基于辛普森数值微分法的成型砂轮廓形设计  

Profile Design of Formed-Grinding Wheel Based on the Simpson Numerical Differential Method

作　　者：黄帅可 王战中 孔德逊 董文杰 Huang Shuaike;Wang Zhanzhong;Kong Dexun;Dong Wenjie(School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学机械工程学院,河北石家庄050043

出　　处：《石家庄铁道大学学报（自然科学版）》2022年第1期100-105,共6页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

摘　　要：随着螺杆转子加工精度要求的提高,对磨削转子用成型砂轮廓形设计精度的要求也越来越高。针对此问题,基于转子端面型线数据,运用辛普森数值微分法,并结合累加弦长参数三次曲线法和牛顿迭代法求解砂轮廓形;进而将求解的砂轮廓形与用局部3次B样条拟合法求解的砂轮廓形进行对比,结果显示用辛普森数值微分法求解的砂轮廓形更准确;随后,采用平均绝对误差和平均绝对百分比误差分别对用辛普森数值微分法和局部3次B样条拟合法求解的砂轮廓形数值进行误差分析,结果显示用辛普森数值微分法求解砂轮廓形的误差明显小于后者的误差,再次说明用辛普森数值微分法求解砂轮廓形的可行性。With the improvement of the machining precision of the screw rotor,the accuracy of profile design of the formed-grinding wheel used for grinding the screw rotor becomes higher and higher.In order to solve this problem,based on the rotor profile data,the profile of formed-grinding wheel was solved with the Simpson numerical differentiation method,combined with the cumulative chord parameter cubic curve method and the newton iteration method in this paper.Then,the profile of formed-grinding wheel calculated with Simpson numerical differentiation method was compared with that calculated with method of local cubic B-spline fitting,and the results showed that the former was more accurate.At the end,the method of mean absolute deviation and the method of mean absolute percentage error were used to analyze the errors of the profile of formed-grinding wheel designed with the method of local cubic B-spline fitting and the Simpson numerical differential method respectively,the results show that the error of formed-grinding wheel calculated with Simpson numerical differential method is smaller than that calculated with the method of local cubic B-spline fitting,so it is feasible to solve the profile of formed-grinding wheel with Simpson numerical differential method.

关 键 词：成型砂轮廓形设计 辛普森数值微分法 累加弦长参数三次曲线法 局部3次B样条拟合法 

分 类 号：TG743[金属学及工艺—刀具与模具]