基于三次NURBS曲面插值的单点线啮合齿轮副建模  

Modeling of single-point line meshing gears based on cubic NURBS surface interpolation

作　　者：陈冲[1] 谷丽瑶 朱鹏程 CHEN Chong;GU Liyao;ZHU Pengcheng(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学机械工程学院,成都610031

出　　处：《机械传动》2025年第2期56-61,78,共7页Journal of Mechanical Transmission

基　　金：中央高校基本科研业务费专项资金(2682020CX33)。

摘　　要：【目的】点线啮合齿轮齿廓方程是复杂的分段函数,运用齿轮齿廓方程建模误差较大。为了更准确地研究齿轮副啮合特性和传动参数,建立了基于三次非均匀有理B样条(Non-Uniform Rational B-Spline, NURBS)曲面插值的单点线啮合齿轮副模型。【方法】根据单点线啮合齿轮副啮合原理以及坐标系变换推导了齿面方程,利用齿面方程获得离散的齿面数据,运用三次NURBS求解离散数据插值而成的曲面控制点矩阵,利用UG二次开发和曲面的控制点矩阵对齿轮进行齿面重构,建立了齿轮副的有限元分析模型,获得齿轮副的瞬时接触线、齿面最大接触应力以及最大弯曲应力的变化曲线,验证了三维模型的准确性。【结果】结果表明,单点线啮合齿轮副主动轮在进入和退出啮合时都未出现边缘接触,且在整个周期内最大接触应力变化比较平缓,最大弯曲应力出现在从动轮和主动轮的齿根过渡曲面附近。[Objective]The gear profile equation of point-line meshing gear is a complex piecewise function,and the modeling error of the gear tooth profile equation is large.In order to more accurately study the meshing characteristics and transmission parameters of the gear pair,a gear pair model of single-point line meshing based on cubic non-uniform rational B-spline(NURBS)surface interpolation was established.[Methods]According to the meshing principle of the gear pair and the coordinate system transformation of the single-point line meshing gear pair,the tooth surface equation was derived to obtain the discrete tooth surface data,the surface control point matrix formed by the interpolation of the discrete data was solved by cubic NURBS,and the tooth surface reconstruction was carried out by using the UG secondary development and the control point matrix of the curved surface;the finite element analysis model of the gear pair was established,the instantaneous contact line,the maximum contact stress of the gear surface and the variation curve of the maximum bending stress were obtained,and the accuracy of the three-dimensional model was verified.[Results]The results show that there is no edge contact between the single-point line meshing gear auxiliary driving wheel when entering and exiting the meshing,the maximum contact stress changes relatively slowly during the whole cycle,and the maximum bending stress occurs near the tooth root transition surface of the driven gear and the driven gear.

关 键 词：单点线啮合齿轮副 齿面重构 啮合特性 接触应力 

分 类 号：TG712[金属学及工艺—刀具与模具]