real-time simulation of flexible multibody dynamics · contents background real-time simulation...

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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 [email protected]

Conclusions

Background

VALMET 865 LM PONSSE ELEPHANTKING


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


Background

Contents

Background





Conclusions

Real-time model

Mechanics Actuators

Controlsystem

Workingprocess

User



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


Global formulationsMechanics

Actuators

Controlsystem

Workingprocess

User


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


MechanicsActuators

Controlsystem

Workingprocess

User

References:A.Avello et. al., 1993

S.M. Issa, K.P. Arczewski., 1998


MechanicsActuators

Controlsystem

Workingprocess

User

iii Qm

ooo Qm dVdpVBe

dtdVQQ

VB

dtdp

oie



MechanicsActuators

Controlsystem

Workingprocess

User



Contents

Background





Conclusions



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


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)



7245 x 7245*/**

0.9369978637953 2.101852520470 2.559024411850 3.732929611370 4.574739592436


Error(*Memory allocation)


[email protected]



• 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



SOFTWARE PACKAGE

*C, Fortran and C++ involves in this packages

UMFPACK, ARPACK, Csparse, LAPACK etc.

Contents

Background





Conclusions



For closed loop -



Main format – Compressed Sparse Column



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





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 · contents background real-time simulation...

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