Tree Topology Modeling For Vehicle Closed-loop Multibody Systems And Computational Efficiency Improvement

Computational multibody dynamics is a new subject that uses modern computer technology to study the dynamics and kinematics of multibody systems.This discipline is widely used in many fields and industries,such as vehicles,robotics,heavy machinery,aerospace,biomechanics.The purpose is to establish mathematical models of large-scale and complex multibody systems which are suitable for numerical solutions and seeking efficient and accurate numerical methods.At present,the most widely used multibody dynamics model in vehicles is established based on the global formulation in terms of Cartesian coordinates.The modeling process of the global formulation is easy to implement,because general Lagrange dynamic equations of all kinds of multibody systems（including open-loop and closed-loop systems）can be formulated by the same procedure.However,this formulation has several disadvantages such as complicated equations of motion and low computational efficiency.In order to solve the issue of low computational efficiency,Spanish scholar Javier García de Jalón proposed a double-step semi-recursive multibody dynamic modeling method in this century.This method is based on relative coordinate system and takes advantage of a topological relationship between components,which uses a set of independent relative coordinates to describe the equations of motion of the multibody systems.Thus,it has higher computational efficiency compared with those global formulations.This dissertation aims to deal with large-scale and complex multibody systems.It takes a 15-DOF sedan vehicle and several multi four-bar mechanisms as the research systems.To achieve the purpose of real-time simulation,this dissertation employs recursive kinematics and dynamics and topology theory to improve the multibody dynamics modeling method,and to develop efficient numerical computing techniques.The contents of this dissertation are summarized as follows:1.According to the detailed structure of the components and the recursive relationship of the closed-loop vehicle multibody system,a variety of vehicle multibody systems tree-topology models based on the joint-cut and rod-removal techniques are established within the framework of the MATLAB/C++platform.By performing the dynamics simulation of each multibody dynamics model,the effectiveness and high efficiency of the rod-removal technique are investigated and verified.The effects of the number of system components,joints,constraint equations on the computational efficiency is evaluated and revealed.2.According to the structure of the lower swing arm of the Macpherson independent suspension,a semi-recursive modeling approach for vehicle multibody system based on the removal of the suspension-arm is proposed.This approach describes the suspension-arm by using two connecting rods and removes them to open the closed-loops based on the rod-removal technique.Thereby the number of system components and the size of the loop-closure constraint equations are reduced,which leads to enhanced computational efficiency of vehicle simulations.3.According to features of the fourth-order Runge-Kutta(4^thRK)and Adams-Bashforth-Moulton（ABM）numerical methods,an iterative refinement technique for solving velocities and accelerations is introduced.By reusing the factorization results of constrained Jacobian matrix and generalized mass matrix,the factorization times of these large-scale matrix are reduced almost 50%.Thereby,the CPU time for solving relative velocities and independent relative accelerations are declined,which improves the computational efficiency of the middle-large multibody systems.