ADAMS_Hydraulics Component Reference

ADAMS/Hydraulics Component Reference

OverviewADAMS/Hydraulics is a modeling and simulating environment for fluid power systems that is a plugin to ADAMS/View. It and its supporting documentation are the result of two years of research and development with MBS Models Oy. A cooperative agreement between MBS Models Oy and MSC.Software has made ADAMS/Hydraulics available for use with MSC.ADAMS.

■ Introducing ADAMS/Hydraulics 3

■ ADAMS/Hydraulics Components 13

■ Density of the Fluid and Bernoulli’s Equation 285

■ ADAMS/Hydraulics Functions 295

■ Command Language Reference 309

■ Run-Time Function Reference 341

■ Index 355

ii ADAMS/Hydraulics Component ReferenceCopyright

The information in this document is furnished for informational use only, may be revised from time to time, and

should not be construed as a commitment by MSC.Software Corporation or MBS Models Oy. MSC.Software

Corporation and MBS Models Oy assume no responsibility or liability for any errors or inaccuracies that may

appear in this document.

Copyright Information

This document contains proprietary and copyrighted information and may not be copied, reproduced, translated,

or reduced to any electronic medium without prior consent, in writing, from MSC.Software Corporation.

©2003 of content by MBS Models Oy.

MBS Models Oy, Eloniemenkatu 17, 08150 Lohja, Finland, tel. +358-19-321000, fax +358-19-321067

©2003 of format and approach by MSC.Software Corporation.

All rights reserved. Printed in the United States of America.

Software/Credits

MSC.ADAMS software is Copyright ©2003 MSC.Software Corporation. All Rights Reserved.

The ADAMS/Hydraulics software module is developed and owned by MBS Models Oy of Finland. Copyright

©2003 MBS Models Oy. MSC.Software Corporation has an exclusive right to sell and market the

ADAMS/Hydraulics software module worldwide. Our special thanks to the Institute of Hydraulics and

Automation of Tampere University of Technology in Finland for their technical support in the development of

the ADAMS/Hydraulics software module.

Trademarks

ADAMS, ADAMS/, ADAMS/Hydraulics, MSC, MSC., MSC.ADAMS, and the MSC.Software logo are either

trademarks or registered trademarks of MSC.Software Corporation in the United States and/or other countries.

All other trademarks are the property of their respective companies.

Government Use

Use, duplication, or disclosure by the U.S. Government is subject to restrictions as set forth in FAR 12.212

(Commercial Computer Software) and DFARS 227.7202 (Commercial Computer Software and Commercial

Computer Software Documentation), as applicable.

1 Introducing ADAMS/Hydraulics

OverviewThis chapter gives you an overview of ADAMS/Hydraulics, including definitions of components in the ADAMS/Hydraulics library of components. The following topics are included:

■ Types of Hydraulic Components, 4

■ Topology, 7

■ Resistances and Volumes, 8

■ Component Modeling, 9

■ Starting ADAMS/Hydraulics, 10

■ Setting System Defaults, 11

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Introducing ADAMS/Hydraulics4

About ADAMS/HydraulicsYou can use ADAMS/Hydraulics to graphically build and refine virtual models of fluid power systems. You can couple models of fluid power systems with models of mechanical systems that are built with ADAMS/View and perform coupled system simulation.

This guide provides you with definitions of key words in ADAMS/Hydraulics and describes each of the components in the ADAMS/Hydraulics component library in alphabetical order. It also provides advanced information on the equations used in ADAMS/Hydraulics.

This guide assumes that you know how to run ADAMS/View or ADAMS/Solver. It also assumes that you have a moderate understanding of hydraulics. To run through a tutorial of ADAMS/Hydraulics, see the guide, Getting Started Using ADAMS/Hydraulics. For information on fluid dynamics, refer to Bibliography on page 353.

Types of Hydraulic ComponentsThe following sections explain the different types of hydraulic components you can use in the ADAMS/Hydraulics:

■ Fluid Component (Essential), 4

■ Volume Components, 5

■ Flow and Volume Components, 6

■ Miscellaneous Components, 7

Fluid Component (Essential)

The fluid component is a special entity. It stores data on fluid properties and formulates equations of state for a fluid. You cannot connect fluid with any other component directly, although other components can reference it. ADAMS/Hydraulics handles this for you automatically. For more information, see Fluid on page 135.



Volume Components

The following table lists the volume components:

The component: Page:

Junction2 161

Junction3 163

Junction4 167

Pressure Source 215

Reservoir 223

Tank 271



Flow and Volume Components

The following table lists the flow components:

The component: Page: The component: Page:

Accumulator 17 Laminar Orifice 171

Check Valve 31 Servovalve 4/3 227

Check Valve with Pilot (to close) 35 Pressure Relief Valve 211

Check Valve with Pilot (to open) 41 One-Way Restrictor Valve 179

Counter Balance Valve with Pilot 47 Orifice 185

Cylinder1 53 Pipe (level 1) 191

Cylinder2 65 Pipe (level 2) 197

Cylinder1f 81 Pressure-Reducing Valve 205

Cylinder2ff 93 Pump/Motor 217

Directional Control Valve 2/2 107 Shuttle Valve 241

Directional Control Valve 3/2 115 Spline Orifice 247

Directional Control Valve 4/3 123 Two-Way Cartridge Valve 273

Flow Source 133 Two-Way Flow Control Valve 279

Generic Pump/Motor 157

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Mixed-Volume Flow Components

The following table lists the mixed-volume flow components:

Miscellaneous Components

The following table lists the miscellaneous components:

TopologyIn ADAMS/Hydraulics, each component has one or more ports. The ports are either:

■ One-way - A one-way port only inputs or outputs data, but not both. An example of a one-way port is a pilot port of a valve; the port inputs (senses) pressure, but does not output anything.

■ Two-way - A two-way port inputs and outputs data. The most common two-way port is a flow-pressure port. Components with fluid volume in them, such as reservoir, input the volumetric flow rate and output (compute) pressure, while resistance-based components commonly input pressure and output (compute) volumetric flow rate.

The element: Page:

Sum of Flows 263

Sum of Flows2 265

Sum of Flows3 267

Sum of Flows4 269

The element: Page:

Force Source 133

One-DOF Translational Mass 175



You can only connect ports to each other if their input and output data types match. ADAMS/Hydraulics allows you to connect only matching port pairs to each other. That is, you cannot directly connect ports of two volumes with each other (both output pressure and input flow rate), instead, you must put a resistance between them, such as an orifice, which inputs volumetric flow rate and outputs pressure. This is similar to mass-force relationships in mechanics. You cannot connect a force to another force directly, you must have a mass between them.

Resistances and VolumesThe basic modeling components of a fluid power system are resistances of flow (an orifice is the simplest real-world example of a resistance) and volumes of fluid. In ADAMS/Hydraulics, resistances and volumes are combined to create simple or complicated models. Some fundamental assumptions about these components include:

■ A flow resistance, such as an orifice, is assumed to have a two-dimensional cross-section area (zero volume). A flow of fluid through this resistance causes a pressure drop. Likewise, a pressure difference that is present over a flow resistance causes a fluid flow.

■ A cross section of an orifice is assumed to be circular; that is, the hydraulic diameter is internally computed from a given cross-section area, assuming this dependency: A

= π*D2/4.

■ A volume always has a finite size.

■ Pressure in a volume is computed based on the equation of state for fluid.

■ Pressure values are always regarded as absolute pressures.



Component ModelingFor flexibility and to have the ability to expand its library, ADAMS/Hydraulics builds component models using a modular approach, where it applies. Figure 1 shows the principle of component modeling used in ADAMS/Hydraulics. In most hydraulic components there is a spool, poppet, or similar mechanical device, whose position is controlled either externally by an input current, manually, or internally through springs, port, and/or control pressures, flow forces, and so on. The position of the spool then adjusts the flow cross-section areas. The flow cross-section area together with a pressure drop over it define the flow rate through the flow cross-section area. Note that ADAMS/Hydraulics ignores any possible transient effects due to a change of the cross-section area.

The spool position model and the flow cross-section area models are specific for each particular component. ADAMS/Hydraulics bases the flow model for most of the component models on the ORIFIC function (see ORIFIC - Flow Through an Orifice on page 304).

Figure 1. Component Modeling in ADAMS/Hydraulics

Input or feedback Spool Position Flow Cross-Section Area

SpoolPositionModel

Flow Cross-Section AreaModel

Flow Model

Component Model

Flow Model

Flow Cross-Section Area Model

Spool Position Model

(Control Model)

Flow



Starting ADAMS/HydraulicsBecause ADAMS/Hydraulics is a plugin for ADAMS/View, ADAMS/Car, ADAMS/Rail, and ADAMS/Engine, you need to load ADAMS/Hydraulics when you use ADAMS/Hydraulics with any of these products.

To start ADAMS/Hydraulics:

1 Start the MSC.ADAMS product in which you are creating your ADAMS/Hydraulics model.

2 From the Tools menu, point to Plugin Manager.

3 Select the Load checkbox next to hydraulics.

4 Select OK.

MSC.ADAMS loads the ADAMS/Hydraulics plugin. If you receive an error message, you might have a problem with your licensing. Contact your system administrator or local MSC.ADAMS expert.

Note: To automatically load ADAMS/Hydraulics each time ADAMS/View starts up, select Load at Startup.



Setting System DefaultsYou can change the following system defaults:

■ Environment pressure - Environment pressure defaults to pressure in STP (standard temperature and pressure, or its equivalent in the

applied unit system). All pressure ports of component models are, by default, connected to environment pressure. Therefore, you can leave any port unconnected, which is functionally equivalent to connecting that port to a tank operating under environment pressure. In other words, you probably use a tank component only if you want the:

❖ Tank pressure to differ from environment pressure.

❖ Tank symbol to appear on the screen.

In the equations in this guide, we use the symbol [force/length2] to refer to

environment pressure.

■ Junction volume - Junctions are basic connection elements located between the component models that output flow rate. Junctions require flow rate as input and then compute (output) pressure at that point of the circuit. ADAMS/Hydraulics treats junctions as small volumes. Junction volume defaults to 1e-6 m3.

■ X penetration tolerance - Without a finite stopping distance, the velocity of a limited travel spool/poppet becomes discontinuous at both ends. To avoid that, ADAMS/Hydraulics applies a virtual impact stiffness to all components with spools or poppets. ADAMS/Hydraulics internally applies appropriate impact properties so that spool/poppet relative penetration does not exceed the value of given X penetration tolerance under normal operating conditions. The lower the value you use for this default, the stiffer the end stops become, and thus, potentially, introduce some numerical difficulties at extremes. The X penetration tolerance defaults to 0.001 (no units).

pSTP 101325( ) Pa=

pe



■ Hysteresis limit - There is an opening-closing hysteresis modeled for most valves with a poppet. The hysteresis limit sets a relative opening limit at which a valve is considered to be open with respect to hysteresis. That is, if the poppet begins to open from the zero position, but returns back before reaching relative position equal to the hysteresis limit, then it returns along the same characteristic curve that it followed when opening. Also, if the poppet opens beyond a given limit, then you can observe hysteresis in its characteristics. The hysteresis limit defaults to 0.001 (no units).

To set the defaults:

1 From the Hydraulics menu, point to Defaults, and then select Set.

The Hydraulics Defaults Set dialog box appears.

2 Set the defaults as desired.

3 Select OK.

2 ADAMS/Hydraulics Components

OverviewThis chapter provides information on each of the components you use in ADAMS/Hydraulics. The following section provides the alphabetical listing and page number for each component:

■ Accumulator, 17

■ Gas-Charged Accumulator, 23

■ Check Valve, 31

■ Check Valve with Pilot (to close), 35

■ Check Valve with Pilot (to open), 41

■ Counter Balance Valve with Pilot, 47

■ Cylinder1, 53

■ Cylinder2, 65

■ Cylinder1f, 81

■ Cylinder2ff, 93

■ Directional Control Valve 2/2, 107



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ADAMS/Hydraulics Components14

■ Flow Source, 133

■ Fluid, 135

■ Force Source, 155

■ Generic Pump/Motor, 157

■ Junction2, 161

■ Junction3, 163

■ Junction4, 167

■ Laminar Orifice, 171

■ One-DOF Translational Mass, 175

■ One-Way Restrictor Valve, 179

■ Orifice, 185

■ Pipe (level 1), 191

■ Pipe (level 2), 197

■ Pressure-Reducing Valve, 205

■ Pressure Relief Valve, 211

■ Pressure Source, 215

■ Pump/Motor, 217

■ Reservoir, 223

■ Servovalve 4/3, 227

■ Shuttle Valve, 241

■ Spline Orifice, 247

■ Spool Valve 4/3p, 251



■ Sum of Flows, 263

■ Sum of Flows2, 265



■ Tank, 271

■ Two-Way Cartridge Valve, 273

■ Two-Way Flow Control Valve, 279


Accumulator17

Accumulator

Screen Icon

Description

ADAMS/Hydraulics assumes that for an accumulator:

■ There is a chamber of ideal gas inside, which is then compressed by the entering flow of fluid.

■ Its internal effective volume is completely occupied by gas at setting pressure and temperature.

■ Temperature has changed from setting temperature to fluid temperature slowly.

■ Pressure has changed from setting pressure to initial operating pressure slowly.

■ The compression process during an analysis is polytropic (from fluid pressure and initial operating pressure).

■ Internal delays and inertial forces can be neglected.

■ Compressibility of gas dominates that of fluid and (fluid inside an accumulator is treated incompressible).

■ Fluid flows into an accumulator through a fixed sized orifice.

Note: For the MSC.ADAMS 2003 release, this component is replaced by the new gas_charged_accumulator component. The original component is available to ensure upward compatibility, but has been removed from the menus. You should stop using this component as it may not be available in future releases of ADAMS/Hydraulics.

P

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Accumulator18

Port Topology

Dialog Box Parameters

The following table shows the values you enter in the Create and Modify Accumulator dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.

For port: Input: Output:

P : pressure at port P [force/length2] : volumetric flow rate out from port P in STP [length3/time]

Table 1. Dialog Box Parameters

For the parameter: Enter: Units: Symbol:

General

Mechanical Volume Effective mechanical volume of the accumulator.

length3

Charging

Set Pressure of Gas Set pressure of gas of the accumulator.

force/length2

Set Temperature of Gas

Set temperature of gas of the accumulator.

temperature

Process

Initial Pressure Initial operating pressure of the accumulator.

force/length2

Polytropic Exponent Exponent for polytropic process. --

pP QPSTP

Veff

pset

Tset

pic

κ

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Accumulator19

States

: Volume of gas inside the accumulator [length3]

ADAMS/Hydraulics Formulation

Gas Compression Process Model

Assuming the following:

■ Accumulator’s internal effective volume is completely occupied by gas at setting pressure and temperature.

■ Temperature has changed from setting temperature to fluid temperature slowly.

■ Pressure has changed from setting pressure to initial operating pressure slowly.

You can write the following equation for the initial operating volume of gas at fluid temperature and initial operating pressure :

(1)

Q=f(A,dp)

Nom Pressure Drop Nominal volumetric flow rate through the accumulator orifice.

length3/time

PA Nom Flowrate Pressure drop at nominal volumetric flow rate.

force/length2

Ref Fluid Density Density of the reference fluid (the fluid used for the measurement).

mass/length3



Qnom

∆pnom

ρref

Vg

T pic

Vic VeffT

Tset---------

pset

pic---------⋅ ⋅=


Accumulator20

If the initial operating pressure is so low that , then the initial operating volume

must be set equal to the total effective volume and the initial operating pressure must be adjusted accordingly, such that:

(2)

(3)

If you assume that the compressibility of gas dominates that of fluid (fluid inside an accumulator is treated incompressible), the equation for volume of gas inside the accumulator is:

(4)

where:

volumetric flow rate of fluid out of the accumulator [length3/time]

density of fluid at initial operating pressure [mass/length3]

If you assume a polytropic compression process during an analysis starting from system pressure and initial operating pressure, you can solve for the instantaneous pressure of gas:

(5)

If you ignore internal delays and inertial forces, you can assume that the internal fluid pressure is equal to that of gas:

(6)

Flow Model

If you assume that fluid flows into an accumulator through a fixed-sized orifice, you can solve the effective cross-section area of accumulator inlet orifice from nominal flow rate values as follows. Default values and are applied for laminar flow

regime, which affects the shape of the flow rate curve only at very low pressure drops.

Vic Veff>

Vic Veff=

pic psetT

Tset---------⋅=

Vg Vic QP td∫+ Vic

m· P

ρic------- td∫+= =

QP

ρic

pg pic

Vic

Vg-------

κ

=

pf pg=

Cd 0.6= Retr 50=


Accumulator21

(7)

ADAMS/Hydraulics calculates the rate in and out of the accumulator using ORIFIC function, such that:

If and then:

(8)

else:

(9)

(10)

Figure 2 on page 22 gives an example of accumulator pressure as a function of fluid volume inside the accumulator. Parameter values in the example are:

■ Set pressure of gas

■ Effective volume of the accumulator

■ Set temperature of gas

■ Fluid temperature

■ Initial operating pressure of the accumulator

■ Polytropic exponent

AQnom

Cd

2∆pnom

ρref-------------------

------------------------------=

Vg Veff= pP pg<

mP·

0=

mP·

ORIFIC 1.0 Cd Retr A pf pP 0, , , ,, ,( )=

QPSTP

mP·

ρfluidSTP

------------------=

pset 100 bar=

Veff 33.5 l=

Tset 293.15 K=

T 293.15 K=

pic 100 bar=

κ 1.4=


Accumulator22

Figure 2. Example of Pressure In Accumulator as a Function of Fluid Volume in the Accumulator

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10 12 14

Pressure [bar]

Fluid Volume [l]

Pressure of Hydropneumatic Accumulator as a Function of Fluid Volume


Gas-Charged Accumulator23

Gas-Charged Accumulator

Screen Icon

Description

ADAMS/Hydraulics assumes that for a gas-charged accumulator:

■ There is a chamber of ideal or real gas inside, which is then compressed by the entering flow of fluid.

■ Its internal effective volume is completely occupied by gas at setting pressure and temperature.

■ Internal delays and inertial forces can be neglected.

■ Compressibility of gas dominates that of fluid (fluid inside an accumulator is treated incompressible).

■ Fluid flows into an accumulator through a fixed-sized orifice.

Port Topology



P

pP QPSTP

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The following table shows the values you enter in the Create and Modify Gas Charged Accumulator dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 26.



General

Mechanical Volume Effective mechanical volume of the accumulator.

length3

Charging

Set Pressure of Gas Set pressure of gas of the accumulator.

force/length2

Set Temperature of Gas

Set temperature of gas of the accumulator.

temperature

Process

Initial Pressure Initial operating pressure of the accumulator.

force/length2

Initial Temperature Initial operating temperature of the accumulator.

temperature

Environment Temperature Function

Temperature outside of the accumulator.

temperature

Process Gas Method to select either real or ideal gas for the accumulator. The options are:■ ideal_gas■ nitrogen

--

Veff

pset

Tset

pic

Tic

Tenv

gas



States

: Volume of gas inside the accumulator [length3]

: Temperature of gas inside the accumulator [temperature]

Heat Transfer Process

Method to characterize the heat transfer process between the accumulator gas and the environment. The options are:■ adiabatic - No heat transfer

(process assumed fast or well isolated).

■ isothermal - Infinite heat transfer (gas temperature remains the same as the environment temperature).

■ custom - Based on a user- defined heat transfer coefficient.

--

Heat Transfer Coefficientcustom

Sets the rate at which heat is transferred between the accumulator gas and the environment.

power/temperature

Q=f(A,dp)

Nom Pressure Drop Nominal volumetric flow rate through the accumulator orifice.

length3/time

PA Nom Flowrate Pressure drop at nominal volumetric flow rate.

force/length2


mass/length3



ItoX

G

Qnom

∆pnom

ρref

Vg

Tg




Gas Compression Process Model

The thermodynamic properties of nitrogen applied here are based on [5].

The governing equation of state for the gas inside the accumulator is:

(11)

where Z = 1 for ideal gas and for real gases.

Assuming that accumulator’s internal effective volume is completely occupied by gas at setting pressure and temperature, then amount of gas can be resolved from the following:

(12)

Initial operating gas volume (starting point for an analysis) computes:

(13)

If the initial operating volume becomes larger than the effective volume of the accumulator , then the initial operating gas volume must be set equal to the total

effective volume and the initial operating pressure must be adjusted accordingly, such that:

(14)

(15)

Note: During static analysis, gas temperature is equal to the environment temperature.

(16)

pgVg ZnRTg=

Z f Tg ρg,( )=

n( )

psetVeff ZnRTset=

Vic

ZnRTic

pic------------------=

Vic Veff>

Vic Veff=

pic

ZnRTic

Vic------------------=

Tg Tenv=



ADAMS/Hydraulics assumes that the compressibility of gas dominates that of fluid (fluid inside an accumulator is treated incompressible) and, therefore, the equation for volume of gas inside the accumulator is:

(17)

(18)

where:

volumetric flow rate of fluid out of the accumulator [length3/time]

density of fluid at initial operating pressure [mass/length3]

The instantaneous pressure of gas computes:

(19)

If you ignore internal delays and inertial forces, you can assume that the internal fluid pressure is equal to that of gas:

(20)

Gas temperature is computed based on the selected heat transfer process.

Vg·

QP

m· P

ρic-------= =

Vg Vic Vg·

td∫+=

QP

ρic

pg

ZnRTg

Vg----------------=

pf pg=



Method: Adiabatic

(21)

where:

thermal pressure coefficient [5, p. 42]

specific heat at constant volume [5, p. 42]

mass of gas

Method: Isothermal

(22)

Method: Custom

(23)

Flow Model

If you assume that fluid flows into an accumulator through a fixed-sized orifice, you can solve the effective cross-section area of accumulator inlet orifice from nominal flow rate values as follows. Default values and are applied for laminar flow


(24)

Tg Tic

γγ0-----pgVg

·

mgcv-----------------–

td∫+=

γγ0-----

cv

mg

Tg Tenv=

Tg Tic

G Tenv Tg–( ) γγ0-----pgVg

·–

mgcv-------------------------------------------------------

td∫+=

Cd 0.6= Retr 50=

AQnom

Cd

2∆pnom

ρref-------------------

------------------------------=



ADAMS/Hydraulics calculates the rate in and out of the accumulator using the ORIFIC function, such that:

If and then:

(25)

else:

(26)

(27)

Vg Veff= pP pg<

mP·

0=

mP·

ORIFIC 1.0 Cd Retr A pf pP 0, , , ,, ,( )=

QPSTP

mP·

ρfluidSTP

------------------=


Check Valve31

Check Valve

Screen Icon

Functional Schematic

Description

ADAMS/Hydraulics assumes that for a check valve:

■ There is no volume inside the valve.

■ The poppet is massless.

■ The flow cross-section area is linearly dependent on poppet position.

Port Topology


A : pressure at port A [force/length2] : volumetric flow rate out from port A in STP [length3/time]

B : pressure at port B [force/length2] : volumetric flow rate out from port B in STP [length3/time]

A B

x

A

(+)

B

(+)

pA QASTP

pB QBSTP


Check Valve32


The following table shows the values you enter in the Create and Modify Check Valve2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 33.



General

Initial Position Initial relative poppet position, --

Q=f(dp)

AB Closing Pressure Drop

Closing pressure drop of the valve. force/length2

AB1 Pressure Drop Pressure drop at first definition volumetric flow rate.

force/length2

AB1 Flowrate First definition volumetric flow rate. length3/time

AB2 Pressure Drop Pressure drop at second definition volumetric flow rate.

force/length2

AB2 Flowrate Second definition volumetric flow rate (at maximum opening).

length3/time

AB Relative Leakage Relative leakage .


mass/length3

Response

Time Constant Opening time constant of the valve. time

Pressure Step Pressure drop for which was given. force/length2

0 x 1≤ ≤ x

∆pc

∆p1

Q1

∆p2

Q2

0 ϒ 1≤ ≤ ϒ

ρref

τ0

τ0 ∆p0


Check Valve33

States

: Relative poppet position [],


Poppet Position Model

ADAMS/Hydraulics assumes that the check valve poppet is massless and closed at . It also assumes that the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:

spring force closing the valve (28)

spring preload (29)

viscous damping force (30)

pressure force opening the valve (31)

pressure force closing the valve (32)

flow force closing the valve (33)

where:

constants (identified internally from input data)

relative poppet velocity [1/time]

effective poppet pressure area [length2]

pressure area ratio ( ), ( ) []

Hysteresis

Hysteresis Ratio Pressure area ratio for hysteresis at ( ), ( ).

Table 3. Dialog Box Parameters (continued)


x 0= ε0 1≤ε0

x 0 x 1≤ ≤

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApεpA=

FpB A– ppB=

Ff k3x pA pB––=

c1 k1 k3, ,

x·

Ap

ε Aclosed Ap⁄ ε 1≤


Check Valve34

ADAMS/Hydraulics calculates the pressure area ratio as follows (see ARATIO - Area Ratio of a Poppet on page 296):

(34)


If you assume that point ( ) corresponds to the maximum opening, you can use that

same point to compute the maximum flow cross-section area of the valve. Default values and are applied for laminar flow regime, which affects the shape of

the flow rate curve only at very low pressure drops.

(35)

Relative flow cross-section area, therefore, computes to:

(36)

Flow Model

ADAMS/Hydraulics defines the flow model for a check valve using the ORIFIC function, such that:

(37)

(38)

(39)

ε ARATIO x xε ε0 closed 0, , , ,( )=

Q2 ∆p2,

Cd 0.6= Retr 50=

Amax

Q2

Cd------

ρref

2∆p2------------=

R LINPWL x ϒ 0, ,( )=

m· AB ORIFIC R Cd Retr Amax pA pB 0, , , ,, ,( )=

QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Check Valve with Pilot (to close)35

Check Valve with Pilot (to close)

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a check valve with pilot (to close):

■ Sum of the pressure areas of ports A and B is equal to pilot pressure area (X).

■ There is no volume inside a valve.

■ Poppet is massless.

■ Flow cross-section area is linearly dependent on the poppet position.

ADAMS/Hydraulics combines the spool position model and the flow cross-section area model in the model of a check valve.

A B

X

X

(+)

A

(+)

x

B (+)



Port Topology


The following table shows the values you enter in the Create and Modify Check Valve with Pilot dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 38.




X : pressure at port X [force/length2] --



General


BA Pressure Area Ratio

Secondary pressure area ratio. --

Q=f(pA)

A Closing Pressure Closing pressure at port A. force/length2

A1 Pressure Pressure at port A at first definition volumetric flow rate.

force/length2

A1 Flowrate First definition volumetric flow rate. length3/time

pA QASTP

pB QBSTP

pX

0 x 1≤ ≤x

rBA

pc

pA1

Q1



States


A2 Pressure Pressure at port A at second definition volumetric flow rate.

force/length2

A2 Flowrate Second definition volumetric flow rate (at maximum opening).

length3/time

AB Relative Leakage

Relative leakage ( ). --

BX Ref Pressure Pressure at ports B and X during measurements.

force/length2


mass/length3

Response


Pressure Step Pressure drop for which was given.

force/length2

Hysteresis


--



pA2

Q2

0 ϒ 1≤ ≤ ϒ

pBXref

ρref

τ0

τ0 ∆p0

x 0= ε0 1≤ε0

x 0 x 1≤ ≤





ADAMS/Hydraulics assumes that the check valve with pilot poppet is massless and closed at . It also assumes the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


spring preload (41)






where



pressure area for port A pressure [length2]


pressure area for port B pressure [length2]

ADAMS/Hydraulics computes pressure area ratio as follows (see ARATIO - Area Ratio of a Poppet on page 296):

(47)

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApAεpA=

FpB ApBpB=

FpX ApA ApB+( )pX–=

Ff k3x pA pB––=

c1 k1 k3, ,

x·

ApA

ε Aclosed ApA⁄ ε 1≤

ApB





If you assume that point ( ) corresponds to the maximum opening, you can use the

same point to compute the maximum flow cross-section area for the valve. Default values and are applied for laminar flow regime, which affects the shape of


(48)

The flow cross-section area, therefore, computes to:

(49)

Flow Model


(50)

(51)

(52)

Q2 pA2,

Cd 0.6= Retr 50=

Amax

Q2

Cd------

ρref

2 pA2 pBXref–( )--------------------------------------=



QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Check Valve with Pilot (to open)41

Check Valve with Pilot (to open)

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a check valve with pilot (to open):

■ Sum of pressure areas of ports A, B, and X is equal to the pressure area of port T.




A B

TX

X

(+)

A

(+)

x

B (+)

T

(+)



Port Topology





T : pressure at port T [force/length2] --

pA QASTP

pB QBSTP

pX

pT



Input Parameters

The following table shows the values you enter in the Create and Modify Check Valve3 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 45.


For the parameter:

Enter: Units: Symbol:

General



Secondary pressure area ratio (B/A). --

XA Pressure Area Ratio

Pilot pressure area ratio (X/A). --

Q=f(pA)



force/length2

A1 Flowrate First definition volumetric flow rate. length3/time


force/length2


length3/time

AB Relative Leakage


0 x 1≤ ≤ x

rBA

rXA

pc

pA1

Q1

pA2

Q2

0 ϒ 1≤ ≤ ϒ



States


BXT Ref Pressure Pressure at ports B, X, and T used during measurements.

force/length2


mass/length3

Response


Pressure Step Pressure drop for which was given. force/length2

Hysteresis


--


For the parameter:


pBXTref

ρref

τ0

τ0 ∆p0

x 0= ε0 1≤ε0

x 0 x 1≤ ≤





ADAMS/Hydraulics assumes that the check valve with pilot poppet is massless and closed at . It also assumes that the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


spring preload (54)




pilot pressure force opening the valve (58)

pressure force closing/opening the valve (59)


where:






pressure area for pilot (port X) pressure [length2]

pressure area for tank (port T) pressure [length2]

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApAεpA=

FpB A– pBpB=

FpX ApXpX=

FpT A– pTpT=

Ff k3x pA pB––=

c1 k1 k3, ,

x·

ApA


ApB

ApX

ApT



ADAMS/Hydraulics computes the area ratio as follows (see ARATIO - Area Ratio of a Poppet on page 296):

(61)





(62)

The flow cross-section area, therefore, computes to:

(63)

Flow Model

ADAMS/Hydraulics defines the flow model for counter balance valve using the ORIFIC function, such that:

(64)

(65)

(66)


Q2 pA2,

Cd 0.6= Retr 50=

Amax

Q2

Cd------

ρref

2 pA2 pBXTref–( )-----------------------------------------=



QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Counter Balance Valve with Pilot47

Counter Balance Valve with Pilot

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a counter balance valve:

■ The sum of the pressure areas of ports A, B, and X is equal to pressure area of port T.


■ Poppet is massless.


A B

X

T

X

(+)

A

(+)

x

B (+)

T

(+)



Port Topology


The following table shows the values you enter in the Create and Modify Counter Balance Valve4p dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 50.





T : pressure at port T [force/length2] --



General



Secondary pressure area ratio (B/A).

--

XA Pressure Area Ratio

Pilot pressure area ratio (X/A). --

Q=f(pA)


pA QASTP

pB QBSTP

pX

pT

0 x 1≤ ≤x

rBA

rXA

pc




force/length2

A1 Flowrate First definition volumetric flow rate.

length3/time


force/length2


length3/time

AB Relative Leakage Relative leakage ( ). --

BXT Ref Pressure Pressure at ports B, X, and T used during measurements.

force/length2


mass/length3

Response

Time Constant Opening time constant of the valve.

time


force/length2

Hysteresis


--



pA1

Q1

pA2

Q2

0 ϒ 1≤ ≤ ϒ

pBXTref

ρref

τ0

τ0 ∆p0

x 0= ε0 1≤ε0



States




ADAMS/Hydraulics assumes that the counter balance valve poppet is massless and closed at . It also assumes that the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


spring preload (68)




pilot pressure force opening the valve (72)

pressure force closing/opening the valve (73)


where:






pressure area for pilot (port X) pressure [length2]

pressure area for tank (port T) pressure [length2]

x 0 x 1≤ ≤

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApAεpA=

FpB A– pBpB=

FpX ApXpX=

FpT A– pTpT=

Ff k3x pA pB––=

c1 k1 k3, ,

x·

ApA


ApB

ApX

ApT



ADAMS/Hydraulics computes the pressure area ratio as follows (see ARATIO - Area Ratio of a Poppet on page 296):

(75)




the flow rate curve only at very low pressure drops:

(76)

Flow cross-section area computes:

(77)

Flow Model

ADAMS/Hydraulics defines the flow model for a counter balance valve using the ORIFIC function, such that:

(78)

(79)

(80)


Q2 pA2,

Cd 0.6= Retr 50=

Amax

Q2

Cd------

ρref

2 pA2 pBXTref–( )-----------------------------------------=



QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Cylinder153

Cylinder1

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a cylinder1:

■ Cylinder1 computes a force value that acts between its end points and consists of pressure, friction, and cushion forces.

