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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
Speakers :Dr. Olivier Brüls, OB, ULgDr. Gaëtan Kerschen, GK, ULgProf. Paul Fisette, PF, UCLDr. Joris Peeters (replacing Prof. Wim Desmet), JP, KULProf. Jean-Claude Samin, JCS, UCLProf. 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 4
Introduction
Prof. J. C. SaminUniversité catholique de Louvain
GraSMech course 2005-2006
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&&&
4
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.
GraSMech – Multibody 14
Different approaches of MBS formalisms
Choice of coordinates
Mechanical principle to generate the
equations
Computer implementation
GraSMech – Multibody 15
Choice of coordinates
Absolute coordinates(a bad example…)
6 bodies:=> 36 differential eq. of motion6 revolute joints:=> 30 algebraic equations
TOTAL : 66 equations (DAE)for a 6 d.o.f. system
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GraSMech – Multibody 16
Choice of coordinates
Absolute coordinates(a good example…)
Main body : 6 absolute coordinates Each bogie frame : 6 absolute coordinates Each wheelset : 6 absolute coordinates
All bodies “elastically” inter-connected6n equations (DAE)
for a 6n d.o.f. system
GraSMech – Multibody 17
Choice of coordinates
6 d.o.f.
6 relative coordinates
=> 6 ODE
Relative coordinates(a good example…)
GraSMech – Multibody 18
Choice of coordinates
Absolute or Relative coordinates ?(a medium example…= reality)
either :
3 relative coordinates
2 constraints
=> 5 DAE
5 absolute coordinates
4 constraints
=> 9 DAE
or :
1 d.o.f.
1 “minimal” coordinate
0 constraints
=> 1 ODE
or :
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GraSMech – Multibody 19
Choice of coordinates
user friendliness…
Wheel carrier
Front of vehicle
Data input :of the reference configuration
Absolute/relative coordinates(user point of view …)
Absolute :• for each center of mass :
• for each body frame : 321 ,, ϑϑϑ
zyx ,,
Relative :• , but in a local body frame
• relative orientation of frames
zyx ,,
GraSMech – Multibody 20
Choice of coordinates
Conclusions
number of equations <=> computer efficiency
+/- user- friendly
kinematical and dynamic equations +/- complicated
+/- easy for MBS computer implementation
= leads to DAE equations
influence on :
GraSMech – Multibody 21
Choice of coordinates
An alternative approach :“natural” coordinates
Rigid body
Set of equivalent punctual masses
used by :Garcia de JalonNikravesh
No need of rotational coordinates !
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GraSMech – Multibody 22
Different approaches of MBS formalisms
Choice of coordinates
Mechanical principle to generate the
equations
Computer implementation
GraSMech – Multibody 23
Which formalism ?
Newton – Euler (basic)
Virtual work or power principle
Lagrange equations
Recursive Newton-Euler algorithm
Recursive “ order N ” algorithm
GraSMech – Multibody 24
Description of a multibody system (basic elements)
Which formalism ?
Topology
Example : « tree-like »
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GraSMech – Multibody 25
Description of a multibody system (basic elements)
Bodies, defined by :
mass
position of the center of mass
body-fixed frame
inertia tensor (with respect to the body-fixed frame)
auxilliary body-fixed frames (attachment points)
Which formalism ?
Ground = fixed reference body (except for space applications)
GraSMech – Multibody 26
Description of a multibody system (basic elements)
Joints, defined between frames attached to bodies
Which formalism ?
revolute
1 relative d.o.f.(rot)
prismatic
1 relative d.o.f.(trans)
GraSMech – Multibody 27
Description of a multibody system (basic elements)
Joints, defined between frames attached to bodies
Which formalism ?
spherical
3 relative d.o.f.(3 rot)
universal
2 relative d.o.f.(2 rot)
cylindrical
2 relative d.o.f.(1 rot + 1 trans)
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GraSMech – Multibody 28
Description of a multibody system (basic elements)
Joints, defined between frames attached to bodies
Which formalism ?
Contact joint
5 relative d.o.f.
or 3 relative d.o.f. (rolling without slip)
Planar
3 relative d.o.f.(1 rot + 2 trans)
Helicoidal (screw)
1 relative d.o.f.(1 rot/trans)
GraSMech – Multibody 29
Description of a multibody system (basic elements)
Force elements, defined between bodies
Which formalism ?
