Dynamic Response of Helical Gear Pairs Under Random Speed Excitation

Helical gear systems are sometimes subjected to random speed excitations in engineering applications, such as gear pairs in wind turbine drivetrains. To investigate the dynamic characteristics of helical gears under random-speed excitation, a dynamic analysis approach is developed. Firstly, the mesh stiffness of the helical gear pair is calculated in the spatial domain using the slicing method combined with the potential energy approach. Subsequently, the K–L expansion is employed to describe the random speed process, According the random rotation speed, the meshing stiffness is transformed into time domain. Finally, a six-degree-of-freedom nonlinear dynamic model of the helical gear pair, incorporating radial, axial, and torsional motions, is established. The vibration responses of a gear pair under random-speed excitations are investigated using Monte Carlo simulations (MCS). The results show that the radial displacement consistently exceeds the axial displacement. The radial displacement exhibits a multimodal distribution, whereas the axial displacement remains more concentrated and approximately symmetric, with only slight changes in its distribution shape across time instants. As the random process's correlation increases, the system response becomes more correlated, revealing stronger statistical coupling. The findings provide a theoretical basis for elucidating the nonstationary dynamic mechanisms of helical gear pairs under random speed excitations.