Unified method for solving mesh problems of circular and noncircular gears (an application of connection between gradient angles in noncircular gears)

摘要

The connection between gradient angles in circular gearing (Cao, 1.987) had been presented by the author on the 7th World Congress on the Theory of Machines and Mechanisms. "Does it hold true in noncircular gearing?" had been asked by earnest audience. The answer is positive. And it is convinced that the mesh problems of circular and noncircular gears can be wholly solved in a unified method by means of three transformations, namely: 1. The transformation of point position (Use coordinates transformation of contact point) 2. The transformation of point direction (Use connections between gradient angles and between pressure angles) 3. The transformation of point curvature (Use formula of Euler-Savary) The first and third transformation have been widely used in circular gearing, but here we extend them so that they can be also used in noncircular gearing. The second transformation is proposed by the author and proved in detail in this paper. With these three transformations, plus a modified method of profile normal, the mesh problem of noncircular gears can be solved in a systematic and correct way. For example, an elliptical gear problem is included to illustrate the use of three transformations and is compared with circular gear step by step for verifying the feasibility in using unified method of solution in both cases.