Example : spring and damper
suspension elements
GraSMech – Multibody 30
Which formalism ?
Newton – Euler (basic)
For each individual body, write :
Newton (vector) equation : xmF &&=∑Euler (vector) equation : HL &=∑
Collect all equations
… easy if absolute coordinates are used …
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GraSMech – Multibody 31
Which formalism ?
Collect all equations
L
M
M
M
M
&&
&&
&&
&&
&&
&&&&
&&
&&
OLLL
LLL
LLL
+
2
2
2
1
1
1
1
1
1
2
2
2
133
132
131
123
122
121
113
112
111
1
1
1
zyx
zyx
mm
mIIIIIIIII
mm
m
ψϕϑ
F=
rely on sparse-oriented numerical methods
Newton – Euler (basic)
GraSMech – Multibody 32
Which formalism ?
Collect all equations in your computer program
L&& +qM vecontributiF= constraintF+
1 contributive torque component
(spring, friction, actuator,…)
5 constraint force/torque components
Newton – Euler (basic)
GraSMech – Multibody 33
Which formalism ?
eliminate (numerically) all constraint force/torque component
=+L&&qM vecontributiF constraintF+J J
complete the dynamical set of equations in your
computer program
with the kinematical joint constraint equations
… lead to a huge amount of equationsbut relatively simple to obtain …
Newton – Euler (basic)
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GraSMech – Multibody 34
Which formalism ?
Newton – Euler (modified)
all internal force/torque of the appending subsystem disappear
for each joint, sum analytically all equations of the « descendant » bodies
I1
ˆ
2I
3I
i
h k
j
Li
Fi
Oi
I1
ˆ
2I
3I
i
h k
j
Li
Fi
Oi
GraSMech – Multibody 35
Which formalism ?
Newton – Euler (modified)
all internal force/torque of the appending subsystem disappear
Translational (vector) joint equation : ),,,( extii FqqqfF &&&=
Rotational (vector) joint equation : ),,,,( extextii LFqqqhL &&&=
project analytically these vector equations onto the joint axis
the joint constraint force/torque components also disappear
GraSMech – Multibody 36
Which formalism ?
Newton – Euler (modified)
implement these analytical results in your computer program
either in implicit form (inverse dynamical model)
),,,,( extext LFqqqQ &&&Φ=
),,,()( extext LFqqcqqMQ &&& +=
or in semi-explicit form (direct dynamical model)
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GraSMech – Multibody 37
Which formalism ?
Virtual power (or work) principle
close to the modifed Newton-Euler approach(and historically inspired by it)
Translational vector equation
I1
ˆ
2I
3I
Gi
hk
jg
Li
Fi
O0i
z i°∆
Oi
GraSMech – Multibody 38
Which formalism ?
Rotational vector equation
I1
ˆ
2I
3I
Gi
hk
jg
Li
Fi
O0i
z i°∆
Oi
Virtual power (or work) principle
GraSMech – Multibody 39
Which formalism ?
Virtual power (or work) principle
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GraSMech – Multibody 40
Which formalism ?
expand the r.h.s. of the equations in terms of the generalized coordinates and their derivatives
implement these analytical results in your computer program
),,,,()( gLFqqcqqMQ extext&&& +=
Virtual power (or work) principle
project analytically these vector equations onto the joint axis
l.h.s.
GraSMech – Multibody 41
Which formalism ?
)( jijoioj qAAA ⋅=
L& +Ω+= )( jjij qωω
L&& += ij ωω
ωωi
ω j
ωω h Xibody i
body j
body h
I1
2I
3I
Base : 0
Ωj
Recursive Newton-Euler algorithmespecially convenient for relative coordinates
first develop a « forward » kinematical recursion
GraSMech – Multibody 42
Which formalism ?
