Influence of Geometric Parameters on the Dynamic Performance of Spiral Bevel Gear

Spiral bevel gears are ubiquitous in numerous power transmission systems. The exigent demands such as high performance, more strength and less noise in helicopter drives can be met by selecting the optimal geometrical design parameters. However, a comprehensive study on the influences of geometric parameters on the transmission system dynamics is not found in the literature. Therefore, in this study, the effects of geometric design parameters such as spiral angle, pressure angle and pitch cone angle on the spiral bevel gear set dynamic characteristics for various boundary conditions are studied. Firstly, the analytical modeling of coupled lateral–axial–torsional vibrations of the spiral bevel gear set is derived theoretically under a few assumptions. Then the emphasis on the effects of geometric parameters on the dynamic characteristics such as critical speeds, coupled mode shapes and unbalance vibration response of the gear pair supported by flexible and rigid boundary conditions are investigated numerically. Under rigid support conditions, it is observed that there is no remarkable influence of geometric parameters on the critical speeds. However, the unbalance response amplitudes at and around the resonance peaks are notably affected. Whereas the critical speeds and unbalance responses are essentially affected by the variation of axial and torsional stiffness at the supports. Meanwhile, the influence of geometric parameters on the critical speeds corresponding to torsional and axial modes is remarkable for the flexible support conditions. Furthermore, the steady state response due to combined torsional and unbalance excitations is also studied, and the results show that the geometric parameters influence the axial, lateral and torsional responses. The results obtained through this study are useful in the design of the spiral bevel gear set.