Dynamics of Rolling Tyre Tread Blocks with Frictional ... · Conclusion •Modular model considers...

Titel

February 10, 2009, Cologne

Tiretech 2010 8

Dynamics of Rolling Tyre Tread Blocks

with Frictional Contact and Wear

Patrick Moldenhauer

Matthias KrögerInstitut of Machine Elements, Design and Manufacturing

Technical University Freiberg

Germany

• Introduction

• Tread block modelling

• Simulation results

• Conclusion


Tiretech 2010 9

Examples of modeled systems with elastomers

Windscreen

wiper

Window seals

Tyre tread blocks

Focus on

friction induced vibrations

seals e.g. in

brake systems

Judder:

comfort problemSqueal:

function problem

Squeal:

comfort problem

Judder: function and

comfort problem


Tiretech 2010 10

• Highly sophisticated 3D models

• Non-linear material description

• Thermo-mechanical coupling

• Numerically very expensive

[Hofstetter 2004]

[Gleu 2001]

[Larsson & Barrelet 2002]

Introduction

• Simple models (1 to 3 DOF)

• Neglect of geometry and structural effects

• Fast calculation

• Mostly add-ons for tyre models

Steady state simulations Dynamic simulations

Stress distribution

Temperature distribution

1D contact element

2 DOF oscillator


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Tread block model

Point contactStructural dynamics


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Module 1 - Craig/Bampton transformation

Additional 10 modal shape functions give an adequate approximation of FE

solution Reduction rate: 78%

Static solution is always fulfilled

1x

1y

Aim: Reduction of DOFs to efficiently calculate dynamic effects

Idea: Combination of static condensation and modal description

Decide: What are primary DOFs

Static shape

functionsModal shape functions


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Local friction characteristic has

to be determined e.g. from

Module 2 – Local friction characteristic

For this example (concrete):

a = 0.8 s/mm

µ∞v = 1.0

µ0v = 1.22

γv = -0.01 s/mm

µ∞p = 0.95

µ0p = 1.3

γp = -8 mm²/N

N)()()(arctan2

),( ,,0,,,0,N

pγ

ppp

vγ

vvvrelrelprelv eμμμeμμμva

πpvμ

• experiments

• analytical models

• numerical simulations

Approximation function depends on relative velocity vrel and local normal pressure pN:

Smoothing term Velocity dependence Pressure dependence

Experiments:

[Gäbel 2009]


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N

NN

Δ

Δ

s

Fc

Few junctions:

large increase of local pressure high deformations small contact stiffness

Many junctions

relatively smaller increase of local pressure small deformations high stiffness

Module 3 - Normal force – displacement characteristic

FN=120 N

FN=60 N

FN=90 N

FN=30 N

Investigation of non-linear force-displacement characteristic

Global contact stiffness

[Gäbel 2009]


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• Local non-linear contact stiffness cK

at each point contact:

• Fit parameters for concrete:

c∞=100 N/mm, k=0.4 mm-1

• Good approximation of measurement

for concrete

)1()(K

ukecuc

Normal force-displacement characteristic Non-linear contact stiffness


Experiments:

[Gäbel 2009]

Non-linear contact stiffness on a concrete surface


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µ(vrel, p, T, ...), cK(u)

Properties of the rough surface are considered by

• Parameter dependent friction characteristic

• Non-linear contact stiffness

Rough surface is modelled as smooth

Fast and efficient contact algorithm

Influence of single asperities passing the contact area is neglected

Numerical efficient treatment of contact mechanics


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Module 4: Wear process

Experimental investigation of wear process

Side views of tread blocks

tested under different conditions

0,23 m/s

0,47 m/s

1,31 m/s

2,62 m/s

0,2 N/mm² 0,4 N/mm² 0,6 N/mm²

Sample mass decreases linearly

with sliding distance

Constant steady wear rate


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Measured steady wear rate

Measured steady friction coefficient


v

0

p

N,0

Nwearwear

Δ

Δkk

v

v

p

pk

s

mη

Description of experimental results by wear law

e.g. [Zhang 2004]