Recursive Newton-Euler algorithmespecially convenient for relative coordinates
first develop a « forward » kinematical recursion
Oi
Oj
dij
body i
body j
body h
zi
I1
2I
3I
pi
pj
Base : 0
L++= )( iiij qzpp
L&& += ij pp
L&&&& += ij pp
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GraSMech – Multibody 43
Which formalism ?
second, develop a « backward » dynamical recursionin vector form
Recursive Newton-Euler algorithm
I
Gibody : , i m
hj
Oi
Fiext
I ii
L exti
-Fj
-Lj
Fi
Li
OjL&& iiji xmFF +=
L& +⋅+= iiji ILL ω
GraSMech – Multibody 44
Which formalism ?
project analytically these vector equations onto the joint axis
iiiii QLF =⋅+⋅ ϕψ
),,,,( jjiiii LFxQ L&&& ωΦ=
l.h.s.
r.h.s.
finally, collect all these dynamical equations :
implicit form (inverse dynamical model)
),,,,,( gLFqqqQ extext&&&Φ=
Recursive Newton-Euler algorithm
note : the semi - explicit form can also be obtained by isolating q&&
GraSMech – Multibody 45
Which formalism ?
Recursive “ order N ” algorithm
a first « forward » kinematical recursion step
a second « backward » dynamical recursion step
a third « forward » recursion step
[ ]),,,()(1extext LFqqcQqMq &&& −= −
explicit form of the dynamical model
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GraSMech – Multibody 46
Which formalism ?
comparison of computational costs(for simulation purpose : explicit form)
... ... ... ... ... ... ... ...
1
2 3
4 5 6 7
8 9 10 11 12 13 14 15
R1
T2 R3
T1 R2 T3 R1
T2 R3 T1 R2 T3 R1 T2 R3
I 3˜
^
Example : a binary tree multibody system
GraSMech – Multibody 47
Which formalism ?
..Minimum number of operations to compute : q
Lagrange andvirtual principles Newton/Euler
recursive
Order(N)
# (+ - x :)
# dof
GraSMech – Multibody 48
Different approaches of MBS formalisms
Choice of coordinates
Mechanical principle to generate the
equations
Computer implementation
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GraSMech – Multibody 49
Computer implementation
Numerical approach
generate numericallyall system equations
according to the generic MBD formalism
solve the system numerically
Numerical implementation
Initial conditionsiterate
MBS description
set of numerical data
including :the particular topologyconstant valuesinitial values qq &,
GraSMech – Multibody 50
Different approaches of MBS formalisms
Symbolic approach
)( and)( qJqh
),( and )( qqcqM &
Generate all system equations :
can also be done by implementingthe MBD formalism in a symbolic
computer program
GraSMech – Multibody 51
Different approaches of MBS formalisms
generate symbolicallyall system equations according to the generic MBD formalism
Specific model equations,given as a sub-routine
Symbolic implementationSymbolic approach
Solveiteratively
Numerical implementation
set of data
MBS description
including :the particular topologysymbols and zeros
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GraSMech – Multibody 52
Principal simulation software
MSC / ADAMS (1973, USA, reference in road vehicles)
LMS / DADS (Belgium, originally USA)
SIMPACK (DLR, Germany, leader in railway dynamics)
In Belgium :
SAMCEF / MECANO (Samtech/ULg, based on finite elements)
ROBOTRAN (UCL, advanced symbolic generation of equations of motion)
EasyDyn (FPMs, free library (GPL) developed for teaching)
GraSMech – Multibody 53
Application examples
GraSMech course 2005-2006
Computer-aided analysis of rigidand flexible multibody systems
GraSMech – Multibody 54
ApplicationsFlexible multibody dynamics
Prof. O. BrülsUniversité de Liè[email protected]
GraSMech course 2005-2006
Finite Element method [Géradin & Cardona ’01]
Samcef-MECANO software
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GraSMech – Multibody 55
Deployable structures
Large space structuresCompact stowed configurationElastic effects:
lightweight designpre-stressingsmall damping
GraSMech – Multibody 56
Deployable structures
Large antennaNo axial symmetry1 kinematic dof !Slow deployment (15 min)1-g test rig ⇒ 0-g behaviour?
GraSMech – Multibody 57
Deployable structures
FE mechanical modelFlexibility (struts + panels)Local stiffnesses & frictionInertial forces = negligible1400 equations
Kinematic analysisImposed angle of the central bodyDriving torque?Forces in the struts?Hinge angles?
