Considering The Friction And Gap Teeth The Impact Behavior Modeling And Analysis

According to the theory of non-linear dynamics and with the application of qualitative and quantitative methods, the gear non-linear characteristics involving with realistic time-varying stiffness, realistic static transmission error, tooth surface and backlash are studied in this paper. The main content is as following:1. The torsional vibration model of gear transmission including realistic time-varying stiffness, realistic static transmission error and tooth surface friction is established. With the assumption that the teeth are in uniform motion on the meshing line and the friction coefficient is constant, the expressions of friction are obtained. Then substituting all the above parameters such as stiffness, STE and surface friction into the torsional vibration model, the final derived differential equations of the system is gained.2. With the application of analytical method and numerical method the solutions of the gear model established above are discussed. Applying a simple Fourier series expression to simulate the time-varying stiffness and static transmission error, and using a high-order polynomial to fit the non-smooth piecewise backlash function. The amplitude-frequency function of the main resonance and 1/2 sub-harmonic are obtained through the application of multiple scale method. The results suggest many non-linear characteristics such as sub-harmonic response, jumping and bifurcation. However using the numerical method to analyze the discrete dynamic model with realistic time-varying stiffness, realistic static transmission error and tooth surface friction. The results through digital calculation show that surface friction causes sudden change and brings additional vibration close to the node point. The effect of other parameters such as velocity, loads and damping to the system is also investigated.3. Explore the impact-collision dynamics of the gear transmission. Introduce the non-linear spring-damper model including energy dissipation to simulate the contact process of teeth. Based on contact-impact theory, non-linear theory and numerical method, bifurcation of the steady-state response and energy dissipation is researched. Numerical results show that the system has very complicated dynamic characteristics, and periodic bifurcation and grazing bifurcation exists with the parameters varying.4. Investigating a gear pair through experiment method. The dynamic transmission error of a pair of standard parameters spur gear is obtained. Then the comparison between theory results and experiment results in spectrum domain verify the validity of the theory research above in some extent.