Modelling and optimization issues in flexible mechanisms

SAMTECH, Integrating CAE towards Professional Solutions

ModellingModelling and optimization issues and optimization issues in flexible mechanismsin flexible mechanisms

M. M. BruyneelBruyneel , F. , F. CugnonCugnon and D. Granvilleand D. Granville

European project

www.rapolac.eu

ACOMEN Conference, 26ACOMEN Conference, 26--28 May 2008, 28 May 2008, LiègeLiège, Belgium, Belgium

www.samcef.comwww.samcef.com

SAMTECH SAMTECH LiègeLiège, Belgium, Belgium

This document is the property of SAMTECH S.A.

SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.

27 May 2008, ACOMEN, Liège,

Overview

SAMCEF for modelling flexible systems

Fidelity levels in the modelling

- at the components level

- at the joints level

Optimization issues in flexible systems

Conclusions




Solution with SAMCEF

SAMCEF is a finite element code able to run multi-body simulations

European project

www.rapolac.eu

Géradin & Cardona (2001). ‘’Flexible multibody dynamics: a finite element approach’’, John Willey & Sons.





Multi-body software- Rigid components- Articulation - joints

Finite element code- Flexible components- Modal reduction(Super Elements)

‘’Flexible systems dynamics’’ ?- Flexible components- Limited to the modal reduction- No interaction between flexible bodies- Rigid joints- 2 environments

+ =

Classicaly (not in SAMCEF)

Limited range of applications





SAMCEF is a finite element code able to run multi-body simulations

SAMCEF MecanoFor flexible systems dynamics- Flexible components- Possible modal reduction- Large displacements- Interaction between flexible bodies- Possible flexible joints - 1 environment

=>

Géradin & Cardona (2001). ‘’Flexible multibody dynamics: a finite element approach’’, John Willey & Sons.

In SAMCEF

…

Wide range of applications

Finite element code- Flexible components- Modal reduction (Super Elements), if needed

Kinematic constraints





SAMCEF solution for Flexible System Dynamics

SAMCEF Field + BOSS quattro (with SAMCEF Field)Analyses: linear static, modal, non linear Finite

Element (material, geometric, contact), Super Elements, flexible mechanisms, control

Optimization: structural (shape, sizing), gains of controllers

Parametric studies

SAMCEF Mecano

Non linear FEA (structure+motion)

All the computations are carried out in a same interface




Overview






Conclusions




Modelling the components

• The different models

MBS (rigid) model Mixed modelSuper Element model

Rigid bar

hinge

Super Element

Finite Element model

FE mesh




• The different models

MBS (rigid) model Mixed model

Check of kinematic loopNo flexibility

Check of kinematic loopFlexibility

System dynamicsStress design

Advanced design (contact, damage)

Decrease the size of themodel, while remaininggeneral where needed

Modelling the components

Super Element model

Check of kinematic loopFlexibility

System dynamicsStress design

Linear material behaviorSmall strains

Finite Element model




Solution with SAMCEF: Master Model concept

MBS (rigid) model

+ Controller+ Super Element

+ Finite Element

Minimum fidelity flexible system model: including flexibility via Super Elements

Master Model

Library of partsinterchangeable components

with different levelsof fidelity

1

2

3b

3a

Minimum fidelity mechatronic model: including a controller and flexibility via Super Elemen ts

Higher fidelity model: including a full FE component

Low fidelity model: including only rigid parts

e.g. damage in case of a

crash




• Results-1200

-1000

-800

-600

-400

-200

0

0 200 400 600 800 1000 1200

forward backward

Imposed rotation at hinge 1 (0° => 90° => 0°)

trajec

tory

Volume FE components

797 sec CPU

Super Elementscomponents

4 sec CPUMixed components

200 sec CPU

Rigidcomponents

3 sec CPU

Solution with SAMCEF: comparison




Flexibility in the model must be taken into account

=> Flexibility and inertia produce vibrations

=> FEM = access to strain and stresses

Precision of the machine

Control strategy

Design of the components

+ Flexibility in the joints (transmit vibrations)

influence

Joints modelling !

