Sinkage is an empirically significant factor in vehicle performance as it can result in an immobile vehicle or significant environmental damage. Bernstein first proposed a pressure-sinkage relationship in 1913, and subsequent work by Janosi and Hanamoto and Hedegus concluded that longitudinal wheel slip also plays a role in sinkage. Shinone, Nakashima, Takatsu, Kasetani, and Matsukawa identified a linear relationship between slip and sinkage on a lightly loaded tire (980 N). In this study, the effects of vertical wheel load, longitudinal wheel slip ratio, and tire inflation pressure on wheel sinkage on loose sand were investigated to relate sinkage to a vehicular operating condition. The test program in this study was conducted using the Cranfield University Single Wheel Tester (SWT) on loose, desert-like sand in the Cranfield Off-Road Dynamics facility soil lane. The SWT uses a closed loop servo-controlled hydraulic actuator to actively control vertical wheel load and twin hydraulic motors to actively control wheel speed. The SWT apparatus is mounted on an independent prime mover tractor unit, which controls forward speed. True forward speed is continuously measured against a fixed reference point and used to calculate the required wheel speed in real time to give the desired slip profile. A series of controlled load tests were conducted using a Goodyear G90 tire on a dry desert sand material. Four discrete inflation pressures (0.69, 1.38, 2.07, and 2.76 bar [10, 20, 30, and 40 psi] and four vertical wheel loads (1, 2, 3, 4, and 5 kN) were chosen to represent the operating range of the tire. Each test run consisted of a continuously decreasing sweep of longitudinal wheel slip ratio (the slip ratio was controlled to decrease linearly from 85% [driven] to −15% [braked]). Although a near-linear increase in sinkage was identified for wheel slip ratios greater than 10%, as Shinone et al. also found, the overall relationship between slip ratio and sinkage was found to be nonlinear.

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