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MODELLING AND SIMULATION OF HEAT GENERATION IN

ELECTRO-HYDROSTATIC ACTUATION SYSTEMS

ohan ANDERSSON*, Petter KRUS*, Katarina NILSSON**, Karl STORCK*

*Department of Mechanical Engineering

Linkoping University

SE-581 8 3 Linkoping, Sweden

**General Systems Research & Development

Saab AB

SE-581 88 Linkoping, Sweden

Abstract

Thermodynamic aspects of hydraulic systems become increasingly important in compact systems where there is noroom for heat exchangers. It is therefore desirable to facilitate temperature predictions at an early stage of the design

process. In this paper two competing concepts of electro-hydrostatic actuation for aircraft applications are studied inorder to examine the necessity of a heat exchanger. To be able to capture the fluid temperature in the system,thermodynamic analyses of hydraulic components have been conducted. For the modelling of hydraulic machines acomprehensive loss-model has been implemented with the intention of accurately model the machine efficiency over awide speed and pressure range. With the help of these models the two systems have been simulated in the HOPSANsimulation package. The systems inputs have been actual pilot commands and aerodynamic loads collected from realmissions. The simulation results show that depending of the ambient temperature and the mission characteristics the

fluid temperature would vary to a great extend, stating the demands of the fluid.

Key Words

Temperature calculation, EHA, modelling, simulation.

Nomenclature

A area [m2]

ao-a4 flow coefficients [misc.]

b0-b6,δ,γ,n0 torque coeffficients [misc.]

B, C, D, E0-E2 density coefficients [misc.]

cpo'kc speciffic heat coefficients [misc.]

cp speciflc heat (constant p) [J/kg K]

cv specific heat (constant v) [J/kg K]

D displacement [m3]

E internal energy [J]

h specific enthalpy [J/kg]

hc Heat transfer coefficient [W/m2Kl

m mass [kg]

m mass flow [kg/s]

n rotational speed [1/s]

p pressure [Pa]

pH high pressure [Pa]

pL low pressure [Pa]

Q rate of heat [W]

Qp, Qm Pump and motor flow [m3/s]

t time [S]

T temperature [℃]

T∞ ambient temperature [℃]

Tcv control volume temperature [℃]

Tp,,Tm pump and motor torque [Nm]

u specific internal energy [J/kg]

Wrate of work [W]

αp expansivity [K-1]

βe compression module [Pa]

ε rate of displacement [-]

ρ density of nuid [kg/m3]

μ viscosity [Ns/m2]

μ40 viscosity at 40℃ [Ns/m2]

μx minimal viscosity [Ns/m2]

v specific volume [m3/kg]

Fluid Power. Forth JHPS International Symposium (C) 1999 JHPS. ISBN4-931070-04-3

537

Introduction

Future development of general aircraft systems isdirected towards highly integrated and power efficientsystems. The More Electric Aircraft (MEA) technologyinvolves for example replacement of the traditionalhydraulic system with local electrically poweredactuation systems, so called Power by Wire (PBW)systems.

Hydraulic actuation has many desirable andessential qualities, for instance: high output forcecapability, effective positioning, quick response, highstiffness and many more. However, conventionaldistributed hydraulic systems have also disadvantagessuch as valve and pump malfunction due tocontamination and wear, fluid leakage, high life-cyclecosts particularly due to high maintenance costs, etc.Furthermore, the tubing is highly exposed to ballisticthreats, such as enemy gunfire, and could easily bedepleted. By introducing PBW systems this exposure isreduced. Other advantages gained by introducing PBWsystems are improved reliability and maintainability,and thereby reduced life-cycle cost. This has been statedby several authors, see for instance Bildstein [1] andNavarro [7].

The dynamic performance of electro-hydrostaticactuators (EHA's) have been studied by several authors,see for example Navarro [7]. It has been shown thatEHA's have the stiffness, accuracy and bandwidthrequired for application on primary flight controlsurfaces.

The thermal aspects of local actuation systems areon the other hand not fully investigated and very muchdependent on the application and the duty cycle. The

question is whether the system has to be cooled down,or warmed up.

In this paper a detailed pump and motor model hasbeen implemented in order to capture the losses inangular machines working at different conditions. Themodel employed has been developed by Rydberg [9].

Thermal modelling of hydraulic components,adapted from Storck [ 10], has been conducted in orderto calculate system temperatures at different operatingconditions. Simultaneously, oil properties such asdensity, viscosity and the specific heat, are modelled asfunctions of temperature and pressure, as described byKjolle [5] and Rodermund [8].