■ Cushions in the both ends of cylinder1 are identical.

■ Cushions prevent cylinder1 from ever reaching its maximum and minimum lengths.

■ Cylinder1 parts are massless. (If mass is needed, you should account for it in the mechanical side of the model.)

■ Cylinder1 walls are flexible.

■ Cylinder1 rod is rigid. (If flexibility is needed, you should account for it in the mechanical side of the model.)

A

A (+)

l

M

(+)

M

(+)


Cylinder154

■ Fluid inside cylinder1 is considered compressible but massless in the mechanical sense.

■ Mechanical motion/acceleration of cylinder1 as a whole does not affect internal flows or fluid movements.

■ The flow cross-section area is a function of any system states to allow modeling of arbitrary end-stop constructions.

■ There is no leakage through the rod sealing.

ADAMS/Hydraulics also assumes [4] that the seal friction has the following properties:

■ Friction force is dependent on pressure difference across a seal.

■ Coulomb friction occurs at zero sliding velocity.

■ At low sliding velocity, the friction force is decreasing until a specific sliding velocity is reached (at this transition area, the friction is changing from

Coulomb to viscous friction).

■ Precompression of seals causes a constant friction force that is not dependent on pressure.

■ Friction force parameters are measured in STP.

vtr( )


Cylinder155

Port Topology


The following table shows the values you enter in the Create and Modify Cylinder1 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 59.


A : pressure at port A [force/length2]

: volumetric flow rate out from port A in STP [length3/time]

Mechanical ■ : upper attachment marker of the cylinder

■ : lower attachment marker of the cylinder

■ : total cylinder force [force]

■ : total pressure force [force]

■ : friction force [force]

■ : cushion force [force]

■ : extension chamber

pressure [pressure]



I MarkerJ Marker

Name of the I and J markers that define the design length of the cylinder (solved internally based on the design position of the cylinder).

length

General

Max Length Maximum length of the cylinder. length

Min Length Minimum length of the cylinder. length

pA QASTP

i marker–

j marker–

F

Fp

Fµ

Fc

pl

l0

lmax

lmin


Cylinder156

A Dead Volume Mechanical volume of extension chamber of the cylinder at minimum length.

length3

Piston Diameter Diameter of piston/inner diameter of the cylinder.

length

A Chamber Initial Pressure

Initial pressure in the extension chamber.

force/length2

A Orifice Diameter Maximum diameter of the output port A flow passage.

length

Static Hold Controls cylinder behavior during static analysis. The options are:■ none - Finds the static

position freely (design length and extension chamber pressure floats).

■ pl - Holds the initial extension chamber pressure (design length floats).

■ l0 - Holds the design length (extension chamber pressure floats).

-- --

End Stops

A Relative Opening Function

Relative opening of the flow cross-section area for flow from port A, .

--



Vldead

Dp

pl0

dA

0 R 1≤ ≤

RA


Cylinder157

Cushion Free Length

Cushion free length (thickness). length

Cushion Relative Stiffness

Cushion relative stiffness. force

Cushion Force Exponent

Cushion force exponent .

--

Cushion Rebound Ratio

Rebound ratio of cushion force, .

Limit Velocity for Rebound

Limit velocity for fully developed hysteresis (rebound force).

length/time

Flexibility

Wall Thickness Cylinder wall thickness. length

Young’s Modulus Modulus of elasticity of the cylinder wall material.

force/length2

Poisson’s Ratio Poisson’s ratio for the cylinder wall material.

--

Losses

Coulomb Friction Force

Dry Coulomb friction due to precompression of seals.

force

Piston Seal Friction Coefficient

Coefficient is the friction force divided by the change in pressure.

length2



lc

kc

0 ec 10≤<ec

0 hc 1≤ ≤hc

vlim

s

E

ϑ

Fµ0

a


Cylinder158

States

: Instantaneous seal - cylinder wall contact location (stiction length) [length]

: Volume of fluid in the extension chamber in STP [length3]

Limit Velocity for Dynamic Friction

Sliding velocity for fully developed dynamic friction.

length/time

Dynamic Friction Decrease

Relative decrease of friction between static to dynamic friction.

--

Seal Shear Stiffness Effective seal shear stiffness. force/length

Damping Coefficient Damping coefficient. force*time/length

Leakages

Relative Clearance of Piston

Relative clearance for laminar leakage over piston ( ).

--

Piston Thickness Piston thickness (for laminar leakage only) ( ).

--



vtr

µD

ksseal

c

0 ϒp≤ϒp

0 Lp<Lp

ls

VlSTP


Cylinder159


Structural Flexibility Model

According to Timoshenko [3], the radial displacement u at the inner surface of a thick-walled cylindrical shape due to an internal pressure increase of is:

(81)

where the outer diameter of the cylinder is:

(82)

For pressure delta, you can write the equation:

(83)

You can also write the equation for effective inner area of the cylinder as a function of pressure, such that:

(84)

Pressure Force Model

ADAMS/Hydraulics computes cylinder length and its time derivative based on the locations and velocities of the cylinder attachment points using the DM and VR functions. For information on these functions, see the ADAMS/Solver (FORTRAN) online help.

(85)

(86)

It computes the design length of the cylinder at the beginning of a simulation as follows:

(87)

The piston pressure area is:

(88)

Λp

uDpΛp

2E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

=

Do Dp 2s+=

Λp p pe–=

Aeff Dp 2u+( )2π4--- 1

p pe–

E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

+ 2

π4---Dp

2= =

l DM i marker– j marker–,( )=

l· VR i marker– j marker– j marker–, ,( )=

l0 DM i marker– j marker–,( )t 0==

Al Aeff=


Cylinder160

It defines the instantaneous mechanical volume of the extension chamber of the cylinder as:

(89)

It also computes the initial volume of fluid in the extension chamber in STP based on the given initial pressure:

(90)

where the function refers to the equation of state for the fluid.

ADAMS/Hydraulics defines the density as mass per unit of volume. It calculates the density of the fluid in the extension chamber of the cylinder as:

(91)

It calculates the pressure of the fluid in the extension chamber of the cylinder using the equation of state for the fluid, such that:

(92)

Following MSC.ADAMS sign convention in which a repelling point-to-point force is positive, you can obtain the following for the total pressure force:

(93)

Friction Force Model

ADAMS/Hydraulics assumes that the maximum static friction force consists of two force components:

(94)

, friction force magnitude over piston seal (95)

The second term of Equation (94) is a constant and represents dry Coulomb friction due to precompression of seals.

Vl l lmin–( )Al Vldead+=

Vlini

ρl0Vl0

ρf luidSTP

------------------f pl0 T,( )

f pSTP TSTP,( )---------------------------------Vl l0( )= =

ρ f p T,( )=

ρl

VlSTP

Vl----------ρfluidSTP

=

pl f ρl T,( )=

Fp pl pe–( )Al=

Fµsta Fµpiston Fµ0+=

Fµpiston a pl pe–=


Cylinder161

If dynamic friction is assumed to be fully developed at sliding velocity of , you can

write the dynamic friction force equation as:

(96)

Knowing that the effective seal shear stiffness is , you can now compute the

maximum shear deformation of seals due to dynamic friction force as:

(97)

If you further assume that there is an additional velocity dependent damping term involved, then the instantaneous friction force acting on the cylinder is:

(98)

(99)

Cushion Force Model

ADAMS/Hydraulics assumes that the cushion force goes to infinity while the cylinder approaches either its maximum or minimum length. The cushion force prevents the cylinder from going beyond its limit length values. Cushion force characteristics are the same on both ends of the cylinder. For an impact against the extension chamber cushion (at the minimum cylinder length), the equations that compute the force are:

(100)

(101)

vtr( )

Fµdyn 1 µD

min l· vtr,( )vtr

----------------------------–

Fµsta=

ksseal( )

∆lµmax

Fµdyn

ksseal--------------=

∆lµ l ls–=

Fµ ksseal∆lµ– cl·– ∆lµmax– ∆lµ ∆lµmax≤ ≤,=

pen max 0 lc lmin+, l–( )=

Fc kcpen

lc pen–-------------------

ecstep l· v– l im 1

hc

2-----+ vlim 1

hc

2-----–, , , ,

=


Cylinder162

Similarly, an impact against the retraction chamber cushion (at the maximum cylinder length) is:

(102)

(103)

STEP functions used in the above equations generate damping through hysteresis by introducing different force characteristics for penetration and rebound.

Cylinder Force

Total force acting in between the cylinder attachment points is simply a sum of pressure, friction, and cushion forces:

(104)


ADAMS/Hydraulics computes the maximum flow cross-section area for flow from port A as follows:

(105)

Flow Model

ADAMS/Hydraulics defines the flow model for flow out from cylinder using the ORIFIC function. Default values and are applied for laminar flow regime,

which affects the shape of the flow rate curve only at very low pressure drops.

(106)

(107)

pen max 0 l lmax l–c

( )–,( )=

Fc k– cpen

lc pen–-------------------


hc

2-----– vlim 1

hc

2-----+, , , ,

=

F Fp Fµ Fc+ +=

AA

πdA2

4----------=

Cd 0.6= Retr 50=

m· A ORIFIC RA Cd Retr AA pl pA 0, , , ,, ,( )=

QASTP

m· A

ρfluidSTP

------------------=


Cylinder163

According to Merritt [1, p. 34], you can compute the laminar flow in annulus between circular shaft and cylinder ( ) as:

(108)

where:

radial clearance [length]

kinematic viscosity of fluid [length2/time]

passage length [length]

eccentricity of shaft [length]

You can assume eccentricity is zero or compensated in the value of relative clearance and define a dimensionless relative clearance as follows:

(109)

From Equations (480) and (525), you can write the equation for laminar leakage flow over the piston as:

(110)

The sum of flow rates from the extension cylinder chamber is, respectively:

(111)

(112)

c D«

m·πDc3

12νL------------- 1

32---

ec--

2+

∆p=

c

ν

L

e

ϒp

ϒp2cD------=

m· lu ϒp3 πD4

96νL-------------

pl pe–( )=

QlSTP

m· lu– m· A–

ρf luidSTP

--------------------------=

VlSTPQlSTP

td∫=


Cylinder164


Cylinder265

Cylinder2

Screen Icon


Description

ADAMS/Hydraulics assumes that for a cylinder2:

■ Cylinder2 computes a force value that acts between its end points and consists of pressure, friction, and cushion forces.

■ Cushions in the both ends of cylinder2 are identical.

■ Cushions prevent cylinder2 from ever reaching its maximum and minimum lengths.

■ Cylinder2 parts are massless. (If mass is needed, you should account for it in the mechanical side of the model.)

■ Cylinder2 walls are flexible.

■ Cylinder2 rods are rigid. (If flexibility is needed, you should account for it in the mechanical side of the model.)

A

B

A (+) B (+)

l

M

(+)

M

(+)


Cylinder266

■ Fluid inside cylinder2 is considered compressible, but massless in the mechanical sense.

■ Mechanical motion/acceleration of cylinder2, as a whole, does not affect internal flows or fluid movements.

■ Flow cross-section areas are functions of any system states to allow modeling of arbitrary end-stop constructions.




■ At low sliding velocity, the friction force is decreasing until a specific sliding

velocity is reached (at this transition area, the friction is changing from




vtr( )


Cylinder267

Port Topology


The following table shows the values you enter in the Create and Modify Cylinder2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 73.




B : pressure at port B [force/length2]

volumetric flow rate out from port B in STP [length3/time]







■ : extension chamber pressure

[pressure]■ : retraction chamber pressure

[pressure]


For the option: Enter: Units: Symbol:

I MarkerJ Marker

Name of the I and J markers that define the design length of the cylinder (solved internally based on design position of the cylinder).

length

pA QASTP

pB QBSTP

i marker–

j marker–

F

Fp

Fµ

Fc

pl

pu

l0


Cylinder268

General



B Dead Volume Mechanical volume of retraction chamber of the cylinder at minimum length.

length3


length3


length

B Rod Diameter Diameter of piston rod above piston. length

A Rod Diameter Diameter of piston rod below piston. length

B Chamber Initial Pressure

Initial pressure in the retraction chamber.

force/length2



force/length2

A Orifice Diameter

Maximum diameter of the output port A flow passage.

length

B Orifice Diameter

Maximum diameter of the output port B flow passage.

length



lmax

lmin

Vudead

Vldead

Dp

dru

drl

pu0

pl0

dA

dB


Cylinder269

Static Hold Controls cylinder behavior during static analysis. The options are:

■ none - Finds static position freely (design length, extension and retraction chamber pressure floats)

■ pl - Holds initial extension chamber pressure (design length and retraction chamber pressure floats)

■ pu - Holds initial retraction chamber pressure (design length and extension chamber pressure floats)

■ pl_and_pu - Holds initial extension and retraction chamber pressure (design length floats)

■ pl_and_l0 - Holds initial extension chamber pressure and design length (retraction chamber pressure floats)

■ pu_and_l0 - Holds initial retraction chamber pressure and design length (extension chamber pressure floats)

-- --




Cylinder270

Static Hold (continued)

■ l0_with_pl - Holds design length by adjusting extension chamber pressure (retraction chamber pressure floats)

■ l0_with_pu - Holds design length by adjusting retraction chamber pressure (extension chamber pressure floats)

-- --

End Stops

A Relative Opening Function

Relative opening of the flow cross-section area for flow from port A,

.

--

B Relative Opening Function

Relative opening of the flow cross-section area for flow from port B,

.

--

Cushion Free Length





Cushion force exponent . --



--



length/time



0 R 1≤ ≤

RA

0 R 1≤ ≤

RB

lc

kc

0 ec 10≤< ec

0 hc 1≤ ≤hc

vlim


Cylinder271

Flexibility


Youngs Modulus Modulus of elasticity of the cylinder wall material.

force/length2

Poissons Ratio Poisson’s ratio for the cylinder wall material.

--

Losses



force



length2

B Rod Seal Friction Coefficient


length2

A Rod Seal Friction Coefficient


length2



length/time



--

Seal Shear Stiffness

Effective seal shear stiffness. force/length



s

E

ϑ

Fµ0

a

bu

bl

vtr

µD

ksseal


Cylinder272

States



: Volume of fluid in the retraction chamber in STP [length3]

Damping Coefficient

Damping coefficient. force*time/length

Leakages


Relative clearance for laminar leakage over piston .

--


--

A Rod Leakage Coefficient

Coefficient of leakage over extension chamber rod seal.

volume/time/pressure

B Rod Leakage Coefficient

Coefficient of leakage over retraction chamber rod seal.




c

0 ϒp≤ϒp

0 Lp<Lp

CArod

CBrod

ls

VlSTP

VuSTP


Cylinder273




(113)


(114)

You can write the equation for pressure delta as:

(115)

You can also write the effective inner area of the cylinder as a function of pressure as:

(116)


ADAMS/Hydraulics computes the cylinder length and its time derivative based on the locations and velocities of the cylinder attachment points using the functions DM and VR. For information on DM and VR functions, see the ADAMS/Solver (FORTRAN) online help.

(117)

(118)

Λp

uDpΛp

2E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

=

Do Dp 2s+=

Λp p pe–=

Aeff Dp 2u+( )2π4--- 1

p pe–

E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

+ 2

π4---Dp

2= =




Cylinder274

Design length of the cylinder is computed in the beginning of a simulation as follows:

(119)

Areas of piston rods are:

(120)

(121)

The piston pressure area for retraction and extension pressures is:

(122)

(123)

The instantaneous mechanical volume of the retraction and extension chamber of the cylinder is:

(124)

(125)

ADAMS/Hydraulics computes the initial volumes of fluid in the retraction and extension chamber in STP based on the given initial pressures in both of the chambers, such that:

(126)

(127)



Aru dru2 π

4---=

Arl drl2 π

4---=

Au Aeff Aru–=

Al Aeff Arl–=

Vu lmax l–( )Au Vudead+=


Vuini

ρu0Vu0

ρf luidSTP

------------------f pu0 T,( )

f pSTP TSTP,( )---------------------------------Vu l0( )= =

Vlini

ρl0Vl0

ρf luidSTP

------------------f pl0 T,( )

f pSTP TSTP,( )---------------------------------Vl l0( )= =

ρ f p T,( )=


Cylinder275

ADAMS/Hydraulics defines density as mass per unit of volume. It calculates the density of the fluid in the retraction and extension chamber of the cylinder as:

(128)

(129)

It also calculates the pressure of the fluid in the retraction and extension chambers of the cylinder using the equation of state for the fluid, such that:

(130)

(131)


(132)


ADAMS/Hydraulics assumes the maximum static friction force consists of three or four force components:

(133)


, friction force magnitude over upper rod seal(135)

, friction force magnitude over lower rod seal(136)

The fourth term of Equation (133) is a constant and represents dry Coulomb friction due to precompression of seals. Force over lower rod seal (Equation 136) is naturally zero in the case of a differential cylinder, which has no lower rod.

ρu

VuSTP

Vu-----------ρf luidSTP

=

ρl

VlSTP


=

pu f ρu T,( )=

pl f ρl T,( )=

Fp plAl puAu– peArl peAru–+=

Fµsta Fµpiston Furod Flrod Fµ0+ + +=

Fµpiston a pl pu–=

Furod bu pu pe–=

Flrod bl pl pe–=


Cylinder276

If you assume that dynamic friction is fully developed at sliding velocity of , you can

then write the equation for dynamic friction force as:

(137)



(138)

If you further assume that there is an additional velocity dependent damping term involved, then the instantaneous friction force acting on the cylinder is:

(139)

(140)

Cushion Force Model

ADAMS/Hydraulics assumes that cushion force goes to infinity while the cylinder approaches either its maximum or minimum length. The cushion force prevents the cylinder from going beyond its limit length values. ADAMS/Hydraulics assumes that the cushion force characteristics are the same on both ends of the cylinder. For an impact against the extension chamber cushion (at the minimum cylinder length), the equations that compute the force are:

(141)

(142)

vtr( )

Fµdyn 1 µD

min l· vtr,( )vtr

----------------------------–

Fµsta=

ksseal( )

∆lµmax

Fµdyn

ksseal--------------=

∆lµ l ls–=



Fc kcpen

lc pen–-------------------

ecstep l· v– lim 1

hc

2-----+ vlim 1

hc

2-----–, , , ,

=


Cylinder277


(143)

(144)


Cylinder Force


(145)


ADAMS/Hydraulics computes the maximum flow cross-section areas for flows from ports A and B as follows:

(146)

(147)


( )–,( )=

Fc k– cpen

lc pen–-------------------


hc

2-----– vlim 1

hc

2-----+, , , ,

=

F Fp Fµ Fc+ +=

AA

πdA2

4----------=

AB

πdB2

4----------=


Cylinder278

Flow Model

ADAMS/Hydraulics defines the flow model for flows out from cylinder using the ORIFIC function. Default values and are applied for laminar flow


(148)

(149)

(150)

(151)

According to Merritt [1, p. 34], you can compute the laminar flow in annulus between the circular shaft and cylinder ( ) as:

(152)

where:

radial clearance [length]

kinematic viscosity of fluid [length2/time]

passage length [length]

eccentricity of shaft [length]

If you assume that the eccentricity is zero or compensated in the value of relative clearance, you can define a dimensionless relative clearance as follows:

(153)

Cd 0.6= Retr 50=

m· A ORIFIC RA Cd Retr AA pl pA 0, , , ,, ,( )=

m· B ORIFIC RB Cd Retr AB pu pB 0, , , ,, ,( )=

QASTP

m· A

ρfluidSTP

------------------=

QBSTP

m· B

ρfluidSTP

------------------=

c D«

m·πDc3

12νL------------- 1

32---

ec--

2+

∆p=

c

ν

L

e

ϒp

ϒp2cD------=


Cylinder279

From Equations (152) and (153), the laminar leakage flow over the piston is:

(154)

Leakage over rods are:

(155)

(156)

The sum of flow rates from retraction and extension cylinder chambers are, respectively:

(157)

(158)

(159)

(160)

m· lu ϒp3 πD4

96νL-------------

pl pu–( )=

m· Arod CArod pl pe–( )=

m· Brod CBrod pu pe–( )=

QlSTP

m· lu– m· A– m· Arod–

ρfluidSTP

-----------------------------------------------=

QuSTP

m· lu m· B– m· Brod–

ρf luidSTP

------------------------------------------=

VlSTPQlSTP

td∫=

VuSTPQuSTP

td∫=


Cylinder280


Cylinder1f81

Cylinder1f

Screen Icon


Description

Note: The difference between the cylinder1 and cylinder1f components is that cylinder1f’s input is the volumetric flow rate directly into the cylinder chamber without an orifice in between. This allows you to:

❖ Input multiple flows into a single cylinder chamber (for example, chained brake cylinders on an aircraft).

❖ Connect pipes and valves with a cylinder without having to add a junction in between.

❖ Easily model flows over the cylinder piston (for example, the pressure relief valve bundled with the piston to protect against cylinder damage).

A

A (+)

l

M

(+)

M

(+)


Cylinder1f82

ADAMS/Hydraulics assumes that:

■ Cylinder1f computes a force value that acts between its end points, consisting of pressure, friction, and cushion forces.

■ Cushions in both ends of cylinder1f are identical.

■ Cushions prevent cylinder1f from ever reaching its maximum and minimum lengths.

■ Cylinder1f parts are massless. (If mass is needed, you should account for it in the mechanical side of the model.)

■ Cylinder1f walls are flexible.

■ Cylinder1f rod is rigid. (If flexibility is needed, you should account for it in the mechanical side of the model.)

■ Fluid inside cylinder1f is considered compressible, but massless in the mechanical sense.

■ Mechanical motion/acceleration of cylinder1f as a whole does not affect internal flows or fluid movements.

■ There is no leakage through the rod sealing.




■ At low sliding velocity, the friction force is decreasing until a specific sliding velocity is reached (at this transition area, the friction is changing from




vtr( )


Cylinder1f83

Port Topology


The following table shows the values you enter in the Create and Modify Cylinder1f dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 86.


A : volumetric flow rate in from port A in STP [length3/time]

: pressure at port A [force/length2]









I MarkerJ Marker


length

General



QASTPpA

i marker–

j marker–

F

Fp

Fµ

Fc

l0

lmax

lmin


Cylinder1f84


length3


length



force/length2

Static Hold Controls cylinder behavior during static analysis. The options are:■ none - Finds the static

position freely (design length and extension chamber pressure floats).

■ pl - Holds the initial extension chamber pressure (design length floats).

■ l0 - Holds the design length (extension chamber pressure floats).

-- --

End Stops

Cushion Free Length





Cushion force exponent .

--



Vldead

Dp

pl0

lc

kc

0 ec 10≤<ec


Cylinder1f85



--



length/time

Flexibility


Young’s Modulus Modulus of elasticity of the cylinder wall material.

force/length2

Poisson’s Ratio Poisson’s ratio for the cylinder wall material.

--

Losses



force



length2



length/time



--

Seal Shear Stiffness Effective seal shear stiffness. force/length

Damping Coefficient Damping coefficient. force*time/length



0 hc 1≤ ≤hc

vlim

s

E

ϑ

Fµ0

a

vtr

µD

ksseal

c


Cylinder1f86

States






(161)


(162)

For pressure delta, you can write the equation:

(163)

Leakages


Relative clearance for laminar leakage over piston ( ).

--


--



0 ϒp≤ϒp

0 Lp<Lp

ls

VlSTP

∆p

uDp∆p

2E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

=

Do Dp 2s+=

∆p p pe–=


Cylinder1f87

You can also write the equation for effective inner area of the cylinder as a function of pressure, such that:

(164)


ADAMS/Hydraulics computes cylinder length and its time derivative based on the locations and velocities of the cylinder attachment points using the DM and VR functions. For information on these functions, see the ADAMS/Solver (FORTRAN) online help.

(165)

(166)

It computes the design length of the cylinder at the beginning of a simulation as follows:

(167)

The piston pressure area is:

(168)

It defines the instantaneous mechanical volume of the extension chamber of the cylinder as:

(169)

It also computes the initial volume of fluid in the extension chamber in STP based on the given initial pressure:

(170)


Aeff Dp 2u+( )2π4--- 1

p pe–

E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

+ 2

π4---Dp

2= =




Al Aeff=


Vlini

ρl0Vl0

ρf luidSTP

------------------f pl0 T,( )

f pSTP TSTP,( )---------------------------------Vl l0( )= =

ρ f p T,( )=


Cylinder1f88

ADAMS/Hydraulics defines the density as mass per unit of volume. It calculates the density of the fluid in the extension chamber of the cylinder as:

(171)

It calculates the pressure of the fluid in the extension chamber of the cylinder using the equation of state for the fluid, such that:

(172)


(173)


ADAMS/Hydraulics assumes that the maximum static friction force consists of two force components:

(174)


The second term of equation (174) is a constant and represents dry Coulomb friction due to precompression of seals.

If dynamic friction is assumed to be fully developed at sliding velocity of , you can

write the dynamic friction force equation as:

(176)

ρl

VlSTP


=

pl f ρl T,( )=

Fp pl pe–( )Al=

Fµsta Fµpiston Fµ0+=

Fµpiston a pl pe–=

vtr( )

Fµdyn 1 µD

min l· vtr,( )vtr

----------------------------–

Fµsta=


Cylinder1f89



(177)

If you further assume that there is an additional velocity-dependent damping term involved, then the instantaneous friction force acting on the cylinder is:

(178)

(179)

Cushion Force Model

ADAMS/Hydraulics assumes that the cushion force goes to infinity while the cylinder approaches either its maximum or minimum length. The cushion force prevents the cylinder from going beyond its limit length values. Cushion force characteristics are the same on both ends of the cylinder. For an impact against the extension chamber cushion (at the minimum cylinder length), the equations that compute the force are:

(180)

(181)


(182)

(183)


ksseal( )

∆lµmax

Fµdyn

ksseal--------------=

∆lµ l ls–=



Fc kcpen

lc pen–-------------------


hc

2-----+ vlim 1

hc

2-----–, , , ,

=


( )–,( )=

Fc k– cpen

lc pen–-------------------


hc

2-----– vlim 1

hc

2-----+, , , ,

=


Cylinder1f90

Cylinder Force

The total force acting in between the cylinder attachment points is simply a sum of pressure, friction, and cushion forces:

(184)

Flow Model

While volumetric flow rate in from port A is given, corresponding mass flow rate is simply:


(185)

where:

■ is radial clearance [length]

■ is kinematic viscosity of fluid [length2/time]

■ is passage length [length]

■ is eccentricity of shaft [length]

You can assume eccentricity is zero or compensated in the value of relative clearance and define a dimensionless relative clearance as follows:

(186)

From equations (480) and (525), you can write the equation for laminar leakage flow over the piston as:

(187)

F Fp Fµ Fc+ +=

m· A QASTPρf luidSTP

=

c D«

m·πDc3

12νL------------- 1

32---

ec--

2+

∆p=

c

ν

L

e

ϒp

ϒp2cD------=

m· lu ϒp3 πD4

96νL-------------

pl pe–( )=


Cylinder1f91

Sum of flow rates to and from extension cylinder chamber is, respectively:

(188)

(189)

QlSTP

m· lu– m· A+

ρf luidSTP

--------------------------=

VlSTPQlSTP

td∫=


Cylinder1f92


Cylinder2ff93

Cylinder2ff

Screen Icon


Description

Note: The difference between the cylinder2 and cylinder2ff components is that cylinder2ff’s inputs are the volumetric flow rates directly into the cylinder chambers without orifices in between. This allows you to:

❖ Input multiple flows into a single cylinder chamber (for example, chained brake cylinders on an aircraft).

❖ Connect pipes and valves with a cylinder without having to add a junction in between.

❖ Easily model flows over the cylinder piston (for example, the pressure relief valve bundled with the piston to protect against cylinder damage).

A

B

A (+) B (+)

l

M

(+)

M

(+)


Cylinder2ff94


■ Cylinder2ff computes a force value that acts between its end points, consisting of pressure, friction, and cushion forces.

■ Cushions in the both ends of cylinder2ff are identical.

■ Cushions prevent cylinder2ff from ever reaching its maximum and minimum lengths.

■ Cylinder2ff parts are massless. (If mass is needed, you should account for it in the mechanical side of the model.)

■ Cylinder2ff walls are flexible.

■ Cylinder2ff rods are rigid. (If flexibility is needed, you should account for it in the mechanical side of the model.)

■ Fluid inside cylinder2ff is considered compressible, but massless in the mechanical sense.

■ Mechanical motion/acceleration of cylinder2ff, as a whole, does not affect internal flows or fluid movements.




■ At low sliding velocity, the friction force is decreasing until a specific sliding

velocity is reached (at this transition area, the friction is changing from




vtr( )


Cylinder2ff95

Port Topology




B volumetric flow rate in from port B in STP [length3/time]

: pressure at port B [force/length2]







QASTPpA

QBSTPpB

i marker–

j marker–

F

Fp

Fµ

Fc


Cylinder2ff96


The following table shows the values you enter in the Create and Modify Cylinder2ff dialog boxes. It also shows the symbols for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 101.



I MarkerJ Marker


length

General



B Dead Volume Mechanical volume of retraction chamber of the cylinder at minimum length.

length3


length3


length

B Rod Diameter Diameter of piston rod above piston. length

A Rod Diameter Diameter of piston rod below piston. length

B Chamber Initial Pressure

Initial pressure in the retraction chamber.

force/length2

l0

lmax

lmin

Vudead

Vldead

Dp

dru

drl

pu0


Cylinder2ff97



force/length2

Static Hold Controls cylinder behavior during static analysis. The options are:

■ none - Finds static position freely (design length, extension and retraction chamber pressure floats).

■ pl - Holds initial extension chamber pressure (design length and retraction chamber pressure floats).

■ pu - Holds initial retraction chamber pressure (design length and extension chamber pressure floats).

■ pl_and_pu - Holds initial extension and retraction chamber pressure (design length floats).

■ pl_and_l0 - Holds initial extension chamber pressure and design length (retraction chamber pressure floats).

■ pu_and_l0 - Holds initial retraction chamber pressure and design length (extension chamber pressure floats).

-- --



pl0


Cylinder2ff98

Static Hold (cont.) ■ l0_with_pl - Holds design length by adjusting extension chamber pressure (retraction chamber pressure floats)

■ l0_with_pu - Holds design length by adjusting retraction chamber pressure (extension chamber pressure floats)

-- --

End Stops

Cushion Free Length





Cushion force exponent . --



--



length/time

Flexibility


Youngs Modulus Modulus of elasticity of the cylinder wall material.

force/length2

Poissons Ratio Poisson’s ratio for the cylinder wall material.

--



lc

kc

0 ec 10≤< ec

0 hc 1≤ ≤hc

vlim

s

E

ϑ


Cylinder2ff99

Losses



force



length2

B Rod Seal Friction Coefficient


length2

A Rod Seal Friction Coefficient


length2



length/time



--

Seal Shear Stiffness

Effective seal shear stiffness. force/length

Damping Coefficient

Damping coefficient. force*time/length



Fµ0

a

bu

bl

vtr

µD

ksseal

c


Cylinder2ff100

States



: Volume of fluid in the retraction chamber in STP [length3]

Leakages


Relative clearance for laminar leakage over piston .

--


--

A Rod Leakage Coefficient

Coefficient of leakage over extension chamber rod seal.


B Rod Leakage Coefficient

Coefficient of leakage over retraction chamber rod seal.




0 ϒp≤ϒp

0 Lp<Lp

CArod

CBrod

ls

VlSTP

VuSTP


Cylinder2ff101




(190)


(191)

You can write the equation for pressure delta as:

(192)

You can also write the effective inner area of the cylinder as a function of pressure as:

(193)


ADAMS/Hydraulics computes the cylinder length and its time derivative based on the locations and velocities of the cylinder attachment points using the functions DM and VR. For information on DM and VR functions, see the ADAMS/Solver (FORTRAN) online help.

