Study On Dynamic Characteristics Of Helical Gear Multi-gap Nonlinear Coupled System

Gear transmission system is an important part of mechanical transmission system. With the scientific and technological progress and the development of machinery industry, the gear system put a higher requirement, high speed, low noise as the direction of development. Strengthen the dynamic study of gear system is an important way to improve the performance of transmission system. Depth study of gear system dynamic parameters, is important to comprehensive analyze the dynamic characteristics of gear transmission system and improve performance of mechanical transmission system.In this paper, helical gear transmission system was studied with gear system dynamics theory, and established a more realistic bend-torsion-axes-swing multi-gap nonlinear coupled gear system model, in full consideration of the nonlinear factors such as time-varying mesh stiffness, transmission error, backlash and bearing clearance. The dynamic equations of system was solved by use of Runge-Kutta numerical integration algorithm, to obtain the results of dynamic response, which were analyzed and compared, and discussed the affect of several dynamic parameters on the dynamic characteristics of system.Firstly, the mechanism of stiffness excitation and error excitation were elaborated, and the time-varying stiffness of meshing was numerical simulated by Fourier series method, to analyze the relationship between time-varying stiffness and gear contact ratio & speed; two types of errors were analyzed and made a numerical simulation. Ultimately two excitations were synthesized as the input of gear system.Secondly, each of several different types of modeling methods and models were analyzed. The bend-torsion-axes-swing nonlinear dynamic model was established by use of lumped parameter method, and the dynamic differential equations based on the model. As the need for numerical calculation, the clearance nonlinear describing function was fitted and the differential equations were dimensionless.Thirdly, based on the numerical theory of the inherent characteristics, the undamped free vibration equation was solved to obtain the numerical results of the natural frequency; and compare with the results of the finite element method to illustrate the theoretical feasibility of the method. Fourth, by comparing a variety of methods for solving the dynamic equations, the model of the gear system was solved by use of the fourth order fixed step Runge-Kutta numerical method to obtain the vibration response of the system, such as time-domain diagram, phase diagram, Poincare map and the FFT graph. Analyzing the characteristics of the response results, and discussing the affect way and level of the parameters, such as gear backlash, driving frequency and the bearing clearance from each two aspects of vibration amplitude and vibration periodicity, to propose reasonable suggestions for the choice of parameter values.Finally, by use of MATLAB's GUI development platform, the analysis tools software was developed including the above analysis methods on the gear system dynamics, which can be interacted with the user.In this paper, dynamic characteristics of helical gear transmission system was studied, and obtained the dynamic characteristics of the corresponding results by a large number of values calculated to provide the basis for further theoretical research and design of high-performance gear system.