GraSMech – Multibody 1 Computer-aided analysis of rigid and flexible multibody systems GraSMech course 2005-2006 GraSMech – Multibody 2 Organization and Teaching team Part I (2005-2006): Modelling approaches and numerical aspects Speakers : Dr. Olivier Brüls, OB, ULg Dr. Gaëtan Kerschen, GK, ULg Prof. Paul Fisette, PF, UCL Dr. Joris Peeters (replacing Prof. Wim Desmet), JP, KUL Prof. Jean-Claude Samin, JCS, UCL Prof. Olivier Verlinden, OV, FPMs Part II (2006-2007): Flexible systems and special topics GraSMech – Multibody 3 Schedule Lessons on wednesday from 14.00 to 18.00 Lesson 1 (February 15) : Part one : Introduction (JCS) + applications (PF,OB,GK,OV) Part two : approach based on Minimal coordinates (OV) Lesson 2 (February 22) : approach based on Cartesian coordinates (OV,JP) Lesson 3 (March 1) : approach based on Finite elements (OB,GK) Lesson 4 (March 8) : approach based on Relative coordinates (PF,JCS) Lesson 5 (March 15) : numerical problems (integration,…) After Easter (April 26 ?) : presentation of projects by students
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GraSMech – Multibody 1
Computer-aided analysis of rigid and flexible multibody systems
GraSMech course 2005-2006
GraSMech – Multibody 2
Organization and Teaching team
Part I (2005-2006): Modelling approaches and numerical aspects
Computer-aided analysis of rigidand flexible multibody systems
GraSMech – Multibody 5
Introduction : multibody applications
Set of articulated bodies
MechanismsRailway vehicles
Robot manipulatorsSpace applications
t
y
GraSMech – Multibody 6
What is a multibody system ?
Multibody System (MBS):
Bodies (rigid or flexible)
Joints
force elements
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GraSMech – Multibody 7
Principle
System defined from technical
elements
Equations of motion built (and eventually solved)
automatically
GraSMech – Multibody 8
Purpose of simulation
To assess the behaviour of a system before its construction
so as to dimension its mechanical elements
so as to optimize its performances
so as to design a controller
…
Computer-aided design tool
To identify possible problems on an existing system
GraSMech – Multibody 9
MBS versus FEM
Multibody approach
- Rigid bodies
- Large motions
MBS with flexible bodieslimit : efficiency versus universality
Why do we need to develop a new theory whereas structural dynamics and finite element theories are well established ?
Finite elements
- Flexible bodies
- Structural and modalanalysis (small motions)
p(t)KqqCqM =++ &&&
0)(
=+=+
g(q,t)λJQ,t)qc(q,qqM T&&&
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GraSMech – Multibody 10
Historical origins
Spacecraft : 1960 Mechanisms : 1970
Robotics : 1980 Flexible bodies : 1990
GraSMech – Multibody 11
Historical origins
The American Explorer I flew in January 1958. Explorer I waslong and narrow like a pencil. It was supposed to rotate around its own centerline, like a pencil spinning about its lead. It was definitely not supposed to rotate end over end, like an airplane propeller or a windmill blade.
GraSMech – Multibody 12
Some unstable satellites
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GraSMech – Multibody 13
Historical origins
First publications :
Hooker and Margulies : « The Dynamical Attitude Equations for a n-Body Satellite », J. Atronautical Sciences, 1965.
Roberson and Wittenburg : « A Dynamical Formalism for an Arbitrary Number of Interconnected Rigid Bodies, with reference to the Satellite Attitude Control », proc. of the 3rd. Int. Congress of Automatic Control, Butterworth and Co., Ltd, London 1967.
GENSYS (Sweden)MEDYNA (Germany, no longer distributed)NUCARS (USA, Association of American Railroads)VOCODYM (France, SNCF and INRETS)VAMPIRE (UK, AEA Technology)SIMPACK (Germany, DLR)MSC.ADAMS/Rail (USA, MEDYNA routines for contact)
Can be considered as reliableERRI benchmark, Manchester benchmarksComparison with measurements
GraSMech – Multibody 80
Wheel-rail Contact - Geometric problem
Contact configuration (position, curvatures, ...) in terms of the lateral displacement
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Difficulties of the geometric problem
Double contact
Discontinuities and contact jumps (several contact points)
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Normal contact force
Options for determination of normal contact force
contact=geometric constraint: N=Lagrange multiplier -> contact zone by Hertz theory
Advantages: ability to tabulate the contact, numerically more stableDrawbacks: not adapted to several contact points, contact area always assumed elliptical
contact=force element with wheel-rail penetration -> contact area and normal force by elastic forces.
