The tooth meshing error produced in the process of gear machining and installation is a kind of displacement type dynamic excitation. The deviation of tooth pitch and tooth profile jointly constitute the deviation of actual meshing tooth profile from the theoretical tooth profile, which leads to the inevitable existence of gap between teeth and the occurrence of gear slapping phenomenon. Therefore, the error excitation and stiffness excitation are also one of the important excitation forms in the process of gear meshing In this paper, the transmission error caused by pitch deviation and tooth profile deviation is considered as meshing transmission error of gear teeth, and the elastic deformation of gear tooth is called static transmission error of gear.
The Fourier series expansion form of static transmission error of gear is as follows:
E0 — mean value of tooth meshing error;
E2j-1 — error variation amplitude;
E2j — error variation amplitude, generally taken as E0 = 0, and the error variation amplitude is obtained according to the machining accuracy of gear teeth.
The pitch curve function, transmission ratio and tooth profile equation of the gear are derived and analyzed. Taking the generating method as the theoretical basis of gear machining of the reducer variable speed integrated gear mechanism, the UG software is redeveloped to simulate the machining process of the non-circular gear, and the three-dimensional model of the face gear is obtained. This chapter not only explains the process of establishing the geometric model of the gear mechanism, but also gives the mathematical expression of the important internal excitation such as the time-varying instantaneous center excitation and the time-varying meshing stiffness of the gear mechanism, which lays a theoretical foundation for the following research on dynamic characteristics.