基于工程应用的直齿圆锥齿轮啮合面的数学建模

推导基于工程应用的直齿圆锥齿轮啮合面的数学模型.以直齿圆锥齿轮的齿形按背锥展开面上的当量圆柱齿轮的齿形加工为依据,首先推导出背锥展开面映射后的空间方程,而后推导出背锥锥面方程,并根据空间方程和锥面方程进一步推导出啮合面的数学方程.该方程的推导为锥齿过渡面、齿根面、切曲线方程和几何约束方程的推导提供了理论依据,它们对形成整体锥齿实体模型是不可缺少的.该模型为锥齿轮的设计、数控加工程序设计以及工程分析（包括接触分析和载荷分配等）提供了理论基础.

Mathematics Modeling Based on The Mating Surface of Straight Bevel Gear in Project Application

The inferential reasoning based on the mathematical model of straight bevel gear mating surface in project application.Takes the tooth profile of straight bevel gear according to unfold surface of the back of bevel gear on equivalent cylindrical gears tooth profile processing as the basis,first infers the spatial equation of unfold surface of the back of bevel gear after mapping,after but infers the conical surface equation of the back of bevel gear,and further infers the mathematics equation of mating surface according to the spatial equation and the conical surface equation.The equation inferential reasoning provides the theory basis for the awl tooth transition surface,the tooth root face,cut the equation of a curve and the geometry restraint equation inferential reasoning,they are essential to formed the overall awl tooth full-scale mockup.The model provides the rationale for the bevel gear design,the numerical control processing programming as well as the project analysis(including contact analysis and load assignment and so on).