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一、前言谐波齿轮传动的啮合理论研究表明,谐波齿轮传动的理论齿形是不能用初等方法描述的数学曲线。这种理论齿形不仅求解复杂,只能获得数值解,而且在工艺上也难以实现。因而必须用一种工艺上易于实现的齿形曲线(即工作齿形曲线)取代理论齿形曲线,且又能保证两者之间的差别极小。为此,就需要采用数值逼近方法来证实工作齿形曲线选取的正确性。在[1]中业已证明,当原始曲线C为四力作用型的圆环变形曲线,柔轮采用渐开线齿形时,只要合理地选择变位系数,则用渐开线曲线作为刚轮的工作齿廓,与其理论齿形曲线间误差极小,且可满足定传动比的要求。但[1]中又指出,采用渐开线齿形的谐波齿轮传动,其正确啮合区间理论上一般不超过5°,啮合弧内的大部分区间均处于尖点啮合状态。那么,尖点啮合所引起的瞬时传动比的变化是否会从
I. INTRODUCTION Research on the meshing theory of harmonic gear drive shows that the theoretical tooth profile of harmonic gear drive is a mathematical curve that can not be described by elementary method. This theory is not only complicated to solve the tooth shape, only to obtain numerical solution, but also difficult to achieve in the process. It is therefore necessary to replace the theoretical profile curve with a toothed profile (ie working profile curve) that is easily achievable in the art and to ensure that the difference between the two is minimal. To this end, we need to use numerical approximation method to confirm the correctness of the work profile selection. It has been proved in [1] that when the original curve C is a four-force-acting ring deformation curve and the involute tooth adopts an involute tooth shape, the involute curve can be used as an involute curve Of the work profile, and its theoretical profile of the curve between the minimum error, and can meet the requirements of the fixed transmission ratio. But [1] also pointed out that the use of involute tooth-shaped harmonic gear drive, the correct range of engagement is generally not more than 5 ° theoretically, most of the intermeshing arc within the cusp engagement state. Then, the cusp caused by the instantaneous gear change will change from