基于鞍点规划理论的圆度及球度误差最小区域法评定新解法  

New Solving Method for Roundness and Sphericity Error Based on Saddle Point Programming Theory

作　　者：王强 汪伟 张鑫 武鸿超 Wang Qiang;Wang Wei;Zhang Xin;Wu Hongchao(School of Mechanical and Electronic Engineering,Jingdezhen Ceramic Institute,Jingdezhen,Jiangxi 333403,China;不详)

机构地区：[1]景德镇陶瓷大学机械电子工程学院,江西省景德镇市333403

出　　处：《工具技术》2022年第11期141-146,共6页Tool Engineering

基　　金：国家自然科学基金(52065028,51705224)。

摘　　要：在形位公差的圆度和球度误差评定方法中,最小区域法是最符合国标中定义形位误差的方法之一。针对目前基于最小区域法建立的数学模型以及相应的求解方法存在局部收敛以及求解迂回等问题,建立了圆度和球度误差评定的鞍点规划模型,并基于鞍点规划理论的最小条件建立了鞍圆和鞍球面误差求解的新算法,通过简单几何分析和有限代数计算即可确定符合最小区域法评定原则的圆度、球度误差以及相应鞍圆、鞍球面的位置和参数。相比于传统优化算法,本文提出的方法避免了优化方法对初始值的依赖性,具有较高的求解稳定性。Among the evaluation methods for roundness and sphericity errors, minimum zone method is the most matching to the definition of form and position tolerance in the national standard.However, current mathematical models and corresponding solving methods have some problems, such as local convergence and circuitous solving procedure.The saddle point programming model is established to evaluate the roundness and sphericity erorrs.A new solving algorithm based on the minimum conditions of saddle point programming theory is presented.The roundness and sphericity errors can be conveniently obtained through simple geometrical analysis and algebraic calculus, as well as the position and dimensions of the saddle circle and saddle sphere.Compared with the traditional optimization methods, the method presented in the paper can prevent the dependence on the initial points, and has high solving stability.

关 键 词：圆度 球度 鞍点规划 最小区域法 优化 

分 类 号：TG801.3[金属学及工艺—公差测量技术] TH115[机械工程—机械设计及理论]