CIRCUIT RACING, TRACK

TEXTURE, TEMPERATURE AND

RUBBER FRICTION

Robin Sharp, Patrick Gruber and

Ernesto Fina

Outline

• General observations

• Grosch's experiments

• Interpretation of Grosch’s results

• Rubber properties

• Persson's hysteresis-loss theory

• Persson's theory versus Grosch's results

• Conclusions

General observations

• Importance of tyre shear forces

• Forces depend on friction between rubber and road

• Racing demands the maximum possible forces

• Forces are functions of -• normal load

• surface nature and texture

• rubber compound

• rubber temperature

• surface temperature

• sliding speed

Observations from motor racing

• Track surfaces not all the same

• “Green” tracks get faster with usage

• Rubber “B” often grips rubber “A” poorly

• Rain on a used track affects the racing line

• New tyres grip well for a short time

• Higher friction tyres have shorter lives

• Rubber and road temperatures are vital

The focus

• Now - how does rubber friction

work?

• Later – how does rubber friction

relate to tyre/road interactions?

Grosch’s experiments

• Flat rubber blocks loaded against smooth

(wavy glass) and rough (silicon carbide)

surfaces – 4 compounds

• Sliding under constant normal load

• Low velocities to avoid heating

• Temperature control -50°C to 100°C

• Sliding speed and friction force

measurements

Fz

V

friction force

loading by weights

moving surface

stationary

rubber block

temperature

regulated box

Grosch’s experiments

4 compounds:

INR, ABR,

SBR, Butyl

energy dissipation by adhesion and/or deformation

Grosch measurements; 4 compounds;

INR, ABR, SBR, Butyl

emery cloth

temperature controlled enclosure

force

measurement

speed-controlled motor

loading on test

rubber block

liquid flow

Lorenz experiments (2011)

Equivalence of energy dissipation and friction force

Grosch results for INR on silicon carbide

(left) and for ABR on glass (right)

T = 90 to -350 C

T = -40 to -580 C

T = 85 to 200 C

T = 10 to -150 C

Log(V/Vref) Vref = 1 cm/s

Friction coefficient

Log(V/Vref) Vref = 1 cm/s

Temperature – frequency / sliding

speed equivalence

• Rubber state depends on temperature

relative to glass-transition temperature, Tg

• Standard temperature, Ts ≈ Tg+500 C

• Williams Landel Ferry (WLF) normalisation

to Ts; plot aTω or aTV (not ω or V), where

S

ST

TT

TTa

5.101

86.8log10

Grosch master curves

• Combining temperature and sliding velocity by WLF

transform gives master curve for ABR on glass;

S

ST

TT

TTa

5.101

86.8log10

WLF transform

T range: -15°C to 80°CResults for

different

temperatures, T

T-compensated

results

1

2

0

1

2

0

200 C

re (1 cm/s)re (1 cm/s)

-4 -2 0 -4 -2 0 -4 0 4 8-8

Grosch master curves for SBR at

200 C on glass and silicon carbide

Log[aTV/Vref] Vref = 1 cm/s

on glasson silicon

carbide

on powdered silicon carbide

adhesion deformationfriction

coefficient

Grosch master curves for ABR at

200 C on glass and silicon carbide

on polished

stainless steelon glass

on silicon

carbide

on powdered

silicon carbide

Log[aTV/Vref] Vref = 1 cm/s

friction

coefficient

Grosch master curves for Butyl at

200 C on glass and silicon carbide

Log[aTV/Vref] Vref = 1 cm/s

on glass

on silicon

carbide

on powdered

silicon carbide

friction

coefficient

Rubber vibration testing

commercial

analyserclose-up

ωLMP

ωLTP

G(ω) = G’(ω)+jG’’(ω)

tan(δ) = G’’(ω)/G’(ω)

Rubber vibration properties

SBR elasticity at constant temperature

maximum loss modulus at ωLMP

maximum ratio at ωLTP

18

Non-linearity (Lorenz)

Amplitude

dependence of

storage (upper)

and loss

(lower) moduli

large strain

large strain

small strain

Non-linearity (Westermann)

carbon

black

filler

storage modulus

Adhesion mechanism

• Smooth surface peak due to adhesion

• Rubber bonds to road; bonds stretch and

break

• All 4 rubbers, VSP≈ 6e-9 ωLMP /(2π) m/s

• Characteristic length, 6e-9 m - molecular

• If bonds break at this stretch, rubber is

forced at ωLMP when V=VSP

Deformation mechanism

• Rough surface peak due to deformation

• All 4 rubbers, VRP≈ 1.5e-4 ωLTP /(2π) m/s

• Characteristic length, 1.5e-4 m, close to mean particle spacing in the surface

• If wavelength is 1.5e-4 m, rubber is forced at ωLTP when V=VRP

• VSP/VRP=6e-9 ωLMP /1.5e-4 ωLTP

• If ωLMP and ωLTP are wide apart, adhesion and deformation peaks are close

Persson’s deformation ideas - simple

(1) sinusoidal surface; waves normal to sliding

(2) rubber deformation from linear elastic theory

(3) calculate energy dissipation for given sliding speed

• wavelength and speed give ω

• temperature gives rubber visco-elastic properties

• expect maximal energy loss at ω = ωLTP

stationary rubber

sliding

speed, V

simple surface

Persson’s deformation ideas - complex

(1) isotropic surface

(2) conformity to short waves depends on long waves

(3) accounting for (1) and (2), integrate energy-loss

contributions from all wavenumbers from qL to q1

• qL non-critical, q1 needs estimating

• divide power by V to get shear force; hence μ

complex surface λ 0

stationary rubber

sliding

speed, V

Persson’s deformation theory

Persson’s notation

• μ, friction coefficient

• C(q), road spectral density function

• P(q), contact area ratio – actual/nominal

• qL, q1, wavenumbers for longest and shortest waves

• Tq, temperature

• E, rubber complex elastic modulus; , Poisson’s ratio

• v, sliding velocity

• σ0, nominal normal stress

Silicon carbide 180 mesh measured

displacement spectrum

SBRubber properties at 200 C

Simulated friction master curves

Reconstructed rubber properties

Simulated friction master curve

Summary and conclusion (1)

• Smooth surface friction - adhesion, not

understood, wide open

• Rough surface friction - deformation

• Persson’s hysteresis mechanics plausible

• Rubber treated as linear viscoelastic

• Amplitude dependence

• Which properties to use?

Summary and conclusion (2)

• Surface represented by displacement

spectrum in range qL to q1

• qL non-critical, q1 uncertain, influenced by

cleanliness and debris

• Which q1 to use?

Summary and conclusion (3)

• With favourable treatment, rough-surface

friction peak realistic with respect to

Grosch

• Below peak, adhesion can account for

differences

• Above peak, predicted friction falls too

much as sliding speed increases

Summary and conclusion (4)

• In racing, “rubbering-in” involves transfer of

rubber to road

• Surface on racing line becomes smoother and

chemistry changes

• Contact area will increase and adhesion will

increase for “same” compounds

• Deformation friction will reduce

• Racing line friction is enhanced but if it rains,

adhesion is impeded - best line changes

Reference

• E. Fina, P. Gruber and R. S. Sharp,

Hysteretic rubber friction: Application of

Persson’s theories to Grosch’s

experimental results,

• ASME Journal of Applied Mechanics

• Vol. 81, No 12, December 2014.