(194)

(195)

Λp

uDpΛp

2E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

=

Do Dp 2s+=

Λp p pe–=

Aeff Dp 2u+( )2π4--- 1

p pe–

E--------------

Do2 Dp

2+

Do2 Dp

2–-------------------- ϑ+

+ 2

π4---Dp

2= =




Cylinder2ff102

Design length of the cylinder is computed in the beginning of a simulation as follows:

(196)

Areas of piston rods are:

(197)

(198)

The piston pressure area for retraction and extension pressures is:

(199)

(200)

Instantaneous mechanical volume of the retraction and extension chamber of the cylinder is:

(201)

(202)

ADAMS/Hydraulics computes the initial volumes of fluid in the retraction and extension chamber in STP based on the given initial pressures in both of the chambers, such that:

(203)

(204)



Aru dru2 π

4---=

Arl drl2 π

4---=

Au Aeff Aru–=

Al Aeff Arl–=

Vu lmax l–( )Au Vudead+=


Vuini

ρu0Vu0

ρf luidSTP

------------------f pu0 T,( )

f pSTP TSTP,( )---------------------------------Vu l0( )= =

Vlini

ρl0Vl0

ρf luidSTP

------------------f pl0 T,( )

f pSTP TSTP,( )---------------------------------Vl l0( )= =

ρ f p T,( )=


Cylinder2ff103

ADAMS/Hydraulics defines density as mass per unit of volume. It calculates the density of the fluid in the retraction and extension chamber of the cylinder as:

(205)

(206)

It also calculates the pressure of the fluid in the retraction and extension chambers of the cylinder using the equation of state for the fluid, such that:

(207)

(208)

Following ADAMS sign convention in which a repelling point-to-point force is positive, you can obtain the following for the total pressure force:

(209)


ADAMS/Hydraulics assumes the maximum static friction force consists of three or four force components:

(210)


, friction force magnitude over upper rod seal (212)

, friction force magnitude over lower rod seal(213)

The fourth term of Equation (210) is a constant and represents dry Coulomb friction due to precompression of seals. Force over lower rod seal (Equation 213) is naturally zero in the case of a differential cylinder, which has no lower rod.

ρu

VuSTP

Vu-----------ρf luidSTP

=

ρl

VlSTP


=

pu f ρu T,( )=

pl f ρl T,( )=

Fp plAl puAu– peArl peAru–+=

Fµsta Fµpiston Furod Flrod Fµ0+ + +=

Fµpiston a pl pu–=

Furod bu pu pe–=

Flrod bl pl pe–=


Cylinder2ff104

If you assume that dynamic friction is fully developed at sliding velocity of , you can

then write the equation for dynamic friction force as:

(214)



(215)

If you further assume that there is an additional velocity-dependent damping term involved, then the instantaneous friction force acting on the cylinder is:

(216)

(217)

Cushion Force Model

ADAMS/Hydraulics assumes that cushion force goes to infinity while the cylinder approaches either its maximum or minimum length. The cushion force prevents the cylinder from going beyond its limit length values. ADAMS/Hydraulics assumes that the cushion force characteristics are the same on both ends of the cylinder. For an impact against the extension chamber cushion (at the minimum cylinder length), the equations that compute the force are:

(218)

(219)

vtr( )

Fµdyn 1 µD

min l· vtr,( )vtr

----------------------------–

Fµsta=

ksseal( )

∆lµmax

Fµdyn

ksseal--------------=

∆lµ l ls–=



Fc kcpen

lc pen–-------------------

ecstep l· v– lim 1

hc

2-----+ vlim 1

hc

2-----–, , , ,

=


Cylinder2ff105


(220)

(221)


Cylinder Force


(222)

Flow Model

While volumetric flow rate in from ports A and B are given, corresponding mass flow rates are simply:

(223)

(224)


(225)

where:

■ is radial clearance [length]

■ is kinematic viscosity of fluid [length2/time]

■ is passage length [length]

■ is eccentricity of shaft [length]


( )–,( )=

Fc k– cpen

lc pen–-------------------


hc

2-----– vlim 1

hc

2-----+, , , ,

=

F Fp Fµ Fc+ +=

m· A QASTPρf luidSTP

=

m· B QBSTPρf luidSTP

=

c D«

m·πDc3

12νL------------- 1

32---

ec--

2+

∆p=

c

ν

L

e


Cylinder2ff106

If you assume that the eccentricity is zero or compensated in the value of relative clearance, you can define a dimensionless relative clearance as follows:

(226)

From Equations (225) and (226), the laminar leakage flow over the piston is:

(227)

Leakage over rods are:

(228)

(229)

The sum of flow rates to and from retraction and extension cylinder chambers are, respectively:

(230)

(231)

(232)

(233)

ϒp

ϒp2cD------=

m· lu ϒp3 πD4

96νL-------------

pl pu–( )=

m· Arod CArod pl pe–( )=

m· Brod CBrod pu pe–( )=

QlSTP

m· lu– m· A m· Arod–+

ρfluidSTP

-----------------------------------------------=

QuSTP

m· lu m· B m· Brod–+

ρf luidSTP

-------------------------------------------=

VlSTPQlSTP

td∫=

VuSTPQuSTP

td∫=


Directional Control Valve 2/2107


Screen Icons


Description

ADAMS/Hydraulics assumes that for a directional control valve 2/2:


■ Spool is massless.

■ Flow characteristics are the same for both flow directions.

A

P

A

P

P (+)

A (+)

f( )

(+)

x



Port Topology


The following table shows the values you enter in the Create or Modify Directional Control Valve 2/2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 111.






Control Input Function

External control input of the valve .

--

X=f(I)

Valve Type Select Open or Closed. --

Initial Position Initial relative spool position, .

--

pP QPSTP

pA QASTP

0 f 1≤ ≤f

K

0 x 1≤ ≤x



I to X Method Method to convert control input function signal to spool position (x). Options:■ direct - Like mechanical

coupling, spool position equals control input value.

■ constant_velocity - First order spool dynamics.

--

Valve Opening Timeconstant_velocity

Switching time for valve opening ( ).

time

Valve Closing Timeconstant_velocity

Switching time for valve closing ( ).

time

A=f(X)

PA X to A Method Method to convert spool position (x) to relative PA flow passage area. The options are:■ linear - Relative opening area is

linearly dependent on relative spool position.

■ nonlinear - Spool under or overlap, radial leakage, and coefficient of nonlinearity define relationship between relative opening area and relative spool position.

■ spline - An arbitrary nonlinear curve defines relationship between relative opening area and relative spool position.

--



ItoX

τo 0>τo

τc 0>τc

XtoAPA



States: Relative spool position [],

PA Xlap(nonlinear)

Relative spool position lap for flow from port P to port A ( ).

--

PA Relative Leakage(nonlinear)

Relative leakage for flow from port P to port A ( ).

--

PA Nonlinearity(nonlinear)

Coefficient of nonlinearity for flow from port P to port A ( ).

--

PA X to A Spline(spline)

Spline name, which defines (x,R)-points for flow from port P to port A ( and ).

--

Q=f(A,dp)

Nom Pressure Drop Pressure drop at nominal volumetric flow rates.

force/length2

PA Nom Flowrate Nominal volumetric flow from port P to port A at full opening.

length3/time

Ref Fluid Density Density of the reference fluid (the fluid used for the measurement of the pressure drop at nominal volumetric flow through the valve).

mass/length3



1– xlap 1< <xlapPA

0 ϒ 1≤ ≤ϒPA

0 NLPA 1<≤NLPA

1– x 1≤ ≤ 0 R 1≤ ≤

SPA

∆pnom

QnomPA

ρref

x 0 x 1≤ ≤





If the valve is normally closed, ADAMS/Hydraulics internally reversed the control input; that is, when . It defines internal control input ( ) as:

(234)

Method: Direct

(235)

Method: Constant Velocity

ADAMS/Hydraulics calculates the relative velocity of spool using the CVS function (see CVS - Constant Velocity Spool on page 300):

(236)


The relative opening of the flow cross-section area from port P to port A is calculated from relative spool displacement (x) with the selected method, linear, nonlinear, or spline.

Method: linear

(237)

Method: nonlinear

(238)

In a real-world valve construction, there are flow restrictions other than the spool opening area itself, which limit the actual flow rate throughput of the valve. For example, if the area of the flow input (or output) passage of the valve is not substantially larger than the maximum spool opening area, it may introduce significant additional flow restriction especially at large spool openings. The coefficient of nonlinearity is intended to be used for flow restrictions other than the spool opening itself.

f 0= fc

fc f if K, 0fc 1 f, if K– 1

= == =

x fc=

x· CVS fc x n τo τc δ 0, , , , , ,( )=

RPA max x 0,( )=

RPA CLWL x xlapPAϒPA NLPA 0, , , ,( )=



Definition of coefficient of nonlinearity

ADAMS/Hydraulics assumes that, beyond laps, the spool opening area increases linearily with respect to the spool movement and that other restrictions remain constant. It also assumes constant pressure drop over the flow passage under investigation, and determines the rate of stationary flow rate increase with respect to the spool movement when the given passage just starts to open (spool just over the lap). Assuming a linear increase of flow rate up to the maximum spool position, estimate how much flow throughput you would get without additional flow restrictions. The coefficient of nonlinearity is defined to be the ratio of the actual maximum flow rate over the estimated unrestricted flow rate.

For further details on the CLWL function, see CLWL - Constant Leakage with Lap on page 298.

Method: spline(239)

A spline holds at least four (x,R)-points to define the relationship between the relative spool position and the relative flow cross-section area. A positive R value at zero x causes the spool to leak. For more information on applied spline-fitting functions, refer to Akima Fitting Method (AKISPL) in the guide, Using the ADAMS/View Function Builder.

You can usually find an operating curve of a specific directional control valve 2/2 in a component manufacturer’s data sheet. Figure 3 on page 113 shows an example of an operating curve of a directional control valve 2/2.

RPA AKISPL x 0 SPA, ,( )=



Figure 3. Example of Operating Curve of Directional Control Valve 2/2

ADAMS/Hydraulics computes the maximum flow cross-section area internally from a

given operating curve point based on Equation (240). It applies default

values and for laminar flow regime, which affects the shape of the

flow rate curve only at very low pressure drops.

(240)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Pressure Drop dp [bar]

Volumetric Flow Q [l/min]

Operating Curve for a 2/2-Directional Control Valve

Qnom,∆pnom( )

Cd 0.6= Retr 50=

Amax

Qnom

Cd-------------

ρref

2∆pnom-------------------=



Flow Model

ADAMS/Hydraulics calculates the flow rate using the ORIFIC function (see ORIFIC - Flow Through an Orifice on page 304), such that:

(241)

(242)

(243)

m· PA ORIFIC R Cd Retr Amax pP pA 0, , , ,, ,( )=

QPSTP

m· PA–

ρfluidSTP

------------------=

QASTP

m· PA

ρfluidSTP

------------------=




Screen Icons


Description

ADAMS/Hydraulics assumes that for a directional control valve 3/2:


■ The spool is massless.


A

P T

A

P T

P (+)

f( )

(+)

xA (+)

T (+)



Port Topology


The following table shows the values you enter in the Create and Modify Directional Control Valve 3/2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 120.




T : pressure at port T [force/length2] : volumetric flow rate out from port T in STP [length3/time]





--

X=f(I)

Valve Type Select Open or Closed. --

Initial Position Initial relative spool position, --

pP QPSTP

pA QASTP

pT QTSTP

0 f 1≤ ≤f

K

0 x 1≤ ≤x



I to X Method Method to convert control input function signal to spool position (x). The options are:■ direct - Like mechanical

coupling, spool position equals control input value.

■ constant_velocity - First-order spool dynamics.

--



time



time

A=f(X)

PA X to A Method Method to convert spool position (x) to relative PA flow passage area. The options are:■ linear - Relative opening area

is linearily dependent on relative spool position.



--



ItoX

τo 0>τo

τc 0>τc

XtoAPA



PA Xlap(nonlinear)


--



--



--



--

AT X to A Method Method to convert spool position (x) to relative AT flow passage area. The options are:■ linear - Relative opening area

is linearily dependent on relative spool position.



--




0 ϒ 1≤ ≤ϒPA

0 NLPA 1<≤

NLPA

1– x 1≤ ≤ 0 R 1≤ ≤

SPA

XtoAAT



AT Xlap(nonlinear)

Relative spool position lap for flow from port A to port T ( ).

--

AT Relative Leakage(nonlinear)

Relative leakage for flow from port A to port T ( ).

--

AT Nonlinearity(nonlinear)

Coefficient of nonlinearity for flow from port A to port T ( ).

--

AT X to A Spline(spline)

Spline name, which defines (-x,R)-points for flow from port A to port T, ( and ).

--

Q=f(A,dp)


force/length2


length3/time

AT Nom Flowrate Nominal volumetric flow from port A to port T at full opening.

length3/time


mass/length3



1– xlap 1< <xlapAT

0 ϒ 1≤ ≤ϒAT

0 NLAT 1<≤

NLAT

1– x 1≤ ≤ 0 R 1≤ ≤

SAT

∆pnom

QnomPA

QnomAT

ρref



States

: Relative spool position [],



If the valve is normally closed, ADAMS/Hydraulics internally reverses the control input; that is, when . It defines the internal control input ( ) as follows:

(244)

Method: Direct

(245)


ADAMS/Hydraulics calculates the relative velocity of the spool using the CVS function (see CVS - Constant Velocity Spool on page 300):

(246)


The relative opening of the flow cross-section areas from port P to port A and from ports A to port T are calculated from relative spool displacement ( ) with the selected method: linear, nonlinear, or spline.

Method: linear

(247)

(248)

Method: nonlinear

(249)

(250)

x 0 x 1≤ ≤

f 0= fc

fc f if K, 0fc 1 f, if K– 1

= == =

x fc=

x· CVS fc x n τo τc δ 0, , , , , ,( )=

x

RPA max x 0,( )=

RAT max x– 0,( )=


RAT CLWL x– xlapATϒAT NLAT 0, , , ,( )=



In a real-world valve construction, there are flow restrictions other than the spool opening area itself, which limit the actual flow rate throughput of the valve. For example, if the area of the flow input (or output) passage of the valve is not substantially larger than the maximum spool opening area, it may introduce significant additional flow restriction, especially at large spool openings. The coefficient of nonlinearity is intended to be used for flow restrictions other than the spool opening itself. For more information, refer to Definition of coefficient of nonlinearity on page 112.

Method: spline(251)

(252)

Each spline holds at least four (x,R)-points to define the relationship between the relative spool position and the relative flow cross-section area. Functions are defined in such a way that all flows can use the same spline definition, if the spool is fully symmetric. A positive R value at zero x causes the spool to leak. For more information on applied spline-fitting functions, refer to Akima Fitting Method (AKISPL) in the guide, Using the ADAMS/View Function Builder.

It internally computes the maximum flow cross-section area for flow from port P to port A from a given operating curve point based on Equation (253), and,

for flow from port A to port T from point , respectively, based on

Equation (254). Default values and are applied for laminar flow

regime, which affects the shape of the flow rate curve only at very low pressure drops:

(253)

(254)


RAT AKISPL x– 0 SAT, ,( )=

QnomPA,∆pnom( )

QnomAT,∆pnom( )

Cd 0.6= Retr 50=

AmaxPA

QnomPA

Cd-------------------

ρref

2∆pnom-------------------=

AmaxAT

QnomAT

Cd-------------------

ρref

2∆pnom-------------------=



Flow Model

ADAMS/Hydraulics calculates flow rates using the ORIFIC function (see ORIFIC - Flow Through an Orifice on page 304), such that:

(255)

(256)

(257)

(258)

(259)

m· PA ORIFIC RPA Cd Retr AmaxPA pP pA 0, , , ,, ,( )=

m· AT ORIFIC RAT Cd Retr AmaxAT pA pT 0, , , ,, ,( )=

QPSTP

m·– PA

ρfluidSTP

------------------=

QASTP

m· PA m· AT–

ρfluidSTP

--------------------------=

QTSTP

m· AT

ρf luidSTP

------------------=




Screen Icon


DescriptionADAMS/Hydraulics assumes that for a directional control valve 4/3:




■ Spool returns to center position when external control is set to zero.

A

P T

B

B (+)

P (+) T (+)

f( )

(+)

xA (+)

T (+)



Port Topology


The following table shows the values you enter in the Create and Modify Directional Control Valve 4/3 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 130.










--

X=f(I)


--

pP QPSTP

pA QASTP

pB QBSTP

pT QTSTP

1– f 1≤ ≤f

0 x 1≤ ≤x



I to X Method Method to convert control input function signal to spool position (x). The options are:■ direct - Like mechanical

coupling, spool position equals control input valve.

■ constant_velocity - First order spool dynamics.

--



time



time

A=f(X)


linearily dependent on relative spool position.



--



ItoX

τo 0>τo

τc 0>τc

XtoAPA



PA Xlap(nonlinear)


--



--



--



--

PB X to A Method Method to convert spool position (x) to relative PB flow passage area. The options are:■ linear - Relative opening area is




--

PB Xlap(nonlinear)

Relative spool position lap for flow from port P to port B ( ).

--




0 ϒ 1≤ ≤ϒPA

0 NLPA 1<≤NLPA

1– x 1≤ ≤ 0 R 1≤ ≤

SPA

XtoAPB

1– xlap 1< <xlapPB



PB Relative Leakage(nonlinear)

Relative leakage for flow from port P to port B ( ).

--

PB Nonlinearity(nonlinear)

Coefficient of nonlinearity for flow from port P to port B ( ).

--

PB X to A Spline(spline)

Spline name, which defines(-x,R)-points for flow from port P to port B, ( and ).

--

AT X to A Method Method to convert spool position (x) to relative AT flow passage area. The options are:■ linear - Relative opening area is




--

AT Xlap(nonlinear)


--



--



0 ϒ 1≤ ≤ϒPB

0 NLPB 1<≤NLPB

1– x 1≤ ≤ 0 R 1≤ ≤

SPB

XtoAAT


0 ϒ 1≤ ≤ϒAT





--



--

BT X to A Method Method to convert spool position (x) to relative BT flow passage area. The options are:■ linear - Relative opening area is




--

BT Xlap(nonlinear)

Relative spool position lap for flow from port B to port T ( ).

--

BT Relative Leakage(nonlinear)

Relative leakage for flow from port B to port T ( ).

--

BT Nonlinearity(nonlinear)

Nonlinearity factor for flow from port B to port T ( ).

--



0 NLAT 1<≤NLAT

1– x 1≤ ≤ 0 R 1≤ ≤

SAT

XtoABT

1– xlap 1< <xlapBT

0 ϒ 1≤ ≤ϒBT

0 NLBT 1<≤NLBT



States


BT X to A Spline(spline)

Spline name, which defines (x,R)-points for flow from port B to port T, ( and ).

--

Q=f(A,dp)


force/length2


length3/time

PB Nom Flowrate Nominal volumetric flow from port P to port B at full opening.

length3/time


length3/time

BT Nom Flowrate Nominal volumetric flow from port B to port T at full opening.

length3/time

PT Nom Flowrate Nominal volumetric flow from port P to port T.

length3/time


mass/length3



1– x 1≤ ≤ 0 R 1≤ ≤

SBT

∆pnom

QnomPA

QnomPB

QnomAT

QnomBT

QnomPT

ρref

x 1– x 1≤ ≤





The valve spool centers itself at zero external input ( ). Positive external input ( ) connects pressure port P to output port A (and B to T) and negative external input ( ) connects pressure port P to output port B (and A to T).

Method: Direct

(260)


ADAMS/Hydraulics calculates the relative velocity of the spool using the CVS function (see CVS - Constant Velocity Spool on page 300):

(261)


The relative opening of the flow cross-section areas from port P to ports A and B and from ports A and B to port T are calculated from relative spool displacement ( ) with the selected method: linear, nonlinear, or spline.

Method: linear

(262)

(263)

(264)

(265)

Method: nonlinear

(266)

(267)

(268)

(269)

f 0=

0 f 1≤<1– f 0<≤

x fc=

x· CVS f x n τo τc δ 0, , , , , ,( )=

x

RPA max x 0,( )=

RPB max x– 0,( )=

RAT max x– 0,( )=

RBT max x 0,( )=


RPB CLWL x– xlapPBϒPB NLPB 0, , , ,( )=


RBT CLWL x xlapBTϒBT NLBT 0, , , ,( )=



In a real-world valve construction, there are flow restrictions other than the spool opening area itself, which limit the actual flow rate throughput of the valve. For example, if the area of the flow input (or output) passage of the valve is not substantially larger than the maximum spool opening area, it may introduce significant additional flow restriction, especially at large spool openings. The coefficient of nonlinearity is intended to be used for flow restrictions other than the spool opening itself. For more information, refer to Definition of coefficient of nonlinearity on page 112.

Method: spline(270)

(271)

(272)

(273)


To identify the five maximum flow cross-section areas for flows P to A, P to B, A to T,

B to T, and P to T, five operating curve points are required as input. The

five maximum flow cross-section areas are computed internally as shown in Equations (274), (7), (276), (277), and (278). Default values and

are applied for laminar flow regime, which affects the shape of the flow rate curve only at very low pressure drops.

(274)

(275)


RPB AKISPL x– 0 SPB, ,( )=


RBT AKISPL x 0 SBT, ,( )=

Qnom,∆pnom( )

Cd 0.6= Retr 50=

AmaxPA

QnomPA

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPB

QnomPB

Cd-------------------

ρref

2∆pnom-------------------=



(276)

(277)

(278)

Flow Model

ADAMS/Hydraulics calculates the flow rates using the ORIFIC function (See “ORIFIC - Flow Through an Orifice” on page 304.), such that:

(279)

(280)

(281)

(282)

(283)

(284)

(285)

(286)

(287)

AmaxAT

QnomAT

Cd-------------------

ρref

2∆pnom-------------------=

AmaxBT

QnomBT

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPT

QnomPT

Cd-------------------

ρref

2∆pnom-------------------=


m· PB ORIFIC RPB Cd Retr AmaxPB pP pB 0, , , ,, ,( )=


m· BT ORIFIC RBT Cd Retr AmaxBT pB pT 0, , , ,, ,( )=

m· PT ORIFIC 1.0 Cd Retr AmaxPT pP pT 0, , , ,, ,( )=

QPSTP

m·– PA m· PB– m· PT–

ρfluidSTP

----------------------------------------------=

QASTP

m· PA m· AT–

ρfluidSTP

--------------------------=

QBSTP

m· PB m· BT–

ρfluidSTP

--------------------------=

QTSTP

m· AT m· BT m· PT+ +

ρfluidSTP

-------------------------------------------=


Flow Source133

Flow Source

Screen Icon

DescriptionFlow source inputs or outputs a predefined volumetric flow from its port A. ADAMS/Hydraulics assumes that there is no resistance in port A and, therefore, the pressure of the flow source is always equal to the input pressure of port A.

Port Topology



AFLOW

pA QASTP


Flow Source134

Dialog Box Parameter

The following table shows the values you enter in the Create and Modify Flow Source dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 134.

ADAMS/Hydraulics FormulationThe formulation of flow source is:

(288)

Tip: Flow source generates a flow rate equal to the value of the “Flowrate Function” with one exception. If the input density (and thus pressure) drops below STP density of the fluid while flow source is absorbing fluid away from the system (sucking), then the flowrate is scaled with the ratio of input density and STP density of the fluid. This prevents flow source from asking mass flow out of a volume, which has no fluid left in it.



User Parameters

Initial Flow Estimate of the initial flow rate of the flow source.

length3/time

Flowrate Function Volumetric flow rate function in STP. length3/time

Qini

Qf

QASTP

Qf Qf 0≥,

min ρA ρSTP,( )ρSTP

------------------------------------Qf

Qf 0<,=


Fluid135

Fluid

Screen Icon

DescriptionIn a hydraulic system, fluid can appear in the form of a liquid or as a combination of liquid and gas. In ADAMS/Hydraulics, fluid has the following properties:

■ Compressibility through the equation of state for a fluid (dependency between density, pressure, and temperature).

■ Nonlinear behavior at low pressure (cavitational effects).

■ Content of dissolvable and undissolvable air.

■ Temperature dependant viscosity.

For fluids, ADAMS/Hydraulics makes the following assumptions:

■ There is a unique pressure-density-temperature relationship (equation of state for a fluid).

■ Density and pressure of a fluid are always greater than zero.

■ The amount of air in a system can be defined as amount of dissolvable and undissolvable air.

■ There is no time delay on air dissolving into or undissolving from fluid.

■ Viscosity of fluid is dependent only on temperature.

■ Dissolved air does not affect the volume of fluid.

■ Air compression and expansion process from standard temperature and pressure to saturation pressure and system temperature has been relatively slow.

■ Air compression and expansion process from saturation pressure to current operating pressure is polytropic during an analysis.

FLUID

f ρ p T, ,( ) 0=

psat T


Fluid136


The following table shows the values you enter in the Create and Modify Fluid dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 138.



Temperature Fluid temperature. Defaults to 293.15 K.

temperature

Equation of State

Eos for Liquid Method

Method to apply for approximation of the equation of state for pure liquid (the only supported method at the moment is Merritt).

--

Ref Density Definition density of the fluid. mass/length3

Ref Temperature Definition temperature of the fluid. temperature

Ref Pressure Definition pressure of the fluid. force/length2

Bulk Modulus The compressibility of the pure liquid. (Merritt [1, p. 21] gives values

MPa of bulk modulus for some pure hydraulic liquids)

force/length2

Thermal Expansion Coefficient

How much pure liquid expands for a raise of one unit of temperature. (Merritt [1, p. 21] gives values

1/K for thermal expansion coefficient for some pure hydraulic liquids.)

1/temperature

T

ρref

Tref

pref

B 1500…2500≈

α 0.0002…0.0003≈

α


Fluid137

Air Content

Air Content Method Method to apply for approximation of air content of the fluid.The only method currently is CCUA (constant content of undissolvable air).

-- --

Air Density at STP Density of air at standard temperature and pressure (STP).

mass/length3

Saturation Pressure Lowest pressure at which dissolvable air is fully dissolved into fluid; that is, when the saturation pressure fluid has stayed in contact with the air long enough to become fully saturated with air.

force/length2

Solubility Coefficient Solubility coefficient for dissolved air.

--

Undissolvable Air Content

Volumetric content of undissolvable air in fluid at standard temperature and pressure (STP), .

--

Polytropic Exponent Polytropic exponent for air compression process.

--

Viscosity

Note that Viscosity is interpolated between given temperature–viscosity points using the method defined by the viscosity_method keyword.



ρaSTP

psat

Sc

0 Cu 1<≤

Cu

κ


Fluid138


Equation of State for Liquid, method = "Merritt"

ADAMS/Hydraulics calculates the density of the pure liquid using the method that Merritt [1, p. 7] proposes, which is:

(289)

where:

definition density of fluid [mass/length3]

bulk modulus of pure liquid [force/length2]

fluid pressure [force/length2]

definition pressure of fluid [force/length2]

thermal expansion coefficient []

fluid temperature [temperature]

definition temperature of fluid [temperature]

Viscosity Method Method to apply for approximation of the viscosity of the fluid (the only method currently is ASTM_D_341-43).

-- --

Temperature Points Temperature values corresponding to viscosity points.

temperature --

Viscosity Points Viscosity values corresponding to temperature points.

length2/time --



ρl ρref 11

B0------ p pref–( ) α T Tref–( )–+=

ρref

B0

p

pref

α

T

Tref


Fluid139

Air Content, method = "CCUA"

ADAMS/Hydraulics defines the volumetric content of dissolvable free air in a fluid as:

(290)

(291)

where:

solubility coefficient []

saturation pressure [force/length2]

standard pressure ( ) [force/length2]

The effective density of the fluid, therefore, is:

(292)

where:

density of air at standard temperature and pressure (STP) [force/length2]

density of pure liquid at standard temperature and pressure (STP)

[force/length2] (defined using the equation of state for liquid)

volumetric content of undissolvable air in fluid []

polytropic exponent []

standard temperature ( ) [temperature]

Cdmax1

1pSTP

Sc psat⋅-------------------+

----------------------------=

Cd Cdmaxp

psat---------

3 ppsat---------

2–

ppsat---------– 1+ 0 p psat≤<,⋅=

Sc

psat

pSTP pSTP 101325 Pa=

ρeff

1ρaSTP

ρlSTP--------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅+

1ρl----

1ρlSTP-------------

pSTP

psat-----------

psat

p---------

1κ---

TTSTP------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅ ⋅ ⋅ ⋅+

---------------------------------------------------------------------------------------------------------------------------------=

ρaSTP

ρlSTP

Cu

κ

TSTP TSTP 293.15 K=


Fluid140

Viscosity, method = "ASTM_D_341-43"

ADAMS/Hydraulics defines the viscosity–temperature relationship using a method based on standard ASTM D 341-43. It defines viscosity as:

(293)

where:

(294)

(295)

(296)

(297)

(298)

(299)

(300)

(301)

and where the symbols are:

first definition temperature [Kelvin]

kinematic viscosity at temperature [centiStoke]

second definition temperature [Kelvin]

kinematic viscosity at temperature [centiStoke]

operating temperature [Kelvin]

Note: This method is unit sensitive. ADAMS/Hydraulics applies the appropriate units for the above interpolation.

ν ee

y3

0.7–=

y3 a bx3+=

a y1 bx1–=

by1 y2–

x1 x2–----------------=

x3 T( )ln=

x1 T1( )ln=

y1 ν1 0.7+( )ln( )ln=

x2 T2( )ln=

y2 ν2 0.7+( )ln( )ln=

T1

ν1 T1

T2

ν2 T2

T


Fluid141

Math Follow-Up

Equation of State for a Fluid

The equation of the state of a liquid cannot be mathematically derived from physical principles [1, p. 6]. ADAMS/Hydraulics defines the pressure of a fluid by the approximation of the equation of state. This approximation defines the relationship:

(302)

where:

pressure of the fluid

density of the fluid

operating temperature

Merritt [1, p. 8] proposes a linearized approximation at , , and for the

equation of a state of a liquid as the first three terms of Taylor’s series for two variables:

(303)

where:

density of the fluid

reference density of the fluid

pressure of the fluid

reference pressure of the fluid

operating temperature

reference temperature of the fluid

or similarly:

(304)

f ρ p T, ,( ) 0=

p

ρ

T

pref ρref Tref

ρ ρrefρ∂p∂

------

Tp pref–( ) ρ∂

T∂------

p

T Tref–( )+ +=

ρ

ρref

p

pref

T

Tref

ρ ρref 11B--- p pref–( ) α T Tref–( )–+=


Fluid142

where, bulk modulus is:

(305)

and:

(306)

ADAMS/Hydraulics assumes that the dissolved air does not affect the volume of fluid. Therefore, the effective density of the fluid (mixture of pure liquid and air) is:

(307)

where:

mass of the pure liquid

mass of air

density of the liquid

volume of the free air

The volume of free air is divided in two components:

(308)

where:

volume of dissolvable free air

volume of undissolvable air

Also, the mass of air is the sum of two components:

(309)

where:

mass of the dissolvable free air

mass of the undissolvable air

B ρrefp∂ρ∂

------

T≡

α 1ρref---------

ρ∂T∂

------

p–≡

ρeff

ml ma+

ml

ρl----- Vfa+

--------------------=

ml

ma

ρl

Vfa

Vfa Vd Vu+=

Vd

Vu

ma md mu+=

md

mu


Fluid143

The volumetric content of dissolvable free air at standard temperature and pressure (STP) is:

(310)

where:

volume of dissolvable free air at standard temperature and pressure (STP)

volume of pure liquid at standard temperature and pressure (STP)

The volume of dissolvable free air at standard temperature and pressure is:

(311)

The analogical definition is used for undissolvable air, which yields:

(312)

where:

volume of undissolvable air in fluid at standard temperature and pressure

(STP)

volumetric content of undissolvable air in fluid at standard temperature and

pressure (STP)

The volumetric content of dissolvable free air is a function of pressure. Henry’s law defines the relationship between the volume of dissolvable free air and pressure as follows:

(313)

where:

solubility coefficient

Cd

VdSTP

VdSTP VlSTP+-----------------------------------=

VdSTP

VlSTP

VdSTP

Cd

1 Cd–--------------- VlSTP⋅=

VuSTP

Cu

1 Cu–--------------- VlSTP⋅=

VuSTP

Cu

VdSTP

VlSTP--------------- Sc

ppSTP-----------⋅=

Sc


Fluid144

The maximum volumetric content of the dissolvable free air is defined assuming that the fluid has stayed for a long time at the saturation pressure in contact with the air, and, therefore, is fully saturated by air. Combining Equation 311 and Henry’s law (Equation 313) yields the following for maximum volumetric content of dissolvable free air:

(314)

where:

saturation pressure – lowest pressure where all the dissolvable air is dissolved

into the fluid

The saturation process of a hydraulic fluid and air depends on, among others, time, fluid agitation, and contact area of fluid and air. To roughly approximate this process and to guarantee continuity at psat, a polynomial fit has been developed. The polynomial fit is third degree function that satisfies:

■ The polynomial fit at

■ The polynomial fit at

■ The derivative over pressure of the polynomial fit at zero satisfies:

■ The derivative over pressure of the polynomial fit at psat satisfies:

Polynomial fit with the above conditions yields:

(315)

Figure 4 on page 145 shows the relative volumetric content of the dissolvable air (Cdmax). The straight line illustrates Henry’s law and the curved line below the straight line shows the polynomial fit applied in ADAMS/Hydraulics.

