基于夹紧性能迭代分析的夹紧力与夹紧点一体化离散设计方法

为了保证工件加工过程的顺利进行，往往采用多重装夹对工件提供合理的夹紧力。因此，需要通过构建工件的装夹模型及其解的存在性分析方法，实现多重装夹布局夹紧性能的判断。将夹紧表面网格化为候选夹紧点的集合，自具有力封闭的第1个候选夹紧点开始，以一定步长选取相邻的两个夹紧力。根据二者力可行的异同，确定当前步长的递减系数，直至步长递减至阈值之内获取当前夹紧点的夹紧力。如此遍历至最后1个具有力封闭的节点，实现“1-夹紧力”的规划。在描述n重夹紧力为1个极径和n-1个极角函数的基础上，将n-1个极角离散为候选微角的集合。在具有力封闭的各个微角处，利用“1-夹紧力”规划算法完成“n-夹紧力”的计算。利用“n-夹紧力”规划方法和力学解析法分别计算典型二重装夹布局的夹紧力，结果表明：二者最大相对误差仅为0.979%. 通过引入离散化思想，将连续型多重装夹设计问题转化为离散型夹紧性能分析问题，不仅适合于形状复杂的工件，而且有利于自动化夹具设计的实现。

Descrete Approach to Integrated Design of Clamping Force and Clamping Point Based on Iterative Analysis of Fixturing Performance

In order to guarantee the successful machining of a workpiece,a multiple fixturing is usually used to assure proper clamping forces.A fixturing model and its analysis method of existence of solutions are formulized to judge the fixturing performance of multiple fixturing layout.A clamping surface is meshed as candidate clamping points,and then two adjacent clamping forces are selected with a given step from the beginning of the first candidate clamping point with force-closure.The decreasing coefficient of the current step can be determined according to the the similarities and differences of selected clamping forces.The clamping force at current clamping point can be obtained until the current step is less than the threshold.The planning of "1-clamping force" is completed after the last clamping point with forceclosure is found.Each polar angle can be discretized into minimum angles by describing n-clamping forces as a function of one polar radius and n-1 polar angles." 1-clamping force" planning algorithm is called to calculate the magnitudes and placements of "n-clamping forces" at each minimum angle with force-closure.Finally,"n-clamping forces" planning algorithm and analytical method are used to calculate the clamping forces for typical double fixturing layout.Results show that the maximum relative errors of "n-clamping forces" planning algorithm is only 0.979％.The proposed method can be used to transform the continuous design issue of multiple clamping forces into the discrete analysis issue of fixturing performance.Therefore,it can not only apply to the complex workpiece,but also benefit the implementation of automated fixture design.