Dynamics of herringbone planetary gear systems under mesh excitations with random cumulative pitch errors

Herringbone planetary gear systems are extensively used in wind turbines and the marine industries, with strict requirements for the vibration level of gear systems. Mesh excitations, primarily driven by cumulative pitch errors, constitute the dominant source of system vibration and noise. Consequently, an improved model for calculating mesh excitations is proposed, considering the impact of random cumulative pitch errors. The validity of the model is confirmed through comparison of calculated and experimental results. On this basis, a lumped-parameter dynamic model of the herringbone planetary gear system with random cumulative pitch errors is established. Then, the impact of the random cumulative pitch errors on mesh excitations under different loading conditions is obtained. The dynamic characteristics of mesh pairs, considering the effects of random cumulative pitch errors, are investigated in detail. The findings suggest that random cumulative pitch errors exert a more pronounced influence on mesh excitations under low-loading conditions. In terms of the frequency spectrum of mesh forces, random cumulative pitch errors of the ring gear lead to the appearance of hunting tooth frequency and its harmonics, as well as rich sidebands around mesh frequency, assembly phase frequency, and their harmonics. The results can provide effective guidance for the low-noise and low-vibration design of herringbone planetary gear systems.