Application to Vehicles Dynamics Taking into account local...

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Application to Vehicles Dynamics

Taking into account local non linearity in MBS models


Introduction

SAMTECH Expertise

SAMTECH Methodology

Application to Vehicle Dynamics

Optimisation

Conclusions

Tables of contents


Introduction


WIA

KATECH

References in the automotive industry


SAMTECH experiences in Automotive

ChassisMachining

PipeEngine

Vehicle Dynamics

Cam shaft

Brakes

Differential

Suspension

Gears


Non

linearity

NVH

Primary Ride Control systems

Handling

Secondary Ride

Misuse

Durability

Frequency

Challenges for simulation

MBS

FEA


Need of reliable CAE solution integrated in the design process

Consequences on final productminimisation of time-to-market

& costs

Prototyping:

Replace real ones by virtual ones

beginning of

design process

NUMERICAL SIMULATION

Simulation in the design process

Project definition Project test

and integration

Vehicle targets

Detailed design

System Test and

verification

System Integration

System Validation

Requirements definition

Global analysis Local

analysis


Modelling chronology

Complexity

Lateral Transient

• sine sweep

• corner entry

Combined manoeuvre

• braking in curve

• gas release

• Lane change

Braking manoeuvreRide and

durabilityLateral Steady state

manoeuvre

• Jturn (step steer)

Body in White

Suspension geometry FEA


System level model for time response

• static,

• kinematic (suspension),

• dynamic (manoeuvres, durability,…)

Necessary to accurately describe the dynamic loads acting on the vehicle

or on vehicle components:

• Driving conditions

• Ride and comfort

• Misuse (kerb hitting),

• …

Global analysis


Local analysis

Static stresses evaluation

Vibration modes computation

Non-Linear Structure Analysis

with contact/friction

Fatigue Analysis

Classical Linear & non-linear Structural Analyses

Need of loads and boundary conditions from Global Analysis

Global-Local coupling


Classical methodology

CAD data MBS (Global analysis)FEA (local analysis)

Super Elements

Replace rigid bodies with SE

Run simulation

Calculate detailed stress

Export node forces time

historyFatigue Prediction

• Superposition of stress

• Cycle counts

• Damage sum

FEA model Rigid bodies model

export

export


Classical methodology

Several different models (local, global)

Several different software (linear FEA, non linear FEA, MBS,…)

Probably several different users/teams

A lot of data transfer

Hypotheses made: - Flexibility in MBS model

- Local non linearity not taken into account

- Transient loads transformed in static loads for FEA model


Linear FEA in

standalone GUI

FEA and MBS in

standalone GUI

FEA and MBS in

unified GUI

Non-Linear

FEA&MBS in KBE

MultiPhysics in

KBE

1980

1990

2000

2010

2020

Integration Level 1

through Interfaces

Integration Level 2

with CAD Based

Pre- and Post-

Processor

Integration Level 3

within the

Engineering

Process

FEA=Finite Element Analysis

SAMTECH evolution

MBS=Multi-Body Simulation

KBE= Knowledge Based Engineering

GUI= Graphical User Interface


SAMCEF Field

Every SAMCEF solver is driven from one common GUI:

SAMCEF Field (FIELD = FInite ELement Desktop)

Need of only one model

CAD Model

(IGES, STEP, Catia, Brep …)Modeler to create your CAD

geometries

Changes

Analysis data

Mesh / Import mesh

Solvers

Post-processing

HTML Report

../../../../SamcefField/V7.3-01/SamcefField/dochtml/us/modeler/index.htm


SAMCEF Capabilities as linear FEM solver

Linear

analysis

Linear FEM capabilities include:

static

composites

Fracture

Modal analysis

Dynamic response

Contact

• Flexible/flexible

• Solid/flexible

Buckling

Meshed part #2

Meshed part #1


Rubber bushing example

MECANO capabilities as non linear FEM solver

Non linear FEM capabilities

include:

Geometric non linearity:

• Large strain

• Large deflection

• …

Material laws (viscoelastic,

hyperelastic, …)

Temperature dependency

…

Large displacement


MECANO capabilities as Rigid MBS solver

Tyre

HingeBushing

Spring

Prismatic

Spherical

Gear and pinion

Library contains over 150 kinematic joints:


3 ways to handle digital control with our tools:

A SAMCEF Mecano model is linearized and transformed into space state matrices to be used by Matlab Simulink

Matlab Simulink controller is exported to a Fortran/C subroutine linked to SAMCEF Mecano

Matlab Simulink is launching Mecano computations to update its structural model

MECANO link with control system


DigitalController

Linear Kinematic Joints

Non Linear

SAMCEF MECANO unique approach


Original methodology of Samcef MECANO

Finite element approach

Implicit solver

Cartesian coordinates (6 dof by nodes)

Rotation vector theory

Joints defined by kinematical constraints

Augmented Lagrangian method

Φ: constraintλ: Lagrangian multiplierp: penalty factork: scaling factor


Explicit conditionally stable

• Solution at t+Δt entirely based on solution at t, meaning that the initial errors are accumulating into further time steps

• Time step has to be smaller than

Implicit – Explicit : what to use ?

