Because the load of gear transmission system fluctuates greatly in the alternating area of tooth number, it will cause vibration and noise of the system; On the other hand, due to the bending deformation and torsional deformation of helical gear under load, the contact of gear teeth along the tooth width direction is uneven, resulting in eccentric load. The tooth profile modification can compensate the pitch deviation in the actual meshing process of helical gear, slow down the fluctuation of meshing stiffness and reduce meshing impact; Tooth modification can effectively improve the uneven distribution of load along the tooth contact line, avoid edge contact, and improve the bearing capacity of helical gear.
The calculation methods of stiffness excitation mainly include material mechanics method, approximate substitution method, slice method, finite element method and so on. Chaari et al. Used the material mechanics method to calculate the meshing stiffness of spur gears by considering the bending deformation, shear deformation, radial compression deformation, Hertz contact deformation and wheel body deformation of spur gears. Liu et al. Adopted the approximate substitution method and used the time-varying of helical gear meshing line to replace the change of meshing stiffness. Due to the large error of the approximate substitution method, ajmi et al. Used the slice method to discretize the helical gear into a slice helical gear along the tooth width direction, and then obtained the elastic deformation and meshing stiffness of each slice helical gear according to the deformation coordination equation, which was compared with the results obtained by the finite element method.
According to the degree of freedom, the dynamic model of helical gear system can be divided into pure torsion model, bending torsion coupling dynamic model and bending torsion shaft pendulum coupling dynamic model. The coupled dynamic model of bending torsion shaft pendulum considers more degrees of freedom than other models, so it can better reflect the real situation of helical gear system. In the early process of gear dynamics modeling, error excitation and stiffness excitation are substituted into the dynamics model for helical gear dynamics analysis. With the deepening of research, Chen et al. Proposed a new nonlinear excitation analytical calculation model integrating the coupling of meshing stiffness and transmission error based on the method of material mechanics, and established the meshing stiffness model of Spur Gear Considering the influence of tooth error. On the basis of Chen, Wang Qibin et al. Extended the model, established an analytical model of spur gear meshing stiffness considering tooth direction modification, and compared it with the finite element method. The results show that the relative error of meshing stiffness solved by the two methods under different modification is no more than 5%.
(1) The nonlinear excitation coupling model of helical gear stiffness and error is established, and the effects of different tooth profile modification amount and tooth profile modification length and different tooth direction modification amount and tooth direction modification length on helical gear meshing stiffness and transmission error are studied. Selecting appropriate modification value can effectively reduce the fluctuation of meshing stiffness in the alternating area of helical gear teeth.
(2) Considering the internal and external excitation of the system, the vibration response law of the system with different tooth profile modification amount and tooth profile modification length and different tooth profile modification amount and tooth profile modification length is studied; With the increase of modification value, the amplitude of vibration acceleration decreases and the formant decreases; When the modification amount continues to increase to a certain value, the vibration acceleration amplitude of the system increases, indicating that there is an optimal modification amount in the system.
(3) Through the experimental research on the dynamic characteristics of the established helical gear transmission system experimental platform, the amplitude frequency curves of vibration acceleration under different working conditions are obtained and compared to verify the correctness of the theoretical model and analysis results.
At present, most of them pay attention to the influence of single modification on the dynamic characteristics of helical gears, and the research object is generally spur gears. The meshing stiffness and tooth error of helical gear is a three-dimensional space problem. The calculation method of meshing stiffness after modification is different from that of spur gear. However, the traditional analytical calculation method does not consider the three-dimensional space position of helical gear meshing line and meshing position when calculating the meshing stiffness of helical gear, so it is impossible to calculate the meshing stiffness and tooth error of helical gear after modification.