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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.

The kinematics and kinetics of a seven degree of freedom vehicle ride model with independent front and rear suspension are developed. Lagrange's equation is used to obtain the mathematical model of the vehicle. The equations of motion are transformed to state space equations in Linear Time Invariant (LTI) form. The effect of Chassis Design Factors (CDF) such as stabilizer bars, stiffness', Dynamic Index in Pitch (DIP) and mass ratio on the vehicle ride quality are investigated. The ride quality of the 3 dimensional vehicle that includes bounce, pitch, roll and unsprung masses motion is demonstrated in time domain response. The vehicle is considered as a Multi-Input-Multi-Output System (MIMO) subjected to deterministic ground inputs. Outputs of interest for the ride quality investigation are vertical and angular displacement and vertical accelerations. Numerical computer simulation analysis is performed using MATLAB® software.

Vehicle Dynamics play an important role in responsiveness of a vehicle. The performance of a vehicle depends on its ride and handling characteristics [1]. Handling is a measure of the directional response of a vehicle and one of the important characteristics from the vehicle dynamics point of view. The directional response of a vehicle depends on the dynamics of the steering system. A good steering control provides an accurate feedback about how the vehicle reacts to the road. In this paper, the powerful techniques of Bond graphs and state equations [2] are used to design and analyze the dynamics of a manual rack and pinion steering system. The author obtains the transfer function between the Angle of rotation of front tire and the Angle of rotation of steering wheel. The overall steering ratio of the bond graph modeled steering system is compared with the overall ratio of a similar vehicle to validate the model.