Study On Manufacturing Hypoid Gears By Generating-line Method

Hypoid gears are widely used to transmit crossed-axis power and motion in vehicles (such as the rear drive-axles of passenger cars and trucks), engineering machineries, ships, aircrafts and other areas. Because of the similarity of the geometrical relationship between hypoid gears and spiral bevel gears, the current methods and machines which are commonly used to manufacture spiral bevel gears can be used to manufacture hypoid gears after calculating and adjusting, and the gear cutting system, which consist of face milling and face hobbing and are used by Gleason Works, is gradually formed. However, the tooth profile curves of spiral bevel gears which are manufactured by face milling or face hobbing are not ideal spherical involutes, so there are theoretical errors on the tooth surfaces. The effects of the error are: (1) transmission ratio is not constant; (2) modification and adjustment of tooth surfaces are complex; (3) designing and manufacturing need to take a longer period; (4) gears can not be interchanged unless in the same batch. Therefore, in order to reduce to effect of the error, the parameters of machine tools and cutting tool need to be modified and improved continuously.Based on the generating principle of spherical involute and the theory of conjugated tooth surfaces, we have proposed a new method of cutting involute gears called generating-line method. This new method can be used to process ideal spherical involute spiral bevel gears that the transmission ratio is constant and gears can be interchanged even in different batches. Moreover this method makes the calculation and adjustment of machine tools settings relatively simple, the processing efficient relatively high, and the controlling of tooth contact areas easily.In order to expand the applying scope of the generating-line method, this paper researched the theory of manufacturing hypoid gears by this new method. Based on analyzing the basic geometry of hypoid gears, the base cones and base planes which are necessary for generating-line method were established, and the geometrical and kinematical relationships between pinion and gear generating lines were proposed, then the formulas of the geometrical parameters of the base cone were studied. Accordingly the basic principle of manufacturing hypoid gears by generating-line method was built.On basis of the process of generating tooth surfaces by this principle, the mathematical model of tooth surfaces was established. Based on the space engagement principle, this paper proved that the pair of tooth surfaces could conjugate exactly in point contact. And then the mathematical model of each side of pinion and gear generating lines which the shape of gear is known as straight line or circular arc was built on basis of the tooth surfaces model.In order to study the processing program of cutting each side of hypoid gears, on the basis of the principle of cutting spiral bevel gear tooth surfaces, the author researched the method of determining the cutting areas and avoiding over-cutting in the condition of the generating lines are straight line, circular arc and plane general curve respectively, then promoted this method to hypoid gears, and proposed the method of determining the cutting areas of each side of pinion and gear and the processing program of cutting. And then the author researched and gathered the necessary motion and structure of machine tools, and built a commonly used six-three axis CNC machine tools to manufacture spiral bevel and hypoid gears by generating-line method.Based on the theoretical studies mentioned above, reference to a pair of Gleason hypoid gears which the designing parameters were known, the author calculated the base cone parameters, cutting areas of each tooth surfaces of pinion and gear, and calculated the equations of gear generating lines and the theoretical pinion generating lines in the condition of setting the gear generating lines as a straight line or circular arc respectively. Because of the theoretical pinion generating lines which were plotted in Matlab looks approximate straight lines or circular arc, in order to improve the cutting efficiency by using the cutting theory of straight line or circular arc generating lines, the methods of substituting simple curves for the complex theoretical pinion generating lines and estimating the errors of substituting were proposed. As the radius of circular arc substituted generating lines were usually not integer, in order to serialize the cutting tool radiuses and simplify the structure of machine tools, the author proposed an optimizing method of rounding the radiuses of circular arc substituted generating lines. It can be seen from the results of the calculating example: the method of substituting generating lines could control the errors under the area of elastic deformation of tooth surfaces, and the method of optimizing substituted generating lines could control the residual errors less than 1% and could make a further optimization, therefore the methods of substituting and optimizing generating lines were both feasible.Through theses studies, the author extended the suitable range of generating-line method to hypoid gears which usually do not have the concept of tooth profile, and accumulated lots of important research data for the further machine tools research and cutting experiments, and also provided a new way to study generating-line method for manufacturing other types of gears. Throughout the full text of this paper, the innovative research works mainly shown in the following areas:1. Built the base cones and base plane for hypoid gears based on the commonly used geometrical relationship, and determined the plane conjugated relationship between the generating lines of pinion and gear, therefore the basic conditions and elements of manufacturing hypoid gears by generating-line method were provided2. Proposed the method of using the theory of manufacturing spiral bevel gears by generating-line method to process hypoid gears. As the theoretical basis and practical experience of manufacturing spiral bevel gears by generating-line method were much more, transforming hypoid gears cutting process to spiral bevel gears could simplify the problems and avoid redundant researches.3. Proposed methods of substituting generating lines and optimization of substituted generating lines. The method of substituting generating lines could avoid cutting the pinion as the generating line was a plane general curve, and would help to play the strengths of generating-line method. The method of rounding optimization of substituted generating lines made the cutting tool radius serialization possible in the further studies of the machine tools, and would help to simplify the design of cutting tools and the configuration of machine tools.