Nonlinear Modeling and Theoretical Development of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

Abstract

This paper describes a nonlinear modeling approach for a double wishbone suspension developed to investigate the nonlinear kinematics and dynamics in the closed, spatial kinematic chain configuration of the suspension. This model is linked to a nonlinear rack and pinion steering subsystem model in order to study the steering nibble (steering wheel rotational vibrations). The suspension mechanism is idealized as a four degree-of-freedom model for a power assisted rack and pinion steering system, with suspension members considered as rigid links and the bushings idealized as linear spring-damper elements. A system of relative coordinates is used in the suspension subsystem model to minimize the number of equations that would be necessary due to the large number of geometrical and kinematic constraints. The equations of motion for the analytical subsystem models are derived symbolically using Maple and solved numerically using Matlab. The results of simulation of the model subjected to a virtual Kinematics and Compliance (K&C) test are compared with the results generated by the developed ADAMS model based on the parameters obtained from a vehicle manufacturer subjected to the same virtual test. Based on the results of the virtual K&C tests and quasi static simulation of the ADAMS model and the analytical models of the vehicle suspension subsystem, the kinematics results match ADAMS model very closely.