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GraSMech – Multibody 58
Deployable structures
a) 1-g model ⇒ experimental validationb) 0-g model ⇒ accurate prediction
GraSMech – Multibody 59
Deployable structures
GraSMech – Multibody 60
Landing gears
Different phasesDeployment / retractionGround impactRollingBreakingTaxiing
Multidisciplinary approachDeformable mechanismTyreHydraulics (shock-absorber, brake, steering)Active / semi-active control
Concorde – nose undercarriage
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GraSMech – Multibody 61
Landing gears
Motivations for modelling:
Optimal design configurationmass
Pre-prototyping checks motionloads, stressesstability (shimmy)complementarity with experimental tests
GraSMech – Multibody 62
Landing gears
Deployment Wheel/ground impact
GraSMech – Multibody 63
Landing gears
Landing of the A380
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GraSMech – Multibody 64
Applications
Prof. P. FisetteUniversité catholique de Louvain
GraSMech course 2005-2006
Hybrid modeling
Dynamical identification
GraSMech – Multibody 65
Bogie actuation : hybrid modeling
« Multibody/Electrical » coupled modelSymbolic generation of the electro-multibody model
Dynamical model of the electrical actuators
Equational-level coupling : same « frequency range »
Application (collab. Bombardier-Transportation, Crespin, France)
Articulated bogie (High speed train)
3-phase induction motor
Effect of the electrical frequency on fatigue problems (chassis)
GraSMech – Multibody 66
Bogie actuation : hybrid modeling
Problem: Torque oscillations lead to fatigue stress
in the bogie frame during acceleration
Force in themotor to chassis - joint
« Electro-multibody » model
Rr1
Rr2
Lr1
Lr2
Lr3
ROTOR
Rr3
Rs1
Rs2
Rs3
Ls1
Ls2 L
s3
us1
us2
us3
STATOR
Msr
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GraSMech – Multibody 67
Semi-active suspension modeling
« Multibody/Hydraulic/Electrical » coupled modelSymbolic generation of the multibody model
Dynamical model of the hydraulic system
Fast simulation (« real time » in Simulink)
Application (collab. Tenneco-Automotive, Saint-Trond)
Audi A6 (more than 80 relative coordinates)
« Kinetic » system : cylinders, pipes, accumulators, …
Behavior and sensitivity analysis
GraSMech – Multibody 68
Semi-active suspension modeling
Problem: Behaviour prediction of this new
suspension system on modern car
« Hydro-multibody » model
Carbody rollWrap excitation
HydraulicDynamics
GraSMech – Multibody 69
Dynamical identification of Tree-like MBS
« Multibody symbolic dynamical model« Inverse dynamics » model
« Reaction dynamics » model
Parameter combination : morphoplogy-dependent
Application (collab. KULeuven)
KUKA Robot identification
( Human body identification )
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GraSMech – Multibody 70
Serial manipulator
Human Body• 20 - 30 dof
« recursive »dynamic model
• … 6 dof
« in extenso »dynamic model
Find ? : Minimal set of dynamical parameters : p
Dynamical identification of Tree-like MBS
GraSMech – Multibody 71
l
jk
d
b
i
i
id
d
i
i
j
lzi
Gi
Bi
O0i
mi =X
mj
mibi =X
mj dij
Ki = Ii −X
mj dij
. dij
j: i j≤
j: i j≤
j: i j≤
“Augmented” body i
Barycentric mass :
Barycentric vector :
Barycentric inertia tensor :
Dynamical identification of Tree-like MBS
Barycentric parameters
GraSMech – Multibody 72
Recursive formulation (origin : Renaud-88 for linear chains)=> Extension to tree-like systems (recursive form)
body i
body j
body k
Fi
Li
Fj
Lj
ωi
kin.
dyn.
