Rubber–Road Contact: Comparison of Physics-Based Theory and Indoor Experiments
For tire designers, rubber friction is a topic of pronounced practical importance. Thus, development of a rubber–road contact model is of great interest. In this research, to predict the effectiveness of the tread compound in a tire as it interacts with the pavement, the physics-based multiscale rubber-friction theories developed by B. Persson and M. Klüppel were studied. The strengths of each method were identified and incorporated into a consolidated model that is more comprehensive and proficient than any single, existing, physics-based approach. In the present work, the friction coefficient was estimated for a summer tire tread compound sliding on sandpaper. The inputs to the model were the fractal properties of the rough surface and the dynamic viscoelastic modulus of rubber. The sandpaper-surface profile was measured accurately using an optical profilometer. Two-dimensional parameterization was performed using one-dimensional profile measurements. The tire tread compound was characterized via dynamic mechanical analysis. To validate the friction model, a laboratory-based, rubber-friction test that could measure the friction between a rubber sample and any arbitrary rough surface was designed and built. The apparatus consisted of a turntable, which can have the surface characteristics of choice, and a rubber wheel in contact with the turntable. The wheel speed, as well as the turntable speed, could be controlled precisely to generate the arbitrary values of longitudinal slip at which the dynamic coefficient of friction was measured. The correlation between the simulation and the experimental results was investigated.ABSTRACT
The axial chromatism technique uses a white light source, in which light passes through an objective lens with a high degree of chromatic aberration. The refractive index of the objective lens will vary in relation to the wavelength of the light. In effect, each separate wavelength of the incident white light will refocus at a different distance from the lens (different height). When the measured sample is within the range of possible heights, a single, monochromatic point will be focalized to form the image. Because of the confocal configuration of the system, only the focused wavelength will pass through the spatial filter with high efficiency, thus, causing all other wavelengths to be out of focus. The spectral analysis is done using a diffraction grating. This technique deviates each wavelength at a different position, intercepting a line of CCD (charge-coupled device), which, in turn, indicates the position of the maximum intensity and allows direct correspondence to the Z height position.
Schematic of the surface-roughness power spectrum of a fractal surface with one scaling region. The slope for q1 > q > q0 is equal to 2Df − 8. qL = 2π/L, where L is the diameter of macroscopic contact area.
Schematic of the surface-roughness power spectrum of a fractal surface with two distinct scaling regions. The slope for q0 < q < q2 is equal to 2Df1 − 8, and the slope for q2 < q < q1 is equal to 2Df2 − 8. qL = 2π/L, where L is the diameter of macroscopic contact area.
Temperature dependence of complex elastic modulus of a viscoelastic material under periodic excitation, where ω is frequency, E is the complex modulus, and T2 < T0 < T1 .
Dynamic friction tester; the drive systems for the disk and the rubber sample, and the force measurement mechanisms.
Dynamic friction tester; control enclosure housing the Kollmorgen AKD drives, the FUTEK load cell amplifiers, the NI DAQ system, and the power supplies.
The viscoelastic modulus master curves for the summer tire tread compound resulting from shifting the real modulus. The reference temperature is T0 = 20 °C.
Power spectral density of surface roughness of 120-grit sandpaper. The measurements were carried out using the Nanovea JR25 optical profilometer, with a lateral resolution of 7 μm. This power spectrum is an average over the power spectra of all the individual line-scan measurements on the surface. A transition wavelength of q2 (≈2π/150 μm) was selected, which separates the macrotexture [C1(q)] and the microtexture [C2(q)] length scales. The fractal dimension was calculated as 2.69 and 2.18 for macrotexture and microtexture, respectively.
Simulated and experimental coefficient of friction with respect to sliding velocity for a summer tire tread compound on sandpaper. For all simulations, the nominal pressure σ0 = 0.4 MPa, and the background temperature T0 = 20 °C (a) The dotted lines show the cold and hot hysteresis friction coefficient values. The dashed lines represent the hot hysteresis friction coefficients for the macro- and microtexture scaling regimes. The solid line is the sum of the hot hysteresis friction coefficients of the macro- and microtexture regions. (b) The dashed line is the adhesive contribution to friction coefficient in the real contact area at maximum magnification A(q1 ). The dotted line shows the total hot friction coefficient (hysteresis + adhesion) for one scaling regime. The solid line is the total hot friction coefficient when two scaling regions are considered. The red dots represent the measured friction coefficients at room temperature (all the other depicted curves are the results of simulation).
Footprint flash temperature at the surface of rubber sliding on sandpaper. The rubber background temperature is T0 = 20 °C. The flash temperature at ζmax is about 50 °C above the rubber background temperature, whereas, at the nominal contact area (ζ = 1), the change in temperature is insignificant.
Real area of contact as a function of sliding velocity.
Effective frictional shear stress as a function of sliding velocity.
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