Simulation Of Multibody System With Linear Graph Theory

The main task of this paper is to research the dynamic modeling, simulation,and software implementation of multibody systems. Computer simulation is acomprehensive technology, which is based on the knowledge from many relativedomains, such as biology, mechanism, mathematics, and computer graphics, database, network communication in computer technology, and so on. The use ofcomputer simulation in engineering is CAE (Computer Aided Engineering). Today,there are a lot of CAE commercial softwares in the both here and abroad. Andalmost all of them are based on the algorithm of finite element and multibodydynamics. Multibody dynamics is a kind of analysis method for multi-body systemdeveloped after 1950s. Because that many multibody dynamic method is easilyexecuted in computer and impropriate less computer resource than finite elementmethod, it became well applied rapidly.The paper analyzed and described different kind of the multibody dynamicmethods. After the research every kind of method, the author founded that, almostall the multibody dynamic method are based on the theory of vector mechanics andanalysis mechanics. Although variational method is a originative method, having alot of advantage, it still needs the development from many relative areas.Lagrangean method, which is based on analysis mechanics, is a very popularmethod in multibody dynamics area. ADAMS, DADS and many other similarcommercial softwares, which are based on Lagrangean method, are well used inboth home and abroad. However, because of the limits of analysis mechanics, theyusually meet a lot of problems when solving comprehensive three dimensionalmechanical systems, especially multiple degree of freedom systems.Vector mechanics is a kind of most intuitionistic method, especially for threedimensional systems. However, for the multibody systems which are constrainedeach other, how to build the mathematical model is a problem. Furthermore,because of based on Cartesian coordinate and Newton second law, the constrainforces, which are not exergonic, will be calculated repetitively, and so thecomputational complexity is increased and the computational efficiency isdecreased. However, the combination with linear graph theory will solve theproblems well.As a result, the method of vectorial mechanics and graph theory is used tomodel and simulate the multi-body system with. This method has many advantagessuch as visual modeling, clear topological structure, convenient forparameterization, saving computational complexity, and so on. Then, the paperdetailed illustrated the procedure of the modeling and solution for multibodysystems, including that creating the translational and rotational sub-graph, theterminal graph of the element, creating of the incidence matrix and building thecut-set matrix using vertex and circuit postulates for solution, and so on.After that, the author compared the algorithmic technique, and decided to usenumerical method for the solution of the software. And the main numerical methodincludes Newton iteration, Runge-Kutta method and so on.Using the methods above, the author compiled a simulation software, which iscompiled with the flat of C++Builder, and suited for the Windows program. Thesoftware can solve the problems for the mechanical systems with any topologicalstructure. It can build the dynamic equations automatically, delete the redundantequations, and calculate with the numerical methods. Furthermore, the software hasa friendly interface and is easy for using.Using the software the paper simulated three systems, and checked the resultout with the data that, experimental data, the result from ADAMS and analyticsolution. And so, the validity of the software is examined.The first system simulated in the paper is the pendulum shock motor vehicletesting system is a real project with FAW, the author took part in the project prepare,experiment, data capture and other works. The result of the simulation software ischecked with the experimental data, and useful for the latter experiment andresearch.The second system simulated in the paper is a double pendulum system, theresult is checked with the result from ADAMS, and the curve is close agreement.The third system simulated in the paper is a slider-crank system, and the resultis checked with the analysis solution. And then, the paper analyzed the work statusof flexible clearance restrains in a high speed situation.In general, the main research findings include that, analyzed every kind of themultibody dynamic methods and chose the method of vector dynamics combinedwith linear graph theory to modeling and simulate a mechanical system, suppliedintegrated element and restrain database, supplied the way to analyze flexibleclearance restrains. Based on the method above, the paper compiled the simulationsoftware. Although having a lot of lack, it still has some advantage in the analysisof flexible clearance restrains compared with ADAMS.