Design sensitivity analysis of multibody systems with special reference to four-wheel steering.

Abstract

Sensitivity analysis methods are investigated for the optimal design of multibody systems. In order to overcome the shortcomings inherent in existing methods, a "mixed" method is developed. The beneficial features of the finite difference and the direct differentiation methods, and equations of motion in the joint coordinates are employed in this method. As a realistic application of the sensitivity analysis, a Four-Wheel-Steering vehicle with complete suspension systems and comprehensive analytical tire model is implemented. This model keeps full nonlinearity in the governing equations of motion for accuracy, and it is simulated using an existing general-purpose multibody dynamics simulation package. However, by using the transient dynamic analysis of the nonlinear model, optimal design parameters are dependent on driving scenarios. Therefore, the transient behavior of the system is represented by a series of steady state configurations. Hence, a steady state analysis procedure which finds a steady state configuration from an arbitrary initial condition is developed. By using the steady state analysis and the sensitivity analysis, the optimal steering ratios between the angles of the front and the rear wheels are obtained over various driving conditions. A steering control strategy is developed for the vehicle simulation to follow a prescribed path. Finally, the simulation results using the optimal steering ratio are compared against the results of the conventional two-wheel steering and the steering ratio based on the linear bicycle model.