The vibration of the gear system will be caused in the process of gear rotation and meshing. If the natural frequency of the gear overlaps or is close to the meshing frequency, resonance will occur. Resonance can produce large dynamic stress at the tooth root and accelerate the fatigue fracture of gear. Especially under high-speed working conditions, resonance failure has become the main failure form of gear.
Therefore, in the design and trial production, we should master its natural frequency and vibration mode in advance, and strive to avoid the meshing vibration frequency. Modal analysis is a method to study the dynamic characteristics of product structures. It is widely used in machinery, civil engineering and other fields. It aims to extract the natural attributes of product structures, including natural frequency, damping ratio and vibration mode, recognize the relationship between system structural parameters, geometric parameters and natural frequency and vibration mode, and provide reference for structural design, vibration fault diagnosis and structural optimization.
Scholars at home and abroad have done a lot of research on the inherent characteristics of gear transmission system. Wang established the dynamic model of planetary gear system, calculated the sensitivity of natural frequency to meshing stiffness by modal analysis method, judged the occurrence of transition by coupling factor, analyzed the parameter instability caused by the change of meshing stiffness by multi-scale method, and obtained the variation law of modal eigenvalue sensitivity, modal transfer criterion and compliance change instability. Lin and Parker studied the modal vibration of single-stage planetary gear trains with different number of planetary gears, analyzed the natural frequencies and vibration modes under various states in detail, and analyzed the sensitivity of the natural characteristics of the system to geometric parameters, meshing stiffness, speed and other factors. Su Bokang and others established the dynamic simulation calculation model and time-frequency-domain test-bed of huipopular planetary gear system, studied the natural characteristics, determined the resonance frequency range of the system, and concluded that the natural frequency of planetary gear system changes differently with the increase of meshing stiffness, and the speed and amplitude increase. Mo Shuai et al. Established the translation torsion coupling dynamic model of the face gear planetary transmission series system by using the lumped parameter method, solved the natural frequency of the system, and studied the effects of meshing stiffness, support stiffness, torsional stiffness and component mass on the natural frequency. Zhang Xiaoping and others used the finite element analysis method to carry out the modal analysis of the double typical normal circular arc gear, calculated the natural frequency under the condition of different number of teeth, modulus and transmission ratio, and concluded that the natural frequency of the pinion presents a large fluctuation change to the modulus and number of teeth, while the large gear is relatively flat. Zhang Lan carried out the modal analysis of involute spur gear and double circular arc gear under constraint. It is concluded that the natural frequency of double circular arc gear is greater than that of spur gear, the effective inertia of Z axis has the greatest influence on the vibration mode, and the effective inertia of spur gear is significantly greater than that of helical gear.
The above research results studied the influence of geometric parameters and system stiffness on the natural characteristics of spur gear, helical gear, planetary gear train and other gear transmission systems by using finite element method and experimental modal method respectively, but most of the relevant studies qualitatively analyzed the influence of the change of geometric factors on the natural frequency, and lacked quantitative research on the primary and secondary order of the factors affecting the natural frequency, It is rare to solve the numerical simplified calculation model of natural frequency of double circular arc gear.
Therefore, how to quantitatively determine the influence of geometric factors on natural frequency and summarize the simplified calculation model of natural frequency of double circular arc gear is an urgent practical problem to be solved. Based on the statistical theory and the modal analysis theory of finite element method, the author establishes a four factor and four level orthogonal experimental model with the geometric parameters of double circular arc gear (modulus, number of teeth, helix angle and tooth width) as independent variables and the constrained modal natural frequency as dependent variables, quantitatively analyzes the influence of geometric parameters on natural frequency, sorts the influence degree according to the F value, and uses the centralized one-time nonlinear regression model, The low order frequency regression equation of constrained mode of double circular arc gear is established.