基于力的存在性与可行性的夹紧力变向增量递减规划算法

根据工件的静力平衡条件与工件-装夹元件之间接触力的方向约束,建立工件装夹方案的力学模型。进一步结合线性规划技术,构建力的存在性分析模型及其求解方法,实现夹紧力是否有解的判断。针对夹紧力有解这一条件,由装夹方案力学模型与线性规划技术推导出力的可行性分析模型及其判断标准,实现给定的夹紧力是否合理的判断。考虑夹紧力的取值范围,以一定步长正向从最小值开始取值,根据当前值与上一次取值之间可行性的差异,确定下一次取值的步长及其方向;若可行性相同则以相同步长继续正向取值,否则以一半步长、反向取值,直至步长的绝对值在阈值范围之内,构建夹紧力变向增量递减的规划算法。该算法将连续型的夹紧力设计问题转化为离散型,不仅利于计算机实现夹紧力的自动化设计,而且还适合于形状复杂的工件。

Planning Algorithm of Clamping Forces for Workpiece Fixturing Scheme Based on Existence and Feasibility of Forces

According to the direction constraints of contact forces between the workpiece and fixturing elements, the static equilibrium condition of the workpiece is considered to establish the fixturing model. In connection with the linear programming technology, the existence model of the force and its solution trick are further formulated to judge whether the existence model has solutions for the independent variable of the clamping force. Under the condition that the clamping force has solutions, the feasibility model of the force feasibility and its judgement criterion are derived form the fixturing model and the linear programming technology. The feasibility model can be used to validate whether the given clamping force is acceptable. With consideration of the value range, the clamping force can be selected as the minimum value with a certain step along the positive direction. According to the feasibility difference of the current selected clamping force with the last one, the step and its direction can be determined for the next selection. If the feasibilities are same, the next clamping force is selected with the same step along the same direction. Or else, it is chosen with the half step along the negative direction. The feasibility of the selected clamping force is iteratively validated until the absolute value of the step is not more than the given threshold value. Thus, the half step with the reverse direction planning method of the clamping force can be suggested to approximate the true clamping force. The proposed method can transform the continuous design problem of clamping forces into the discrete one. Therefore, it can not only benefit the development of computer aided clamping force design, but also apply to the complex workpiece.