Impact of system-level factors on planetary gear set behavior

Planetary gear sets are used commonly in many diverse product applications. Their compact and co-axial design and ratio flexibility make them preferable to counter-shaft gear drives. Planetary gear sets are complex, multi-mesh systems formed by multiple branches of planet gears that are in mesh with a sun gear and a ring gear and are held by a common carrier through needle bearings and planet pins. Their design presents unique challenges stemming from a number of system-level issues, including their planet load sharing behavior, dynamic response, rim deflections, and spline/support conditions. This study investigates the influence of several-system level factors on gear stresses, and quantifies their impact on the resultant bending fatigue lives of the gears in planetary gear sets.; This study provides both experimental and theoretical investigations of the influence of several system-level factors on gear stresses, and quantifies their impact on the resultant bending fatigue lives of the gears in planetary gear sets. For the experimental investigations, a set of precise test fixtures that utilizes a power-circulatory arrangement is designed and implemented in a high-speed transmission dynamometer. Sets of precision planetary gear sets with desired variations were designed and built, including number of planets, carrier pinhole position errors, and internal gear rim thickness. Multi-channel strain and deflection measurement data collection and analysis systems are implemented for measurement of gear root strains and planet load sharing. Deformable-body models of planetary gear sets, based on a finite element formulation and designed to account for the same variations, are developed for the same systems.; As the first system-level influence, planet load sharing behavior of 3 to 6-planet gear sets having various amounts of intentional manufacturing errors is investigated experimentally. The deformable-body model predictions are shown to agree well with the measurements. A more computationally efficient, discrete transverse-torsional model of planet load sharing is proposed and shown to match well the experimental and deformable-body model results. Using the discrete planet load-sharing model, a set of closed-form design formulae are derived and used to predict statistical variations of planet loads. Experimental and theoretical results show clearly that a 3-planet system is completely insensitive to the manufacturing errors, provided that at least one central member floats radially. For systems having more than three planets, planet load sharing is a very relevant issue that becomes more significant with increased number of planets in the gear set, as the sensitivity of the gear set to the manufacturing errors increase with increased number of planets.; The second investigation focuses on the combined influence of gear rim deflections and spline conditions on the gear stresses and planet load sharing. As a representative example, rim thickness of the ring gear is varied and the changes in the rim defections, and root and hoop strains of the ring gear are measured for carriers having any number of planets and manufacturing errors. The experiments show that a more flexible ring does not eliminate unequal planet load sharing conditions, while it increases ring gear stresses and deflections significantly. When the rim thickness is reduced beyond a certain value, hoop effects became more dominant than tooth bending and the influence of splines on gear stresses become more significant. Stress predictions of the deformable-body model with the same flexible ring gears agree well with the experiments.; At the end, the impact of system level influences on gear bending fatigue lives are investigated by employing a stress-life based fatigue life model. Critical points at each gear root are determined and the lives of gear components with various load sharing conditions and rim thickness values are predicted. This bending fatigue life model...