circuit racing, track texture, temperature and rubber friction racin… · circuit racing, track...
TRANSCRIPT
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.