Modelling of hydraulic machines

The efficiency of hydraulic machines can be calculatedusing different models and approaches. In this paper adetailed model, especially developed for axial pistonpumps, is employed, see Rydberg [9]. The flow andtorque equations according to the Rydberg model are

given in equations (1) and (2) for a pump case. In themotor case the losses would be working in the oppositedirection.

(1)

(2)

The first loss terms in equations (1) and (2), indexed 0,are only used in regression analysis in order todetermine the other loss coefficients, and are usuallysmall. The second loss term of the flow equationhandles compression losses in the machine due to thedisplacement and the dead volumes. The third termmodels ordinary laminar leakage, whereas the fourthterm emulates leakage due to load dependent changes inclearances.

In the torque equation (2), the first loss term is aconstant friction term depending on the pressuredifference, whereas the second term depends only onthe low pressure PL. The third term represents a varyingcolumbian friction appearing at low speeds. Thereafteris a viscous friction term, and finally a term that modelsacceleration and flow losses depending on the square ofthe rotational speed. Typical efficiencies obtained bythese equations are given in Figure I.

The hydraulic machine in an electro-hydrostaticactuator has to operates as both pump and motor atvarious operating conditions. The pressure differencecould vary between a couple of bars up to more than200 bars and the speed may vary within the range of +/-8000 rpm. This of course put great demands on themodel of the hydraulic machine, as much of the lossesarise from the machine.

Figure 1: Pump efficiencies at 200 bar calculated fromequation (1) and (2).

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Thermal modelling of hydraulic

components

In order to make a thorough examination of the systemsto be studied, thermodynamic aspects have to be takeninto consideration. The mathematical background forthermal modelling of hydraulic components and systemscould be found in for instance Storck [10], Svensson etal. [11], Dorey and Harris [31, and MancO and Nervegna

[6]. The basic equation for calculation of temperaturesin hydraulic systems is the first law of thermodynamicsapplied on a control volume, as described in Figure 2and equation (3).

Figure 2: Control volume considered when deriving the

thermodynamic expressions.

As indicated in Figure 2 the control volume might have

multiple inlet and output nodes.

(3)

In order to evaluate equation (3), an expression for thespecific enthalpy has to be derived. According to VanWylen and Sonntag [12] the specific enthalpy for a puresubstance can be expressed as:

h=h(T, p) (4)

and therefore

(5)

The first derivative is recognised as the specific heat

capacity at constant pressure C,, see equation (6).

(6)

From Van Wylen and Sonntag [12) equation (7) isobtained as an expression for the second derivative.

(7)

The expansivity is defined by equation (8).

(8)

Combining equations (5)-(8) yields

(9)

Linearising equation (9) and replacing the fluid

properties with their mean values over the controlvolume (indicated by barred notation) yields

(10)

The energy E constitutes the sum of the internal,

potential and kinetic energy of the control volume. If thepotential and the kinetic energy are neglected togetherwith the time rate of change in mass within controlvolume, the energy change could be express accordingto equation (11).

(11)

The internal specific energy u can be expressed as afunction of temperature and specific volume, i. e.u=u(T,v). Generally the influence of changingtemperature has a much large impact on the internalenergy than the specific volume and thus du could beexpressed in accordance to equation (12).

(12)

Introducing the specific heat capacity at constantvolume defined by equation (13).

(13)

Combining equation (11)-(13) yields

(14)

In the upcoming chapters equations (3),(10) and (14)are applied to the different hydraulic components vitalto the studied systems.

Fluid power machines

As the amount of fluid enclosed in a machine is usuallysmall the internal energy is neglected, i.e. dEldt=0. Thefirst law of thermodynamics, equation (3) and equation

(10) then yields

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(15)

Where the heat transfer and work are given by equation

(16) and (17) respectively.

Q=hcA(T∞-TCv) (16)

W=Tp2πn (17)

The torque Tp in equation (17) is given by the torqueequation (2). It is ensured that the work is negative inthe pump case and positive in the motor case.

Valves

From a thermodynamic point of view different types ofvalves are looked upon as simple orifices. Naturallythere is no work involved in the throttling process of anorifice, i.e. w=0. As the orifice has a very limitedspatial extension there are no heat losses to the

environment, i.e. Q=0. The internal energy storage

could also be neglected, i. e. dE/dt=0. The mass flows in

and out of the orifice are equal, min=mout. The first

law of thermodynamics, equation (3) and equation (10)then yields the expression for temperature calculation ofan orifice (18).

