基于线性规划的工件稳定性建模及其应用

工件在实现定位后，在加工过程中将要受到工件重力和切削力等外力的作用。为使工件保持定位精度与生产安全性，必须保证工件在整个加工过程中具有稳定性。系统地讨论了工件稳定性建模及其求解方法，在摩擦锥线性近似以及变量非负转换的基础上，提出了工件稳定性的定量判断准则；利用线性规划方法对工件稳定性模型进行分析。结果表明，稳定性模型不仅能够验证工件的稳定性，而且还能够分析夹紧力大小、作用点以及夹紧顺序的合理性。这种方法既适用于夹具夹持稳定性分析，也适用于机械手的抓取稳定性分析。

MODELING AND APPLICATION OF WORKPIECE STABILITY BASED ON THE LINEAR PROGRAMMING METHOD

After being located on a machine bed or a fixture, a workpiece will be subject to gravity, cutting and inertial force during the machining operation. In order to keep the locating precision and the machining safety, it is necessary to maintain the workpiece stability during the entire machining process. A general framework is established to analyze the workpiece stability. Based on the linear approximation of the friction cone and variable transformation, a quantitive criterion is established to verify the workpiece stability. The linear programming method is employed to solve the problem. Results show that the proposed method, in addition to the verification of the work-piece stability, can be used to study the feasibility of the magnitude, placement of clamping forces and clamping sequence. The method is also suitable to the analysis of the robot hand grasp stability.