application examples and potential for explicit finite elements in the analysis of friction brakes

5th European HTC in Bonn

Knorr-Bremse Group WANG (R/LTA), 5. Nov. 2011 Seite 1

Application examples and potential for explicit

finite elements in the analysis of friction brakes

Jiasheng WANG

Technical Analysis & Simulations,

Knorr-Bremse Sfs, Germany



Outline

Introduction of the company

Why use explicit finite elements to simulate a brake?

Theory background

Practical considerations

Application examples

Future perspective and potential applications



Company Introduction

Founded: in 1905

Experience: 100 years of innovation

Nearly 17,000 employees

Turnover approximately EUR 3.7 billion

R & D 4.9% of revenue

Investments of EUR 140 million

Locations Over 60 locations in 25 countries

Corporate divisions:

rail and commercial vehicles

Market and technology leader with two pillars:

- Braking systems for rail vehicles + On-Board Systems - Braking systems for commercial vehicles + torsional vibration dampers




• Explicit finite elements are typically used for modelling highly dynamic

events such as crash or impact problems.




• During a normal service braking process or an emergency braking process, the brake pressure

has to be increased in very short time duration, which means the explicit analysis is in principle

well suited for such a kind of simulation.

Truck disc brake slows down or stops the rotation of the truck wheels due to

friction from the brake pads.




• Secondly, under actual driving condition the brake assembly is often subjected to vibration loads

which come from the wheels and axle. Thus, in the product development phase, an equivalent

vibration test with certain frequencies has to be done.

Red: measured result

Blue: simulated result

Vertical shake test for a whole truck brake assembly

Body

Axle

System Reaktion (on highway)




• Further, an explicit dynamic analysis may also be used to model some highly nonlinear

phenomena.

• Nonlinearities may stem not only from the materials (for example, rubber parts), but also from the

contact (for example, big relative displacement) and from the geometric (for example, highly

deformation).

Material Contact Geometric



Theoretical background (simplified)

• The equation of motion

• Implicit static calculation • Explicit calculation without damping



Theoretical background (in detail)

)(),(int tFuuFuM ext

11

12

2121

)1(

)(

nnnn

nnnnn

ututuu

utututuu

)(),(111int1 fffm

nextnnntFuuFuM

n

m

n

m

n

n

f

n

f

n

n

f

n

f

n

uuu

uuu

uuu

m

f

f

11

11

11

)1(

)1(

)1(

),,,,( 11

321

nnnnnn ttuuuRhsuKcCcMc

221

41

21

11

12

fm

fm01 qAAqq nnn

)()~

,~(111int1 fffm

nextnnntFuuFuM

n

m

n

m

n

n

f

n

f

n

n

f

n

f

n

uuu

uuu

uuu

m

f

f

11

11

11

)1(

~)1(

~

~)1(~

),,,,( 11

1

nnnnnn ttuuuRhsuMc

nnn

nnnn

utuu

ututuu

)1(~

)(~

1

2121

111

1211

~

~

nnn

nnn

utuu

utuu

12

3

)2()1(

35

1

122

fmm

Conclusion:

Intern force stays on the left side

[M+C+K]x=b must be solved

Intern force is moved to the right side

Mx=b must be solved

Implicit time integration Explicit time integration

Time Discretisation Predictor

Corrector

Newton-Raphson

uu

uuFu

u

uuFuuFuuF

C

ttitti

K

ttittittittinn

ii

11

),(),(),(),(

11int11int11int11int



Practical considerations

Implicit Explicit

(-) (non diagonal) (+) (Diagonal matrix)

(-) Low robustness (Divergence)

(+) High robustness

High nonlinear materials, intensive

contact, large displacement

(-) High memory (+) Low memory (High and coupled

nonlinearity)

(-) Relatively high cost

high CPU , high memory

(+) Relatively low cost

Low CPU , low memory

(+) Always stable (-) Conditional stability

(+) Min. element size unlimited (-) Min. element size limited

(Mass scaling required)

(+) default with nonlinear elements (-) Locking effect by using linear

tetrahedrons, hexahedrons not easy

(+) stress result very precise (-) stress result not so accurate

(+) large time step (-) small time step

[Reference: Altair Engineering, Inc., Radioss Theory Manual ]



Application example 1

Exp. 1: Shake Test of a

whole truck brake assembly

Brake bracket was broken




Exp. 2: Simulation of an

endurance test of a membrane




t=0ms t=70ms t=120ms

Exp. 3: Brake pressure distribution



Future perspective and potential applications

• The size of the model time step has to be chosen small enough to accommodate the element time

step of the smallest element. Hence the smallest time step determines the performance of the

whole model .

• A further technology which is called "multi-domain" would be able to subdivide domains based on

time step (mesh size). Each domain uses its own time step. The CPU time could be decreased

significantly and the computation accuracy may be increased by refining the mesh locally.

• Explicit CFD and fluid-structure interaction may also be applied for simulation of brake valves.

(ALE, SPH etc.)

[Reference: HW-Tutorial RD3590]

Fluid Flow through a Rubber Valve



• Thank you for your listening!

Jiasheng WANG

Knorr Bremse SfS

Technical Analysis/Simulations (R/LTA)

Moosacher Straße 80, D-80809 München

Phone +49 89 3547 180245

EFax +49 89 35647 180245

mailto: [email protected]

http://www.knorr-bremse.com

http://www.knorr-bremse.com/






Contact force between

the bracket and the flat spring

(explicit FEM analysis)




Contact pressure between the brake pad and the brake disk

application examples and potential for explicit finite elements in the analysis of friction brakes

Business

u t t u u u u

f u f u n u n

u u n t

mu n u n

u n predictoru n

u n tu n t

f u n ff

u t t f int