(18)

Volumes

As for orifices no work has to be considered in thevolume. On the other hand the heat exchange and theinternal energy has to be taken into account. In additionthere is no pressure difference over a volume so thesecond term of equation (10) equals zero. For thevolume equation (3), (10) and (14) yields

(19)

It is assumed to be a perfect mixing in the volume, i.e.

the temperature in the volume equalises instantly as

fluid enters the volume. Fluid leaving the volume is

considered having the temperature of the volume, i. e.

T0ut = Tc,,. The temperature T at the time t+•¢t is

calculated using the explicit scheme shown in equation

(20).

(20)

where At is the time step employed in the simulation.

A pressurised volume with multiple inputs has been

employed as a tank.

Modelling of fluid properties

As previously described the fluid temperature iscalculated with the help of flow and pressure. Byexpressing fluid properties such as viscosity and densityas functions of the temperature, the flow and pressurewill in turn be somewhat affected by the temperature.

From Kjolle [5], an expression for fluid density,equation (21) are adopted.

(21)

The parameters in equation (21) are tabulated in [5] fora wide range of fluids. Furthermore, Kjolle gives anexpression for the heat capacity represented byequation (22).

(22)

The derivative a 2v/aT 2 can be obtained by invertingequation (21) and deriving it two times with respect tothe temperature. In a similar manner an expression forav/aT in equation (7) and (8) could be obtained, andthus an expression for the expansivity is derived.

An expression for the temperature dependency ofthe viscosity is given by Rodermund [8] as shown inequation (23)

(23)

where

(24)

(25)

μ40denotes the viscosity at 40℃ andμx is the minimal

viscosity of the fluid.

Experimental verifications of the models in this

paper are given in Svensson et a1.[11].

Actuation systems

In this paper two different concepts of electrical

actuation systems are studied. These are the Electro-

Hydrostatic Actuator(EHA)with a fixed hydraulic

pump(EHA-FP), and with a variable displacement

pump(EHA-VP). Each systems consist of an electric

motor driving the hydraulic pump, a hydraulic cylinder,

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anti-cavitation check valves, pressure relief valves, aby-pass damper and a pressurised reservoir, as depicted

simplified in Figure 3. In the case of the EHA-FPconcept the movement is controlled by a

DC-servo motor and in the EHA-VP concept by a

hydraulic servo pump. In the EHA-FP concept theelectric motor is controlled by a high power signal. On

the contrary a low power signal is sufficient to controlthe displacement of the pump in the EHA-VP system.

Figure 3: Electro-hydrostatic actuator concepts withfixed and variable displacement pumps.

Simulations of the two different competingconcepts have been carried out in the HOPSANsimulation package [4]. The model library has beenextended with a more comprehensive hydraulic machinemodel together with the capability to handle thermalaspects in hydraulic systems. The HOPSAN model ofthe EHA-FP concept is shown in Figure 4.

Figure 4: HOPSAN model of the Electro-hydrostaticactuator with fixed pump.

The inputs to the simulation model is given bysignal generators, the "G-boxes" in Figure 4. The

position command is given by the signal generator at thetop. In this case, the commands given by the pilottrough the flight control computer. The other signal

generator generates the force acting on the actuator. The

forces are calculated from measured aerodynamic loads

from a flight simulator during a simulated flight. As the

cylinder is sometimes working against the aerodynamic

loads and sometimes with them the hydraulic machine

has to work as both pump and motor. The movement

and the force are very oscillating forcing the machine to

constantly change from pump to motor operation.

System optimisation

Optimisation has been employed in order determine

component sizes and control parameters for optimal

system performance. Both systems have been optimised

using the same objective function formulation in order

to minimise weight, cost andenergy consumption and

simultaneously keeping the control error low. A duty

cycle containing dimensioning manoeuvres has been

employed for the optimisation to assure high stiffness

and accuracy. In the optimisation procedure a non-

gradient optimisation method is coupled to the

simulation as described in Andersson et al.[1].

Simulation results

The two systems have been studied during two different

duty cycles. The first duty cycle is an ordinary mission,

which is associated with low energy consumption.

Secondly, an extreme mission is studied where more

energy is required in order to control the aircraft.