Gi =Xj∈ ı
Gj−Fiext+βi .biz+ mi γi
Fi = miα∗i+Gi
L i =Xj∈ ı
(L j +edijz .Gj)−L iext−ediiz .Fiext
+ K iz . ωi+ ωi .K i
z .ωi+ebiz .αi
Qqqq =δϕ ),,( &&&
Dynamical identification of Tree-like MBS
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GraSMech – Multibody 73
Minimal set of body j parameters Redefinition of parent body i parametersmj (mi := mi)
bj1, bj2, b
j3 (bi := bi)
/ Ki :=Ki +Kj
Minimal set of body j parameters Redefinition of parent body i parameters/ (mi := mi)
bj1, bj2 bi := bi + bj3 ϕ
j
Kj12,K
j13,K
j23,K
jd,K
j33 Ki :=Ki − bj3(d
ij. φ
j+ φ
j. d
ij)−Kj
s φj. φ
j
with Kjd = Kj
11 −Kj22 with Kj
s = Kj11 + Kj
22
Prismatic joint : combination and report rules
Revolute joint : combination and report rules
Set of parameters : p
Dynamical identification of Tree-like MBS
GraSMech – Multibody 74
1. Symbolic Computation of the theoretical combination rules
2. Symbolic Inverse or Reaction Dynamics
4. Detection of the « zero » columns in D
,,,,,,,,
,,,,,,,11*1*1*1*1133
3333333
dyyyzxzxyzxsy
dyyyzxzxyzx
KKKKKbbKb
KKKKKbbp =
correspond to parameters that must be removed from p
5. Results : => Minimal Parameters set δ ∗
=> Identification Matrix ϕ ∗ Qqqq =*),,(* δϕ &&&
=
xxxxxxxx
xxxxxxxxxxxx
D
0...00...0
.....................0...00...00...0
Partial derivative matrix D3. Symbolic Differentiation w.r. to p
Dynamical identification of Tree-like MBS
GraSMech – Multibody 75
Internal model inverse dynamicsExternal model reaction dynamics1 2 3 4 5 6
nr. parameter exact parameter σi σe σcvalue
P1 Kr111 32.0920 0.0916 0.0873 0.0611P2 Kd2 −12.3614 0.0906 0.0332 0.0304P3 K2
12 0.6174 0.1150 0.0351 0.0313P4 Kr213 1.5078 0.1231 0.0528 0.0467P5 K2
23 −0.2974 0.0990 0.0439 0.0423P6 b31 0.0580 0.0259 0.0080 0.0075P7 b32 2.5780 0.0392 0.0111 0.0107P8 Kd3 2.2511 0.0818 0.0322 0.0296P9 K3
12 0.5953 0.0909 0.0239 0.0227P10 K3
13 −0.2978 0.0562 0.0251 0.0237… … … … … …
Standard deviation
KUKA IR 361: Dynamic Parameter Estimation Combining Internal and External models
Dynamical identification of Tree-like MBS
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GraSMech – Multibody 76
2D volley-ball motion
Parameter estimation : mean error (%)
3. trunk
2. thigh
1. shank
5. arm
4. head 6. forearm
I1
I3
Reaction measurement at the foot
Reaction measurement at the trunk
error [%]
error [deg]
error [%]
error [deg]
GraSMech – Multibody 77
ApplicationsRailway vehicles
Prof. O. VerlindenFaculté polytechnique de Mons
GraSMech course 2005-2006
GraSMech – Multibody 78
Building railway vehicle models
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GraSMech – Multibody 79
Principal dedicated softwares
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
GraSMech – Multibody 81
Difficulties of the geometric problem
Double contact
Discontinuities and contact jumps (several contact points)
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GraSMech – Multibody 82
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
GraSMech – Multibody 83
Tangential contact forces
GraSMech – Multibody 84
Assessment of performances
Major concernsStability, critical speedRide quality – comfortUIC 518 criteria (tests): stability, track loads, derailment
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
GraSMech – Multibody 86
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
30
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
GraSMech – Multibody 96
Derailment study
33
GraSMech – Multibody 97
Y/Q for Minneapolis
GraSMech – Multibody 98
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
35
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)
« Hardware in the loop » analysis
Others (Haptic systems, games, …)
GraSMech – Multibody 107
Multibody Real time computation
Example : semi-active control of car
Non-Model-based controller …=> Model-based controller
KUL-PMA
GraSMech – Multibody 108
Multibody Education via projects !
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)
at the basis of the final examination
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GraSMech – Multibody 109
Multibody Education via projects !
…numerical methods…a « real » system
… a group
…theoretical formalisms
….a CAD system
Given …
….programming tools
…system parameterization…system animation …system analysis
… Produce
GraSMech – Multibody 110
Problem to solve : truck “jacknifing”
GraSMech – Multibody 111
Typical Results
… …
Solved !
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GraSMech – Multibody 112
Problem to solve : Sidecar side-skidding
Solved ?