Cdmax1

1pSTP

Sc psat⋅-------------------+

----------------------------=

psat

f 0( ) Cdmax=

f psat( ) 0=

df 0( )dp

-------------Cdmax

psat---------------–=

df psat( )dp

------------------- 0=

Cd Cdmaxp

psat---------

3 ppsat---------

2–

ppsat---------– 1+ 0 p psat≤<,⋅=


Fluid145

Figure 4. Polynomial Fit for the Relative Volumetric Content Of Dissolvable Air

ADAMS/Hydraulics assumes that the air compression and expansion process from standard temperature and pressure to saturation pressure and system temperature

has been relatively slow (recall that, by definition, saturation pressure is the pressure at which fluid had stayed a relatively long time in contact with air).

(316)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Relative Amount of Undissolved Air

Relative Pressure

Polynomial Fit for Amount of Dissolvable Air

psat T

V1 VSTP

pSTP

psat-----------

TTSTP------------⋅ ⋅=


Fluid146

During actual operation (simulation), the air compression and expansion process in a hydraulic system is assumed polytropic, that is:

(317)

For the volume of the dissolvable free air at pressure p, this yields:

(318)

and, similarly, for undissolvable air:

(319)

Equation (311) yields the following for mass of the dissolvable air:

(320)

and Equation (312) yields:

(321)

Equations (308), (311), (312), (318), and (319) yield the following for the volume of free air:

(322)

and Equations (309), (320), and (321) yield the following for the mass of air:

(323)

V V1

psat

p---------

1κ---

=

Vd VdSTP

pSTP

psat-----------

TTSTP------------

psat

p---------

1κ---

⋅ ⋅ ⋅=

Vu VuSTP

pSTP

psat-----------

TTSTP------------

psat

p---------

⋅ ⋅

1κ---

⋅=

md

Cd

1 Cd–---------------

ρaSTP

ρlSTP-------------- ml⋅ ⋅=

mu

Cu

1 Cu–----------------

ρaSTP

ρlSTP---------------- ml⋅ ⋅=

Vfa

ml

ρlSTP-------------

pSTP

psat-----------

psat

p---------

⋅

1κ---

TTSTP------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅ ⋅ ⋅=

ma ml

ρaSTP

ρlSTP--------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅ ⋅=


Fluid147

From Equations (307), (322), and (323), the effective density of the fluid is:

(324)

In Figure 5 on page 148, there is a sample plot of a equation of state for fluid with following parameters:

■ Bulk modulus of pure liquid

■ Reference density of the pure liquid kg/m3

■ Reference pressure of the pure liquid

■ Reference temperature of the pure liquid

■ Thermal expansion coefficient

■ Saturation pressure

■ Solubility coefficient

■ Density of the air at STP kg/m3

■ Volumetric content of undissolvable air

■ Polytropic exponent

ρeff

1ρaSTP

ρlSTP--------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅+

1ρl----

1ρlSTP-------------

pSTP

psat-----------

psat

p---------

1κ---

TTSTP------------

Cd

1 Cd–---------------

Cu

1 Cu–---------------+

⋅ ⋅ ⋅ ⋅+

---------------------------------------------------------------------------------------------------------------------------------=

B 1900.0 MPa=

ρref 900.0=

pref 1.0 bar=

Tref 293.15 K=

α 0.00028 1/K=

psat 2.0 bar=

Sc 0.08=

ρaSTP 1.2=

Cu 0.002=

κ 1.4=


Fluid148

Figure 5. A Sample Plot of Equation of State for a Fluid

Fluid Density as a Function of Pressure and Temperature

0100000

200000300000

400000500000

600000700000

800000900000

1e+06

273.15283.15

293.15303.15

313.15323.15

333.15343.15

353.15363.15

0

200

400

600

800

1000

Pressure [Pa]

Temperature [K]

Density [kg/m3]


Fluid149

Figure 6 shows an example of density of a fluid as a function of pressure and saturation pressure of dissolvable air. The parameter values are the same as in previous example except the temperature, which is constant .

Figure 7 on page 150 shows an example of density of a fluid as a function of pressure and the volumetric content of undissolvable air. The parameter values are the same as in Figure 6.

Figure 6. An Example of Density of a Fluid as a Function of Pressure and Saturation Pressure

T 293.15 K=

Fluid Density as a Function of Pressure and Saturation Pressure

020000

4000060000

80000100000

120000140000

160000180000

200000

0100000

200000300000

400000500000

600000700000

800000900000

0100200300400500600700800900

1000

Pressure [Pa]

Saturation Pressure [Pa]

Density [kg/m3]


Fluid150

Figure 7. An Example of Density of a Fluid as a Function of Pressureand Volumetric Content of Undissolvable Air

Fluid Density as a Function of Pressure and Volumetric Content of Undissolvable Air

050000

100000150000

200000250000

300000350000

400000450000

500000

00.1

0.20.3

0.40.5

0.60.7

0.80.9

0

500

1000

Pressure [Pa]

Content of Undissolvable Air

Density [kg/m3]


Fluid151

Figure 8 shows an example of effective bulk modulus of a fluid for set of values of volumetric content of undissolvable air ( = 0.0 – 5.0%). All the other parameter values

except the volumetric content of undissolvable air are the same as in Figure 6 on page 149.

Figure 8. An Example of Effective Bulk Modulus for a Fluid

Cu

0

1e+08

2e+08

3e+08

4e+08

5e+08

6e+08

7e+08

8e+08

9e+08

1e+09

1.1e+09

1.2e+09

1.3e+09

1.4e+09

1.5e+09

1.6e+09

1.7e+09

1.8e+09

1.9e+09

2e+09

0 5e+06 1e+07 1.5e+07 2e+07 2.5e+07 3e+07

Effective Bulk Modulus [Pa]

Pressure [Pa]

Effective Bulk Modulus as a Function of Pressure

Cu=0.0

Cu=0.001

Cu=0.005

Cu=0.01

Cu=0.02

Cu=0.03

Cu=0.04

Cu=0.05


Fluid152

ViscosityADAMS/Hydraulics interpolates or extrapolates the value of viscosity of a fluid at a given operating temperature based on definition points.The method is based on standard ASTM D 341-43.

Standard ASTM D 341-43 introduces a compact method of approximating viscosity of a fluid with only a couple of definition points and at the same allows users to define viscosity of a fluid based on empirical data.

Figure 9. An Example of Fluid Viscosity as a Function of Temperature

10

100

1000

10000

233.15 253.15 273.15 293.15 313.15 333.15 353.15 373.15 393.15

Viscosity [cSt]

Temperature [K]

Viscosity of Fluid as a Function of Temperature (ESSO HYDRAULIC OIL J26)


Fluid153

Figure 9 on page 152 shows an example of a viscosity plot with the following definition points. Interpolation is applied three times independently for pairs of points (1&2, 2&3, and 3&4). In Figure 9, there are three full curves shown, but naturally only the sections in between definition points are used for interpolation. For temperatures T < T1 and T > T4 extrapolation is applied.

■ ...

■ ...

■ ...

■ ...

T1 233.15 K= ν1 1200.0 cSt=

T2 273.15 K= ν2 78.0 cSt=

T3 313.15 K= ν3 26.0 cSt=

T4 373.15 K= ν4 10.1 cSt=


Fluid154


Force Source155

Force Source

Screen Icon

DescriptionForce source generates a translational force as a user-defined function of any system states. A force source is usually connected to a translational one degree-of-freedom mass.

Port Topology


The following table shows the values you enter in the Create and Modify Force Source dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.


The formulation of force source component is:

(325)


F -- : translational force [force]



User Parameters

Initial Force Estimate of the initial force of the force source.

force

Force Function Force function. force

FF

F

Fini

F

F F ( )=


Force Source156


Generic Pump/Motor157

Generic Pump/Motor

Screen Icon

DescriptionADAMS/Hydraulics assumes that for a generic pump/motor:

■ Positive torque on the output/input shaft corresponds to the positive direction of rotation.

■ Positive direction of rotation of the output/input shaft corresponds to the flow from port A to port B.

■ Pump/motor torque and flow characteristics are supplied through functions (including losses).

■ There is no leakage outside ports A and B.

■ There is no volume inside a pump/motor.

■ Mass properties of a pump/motor belong to the mechanical portion of the model.

■ Mechanical motion/acceleration of a pump/motor, as a whole, does not affect internal flows or fluid movements.

A

B



Port Topology


The following table shows the values you enter in the Create and Modify Generic Pump Motor2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 159.



B : pressure at port B [force/length2] : volumetric flow rate out from port B in STP [c]

Mechanical : angular velocity of the output/input shaft [angle/time]

: output torque [force*length]



Torque Model Parameters

Initial Torque Estimate of the initial torque. force*length

Torque Function Torque function ( )

force*length

Flow Model Parameters

Initial Flowrate Estimate of the volumetric flow rate length3/time

Flowrate Function Volumetric flow rate function ( )

length3/time

pA QASTP

pB QBSTP

ωAB Tout

Tini

Tf f ∆pAB ωAB,( )=

Tf

Qini

Qf f ∆pAB ωAB,( )=

Qf



ADAMS/Hydraulics FormulationPressure drop is defined as:

(326)

Torque Model Parameters

Total torque of a pump/motor is simply:

(327)

Flow Model

The mass flow rate that the generic pump/motor generate/requires is:

(328)

where fluid density is computed from equation of state for the fluid:

(329)

The flow rate out of ports A and B is:

(330)

(331)

Initial Angular Velocity Estimate of the angular velocity of the input shaft

angle/time

Angular Velocity Function

Angular velocity of the input shaft radians/time



ωABini

ωAB

∆pAB pA pB–=

Tout Tf=

m· f ρQfρ ρA if Qf 0ρ

≥,ρB if Qf 0<,

==

=

ρ f p T,( )=

QASTP

m· f–

ρfluidSTP

------------------=

QBSTP

m· f

ρfluidSTP

------------------=


Junction2161

Junction2

Screen Icon

DescriptionJunction is a connecting component that acts between two resistance elements. It serves three purposes:

■ Enables straightforward and flexible topology of a model.

■ Is a point in a fluid power circuit at which pressure is computed, and, therefore, can be observed.

■ Allows you to take into account effects of small volumes of fluid in between hydraulics components. For example, even if your valve is assembled with your cylinder, a flow passage with a define volume is typically needed. Compliance of fluid stored into that passage may become significant in some cases, when the cylinder approaches its end stops and doesn’t have built-in dead volumes of fluid.

Port Topology



: pressure of the fluid in the junction [force/length2]

B : volumetric flow rate in from port B in STP [length3/time]


A B

QASTPp

QBSTPp


Junction2162


The following table shows the values you enter in the Create and Modify Junction2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 162.

States

: Volume of fluid in the junction in STP [length3]


ADAMS/Hydraulics calculates the density of the fluid in a junction as:

(332)

It calculates the pressure of the fluid in the junction using the equation of state for the fluid:

(333)

For more information about the fluid and pressure calculation, see Fluid on page 135.



Initial Pressure Initial pressure in the junction. force/length2

Volume Selector Select Apply default volume or Specify volume.

--

Volume Mechanical volume of the junction. Only available if you selected Specify volume above. Defaults to value of Junction Volume in Setting System Defaults on page 11.

length3

pini

K

Vmec

VfluidSTP

ρmfluid

Vmec--------------

VfluidSTPinipini T,( ) QASTP

QBSTP+( ) td∫+

Vmec-----------------------------------------------------------------------------------------------ρf luidSTP

= =

p f ρ T,( )=


Junction3163

Junction3

Screen Icon

DescriptionA junction is a connecting component that acts between two resistance elements. It serves three purposes:

■ It enables straightforward and flexible topology of a model.

■ It is a point in a fluid power circuit at which pressure is computed and, therefore, can be observed.


Port Topology

For port: Input: Output





C : volumetric flow rate in from port C in STP [length3/time]


A B

C

QASTPp

QBSTPp

QCSTPp


Junction3164


The following table shows the values you enter in the Create and Modify Junction3 dialog boxes. It also shows the symbols for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 164.

States




(334)





--

Volume Mechanical volume of the junction. Available only if you select Specify volume. Defaults to value of Junction Volume in Setting System Defaults on page 11.

length3

pini

K

Vmec

VfluidSTP

ρmfluid

Vmec--------------=


QBSTPQCSTP

+ +( ) td∫+

Vmec------------------------------------------------------------------------------------------------------------------ρf luidSTP

=


Junction3165


(335)


p f ρ T,( )=


Junction3166


Junction4167

Junction4

Screen Icon

DescriptionA junction is a connecting component that acts between two resistance elements. It serves three purposes:

■ It enables straightforward and flexible topology of a model.

■ It is a point in a fluid power circuit at which pressure is computed and, therefore, can be observed.


Port Topology








D : volumetric flow rate in from port D in STP [length3/time]


A B

C

D

QASTPp

QBSTPp

QCSTPp

QDSTPp


Junction4168


The following table shows the values you enter in the Create and Modify Junction4 dialog boxes. It also shows the symbols for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.

States




(336)





--

Volume Mechanical volume of the junction. Available only if you select Specify volume. Defaults to value of Junction Volume in Setting System Defaults on page 11.

length3

pini

K

Vmec

VfluidSTP

ρmfluid

Vmec--------------=


QBSTPQCSTP

QDSTP+ + +( ) td∫+

Vmec--------------------------------------------------------------------------------------------------------------------------------------ρfluidSTP

=


Junction4169


(337)


p f ρ T,( )=


Junction4170


Laminar Orifice171

Laminar Orifice

Screen Icon

Description

ADAMS/Hydraulics models a laminar orifice as a circular tube with a small diameter when compared to the length of the orifice. You can model other cross-section shapes by entering an equivalent diameter. There are also optional turbulent entrance and/or exit pressure drop defined in the laminar orifice.


■ The diameter of laminar orifice is much smaller than its length.

■ The orifice has no volume.

■ The cross section of a laminar orifice is circular (the hydraulic diameter for a circular cross section is ).

Port Topology




A B

LAMINAR

Dh D=

pA QASTP

pB QBSTP


Laminar Orifice172


The following table shows the values you enter in the Create and Modify Laminar Orifice dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.


Pressure Drop Model

The pressure drop due to laminar flow through the orifice is:

(338)

where:

density of the fluid at pressure [force/length2] (at pressure , if flow

direction is from B to A)

kinematic viscosity of the fluid at fluid temperature [length2/time]

volumetric flow rate [length3/time]



Pressure Drop Model Parameters

Length Orifice length. length

Hydraulic Diameter Hydraulic diameter of the orifice. length

Loss Coefficient Entrance/exit loss coefficient. --


N of Orifices in Parallel Number of identical laminar orifices in parallel.

--

L

Dh

K

N

∆pl128νρL

πDh4

-------------------Q=

ρ pA pB

ν

Q


Laminar Orifice173

ADAMS/Hydraulics assumes a circular cross section for laminar orifices. For a circular cross section, the hydraulic diameter is the same as the geometrical diameter. That is:

(339)

Turbulent pressure drop due to entrance/exit losses is:

(340)

Flow Model

Volumetric flow rate through one laminar orifice is solved from the equation:

(341)

The sum of volumetric flows through N laminar orifices computes as:

(342)

(343)

(344)

Aπ4---Dh

2=

∆pt Kρ2---

QA----

2=

pA pB– ∆pl ∆pt+=

m· AB NρQ=

QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Laminar Orifice174

ADAMS/Hydraulics Component Reference 175

One-DOF Translational Mass

Screen Icon

DescriptionA force input from port A accelerates a one-degree-of-freedom (DOF) translational mass. Mass position can be either limited or unlimited depending on how you specify it. A positive force causes positive acceleration.

Port Topology


F : translational force at port F [force]

--

X -- : position of mass [length]

V -- : velocity of mass [length/time]

ACC -- : acceleration of mass [length/time2]

FM

FF

X

v

a


One-DOF Translational Mass176


The following table shows the values you enter in the Create and Modify Mass1 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 177.



General

Mass Mass of one-DOF mass. mass

Initial Position Initial position of mass. length

Initial Velocity Initial velocity of mass. length/time

Bounds

Lower Bound Position Lower bound of X. length

Upper Bound Position Upper bound of X. length

Force at Penetration dx Force at penetration (if you set it to zero, then boundary surfaces do not limit the mass position).

force

Penetration dx Penetration length at which force equals .

length

Force Exponent Exponent of the force deformation characteristics.

--

Max Damping Coefficient

Maximum damping coefficient of boundary surface.

force*time/length

m

Xini

vini

Xl

Xu

dX FdX

FdX

dX

e

c




The formulation of one-DOF translational mass component is:

(345)

(346)

(347)

For information on the MSC.ADAMS BISTOP function, refer to the ADAMS/Solver (FORTRAN) online help.

Penetration for Max Damping

Boundary penetration at which full damping is applied.

length



d

a

FF BISTOP X v Xl Xu

FdX

dX( )e-------------- e c d, , , , , , ,

+

m------------------------------------------------------------------------------------------------------ if FdX 0>( )

a

,

FF

m------ if FdX 0≤( ),

=

=

v vini a td∫+=

X Xini v td∫+=


One-Way Restrictor Valve179

One-Way Restrictor Valve

Screen Icon


DescriptionADAMS/Hydraulics assumes the following for a one-way restrictor valve:

■ There is an adjustable-size orifice and a check valve built parallel to one and other.

■ The orifice is symmetrical for both flow directions.



■ Flow cross-section area is linearly dependent on poppet position.

A B

A

(+)

B

(+)

x

R(+)



Port Topology





: output =volumetric flow rate out from port B in STP [length3/time]

pA QASTP

pB QBSTP




The following table shows the values you enter in the Create and Modify Restrictor Valve2 dialog boxes. It also shows the symbols for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 183.


For the parameter:


General

Initial Position Initial relative poppet position, .

--

Q=f(dp)



AB1 Pressure Drop Pressure drop at the first definition volumetric flow.

force/length2

AB1 Flowrate First definition volumetric flow rate A to B (check valve+orifice).

length3/time

AB2 Pressure Drop Pressure drop at the second definition volumetric flow rate.

force/length2

AB2 Flowrate Second definition volumetric flow rate A to B (at maximum opening, check valve+orifice).

length3/time

AB Relative Leakage


BA Nom Pressure Drop

Pressure drop at nominal volumetric flow rate from port B to port A.

force/length2

0 x 1≤ ≤x

∆pc

∆p1

QAB1

∆p2

QAB2

0 ϒ 1≤ ≤ ϒ

∆pnomBA



States


BA Nom Flowrate Nominal volumetric flow rate from port B to port A (orifice) at full opening.

length3/time

Relative Opening Function

Relative opening of the flow cross-section area of the orifice .

--


mass/length3

Response



force/length2

Hysteresis


--


For the parameter:


QnomBA

0 R 1≤ ≤R

ρref

τ0

τ0 ∆p0

x 0= ε0 1≤ε0

x 0 x 1≤ ≤





ADAMS/Hydraulics assumes that the one-way restrictor valve poppet is massless and closed at . It also assumes the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


spring preload (349)





where:






(354)

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApεpA=

FpB A– ppB=

Ff k3x pA pB––=

c1 k1 k3, ,

x·

Ap






You can compute the flow cross-section area of the orifice from given nominal flow rate and pressure drop over the orifice as follows. Default values and


(355)

If you assume that point ( ) corresponds to the maximum opening, you can use

the same point to compute the maximum flow cross-section area for the check valve flow passage as follows:

(356)

The flow cross-section area computes as:

(357)

Flow Model

ADAMS/Hydraulics defines the flow model for a one-way restrictor valve using the ORIFIC function, such that:

(358)

(359)

(360)

(361)

Cd 0.6= Retr 50=

AmaxBA

QnomBA

Cd-------------------

ρref

2∆pnomBA-------------------------=

QAB2 ∆p2,

Apmax

QAB2

Cd-------------

ρref

2∆p2------------ AmaxBA–=

Rp LINPWL x ϒ 0, ,( )=

m· ABo ORIFIC R Cd Retr AmaxBA pA pB 0, , , ,, ,( )=

m· ABcv ORIFIC Rp Cd Retr Apmax pA pB 0, , , ,, ,( )=

QASTP

m· ABo– m· ABcv–

ρfluidSTP

---------------------------------------=

QBSTP

m· ABo m· ABcv+

ρf luidSTP

-----------------------------------=


Orifice185

Orifice

Screen Icon

Description

An orifice is a sudden restriction of short length (ideally zero length for a sharp-edged orifice) in a flow passage and can have a fixed or variable area [1, p. 39].


■ The orifice has no volume.

■ The cross section of an orifice is circular (the hydraulic diameter for a circular cross section is ).

Applying the given formulation to the compressible flow (varying density) is a simplification and, therefore, not absolutely accurate from a theoretical point of view. The formulation of a true compressible flow leads to very complicated equations, which prove to be impractical. Recalling that an orifice acts basically as a time constant within a fluid power circuit, and that, in most cases, measured parameters are based on the assumption of incompressible flow, you conclude that:

■ The given formulation is still valid for a wide range of pressure drop within the neighborhood of the reference pressure drop for which parameters were measured.

■ The small error in the time constant of an orifice is mostly compensated in the parameters used because of measurement practices.

A B

Dh D=


Orifice186

Port Topology


The following table shows the values you enter in the Create and Modify Orifice dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 187.





: volumetric flow rate out from port B in STP [length3/time]



Flow Cross-Section Area Model Parameters


Ratio of effective cross-section area of the orifice ( ) and the cross-section area of the orifice at maximum opening ( ),

--

Max Hydraulic Diameter

Maximum hydraulic diameter of the orifice

length

Discharge Coefficient

Discharge coefficient of the orifice. (Discharge coefficient is usually defined using component manufacturers information. Merritt [1, p. 42] gives an estimate of a typical discharge coefficient for an orifice:

.)

--

pA QASTP

pB QBSTP

A

Amax 0 R 1≤ ≤

R

Dhmax

Cd 0.6≈

Cd


Orifice187



ADAMS/Hydraulics assumes a circular cross section for an orifice. For a circular cross section, the hydraulic diameter is the same as the geometrical diameter. That is:

(362)

Flow Model

You can merge the effect of entrance/exit loss coefficient and effect of multiple orifices in a row into the value of discharge coefficient to achieve equivalent flow characteristics. Equivalent discharge coefficient is:

(363)

ADAMS/Hydraulics defines the flow model for an orifice using the ORIFIC function, such that:

(364)


Reynolds Transient Reynolds number at which the flow turns from laminar to turbulent.

--

Loss Coefficient Entrance/exit loss coefficient. Usually used if orifice is connected to a large reservoir.

--

N of Orifices in Series

Number of identical orifices in a row. --



Retr

K

N

Amaxπ4---Dhmax

2=

Cdeq

Cd

N KCd2+

-------------------------=

m· AB ORIFIC R Cdeq Retr Amax pA pB 0, , , ,, ,( )=


Orifice188

(365)

(366)

Math Follow-Up

For a detailed description of the mathematical background of the ORIFIC function, see ORIFIC - Flow Through an Orifice on page 304.

Resistance or loss coefficient K refers to those energy losses caused by bends, fittings, and sudden changes in flow cross section. These losses are empirically described by [1, p. 46]:

(367)

where:

fluid velocity [length/time]

gravitational constant [length/time2]

volumetric flow rate [length3/time]

flow passage area [length2]

Pressure loss over N orifices in a row and a one-time entrance/exit pressure loss defined by K can be combined to yield:

(368)

QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=

HL Ku2

2g------

K2g------

QA----

2= =

u

g

Q

A

pA pB– Kρ2---

QA----

2N

ρ2---

QCdA----------

2+=


Orifice189

From Equation (368), you can write the following equation for the mass flow through a row of orifices:

(369)m· ρQ A2ρ pA pB–( )

KN

Cd2

------+

------------------------------ CdA2ρ pA pB–( )

N KCd2+

------------------------------= = =


Orifice190


Pipe (level 1)191

Pipe (level 1)

Note: ADAMS/Hydraulics uses the term pipe to refer to both pipes and hoses.

Screen Icon


Description

A level 1 pipe model is functionally a combination of two orifices and a reservoir. It takes into account:

■ Nonlinear pipe friction

■ Exit and entrance losses of the pipe

■ Capacitance, fluid, and wall flexibility of the pipe

The pipe omits all inertial effects of fluid inside it.

Port Topology






A B

A

(+)

B

(+)

pA QASTP

pB QBSTP


Pipe (level 1)192


The following table shows the values you enter in the Create and Modify Pipe 1 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 194.



General

Length Pipe length. length

Diameter Inner diameter of the pipe. length

Initial Pressure Initial pressure in the pipe at the beginning of the simulation. Initial volume of the fluid ( ) in STP in the pipe is computed based on that.

force/length2

Losses

Loss Length Effective length, added to the pipe physical length, which represents additional pressure loss over the pipe.

length

A Exit Loss Coefficient of one-time pressure loss at the A end of pipe for exiting flow

--

A Entrance Loss Coefficient of one-time pressure loss at the A end of pipe for entering flow

.

--

L

D

Vini

pini

Lloss

0 λAexit 1≤ ≤ 0 No loss= 1 All kinetic energy lost at exit=,( ),

λAexit

0 λAentr≤ 0 No loss=( ),

λAentr


Pipe (level 1)193

B Exit Loss Coefficient of one-time pressure loss at the B end of pipe for exiting flow

--

B Entrance Loss Coefficient of one-time pressure loss at the B end of pipe for entering flow

.

--

Flexibility

Flexibility Type Pipe the wall flexibility type. The options are:■ linear - Pipe radius expands

linearly with respect to pressure.

■ nonlinear - Pipe radius expands nonlinearly with respect to pressure.

--

Wall Thicknesslinear

Pipe wall thickness. length

Youngs Moduluslinear

Modulus of elasticity of the pipe wall material.

force/length2

Poissons Ratiolinear

Poisson’s ratio for the pipe wall material.

--

Flexibility Coefficientsnonlinear

Coefficients of structural flexibility polynomial.

--



0 λBexit 1≤ ≤ 0 No loss= 1 All kinetic energy lost at exit=,( ),

λBexit

0 λBentr≤ 0 No loss=( ),

λBentr

flextype

s

E

ϑ

ai


Pipe (level 1)194

States

: Volume of fluid inside the pipe (reservoir) in STP [length3]


Capacitance Model

In the following explanations, pressure delta is defined as:

(370)

Method: Linear


(371)

where:

(372)

The effective volume of the pipe as a function of pressure is:

(373)

Method: Nonlinear

The effective volume of the pipe as a function of pressure is computed based on given flexibility coefficients as follows:

(374)

VrSTP

Λp p pe–=

Λp

uDΛp2E

------------Do

2 D2+

Do2 D2–

-------------------- ϑ+

=

Do D 2s+=

Veff D 2u+( )2π4---L 1

p pe–

E--------------

Do2 D2+

Do2 D2–

-------------------- ϑ+

+ 2

π4---D2L= =

Veff 1 ai

p pe–

pSTP--------------

i

i 1=

n

∑+ π

4---D2L=


Pipe (level 1)195

Initial volume of fluid in the pipe in STP is computed based on the given initial pressure:

(375)


ADAMS/Solver calculates the instantaneous volume of fluid in STP in the pipe as:

(376)

ADAMS/Hydraulics defines density as the mass per unit of volume. Density of the fluid in the pipe (reservoir) is:

(377)

Using the equation of state for the fluid, the pressure of the fluid in the pipe (reservoir) is:

(378)

Flow Resistance Model

Resistance of the pipe over a length of (l) takes the following form:

(379)

where:

, effective friction length of the pipe [length]

friction coefficient of the pipe []

flow velocity of the fluid [length/time]

Vini

ρiniVpe

ρfluidSTP

------------------f pini T,( )

f pSTP TSTP,( )---------------------------------

π4---D2L= =

ρ f p T,( )=

VrSTPVini

m· A m· B+( ) td∫ρfluidSTP

----------------------------------–=

ρr

VrSTP

Veff-----------ρf luidSTP

=

pr f ρr T,( )=

∆p λρ lD----

v2

2----- λρ l

D----

Q2

2πD2

4----------

2----------------------= =

l L Lloss+

λ

v


Pipe (level 1)196

For laminar regime, the friction factor according to the Hagen-Poiseuille law is:

(380)

and for turbulent regime according to Prandtl’s universal law of friction for smooth pipes:

(381)

Additional pressure drops due to exit and entrance losses are computed with the following equations:

(382)

Entrance loss is caused by the fact that, the effective flow cross-section area may grow smaller than the area of the pipe itself, due to the flow patterns of the input flow. The exit loss defines how much of the pipe flow’s kinetic energy is being lost at exit. Exit loss is typically 1 (100% lost).

λ 64Re------=

1

λ------- 2 Re λ( )log 0.8–=

∆pA

λAexitρvA

2

2-------- for flow out of pipe,

λAentrρvA

2

2-------- for flow in to pipe,

=

∆pB

λBexitρvB

2


λBentrρvB

2


=


Pipe (level 2)197

Pipe (level 2)

Note: ADAMS/Hydraulics uses the term pipe to refer to both pipes and hoses.

Screen Icon

Description

Level 2 pipe models are fairly complicated dynamic pipe models, which consist of a large number of coupled differential state variables. A real world pipe is a highly nonlinear continuous flexible structure with a widely spread set of eigenfrequencies. A math model of a dynamic pipe tends to discretize the continuous nature of a pipe more or less in any case and, thus, only take into account a finite number of lowest eigenfrequencies in its response. Due to that and other complex physical phenomenas involved, it should be understood that a dynamic pipe model is an approximation, even at its best.

There are three different versions of the dynamic pipe model implemented in this version. They differ in the way they connect with the rest of the system (different port types).

■ pipe_2pp: inputs pressures and outputs flow rates

■ pipe_2ff: inputs flow rates and outputs pressures

■ pipe_2pf: A port inputs pressure and outputs flow rate; B port does the opposite, inputs flowrate and outputs pressure

The level 2 pipe models can handle:

■ Fluid inertial effects

■ Nonlinear pipe friction

■ Waterhammer (pressure spikes)

■ Acceleration/deceleration of fluid

■ Eigenfrequency analysis (ADAMS/Linear and ADAMS/Vibration)

■ Pressure dependency of eigenfrequencies

■ Exit and entrance losses of the pipe

■ Capacitance, fluid and wall flexibility of the pipe

■ Speed of sound (or pressure wave) in a pipe causing time delays to the response of the pipe

A B


Pipe (level 2)198

Port Topology


pipe_2pp





pipe_2pf





pipe_2ff





pA QASTP

pB QBSTP

pA QASTP

QBSTPpB

QASTPpA

QBSTPpB


Pipe (level 2)199


The following table shows the values you enter in the Create and Modify Pipe 2 dialog boxes. It also shows the symbols for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 201.



General

Length Pipe length. length

Diameter Inner diameter of the pipe. length

Initial Pressure Initial pressure in the pipe at the beginning of the simulation. Initial volume of the fluid ( ) in STP in the pipe is computed based on that.

force/length2

Initial Flowrate Initial volumetric flow rate through the pipe at the beginning of the simulation. Positive flow direction is from A to B (sets initial fluid kinetic energy).

length3/time

Number of Divisions Defines the number of segments a pipe is being discretized internally. The higher the number, the more accurate the results, but at an expense of computational effort.

