A Stiff Equations Solution Method Of Multi-body System Dynamics Based On Quantized State System

Multi-body system dynamics provides powerful theoretical tools and technical support for dynamic performance evaluation and optimization of a large number of mechanical systems in the fields of machinery,aviation,aerospace,weapons,robots and so on.It is one of the hotspots and difficulties in the field of mechanics.In the process of multi-body system motion,the dynamic equation is rigid because of the large difference of characteristic parameters between different components,or the coupling between the large-scale motion of flexible body and the small elastic deformation of the component itself.The solution of this kind of rigid equation is one of the difficult problems in dynamic control of multibody systems.At present,the common solution of dynamic equation of multi-body system is numerical integration method based on time discretization.When the dynamic equation is rigid,considering the stability ofcalculatoon and other factors,it is necessary to use implicit algorithm compulsorily,which makes the process cumbersome and complex,and the calculation cost significantly increased.To solve this problem,based on the Q uantized State System(QSS),a multi-point correction explicit algorithm(MCQSS)is proposed in this paper.The algorithm uses two hysteretic quantization functions to discretize the state variables of the system,and introduces the idea of multi-point correction to modify the derivatives of the state variables,which makes the time nodes of each step more precise and effectively improves the accuracy and stability of the algorithm.At the same time,it retains the characteristic that the explicit calculation of QSS algorithm does not need iteration.The simulation efficiency of the algorithm is improved.In order to verify the effectiveness of the proposed multi-point correction oxplicit algorithm based on quantized state system in the process of multi-body system dynamics solution,the feasibility of the algorithm is proved by the simulation of double pendulum system.After that,the application of the boom system of concrete pump truck,a complex rigid-flexible coupling multi-body system,is analyzed.As a typical multi-body system,the arm bars of the boom system have obvious elastic deformation in the course of motion.Therefore,the flexible dynamic equation of the boom system has strong non-linearity or rigid-flexible coupling,which makes the dynamic equation present rigid characteristics.Through numerical solution of flexible boom system,MCQSS algorithm is compared with traditional numerical integration method and QSS method in terms of simulation accuracy and simulation efficiency.The results show that MCQSS algorithm can effectively improve simulation accuracy while ensuring simulation efficiency.The performance of MCQSS algorithm is superior to traditional method and QSS method.