The theory of spiral bevel gear was put forward by E. wiidhaber, M.L. Baxter and other outstanding scientists of Gleason company in the United States. In 1874, William Gleason, the founder of Gleason company, invented the world’s first bevel gear planer. In 1913, the spiral bevel gear machining machine tool with circular arc longitudinal tooth line was successfully developed and began to be used in the automotive industry in 1915. Then, with the development of the automotive industry and other industries, the Gleason spiral bevel gear manufacturing system, which guided the pioneer of the world spiral bevel gear manufacturing industry, was formed.
In the late 1950s, China received the assistance of the former Soviet Union and introduced the manufacturing technology of spiral bevel gears made by Gleason. China’s spiral bevel gear processing machine tools were produced by Tianjin No. 1 machine tool factory, and China’s standard and complete equipment of spiral bevel gears based on Gleason system were formed. In the 1970s, the former Ministry of machinery industry organized many domestic scientific research institutes and universities to tackle the key problems of Gleason spiral bevel gear technology, which not only successfully decoded Gleason technology, but also had innovation and development. In this work, professors Zheng Changqi, Zeng Tao, Wu Xutang, Dong Xuezhu, Wang Xiaochun and Liang Guiming have laid a foundation for the development of spiral bevel gear technology in China. Until today, these technologies still play an important role in China’s spiral bevel gear manufacturing industry.
Based on the “local conjugate method”, the traditional Gleason technology first cuts out the gear tooth surface according to a certain method, selects a calculation reference point on the gear tooth surface, and determines the first-order and second-order contact parameters such as position vector, normal vector and normal curvature of the reference point of the small gear tooth surface completely conjugate with the gear tooth surface by using the parameters of the generating wheel of the large wheel, and then modifies the normal curvature of the reference point of the small gear tooth surface according to the requirements of the contact area, Determine the processing parameters of small wheel gear cutting. Zheng Changqi studied the design and machining of spiral bevel gear, deduced various calculation formulas of spiral bevel gear tooth contact analysis, and expounded the application method of local conjugate principle in determining tooth surface contact spot, V / h adjustment value and motion curve. Zeng Tao discussed the “pitch analysis method”, which reduced the blank design and tooth cutting calculation of spiral bevel gear to the calculation of the pitch parameters and node curvature of an quasi hyperbolic gear, and thus deduced all the formulas of each calculation card of Gleason company. Using the principle of equidistant conjugate surface, Gao yetian et al. Expounded the compiling principle and method of Gleason’s spiral bevel gear modification machining adjustment card. Wu Xutang studied the basic principles and corresponding machine tool adjustment of tool inclination half development, tool inclination full development, denatured half development and denatured full development of hypoid gear. The results obtained are the same as those calculated by Gleason calculation card. Dong Xuezhu studied a simple calculation method of cutting adjustment with the center of the contact area of the tooth surface as the reference point, and applied it to the machining methods of spiral bevel gear, such as tool inclination half development, tool inclination full development, denatured half development, denatured full development and so on.
The traditional Gleason technology is very difficult to determine the reasonable curvature correction amount of tooth surface reference point. It must be corrected repeatedly to obtain satisfactory meshing performance, and the calculation is very cumbersome, which is difficult for ordinary technicians to master. In the late 1970s, Professor Litvin proposed the “local synthesis method” gear cutting technology independent of Gleason technology. Firstly, preset the second-order contact parameters of three tooth surfaces, namely, the first derivative of transmission ratio, the contact trace direction of gear tooth surface and the length of the long half axis of instantaneous contact ellipse, and then deduce the principal curvature and principal direction of the reference point of small gear tooth surface by using the relationship between the principal curvature and principal direction of point contact tooth surface, Determine the processing parameters of the small wheel. Using the local synthesis method, the meshing performance of spiral bevel gear pair at and near the reference point can be effectively pre controlled. In addition, Professor Litvin also proposed a preset parabolic transmission error to absorb the linear transmission error caused by installation error and reduce the vibration and noise of spiral bevel gear pair. The local synthesis method can pre control the meshing characteristics near the reference point of the tooth surface, but the meshing performance of the tooth surface area far from the reference point can not be controlled, so there will be serious bending of the contact trace and drastic changes in the length of the long semi axis of the contact ellipse, resulting in third-order or higher-order contact defects such as diamond, fishtail, fan, triangle and trapezoid in the tooth surface contact area.