--

L

D

Vini

pini

QfiniSTP

N


Pipe (level 2)200

Losses

Loss Length Effective length, added to the pipe physical length, which represents additional pressure loss over the pipe.

length

A Exit Loss Coefficient of one-time pressure loss at the A end of pipe for exiting flow

--

A Entrance Loss Coefficient of one-time pressure loss at the A end of pipe for entering flow

--

B Exit Loss Coefficient of one-time pressure loss at the B end of pipe for exiting flow

--

B Entrance Loss Coefficient of one-time pressure loss at the B end of pipe for entering flow

--



Lloss

0 λAexit 1≤ ≤ 0 No loss= 1 All kinetic energy lost at exit=,( ),

λAexit

0 λAentr≤ 0 No loss=( ),

λAentr

0 λBexit 1≤ ≤ 0 No loss= 1 All kinetic energy lost at exit=,( ),

λBexit

0 λBentr≤ 0 No loss=( ),

λBentr


Pipe (level 2)201


Capacitance Model

For the following explanations, pressure delta is defined as:

(383)

Flexibility

Flexibility Type Pipe wall flexibility type. Options:■ linear - Pipe radius expands

linearly with respect to pressure

■ nonlinear - Pipe radius expands nonlinearly with respect to pressure

--

Wall Thicknesslinear

Pipe wall thickness. length

Youngs Moduluslinear

Modulus of elasticity of the pipe wall material.

force/length2

Poissons Ratiolinear

Poisson’s ratio for the pipe wall material.

--

Flexibility Coefficientsnonlinear

Coefficients of structural flexibility polynomial.

--



flextype

s

E

ϑ

ai

Λp p pe–=


Pipe (level 2)202

Method: Linear


(384)

where:

(385)

The effective volume of the pipe as a function of pressure is:

(386)

Method: Nonlinear

The effective volume of the pipe as a function of pressure is computed based on given flexibility coefficients as follows:

(387)

Flow Resistance Model

Resistance of the pipe flow over a length of (l) takes the following form:

(388)

where:

, effective friction length of the pipe [length]

friction coefficient of the pipe []

flow velocity of the fluid [length/time]

Λp

uDΛp2E

------------Do

2 D2+

Do2 D2–

-------------------- ϑ+

=

Do D 2s+=

Veff D 2u+( )2π4---L 1

p pe–

E--------------

Do2 D2+

Do2 D2–

-------------------- ϑ+

+ 2

π4---D2L= =

Veff 1 ai

p pe–

pSTP--------------

i

i 1=

n

∑+ π

4---D2L=

∆p λρ lD----

v2

2-----=

l L Lloss+

λ

v


Pipe (level 2)203

For laminar regime, the friction factor according to the Hagen-Poiseuille law is:

(389)

and for turbulent regime according to Prandtl’s universal law of friction for smooth pipes:

(390)

Additional pressure drops due to exit and entrance losses are computed with the following equations:

(391)

Entrance loss is caused by the fact that, the effective flow cross-section area may grow smaller that the area of the pipe itself, due to the flow patterns of the input flow. The exit loss defines how much of the pipe flow’s kinetic energy is being lost at exit. Exit loss is typically 1 (100% lost).

λ 64Re------=

1

λ------- 2 Re λ( )log 0.8–=

∆pA

λAexitρvA

2


λAentrρvA

2


=

∆pB

λBexitρvB

2


λBentrρvB

2


=


Pipe (level 2)204


Pressure-Reducing Valve205

Pressure-Reducing Valve

Screen Icon


Description

For a pressure-reducing valve, ADAMS/Hydraulics assumes that:



■ The spool geometry fully compensates for the pressure force at port A.

■ The flow cross-section area is linearly dependent on the spool position.

■ There are no leakages (other than given flow from port B to T, which can be set to zero as well).

A B

T

B (+)

A (+)

x

Spool is at openposition (x=1).

T

(+)



Port Topology


The following table shows the values you enter in the Create and Modify Pressure Reducing Valve3 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 208.







General


Q=f(pB)

A Ref Pressure Pressure at port A during measurements.

force/length2

B1 Pressure First set pressure (port B). It is the pressure at port B at which the spool begins to close its flow cross-section area.

force/length2

pA QASTP

pB QBSTP

pT QTSTP

0 x 1≤ ≤x

pAref

pBset1



B1 Flowrate Volumetric flow corresponding to the first set pressure point .

length3/time

B2 Pressure Second set pressure (port B). force/length2

B2 Flowrate Volumetric flow corresponding to the second set pressure point

.

length3/time

B3 Pressure Third set pressure (port B) force/length2

B3 Flowrate Volumetric flow corresponding to the third set pressure point .

length3/time


BT Nom Pressure Drop

Pressure drop at nominal volumetric flow from port B to port T.

force/length2

BT Nom Flowrate Nominal volumetric flow from port B to port T.

length3/time

T Ref Pressure Pressure at port T during measurements.

force/length2

Ref Fluid Density Density of the reference fluid, the fluid used for the measurement.

mass/length3

Response


time



pBset1

QBset1

pBset2

pBset2

QBset2

pBset3

pBset3

QBset3

0 ϒ 1≤ ≤ ϒ

∆pnomBT

QnomBT

pTref

ρref

τ0



States




ADAMS/Hydraulics assumes that the pressure-reducing valve spool is massless and closed at . It also assumes that the following forces act on the spool of the valve (positive force moves to positive direction) and, thus, determine its position:

spring force opening the valve (392)

spring preload at x=1 (valve open) (393)




where:


pressure area for port B (and port T) pressure [length2]


force/length2



τ0 ∆p0

x 0 x 1≤ ≤

x 0=

x

Fs k– 1 x 1–( )=

Fs0 F0=

Fd c1x·–=

Fp ApB– pB pT–( )=

Ff k3x pA pB––=

c1 k1 k3, ,

ApB




Default values and are applied for laminar flow regime, which

affects the shape of the flow rate curve only at very low pressure drops.

Maximum effective flow cross-section area for flow from port B to T is:

(397)

Maximum flow cross-section area is computed internally as follows:

(398)

Relative flow cross-section area computes to:

(399)

Flow Model

ADAMS/Hydraulics defines the flow model for a pressure-reducing valve using the ORIFIC function, such that:

(400)

(401)

(402)

(403)

(404)

Cd 0.6= Retr 50=

AmaxBT

QnomBT

Cd

2∆pnomBT

ρref-------------------------

------------------------------------=

Amax

QBset1

Cd

2 pAref pBset1–( )ρref

-----------------------------------------

----------------------------------------------------=



m· BT ORIFIC 1.0 Cd Retr AmaxBT pB pT 0, , , ,, ,( )=

QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB m· BT–

ρfluidSTP

--------------------------=

QTSTP

m· BT

ρf luidSTP

------------------=


Pressure Relief Valve211

Pressure Relief Valve

Screen Icon


Description

ADAMS/Hydraulics assumes that for a pressure relief valve:




Port Topology




A B

x

A

(+)

B

(+)

pA QASTP

pB QBSTP




The following table shows the values you enter in the Create and Modify Pressure Relief Valve dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 213.



General


Q=f(dp)



AB1 Pressure Drop Pressure drop at the first definition volumetric flow rate.

force/length2

AB1 Flowrate First definition volumetric flow rate.

length3/time

AB2 Pressure Drop Pressure drop at the second definition volumetric flow rate.

force/length2

AB2 Flowrate Second definition volumetric flow rate (at maximum opening).

length3/time



mass/length3

0 x 1≤ ≤x

∆pc

∆p1

Q1

∆p2

Q2

0 ϒ 0.5≤ ≤ ϒ

ρref



States and Output




ADAMS/Hydraulics assumes that the pressure relief valve poppet is massless and closed at . It also assumes that the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


spring preload (406)





Response


time


force/length2

Hysteresis


--



τ0

τ0 ∆p0

x 0= ε0 1≤ε0

x 0 x 1≤ ≤

x 0=

x

Fs k1x–=

Fs0 F0–=

Fd c1x·–=

FpA ApεpA=

FpB A– ppB=

Ff k3x pA pB––=



where:constants (identified internally from input data)





(411)


If you assume that point ( ) corresponds to the maximum opening, you can use the



(412)

Relative flow cross-section area is:

(413)

Flow Model


(414)

(415)

(416)

c1 k1 k3, ,

x·

Ap



Q2 ∆p2,

Cd 0.6= Retr 50=

Amax

Q2

Cd------

ρref

2∆p2------------=



QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Pressure Source215

Pressure Source

Screen Icon

Description

A pressure source acts like a tank with varying pressure. A function defines its pressure regardless of the amount of flow in or out.

Port Topology


The following table shows the values you enter in the Create and Modify Pressure Source dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 215.


The formulation of pressure source component is:

(417)



: pressure of the pressure source [force/length2]



User Parameters

Initial Pressure Estimate of the initial pressure of the pressure source.

force/length2

Pressure Function Pressure function. force/length2

AP

QASTPp

pini

pf

p max pf 0,( )=


Pressure Source216


Pump/Motor217

Pump/Motor

Screen Icon

DescriptionADAMS/Hydraulics assumes that for a pump/motor:

■ Positive torque on the output/input shaft corresponds to the positive direction of rotation.

■ Positive direction of rotation of the output/input shaft corresponds to the flow from port A to B.

■ Pump/motor torque losses consist of a viscous damping torque, a friction torque due to pressure forces, and a constant friction torque.

■ Leakage characteristics to drain (T) from both ports, A and B, are the same.

■ There is no volume inside a pump/motor.

■ Mass properties of a pump/motor belong to the mechanical portion of the model.

■ Mechanical motion/acceleration of a pump/motor, as a whole, does not affect internal flows or fluid movements.

Port Topology






A

B

T

pA QASTP

pB QBSTP


Pump/Motor218


The following table shows the values you enter in the Create and Modify Pump/Motor3 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 220.

T : pressure at port T [force/length2]

: volumetric flow rate out from port T in STP [length3/time]

Mechanical -- ■ : output torque [force*length]

■ : output torque of an ideal

pump/motor [force*length]

■ : shear torque [force*length]

■ : internal friction torque

[force*length]




Relative volumetric displacement of the pump/motor,

.

--

Angular Velocity Function

Angular velocity of the output/input shaft.

radians/time


pT QTSTP

Tout

Tideal

Ts

Tµ

0 R 1≤ ≤

R

ωAB


Pump/Motor219

General

Max Volumetric Displacement

Maximum volumetric displacement of the pump/motor.

volume/angle

Initial Control Input Estimate of the initial relative volumetric displacement,

.

--

Initial Angular Velocity

Estimate of the initial angular velocity of the output/input shaft.

angle/time

Losses

Shear Damping Coefficient

Dimensionless (shear) damping coefficient.

--

Internal Friction Coefficient

Dimensionless internal friction coefficient.

--

Coulomb Friction Torque

Coulomb friction torque. force*length

Limit Angular Velocity for Friction

Angular velocity for fully developed Coulomb friction torque.

angle/time

Leakage

Internal Leakage Coefficient

Internal (from A to B) leakage coefficient.


External Leakage Coefficient

External (from A and B to T) leakage coefficient.




VRADmax

0 Rini 1≤ ≤

Rini

ωABini

Cs

Cf

TC

ωl im

Cint

Cext


Pump/Motor220


Torque Model

Volumetric displacement of the pump/motor is:

(418)

Torque required/generated by an ideal pump/motor is:

(419)

Torque loss due to shear of fluid in narrow clearance is:

(420)

where fluid density is computed from equation of state for the fluid:

(421)

Internal friction torque due to pressure forces normal to direction of movement (typical in piston pumps / motors) and Coulomb friction is:

(422)

Total torque of a pump/motor is simply the sum of torque of an ideal pump/motor and the losses is:

(423)

Flow Model

The mass flow rate generated/required by an ideal pump/motor is:

(424)

Internal (laminar) leakage flow rate from port A to port B is:

(425)

VRAD RVRADmax=

Tideal VRAD pA pB–( )=

Ts CsV–RAD

ρνωAB

ρ ρA if pA pB

ρ≥,

ρB if pB pA>,

===

ρ f p T,( )=

Tµ CfV–RADmax

pA pB+( ) TC–( )step ωAB ω– l im 1– ωlim 1, , , ,( )=

Tout Tideal Ts Tµ+ +=

m· ideal ρVRADωABρ ρA if ωAB 0ρ

≥,ρB if ωAB 0<,

==

=

m· int ρCint pA pB–( )ρ ρA if pA pBρ

≥,ρB if pB pA>,

==

=


Pump/Motor221

External (laminar) leakage flow rate from ports A and B to port T is:

(426)

(427)

The flow rate out of each independent port is:

(428)

(429)

(430)

m· extAT ρCext pA pT–( )ρ ρA if pA pTρ

≥,ρT if pT pA>,

==

=

m· extBT ρCext pB pT–( )ρ ρB if pB pTρ

≥,ρT if pT pB>,

==

=

QASTP

m· ideal– m· int– m· extAT–

ρf luidSTP

----------------------------------------------------------=

QBSTP

m· ideal m· int m· extBT–+

ρfluidSTP

------------------------------------------------------=

QTSTP

m· extAT m· extBT+

ρf luidSTP

----------------------------------------=


Pump/Motor222


Reservoir223

Reservoir

Screen Icon

Description

In ADAMS/Hydraulics, a reservoir is a constant or variable volume component in which pressure of the fluid is calculated.


■ A reservoir has a constant or variable volume (finite) volume.

■ Velocity of the fluid in a reservoir is zero.

■ Fluid pressure in a reservoir is a function of density and temperature.

Port Topology


A : volumetric flow rate out from port A in STP [length3/time]

: pressure of the fluid in the reservoir [force/length2]

B : volumetric flow rate out from port B in STP [length3/time]

: pressure of the fluid in the reservoir [force/length2]

A B

QASTPp

QBSTPp


Reservoir224


The following table shows the values you enter in the Create and Modify Reservoir2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 225.

States

: Volume of fluid in the reservoir in STP [length3]



General

Initial Volume Initial volume (STP) of the reservoir at the beginning of the simulation.

length3

Volume in STP Function

Mechanical volume (STP) of the reservoir; can be a function of any system variables.

length3

Initial Pressure Initial pressure in the reservoir at the beginning of the simulation. The system calculates initial volume of the fluid in the reservoir from the given initial pressure.

force/length2

Flexibility

Flexibility Coefficients Coefficients of structural flexibility polynomial.

--

VSTPini

VSTP

ViniSTP

pini

ai

VfluidSTP


Reservoir225


Pressure dependency (structural flexibility) of mechanical volume is given as a polynomial:

(431)

ADAMS/Hydraulics calculates the density of the fluid in a reservoir as:

(432)

It calculates the pressure of the fluid in the reservoir using the equation of state for the fluid:

(433)


Vmec VSTP 1 ai

p pe–

pSTP--------------

i

i 1=

n

∑+

=

ρmfluid

Vmec--------------

VSTPiniQASTP

QBSTP+( ) td∫+

Vmec-------------------------------------------------------------------ρfluidSTP

= =

p f ρ T,( )=


Reservoir226


Servovalve 4/3227

Servovalve 4/3

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a servovalve 4/3:


■ The flow characteristics are the same for both flow directions.

■ The spool returns to center position when the external control is set to zero.

Positive relative spool postition ( ) connects pressure port P to output port A (and B to T), and negative relative spool postition ( ) connects pressure port P to output port B (and A to T). Positive control input function signal moves spool to positive direction.

A

P T

B

B (+)

P (+) T (+)

f( )

(+)

xA (+)

T (+)

0 x 1≤<1– x 0<≤


Servovalve 4/3228

Port Topology


The following table shows the values you enter in the Create Servovalve dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation on page 235.


P : pressure at port P [force/length2]

: volumetric flow rate out from port P in STP [length3/time]





T : pressure at port T [force/length2]

: volumetric flow rate out from port T in STP [length3/time]

pP QPSTP

pA QASTP

pB QBSTP

pT QTSTP


Servovalve 4/3229





--

X=f(I)


--

I to X Method Method to convert control input function signal to spool position (x). The options are:■ voice_coil - Second-order spool

dynamics, spring-mass system, spring centered.

■ nozzle_flapper - Third-order spool dynamics.

--

Eigenfrequencyvoice_coil

Eigenfrequency of the valve. 1/time

Relative Dampingvoice_coil

Relative damping of the valve; value of one equals critical damping.

--

Flapper Eigenfrequencynozzle_flapper

Eigenfrequency of the flapper. 1/time

Flapper Relative Dampingnozzle_flapper

Relative damping of the flapper; value of one equals critical damping.

--

1– f 1≤ ≤f

1– x 1≤ ≤x

ItoX

feigen

ζ

feigfl

ζf l


Servovalve 4/3230

Proportional Bandnozzle_flapper

Maximum relative flapper position (full opening of the

nozzle).

--

Ref Relative Velocity nozzle_flapper

Spool-saturated velocity; that is, spool velocity at maximum relative flapper position (nominal pressure drop over the valve).

1/time

A=f(X)




■ spline - An arbitrary nonlinear curve defines relation between relative opening area and relative spool position.

--

PA Xlap(nonlinear)


--



0 zmax 1<≤zmax

feigfl

XtoAPA



Servovalve 4/3231



--



--



--





--

PB Xlap(nonlinear)


--



--



0 ϒ 1≤ ≤ϒPA

0 NLPA 1<≤NLPA

1– x 1≤ ≤ 0 R 1≤ ≤

SPA

XtoAPB


0 ϒ 1≤ ≤ϒPB


Servovalve 4/3232



--



--





--

AT Xlap(nonlinear)


--



--



--



0 NLPB 1<≤NLPB

1– x 1≤ ≤ 0 R 1≤ ≤

SPB

XtoAAT


0 ϒ 1≤ ≤ϒAT

0 NLAT 1<≤NLAT


Servovalve 4/3233



--





--

BT Xlap(nonlinear)


--



--



--



1– x 1≤ ≤ 0 R 1≤ ≤

SAT

XtoABT


0 ϒ 1≤ ≤ϒBT

0 NLBT 1<≤NLBT


Servovalve 4/3234

States


: Relative spool velocity [1/time]



--

Q=f(A,dp)


force/length2


length3/time


length3/time


length3/time


length3/time

PT Nom Flowrate Nominal volumetric flow from port P to port T at full opening.

length3/time


mass/length3



1– x 1≤ ≤ 0 R 1≤ ≤

SBT

∆pnom

QnomPA

QnomPB

QnomAT

QnomBT

QnomPT

ρref

x 1– x 1≤ ≤

x·


Servovalve 4/3235



The valve spool centers itself at zero external input ( ). Positive external input ( ) connects pressure port P to output port A (and B to T) and negative external input ( ) connects pressure port P to output port B (and A to T).

Method: Voice Coil

A second-order transfer function computes the spool position:

(434)

(435)

Method: Nozzle Flapper

Functional schematic of a nozzle flapper driven servovalve spool.

f 0=

0 f 1≤<1– f 0<≤

ω 2πfeigen=

x s( ) ω2

s2 2ζωs ω2+ +-------------------------------------I s( )= 1– x 1≤ ≤,

x

pp pt

Q1a Q1b

Q2bQ2a

T

p1a p1b


Servovalve 4/3236

The nozzle flapper itself is regarded as a second-order dynamic system. External control input (torque T) and spool position feedback act as forces on the flapper against the centering spring of the flapper (not shown in the schematic). Flapper acceleration, velocity, and position computes:

(436)

(437)

(438)

Spool velocity is then linearily dependent on flapper position at a constant pressure drop over the valve.

(439)

(440)

A nozzle-flapper construction always causes certain amount of leakage from port P to T. ADAMS/Hydraulics does not enforce this, but we recommend that you include it in the value of PT Nom Flowrate.



z·· feigfl2

I x– z–( ) 2ζf lfeigflz·–=

z· z··∫=

z z·∫=zmax– z zmax≤ ≤

x· x· refz

zmax-----------

2 pp pt–( )ρp

2 p∆ PTnomρref

---------------------------------------=

x x·∫=1– x 1≤ ≤

x


Servovalve 4/3237

Method: linear

(441)

(442)

(443)

(444)

Method: nonlinear

(445)

(446)

(447)

(448)

In a real-world valve construction, there are flow restrictions other than the spool opening area itself, which limit the actual flow rate throughput of the valve. For example, if the area of the flow input (or output) passage of the valve is not substantially larger than the maximum spool opening area, it may introduce significant additional flow restriction, especially at large spool openings. The coefficient of nonlinearity is intended to be used for flow restrictions other than the spool opening itself. for more information, refer to Definition of coefficient of nonlinearity on page 112.

Method: spline(449)

(450)

(451)

(452)

Each spline holds at least four (x,R)-points to define the relationship between the relative spool position and the relative flow cross-section area. Functions are defined in such a way that all flows can use the same spline definition, if the spool is fully symmetric. A positive R value at zero x causes the spool to leak. For more information on applied

RPA max x 0,( )=

RPB max x– 0,( )=

RAT max x– 0,( )=

RBT max x 0,( )=










Servovalve 4/3238

spline-fitting functions, refer to Akima Fitting Method (AKISPL) in the guide, Using the ADAMS/View Function Builder.

To identify the five maximum flow cross-section areas for flows P to A, P to B, A to T, B to T, and P to T, five operating curve points at full opening of the spool

are required as input. The five maximum flow cross-section areas are computed internally as shown in Equations (453)-(457):

(453)

(454)

(455)

(456)

(457)

Flow Model

ADAMS/Hydraulics calculates flow rates using the ORIFIC function (ORIFIC - Flow

Through an Orifice on page 304). Default values and are applied

for laminar flow regime, affects the shape of the flow rate curve only at very low pressure drops.

(458)

(459)

(460)

(461)

Qnom,∆pnom( )

AmaxPA

QnomPA

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPB

QnomPB

Cd-------------------

ρref

2∆pnom-------------------=

AmaxAT

QnomAT

Cd-------------------

ρref

2∆pnom-------------------=

AmaxBT

QnomBT

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPT

QnomPT

Cd-------------------

ρref

2∆pnom-------------------=

Cd 0.6= Retr 50=






Servovalve 4/3239

(462)

(463)

(464)

(465)

(466)


QPSTP


ρfluidSTP

----------------------------------------------=

QASTP

m· PA m· AT–

ρfluidSTP

--------------------------=

QBSTP

m· PB m· BT–

ρfluidSTP

--------------------------=

QTSTP


ρfluidSTP

-------------------------------------------=


Servovalve 4/3240


Shuttle Valve241

Shuttle Valve

Screen Icon


Description

For a shuttle valve, ADAMS/Hydraulics assumes that:

■ Flow passages from A to C and B to C are the same.

■ Moving the poppet along the x-axis opens the other flow passage as much as it closes the other passages.



■ The flow cross-section area is linearly dependent on poppet position.

■ There are no leakages.

A B

C

A

(+)

C (+)

B

(+)

x


Shuttle Valve242

Port Topology


The following table shows the values you enter in the Create and Modify Shuttle Valve3 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.




C : pressure at port C [force/length2] : volumetric flow rate out from port C in STP [length3/time]



General


Q=f(dp)

A1 Pressure Pressure at port A corresponding to full opening.

force/length2

AC Nom Flowrate Nominal volumetric flow rate through the valve at full opening.

length3/time

B Cracking Pressure Cracking pressure of the valve (port B).

force/length2

pA QASTP

pB QBSTP

pC QCSTP

0 x 1≤ ≤x

pA1

Qnom

pc


Shuttle Valve243

States


If you assume that the poppet is at under given pressures in ports A and C,

and respectively, you can define cracking pressure at port B as the pressure,

which begins to move poppet towards port A, allowing flow from port B to C.

C Ref Pressure Pressure at port C used during measurements.

force/length2


mass/length3

Response


time

B Pressure Step Pressure increase of port B for which was given.

force/length2



pCref

ρref

τ0

τ0

∆p0

x 0 x 1≤ ≤

x 1= pA1( )

pCref( ) pc( )


Shuttle Valve244



ADAMS/Hydraulics assumes the shuttle valve poppet is massless. Flow passage from A to C is fully open at and closed at , flow from B to C is symmetrical, but opposite. ADAMS/Hydraulics also assumes the following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:


pressure force from port A (468)

pressure force from port B (469)

flow force closing flow from A to C (470)

flow force closing flow from B to C (471)

where:


pressure area for port A (and port B) pressure [length2]


Default values and are applied for laminar flow regime (affects the

shape of the flow rate curve only at very low pressure drops).

Maximum effective flow cross-section area for the flow from port A to C is:

(472)

ADAMS/Hydraulics assumes the flow passage from B to C is the same; that is, the same maximum flow cross-section area applies.

x 1= x 0=

x

Fd c1x·–=

FpA ApApA=

FpB ApApB–=

FfA k3x pA pC––=

FfB k3 1 x–( ) pB pC–=

c1 k3,

ApA

Cd 0.6= Retr 50=

Amax

Qnom

Cd

2 pA1 pCref–( )ρref

-----------------------------------

----------------------------------------------=


Shuttle Valve245

Flow Model

ADAMS/Hydraulics defines the flow model for a shuttle valve using the ORIFIC function, such that:

(473)

(474)

(475)

(476)

(477)

m· AC ORIFIC x Cd Retr Amax pA pC 0, , , ,, ,( )=

m· BC ORIFIC 1 x– Cd Retr Amax pB pC 0, , , ,, ,( )=

QASTP

m· AC–

ρfluidSTP

------------------=

QBSTP

m· BC–

ρfluidSTP

------------------=

QCSTP

m· AC m· BC+

ρf luidSTP

----------------------------=


Shuttle Valve246


Spline Orifice247

Spline Orifice

Screen Icon

DescriptionA spline orifice is an element that uses a spline to describe the dependency between pressure drop and volumetric flow rate through an orifice.


■ The spline orifice has no volume.

■ The flow behaves the same in both flow directions: A to B and B to A.

Port Topology




A B

SPLINE

pA QASTP

pB QBSTP


Spline Orifice248


The following table shows the values you enter in the Create and Modify Spline Orifice dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.



Flowrate Spline Spline name, which defines ( , )-points for flow from port A to port B ( and ).

Pressure drop is defined to be positive for flow from port A to port B. You must define your spline so that:

■ Positive flowrate vlaues correspond to positive pressure drop values.

■ Negative flowrate values correspond to negative pressure drop values (needed only with the “full” option).

■ It always passes through zero (0,0).

--dp QSTP

0 dp≤ 0 QSTP≤

SAB


Spline Orifice249

Fluid viscosity is used as the z-value for spline . Therefore, for a spline orifice, you

can define different characteristics for different fluid viscosities by using a three-dimensional spline instead of a two-dimensional spline. For more information on splines, refer to the ADAMS/Solver (FORTRAN) online help or the guide, Using the ADAMS/View Function Builder.

Apply Spline As Defines how to apply given spline data. The available options are.

■ symmetric - Defines flowrate from port B to port A as similar to that of port A to port B. Positive half of the spline defines flow characteristics both ways.

■ full - Uses full spline to define flow characteristics

■ oneway - Defines flowrate from port B to port A as closed. Positive half of the spline defines flow characteristics from port A to port B.

-- --


Ratio of the actual flowrate through the orifice and the nominal flowrate given by the flowrate spline (0 ≤ R ≤ 1).

-- R



SAB


Spline Orifice250


ADAMS/Hydraulics defines the flow model for spline orifice using the MSC.ADAMS AKISPL function. For the:

Symmetric option

(478)

(479)

(480)

Full option

(481)

(482)

(483)

Oneway option

(484)

(485)

(486)

where:

Kinematic viscosity of fluid

QABSTPRsign pA pB–( )akispl pA pB– ν SAB, ,( )=

QASTPQABSTP

–=

QBSTPQABSTP

=

QABSTPRakispl pA pB ν SAB, ,–( )=

QASTPQABSTP

–=

QBSTPQABSTP

=

QABSTPRakispl max pA pB 0,–( )ν SAB,( )=

QASTPQABSTP

–=

QBSTPQABSTP

=

ν


Spool Valve 4/3p251

Spool Valve 4/3p

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a spool valve 4/3p:

■ There is no volume inside a valve other than pilot volumes in the ends of the spool.


Positive relative spool position ( ) connects pressure port P to output port A (and B to T) and negative relative spool position ( ) connects pressure port P to output port B (and A to T). Positive flow in to the pilot port XA moves spool to positive direction, thus, connecting pressure port P to output port A (and B to T). Positive flow in to the pilot port XB does the opposite.

A

P T

B

XBXA

B (+)

P (+) T (+)

xA (+)

T (+)

XB

(+)

XA

(+)

0 x 1≤<1– x 0<≤


Spool Valve 4/3p252

Port Topology


The following table shows the values you enter in the Create and Modify Spool Valve 4/3p dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.






XA : volumetric flow rate in from pilot port XA in STP [length3/time]

: pressure at pilot port XA [force/length2]

XB : volumetric flow rate in from pilot port XB in STP [length3/time]

: pressure at pilot port XB [force/length2]



X=f(I)


--

Initial X Pressure Initial pressure in the pilot ports. force/length2

pP QPSTP

pA QASTP

pB QBSTP

pT QTSTP

QXASTPpXA

QXBSTPpXB

0 x 1≤ ≤xini

pini


Spool Valve 4/3p253

Spool Type Massless (First order). --

Spool Half Stroke Length of spool stroke from center to either end.

length

Spool Piston Area Effective pressure drive area of the spool.

length2

XA Dead Volume Smallest volume of the XA pilot chamber.

length3

XB Dead Volume Smallest volume of the XB pilot chamber.

length3

A=f(X)





--



spool_type

l1 2⁄

Ap

VXAdead

VXBdead

XtoAPA


Spool Valve 4/3p254

PA Xlap(nonlinear)


--



--



--


Spline name, which defines (x,R)-points for flow from port P to port A( and ).

--





--

PB Xlap(nonlinear)


--




0 ϒ 1≤ ≤ϒPA

0 NLPA 1<≤NLPA

1– x 1≤ ≤ 0 R 1≤ ≤

SPA

XtoAPB



Spool Valve 4/3p255



--



--



--





--

AT Xlap(nonlinear)


--



--



0 ϒ 1≤ ≤ϒPB

0 NLPB 1<≤NLPB

1– x 1≤ ≤ 0 R 1≤ ≤

SPB

XtoAAT


0 ϒ 1≤ ≤ϒAT


Spool Valve 4/3p256



--



--





--

BT Xlap(nonlinear)


--



--



--



0 NLAT 1<≤NLAT

1– x 1≤ ≤ 0 R 1≤ ≤

SAT

XtoABT


0 ϒ 1≤ ≤ϒBT

0 NLBT 1<≤NLBT


Spool Valve 4/3p257



--

Q=f(A,dp)


force/length2


length3/time


length3/time


length3/time


length3/time

PT Nom Flowrate Nominal volumetric flow from port P to port T.

length3/time


mass/length3



1– x 1≤ ≤ 0 R 1≤ ≤

SBT

∆pnom

QnomPA

QnomPB

QnomAT

QnomBT

QnomPT

ρref


Spool Valve 4/3p258

States


: Volume of fluid in the XA pilot chamber in STP [length3]

: Volume of fluid in the XB pilot chamber in STP [length3]



Instantaneous mechanical volumes of the pilot chambers of the spool valve are:

(487)

(488)

ADAMS/Hydraulics computes the initial volumes of fluid in the pilot chambers in STP based on the given initial X pressure, such that:

(489)

(490)


Instantaneous fluid volumes in the pilot chambers are:

(491)

(492)

x 1– x 1≤ ≤

VXASTP

VXBSTP

VXA 1 x+( )l1 2⁄ Ap VXAdead+=

VXB 1 x–( )l1 2⁄ Ap VXBdead+=

VXASTP

ini ρXAiniVXAini

ρf luidSTP

---------------------------f pini T,( )

f pSTP TSTP,( )---------------------------------VXA xini( )= =

VXBSTP

ini ρXBiniVXBini

ρf luidSTP

---------------------------f pini T,( )

f pSTP TSTP,( )---------------------------------VXB xini( )= =

ρ f p T,( )=

VXASTPVXASTP

iniQXASTP

td∫+=

VXBSTPVXBSTP

iniQXBSTP

td∫+=


Spool Valve 4/3p259

A massless spool always takes a position where pilot pressures acting on the end of the spool are equal (provided that the spool is not at either end of its travel). Therefore, relation of equation (493) hold.

