基于更新Kriging模型的双重螺旋法加工齿面的重构方法

Tooth surface reconstructing method of spiral bevel gear generated by duplex helical method based on renewal Kriging model

针对双重螺旋法加工的螺旋锥齿轮采用常用样条曲线重构误差较大、影响啮合仿真精度的问题,基于更新Kriging模型提出一种提高齿面重构精度的方法。根据双重螺旋法成型原理,推导大、小轮齿面方程,由此提取出小轮齿面的型值点,并对其归一化,然后基于高斯核的Kriging模型进行重构,以复相关系数为约束条件,评判重构结果、更新样本点集,通过循环Kriging模型得到控制顶点,最后通过蒙面法重构齿面。以双重螺旋法加工的螺旋锥齿轮小轮齿面为例,比较基于更新Kriging模型的重构方法与常用样条曲线所建模型的重构精度。研究结果表明:更新Kriging模型提高了齿面重构精度。

To overcome the impact of large errors on the precision of reconstruction in the tooth surface of outputted model after simulation processfor spiral bevel gears generated by duplex helical method,a fitting method based on renewal Kriging model was proposed.According to the forming principle of duplex helical method,the tooth surface equations of gear and pinion were established,and thus the initial data points on the tooth surface of pinion were extracted.Then they were treated with normalization,and fitting by the model of Kriging with the Gaussian kernel.Taking multiple correlation coefficients of the fitting data as constraints,the results of reconstruction were judged,and then the set of sample points was renewed.With this fitting method being circulated,control vertexes were obtained.Finally,the reconstruction of tooth surface was accomplished through skinning method.Taking a pinion tooth surface of spiral bevel gear drive manufactured by duplex helical method for example,the accuracy of reconstruction models generated by this method was compared with that of the common spline curve fitting method.Ther esults show that the precision of the proposed ideas has goocl superiority.