中文摘要：

基于齿轮啮合原理,从变厚齿轮的加工原理出发,采用齐次坐标表达式首先建立了齿条刀在其法平面内的数学模型,然后运用坐标矩阵变换关系将其转换到端面坐标系内,进而运用齿条的节平面与齿轮的分度圆柱为无滑动的纯滚动关系,基于齿条刀与变厚齿轮之间的相互啮合关系推导出了变厚齿轮的参数化数学模型,并在此基础上基于变厚齿轮啮合的连续切触条件提出了变厚齿轮传动的啮合模型,该模型可以用于模拟交错轴、平行轴及相交轴的变厚齿轮传动,为变厚齿轮传动啮合特性、接触特性的进一步研究提供了理论基础。

英文摘要：

Homogeneous coordinate is adopted first to establish a mathematical model of rack cutter and conical involute gear based on theory of gear meshing and machining of conical involute gear,which will be then transformed into the end coordinate system by applying coordinate matrixing.After that a parametric mathematical model for the conical involute gear is deduced based on meshing between the rack and the conical involute gear by adopting nonslipping pure rolling between pitch plane of the rack and graduated cylinder of the gear.Based on continuous contact of the gear meshing,a meshing model for the conical involute gear transmission is proposed.The meshing model of conical involute gear can be used to simulate the conical involute gear with crossed,intersected and parallel axes,which provides effective theoretical basis for further study on the engagement properties and contacting characteristics of conical involute gear transmission.