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
Grosch s experiments temperature regulated box F z loading by weights 4 compounds: INR, ABR, SBR, Butyl friction force V moving surface stationary rubber block energy dissipation by adhesion and/or deformation
Grosch measurements; 4 compounds; INR, ABR, SBR, Butyl speed-controlled motor temperature controlled enclosure emery cloth liquid flow loading on test rubber block force measurement
Lorenz experiments (2011) Equivalence of energy dissipation and friction force
Grosch results for INR on silicon carbide (left) and for ABR on glass (right) Friction coefficient T = 85 to 20 0 C T = -40 to -58 0 C T = 90 to -35 0 C T = 10 to -15 0 C Log(V/V ref ) V ref = 1 cm/s Log(V/V ref ) V ref = 1 cm/s
Temperature frequency / sliding speed equivalence Rubber state depends on temperature relative to glass-transition temperature, T g Standard temperature, T s T g +50 0 C Williams Landel Ferry (WLF) normalisation to T s ; plot a T ω or a T V (not ω or V), where log 10 a T 8.86 T 101.5 T T S T S
Grosch master curves Combining temperature and sliding velocity by WLF transform gives master curve for ABR on glass; 2 T range: -15 C to 80 C Results for different temperatures, T 2 T-compensated results 1 1 20 0 C 0 WLF transform 0-4 -2 0-4 -2 0-8 -4 0 4 8 re (1 cm/s) re (1 cm/s) log 10 a T 8.86 T TS 101.5 T T S
Grosch master curves for SBR at 20 0 C on glass and silicon carbide friction coefficient on glass adhesion deformation on silicon carbide on powdered silicon carbide Log[a T V/V ref ] V ref = 1 cm/s
Grosch master curves for ABR at 20 0 C on glass and silicon carbide friction coefficient on polished stainless steel on glass on silicon carbide on powdered silicon carbide Log[a T V/V ref ] V ref = 1 cm/s
Grosch master curves for Butyl at 20 0 C on glass and silicon carbide friction coefficient on silicon carbide on glass on powdered silicon carbide Log[a T V/V ref ] V ref = 1 cm/s
Rubber vibration testing commercial analyser close-up
Rubber vibration properties ω LMP G(ω) = G (ω)+jg (ω) tan(δ) = G (ω)/g (ω) ω LTP
SBR elasticity at constant temperature maximum loss modulus at ω LMP maximum ratio at ω LTP 18
Non-linearity (Lorenz) small strain large strain Amplitude dependence of storage (upper) and loss (lower) moduli large strain
Non-linearity (Westermann) storage modulus carbon black filler
Adhesion mechanism Smooth surface peak due to adhesion Rubber bonds to road; bonds stretch and break All 4 rubbers, V SP 6e-9 ω LMP /(2π) m/s Characteristic length, 6e-9 m - molecular If bonds break at this stretch, rubber is forced at ω LMP when V=V SP
Deformation mechanism Rough surface peak due to deformation All 4 rubbers, V RP 1.5e-4 ω LTP /(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 ω LTP when V=V RP V SP /V RP =6e-9 ω LMP /1.5e-4 ω LTP If ω LMP and ω LTP 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 = ω LTP stationary rubber simple surface sliding speed, V
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 q L to q 1 q L non-critical, q 1 needs estimating divide power by V to get shear force; hence μ stationary rubber complex surface λ 0 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 q L, q 1, wavenumbers for longest and shortest waves T q, temperature E, rubber complex elastic modulus;, Poisson s ratio v, sliding velocity σ 0, nominal normal stress
Silicon carbide 180 mesh measured displacement spectrum
SBRubber properties at 20 0 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 q L to q 1 q L non-critical, q 1 uncertain, influenced by cleanliness and debris Which q 1 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.