Advantages: naturally adapted to several contact pointsDrawbacks: computational burden, stiff motion equations
Main design variablesGlobal layout (distribution of bogies)Primary suspensions and contact geometry (stability and track loads)Secondary suspension (comfort)
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GraSMech – Multibody 85
Stability – kinematic yaw
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Linear analyses
Equations of motion can be linearized about a stationnary motion -> study of small perturbations
GraSMech – Multibody 87
Root locus
Root locus: evolution of poles (roots) with velocity
Unstable(Re>0)
Stable(Re<0)
10% limit
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GraSMech – Multibody 88
Root locus of a bogie
There exists a critical speed !
GraSMech – Multibody 89
Critical speed vs concity
GraSMech – Multibody 90
Tramway of Minneapolis
Rigid wheelsets
Independent wheels
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GraSMech – Multibody 91
Tramway of Minneapolis
Pole leading to instability at low conicity
GraSMech – Multibody 92
Tramway of Minneapolis
Pole leading to instability at high conicity
GraSMech – Multibody 93
Nonlinear stability analysis
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GraSMech – Multibody 94
Cityrunner
Short carbodies: adapted to tortuous networksMore carbodies than bogiesCentral carbody not connected to the railComfort of the central carbody driven by the global dynamics of the vehicle
GraSMech – Multibody 95
Cityrunner
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Derailment study
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Y/Q for Minneapolis
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Conclusions
Reliable commercial softwares exist with many possiblitiesThey are classically used in industry
Attention to modelling mistakes !A prototype will always be built for final validation
GraSMech – Multibody 99
Today Challenges
GraSMech course 2005-2006
Multi – physics modeling and simulation
Real time computation
optimization, «hardware in the loop» simulations, …
Parameter identification
Education
…
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GraSMech – Multibody 100
Perspectives: multiphysics
Mechatronics = science of motion controlMechanismActuators Sensors Control law Cars (suspension, ESP…)
Large manipulators
High-speedmachines
Magnetic bearings
GraSMech – Multibody 101
Perspectives: multiphysics
Integrated analysis and designMultibody dynamicsElectronicsHydraulicsPneumaticsElectrical circuitsPiezoelectricityMagnetics…
Next step: micro-mechatronicsnew technologies / new physical effects
Radial comb motor
Bistable mechanism
Micropump
GraSMech – Multibody 102
Multibody System Optimization
Optimization of « dynamical » performancesFast computation of the cost function (ex. symbolic model)
Optimization algorithms : deterministic or stochastic methods
Geometrical/morphological optimization of mechanismsRobust assembly method (loop closure)
Problem of local optima (related to mechanism reconfiguration)
Problem of computer time (=> parallel computation)
Illustration Car suspension
Planar mechanism
Acherman steering mechanism
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GraSMech – Multibody 103
Suspension geometricaloptimization
for lateral dynamicstability
Test : lane changeat 65 km/h
Multibody System Optimization
Student final project
GraSMech – Multibody 104
Multibody System Optimization
Optimal design of path-following mechanisms• Deformation of mechanism to circumvent assembling constraints
• objective : strain energy of the bars• parameters : natural lengths of the springs
Non-Linear Least Squares Optimization
Use of natural coordinates
Initial Optimal
GraSMech – Multibody 105
Multibody System Optimization
• Different starting points different local optima
• Example : Six-bar steering linkage mechanismto fulfill the Ackermann condition
Other design criteria to choose best mechanim(e.g. robust design)
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GraSMech – Multibody 106
Multibody Real time computation
For « greedy » simulations, such as:Sensitivity analysis
Identification process (many run of the model / many « exciting »trajectories
Optimzation of a dynamic transient behaviour
For real « Real time » requirementReal time control of robots (including an inverse dynamic model)
At the end of a MBS project, students should be able to:formulate consistent hypotheses (Engineering)manipulate 3D kinematic tools (Physics)use the Newton-Raphson method to find system equilibrium (Numerical methods)build a well-structured simulation program (Programming)make a 3D drawing of the vehicle and a 3D virtual animationanalyse their results (Physics)question their model (Engineering)