Constructing Equations of Motion for a Vehicle Rigid Body Model

Abstract

This paper focuses on generating equations of motion for a Vehicle model. The generated equations can be used for rigid body analysis such as vibration analysis, frequency domain analysis, and time domain analysis. The paper starts with the equations of motion of a 6- degree-of-freedom (DOF) system and demonstrates detailed approach in building the equations. Next, the equations of motion are built for a 12-DOF vehicle model, which can be used as an approximated Vehicle model in most cases. Finally, the rigid body of an accurate Vehicle model is created and the equations of motion are constructed following the presented method. Nomenclature efficient rigid body models and used them for perturbation analysis and simulation of systems with frictional contacts. Hegazy et. al. (2) presented a complicated vehicle model for nonlinear rigid body analysis. This model had 94 degrees of freedom and comprised front/rear suspensions, steering system, wheels/tires, and vehicle inertia. The model was successfully used for the vehicle handling analysis. Zhang et. al. (3) used flexible and rigid beams to create a vehicle model which was used for road surface analyses in order to find dynamic properties of the vehicle chassis/suspension system. Pereira et. al.(4) presented a multibody dynamic model for train vehicles and constructed formulations based on it. The model and the formulations were used for crashworthiness analysis and design of the train vehicles. Mousseau et. al. (5) successfully developed a comprehensive vehicle dynamics model for simulating the dynamics response of ground vehicles on different road surfaces. In their research, the multibody system simulations (MSS) program was used to simulate the vehicle and a nonlinear finite element model was used for the tires. Lee et. al. (6) created a computer model for a vehicle system and used it for frequency response analyses. The computer model consisted of vehicle body, suspension systems, and tires. A coupled formulation is also obtained for the vehicle model by using the modal synthesis technique. Hunt (7) devised a method of creating a multi-axle vehicle model and used this model to represent all vehicles on the road for vibration analysis. The effects of vehicle mass, speed, and wheelbase on its ground vibration were discussed. Ibrahim et. al. (8) applied finite element method to create a truck frame model in order to analyze the vehicle dynamic responses. The effects of the frame flexibility on the ride vibration behavior of trucks were investigated through the FE model.