| With the increasing complexity of mechanical engineering and the development of computer aided technology,multi-body system dynamics simulation has been widely used and paid attention to.Among them,dynamic modeling and numerical calculation are important research contents,both of which need to choose appropriate modeling methods and design more efficient and stable numerical algorithm of dynamic equations to meet the needs of practical engineering.In this paper,the differential algebraic equations corresponding to the direction vector model of multi-body system dynamics are studied,and the simulation algorithms of multi-step block scheme and L-stable block scheme are constructed.The direction vector coordinates in natural coordinates have the characteristics of flexible selection of coordinates,moderate number of coordinates,linear Jacobi matrix of constraint,constant mass matrix of equation,and no Coriolis inertial force and centrifugal force in dynamic equation.Based on these unique advantages,the direction-vector method is used to describe the multi-body system,and the differential algebraic equations with different indices are obtained.Then,the high-precision and high-stability multi-step block schemes and L-stable block schemes are constructed based on the equidistant nodes and not equidistant nodes to solve the problems.The block scheme is constructed by Taylor expansion of all variables in the equation at A certain time,and A coefficient matrix containing undetermined parameters is obtained.The undetermined parameters are obtained according to the stability requirements.The scheme is simple,easy to understand,and meets both A-stable and L-stable requirements.In this paper,a two-link manipulator and a slider crank mechanism are taken as examples to compare and analyze the method of combining direction vector with block scheme simulation,so as to provide a new method for the study of multi-body system dynamics simulation. |
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