Lmin: smallest element dimension

Cd:characteristc speed

• If the time step is greater than Δtcr, non physical oscillations appear in the results

• As CPU time is inversely proportional to time step size, calculation can be very long

• Or a compromise needs to be found between CPU time and accuracy

Explicit Schemes are well suited for very fast dynamic phenomena (crash)


Implicit unconditionally stable

• Use equilibrium at t, t+Δt to solve solution at t+Δt

• Time step only depends on the frequencies you want to represent (curves must be properly described)

• Results are more stable and simulation is faster for longer runs (no simulation time limit)

• Several schemes exist with different behaviour regarding numerical damping

Implicit – Explicit : what to use ?

Implicit schemes are well suited for dynamic analysis with longer phenomena (vehicle dynamics, engine dynamics…)


Implicit time integration

• Newmark

• HHT

• Chung-Hulbert …

Resolution of potentially large problems

• Sparse solver

• Mumps solver

• Parallel solver

SAMCEF MECANO solvers

• 4 sections of fuselage

• 18,580,217 dof's

• 2,521,568 shells elem.

• 3,092,810 elem. In total

• 28 h 30' on a cluster

of 10 nodes.

• 7 time steps, 5 rejected,

57 iterations up to 91% of the load

• Intel(R) Core(TM) 2.67 GHz

• 12 Gb per node


Generalised non-linear mechanical tool box

Integration of design & verification engineering in a common environment

Strong coupling between FEM & MBS

MECANO = MBS features inside a FEM code

NOT flexibility inside MBS code

SAMCEF MECANO advantages

Non-Linear FEA & S.E.

Contact/FrictionRigid/Flexible kinematical joints


Application to

Vehicle Dynamics


Nowadays virtual prototyping plays greater role in vehicle design

Better accuracy needed to predict the vehicle performances based on CAE estimations and results

Challenges faced for vehicle dynamics:• Local non linearity• Frequency domain coverage• Multi disciplinary

Data exchange between platforms • MBS • FEA• Control systems• Fatigue program

Vehicle dynamics context

Virtual Real

Simulation


NVH

Handling

Vehicle dynamics context

Durability

Ride and comfort

Misuse

Kinematics

Control systems


4 wheels

model

Model complexity

Number of parameters

Results accuracy

100%

Bicycle model

MBS

model

MBS

model

with SE

MBS model

with FEA

MBS model

with FEA

and meshed

tyres

-60

-40

-20

0

20

40

60

-20 -10 0 10 20

MBSTest

Mecano


Possible sources of non linearity in a vehicle

Tyre

Bushing

Damper

Spring

Bump or rebound stop

Chassis flexibility

Aerodynamic forces Friction

Power steering

Antiroll bar

Brakes(contact,

friction and temperature)

Pre-stress

Free play

Local plasticity

http://upload.wikimedia.org/wikipedia/commons/7/7b/Plain-bearing_DIN-ISO4379_Type-G.png


Rigid body or Flexible

Possibility to import mesh from external sources- Created in another model by SAMCEF- NASTRAN- ANSYS

When objects are defined as rigid, SAMCEF Field automatically creates:

• One node at the Centre of Gravity

• One node at each “interface” with other objects or the ground

• Mass and inertia of the object are assigned to the CoG

• Extra masses and inertias can be manually assigned


Different types of Elements for different levels of models

• Lumped mass and Inertias

• Rigid body elements

• Super elements (elastic bodies)

• Joint elements

• Real Flexible Finite Elements

Easy switch from one model type to another

Choice must be done following the requested level of precision …

First rigid approach can be done improving model in following analyses …

Large modelling capabilities

Motion (rigid) model

Super Element model

FEA model

Mixed model

CAD model


Use of parts

Substructures (parts): - are easily tuneable- can be stored in libraries and reused later

Model Substructure Parameters Data

• front suspension

• rear suspension

• Chassis

• Steering system

• Powertrain

• ...

Attachment points

Material

Tyre

Spring

Damper

…


Super- Elements: Craig and Bampton Component Mode Synthesis

Elastic bodies represented by static deformations and vibration modes (Mecano large rotations sub-modelling formulation)

Reduction of the number of d.o.f. -> calculation time reduction by generation of the reduced stiffness matrix, the related load vectors and/or the mass and damping matrices.