• Conclusions

Very important since weight is to be decreased !

Solution with SAMCEF: conclusion




• Flexibility must be modelled at the joints level

Joints transmit vibrations !

Modelling the joints




• Full finite elements model of the component and the joint

Examples




• Finite element model of the joints

Examples

Courtesy of01dB - METRAVIB




Overview






Conclusions




Optimization with BOSS quattro

Structural optimization

Kinematic loopoptimization

Controleroptimization

e.g. optimal position of joints in the mechanism

e.g. optimal size and shapeof components

BOSS quattro = open architecture= task manager

Some semi-analyticalsensitivities for linear and non linear analyses

possibility to run finite differencesin parallel

Sensitivity analysis

+

+

e.g. optimal gains of a PID

Trajectory




Example: controller optimization

• The dynamic of the controller is embarked in the model

• A step of 45 degrees is imposed to tune the gains of the controller

• An external controller could be defined (with Simulink, or other) based on a linearized model and used in SAMCEF Field

• PID available in SAMCEF Field => 3 gains to find

• Rigid model: the rotation at one hinge is controlled with a PID

• The rotation at one hinge is controlled (hinge between the baseframe and the rotating column)





• Definition of the optimization problem solved in BOSS quattro

( )2,,

min ∑ −i

targetii

KDKIKPdd

iii ddd ≤≤

jjj KKK ≤≤ DIPj ,,=

0

10

20

30

40

50

60

0 1 2 3 4 5 6

Avoid overshoot

Decrease rise time

d i

i = time






• Results of the optimization problem solved in BOSS quattro

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40

Iterations

Rel

ativ

e g

ain

s o

f th

e P

ID

KP KI KD

-1

1

3

5

7

9

11

0 5 10 15 20 25 30 35 40

Iterations

Ob

jec

tiv

e f

un

cti

on

45°KP ≠ 0, KI ≠ 0, KD ≠ 0





-1

1

3

5

7

9

11

0 5 10 15 20 25 30 35 40

Iterations

Ob

jec

tiv

e f

un

cti

on

45°





• Flexible-Rigid model: the rotation at one hinge is controlled with a PID

0

2

4

6

8

10

12

0 2 4 6

Time (sec.)

Ro

tati

on

an

gle

(d

eg.)

Process Variable Set Point

0

10

20

30

40

50

0 2 4 6

Time (sec.)

Rot

atio

n an

gle

(deg

.)


0

20

40

60

80

100

0 2 4 6

Time (sec.)

Ro

tati

on

an

gle

(d

eg.)


0

10

20

30

40

50

0 2 4 6

Time (sec.)

Rot

atio

n an

gle

(deg

.)


0

10

20

30

40

50

0 2 4 6

Time (sec.)

Ro

tati

on

an

gle

(d

eg.)


0

10

20

30

40

50

0 2 4 6

Time (sec.)

Ro

tati

on

an

gle

(d

eg.)

Process variable Set Point





The RAPOLAC project

• Some improvements of the model

• To use several controllers

• To use (external) controllers defined with Simulink (or other)

• Flexibility of the robot

• Dynamic of the controller

• Inertia of the robotSensors at the hand tip

and actuators at the hinges

Sensor

Actuator

• Up-to-now co-located control => rather use non co-located control

• Goal: To follow trajectories

with SAMCEF

• Collaboration with KUKA Roboter




Conclusions

• Flexibility in the components

• via Super Elements

• via Finite Element model

• Flexibility in the joints

• Interaction between flexible bodies (e.g. contact)

=> Transmission of vibrations between flexible bodies

• Optimisation

• Available tools should be validated for sizing and shape optimization

• An important issue at an industrial level : TOPOLOGY OPTIMIZATION offlexible systems – including transient (dynamic) considerations

Modelling and optimization issues in flexible mechanisms

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