Post on 30-Jul-2018
www.lut.fi
Lappeenranta University of Technology
Real-time simulation of flexible multibody dynamics
Aki Mikkola, Ezral Bin Baharudin and Asko Rouvinen
Lappeenranta University of Technology Mevea Ltd, www.mevea.com
Contents
Background
Real-time Simulation
Description of Flexible bodies
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Conclusions
Background
VALMET 865 LM PONSSE ELEPHANTKING
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Background
VALMET 865 LM PONSSE ELEPHANTKING
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Collaborate with:Simulator Use – R&D
• Verify customer needs andavailable technologies early (e.g. hybrids, energy recovery etc.)
• Perform virtual testing, simulation andoptimization (e.g. energy losses, fuelconsumption etc.)
• Avoid costly prototypes andlong iterations
• Develop better solutions, faster and with lower cost
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Background
Contents
Background
Real-time Simulation
Description of Flexible bodies
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Conclusions
Real-time model
Mechanics Actuators
Controlsystem
Workingprocess
User
Real-time Simulation
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Augmented formulation
0 λCQQqM qT
ev
c
veT
QQQ
λq
CCM
q
q 00C
Embedding technique
0 eT
vTT
iT QBQBMDBqMBB
Penalty method
CΩCΩμCqCαCqMqαCCM qqqq2
1 2 t
Tii
T
Real-time Simulation
Global formulationsMechanics
Actuators
Controlsystem
Workingprocess
User
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Topological methods
T T
10
bNn n n
n nn n n n n n n
m I 0 u 0 F
u ω0 J ω ω J ω T
T 0 q Mq C QIn compact form
q Rz+b
With help of ’Velocity Transformation Matrix R’ velocity and acceleration can be written as
q Rz Rz+b
T T T T T
T T( ) ( )
R MRz R MRz R Mb R C R QR Q C R M Rz b
Substituing all the variables into the compact formlead to
Real-time Simulation
MechanicsActuators
Controlsystem
Workingprocess
User
References:A.Avello et. al., 1993
S.M. Issa, K.P. Arczewski., 1998
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
MechanicsActuators
Controlsystem
Workingprocess
User
iii Qm
ooo Qm dVdpVBe
dtdVQQ
VB
dtdp
oie
Real-time Simulation
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
MechanicsActuators
Controlsystem
Workingprocess
User
Real-time Simulation
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Real-time Simulation
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Real-time Simulation
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Contents
Background
Real-time Simulation
Description of Flexible bodies
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Conclusions
Description of Flexible bodies
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Description of Flexible bodies
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
REDUCTION METHODS
Guyan Reduction
T
T
can be represent as
ss smr
ms mm
ss smr
ms mm
G
K K LK L I
K K I
M M LM L I
M M I
LL
I
Krylov Subspace
2 1
1 2 3
( , ) , , , ...,
, , , ...,
mm
m
r
r
span
span
T
T
A b b Ab A b A b
v v v v
M = V MV
K = V KV
Craig-Bampton
T
T
0
R L
r CB CB
r CB CB
IB Φ
K Φ KΦ
M Φ MΦ
Looking for
Ф / V / L
Description of Flexible bodies
Real-time simulation of flexible multibody dynamics
In Matlab codeMatrix test (K, M) ASNYS Guyan (Hz) Craig-Bampton (Hz) Krylov Subspace (Hz)
60 x 60(reduce to 10)
8.300052.0095
145.6029285.2588471.4364
8.300452.5328
160.7633311.7753574.3402
8.300052.0095
145.6029285.2588471.4364
8.300052.0095
145.6029285.2588471.4364
243 x 243(reduce to 50)
2075.411566503662075.411567419726100.638573356616100.6385737116613227.374715433
6136.449611295.830412573.372023665.402126646.7124
2075.41162075.41166100.63866100.6386
13227.3747
2075.41412075.41656100.77896100.8073
13228.5620
3147 x 3147(Reduce to 100)
12.5274417130817412.741683101744815.2633176098634218.5829012047296720.92137855707649
9.860812.586312.738716.116636.8489
12.527612.741815.263418.582720.9214
12.527412.741815.263318.582920.9214
5250 x 5250*/**(Cargotec model)
0.9369978637953 2.101852520470 2.559024411850 3.732929611370 4.574739592436
Error(#Memory allocation)
Error(#Memory allocation)
Error(#Memory allocation)
7245 x 7245*/**
0.9369978637953 2.101852520470 2.559024411850 3.732929611370 4.574739592436
Error(#Memory allocation)
Error(*Memory allocation)
Error(#Memory allocation)
mikkola@lut.fi
Description of Flexible bodies
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
• C programming instead of MATLAB • Solver which can do eigenvalue analysis for large and
sparse matrices.
Mass & Stiffness matrices partition process (Dofs to remove) Tr
asnf
orm
atio
n m
atri
x
Guyan reduction
Craig-Bampton
Krylov Subspace
Mass matrix
reduction
Stiffness matrix
reduction
Eig
enan
alys
is
Dev
elop
new
mod
el
base
d on
solv
er’s
re
sults
Solver code written in C
Ex: FEM Private / Commercial Software
Description of Flexible bodies
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
SOFTWARE PACKAGE
*C, Fortran and C++ involves in this packages
UMFPACK, ARPACK, Csparse, LAPACK etc.
Contents
Background
Real-time Simulation
Description of Flexible bodies
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Conclusions
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
For closed loop -
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Main format – Compressed Sparse Column
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
H8 Tree Harvester descriptions Lagrange Recursive, R
Number of bodies 30 30
Generalized coordinates 180 180
Joint coordinates - 35
Constraint equations 153 8
Number of DOFs 27 27
Number of entries of Cq, Nc (Rows x Columns)
27540 1440
Number of non-zero elements, NNZc 1128 78
Contents
Background
Real-time Simulation
Description of Flexible bodies
Offshoot of the Project
Real-time simulation of flexible multibody dynamics mikkola@lut.fi
Conclusions
Conclusions
Real-time simulation can be used in development of new products/concepts
• Real-time simulation allows to test new software versions • Design concepts can be tested reliable and fast manner using real customers and their needs other manufacturers
• Smart connected products
Flexible bodies can be descripted in real-time simulation by employing modal reduction approaches.
In this study, a software based on C programming was develop
Real-time simulation of flexible multibody dynamics mikkola@lut.fi