弧齿锥齿轮机床加工参数逆向求解的算法研究  

Research of Inversion Algorithm of Machine-tool Machining Parameter for Spiral Bevel Gear

作　　者：蔡香伟[1] 方宗德[1] 

机构地区：[1]西北工业大学机电学院,陕西西安710072

出　　处：《机械传动》2015年第3期5-8,14,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51175423;51375384)

摘　　要：研究了弧齿锥齿轮小轮机床加工参数反求的算法实现问题。推导了变性法加工的弧齿锥齿轮小轮齿面方程,建立了理论齿面向目标齿面逼近的最小二乘法优化模型,采用基于置信域策略的Levenberg-Larquardt迭代算法反求小轮的机床加工参数,并与广义逆矩阵法、截断奇异值分解法进行了比较。以小轮的某种修形齿面为例,3种算法识别的齿面与目标齿面的残余偏差平法和分别为1.472 3×10-3 mm2、8.296 9×10-4 mm2、1.499 3×10-5 mm2。结果表明,相对于前两种识别算法,采用基于置信域策略的Levenberg-Marquardt迭代算法可以大大提高齿面逼近的精度。该迭代算法为弧齿锥齿轮的齿面误差修正技术及齿面主动修形设计提供了应用基础。The inversion algorithm of pinion machine-tool machining parameter for spiral bevel gear is investigated.The pinion tooth surface equation of spiral bevel gear generated by modified-roll method is deduced,the least squares optimization model of the tooth surface is established in order to obtain predesigned target surface,and it is solved by using the levenberg-marquardt method with trust region strategy,and the generalized inverse matrix method and truncated singular value decomposition method are also used to identify the machine-tool machining parameter separately.A numerical example shows the effects of tooth surface approximation,according to the three algorithms,the sum of squared errors between the identified surface and target surface is followed by 1.472 3×10^-3 mm^2,8.296 9×10^-4 mm^2 and 1.499 3×10^-5 mm^2,the result reveals that the levenberg-marquardt algorithm can greatly improve the accuracy of the tooth surface approximation with respect to the first two methods.This iterative algorithm can be used for tooth surface deviation correction and active modification design of spiral bevel gear.

关 键 词：弧齿锥齿轮 机床调整参数 齿面逼近 Levernberg-Marquardt算法 

分 类 号：TG61[金属学及工艺—金属切削加工及机床]