A Gear Mesh Dynamic Model for Analyzing the Nonlinear Vibrations of Spur Gears Supported by Compliant Shafts

A gear mesh dynamic model of spur gears is presented in this paper. Initially, the influence of variation in center distance due to geometric eccentricity, assembly error and bending deformation of shaft on gear mesh parameters such as pressure angle, backlash and time-varying mesh stiffness were determined. Then, the gear mesh dynamic model was formulated by replacing the constant backlash and time-varying mesh stiffness under quasi-static conditions of the previous model with continuously calculated time-varying backlash and time-varying mesh stiffness under dynamic conditions. A six-degree-of-freedom lateral-torsional coupled nonlinear dynamic model was established with the gear mesh dynamic model. A gear pair was analyzed to demonstrate and qualify the impact of shaft stiffness and operating conditions on the differences between the dynamic responses predicted by the nonlinear dynamic model established in this study and the previous nonlinear dynamic model. The results showed clear differences between the dynamic responses predicted by different models, especially for the gear rotor bearing system with high compliant shafts. A strong coupling effect between dynamic response and gear mesh parameters was found. The comparison between the gear mesh forces within a wide range of torque and speed also revealed differences, especially in the vicinity of the primary resonance speed and 1/3 of this speed. With increasing torque, the differences increased and the range of speeds corresponding to same difference also increased. The differences reached to a minimum near half of the resonance speed under different input torques.