圆柱齿轮传动的三维接触分析

本文用三维有限元、柔度矩阵及数学规划方法对直齿和斜齿齿轮的齿面接触状况进行了三维分析。分析时计及了轮齿变形，轴和轴承的变形，以及被计算齿轮同一轴上其它同时工作齿轮的影响，通过分析计算获得了载荷在同时啮合各齿对之间的分配，载荷在轮齿接触线上的分布，以及载荷作用下齿轮副的传动误差，为齿轮系统的动、 静强度设计提供了精确而可靠的理论依据。

3-D Tooth Contact Analysis of Helical Gears

The tooth contact analysis (TCA) of spur and helical gears can beconsidered as a plane problem 1] under ideal conditions. Under serviceconditions errors exist and the TCA becomes a non-linear 3-D problem. Foraviation gearing, high reliability is mandatory and the problem must betreated as a non-linear 3-D problem. Very recently, the finite element method (FEM) and the iterative methodhave been applied to the TCA 2],3],4]. There still exist three shortcomingsin their methods: (1) they can only solve linear 3-D problem; (2) they do notconsider deformation of supports and (3) the calculations required by themare too tedious to be used in engineering. Though for obvious reasons the 1978 paper by Conry 5] is not applicableto solution of the above-mentioned non-linear 3-D problem, his idea ofmathematical programming is highly useful. The authors combine Conry's ideawith 3-D FEM and flexibility matrix to solve the non-linear 3-D problem. The compound deformation, including the deformation of gears and theirsupports, and compound errors, including various types of mesh errors, areconsidered. A computer program has been prepared by the authors, which consists ofthe auto-generator of finite element mesh, the calculation of flexibility matrix,and the auto-arrangement and solution of mathematical programming. Onlythe parameters of gearing and the working conditions are required as input,and then the load distribution on the whole tooth face and the transmissionerror can be obtained. Therefore, the authors believe they have provided a rather complete TCAmethod for accurate design of high-strength aviation gearings.