Finite Element Dynamic Analysis Of The Rear Axle System

In this paper, a three dimensional finite element method is developed for the dynamic and vibration analysis of the rear axle system. The method allows for the dynamic modeling of several components of the axle system including the input shaft, the output shafts, the control arms, track bar, tires, bearings, bushings, and helical springs and dashpots of the suspension system. The input and output shafts, the control arms, and the track bar are modeled using three dimensional finite elements. Beam elements, each of which has two nodes and twelve degrees of freedom, are used in the finite element discretization. The formulation developed in this paper takes into account the effect of the angular velocities of the rotating input and output shafts. It is shown in this investigation that in order to model the effect of the angular velocities of the rotating shafts, a non-conventional finite element formulation must be used. This formulation leads to a stiffness matrix which is expressed explicitly in terms of the angular velocities. A set of matrices, called inertia shape integrals must be evaluated for each finite element of the rotating shafts. The inertia shape integrals of the shafts are obtained by assembling the inertia shape integrals of their elements. The bearings, bushings, tires, and helical springs of the suspension systems are modeled using discrete spring-damper elements. The carrier is treated as a rigid body which has six degrees of freedom. The carrier equations of motion are obtained using the three dimensional Newton-Euler equations. Using the Lagrangian dynamics and the finite element method, the equations of motion of the components of the axle system are developed and used to define the equations of motion of the axle system. The resulting equations are used to predict the natural frequencies and mode shapes of a model of the axle system that includes significant details. Excellent agreement was found between some of the natural frequencies predicted using the model developed in this investigation and the natural frequencies determined experimentally. A parametric study is also, performed in order to investigate the effect of the system parameters on the natural frequencies and mode shapes. Among the parameters, which are considered in this numerical investigation, is the carrier inertia, the angular velocities of the rotating shafts, the bushing stiffness, the bearing stiffness, the tire stiffness, and the stiffness of the helical spring of the suspension system.