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本文以赫芝接触理论为基础,提出了求跑合后园弧齿轮接触应力的一种近似方法。园弧齿轮接触区上载荷分布规律,是个多因素较为复杂的问题,在对实际齿面接触区形状分析研究的基础上,国内外不少研究人员认为,把载荷分布按弹性力学中两个弹性体的接触理论处理为盖在椭园接触区域上的半椭球形分布较接近实际,但是,由于园弧齿轮在工作之前先经过跑合,结果直接用理论当量法曲率计算接触区尺寸所得椭园接触区半轴长可能不等于园弧齿轮的接触弧长,由于目前还没有求跑合后齿面形状及当量曲率的十分成熟的方法,特别是对跑合的机理还不十分清楚,从而给实际接触应力分析带来困难,本文经过慎密分析和深入研究,假定在跑合过程中,沿齿宽方向的当量主曲率 knτ不发生变化,(因为沿齿宽方向曲率半径较大,不致于因跑合而发生明显变化),沿齿高方向的当量主曲率 kn 发生变化,使接触区逐步扩大,最后沿整个接触弧长贴合,这是和跑合过程,跑合要求相一致的,因此,园弧齿轮的接触问题可以归结为一个这样的特殊的接触问题:已知沿一个方向的接触区椭园半轴长和另一个方向的当量主曲率,求另一个方向的接触区椭园半轴长。
Based on Höch contact theory, this paper presents an approximate method to find out the contact stress of circular arc gear after running. The distribution of load on circular arc gear is a complicated problem with many factors. Based on the analysis of the shape of the actual contact area, many researchers at home and abroad think that the distribution of load can be divided into two elasticities However, since the circular arc gear runs and runs before the work, the result is that the ellipsoid obtained by directly calculating the contact zone size by the theoretical equivalent curvature The half-shaft length of the contact zone may not be equal to the contact arc length of the circular arc gear. Since there is not a very mature method for determining the shape of the tooth surface and the equivalent curvature after running and closing, especially the mechanism of running-in is not very clear, Actual contact stress analysis difficult, this paper through careful analysis and in-depth study, assuming that in the process of running together, along the tooth width direction equivalent primary curvature knτ does not change (because along the tooth width direction of the larger radius of curvature, not to Due to run-in and significant changes occur) along the tooth height direction equivalent primary curvature kn change, so that the contact area gradually expanded, and finally along the entire contact arc length fit, which is running together Therefore, the contact problem of circular arc gear can be summarized as a special contact problem: the principal principal curvature of the equivalent of the known half-length of the contact zone in one direction and the other direction The contact area in the other direction is elliptical and semi-axial length.