Study On The Nonliner Osillations Of Beveloid Gear System

Up to now, only few researches aim at the theory of nonlinear vibration of beveloid gears with parallel axes. The paper mainly focuses on the nonlinear vibration property of them. The paper could finally provide the theoretical foundation of the reduction of vibration as well as noise in the real application of beveloid gears.As the dynamic excitation of the gear system is the main reason of vibration and noise, the time-varying stiffness, transmission error and backlash have been considered in the model. Stiffness excitation of gears is time-varying. Time-varying mesh stiffness is made by Ishikawa formula, then expanded into the form of Fourier series. The paper makes time-varying mesh stiffness parametric, and analyzes the forming reason of error excitation and backlash. Backlash can be easily calculated by polynomial fitting.In the light load, oscillatory system of beveloid gears with parallel axes have been simplified as the dynamic model. The frequency-response equation and first order approximate solution in the steady-state of the primary resonance, secondary resonance and combination resonance caused by internal, external and parametric excitation have been obtained based on the method of multiple-scales. The corresponding frequency-response curves have been presented. The effect of different physical parameters, such as external load and damping, on steady-state response has been analyzed. Combined with the numerical method, curve of time-displacement and phase plane have been drawn under the primary resonance, secondary resonance. Scanning curves have been drawn under different rotational speed and analyzed.In the heavy or moderate load, considering a small metacentric angle, the system of beveliod gear produces axial force. The paper sets up the dynamic model with axial, transverse bending and torsional vibration for beveloid gear system. The frequency factors have been analyzed by the method of multiple-scales. The steady response has been obtained by means of numerical method. Scanning curves have been drawn under different rotational speed and analyzed.