Nonlinear factors such as backlash and time-varying meshing stiffness inevitably exist in gear meshing process, which belongs to the research scope of non-linear dynamics.According to the analysis results of domestic and foreign scholars, all kinds of phenomena such as amplitude jump, subharmonic, superharmonic resonance, bifurcation and chaotic motion which are possessed by non-linear dynamics also exist in the non-linear dynamic model of gear transmission system.
In foreign countries, the amplitude jump characteristics of non-linear time-invariant model of gear transmission system and complex motion forms including subharmonic resonance and chaotic motion are analyzed by numerical solution and analytical method respectively, which verifies the feasibility of simulation of gear non-linear vibration characteristics by numerical method.
Then, based on the nonlinear time-varying model, the coupling effect between time-varying stiffness and tooth side clearance and bearing clearance is analyzed.For the non-linear time-varying model of planetary gear drive, harmonic balance method and numerical method are used to analyze the amplitude jump characteristics respectively.
Considering the influence of friction, the influence of friction on system subharmonic, superharmonic resonance and stability is calculated and analyzed by analytical method.For the non-linear dynamic model of, amplitude jump, subharmonic vibration and chaotic motion are also found by numerical calculation.
Non-linear vibration response and amplitude jump characteristics of DOF nonlinear dynamic model were analyzed by multi-scale harmonic balance method and numerical method respectively.Incremental harmonic balance method and numerical method are used to analyze vibration response and amplitude jump characteristics of single-degree-of-freedom gears.Considering the non-linear oil film force between gears, the jump characteristics of gears are analyzed by numerical method.
For two-stage fixed-axle gear drive system with degrees of freedom, the tooth detachment, unilateral impact and bilateral impact under different clearance conditions are analyzed numerically.Considering non-linear bearing support, non-linear dynamic analysis methods such as section diagram, exponent, phase plane diagram and global bifurcation diagram are used to analyze non-linear vibration forms such as periodic motion, subharmonic motion and chaotic motion of the system.
Considering the lubrication between teeth, the non-linear vibration characteristics of gears including tooth removal and amplitude jump are analyzed by numerical method.Considering dynamic tooth side clearance and friction, the impact state, global bifurcation and chaos characteristics under different dynamic models were analyzed by numerical method.Considering the time-varying meshing damping between the teeth, the gear skip characteristics are analyzed based on the validation model.
The bifurcation and chaos characteristics of degree-of-freedom non-linear gear drive system are analyzed by analytical method, and the correctness of the analytical method is verified by numerical method combined with phase plane diagram and time-domain frequency-domain curve.Considering random assembly clearance, the complex motion state of gears with different parameters is analyzed by using global bifurcation diagram and maximum index.
In China, Wang Sanmin et al. analyzed various periodic and chaotic responses of the system by using step-variable Runge-Kutta method combined with frequency spectrogram, cross-section diagram and maximum index, taking into account tooth surface friction, tooth side clearance and time-varying meshing stiffness.Zhang Lochuai and others studied the relationship between chaotic motion, periodic motion and quasi-periodic motion of gear rotor bearing coupling system and rotational speed.
Aiming at the nonlinear time-varying dynamic model with clearance and time-varying stiffness, etc., Zhang Zhiying studied the bifurcation structure of periodic and chaotic motions in parameter plane, and discussed the multiple periodic solutions in system space as well as the effects of damping parameters and excitation frequency on the periodic solutions of the system.Liu Mengjun and others analyzed the characteristics of system attractor changing with damping ratio, clearance and other parameters by using the sectional linear clearance gear model and calculated the index by the definition method.Chen Siyu et al. considered three different gap forms, i.e. constant gap, time-varying gap and random gap.The time-domain response and amplitude-frequency response of the system are analyzed by means of numerical simulation.
Tang Jinyuan and others studied the global characteristics of single-degree-of-freedom nonlinear gear system based on the cell mapping method.Considering random assembly clearance, Lu Jianwei and others analyzed the non-linear vibration behavior of gear pair system by bifurcation diagram and maximum index.Sun Tao et al. analyzed the non-linear frequency response characteristics of planetary gear transmission system by harmonic balance method.
Sun Zhimin and others studied the chaos and bifurcation behavior of star gear drive system under strong non-linear excitation.Li Tongjie et al. analyzed the periodic solution and its stability, local and global bifurcation characteristics and vibration strength stability of planetary gear transmission system.