(493)

From equations (487), (488) and (493) we find that

(494)



Method: linear

(495)

(496)

(497)

(498)

Method: nonlinear

(499)

(500)

(501)

(502)

In a real-world valve construction, there are flow restrictions other than the spool opening area itself, which limit the actual flow rate throughput of the valve. For example, if the area of the flow input (or output) passage of the valve is not substantially larger than the maximum spool opening area, it may introduce significant additional flow restriction,

VXASTP

VXA----------------

VXBSTP

VXB----------------=

xVXASTP

VXBSTP–

VXASTPVXBSTP

+-------------------------------------

VXBSTPV

XAdeadVXASTP

VXBdead

–

l1 2⁄ Ap VXASTPVXBSTP

+( )------------------------------------------------------------------------------–=

x

RPA max x 0,( )=

RPB max x– 0,( )=

RAT max x– 0,( )=

RBT max x 0,( )=






Spool Valve 4/3p260

especially at large spool openings. The coefficient of nonlinearity is intended to be used for flow restrictions other than the spool opening itself. For more information, refer to Directional Control Valve 2/2 on page 107.

Method: spline(503)

(504)

(505)

(506)


To identify the five maximum flow cross-section areas for flows P to A, P to B, A to T, B to T, and P to T, five operating curve points at full opening of the spool

are required as input. The five maximum flow cross-section areas are computed internally as shown in Equations (507)-(511). Default values and


(507)

(508)

(509)





Qnom,∆pnom( )

Cd 0.6= Retr 50=

AmaxPA

QnomPA

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPB

QnomPB

Cd-------------------

ρref

2∆pnom-------------------=

AmaxAT

QnomAT

Cd-------------------

ρref

2∆pnom-------------------=


Spool Valve 4/3p261

(510)

(511)

Flow Model

ADAMS/Hydraulics calculates the flow rates using the ORIFIC function (see ORIFIC - Flow Through an Orifice on page 304), such that:

(512)

(513)

(514)

(515)

(516)

(517)

(518)

(519)

(520)

AmaxBT

QnomBT

Cd-------------------

ρref

2∆pnom-------------------=

AmaxPT

QnomPT

Cd-------------------

ρref

2∆pnom-------------------=






QPSTP


ρfluidSTP

----------------------------------------------=

QASTP

m· PA m· AT–

ρfluidSTP

--------------------------=

QBSTP

m· PB m· BT–

ρfluidSTP

--------------------------=

QTSTP


ρfluidSTP

-------------------------------------------=


Spool Valve 4/3p262

Pilot Pressure Model

ADAMS/Hydraulics defines density as mass per unit of volume. It calculates the density of the fluid in the pilot chambers of the spool valve as:

(521)

(522)

Pilot chamber pressures are then computed using the equation of state for the fluid, such that:

(523)

(524)

ρXA

VXASTP

VXA---------------ρfluidSTP

=

ρXB

VXBSTP

VXB---------------ρfluidSTP

=

pXA f ρXA T,( )=

pXB f ρXB T,( )=


Sum of Flows263

Sum of Flows

Screen Icon

DescriptionSum of flows sums flow rates A and B into flow rate C.

Note: For the MSC.ADAMS 2003 release, this component is replaced by the new sum_of_flows2 component. The original component is available to ensure upward compatibility, but it has been removed from the menus. You should stop using this component, as it may be dropped in a future release of ADAMS/Hydraulics.

Port Topology



: pressure at port C [force/length2]


: pressure at port C [force/length2]

C : pressure at port C [force/length2] : volumetric flow rate out from port C in STP [length3/time]

BC

A

QASTPpC

QBSTPpC

pC QCSTP


Sum of Flows264


(525)

(526)

(527)

pA pC=

pB pC=

QCSTPQASTP

QBSTP+=


Sum of Flows2265

Sum of Flows2

Screen Icon

DescriptionSum of flows2 sums flow rates A and B into flow rate P.

Port Topology


(528)

(529)

(530)



: pressure at port P [force/length2]




A

P

B

QASTPpP

QBSTPpP

pP QPSTP

pA pP=

pB pP=

QPSTPQASTP

QBSTP+=


Sum of Flows2266


Sum of Flows3267

Sum of Flows3

Screen Icon

DescriptionSum of flows3 sums flow rates A, B, and C into flow rate P.

Port Topology


(531)

(532)

(533)

(534)









BP

A

C

QASTPpP

QBSTPpP

QCSTPpP

pP QPSTP

pA pP=

pB pP=

pC pP=

QPSTPQASTP

QBSTPQCSTP

+ +=


Sum of Flows3268


Sum of Flows4269

Sum of Flows4

Screen Icon

DescriptionSum of flows4 sums flow rates A, B, C, and D into flow rate P.

Port Topology








D : volumetric flow rate in from port D in STP [length3/time]



B

P

A

C

D

C

QASTPpP

QBSTPpP

QCSTPpP

QDSTPpP

pP QPSTP


Sum of Flows4270


(535)

(536)

(537)

(538)

(539)

pA pP=

pB pP=

pC pP=

pD pP=

QPSTPQASTP

QBSTPQCSTP

QDSTP+ + +=


Tank271

Tank

Screen Icon

Description

The tank is assumed to be a reservoir with an infinite volume. Therefore, it maintains constant pressure that is independent of the amount of flow in or out of it.

Port Topology


The following table shows the values you enter in the Create and Modify Tank dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.


The formulation of the tank component is:

(540)


T : volumetric flow rate in from port T in STP [length3/time]

: pressure of the fluid in the tank [force/length2]



Tank Pressure Tank pressure. force/length2

T

QTSTPp

pt

p pt=


Tank272


Two-Way Cartridge Valve273

Two-Way Cartridge Valve

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a two-way cartridge valve:


■ The poppet (or spool) is massless.

■ The control orifice dominates the damping characteristics.

■ The control volume above the poppet (or spool) is small enough to be regarded as incompressible.

■ Changes of flow due to changing volumes on both sides of the poppet (or spool), while the poppet (or spool) is moving, are negligible.

A

B

X

X

(+)

A

(+)

x

B (+)



Port Topology


The following table shows the values you enter in the Create Cartridge Valve3p dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.







General

Initial Position Initial relative poppet or spool position,

--

Spring Stiffness Spring stiffness. force/length

Spring Precompression Spring precompression. length

Max Opening Maximum movement (opening) of poppet/spool.

length

Diameter Diameter of the poppet (or spool). length

Valve Type Valve type, either poppet or spool.

--

Jet Angle Jet angle (fixed at 69 degrees for spool-type valves).

angle


pA QASTP

pB QBSTP

pX

0 x 1≤ ≤x

k

X0

Xmax

DC

valve_type

α

0 ϒ 1≤ ≤ ϒ



States

: Relative poppet/spool position [],


Poppet/Spool Position Model

ADAMS/Hydraulics assumes that the two-way cartridge valve poppet (or spool) is massless and closed at . It also assumes that the following forces act on the poppet (or spool) of the valve (positive force moves to positive direction) and, thus, determine its position.

You can assume that the control orifice dominates the damping characteristics of the poppet (or spool), and we have, therefore, omitted the velocity-dependent force terms (viscous damping and friction) from the force balance equation. You can further assume that the control volume above the poppet (or spool) is small enough to be regarded incompressible. We ignore the changes of flow due to changing volumes on both sides of the poppet (or spool), while the poppet (or spool) is moving.


spring preload closing the valve (542)

pressure force opening the valve (A) (543)

Pilot

CA Pressure Area Ratio

Counter pressure area ratio, .

--

X Orifice Diameter Diameter of the control orifice. length

Hysteresis


--



rCA ApC ApA⁄=rCA

DX

x 0= ε0 1≤ε0

x 0 x 1≤ ≤

x 0=

x

Fs kX–=

Fs0 kX0–=

FpA ApAεpA=



pressure force opening the valve (B) (544)

pressure force closing the valve (C) (545)

flow force closing/opening the valve (546)

where:



: pressure area ratio ( ), ( ) []

effective flow cross-section area [length2]

fluid density at port A pressure [mass/length3]

According to Merritt [1, p. 103], jet angle for a spool type orifice equals to 69 degrees at openings considerably higher than radial clearance of spool.

The poppet/spool position is:

(547)


(548)

FpB ApBpB=

FpC A– pCpC=

Ff m·– vf min α 69°,( )( )cos vA–( ) 2CdA pA pB–( ) min α 69°,( )( )cos–m· AB

2

ρf pA( )ApA-------------------------+= =

ApA

ApB

ε Aclosed ApA⁄ ε 1≤

A

ρf pA( )

X Xmaxx=





Effective diameter of poppet/spool is:

(549)

In the case of a spool-type valve, effective flow cross-section area is:

(550)

In the case of a poppet-type valve, effective flow-cross section is:

(551)

Further, the maximum flow cross-section area is limited to that of port A:

(552)

Flow Model

ADAMS/Hydraulics defines the flow model for a two-way cartridge valve using the ORIFIC function. Default values and are applied for laminar flow


(553)

(554)

(555)

DA

DC2

rCA--------=

A πDAXmaxLINPWL x ϒ 0, ,( )=

A πDAXmax α 1X

2DA---------- 2αsin–

sin LINPWL x ϒ 0, ,( )= 0 α 90°< <,

A ApA≤

Cd 0.6= Retr 50=

m· AB ORIFIC 1.0 Cd Retr A pA pB 0, , , ,, ,( )=

QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=


Two-Way Flow Control Valve279

Two-Way Flow Control Valve

Screen Icon


DescriptionADAMS/Hydraulics assumes that for a two-way flow control valve:



■ The flow cross-section area is linearly dependent on spool position.

■ There are no leakages.

A B

A

(+)

B

(+)

xSpool is in openposition (x=1)



Port Topology


The following table shows the values you enter in the Create Flow Control Valve 2 dialog boxes. It also shows the symbol for the different parameters as they appear in the equations in ADAMS/Hydraulics Formulation.






General


Q=f(pA)

AB1 Pressure Drop Pressure drop at the first definition volumetric flow (spool begins limiting flow through the valve).

force/length2

AB1 Flowrate First definition volumetric flow rate.

length3/time

AB2 Pressure Drop Pressure drop at the second definition volumetric flow.

force/length2

pA QASTP

pB QBSTP

0 x 1≤ ≤x

∆p1

Q1

∆p2



States


AB2 Flowrate Second definition volumetric flow rate.

length3/time

AB3 Pressure Drop Pressure drop at the third definition volumetric flow.

force/length2

AB3 Flowrate Third definition volumetric flow rate.

length3/time

Ratio of Pressure Drops

Ratio of pressure drop over the orifice and pressure drop over the valve at full opening of the spool,

.

--


mass/length3

Response

AB1 Flowrate Change Rate

Flow rate change over time at caused by a sudden

pressure drop from to .

[length3/time/time]



Q2

∆p3

Q3

0 rref 1< <

rref

ρref

Q1( )∆p1 ∆p2

Q· 1

x 0 x 1≤ ≤





Assume the following:

■ Two-way flow control valve poppet is massless and closed at .

■ The following forces act on the poppet of the valve (positive force moves to positive direction) and, thus, determine its position:

spring force opening the valve (556)

spring preload at x=1 (valve open) (557)




where:

constants


pressure drop over the orifice [force/length2]

: pressure drop over the spool [force/length2]


If you assume that point ( ) corresponds to the pressure drop at which the spool

begins limiting flow through the valve still at the maximum opening, you can use that point to compute the maximum flow cross-section area for the valve. Default values

and are applied for laminar flow regime, which affects the shape of


(561)

x 0=

x

Fs k– 1 x 1–( )=

Fs0 F0=

Fd c1x·–=

Fp ApB– ∆pori=

Ff k3x ∆ps–=

c1 k1 k3, ,

ApB

∆pori

∆ps

Q1 ∆p1,

Cd 0.6= Retr 50=

Amax

Q1

Cd

2 1 rref–( )∆p1

ρref-----------------------------------

----------------------------------------------=



ADAMS/Hydraulics internally solves the product of discharge coefficient and flow cross-section area of the orifice from:

(562)

The ratio of the effective flow cross-section areas is:

(563)

Equivalent and relative flow cross-section areas for the valve are, respectively:

(564)

(565)

Flow Model

ADAMS/Hydraulics defines the flow model for a two-way flow control valve using the ORIFIC function (see ORIFIC - Flow Through an Orifice on page 304), such that:

(566)

(567)

(568)

CdoAo

Q1

2rref∆p1

ρref---------------------

--------------------------=

ra

CdAmax

CdoAo-------------------=

Aeq

Amaxx

1 ra2x2+

------------------------=

RAeq

Amax------------=


QASTP

m· AB–

ρfluidSTP

------------------=

QBSTP

m· AB

ρfluidSTP

------------------=

A Density of the Fluid and Bernoulli’s Equation

OverviewWuori [2, p. 36] gives the general Bernoulli’s equation as:

(569)

where:

: average velocity of flow

: time

: length along the flow path

: energy of the body force (for example, gravity)

: fluid density

: fluid pressure

If the unstationary term and energy of the body force

are ignored, Equation (385) yields:

(570)

where the density ( ) is actually a function of temperature ( ) and pressure ( ). Therefore, Equation (386) should be integrated with the embedded equation of state for a fluid, which leads to a rather complicated formulation for flow. This is impractical, because in most cases the input data that are available for modeling an orifice are derived from

v∂t∂

----- sv

2

2----- U

1ρ--- pd∫+ + +d∫ constant=

v

t

s

U

ρ

p

v∂t∂

----- sd∫ U

v2

2-----

1ρ--- pd∫+ constant=

ρ T

p


Density of the Fluid and Bernoulli’s Equation286

measurements using the simplified form of Bernoulli’s equation.

In the fluid power system used in ADAMS/Hydraulics, the density of the fluid is variable. To keep the formulation of the equations flexible and efficient, the flow through an orifice is defined using the simplified Bernoulli-based equation, and the density of the fluid ( ) is assumed to be (the density of the incoming flow).

Flow at Low Reynolds NumbersThe Reynolds number is a unitless ratio of inertia force to viscous force of a fluid flow. The definition of Reynolds number is given as:

(571)

where:: fluid density

: average velocity of flow

: characteristic dimension of a particular flow situation

: absolute viscosity of fluid

Laminar FlowThe flow at low Reynolds numbers appears to be directly proportional to the square root of Reynolds number:

(572)

where:: volumetric flow rate

: discharge coefficient for laminar flow

: flow section area

: density of the fluid

: pressure 1

: pressure 2

ρ ρ1

Reρva

µ---------=

ρ

v

a

µ

Q CdlA2ρ--- p1 p2–( ) δ ReA

2ρ--- p1 p2–( )= =

Q

Cdl

A

ρ

p1

p2



: laminar flow coefficient

: Reynolds number

Kinematic viscosity of fluid is defined as a ratio of absolute viscosity and fluid density:

(573)

Consider a circular cross section of a pipe in which the laminar flow takes place. The characteristic length used for Reynolds number is inside the pipe diameter D, and the average flow velocity is the volumetric flow rate divided by the pipe area. By combining Equations (571) and (573), Reynolds number can be written as:

(574)

where:

: volumetric flow rate

: hydraulic diameter

: kinematic viscosity of fluid

Now the discharge coefficient from Equation (572) can be given as:

(575)

and Equation (572) becomes:

(576)

from which we can derive for mass flow:

(577)

δ

Re

ν µρ---=

RevDh

ν---------

QDh

Aν-----------

4QπDhν--------------= = =

Q

Dh

ν

Cdl δ 4QνπDh--------------=

ρQ δ 4QνπDh--------------

πDh2

4---------- 2ρ p1 p2–( )=

ρ2Q

2 δ24Qπ2

Dh4

νπDh16---------------------------2ρ p1 p2–( )=



(578)

To keep the discharge coefficient continuous at Reynolds number , Equation (579)

must hold:

(579)

where:

: discharge coefficient at turbulent flow (constant)

Equation (578) now reads:

(580)

Polynomial Fit for Discharge CoefficientTo keep the transition between laminar and turbulent flow smooth a polynomial fit for discharge coefficient has been developed. A general third degree polynomial form for volumetric flow rate reads:

(581)

where:

: flow section area

: kinematic viscosity

: Reynolds number for transition flow

: hydraulic diameter

: pressure 1

m· ρQδ2πDh

3

2ν---------------- p1 p2–( )= =

Retr

δCd

Retr

--------------=

Cd

m·Cd

2πDh3

2Retrν----------------- p1 p2–( )=

QAνRetr

Dh----------------- a

p1 p2–

∆p0----------------- b

p1 p2–( )

∆p02

---------------------2

cp1 p2–( )3

∆p03

------------------------+ +

=

A

ν

Retr

Dh

p1



: pressure 2

: limit pressure drop for pure turbulent flow

: constants

Derivative of Equation (581) over pressure difference becomes:

(582)

From the definition of the Reynolds number:

(583)

where:

: flow velocity at Reynolds number

According to Merritt [1, p. 41], turbulent volumetric flow rate through a circular orifice at Reynolds number can be presented as:

(584)

Using Equation (583), the volumetric flow rate can also be given as:

(585)

From Equations (584) and (585), you can solve for pressure drop at Reynolds number :

(586)

p2

∆p0

a b c, ,

dQdp-------

AνRetr

Dh----------------- a

∆p0--------- 2b

p1 p2–

∆p02

----------------- 3cp1 p2–( )2

∆p03

------------------------+ +

=

vtr

RetrνDh

-------------=

vtr Retr

Retr

Qtr Cd

πDh2

4----------

2∆ptr

ρ--------------=

Qtr AvRetrνπDh

4------------------------= =

Retr

∆ptr

ρRetr2 ν2

2Dh2Cd

2--------------------=



You can define the limit pressure drop for pure turbulent flow as:

(587)

Now the derivative of Equation (582) becomes:

(588)

and further:

(589)

To fit a third-order polynomial between laminar and turbulent flows, the polynomial must satisfy:

■ Laminar flow Equation (580) and its first-order derivative at zero pressure

■ Turbulent flow rate Equation (584) and its first-order derivative at , which

yields:

(590)

(591)

(592)

(593)

∆p0

∆p0 ξ2∆ptr ξ2ρRetr2 ν2

2Dh2Cd

2--------------------= =

dQdp-------

AνRetr

Dh-----------------

2Dh2Cd

2

ξ2ρRetr2 ν2

------------------------- a 2bp1 p2–

∆p0----------------- 3c

p1 p2–( )2

∆p02

------------------------+ +

⋅=

dQdp-------

2ACd2Dh

ξ2Retrρν

----------------------- a 2bp1 p2–

∆p0----------------- 3c

p1 p2–( )2

∆p02

------------------------+ +

=

∆p0

Q 0( ) 0=

dQdp------- 0( )

2Cd2ADh

ρνRetr---------------------=

Q ∆p0( ) CdA2∆p0

ρ------------

ξARetrνDh

---------------------= =

dQdp------- ∆p0( )

CdA

2ρ∆p0

--------------------Cd

2ADh

ξRetrρν--------------------= =



Equations (581) and (582) at and yield:

(594)

(595)

(596)

(597)

Equation (594) always satisfies Equation (590). From Equations (591) and (595), you get these unequal values:

(598)

Equations (592) and (596) require these equal values:

(599)

and, finally, from Equations (593) and (597), you get:

(600)

Solving Equations (599) and (598) for constant c:

(601)

Combining this with Equations (600) and (598) yields:

(602)

from which you can solve for constant b:

(603)

p 0= p ∆p0=

Q 0( ) 0=

dQdp------- 0( ) a

2ACd2Dh

ξ2Retrρν

-----------------------=

Q ∆p0( )AνRetr

Dh----------------- a b c+ +( )=

dQdp------- ∆p0( )

2ACd2Dh

ξ2ρνRetr

----------------------- a 2b 3c+ +( )=

a ξ2=

ξ a b c+ +=

ξ 2a 4b 6c+ +=

c ξ ξ2– b–=

ξ 2ξ24b 6ξ 6ξ2

– 6b–+ +=

b52---ξ 2ξ2

–=



Substituting b back to Equation (601), c becomes:

(604)

Now knowing the constants a, b, and c, you can write the following for the original polynomial (581):

(605)

Recalling the physical background of the polynomial fit, the change of the sign of the second-order derivative of the polynomial fit suggests waviness of the polynomial. Therefore, you can assume a smooth change in the first-order derivative of the polynomial. In math terms, this is expressed:

(606)

The second-order derivative of the polynomial reads:

(607)

from which you can derive unequal values:

(608)

Now you can define a new variable x, and substitute b and c from Equations (603) and (604), respectively:

(609)

c ξ ξ2–

52---ξ– 2ξ2

+ ξ2 32---ξ–= =

QAνRetr

Dh----------------- ξ2p1 p2–

∆p0-----------------

52---ξ 2ξ2

– p1 p2–( )2

∆p02

------------------------ ξ2 32---ξ–

p1 p2–( )3

∆p03

------------------------+ +=

d2Q

dp2

---------- 0 0 p ∆p0≤ ≤,≤

d2Q

dp2

----------2ACd

2Dh

ξ2Retrρν

----------------------- 2b1

∆p0--------- 6c

p1 p2–

∆p02

-----------------+

0≤=

2b 6cp1 p2–

∆p0----------------- 0≤+

xp1 p2–

∆p0----------------- 0 x 1≤ ≤,=



Equation (608) then yields:

(610)

and further:

(611)

Using limited values of x (one and zero), you get two unequal equations for , namely Equations (612) and (613):

(612)

(613)

from which you can solve for :

(614)

For the sake of efficiency, choose . Then, Equation (605) shrinks to a second-

degree polynomial:

(615)

5ξ 4ξ2– 6ξ2

x 9ξx 0≤–+

6ξ 9–( )x 4ξ 5–≤

ξ

6ξ 9– 4ξ 5–≤

0 4ξ 5–≤

ξ

54--- ξ 2≤ ≤

ξ 32---=

Q3AνRetr

4Dh--------------------- 3

p1 p2–

∆p0-----------------

p1 p2–( )2

∆p02

------------------------–

=

B ADAMS/Hydraulics Functions

OverviewThe functions presented here are referenced by multiple component models and are callable from component models. These functions are compact, expandable building blocks for component models.

Table 39 lists the functions by type. The section that follows lists the functions alphabetically and describes how to use them.

Table 39. Functions in ADAMS/Hydraulics

Function Types: Function Names:

Flow ■ ORIFIC - Flow Through an Orifice

Relative Flow Cross-Section Area

■ CLWL - Constant Leakage with Lap

■ LINPWL - Linear Poppet Opening Area With Leakage

Spool Positioning ■ CVS - Constant Velocity Spool

Hysteresis ■ ARATIO - Area Ratio of a Poppet


ADAMS/Hydraulics Functions296

ARATIO - Area Ratio of a Poppet

ARATIO assumes that hysteresis of a poppet type valve is caused by a change in the effective pressure area at the opening. Let the effective area be when the poppet is

closed and when the poppet is open. Assume that the transition between these two

areas occurs at a relative poppet movement of when the poppet is opening.

While closing, assume that the pressure area maintains its maximum value until the poppet is fully closed. The decision about whether or not the valve is closed is based on the valve’s position at a previous, successful timestep. Therefore, in some cases, the formulation is slightly dependent on the integration step size (for example, when the poppet is almost closed, but then starts to open again, it may occur that “almost closed” becomes closed when using a different integration step size).

Define:

(616)

Syntax

The syntax for ARATIO is:

(617)

where:

: relative poppet position [],

: relative valve poppet position limit for hysteresis []

: pressure area ratio for hysteresis at ( ), ( ) []

: closed flag []0 = valve was open at previous integration step1 = valve was closed at previous integration step

: differencing identifier []

Ac( )

Ap( )

0 x x≤ ≤ ε( )

εAc

Ap------=

ε ARATIO x xε ε0 closed idif, , , ,( )=

x 0 x 1≤ ≤

xε

ε0 x 0= ε0 1≤

closed

idif




If ( ):

(618)

otherwise:

(619)

For further information on the MSC.ADAMS STEP function, see the guide, Using the ADAMS/View Function Builder.

closed

ε step x 0.0 ε0 xε 1.0, , , ,( ) 0 x xε≤ ≤,=

ε 1=



CLWL - Constant Leakage with Lap

The CLWL function returns the relative opening of a flow passage as a function of relative spool displacement.

Syntax

The syntax for CLWL is:

(620)

where:

: relative spool displacement ( ) []

: relative spool displacement lap ( ) []

: relative leakage ( ) []


R CLWL x xlap ϒ idif, , ,( )=

x x 1≤

xlap 1– xlap 1< <

ϒ 0 ϒ 1≤ ≤

idif




CLWL is defined as:

(621)

Figure 10 shows an example of CLWL output as a function of relative spool displacement with the following parameter values:

■ Relative spool displacement lap and

■ Relative leakage

Figure 10. Example of CLWL Function Output as a Function of Relative Spool Displacement

CLWL maxx xlap–( ) 1 ϒ–( )⋅

1 xlap–--------------------------------------------- 0,

ϒ+=

xlap 0.05= xlap 0.05–=

ϒ 0.04=

0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8 1

CLWL []

Spool Displacement []

Constant Leakage with Lap Model Output as a function of Spool Displacement



CVS - Constant Velocity Spool

The constant velocity spool (CVS) function drives the spool from one end to another, switching at a given time at a constant velocity. CVS assumes that the spool accelerates/decelerates relatively fast to that constant speed. Independent switching times are defined both away from ( ) and to ( ) the center position. CVS returns the

instantaneous relative velocity of the spool.

Syntax

The syntax for CVS is:

(622)

where:

: control input for the spool displacement []

: relative valve spool displacement []

: center position flag ( ) []0 = no center position, only ends1 = spool has three positions, center and two ends

: switching time for spool opening ( ) [time]

: switching time for spool closing ( ) [time]

: relative acceleration/deceleration length at negative and positive end ( ) []


Opening refers to movement away from the center position. Closing refers to motion towards the center position.

τo τc

x· CVS f x n τo τc δ idif, , , , , ,( )=

f

x

n n 0 or 1=

τo τo 0>

τc τc 0>

δ δ 0>

idif




The control input is internally limited between -1 or 0 and 1.

(623)

The CVS function is defined as:

, for opening and (624)

, for closing. (625)

flim min 1 max f 0,( ),( ) if n = 0 flim min 1 max f 1–,( ),( ) if n = 1 ,=

,=

CVSmin

flim x–( )δ

---------------------- 1,

τo-------------------------------------------=

CVSmin

flim x–( )δ

---------------------- 1,

τc-------------------------------------------=



LINPWL - Linear Poppet Opening Area With Leakage

The LINPWL function returns the relative opening area of a valve as a function of relative poppet displacement. LINPWL assumes a linear relationship between the opening area and the poppet displacement other than in the closed position, where leakage dominates.

Syntax

The syntax for LINPWL is:

(626)

where:

: relative poppet displacement ( ) []

: relative leakage ( ) []



With conditions:

(627)

You can obtain a second order polynomial for relative opening area:

(628)

Choose for leakage transition length constant. With the above definitions, you can write for LINPWL:

If ( )

(629)

R LINPWL x ϒ idif, ,( )=

x x 1≤

ϒ 0 ϒ 1≤ ≤

idif

R 0( ) ϒR nϒ( ) nϒR’ nϒ( ) 1

===

R ϒ 12n---–

xϒ

nϒ( )2--------------x2+ + 0 x nϒ≤ ≤,=

n 2=

0 x 2ϒ≤ ≤

R ϒ 14ϒ-------x2+=



Otherwise, if ( ) (this is defined only for completeness, x should have negative values), then:

(630)

otherwise:

(631)

Figure 11 shows an example of the LINPWL function output as a function of relative poppet displacement using the parameter values: relative leakage .

Figure 11. Example of Linpwl Output as a Function of Relative Poppet Displacement

x 0<

R ϒ=

R x=

ϒ 0.02=

0

0.02

0.04

0.06

0.08

0.1

0 0.02 0.04 0.06 0.08 0.1

LINPWL []

Poppet Displacement []

Linear Poppet Opening Area with Leakage as a function of Poppet Displacement



ORIFIC - Flow Through an Orifice

The ORIFIC function computes mass flow rate through a passage with area of Amax, having a relative opening of R, and known pressures, pin and pout, before and after it. The ORIFIC function refers to fluid data internally.

Syntax

The syntax for ORIFIC is:

(632)

where:

: relative opening of the orifice [],

: discharge coefficient []

: Reynolds number at transition flow []

: maximum flow cross-section area [length2]

: pressure at input port [force/length2]

: pressure at output port [force/length2]



Instantaneous flow cross-section area of an orifice is:

(633)

where:

flow cross-section area of the orifice [length2]

hydraulic diameter of the orifice [length]

m· ORIFIC R Cd Retr Amax pin pout idif, , , ,, ,( )=

R 0 R 1≤ ≤

Cd

Retr

Amax

Pin

Pout

idif

A

AπDh

2

4---------- R= Amax=

A

Dh



From Equation (633):

(634)

The limit pressure drop for pure turbulent flow ( ) writes (see Density of the Fluid and

Bernoulli’s Equation on page 285):

(635)

where:

: density of the fluid at pressure [force/length2]

: kinematic viscosity of the fluid at fluid temperature [length2/time]

Formulation applied in ADAMS/Hydraulics for mass flow through an orifice is:

, when: (636)

, when:

(637)

(638)

where:

: mass flow towards pressure [mass/time]

: mass flow towards pressure [mass/time]

: pressure 1 [force/length2]

: pressure 2 [force/length2]

For further description of the applied flow formulation at low pressures, see Density of the Fluid and Bernoulli’s Equation on page 285.

Dh 2RAmax

π----------------=

∆p0

∆p0

9ρ1Retr2 ν1

2

8Dh2Cd

2-------------------------=

ρ1 p1

ν1

m2·

CdA 2ρ1 p1 p2–( )= p1 p2–( ) ∆p0≥

m· 2

3ρ1πDhν1Retr

16------------------------------------

p1 p2–

∆p0----------------- 3

p1 p2–

∆p0-----------------–

⋅=

p1 p2–( ) ∆p0<

m· 1 m· 2–=

m· 1 p1

m· 2 p2

p1

p2



Math Follow-UpMerritt [1, p. 40–41] gives an equation for turbulent volumetric flow (flow at high Reynolds numbers) through an orifice based on Bernoulli’s equation:

(639)

where:

: volumetric flow through the orifice

: density of the fluid

In Equation (639), density of the fluid is assumed constant. For the mass flow, Equation (639) yields:

(640)

It has been found that Equation (639) is not valid for low Reynolds numbers. Attempts have been made to extend this equation to the laminar region by plotting discharge coefficient as a function of the Reynolds number. For , many investigators have found the discharge coefficient to be directly proportional to the square root of the Reynolds number [1, p. 43]:

(641)

where:

: discharge coefficient for laminar flow

: laminar flow coefficient

: Reynolds number

To make the transition from laminar flow to turbulent smooth, a polynomial fit has been developed. For more information concerning turbulent and laminar flow and the polynomial fit see Density of the Fluid and Bernoulli’s Equation on page 285.

Q CdA2ρ--- p1 p2–( )=

Q

ρ

m· ρQ CdA 2ρ p1 p2–( )= =

Re 10<

Cdl δ Re=

Cdl

δ

Re



Figure 12 shows an example of a mass flow through an orifice as a function of pressure drop ( ) and Reynolds number at transition flow ( ). The values for the

parameters in the example are:

■ Density of the fluid

■ Kinematic viscosity of the fluid

■ Discharge coefficient of the orifice

■ Hydraulic diameter of the orifice

Figure 12. Example of Mass Flow Through an Orifice as a Function of Pressure Drop and Reynolds Number at Transition Flow

p1 p2– Retr

ρ 900 kg/m3

=

ν 50 cSt=

Cd 0.6=

Dh 1.5 mm=

Example of Mass Flow Through an Orifice

010

2030

4050

0500

10001500

20002500

30003500

4000

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Pressure Drop [MPa]

Re_tr []

Mass Flow [kg/s]

C Command Language Reference

OverviewThe following appendix lists the commands available in ADAMS/View for executing ADAMS/Hydraulics. For more information on entering commands, refer to the ADAMS/View online help.


