Nonlinear Modeling and Experimental Validation of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

Abstract

This paper describes the model integration and validation that followed the development of nonlinear models of a tire with non-uniformities, a double wishbone suspension and rack-and-pinion power steering. These submodels are integrated to investigate the effects of variation of tire, suspension and steering parameters on the transmission of tire forces acting on the wheel spindle to the steering system and vehicle chassis. The tire model is based on a rigid ring model which includes mass imbalance and balancing mass. The suspension is idealized as rigid links with seven degrees-of-freedom and the bushings are represented by spring-damper elements. The equations of motion are derived using the Lagrange multiplier method in Maple, and solved numerically using Matlab DAE solver. The steering system is idealized as a four degree-of-freedom system and considers motion of the rack, rack housing, pinion gear and steering wheel. Nonlinear compliant friction is considered between the pinion gear / rack, and the steering column / chassis interfaces. The analytical model is used to develop a quantitative measure of the relative importance of the parameters such as mass/inertia, suspension bushing stiffness and damping, torsion bar stiffness and damping, rack friction and damping, to the force transmissibility to the vehicle chassis and the steering system. Experimental results include a modal analysis, a shop-testing and road testing, which are used to cross verify the numerical simulations. The testing shows the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear variation of the nibble phenomenon with vehicle speed and tire imbalance. Results obtained from simulation matches well with the experimental measurements.