Naturally the second case is characterised by larger

losses leading to higher system temperature. In order to

find dimensioning operating conditions the systems

have been studied at two different ambient

temperatures. The first case should emulate a hot

summer day when the initial system temperature and the

ambient temperature both equals 40•Ž. The second case

is a winters day where the initial systems temperature is

-20•Ž and the ambient temperature at operating altitude

equals -50•Ž. Simulation results for the various test

cases are shown for the EHA-FP system in Figure 5 and

EHA-VP system in Figure 6.

Figure 5: EHA-FP system temperature for different dutycycles at various ambient temperatures.

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Figure 6: EHA-VP system temperature for different duty

cycles at various ambient temperatures.

As the flying time of these missions are 50 minutes,

a stationary temperature is not reached for all cases.

From the graphs it can be seen that the system

temperature would vary from between -35•Ž to 100•Ž

depending on the duty-cycle. The EHA-VP system

shows a higher system temperature for all duty-cycles.

Discussion

Since the pump in the EHA-VP concept is constantly

running with a rather high speed this concept is

associated with a larger amount of losses, resulting in

higher system temperature. This has the greatest impact

on the normal flight case where the energy consumption

is proportionately low, as seen when comparing the

dash-dotted lines in Figure 5 and 6.

Besides the objectives to design the system to be

light weight with a low energy consumption the fluid

temperature has to be considered. By introducing a

smooth opening shut-off valve in parallel with the

cylinder a circulating flow could be achieved in order to

warm the fluid at extreme temperatures.

In this paper only the thermodynamic aspects of the

hydraulic system has been studied. Temperature

increase in the electric system due to losses and

regenerative power has been left for future studies.

Conclusion

Thermodynamic aspects of hydraulic systems becomes

important when the system has to be compact and light

weight, as in the case of an electro-hydrostatic actuator.

In this paper thermal modelling of hydraulic

components have been conducted in order to predict the

system temperature at an early stage of the design

process.

Two different EHA concepts have been modelled

and simulated under various operating conditions.

Calculations show that the fluid temperature will vary to

a great extend depending on duty-cycle and ambient

temperature. It has also been shown that the EHA-FP

concept has a better efficiency than the EHA-VPconcept, leading two a lower system temperature.However, for this application the problem will not be tokeep the fluid from overheating but rather to keep itwarm enough.

References

[1] Andersson J., Krus P., Nilsson K., Optimization asa Support for Selection and Design of AircraftActuation Systems, Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysisand Optimization, St. Louis, September 2-4, 1998.

[2] Bildstein M., Application of electro-hydrostaticactuators (EHA) for future aircraft primary flightcontrols 1. Internationales FluidtechnischesKolloquium, Aachen, Germany, 1998.

[3] Dorey R. E. and Harris R. M., Thermodynamicdetermination of power losses in hydrauliccomponents, 2nd International Conference on FluidPower Transmission and Control, Hangzhou,China, March 20-22, 1989.

[4] Hopsan, A Simulation Package, User's Guide,Technical Report LITH-IKP-R-704, Div. of Fluidand Mech. Eng. Systems, Dept. of Mech. Eng.,Linkoping University, Sweden, 1991.

[5] Kjolle P., Relationship of pvT Conditions and cv ofOils for Thermodynamic Measurements, NELReport No 658, National Engineering Laboratory,Norway, 1978.

[6] Manco S. and Nervegna N., Theoretical andExperimental Studies on the ThermodynamicEfficiency of an Hydraulic Pump, in Proc. ofASME Fluid Power Systems and Technology, SanFransisco, November 12-17, 1995.

[7] Navarro R., Performance of an Electro-HydrostaticActuator on the F-18 Systems Research Aircraft,NASA/TM-97-206224, 1997.

[8] Rodermund H. Berechnung der Temperatur-abhangigkeit der Viskositat von Mineralolen ausdem Viskositatsgrad, Schmiertechnik andTribologie, vol2, pp.56-57, 1978.

[9] Rydberg K., On performance optimization anddigital control of hydrostatic drives for vehicleapplications, Ph.D. thesis, Linkoping Universit,Linkoping Sweden, 1983.

[10] Storck K., Thermal system analysis- heat transferin glass forming and fluid temperature-controlsystems, Ph. D. thesis, Linkoping University,Linkoping, Sweden, 1998.

[11] Svensson H., Andersson J., Rydberg K-E.,Modeling of Losses and Temperature Calculationsin Fluid Power Systems, The Fifth ScandinavianInternational Conference on Fluid Power,Linkoping, Sweden, May 28-30, 1997.

[12] Van Wylen G. P.and Sonntag R. E., Fundamentalsof classical thermodynamics, John Whiley & Sons,1985.

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