Command Language Reference310

!N/A = default not available

!N/A = default not available

hydraulics defaults set & junction_volume = (eval(1.0E-6(meter**3))) & ! < real:gt=0 > environment_pressure = (eval(101325(Newton/meter**2))) &! < real:gt=0 > x_penetration_tolerance = 0.001 & ! < real:gt=0 > hysteresis_limit = 0.001 & ! < real:gt=0 > model_name = (default model) ! < model:A >

hydraulics connect & i_port_name = N/A & ! < hyd_port > j_port_name = N/A ! < hyd_port >

hydraulics disconnect single_port & port_name = N/A ! < hyd_port >

hydraulics disconnect all_ports & entity_name = N/A ! < hyd_entity >

hydraulics copy & entity_name = N/A & ! < hyd_entity > new_entity_name = N/A ! < new_hyd_entity >

hydraulics rename & entity_name = N/A & ! < hyd_entity > new_entity_name = N/A ! < new_hyd_entity >

hydraulics delete & entity_name = N/A ! < hyd_entity >

hydraulics reorient & entity_name = N/A & ! < hyd_entity > orientation = N/A ! < real:C=1 >

hydraulics create accumulator & accumulator_name = N/A & ! < new_hyd_accumulator > location = 0,0,0 & ! < location > mechanical_volume = (eval(1e-2(meter**3))) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > polytropic_exponent = 1.4 & ! < real:gt=0 > set_pressure_of_gas = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > set_temperature_of_gas = 293.15 & ! < real:gt=0 > nom_pressure_drop = (eval(10e5(Newton/meter**2))) & ! < real:gt=0 >



PA_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify accumulator & accumulator_name = N/A & ! < hyd_accumulator > location = (current value) & ! < location > mechanical_volume = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 > polytropic_exponent = (current value) & ! < real:gt=0 > set_pressure_of_gas = (current value) & ! < real:gt=0 > set_temperature_of_gas = (current value) & ! < real:gt=0 > nom_pressure_drop = (current value) & ! < real:gt=0 > PA_nom_flowrate = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create counter_balance_valve4p & counter_balance_valve4p_name = N/A & ! < new_hyd_counter_balance_valve4p > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > A_closing_pressure = (eval(3e5(Newton/meter**2))) & ! < real:gt=0 > A1_pressure = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > A1_flowrate = (eval(1.414e-3(meter**3/second))) & ! < real:gt=0 > A2_pressure = (eval(21e5(Newton/meter**2))) & ! < real:gt=0 > A2_flowrate = (eval(3.14e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > BXT_ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > BA_pressure_area_ratio = 0.9 & ! < real:ge=0 > XA_pressure_area_ratio = 2.0 & ! < real:ge=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify counter_balance_valve4p & counter_balance_valve4p_name = N/A & ! < hyd_counter_balance_valve4p > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > A_closing_pressure = (current value) & ! < real:gt=0 > A1_pressure = (current value) & ! < real:gt=0 > A1_flowrate = (current value) & ! < real:gt=0 > A2_pressure = (current value) & ! < real:gt=0 > A2_flowrate = (current value) & ! < real:gt=0 >



AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > BXT_ref_pressure = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > BA_pressure_area_ratio = (current value) & ! < real:ge=0 > XA_pressure_area_ratio = (current value) & ! < real:ge=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create cartridge_valve3p & cartridge_valve3p_name = N/A & ! < new_hyd_cartridge_valve3p > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > spring_stiffness = (eval(10(Newton/mm))) & ! < real:gt=0 > spring_precompression = (eval(10mm)) & ! < real:ge=0 > max_opening = (eval(6mm)) & ! < real:gt=0 > diameter = (eval(8mm)) & ! < real:gt=0 > valve_type = poppet & ! < list(poppet,spool) > jet_angle = (eval(50degrees)) & ! < real:gt=0 > CA_pressure_area_ratio = 1.0 & ! < real:ge=1.0 > X_orifice_diameter = (eval(5mm)) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify cartridge_valve3p & cartridge_valve3p_name = N/A & ! < hyd_cartridge_valve3p > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > spring_stiffness = (current value) & ! < real:gt=0 > spring_precompression = (current value) & ! < real:ge=0 > max_opening = (current value) & ! < real:gt=0 > diameter = (current value) & ! < real:gt=0 > valve_type = (current value) & ! < list(poppet,spool) > jet_angle = (current value) & ! < real:gt=0 > CA_pressure_area_ratio = (current value) & ! < real:ge=1.0 > X_orifice_diameter = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >



hydraulics create check_valve2 & check_valve2_name = N/A & ! < new_hyd_check_valve2 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (eval(2e5(Newton/meter**2))) &! < real:gt=0 > AB1_pressure_drop = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > AB1_flowrate = (eval(1.414e-3(meter**3/second))) & ! < real:gt=0 > AB2_pressure_drop = (eval(20e5(Newton/meter**2))) & ! < real:gt=0 > AB2_flowrate = (eval(3.14e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify check_valve2 & check_valve2_name = N/A & ! < hyd_check_valve2 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (current value) & ! < real:gt=0 > AB1_pressure_drop = (current value) & ! < real:gt=0 > AB1_flowrate = (current value) & ! < real:gt=0 > AB2_pressure_drop = (current value) & ! < real:gt=0 > AB2_flowrate = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > ref_fluid_density = (current value) & ! < real:gt=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create check_valve3p & check_valve3p_name = N/A & ! < new_hyd_check_valve3p > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > A_closing_pressure = (eval(3e5(Newton/meter**2))) & ! < real:gt=0 > A1_pressure = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > A1_flowrate = (eval(1.414e-3(meter**3/second))) & ! < real:gt=0 > A2_pressure = (eval(21e5(Newton/meter**2))) & ! < real:gt=0 > A2_flowrate = (eval(3.14e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > BX_ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 >



BA_pressure_area_ratio = 0.1 & ! < real:ge=0:le=1 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify check_valve3p & check_valve3p_name = N/A & ! < hyd_check_valve3p > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > A_closing_pressure = (current value) & ! < real:gt=0 > A1_pressure = (current value) & ! < real:gt=0 > A1_flowrate = (current value) & ! < real:gt=0 > A2_pressure = (current value) & ! < real:gt=0 > A2_flowrate = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > BX_ref_pressure = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > BA_pressure_area_ratio = (current value) & ! < real:ge=0:le=1 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create check_valve4p & check_valve4p_name = N/A & ! < new_hyd_check_valve4p > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > A_closing_pressure = (eval(3e5(Newton/meter**2))) & ! < real:gt=0 > A1_pressure = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > A1_flowrate = (eval(1.414e-3(meter**3/second))) & ! < real:gt=0 > A2_pressure = (eval(21e5(Newton/meter**2))) & ! < real:gt=0 > A2_flowrate = (eval(3.14e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=1 > BXT_ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > BA_pressure_area_ratio = 0.9 & ! < real:ge=0 > XA_pressure_area_ratio = 2.0 & ! < real:ge=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >



hydraulics modify check_valve4p & check_valve4p_name = N/A & ! < hyd_check_valve4p > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > A_closing_pressure = (current value) & ! < real:gt=0 > A1_pressure = (current value) & ! < real:gt=0 > A1_flowrate = (current value) & ! < real:gt=0 > A2_pressure = (current value) & ! < real:gt=0 > A2_flowrate = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=1 > BXT_ref_pressure = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > BA_pressure_area_ratio = (current value) & ! < real:ge=0 > XA_pressure_area_ratio = (current value) & ! < real:ge=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create cylinder1 & cylinder1_name = N/A & ! < new_hyd_cylinder1 > location = 0,0,0 & ! < location > i_marker = N/A & ! < marker > j_marker = N/A & ! < marker > max_length = (eval(1meter)) & ! < real:gt=0 > min_length = (eval(0.6meter)) & ! < real:gt=0 > A_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > piston_diameter = (eval(0.05meter)) & ! < real:gt=0 > A_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > A_orifice_diameter = (eval(1e-2(meter))) & ! < real:ge=0 > cushion_free_length = (eval(0.005meter)) & ! < real:gt=0 > cushion_relative_stiffness = (eval(10000Newton)) & ! < real:gt=0 > cushion_force_exponent = 2.0 & ! < real:gt=0 > cushion_rebound_ratio = 0.0 & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (eval(0.01(meter/second))) & ! < real:gt=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(0.005meter)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > apply_mechanical_losses = no & ! < list(yes,no) > Coulomb_friction_force = 0.0 & ! < real:ge=0 > piston_seal_friction_coefficient = 0.0 & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (eval(1e-2(meter/second))) &! < real:gt=0 > dynamic_friction_decrease = 0.1 & ! < real:ge=0 >



seal_shear_stiffness = (eval(10(Newton/mm))) & ! < real:gt=0 > damping_coefficient = 0.0 & ! < real:ge=0 > apply_leakage = no & ! < list(yes,no) > relative_clearance_of_piston = 0.0 & ! < real:ge=0 > piston_thickness = (eval(0.020meter)) & ! < real:gt=0 > static_hold = none & ! < list(none,pl,l0) > A_relative_opening_function = "1.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify cylinder1 & cylinder1_name = N/A & ! < hyd_cylinder1 > location = (current value) & ! < location > i_marker = (current value) & ! < marker > j_marker = (current value) & ! < marker > max_length = (current value) & ! < real:gt=0 > min_length = (current value) & ! < real:gt=0 > A_dead_volume = (current value) & ! < real:ge=0 > piston_diameter = (current value) & ! < real:gt=0 > A_chamber_initial_pressure = (current value) & ! < real:gt=0 > A_orifice_diameter = (current value) & ! < real:ge=0 > cushion_free_length = (current value) & ! < real:gt=0 > cushion_relative_stiffness = (current value) & ! < real:gt=0 > cushion_force_exponent = (current value) & ! < real:gt=0 > cushion_rebound_ratio = (current value) & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (current value) & ! < real:gt=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > apply_mechanical_losses = (current value) & ! < list(yes,no) > Coulomb_friction_force = (current value) & ! < real:ge=0 > piston_seal_friction_coefficient = (current value) & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (current value) & ! < real:gt=0 > dynamic_friction_decrease = (current value) & ! < real:ge=0 > seal_shear_stiffness = (current value) & ! < real:gt=0 > damping_coefficient = (current value) & ! < real:ge=0 > apply_leakage = (current value) & ! < list(yes,no) > relative_clearance_of_piston = (current value) & ! < real:ge=0 > piston_thickness = (current value) & ! < real:gt=0 > static_hold = (current value) & ! < list(none,pl,l0) > A_relative_opening_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create cylinder1f & cylinder1f_name = N/A & ! < new_hyd_cylinder1f >



location = 0,0,0 & ! < location > i_marker = N/A & ! < marker > j_marker = N/A & ! < marker > max_length = (eval(1meter)) & ! < real:gt=0 > min_length = (eval(0.6meter)) & ! < real:gt=0 > A_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > piston_diameter = (eval(0.05meter)) & ! < real:gt=0 > A_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > cushion_free_length = (eval(0.005meter)) & ! < real:gt=0 > cushion_relative_stiffness = (eval(10000Newton)) & ! < real:gt=0 > cushion_force_exponent = 2.0 & ! < real:gt=0 > cushion_rebound_ratio = 0.0 & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (eval(0.01(meter/second))) & ! < real:gt=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(0.005meter)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > apply_mechanical_losses = no & ! < list(yes,no) > Coulomb_friction_force = 0.0 & ! < real:ge=0 > piston_seal_friction_coefficient = 0.0 & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (eval(1e-2(meter/second))) &! < real:gt=0 > dynamic_friction_decrease = 0.1 & ! < real:ge=0 > seal_shear_stiffness = (eval(10(Newton/mm))) & ! < real:gt=0 > damping_coefficient = 0.0 & ! < real:ge=0 > apply_leakage = no & ! < list(yes,no) > relative_clearance_of_piston = 0.0 & ! < real:ge=0 > piston_thickness = (eval(0.020meter)) & ! < real:gt=0 > static_hold = none & ! < list(none,pl,l0) > fluid_name = N/A ! < hyd_fluid >

hydraulics modify cylinder1f & cylinder1f_name = N/A & ! < hyd_cylinder1f > location = (current value) & ! < location > i_marker = (current value) & ! < marker > j_marker = (current value) & ! < marker > max_length = (current value) & ! < real:gt=0 > min_length = (current value) & ! < real:gt=0 > A_dead_volume = (current value) & ! < real:ge=0 > piston_diameter = (current value) & ! < real:gt=0 > A_chamber_initial_pressure = (current value) & ! < real:gt=0 > cushion_free_length = (current value) & ! < real:gt=0 > cushion_relative_stiffness = (current value) & ! < real:gt=0 > cushion_force_exponent = (current value) & ! < real:gt=0 > cushion_rebound_ratio = (current value) & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (current value) & ! < real:gt=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) >



wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > apply_mechanical_losses = (current value) & ! < list(yes,no) > Coulomb_friction_force = (current value) & ! < real:ge=0 > piston_seal_friction_coefficient = (current value) & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (current value) & ! < real:gt=0 > dynamic_friction_decrease = (current value) & ! < real:ge=0 > seal_shear_stiffness = (current value) & ! < real:gt=0 > damping_coefficient = (current value) & ! < real:ge=0 > apply_leakage = (current value) & ! < list(yes,no) > relative_clearance_of_piston = (current value) & ! < real:ge=0 > piston_thickness = (current value) & ! < real:gt=0 > static_hold = (current value) & ! < list(none,pl,l0) > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create cylinder2 & cylinder2_name = N/A & ! < new_hyd_cylinder2 > location = 0,0,0 & ! < location > i_marker = N/A & ! < marker > j_marker = N/A & ! < marker > max_length = (eval(1meter)) & ! < real:gt=0 > min_length = (eval(0.6meter)) & ! < real:gt=0 > B_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > A_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > piston_diameter = (eval(0.05meter)) & ! < real:gt=0 > B_rod_diameter = (eval(0.01meter)) & ! < real:gt=0 > A_rod_diameter = 0.0 & ! < real:ge=0 > B_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > A_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > A_orifice_diameter = (eval(1e-2(meter))) & ! < real:ge=0 > B_orifice_diameter = (eval(1e-2(meter))) & ! < real:ge=0 > cushion_free_length = (eval(0.005meter)) & ! < real:gt=0 > cushion_relative_stiffness = (eval(10000Newton)) & ! < real:gt=0 > cushion_force_exponent = 2.0 & ! < real:gt=0 > cushion_rebound_ratio = 0.0 & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (eval(0.01(meter/second))) & ! < real:gt=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(0.005meter)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > apply_mechanical_losses = no & ! < list(yes,no) > Coulomb_friction_force = 0.0 & ! < real:ge=0 > piston_seal_friction_coefficient = 0.0 & ! < real:ge=0 > B_rod_seal_friction_coefficient = 0.0 & ! < real:ge=0 >



A_rod_seal_friction_coefficient = 0.0 & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (eval(1e-2(meter/second))) &! < real:gt=0 > dynamic_friction_decrease = 0.1 & ! < real:ge=0 > seal_shear_stiffness = (eval(10(Newton/mm))) & ! < real:gt=0 > damping_coefficient = 0.0 & ! < real:ge=0 > apply_leakage = no & ! < list(yes,no) > relative_clearance_of_piston = 0.0 & ! < real:ge=0 > piston_thickness = (eval(0.020meter)) & ! < real:gt=0 > static_hold = none & ! < list(none,pl,pu,pl_and_pu,pl_and_l0,pu_and_l0) > A_relative_opening_function = "1.0" & ! < analysis_function:c=0 > B_relative_opening_function = "1.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify cylinder2 & cylinder2_name = N/A & ! < hyd_cylinder2 > location = (current value) & ! < location > i_marker = (current value) & ! < marker > j_marker = (current value) & ! < marker > max_length = (current value) & ! < real:gt=0 > min_length = (current value) & ! < real:gt=0 > B_dead_volume = (current value) & ! < real:ge=0 > A_dead_volume = (current value) & ! < real:ge=0 > piston_diameter = (current value) & ! < real:gt=0 > B_rod_diameter = (current value) & ! < real:gt=0 > A_rod_diameter = (current value) & ! < real:ge=0 > B_chamber_initial_pressure = (current value) & ! < real:gt=0 > A_chamber_initial_pressure = (current value) & ! < real:gt=0 > A_orifice_diameter = (current value) & ! < real:ge=0 > B_orifice_diameter = (current value) & ! < real:ge=0 > cushion_free_length = (current value) & ! < real:gt=0 > cushion_relative_stiffness = (current value) & ! < real:gt=0 > cushion_force_exponent = (current value) & ! < real:gt=0 > cushion_rebound_ratio = (current value) & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (current value) & ! < real:gt=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > apply_mechanical_losses = (current value) & ! < list(yes,no) > Coulomb_friction_force = (current value) & ! < real:ge=0 > piston_seal_friction_coefficient = (current value) & ! < real:ge=0 > B_rod_seal_friction_coefficient = (current value) & ! < real:ge=0 > A_rod_seal_friction_coefficient = (current value) & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (current value) & ! < real:gt=0 > dynamic_friction_decrease = (current value) & ! < real:ge=0 > seal_shear_stiffness = (current value) & ! < real:gt=0 >



damping_coefficient = (current value) & ! < real:ge=0 > apply_leakage = (current value) & ! < list(yes,no) > relative_clearance_of_piston = (current value) & ! < real:ge=0 > piston_thickness = (current value) & ! < real:gt=0 > static_hold = (current value) & ! < list(none,pl,pu,pl_and_pu,pl_and_l0,pu_and_l0) > A_relative_opening_function = (current function) & ! < analysis_function:c=0 > B_relative_opening_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create cylinder2ff & cylinder2ff_name = N/A & ! < new_hyd_cylinder2ff > location = 0,0,0 & ! < location > i_marker = N/A & ! < marker > j_marker = N/A & ! < marker > max_length = (eval(1meter)) & ! < real:gt=0 > min_length = (eval(0.6meter)) & ! < real:gt=0 > B_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > A_dead_volume = (eval(0.0(meter**3))) & ! < real:ge=0 > piston_diameter = (eval(0.05meter)) & ! < real:gt=0 > B_rod_diameter = (eval(0.01meter)) & ! < real:gt=0 > A_rod_diameter = 0.0 & ! < real:ge=0 > B_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > A_chamber_initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > cushion_free_length = (eval(0.005meter)) & ! < real:gt=0 > cushion_relative_stiffness = (eval(10000Newton)) & ! < real:gt=0 > cushion_force_exponent = 2.0 & ! < real:gt=0 > cushion_rebound_ratio = 0.0 & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (eval(0.01(meter/second))) & ! < real:gt=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(0.005meter)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > apply_mechanical_losses = no & ! < list(yes,no) > Coulomb_friction_force = 0.0 & ! < real:ge=0 > piston_seal_friction_coefficient = 0.0 & ! < real:ge=0 > B_rod_seal_friction_coefficient = 0.0 & ! < real:ge=0 > A_rod_seal_friction_coefficient = 0.0 & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (eval(1e-2(meter/second))) &! < real:gt=0 > dynamic_friction_decrease = 0.1 & ! < real:ge=0 > seal_shear_stiffness = (eval(10(Newton/mm))) & ! < real:gt=0 > damping_coefficient = 0.0 & ! < real:ge=0 > apply_leakage = no & ! < list(yes,no) > relative_clearance_of_piston = 0.0 & ! < real:ge=0 > piston_thickness = (eval(0.020meter)) & ! < real:gt=0 > static_hold = none & ! < list(none,pl,pu,pl_and_pu,pl_and_l0,pu_and_l0) >



fluid_name = N/A ! < hyd_fluid >

hydraulics modify cylinder2ff & cylinder2ff_name = N/A & ! < hyd_cylinder2ff > location = (current value) & ! < location > i_marker = (current value) & ! < marker > j_marker = (current value) & ! < marker > max_length = (current value) & ! < real:gt=0 > min_length = (current value) & ! < real:gt=0 > B_dead_volume = (current value) & ! < real:ge=0 > A_dead_volume = (current value) & ! < real:ge=0 > piston_diameter = (current value) & ! < real:gt=0 > B_rod_diameter = (current value) & ! < real:gt=0 > A_rod_diameter = (current value) & ! < real:ge=0 > B_chamber_initial_pressure = (current value) & ! < real:gt=0 > A_chamber_initial_pressure = (current value) & ! < real:gt=0 > cushion_free_length = (current value) & ! < real:gt=0 > cushion_relative_stiffness = (current value) & ! < real:gt=0 > cushion_force_exponent = (current value) & ! < real:gt=0 > cushion_rebound_ratio = (current value) & ! < real:ge=0:le=1 > limit_velocity_for_rebound = (current value) & ! < real:gt=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > apply_mechanical_losses = (current value) & ! < list(yes,no) > Coulomb_friction_force = (current value) & ! < real:ge=0 > piston_seal_friction_coefficient = (current value) & ! < real:ge=0 > B_rod_seal_friction_coefficient = (current value) & ! < real:ge=0 > A_rod_seal_friction_coefficient = (current value) & ! < real:ge=0 > limit_velocity_for_dynamic_friction = (current value) & ! < real:gt=0 > dynamic_friction_decrease = (current value) & ! < real:ge=0 > seal_shear_stiffness = (current value) & ! < real:gt=0 > damping_coefficient = (current value) & ! < real:ge=0 > apply_leakage = (current value) & ! < list(yes,no) > relative_clearance_of_piston = (current value) & ! < real:ge=0 > piston_thickness = (current value) & ! < real:gt=0 > static_hold = (current value) & ! < list(none,pl,pu,pl_and_pu,pl_and_l0,pu_and_l0) > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create directional_control_valve2w2 & directional_control_valve2w2_name = N/A & ! < new_hyd_directional_control_valve2w2 > location = 0,0,0 & ! < location > valve_type = closed & ! < list(open,closed) > initial_position = 0.0 & ! < real:ge=0:le=1 > valve_opening_time = (eval(5ms)) & ! < real:gt=0 >



valve_closing_time = (eval(5ms)) & ! < real:gt=0 > PA_xlap = 0.0 & ! < real:gt=-1:lt=1 > PA_relative_leakage = 0.0 & ! < real:ge=0:le=1 > nom_pressure_drop = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > PA_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > control_input_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify directional_control_valve2w2 & directional_control_valve2w2_name = N/A & ! < hyd_directional_control_valve2w2 > location = (current value) & ! < location > valve_type = (current value) & ! < list(open,closed) > initial_position = (current value) & ! < real:ge=0:le=1 > valve_opening_time = (current value) & ! < real:gt=0 > valve_closing_time = (current value) & ! < real:gt=0 > PA_xlap = (current value) & ! < real:gt=-1:lt=1 > PA_relative_leakage = (current value) & ! < real:ge=0:le=1 > nom_pressure_drop = (current value) & ! < real:gt=0 > PA_nom_flowrate = (current value) & ! < real:ge=0 > ref_fluid_density = (current value) & ! < real:gt=0 > control_input_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create directional_control_valve3w2 & directional_control_valve3w2_name = N/A & ! <new_hyd_directional_control_valve3w2 > location = 0,0,0 & ! < location > valve_type = closed & ! < list(open,closed) > initial_position = 0.0 & ! < real:ge=0:le=1 > valve_opening_time = (eval(5ms)) & ! < real:gt=0 > valve_closing_time = (eval(5ms)) & ! < real:gt=0 > PA_xlap = 0.0 & ! < real:gt=-1:lt=1 > PA_relative_leakage = 0.0 & ! < real:ge=0:le=1 > AT_xlap = 0.0 & ! < real:gt=-1:lt=1 > AT_relative_leakage = 0.0 & ! < real:ge=0:le=1 > nom_pressure_drop = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > PA_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > AT_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > control_input_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify directional_control_valve3w2 & directional_control_valve3w2_name = N/A & ! < hyd_directional_control_valve3w2 >



location = (current value) & ! < location > valve_type = (current value) & ! < list(open,closed) > initial_position = (current value) & ! < real:ge=0:le=1 > valve_opening_time = (current value) & ! < real:gt=0 > valve_closing_time = (current value) & ! < real:gt=0 > PA_xlap = (current value) & ! < real:gt=-1:lt=1 > PA_relative_leakage = (current value) & ! < real:ge=0:le=1 > AT_xlap = (current value) & ! < real:gt=-1:lt=1 > AT_relative_leakage = (current value) & ! < real:ge=0:le=1 > nom_pressure_drop = (current value) & ! < real:gt=0 > PA_nom_flowrate = (current value) & ! < real:ge=0 > AT_nom_flowrate = (current value) & ! < real:ge=0 > ref_fluid_density = (current value) & ! < real:gt=0 > control_input_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create directional_control_valve4w3 & directional_control_valve4w3_name = N/A & ! < new_hyd_directional_control_valve4w3 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=-1:le=1 > valve_opening_time = (eval(5ms)) & ! < real:gt=0 > valve_closing_time = (eval(5ms)) & ! < real:gt=0 > PA_xlap = 0.0 & ! < real:gt=-1:lt=1 > PA_relative_leakage = 0.0 & ! < real:ge=0:le=1 > PB_xlap = 0.0 & ! < real:gt=-1:lt=1 > PB_relative_leakage = 0.0 & ! < real:ge=0:le=1 > AT_xlap = 0.0 & ! < real:gt=-1:lt=1 > AT_relative_leakage = 0.0 & ! < real:ge=0:le=1 > BT_xlap = 0.0 & ! < real:gt=-1:lt=1 > BT_relative_leakage = 0.0 & ! < real:ge=0:le=1 > nom_pressure_drop = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > PA_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > PB_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > AT_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > BT_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > PT_nom_flowrate = 0.0 & ! < real:ge=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > control_input_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify directional_control_valve4w3 & directional_control_valve4w3_name = N/A & ! < hyd_directional_control_valve4w3 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=-1:le=1 > valve_opening_time = (current value) & ! < real:gt=0 > valve_closing_time = (current value) & ! < real:gt=0 >



PA_xlap = (current value) & ! < real:gt=-1:lt=1 > PA_relative_leakage = (current value) & ! < real:ge=0:le=1 > PB_xlap = (current value) & ! < real:gt=-1:lt=1 > PB_relative_leakage = (current value) & ! < real:ge=0:le=1 > AT_xlap = (current value) & ! < real:gt=-1:lt=1 > AT_relative_leakage = (current value) & ! < real:ge=0:le=1 > BT_xlap = (current value) & ! < real:gt=-1:lt=1 > BT_relative_leakage = (current value) & ! < real:ge=0:le=1 > nom_pressure_drop = (current value) & ! < real:gt=0 > PA_nom_flowrate = (current value) & ! < real:ge=0 > PB_nom_flowrate = (current value) & ! < real:ge=0 > AT_nom_flowrate = (current value) & ! < real:ge=0 > BT_nom_flowrate = (current value) & ! < real:ge=0 > PT_nom_flowrate = (current value) & ! < real:ge=0 > ref_fluid_density = (current value) & ! < real:gt=0 > control_input_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create flow_control_valve2 & flow_control_valve2_name = N/A & ! < new_hyd_flow_control_valve2 > location = 0,0,0 & ! < location > initial_position = 1.0 & ! < real:ge=0:le=1 > AB1_pressure_drop = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > AB1_flowrate = (eval(4e-3(meter**3/second))) & ! < real:gt=0 > AB2_pressure_drop = (eval(40e5(Newton/meter**2))) & ! < real:gt=0 > AB2_flowrate = (eval(3.95e-3(meter**3/second))) & ! < real:gt=0 > AB3_pressure_drop = (eval(45e5(Newton/meter**2))) & ! < real:gt=0 > AB3_flowrate = (eval(3.9e-3(meter**3/second))) & ! < real:gt=0 > ratio_of_pressure_drops = 0.7 & ! < real:gt=0:lt=1 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > AB1_flowrate_change_rate = (eval(-0.03(meter**3/second**2))) & ! < real:lt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify flow_control_valve2 & flow_control_valve2_name = N/A & ! < hyd_flow_control_valve2 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > AB1_pressure_drop = (current value) & ! < real:gt=0 > AB1_flowrate = (current value) & ! < real:gt=0 > AB2_pressure_drop = (current value) & ! < real:gt=0 > AB2_flowrate = (current value) & ! < real:gt=0 > AB3_pressure_drop = (current value) & ! < real:gt=0 > AB3_flowrate = (current value) & ! < real:gt=0 > ratio_of_pressure_drops = (current value) & ! < real:gt=0:lt=1 > ref_fluid_density = (current value) & ! < real:gt=0 >



