Research On Nonlinear Dynamic Characteristics Of A Spur Gear Rotor System Considering Tip Relief

Gear rotor system is the main transmission system in rotating machinery and is one of the most widely used movement transmission devices in all sorts of mechanical equipment. Vibration and noise are always caused during the power transmission due to the manufacturing errors, assembly errors and tooth deformations. Tooth profile modification (TPM) is an effective method to optimize contact patterns, compensate for manufacturing errors and reduce the vibration and noise of gear system. Considering the tip relief, a quasi-static finite element model (FEM) of a spur gear pair in mesh is established by ANSYS software, and the time-varying mesh stiffness (TVMS), static transmission error (STE) are calculated. Then a dynamic model of a geared-rotor system is proposed by MATLAB software. The model consists of finite element models of shaft structures combined with a discrete model of a spur gear pair. Considering TVMS, STE, load torque and gear backlash, the natural characteristics and vibration responses of the geared rotor system are analyzed. The main contents are as follows:(1) Considering the tip relief, a quasi-static FEM of a spur gear pair in mesh is established by ANSYS software. With the elastic deformation of the tooth under a constant applied load taken into account only, TVMS and STE with different amounts of tip relief and different loads are calculated based on the FEM and this will provide data support for the dynamic characteristics analysis of the geared-rotor system. The amplitude of TVMS and STE changes with different loads, the abrupt change near transition regions between single-and double-tooth engagements becomes slow, and the higher harmonics of the mesh frequency decrease after tip relief.(2) The dynamic meshing model of a spur gear pair is established, and when it is combined with a rotor system, a FEM of a spur geared rotor system is formed. Assuming the mesh stiffness is time-invariant, a number of primary resonances and some super-harmonic resonances about lateral-torsional coupling vibration are excited by fundamental and higher order terms of STE. In the vibration responses of the system, considering constant load torque, only the fundamental harmonic of TVMS will result in the fundamental and higher order meshing frequency. Besides, the fundamental, double and composed frequency about time-varying mesh stiffness and shaft frequency will coexist if the torque fluctuate along sinusoidal wave.(3) The effect of different amounts of tip relief under different loads on vibration responses is discussed. The dynamic response amplitude, acceleration amplitude fluctuation, vibration and impact will reduce after tip relif. The optimal amount of tip relif under different loads is different, and it is not always better for a greater amount of tip relief.(4) Considering the gear backlash, a single-degree-of-freedom dynamic model about the alternating rotating displacement is established. Hard nonlinear phenomenon and double-sided impact between gear pairs disappear with the increase of the gear backlash. The amplitude of the amplitude frequency responses decreases, hard nonlinear phenomenon and jump phenomenon disappear with the increase of the viscous damping ratio.. The amplitude of the amplitude frequency responses increases with the increase of load torque, and hard nonlinear phenomenon becomes evident. Jump phenomenon does not appear in the studied geared-rotor system, because the influence of backlash on the vibration response is dependent on system parameters.Based on the numerical simulation, dynamic characteristics of a spur gear-rotor system is studied, and the results could provide theoretical basis for dynamic response calculation and structure design.