Mobility Boundaries for the Wheel Normal Reaction

When a vehicle moves over uneven ground, motion of the sprung and unsprung masses causes dynamic shifting in the load transmitted to the ground, making the normal reaction in the tire-soil patch a continuously changing wheel parameter that may affect vehicle performance. At high loads, sinkage of the wheel can become high as the wheel digs into the soil. At low loads, the wheel can have difficulty acquiring sufficient traction. Additionally, steerability of the wheel can be diminished at very low loads. Controlling the damping forces in the suspension that is usually used to improve ride quality and stabilize motion of the sprung mass can result in an increase in the dynamic variation of the wheel normal reaction and cause vehicle performance deterioration. In this paper, a method is developed to establish boundary constraints on the dynamic normal reaction to maintain reasonable tire-terrain mobility characteristics. Using an inverse dynamics approach, a time history of the dynamic normal reaction in the tire contact patch is recovered from assigned kinematic characteristics of the sprung mass and wheel longitudinal dynamics. Maximum and minimum constraints identify critical areas for continued mobility on a stochastic distribution of uneven terrain modeled with a varying height profile and traction properties. Maximum values of the normal reaction are those which exceed the soil bearing capacity and cause soil damage. Minimum values of the normal reaction are those which limit the maximum circumferential wheel force and, thus, lead to excessive tire slippage and mobility loss if the resistance to motion requires more traction than the wheel can provide due to reduced friction with the ground.