夹具定位分析的双边二次方法

New Quadratic Method of Workpiece Positioning Analysis

传统的夹具定位分析方法都是基于点模型描述的,而不考虑工件和定位元的曲率影响,即使CARLSON提出的二次方法也只是考虑了工件局部曲率的影响,但是当定位元的局部曲率和工件的局部曲率相当时,定位元的局部曲率对夹具定位精度的影响很大。基于此,定义面—面有向距离函数,分析面—面有向距离函数的微分性质,由此推导出面—面有向距离函数的二阶泰勒展开式。在此基础上,给出夹具定位的二次敏感度方程,提出一种双边二次的夹具定位分析方法。该方法不仅考虑了工件局部曲率对定位精度的影响,还考虑了定位元局部曲率对定位精度的影响。仿真试验表明,该方法比线性方法、CARLSON的二次方法的分析精度高。

The conventional methods for fixture analysis are based on the point-kinematic model,which ignores the curvatures of workpiece and locators.Even if CARLSON presented a quadratic method considering the curvature of workpiece,the effect of locators＇ curvatures should not be neglected especially when the locators＇ curvature is large with respect to the workpiece curvature.The signed distance function from surface to surface is defined,the first and second differential properties are analyzed and its 2nd Taylor expansion is derived.Then the new quadratic sensitivity equations are derived and a new method of fixtures locating analysis is presented.The proposed method considers not only the curvature of workpieces but also that of locators.The examples show that the proposed method has higher precision than the linear method and the CARLSON＇s method.