一种矩阵秩运算的自由曲面轮廓度评定方法  

Tolerance Evaluation of Free Surface Based on Matrix Rank

作　　者：黄美发[1,2] 丁国臻 唐哲敏 江艳燕 HUANG Mei-fa;DING Guo-zhen;TANG Zhe-min;JIANG Yan-yan(School of Mechanical and Electrical Engineering,Guilin University of Electronic Technology,Guangxi Guilin 541004,China;Guangxi Key Laboratory of Manufacturing Technology,Guangxi Guilin 541004,China;Beihai Campus,Guilin University of Electronic Technology,Guangxi Beihai 536005,China)

机构地区：[1]桂林电子科技大学机电工程学院,广西桂林541004 [2]广西制造系统与先进制造技术重点实验室,广西桂林541004 [3]桂林电子科技大学北海校区,广西北海536005

出　　处：《机械设计与制造》2022年第6期184-188,共5页Machinery Design & Manufacture

基　　金：国家自然科学基金项目(51765012);桂林电子科技大学研究生科研创新项目(2019YCXS011)。

摘　　要：为了能够提高自由曲面轮廓度评定的精度与效率,提出一种将空间齐次坐标变换矩阵与刚体运动学相结合,从而保证测点集始终在理想零件模型的边界作用下向最小区域变动,并通过方程组解的特性来模拟实际量具测量过程的评定方法。采用系数矩阵与增广矩阵的秩分析每个测点的运动情况来确定每一阶段测点集的变动方向,依据各阶段测点集的自由度来判断评定过程是否满足终止条件,最后通过使用螺旋桨叶片自由曲面为工程实例来验证该方法的有效性。In order to improve the precision and efficiency of evaluating the profile of complex curved surface,an evaluation method is proposed,which combines the spatial homogeneous coordinate transformation matrix with rigid body kinematics,ensures that the measuring point set always changes to the minimum area under the boundary action of the ideal part model,and simulates the actual measuring process of measuring tools through the characteristics of the equations solution. The rank analysis of coefficient matrix and augmented matrix is used to determine the change direction of the measuring point set at each stage. According to the degree of freedom of the set of measuring points in each stage to determine whether the evaluation process meets the termination conditions. Finally,the validity of the method is verified by using the free surface of propeller blade as an engineering example.

关 键 词：自由曲面轮廓度 齐次坐标变换 刚体运动学 矩阵秩运算 

分 类 号：TH16[机械工程—机械制造及自动化] TH161