Dynamic Characteristics of Double-Helical Planetary Gear Sets Under Time-Varying Mesh Stiffness

Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform（ TW） and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs（ degree of freedom） are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness（ SW）,the results show that dynamical factors and perturbation under the excitation of TW（ β < β0） are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet（ R- P） is stronger than sun-planet（ S-P） which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.