A dynamic model of a double-helical planetary gear set

A linear, time-invariant model of a double-helical planetary gear set is proposed in this paper. The model formulation allows the analysis of a gear set with any number of planets, any planet phasing and spacing configurations and any support conditions. Torsional, transverse, axial and rotational (rocking) motions of gears and the planet carrier are included in this three-dimensional model. Planets are allowed to be positioned equally or unequally spaced around the sun gear. The natural modes are computed by solving the corresponding Eigen value problem. The modal summation technique is used to find the forced response due to periodic gear mesh excitations under constant or proportional modal damping conditions. An example gear set consisting of four equally-spaced planets is considered at the end to demonstrate the influence of key design parameters including right-to-left stagger angle, and support conditions on the dynamic response of the double-helical planetary gear system. Numerous modes with dominant tilting motions are predicted to underline the essence of using a 3D formulation for double helical gears. Staggering of gear teeth is shown to impact the dynamic response of the gear system substantially. Different values of stagger are shown excite different types of modes, resulting in different dynamic response curves. It is also found that left and right sides of double helical gears can carry equal or different dynamic load amplitudes based on the right-to-left stagger values. Likewise the influence of the sun support conditions is shown to be more pronounced for the case of a non-zero stagger.