At present, the commonly used spiral bevel gears are mainly Gleason system represented by Gleason company and equal height gear system represented by orecon company in Switzerland. Among them, Gleason spiral bevel gears generally have better strength performance. Gleason gear system has great advantages both at home and abroad. This paper is based on Gleason spiral bevel gear.
Since Gleason invented spiral bevel gear and first put forward the meshing theory of spiral bevel gear in the 1940s, for the consideration of commercial interests, Gleason blocked the complete technology of spiral bevel gear made by Gleason, forcing China to make a lot of exploration on these contents. In the early 1970s, China organized a number of scholars, professors and scientific research institutes to study Gleason technology, and listed “Gleason complete set of technology research” as a key topic for research, and achieved outstanding research results. Among them, Professor Yan Zhida and Professor Wu Xutang systematically studied the mathematical basic theory of the meshing principle of spiral bevel gears, and deduced the induced normal curvature formula of the conjugate surface of gears, which laid a solid foundation for a thorough understanding of Gleason technology. Professor Zheng Changqi and Professor Zeng Tao also studied the machining principle of spiral bevel gear. After the “Seventh Five Year Plan” and “Eighth Five Year Plan”, China has preliminarily mastered the theoretical basis and processing principle of Gleason spiral bevel gear, and established the technical and industrial system of spiral bevel gear.
With the development of modern industry, aviation, aerospace and automobile have higher and higher requirements for the dynamic performance of spiral bevel gears. How to obtain spiral bevel gears with low vibration and noise and high reliability and improve the dynamic performance of spiral bevel gears become more and more important. Therefore, it has attracted extensive research by experts and scholars at home and abroad.
In 1978, Gleason company published the principle and method of tooth surface contact analysis (TCA). Without considering the factors such as loading deformation and error, the shape and position of tooth surface contact spots were simulated by computer using the tooth surface meshing principle and machining principle. Chinese scholars have also studied TCA method one after another. However, since TCA method is based on ignoring the load and only analyzes the dynamics from the perspective of spatial geometry, this method is difficult to meet the requirements when it is necessary to conduct a more in-depth study on the vibration and noise of spiral bevel gears.
In 1981, krezer published the principle and method of contact analysis of loaded tooth surface of spiral bevel gear (LTCA). On the basis of TCA, considering the loading situation and using the contact principle of spatial curved surface, krezer calculated the contact spot and transmission error of spiral bevel gear tooth surface, and qualitatively judged the gear vibration according to the shape and position of contact spot and experience. After that, this dynamic analysis method has been studied and improved at home and abroad. However, the method of judging the vibration of spiral bevel gear by using contact spot and transmission error has three shortcomings: first, the position and shape of contact spot is a fuzzy concept, which can not quantitatively judge the vibration performance of spiral bevel gear; Second, because the transmission error does not consider the component of tooth meshing cycle, it is not completely accurate to judge the vibration performance of spiral bevel gear by transmission error; Third, this research method still belongs to the category of static research and does not involve dynamic analysis.
Using the concentrated parameter method to establish the dynamic model of gear system and solve the multi degree of freedom vibration equation can quantitatively study and analyze the vibration response of gear, which has high research value. Since tuplin first proposed the gear dynamics model, a new era of gear dynamics research has been created. The gear transmission system has been regarded as an elastic mechanical vibration system. Based on the vibration theory, the dynamic characteristics of the gear system under the effects of transmission error, time-varying meshing stiffness and meshing impact are analyzed. After that, people gradually improve the analysis model of gear system dynamics, and gradually develop from linear vibration model to nonlinear vibration model, which makes the research of gear dynamics more in-depth. Kahraman studied spur gear, proposed a dynamic vibration equation considering transmission error and tooth side clearance, and then solved it by harmonic balance method, and analyzed the nonlinear dynamic characteristics of gear system. Then Gosselin C and others introduced this method into the dynamic analysis of spiral bevel gears. Domestic scholars have also done a lot of research on the method of solving the dynamic equation. Wang Sanmin et al. Considered the time-varying meshing stiffness and ruler side clearance, established the 8-DOF nonlinear dynamic model of the spiral bevel gear transmission system, and then solved the equation by using the a operator algorithm, obtained the dynamic response of the spiral bevel gear system, and found the phenomenon of chaos Jump phenomenon of relative rotation error. Wang Lihua et al. Established an 8-DOF nonlinear dynamic model of spiral bevel gear transmission considering transmission error, ruler side clearance and time-varying meshing stiffness by using the centralized mass method, solved the dynamic equation by using the 4-5 order Runge Kutta variable step numerical integration method, and analyzed the dynamic characteristics of spiral bevel gear system.