Professor Wang Xiaochun established the relationship between the second-order and third-order geometric parameters of two line contact conjugate surfaces, and gave the specific calculation method; The curvature tensor and moving frame method are used to analyze the third-order contact of the surface meshed by two points; The third-order contact characteristics of two point meshing tooth surfaces during V / h test are analyzed; The third-order contact parameters of spiral bevel gear are optimized by using the redundant optional parameters of the machining machine tool, and the overall meshing characteristics of the tooth surface are controlled by the third-order contact parameters of the reference point, so as to realize the ideal contact performance in the whole transmission process. This method is called the third-order transmission performance pre control method. This method is a very effective tool for analyzing, researching, designing and manufacturing high-quality local point contact tooth surface; Moreover, based on the third-order contact theory of tooth surface, the calculation formula of the sensitivity of the contact point position of point contact tooth surface to installation error is deduced; Furthermore, the design method of low noise and low sensitivity transmission performance of spiral bevel gear is proposed. In this method, the parameters related to the error sensitivity of gear pair are selected from the third-order contact characteristics as the third-order optimization objective, and the assignment principle is given; The third-order contact analysis theory is an effective tool to study and manufacture high-quality local point meshing tooth surface. Professor Fang Zongde introduced the local synthesis method into China and proposed the global optimization design based on local synthesis. Firstly, the first-order and second-order contact parameters of the reference point of the tooth surface are pre controlled. At the same time, considering the contact marks and transmission errors of the spiral bevel gear pair when meshing at the small end, middle end and large end, the third-order contact defects of the spiral bevel gear pair are eliminated by optimizing the optional processing parameters.
The shape and amplitude of transmission error curve and the shape of tooth surface impression directly affect the motion characteristics, transmission efficiency and bearing capacity of spiral bevel gear pair, and have an important impact on the vibration, noise and working characteristics of spiral bevel gear pair. Stadtfeld h J. and Pei Yu Wang proposed to replace the traditional quadratic parabola transmission error with a high-order transmission error curve to improve the dynamic performance of spiral bevel gears. Alfonso Fuentes and Litvin proposed to design the tooth surface impression as a straight line on the basis of local synthesis method to reduce the sensitivity of tooth surface installation error; The amplitude of geometric transmission error at the conversion point of tooth pair is controlled to reduce the vibration and noise during meshing; By optimizing the second-order and third-order denaturation coefficients of the small wheel, the tooth mark and transmission error amplitude are controlled. Wu Xuncheng and others put forward the active design method of tooth surface based on functional requirements. Given the equation of transmission error and the track of tooth surface impression, the first-order and second-order parameters of tooth surface can be designed. The contact trace in the process of tooth surface meshing and the size of the long axis of instantaneous contact ellipse can be designed directly, and the high-order acceleration can be designed according to the needs; Thus, the transmission error curves with various change laws and shapes are obtained, so as to obtain the required tooth surface. The tooth surface obtained by this design can only be realized by using the full numerical control spiral bevel gear machine tool. Su Zhijian et al. Proposed the design of hypoid gear based on the parametric representation of tooth surface. NURBS (non-uniform rational B-spline) surface is constructed according to the coordinates of discrete points of tooth surface. According to the active design principle of hypoid gear, the key technologies of NURBS representation of known tooth surface and designing unknown tooth surface under the conditions of tooth surface contact trace and transmission ratio function are solved. Yang Hongbin, Zhou Yanwei and Deng Xiaozhong put forward the design method of high coincidence spiral bevel gear and carried out experimental research. Through the inclination of the contact path direction of the tooth surface, the coincidence degree is increased, which can effectively improve the dynamic characteristics of spiral bevel gear and improve the tooth strength, so as to improve the stability and bearing capacity of meshing transmission of spiral bevel gear pair. Wei Bingyang and others put forward the design of high-order transmission error. Combined with the bearing transmission error, the spiral bevel gear has good dynamic performance and relatively low error sensitivity under different load conditions. Cao Xuemei and others put forward the active design method of the tooth surface of spiral bevel gear. Combined with the “local conjugate method” and “local synthesis method”, it can ensure that the tooth surface can meet the requirements of the pre-designed transmission error and tooth surface contact path in the whole meshing process, so as to achieve the whole process control of the meshing quality of the tooth surface.