The Stiffness Study And Structure Optimization Of Half-tooth Master Gear

Gear is one of important transmission parts which are widely used in engineering. Gear single-flank testing and double-flank testing are two common gear measuring methods. The former method is based on tangential composite deviations of tooth flank, while another is based on radial composite deviations of tooth flank. The measuring elements tested by these two measuring methods are different, as well as the measuring instruments. So far, there’s no one measuring instrument which can complete the synchronous testing both of tangential composite deviations and radial composite deviations. Thus, an original master gear and method were presented by our research group, which realized single-flank testing and double-flank testing synchronously. Thus, the tangential composite deviations and radial composite deviations can be obtained with one measurement process, and the measurement efficiency can be improved greatly. The original master gear was comprised of two same structure half-tooth master gears whose tooth stiffness was evidently weaker than the traditional gear tooth, which will influence the measurement accuracy and the applicability of this measuring method. The main aim of this paper is to improve the tooth stiffness of half-tooth master gear in order to reduce this influence. The main research contents of this paper are as follows:By structural analysis of half-tooth master gear, it was certain that half-tooth groove depth was the main factor influencing tooth stiffness. On the basis, through deformation analyses of gear tooth cantilevered ends of half-tooth master gears, under the condition of specific parameters and different half-tooth groove depth, the change of gear tooth cantilevered end deformation with half-tooth groove depth was obtained. Then the optimal half-tooth groove depth making gear tooth cantilevered end stiffness maximum was determined. Imitating the above analysis methods, the relationships between the optimal half-tooth groove depth and number of teeth, tooth width and gear module were obtained. Then, the empirical equations between optimal half-tooth groove depth and the number of teeth, tooth width and gear module were found by data-fitting. Finally, the accuracy of the empirical equation was verified by an example.For the fact that the tooth stiffness of half-tooth master gear is evidently weaker than the traditional gear tooth, one method, assembling annular plate at gear tooth cantilevered end of the half-tooth master gear to improve the tooth stiffness, was put forward. The structure scheme, processing technology and bearing capacity of annular plate were analyzed. And the feasibility and validity of the method to improve tooth stiffness were verified by analysis of gear tooth cantilevered end deformation before and after assembling annular plate. On the basis, through analyzing the relationship between the half-tooth groove depth and the deformation of gear tooth non-cantilevered end, the structure of half-tooth master gear was improved by changing the half-tooth groove depth.On the issue that the non-uniform change of tooth stiffness along tooth width direction of half-tooth master gear, an optimization algorithm about the sizes of half-tooth groove depth, the axial thickness and size difference between inner diameter and outer diameter of annular plate was put forward in this paper. Sizes of annular plate and half-tooth groove depth, determined by the above optimization algorithm, can make the stiffness of the terminals of gear tooth cantilevered, non-cantilevered end and the middle of gear tooth cantilevered end equal. Thus, the uniformity of the tooth stiffness along tooth width direction of half-tooth master gear can be improved. Two examples of optimization algorithm under different loading modes were given in this paper.The research on the tooth stiffness of half-tooth master gear contributed to improve the practicability of half-tooth master gear in engineering. Relevant research results have been applied for patents.