No consideration of

friction coefficient


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h

v

0

p

N,0

N

N

0Nwear),(

1),(*

kk

v

v

p

p

pvμkpvη

k0 =0.735 mg/m

kp =1

kv=0.49

pN,0 = 1 N/mm²

v0 = 1 mm/s

Measured wear rate

Measured friction coefficient

v

0

p

N,0

Nwearwear

Δ

Δkk

v

v

p

pk

s

mη

Description of experimental results by wear law

e.g. [Zhang 2004]

No consideration of

friction coefficient

Introduction of µ-related wear rate),(

),(),(*

N

NNwear

pvμ

pvηpvη

µ-related wear rate



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• Wear law is formulated time-dependent

at each local contact element

• Local wear results in decrease of non-

linear spring length

• Stiffness of non-linear springs remains

unchanged

• Contact algorithm remains unchanged

1v

0

p

N,0

N,

w,

1)(

k

i

k

i

i

i

iv

v

p

pμ

Aρt

.

Implementation of wear law into tread block model

k0 =0.735 mg/m

kp =1

kv=0.49

pN,0 = 1 N/mm²

v0 = 1 mm/s


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Introduction

Run-in Sticking Sliding Snap-out

Rotation, Torque

Aim of tread block model is the simulation of

• Passage of tread block through contact patch

• Interaction between structural dynamics, friction and wear

• High-frequency tread block dynamics during sliding and rolling

• Glass surface

• Normal force: 60 N

• Vehicle velocity: 10 mm/s

• Rel. Velocity: 5 mm/s

• Mean COF: 0.8

HS investigations from

[Lindner 2005]


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Rolling motion

Steel belt determines

rolling behaviour of tyre

tread (Displacement

controlled simulation)

Centrifugal forces are

small compared to the

contact forces

Effect of inertia by

change of guide velocity

neglected

Description of

tread block as fixed

system with reduced

system matrices


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Simulation of rolling tread block

Approximation of FE calculated belt

flattening by polynomial function

Coordinate x [mm]

Chronological view of tread block deformation

under driving slip

Co

ord

. y[m

m]

Simulation with driving slip

vgl = 1 m/s, pN = 0,8 N/mm²


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Approximation of FE calculated belt

flattening by polynomial function

Coordinate x [mm]

Chronological view of tread block deformation

under driving slip

Co

ord

. y[m

m]

Simulation with driving slip

vgl = 1 m/s, pN = 0,8 N/mm²


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• Allocation of sticking, sliding and snap-out phase

• Sticking zone decreases with increasing slip

• No sticking occurs for high slip

Deformation behaviour of leading edge under variation of tyre braking slip

Normal pressure pN = 1,0 N/mm², Vehicle velocity vC = 20 m/s

C

C

v

rωvS

Slip definition


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Deformation behaviour of leading edge under variation of tyre slip


C

C

v

rωvS

Slip definition


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C

C

v

rωvS

Slip definition


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C

C

v

rωvS

Slip definition


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• During sticking nearly linear increase of friction force

• Overall friction forces increases with increasing slip

• Saturation for higher slip values

Tread block contact forces under variation of tyre slip



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• Sticking zone decreases with increasing vehicle velocity

• Deformation velocity increases with increasing vehicle velocity

• Stick-Slip vibrations occur during sliding phase

at 602 Hz and 952 Hz

Deformation behaviour of leading edge under variation of vehicle velocity

Normal pressure pN = 0,8 N/mm², Constant tyre braking slip S = 0,02

C

C

v

rωvS

Slip definition


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C

C

v

rωvS

Slip definition


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C

C

v

rωvS

Slip definition


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• Sticking zone approx. constant






C

C

v

rωvS

Slip definition


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Conclusion

• Modular model considers structural dynamics, parameter

dependent friction, non-linear contact stiffness and wear

• Craig/Bampton transformation allows efficient calculation of the

tread block dynamics

• Rough surface is modelled as smooth with respective non-linear

contact stiffness and local friction characteristic

• Experimentally identified non-linear friction characteristic and wear

law are implemented

• Implementation of global tyre kinematics allows deeper insight into

processes in the tyre contact patch including stick-slip phenomena

Thanks to Deutsche Forschungsgemeinschaft (DFG FOR492)

Forschergruppe “Dynamical contact problems with friction of elastomers”

Dynamics of Rolling Tyre Tread Blocks with Frictional ... · Conclusion •Modular model considers...

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