This paper analyzes the vibration characteristics and dynamics of involute straight bevel gear transmission, discusses the tooth modification and gear dynamics theory, establishes the accurate three-dimensional model and vibration mathematical model of straight bevel gear, and simulates and analyzes the influence of modification on the dynamic behavior of straight bevel gear system by using dynamics analysis software, In order to improve the accuracy and stability of straight bevel gear transmission through tooth profile modification technology, and reduce the vibration, noise and impact in the working process of straight bevel gear. The main work and research results are summarized as follows:
(1) Based on the spherical involute equation of straight bevel gear, the spherical involute coordinates of large and small ends of gear teeth are solved by Matlab tool programming, which is imported into SolidWorks 3D modeling software to generate spherical involute, and then the accurate modeling of straight bevel gear is completed through mirror image, surface filling, surface stitching, rotation and other operations. According to the determined modification parameters and using the functions of surface deletion, the three-dimensional parametric models of tooth profile arc curve modification and tooth direction equidistant modification of straight bevel gear are established. This technology avoids the large error caused by using other curves (such as back cone involute) or fast modeling software (Mindy tool set), and provides an accurate three-dimensional model of straight bevel gear before and after modification for the dynamic simulation analysis of straight bevel gear.
(2) Under the environment of RomaxDesigner, the dynamic simulation model of straight bevel gear is established. Through setting working conditions, defining constraints and dynamic analysis, the transmission error, dynamic contact load and dynamic response curve of straight bevel gear before and after modification are obtained under specific working conditions. Comparing the dynamic performance of the straight bevel gear before and after modification, it can be seen that the tooth modification can effectively improve the transmission performance of the straight bevel gear, reduce the vibration, noise and impact in the transmission process of the straight bevel gear, and the tooth equidistant modification is better than the circular arc modification gear in reducing the dynamic load of the straight bevel gear and improving the dynamic performance of the straight bevel gear. Analyzing and studying the influence of modification on the dynamic performance of straight bevel gear has reference and guiding value for perfecting the modification theory of straight bevel gear.
(3) In view of the great influence of the axial vibration of the straight bevel gear on the working performance of the gear, based on the nonlinear dynamics theory of the straight bevel gear, the mathematical model of the multi degree of freedom modified straight bevel gear considering the meshing stiffness and meshing damping is established, and the corresponding dynamic differential equations of the straight bevel gear are listed according to Newton’s law, The nonlinear parameters of straight bevel gear system are determined. As the fitting degree of the polynomial curve is higher and higher than that of the original curve, the fitting degree of the polynomial curve can be calculated by MATLAB. On the contrary, in order to reduce the fitting degree of the polynomial curve, the fitting degree of the polynomial curve becomes higher and higher, The tooth clearance function is approximated by cubic polynomial.
Because the meshing stiffness curve of straight bevel gear has no step change and the overall change range of stiffness is small, the dynamic equation of straight bevel gear system can be solved by referring to the method of linear differential equation, and the meshing damping of straight bevel gear can be solved by using the existing empirical formula. The dynamic equation of straight bevel gear is complex and difficult to solve. Only several methods of solving the dynamic equation are discussed, and the expressions of displacement and velocity response of the system are solved by using the inverse operator decomposition method.