并联机构静刚度特性的分析与求解研究

Analysis and Solution of Static Stiffness Characteristics of Parallel Mechanism

目的从机构的整机刚度特性入手,对3-TPT并联机构的刚度进行研究,解决并联机构刚度特性难以分析与评判的问题,为并联机构的进一步优化设计做出良好铺垫。方法运用虚功原理,对并联机构的力学雅可比矩阵进行求解;建立刚度模型,求解机构支链各部件的轴向刚度,进而得到支链刚度以及整机刚度矩阵,并对各个部件对支链刚度的影响进行分析;选取并联机构工作空间上的点,进行刚度矩阵的求解,研究矩阵的相关规律;运用最小特征值和静刚度性能商法,基于MATLAB软件进行工作空间上机构刚度分布的仿真,并对比两种评价方法的优劣。结果仿真结果表明,并联机构在z轴方向具有更高的刚度,随着远离z轴,机构的刚度不断下降,且下降速度呈现越远离下降越快的趋势。结论对于评价方法,可以在最小特征值法的基础上进行机构结构优化,静刚度性能商法则在优化结果的验证以及更深入的研究中展现更好的明晰性;对于优化设计,可以对机构x,y两个方向的刚度进行提升。

In view of the stiffness characteristic of the whole machine,the stiffness of 3-TPT parallel mechanism is studied.The problem that it is difficult to analyze and judge the stiffness characteristics of parallel mechanism is solved,and a good bedding for the further optimization of parallel mechanism design is made.The virtual work principle is used to solve mechanical jacobian matrix of parallel mechanism.The stiffness model is established to solve the axial stiffness of each part of the branch chain of the mechanism,and then the stiffness matrix of the branch chain and the whole machine is obtained.The influence of each part on the stiffness of the branch chain is analyzed.Select the points on the workspace of parallel mechanism,solve the stiffness matrix,and study the correlation law of the matrix.Two method,the minimum eigenvalue and performance quotient of static stiffness are used to simulate the stiffness distribution of the mechanism in the workspace based on MATLAB software,analyze the simulation results,and compare the advantages and disadvantages of the two evaluation methods.The simulation results show that the parallel mechanism has a higher stiffness in the z-axis direction,and the farther away from the z-axis,the faster the descending speed will be.As for the evaluation method,it is believed that the optimization of mechanism structure can be carried out on the basis of the minimum eigenvalue method,and the static stiffness performance quotient method can show better clarity in the verification of optimization results and further research.For optimal design,the stiffness of mechanism x and y can be improved.