State Space Formulation by Bond Graph Models for Vehicle System Dynamics 2008-01-0430

Modeling and simulation of dynamic systems is not always a simple task. In this paper, the mathematical model of a 4 Degree Of Freedom (DOF) ride model is presented using a bond-graph technique with state energy variables. We believe that for the physical model as described in this research, the use of a bond-graph approach is the only feasible solution. Any attempt to use classical methods such as Lagrange equations or Newton's second law, will create tremendous difficulties in the transformation of a set of second order linear differential equations to a set of first order differential equations without violating the existence and the uniqueness of the solution of the differential equations, the only approach is the elimination of the damping of the tires, which makes the model unrealistic.

The bond-graph model is transformed to a mathematical model. Matlab is used for writing a computer script that solves the engineering problem. This research concentrates on the investigation of the effect of the change of the weight distribution on the ride quality of the system, namely effect of the Dynamic Index in Pitch (DIP) on ride performance. This paper compares the effect of DIP = 0.5 (peculiar to sports car) to DIP=1 (peculiar to regular mid-size cars) on the bounce velocity, bounce acceleration, pitch velocity, and pitch acceleration on ride quality via eigenvalues, peak and steady state values. A table of main results summarizes the results of this research.