Super Elements

Real part

Finite Elements52000 dof

Super Elements2000 dof


Linearity: Chassis flexibility

First torsion mode forReinforcement to introduce

(for suspensions)

Carbon :

• MTM49-3/CF1103 (hot parts)

• VTM264FRB/CF1103

Aluminium honeycomb (Nomex)

36.2 Hz


-60

-40

-20

0

20

40

60

-20 -10 0 10 20

Body transmitted force

(Upper Support Moment (Nm))

Body transmitted force

SAMCEF

MBD solver

Test

Wh

eel str

oke(m

m)

Non linearity: the coil spring

Coil springs have a non-linear behaviour due to large displacements

Transmitted forces display an hysteretic behaviour

A classical “MBS like” spring element cannot represent this effect


Non linearity: the tyre

TNO Tyre model (Pacejka Magic Formula and SWIFT) is currently being implemented

Contacts have been initiated with• COSIN (FTIRE)• CDTIRE• RMOD-K

Road models will be available with

www.opencrg.org

Projects with meshed tyres are on going

http://www.opencrg.org/


The Imperia GP (www.greenpropulsion.be)

Vehicle dynamics example

http://www.greenpropulsion.be/


Rigid Multi Body Simulation allows:• Short calculation time• Investigation of an important number of designs covering several input variables and their full range of interest

Motion in FEA – Rigid vehicle

MBS approach:

Front and rear double wishbone suspensions

Front and rear antiroll bar

Joints:• hinges• bushing• non linear springs• non linear dampers

Non linear tyre model (Pacejka Magic Formula)


Enables optimization of:- Ride and Comfort performance - Handling performance

Motion in FEA – Flexible vehicle

Flexible approach: Meshed wishbones

Possibly meshed spring

Compromise between the two !!


Super-Element for large car

body model (shell)

Flexible mechanisms for suspension Wheels, beams, springs, sliders,

spherical joints…

Car body and suspension modeling

Modeling of misuse

Car riding (30Km/h) over an obstacle (25cm height)


Welding Spots Optimization

Welding spots idealized with small beam elements Sizing optimization on a car bodyDesign variables: discrete beam propertiesObjective:minimize number of welding spotsConstraints on given displacements

5000 variables


Motion in FEA – Rigid vs Flexible vehicle with MECANO

Flexible approach

Physical suspension compliance definitions:• FEA parts• non linear 3D bushings• elastomer

Greater details improve the accuracy of the results:• Higher frequency contents• Higher number of cycles for fatigue performance assessment

No need to re-measure the suspension if

• geometry changes (attachment point)

• part redesigned (new FEA model)

• fatigue can be integrated early in the design process

Better modularity

Rigid MBS


Test rig modelling

Any test rig can be defined and used- Kinematics and Compliance- 4 post rig- Durability

Modelling Rig helps model validation

Camber Angle Toe Angle


0.E+00

2.E+06

4.E+06

6.E+06

8.E+06

1.E+07

1.E+07

1.E+07

0.13

7.16

14.2

21.2

28.2

35.3

42.3

49.3

56.4

63.4

70.4

77.5

84.5

91.5

98.6

106

113

120

EQUIVALENT STRESS [MPa]

CY

CL

ES

STEEL EN-S355 S-N CURVE

Sfl(74); 5.00E+06; 74

Sfl(160); 5.00E+06; 160

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

CYCLES

AL

TE

RN

AT

ING

ST

RE

SS

[M

Pa]

Step 4:

RFC of stress cycles

Durability

Step 6:

Input in S-N material data

i

b

ii i

i

kS

dSPE

N

nDE

)p(S T)( i

Step 5:

Computation of fatigue damage:

Step 1:

Import Loads for FEM computation from aeroelastic behaviour

Step 2:

Stress computation by FEM

Step 3:

Stress transients in hot spots


Virtual Proving Ground capabilities

Possibility to use different level complexity

• Rigid body

• Super elements

• Meshed parts with non linear behaviour

Possibility to use advanced tyre models

• Commercial models

• Meshed tyres

Possibility to use advanced road models

(From www.opencrg.org)

http://www.opencrg.org/


A few thousands of

contacts

static contact wheel - track

dynamic contact wheel - track

Other example of vehicle dynamics


Chaining enables you to "chain" or "link" two calculations together, using the results of the first calculations as an input for the second.

Solver capabilities: chaining

Modal

Linear transient

and harmonic response

Thermal

Response to random forces

Vibro acoustic


SAMCEF Mecano enables you to increase:

Your simulation non linearity range

Your simulation frequency range

Pushing the limits of virtual prototyping

Increasing confidence you have in simulation results

Conclusions

Application to Vehicles Dynamics Taking into account local...

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