AB1_flowrate_change_rate = (current value) & ! < real:lt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create flow_source & flow_source_name = N/A & ! < new_hyd_flow_source > location = 0,0,0 & ! < location > initial_flow = 0 & ! < real > flowrate_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify flow_source & flow_source_name = N/A & ! < hyd_flow_source > location = (current value) & ! < location > initial_flow = (current value) & ! < real > flowrate_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create fluid & fluid_name = N/A & ! < new_hyd_fluid > location = 0,0,0 & ! < location > temperature = 293.15 & ! < real:gt=0 > eos_for_liquid_method = Merritt & ! < list(Merritt) > ref_density = (eval(900(kg/meter**3))) & ! < real:gt=0 > ref_temperature = 293.15 & ! < real:gt=0 > ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > bulk_modulus = (eval(1.9E9(Newton/meter**2))) & ! < real:gt=0 > thermal_expansion_coefficient = 2.8E-04 & ! < real:gt=0 > air_content_method = CCUA & ! < list(CCUA) > air_density_at_STP = (eval(1.2(kg/meter**3))) & ! < real:gt=0 > saturation_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > solubility_coefficient = 0.08 & ! < real:gt=0 > undissolvable_air_content = 0.002 & ! < real:ge=0:lt=1 > polytropic_exponent = 1.4 & ! < real:gt=0 > viscosity_method = ASTM_D_341_43 & ! < list(ASTM_D_341_43) > temperature_points = 233.15,313.15,373.15 & ! < real:gt=0:c=2,0 > viscosity_points = (eval(1(mm**2/sec)*{1100.0,27.0,10.5})) & ! < real:gt=0:c=2,0 >

hydraulics modify fluid & fluid_name = N/A & ! < hyd_fluid > location = (current value) & ! < location > temperature = (current value) & ! < real:gt=0 > eos_for_liquid_method = (current value) & ! < list(Merritt) > ref_density = (current value) & ! < real:gt=0 > ref_temperature = (current value) & ! < real:gt=0 > ref_pressure = (current value) & ! < real:gt=0 > bulk_modulus = (current value) & ! < real:gt=0 >



thermal_expansion_coefficient = (current value) & ! < real:gt=0 > air_content_method = (current value) & ! < list(CCUA) > air_density_at_STP = (current value) & ! < real:gt=0 > saturation_pressure = (current value) & ! < real:gt=0 > solubility_coefficient = (current value) & ! < real:gt=0 > undissolvable_air_content = (current value) & ! < real:ge=0:lt=1 > polytropic_exponent = (current value) & ! < real:gt=0 > viscosity_method = (current value) & ! < list(ASTM_D_341_43) > temperature_points = (current value) & ! < real:gt=0:c=2,0 > viscosity_points = (current value) & ! < real:gt=0:c=2,0 >

hydraulics create force_source & force_source_name = N/A & ! < new_hyd_force_source > location = 0,0,0 & ! < location > initial_force = 0.0 & ! < real > force_function = "0.0" & ! < analysis_function:c=0 >

hydraulics modify force_source & force_source_name = N/A & ! < hyd_force_source > location = (current value) & ! < location > initial_force = (current value) & ! < real > force_function = (current function) & ! < analysis_function:c=0 >

hydraulics create generic_pump_motor2 & generic_pump_motor2_name = N/A & ! < new_hyd_generic_pump_motor2 > location = 0,0,0 & ! < location > initial_torque = 0.0 & ! < real > initial_flowrate = 0.0 & ! < real > initial_angular_velocity = 0.0 & ! < real > torque_function = "0.0" & ! < analysis_function:c=0 > flowrate_function = "0.0" & ! < analysis_function:c=0 > angular_velocity_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify generic_pump_motor2 & generic_pump_motor2_name = N/A & ! < hyd_generic_pump_motor2 > location = (current value) & ! < location > initial_torque = (current value) & ! < real > initial_flowrate = (current value) & ! < real > initial_angular_velocity = (current value) & ! < real > torque_function = (current function) & ! < analysis_function:c=0 > flowrate_function = (current function) & ! < analysis_function:c=0 > angular_velocity_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >



hydraulics create junction2 & junction2_name = N/A & ! < new_hyd_junction2 > location = 0,0,0 & ! < location > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > apply_default_volume = apply & ! < list(apply,specify) > volume = (eval(1e-6(meter**3))) & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify junction2 & junction2_name = N/A & ! < hyd_junction2 > location = (current value) & ! < location > initial_pressure = (current value) & ! < real:gt=0 > apply_default_volume = (current value) & ! < list(apply,specify) > volume = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >


hydraulics modify junction3 & junction3_name = N/A & ! < hyd_junction3 > location = (current value) & ! < location > initial_pressure = (current value) & ! < real:gt=0 > apply_default_volume = (current value) & ! < list(apply,specify) > volume = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >


hydraulics modify junction4 & junction4_name = N/A & ! < hyd_junction4 > location = (current value) & ! < location > initial_pressure = (current value) & ! < real:gt=0 > apply_default_volume = (current value) & ! < list(apply,specify) > volume = (current value) & ! < real:gt=0 >



fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create laminar_orifice & laminar_orifice_name = N/A & ! < new_hyd_laminar_orifice > location = 0,0,0 & ! < location > length = (eval(100mm)) & ! < real:gt=0 > hydraulic_diameter = (eval(5mm)) & ! < real:gt=0 > loss_coefficient = 0.0 & ! < real:ge=0 > n_of_orifices_in_parallel = 1 & ! < integer:ge=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify laminar_orifice & laminar_orifice_name = N/A & ! < hyd_laminar_orifice > location = (current value) & ! < location > length = (current value) & ! < real:gt=0 > hydraulic_diameter = (current value) & ! < real:gt=0 > loss_coefficient = (current value) & ! < real:ge=0 > n_of_orifices_in_parallel = (current value) & ! < integer:ge=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create mass1 & mass1_name = N/A & ! < new_hyd_mass1 > location = 0,0,0 & ! < location > mass = (eval(1kg)) & ! < real:gt=0 > initial_position = 0.0 & ! < real > initial_velocity = 0.0 & ! < real > apply_bounds = no & ! < list(yes,no) > lower_bound_position = 0.0 & ! < real > upper_bound_position = 0.0 & ! < real > force_at_penetration_dx = 0.0 & ! < real:ge=0 > penetration_dx = (eval(1mm)) & ! < real:gt=0 > force_exponent = 1.0 & ! < real:gt=0 > max_damping_coefficient = 0.0 & ! < real:ge=0 > penetration_for_max_damping = (eval(0.1mm)) & ! < real:gt=0 >

hydraulics modify mass1 & mass1_name = N/A & ! < hyd_mass1 > location = (current value) & ! < location > mass = (current value) & ! < real:gt=0 > initial_position = (current value) & ! < real > initial_velocity = (current value) & ! < real > apply_bounds = (current value) & ! < list(yes,no) > lower_bound_position = (current value) & ! < real > upper_bound_position = (current value) & ! < real > force_at_penetration_dx = (current value) & ! < real:ge=0 >



penetration_dx = (current value) & ! < real:gt=0 > force_exponent = (current value) & ! < real:gt=0 > max_damping_coefficient = (current value) & ! < real:ge=0 > penetration_for_max_damping = (current value) & ! < real:gt=0 >

hydraulics create orifice & orifice_name = N/A & ! < new_hyd_orifice > location = 0,0,0 & ! < location > max_hydraulic_diameter = (eval(5mm)) & ! < real:gt=0 > discharge_coefficient = 0.6 & ! < real:gt=0:le=1 > Reynolds_transient = 50 & ! < real:gt=0 > loss_coefficient = 0.0 & ! < real:ge=0 > n_of_orifices_in_series = 1 & ! < integer:ge=1 > relative_opening_function = "1.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify orifice & orifice_name = N/A & ! < hyd_orifice > location = (current value) & ! < location > max_hydraulic_diameter = (current value) & ! < real:gt=0 > discharge_coefficient = (current value) & ! < real:gt=0:le=1 > Reynolds_transient = (current value) & ! < real:gt=0 > loss_coefficient = (current value) & ! < real:ge=0 > n_of_orifices_in_series = (current value) & ! < integer:ge=1 > relative_opening_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pipe_1 & pipe_1_name = N/A & ! < new_hyd_pipe_1 > location = 0,0,0 & ! < location > length = (eval(1meter)) & ! < real:gt=0 > diameter = (eval(10mm)) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > loss_length = 0.0 & ! < real:ge=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(3mm)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pipe_1 & pipe_1_name = N/A & ! < hyd_pipe_1 > location = (current value) & ! < location > length = (current value) & ! < real:gt=0 > diameter = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 >



loss_length = (current value) & ! < real:ge=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pipe_2ff & pipe_2ff_name = N/A & ! < new_hyd_pipe_2ff > location = 0,0,0 & ! < location > length = (eval(1meter)) & ! < real:gt=0 > diameter = (eval(10mm)) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > initial_flowrate = (eval(0.0(meter**3/second))) & ! < real > number_of_divisions = 10 & ! < integer:ge=10 > loss_length = 0.0 & ! < real:ge=0 > A_exit_loss = 0.0 & ! < real:ge=0:le=1 > A_entrance_loss = 0.0 & ! < real:ge=0 > B_exit_loss = 0.0 & ! < real:ge=0:le=1 > B_entrance_loss = 0.0 & ! < real:ge=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(3mm)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pipe_2ff & pipe_2ff_name = N/A & ! < hyd_pipe_2ff > location = (current value) & ! < location > length = (current value) & ! < real:gt=0 > diameter = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 > initial_flowrate = (current value) & ! < real > number_of_divisions = (current value) & ! < integer:ge=10 > loss_length = (current value) & ! < real:ge=0 > A_exit_loss = (current value) & ! < real:ge=0:le=1 > A_entrance_loss = (current value) & ! < real:ge=0 > B_exit_loss = (current value) & ! < real:ge=0:le=1 > B_entrance_loss = (current value) & ! < real:ge=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >



hydraulics create pipe_2pf & pipe_2pf_name = N/A & ! < new_hyd_pipe_2pf > location = 0,0,0 & ! < location > length = (eval(1meter)) & ! < real:gt=0 > diameter = (eval(10mm)) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > initial_flowrate = (eval(0.0(meter**3/second))) & ! < real > number_of_divisions = 10 & ! < integer:ge=10 > loss_length = 0.0 & ! < real:ge=0 > A_exit_loss = 0.0 & ! < real:ge=0:le=1 > A_entrance_loss = 0.0 & ! < real:ge=0 > B_exit_loss = 0.0 & ! < real:ge=0:le=1 > B_entrance_loss = 0.0 & ! < real:ge=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(3mm)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pipe_2pf & pipe_2pf_name = N/A & ! < hyd_pipe_2pf > location = (current value) & ! < location > length = (current value) & ! < real:gt=0 > diameter = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 > initial_flowrate = (current value) & ! < real > number_of_divisions = (current value) & ! < integer:ge=10 > loss_length = (current value) & ! < real:ge=0 > A_exit_loss = (current value) & ! < real:ge=0:le=1 > A_entrance_loss = (current value) & ! < real:ge=0 > B_exit_loss = (current value) & ! < real:ge=0:le=1 > B_entrance_loss = (current value) & ! < real:ge=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pipe_2pp & pipe_2pp_name = N/A & ! < new_hyd_pipe_2pp > location = 0,0,0 & ! < location > length = (eval(1meter)) & ! < real:gt=0 > diameter = (eval(10mm)) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > initial_flowrate = (eval(0.0(meter**3/second))) & ! < real > number_of_divisions = 10 & ! < integer:ge=10 >



loss_length = 0.0 & ! < real:ge=0 > A_exit_loss = 0.0 & ! < real:ge=0:le=1 > A_entrance_loss = 0.0 & ! < real:ge=0 > B_exit_loss = 0.0 & ! < real:ge=0:le=1 > B_entrance_loss = 0.0 & ! < real:ge=0 > apply_wall_flexibility = no & ! < list(yes,no) > wall_thickness = (eval(3mm)) & ! < real:gt=0 > youngs_modulus = (eval(210e9(Newton/meter**2))) & ! < real:gt=0 > Poissons_ratio = 0.3 & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pipe_2pp & pipe_2pp_name = N/A & ! < hyd_pipe_2pp > location = (current value) & ! < location > length = (current value) & ! < real:gt=0 > diameter = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 > initial_flowrate = (current value) & ! < real > number_of_divisions = (current value) & ! < integer:ge=10 > loss_length = (current value) & ! < real:ge=0 > A_exit_loss = (current value) & ! < real:ge=0:le=1 > A_entrance_loss = (current value) & ! < real:ge=0 > B_exit_loss = (current value) & ! < real:ge=0:le=1 > B_entrance_loss = (current value) & ! < real:ge=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > wall_thickness = (current value) & ! < real:gt=0 > youngs_modulus = (current value) & ! < real:gt=0 > Poissons_ratio = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pump_motor3 & pump_motor3_name = N/A & ! < new_hyd_pump_motor3 > location = 0,0,0 & ! < location > max_volumetric_displacement = (eval(0.05e-3(meter**3/rad))) & ! < real:gt=0 > initial_control_input = 0.0 & ! < real:ge=0:le=1 > initial_angular_velocity = 0.0 & ! < real > apply_mechanical_losses = no & ! < list(yes,no) > shear_damping_coefficient = 0.0 & ! < real:ge=0 > internal_friction_coefficient = 0.0 & ! < real:ge=0 > Coulomb_friction_torque = 0.0 & ! < real:ge=0 > limit_angular_velocity_for_friction = (eval(1(rad/second))) &! < real:gt=0 > apply_leakage = no & ! < list(yes,no) > internal_leakage_coefficient = 0.0 & ! < real:ge=0 > external_leakage_coefficient = 0.0 & ! < real:ge=0 > control_input_function = "0.0" & ! < analysis_function:c=0 >



angular_velocity_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pump_motor3 & pump_motor3_name = N/A & ! < hyd_pump_motor3 > location = (current value) & ! < location > max_volumetric_displacement = (current value) & ! < real:gt=0 > initial_control_input = (current value) & ! < real:ge=0:le=1 > initial_angular_velocity = (current value) & ! < real > apply_mechanical_losses = (current value) & ! < list(yes,no) > shear_damping_coefficient = (current value) & ! < real:ge=0 > internal_friction_coefficient = (current value) & ! < real:ge=0 > Coulomb_friction_torque = (current value) & ! < real:ge=0 > limit_angular_velocity_for_friction = (current value) & ! < real:gt=0 > apply_leakage = (current value) & ! < list(yes,no) > internal_leakage_coefficient = (current value) & ! < real:ge=0 > external_leakage_coefficient = (current value) & ! < real:ge=0 > control_input_function = (current function) & ! < analysis_function:c=0 > angular_velocity_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pressure_reducing_valve3 & pressure_reducing_valve3_name = N/A & ! < new_hyd_pressure_reducing_valve3 > location = 0,0,0 & ! < location > initial_position = 1.0 & ! < real:ge=0:le=1 > A_ref_pressure = (eval(201e5(Newton/meter**2))) & ! < real:gt=0 > B1_pressure = (eval(101e5(Newton/meter**2))) & ! < real:gt=0 > B1_flowrate = (eval(5e-4(meter**3/second))) & ! < real:gt=0 > B2_pressure = (eval(111e5(Newton/meter**2))) & ! < real:gt=0 > B2_flowrate = (eval(2.5e-4(meter**3/second))) & ! < real:gt=0 > B3_pressure = (eval(121e5(Newton/meter**2))) & ! < real:gt=0 > B3_flowrate = 0.0 & ! < real:ge=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > BT_nom_pressure_drop = (eval(35e5(Newton/meter**2))) &! < real:gt=0 > BT_nom_flowrate = 0.0 & ! < real:ge=0 > T_ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > time_constant = (eval(3e-3(second))) & ! < real:gt=0 > pressure_step = (eval(10e5(Newton/meter**2))) & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pressure_reducing_valve3 & pressure_reducing_valve3_name = N/A & ! < hyd_pressure_reducing_valve3 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > A_ref_pressure = (current value) & ! < real:gt=0 >



B1_pressure = (current value) & ! < real:gt=0 > B1_flowrate = (current value) & ! < real:gt=0 > B2_pressure = (current value) & ! < real:gt=0 > B2_flowrate = (current value) & ! < real:gt=0 > B3_pressure = (current value) & ! < real:gt=0 > B3_flowrate = (current value) & ! < real:ge=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > BT_nom_pressure_drop = (current value) & ! < real:gt=0 > BT_nom_flowrate = (current value) & ! < real:ge=0 > T_ref_pressure = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pressure_relief_valve2 & pressure_relief_valve2_name = N/A & ! < new_hyd_pressure_relief_valve2 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (eval(2e5(Newton/meter**2))) & ! < real:gt=0 > AB1_pressure_drop = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > AB1_flowrate = (eval(1.414e-3(meter**3/second))) & ! < real:gt=0 > AB2_pressure_drop = (eval(20e5(Newton/meter**2))) & ! < real:gt=0 > AB2_flowrate = (eval(3.14e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pressure_relief_valve2 & pressure_relief_valve2_name = N/A & ! < hyd_pressure_relief_valve2 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (current value) & ! < real:gt=0 > AB1_pressure_drop = (current value) & ! < real:gt=0 > AB1_flowrate = (current value) & ! < real:gt=0 > AB2_pressure_drop = (current value) & ! < real:gt=0 > AB2_flowrate = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > ref_fluid_density = (current value) & ! < real:gt=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 >



apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create pressure_source & pressure_source_name = N/A & ! < new_hyd_pressure_source > location = 0,0,0 & ! < location > initial_pressure = (eval(1.0e5(Newton/meter**2))) & ! < real:gt=0 > pressure_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify pressure_source & pressure_source_name = N/A & ! < hyd_pressure_source > location = (current value) & ! < location > initial_pressure = (current value) & ! < real:gt=0 > pressure_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create reservoir2 & reservoir2_name = N/A & ! < new_hyd_reservoir2 > location = 0,0,0 & ! < location > initial_volume = (eval(1.0e-3(meter**3))) & ! < real:gt=0 > initial_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > apply_wall_flexibility = no & ! < list(yes,no) > flexibility_coefficients = 0.0 & ! < real:c=0 > volume_in_STP_function = ".c.initial_volume" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify reservoir2 & reservoir2_name = N/A & ! < hyd_reservoir2 > location = (current value) & ! < location > initial_volume = (current value) & ! < real:gt=0 > initial_pressure = (current value) & ! < real:gt=0 > apply_wall_flexibility = (current value) & ! < list(yes,no) > flexibility_coefficients = (current value) & ! < real:c=0 > volume_in_STP_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create restrictor_valve2 & restrictor_valve2_name = N/A & ! < new_hyd_restrictor_valve2 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (eval(2e5(Newton/meter**2))) & ! < real:gt=0 > AB1_pressure_drop = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > AB1_flowrate = (eval(2.2e-3(meter**3/second))) & ! < real:gt=0 > AB2_pressure_drop = (eval(20e5(Newton/meter**2))) & ! < real:gt=0 >



AB2_flowrate = (eval(3.927e-3(meter**3/second))) & ! < real:gt=0 > AB_relative_leakage = 0.0 & ! < real:ge=0:le=0.5 > BA_nom_pressure_drop = (eval(20e5(Newton/meter**2))) & ! < real:gt=0 > BA_nom_flowrate = (eval(7.85e-4(meter**3/second))) & ! < real:ge=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > pressure_step = (eval(11e5(Newton/meter**2))) & ! < real:gt=0 > apply_hysteresis = no & ! < list(yes,no) > hysteresis_ratio = 1.0 & ! < real:gt=0:le=1 > relative_opening_function = "1.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify restrictor_valve2 & restrictor_valve2_name = N/A & ! < hyd_restrictor_valve2 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > AB_closing_pressure_drop = (current value) & ! < real:gt=0 > AB1_pressure_drop = (current value) & ! < real:gt=0 > AB1_flowrate = (current value) & ! < real:gt=0 > AB2_pressure_drop = (current value) & ! < real:gt=0 > AB2_flowrate = (current value) & ! < real:gt=0 > AB_relative_leakage = (current value) & ! < real:ge=0:le=0.5 > BA_nom_pressure_drop = (current value) & ! < real:gt=0 > BA_nom_flowrate = (current value) & ! < real:ge=0 > ref_fluid_density = (current value) & ! < real:gt=0 > time_constant = (current value) & ! < real:gt=0 > pressure_step = (current value) & ! < real:gt=0 > apply_hysteresis = (current value) & ! < list(yes,no) > hysteresis_ratio = (current value) & ! < real:gt=0:le=1 > relative_opening_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create shuttle_valve3 & shuttle_valve3_name = N/A & ! < new_hyd_shuttle_valve3 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=0:le=1 > A1_pressure = (eval(36e5(Newton/meter**2))) & ! < real:gt=0 > AC_nom_flowrate = (eval(1e-2(meter**3/second))) & ! < real:ge=0 > B_cracking_pressure = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > C_ref_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > time_constant = (eval(3ms)) & ! < real:gt=0 > B_pressure_step = (eval(10e5(Newton/meter**2))) & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >



hydraulics modify shuttle_valve3 & shuttle_valve3_name = N/A & ! < hyd_shuttle_valve3 > location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=0:le=1 > A1_pressure = (current value) & ! < real:gt=0 > AC_nom_flowrate = (current value) & ! < real:ge=0 > B_cracking_pressure = (current value) & ! < real:gt=0 > C_ref_pressure = (current value) & ! < real:gt=0 > ref_fluid_density = (current value) & ! < real:gt=0 > time_constant = (current value) & ! < real:gt=0 > B_pressure_step = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create spline_orifice & spline_orifice_name = N/A & ! < new_hyd_spline_orifice > location = 0,0,0 & ! < location > flowrate_spline = N/A & ! < spline > apply_spline_as = symmetric & ! < list(symmetric,full,oneway) > relative_opening_function = "1.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify spline_orifice & spline_orifice_name = N/A & ! < hyd_spline_orifice > location = (current value) & ! < location > flowrate_spline = (current value) & ! < spline > apply_spline_as = (current value) & ! < list(symmetric,full,oneway) > relative_opening_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create sum_of_flows & sum_of_flows_name = N/A & ! < new_hyd_sum_of_flows > location = 0,0,0 & ! < location > fluid_name = N/A ! < hyd_fluid >

hydraulics modify sum_of_flows & sum_of_flows_name = N/A & ! < hyd_sum_of_flows > location = (current value) & ! < location > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create sum_of_flows2 & sum_of_flows2_name = N/A & ! < new_hyd_sum_of_flows2 > location = 0,0,0 & ! < location > fluid_name = N/A ! < hyd_fluid >

hydraulics modify sum_of_flows2 & sum_of_flows2_name = N/A & ! < hyd_sum_of_flows2 >



location = (current value) & ! < location > fluid_name = (current fluid) ! < hyd_fluid >


hydraulics modify sum_of_flows3 & sum_of_flows3_name = N/A & ! < hyd_sum_of_flows3 > location = (current value) & ! < location > fluid_name = (current fluid) ! < hyd_fluid >


hydraulics modify sum_of_flows4 & sum_of_flows4_name = N/A & ! < hyd_sum_of_flows4 > location = (current value) & ! < location > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create servovalve4w3 & servovalve4w3_name = N/A & ! < new_hyd_servovalve4w3 > location = 0,0,0 & ! < location > initial_position = 0.0 & ! < real:ge=-1:le=1 > eigenfrequency = (eval(80(1/second))) & ! < real:gt=0 > relative_damping = 0.1 & ! < real:ge=0 > PA_x_to_A_spline = N/A & ! < spline > PB_x_to_A_spline = N/A & ! < spline > AT_x_to_A_spline = N/A & ! < spline > BT_x_to_A_spline = N/A & ! < spline > nom_pressure_drop = (eval(35e5(Newton/meter**2))) & ! < real:gt=0 > PA_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > PB_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > AT_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > BT_nom_flowrate = (eval(1e-3(meter**3/second))) & ! < real:ge=0 > PT_nom_flowrate = 0.0 & ! < real:ge=0 > ref_fluid_density = (eval(900(kilogram/meter**3))) & ! < real:gt=0 > control_input_function = "0.0" & ! < analysis_function:c=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify servovalve4w3 & servovalve4w3_name = N/A & ! < hyd_servovalve4w3 >



location = (current value) & ! < location > initial_position = (current value) & ! < real:ge=-1:le=1 > eigenfrequency = (current value) & ! < real:gt=0 > relative_damping = (current value) & ! < real:ge=0 > PA_x_to_A_spline = (current value) & ! < spline > PB_x_to_A_spline = (current value) & ! < spline > AT_x_to_A_spline = (current value) & ! < spline > BT_x_to_A_spline = (current value) & ! < spline > nom_pressure_drop = (current value) & ! < real:gt=0 > PA_nom_flowrate = (current value) & ! < real:ge=0 > PB_nom_flowrate = (current value) & ! < real:ge=0 > AT_nom_flowrate = (current value) & ! < real:ge=0 > BT_nom_flowrate = (current value) & ! < real:ge=0 > PT_nom_flowrate = (current value) & ! < real:ge=0 > ref_fluid_density = (current value) & ! < real:gt=0 > control_input_function = (current function) & ! < analysis_function:c=0 > fluid_name = (current fluid) ! < hyd_fluid >

hydraulics create tank & tank_name = N/A & ! < new_hyd_tank > location = 0,0,0 & ! < location > tank_pressure = (eval(101325(Newton/meter**2))) & ! < real:gt=0 > fluid_name = N/A ! < hyd_fluid >

hydraulics modify tank & tank_name = N/A & ! < hyd_tank > location = (current value) & ! < location > tank_pressure = (current value) & ! < real:gt=0 > fluid_name = (current fluid) ! < hyd_fluid >

D Run-Time Function Reference

OverviewThis appendix lists the states available for referencing from within ADAMS/Hydraulics components. For more information on building run-time functions, see the guide, Using the ADAMS/View Function Builder.


Run-Time Function Reference342

IntroductionRun-time functions allow you to specify mathematical relationships between the simulation states that directly define the behavior of the system.You can work with run-time functions from boxes that expect run-time functions. You build a run-time function in the Function Builder and then insert the function in the box that accepts run-time functions. ADAMS/Hydraulics components allow you to reference their states by their name directly in your run-time function expressions.

If you want to make your run-time function dependent on an ADAMS/Hydraulics state, you can either type the name reference of the state directly into your function expression, or, if you are working in the Function Builder, do the following:

1 Set the Getting Object Data pull-down menu to Measures.

2 Right-click in the corresponding text box.

3 Select Browse or Guesses to display the valid states available for your component.

❖ Browse - Displays the Database Navigator with each state grouped by component.

❖ Guesses - Displays a subset of available state references.

For example, let’s say you want to find the pressure drop over a check valve. You could simply write your function expression as follows:

.my_model_name.my_check_valve_name.B_pressure -

.my_model_name.my_check_valve_name.A_pressure



ADAMS/Hydraulics State References

Table 40. State References

Component: State name:

accumulator gas_volumeP_pressureP_flowrategas_pressure

counter_balance_valve4p relative_positionA_pressureA_flowrateB_pressureB_flowrateX_pressureT_pressurecartridge_valve3prelative_positionA_pressureA_flowrateB_pressureB_flowrateX_pressurespring_forceflow_force

check_valve2 relative_positionA_pressureA_flowrateB_pressureB_flowrate

check_valve3p relative_positionA_pressureA_flowrateB_pressureB_flowrateX_pressure



check_valve4p relative_positionA_pressureA_flowrateB_pressureB_flowrateX_pressureT_pressure

cylinder1 A_relative_opening_functionstiction_lengthA_chamber_fluid_volume_in_STPcylinder_lengthcylinder_velocityA_pressureA_flowratecylinder_forcepressure_forcefriction_forcecushion_forceA_chamber_pressure

cylinder1f stiction_lengthA_chamber_fluid_volume_in_STPcylinder_lengthcylinder_velocityA_flowrateA_pressurecylinder_forcepressure_forcefriction_forcecushion_force

Table 40. State References (continued)




cylinder2 A_relative_opening_functionB_relative_opening_functionstiction_lengthA_chamber_fluid_volume_in_STPB_chamber_fluid_volume_in_STPcylinder_lengthcylinder_velocityA_pressureA_flowrateB_pressureB_flowratecylinder_forcepressure_forcefriction_forcecushion_forceB_chamber_pressureA_chamber_pressure

cylinder2ff stiction_lengthA_chamber_fluid_volume_in_STPB_chamber_fluid_volume_in_STPcylinder_lengthcylinder_velocityA_flowrateA_pressureB_flowrateB_pressurecylinder_forcepressure_forcefriction_forcecushion_force





directional_control_valve2w2 control_input_functionrelative_positionP_pressureP_flowrateA_pressureA_flowrate

directional_control_valve3w2 control_input_functionrelative_positionP_pressureP_flowrateA_pressureA_flowrateT_pressureT_flowrate

directional_control_valve4w3 control_input_functionrelative_positionP_pressureP_flowrateA_pressureA_flowrateB_pressureB_flowrateT_pressureT_flowrate

flow_control_valve2 relative_positionA_pressureA_flowrateB_pressureB_flowrate

flow_source flowrate_functionA_pressureA_flowrate





fluid

force_source force_functionF_force

generic_pump_motor2 torque_functionflowrate_functionangular_velocity_functionA_pressureA_flowrateB_pressureB_flowrateoutput_torque

junction2 density_ratioA_flowrateA_pressureB_flowrateB_pressure

junction3 density_ratioA_flowrateA_pressureB_flowrateB_pressureC_flowrateC_pressure





junction4 density_ratioA_flowrateA_pressureB_flowrateB_pressureC_flowrateC_pressureD_flowrateD_pressure

laminar_orifice A_pressureA_flowrateB_pressureB_flowrate

mass1 positionvelocityF_forceacceleration

orifice relative_opening_functionA_pressureA_flowrateB_pressureB_flowrate

pipe_1 density_ratioA_pressureA_flowrateB_pressureB_flowrate

pipe_2ff A_flowrateA_pressureB_flowrateB_pressure





pipe_2pf A_pressureA_flowrateB_flowrateB_pressure

pipe_2pp A_pressureA_flowrateB_pressureB_flowrate

pump_motor3 control_input_functionangular_velocity_functionA_pressureA_flowrateB_pressureB_flowrateT_pressureT_flowrateoutput_torqueoutput_torque_idealshear_torquefriction_torque

pressure_reducing_valve3 relative_positionA_pressureA_flowrateB_pressureB_flowrateT_pressureT_flowrate

pressure_relief_valve2 relative_positionA_pressureA_flowrateB_pressureB_flowrate





pressure_source pressure_functionA_flowrateA_pressure

reservoir2 volume_in_STP_functionfluid_volume_in_STPA_flowrateA_pressureB_flowrateB_pressuredensity_ratio

restrictor_valve2 relative_opening_functionrelative_positionA_pressureA_flowrateB_pressureB_flowrate

shuttle_valve3 relative_positionA_pressureA_flowrateB_pressureB_flowrateC_pressureC_flowrate

spline_orifice relative_opening_functionA_pressureA_flowrateB_pressureB_flowrate





sum_of_flows A_flowrateA_pressureB_flowrateB_pressureC_pressureC_flowratedensity_ratio

sum_of_flows2 A_flowrateA_pressureB_flowrateB_pressureP_pressureP_flowratedensity_ratio

sum_of_flows3 A_flowrateA_pressureB_flowrateB_pressureC_flowrateC_pressureP_pressureP_flowratedensity_ratio





sum_of_flows4 A_flowrateA_pressureB_flowrateB_pressureC_flowrateC_pressureD_flowrateD_pressureP_pressureP_flowratedensity_ratio

servovalve4w3 control_input_functionrelative_positionrelative_velocityP_pressureP_flowrateA_pressureA_flowrateB_pressureB_flowrateT_pressureT_flowrate

tank T_flowrateT_pressuredensity_ratio



Bibliography

[1] Merritt, Herbert E.: Hydraulic Control Systems. New York 1967, John Wiley & Sons, Inc., p. 358.

[2] Wuori, Paul A.: Virtausmekaniikan Perusteet. Espoo 1990, Otatieto Oy, p. 159.

[3] Timoshenko, S., Strength of Materials, 2nd ed., Part II. New York, Van Nostrand.

[4] Ellman A.U., Koivula T.S., Vilenius M.J., Hydraulic cylinder seal friction - comparison of two seal designs, 15th International Conference on Fluid Sealing, Maastricht, The Netherlands on 16-18 September 1997.

[5] Sychev V.V., Vasserman A.A., Kozlov A.D., Spiridonov G.A., Tsymarny V.A.: Thermodynamic Properties of Nitrogen, 1987, Hemisphere Publishing Corporation


Bibliography354


Index355

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

Index

AAccumulator, using 17

ADAMS/Hydraulicsassumptions in 8command language for executing 309function expressions 341setting defaults 11topology 7

ARATIO (area ratio of a poppet) function, using 296

Assumptions in ADAMS/Hydraulics 8

BBernoulli’s equation, defined 285

CCheck valve with pilot (to close), using 35

Check valve with pilot (to open), using 41

Check valve, using 31

CLWL (constant leakage with lap) function, using 298

Coefficient, discharge for polynomial fit 288

Command language for executing ADAMS/Hydraulics 309

Component modeling, described 9Components

accumulator 17check valve 31check valve with pilot (to close) 35check valve with pilot (to open) 41counter balance valve with pilot 47cylinder1 53cylinder1f 81cylinder2 65


Index356

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

cylinder2ff 93directional control valve 2/2 107directional control valve 3/2 115directional control valve 4/3 123flow source 133fluid 135force source 155gas-charged accumulator 23generic pump/motor 157junction2 161junction3 163junction4 167laminar office 171one-DOF translational mass 175one-way restrictor valve 179orifice 185pipe (level 1) 191pipe (level 2) 197pressure source 215pressure-reducing valve 205pressure-relief valve 211pump/motor 217reservoir 223servovalve 4/3 227shuttle valve 241spline orifice 247spool valve 4/3 251sum of flows 263sum of flows 2 265sum of flows 3 267sum of flows 4 269tank 271theory of modeling 9two-way cartridge valve 273two-way flow control valve 279types of 4

Counter balance valve with pilot, using 47


Index357

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

CVS (constant velocity spool) function, using 300

Cylinder1, using 53

Cylinder1f, using 81

Cylinder2, using 65

Cylinder2ff, using 93

DDefaults, setting 11

Directional control valve 2/2, using 107



Discharge coefficient, polynomial fit for 288

EEnvironment pressure, setting defaults for 11

Equation, Bernoulli’s defined 285

Essential component, explained 4

FFlow and volume components, listed 6Flow source, using 133

Flow, defined for low Reynolds numbers 286

Fluidoverview of 4using 135

Force source, using 155

Function expressions for ADAMS/Hydraulics 341

FunctionsARATIO (area ratio of a poppet) 296CLWL (constant leakage with lap) 298CVS (constant velocity spool) 300LINPWL (linear poppet opening area with leakage) 302ORIFIC (flow through an orifice) 304


Index358

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

GGas-charged accumulator, using 23

Generic pump/motor, using 157

HHydraulic components, See Components

Hysteresis limit, setting defaults for 12

JJunction volume, setting defaults for 11

Junction2, using 161



LLaminar orifice, using 171

LINPWL (linear poppet opening area with leakage) function, using 302

MMass1, using 175

Miscellaneous components, listing of 7Mixed-volume flow components, listed 7

OOne-DOF translational mass, using 175

One-way port, described 7One-way restrictor valve, using 179

ORIFIC (flow through an orifice) function, using 304

Orifice, using 185


Index359

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

PPipe (level 1), using 191

Pipe (level 2), using 197

Polynomial fit for discharge coefficient, described 288

Ports, types of 7Pressure source, using 215

Pressure-reducing valve, using 205

Pressure-relief valve, using 211

Pump/motor, using 217

RReservoir, using 223

Resistances in ADAMS/Hydraulics 8Restrictor valve2, using 179

Reynolds numbers, using 286

SServovalve 4/3, using 227

Shuttle valve, using 241

Spline orifice, using 247

Spool valve 4/3, using 251

Starting ADAMS/Hydraulics 10

Sum of flows 2, using 265



Sum of flows, using 263

System defaults, setting 11


Index360

A - B

U - V

W - Z

C - D

E - F

G - H

I - J

K - L

S - T

Q - R

O - P

M - N

TTank, using 271

Topology of ADAMS/Hydraulics 7Two-way cartridge valve, using 273

Two-way flow control valve, using 279

Two-way port, described 7Types of hydraulic components 4

VVolume components, listed 5Volumes in ADAMS/Hydraulics 8

XX penetration tolerance, setting defaults for 11

ADAMS_Hydraulics Component Reference

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