The original spiral bevel gear design was based on geometry and kinematics. Because spiral bevel gear is a load-bearing component in mechanical components, in order to further improve the performance of spiral bevel gear, mechanical analysis was also introduced into the research field of spiral bevel gear. Therefore, the strength analysis of various spiral bevel gears is an important research content for gear designers. The traditional strength analysis of spiral bevel gear is a semi analytical method based on experiment. The theoretical basis of contact stress calculation is Hertz contact theory. Hertz contact theory contains several assumptions, mainly including that only slight deformation occurs in the contact area, the contact area is oval, the contacting object is regarded as an elastic half space, and only distributed vertical compressive stress acts on the contact surface. Based on the above assumptions, Hertz obtains the contact stress calculation formula. Since Hertz contact stress calculation formula is an approximate calculation formula, in practical application, it is generally necessary to modify the formula according to the characteristics of spiral bevel gears. At present, when designing gears, gear workers generally use DIN standards, ISO standards, ASME standards and national standards GB / T.
For the calculation of the bending strength of spiral bevel gear, the gear tooth is generally regarded as a thick plate cantilever beam, and then the calculation formula of bending stress of specific spiral bevel gear is obtained after modifying the formula according to the cantilever beam calculation formula in material mechanics and combined with experiments. Because the bending condition and contact condition of spiral bevel gear usually affect each other, and the theoretical formulas for contact stress calculation and bending stress calculation are based on multiple assumptions, in practice, a large number of experiments are needed to obtain the available stress calculation formulas. Since the 1970s, the finite element method as a computational mechanics method has developed very rapidly. Because the finite element method has better adaptability to various engineering problems than the analytical method and can obtain more accurate data in a shorter time than the experimental method, in addition to the traditional semi empirical method, there are more and more studies on the stress condition of spiral bevel gear by using the finite element method, and in most cases, more satisfactory results can be obtained.
Scholars at home and abroad have carried out a lot of research on the stress condition of spiral bevel gears and obtained many valuable results. Gonzalez Perez and others put forward an analytical stress analysis method for local loaded contact of spiral bevel gears based on Hertz theory, but the inherent assumptions of Hertz theory make the stress analysis by this method different. Therefore, the author compares the results of contact analysis by finite element method and analytical method, The effectiveness of the above analytical method for stress analysis of involute gear is verified. Based on a gear pair contact model including tooth surface modification, spiral bevel gear machining error and tooth surface contact deformation, Zhang et al. Proposed a method to analyze the contact and load distribution of staggered shaft helical gear by using the finite element method. Compared with the traditional tooth surface contact analysis method, this method is used to analyze the transmission error of spiral bevel gear, Contact characteristics and contact load distribution are closer to reality. Bajpai et al. Comprehensively used the finite element method and Archard wear equation to predict the wear of the contact surface of spiral bevel gear. At the same time, they developed an iterative numerical method to calculate the change of the contact condition of spiral bevel gear caused by tooth surface wear, established the calculation model of tooth surface wear of parallel shaft gear, and compared it with the experiment. The results show that the calculation results are more in line with the actual situation, From the analysis and experimental results, it is concluded that the initial geometry of spiral bevel gear pair will affect the wear of spiral bevel gear to a great extent. Litvin et al. Used the finite element method to carry out the tooth surface loading contact analysis on the parallel axis, intersecting axis and staggered axis gear pairs of various new tooth profiles, and obtained the important data such as the contact stress, bending stress and contact point trajectory during the transmission of spiral bevel gear. According to the finite element analysis results, some spiral bevel gear pairs were optimized.
Using mathematical method and finite element method, Japanese scholar Li obtained the surface contact stress distribution and gear pair deformation of spiral bevel gear pair during internal and external meshing of involute gear transmission, developed the finite element program for tooth surface contact analysis and strength calculation, and proved the correctness of the program through experiments. For spiral bevel gears, krenzer puts forward the analysis model of spiral bevel gears under load. Bibel et al. Calculated the contact stress of spiral bevel gear by using the finite element method. Gosselin et al. Proposed a method to calculate the load distribution and transmission error of spiral bevel gear based on bearing tooth surface contact analysis, Hertz contact model and finite element square analysis model. Sheveleva et al. Put forward a method to deal with the contact surface and contact interval by meshing, and then calculate the contact trajectory, transmission error, contact area and contact stress through the grid model. Teixeira Alves et al. Proposed a method to calculate the bending deformation of spiral bevel gear teeth by using interpolation function. Compared with the finite element method, this method can save a lot of calculation time.
Simon introduced Hertz theory and compatibility conditions into the geometry research of spiral bevel gear, proposed the calculation models of load distribution on the tooth surface and load distribution between teeth of spiral bevel gear and long epicycloid bevel gear, compared them with the results of finite element analysis, and proposed an optimization algorithm for the tooth profiles of these bevel gears. Mermoz et al. Proposed to optimize the tooth surface topology of spiral bevel gear by using nonlinear finite element model. At the same time, a numerical analysis method for the influence of the tangent length of each tooth along the tooth contour of the machine tool is proposed. De Vaujany and others studied the variation of transmission error of circular arc bevel gear under load by using the comprehensive method of numerical analysis and experimental research.
Based on the theory of linear elastic fracture mechanics, spievak et al. Proposed a method to predict the crack propagation of spiral bevel gear with arbitrary shape by using the boundary element method, compared the calculation with the experimental situation, and discussed the sensitivity of the calculation results to the change of load and the parameters of crack growth model. Based on the work of spievak et al., Ural et al. Proposed a method for crack propagation of arbitrary shape by using the finite element method and the theory of linear elastic fracture mechanics. The calculation method has high efficiency and good convergence. Wang et al. Proposed a method to analyze the 3D dynamic contact of spiral bevel gear by using the finite element method under the condition of comprehensively considering friction, spiral bevel gear backlash and time-varying stiffness.