Modelling and optimization issues in flexible mechanisms
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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, Page 2
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 3
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.
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 4
Solution with SAMCEF
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 5
Solution with SAMCEF
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 6
Solution with SAMCEF
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 7
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 8
Modelling the components
• The different models
MBS (rigid) model Mixed modelSuper Element model
Rigid bar
hinge
Super Element
Finite Element model
FE mesh
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 9
• 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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 10
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 11
• 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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 12
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 13
• Flexibility must be modelled at the joints level
Joints transmit vibrations !
Modelling the joints
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 14
• Full finite elements model of the component and the joint
Examples
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 15
• Finite element model of the joints
Examples
Courtesy of01dB - METRAVIB
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 16
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 17
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 18
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 19
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)
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 20
• Rigid model: the rotation at one hinge is controlled with a PID
• 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
Example: controller optimization
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 21
• Rigid model: the rotation at one hinge is controlled with a PID
• 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
Example: controller optimization
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 22
-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°
Example: controller optimization
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 23
• 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
.)
Process Variable Set Point
0
20
40
60
80
100
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
.)
Process Variable Set Point
0
10
20
30
40
50
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.)
Ro
tati
on
an
gle
(d
eg.)
Process variable Set Point
Example: controller optimization
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 24
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
This document is the property of SAMTECH S.A.
SAMTECH, Integrating CAE towards Professional Solutions Michaël Bruyneel et al.
27 May 2008, ACOMEN, Liège, Page 25
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
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