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In this study, a theoretical investigation on the overall loaded motion transmission error of planetary gear sets is presented. Planetary gear set load distribution model is employed to predict the input-to-output transmission error of planetary gear sets having distinct planet phasing conditions, to establish nominal transmission error behavior. Impact of carrier manufacturing errors resulting in unequal planet-to-planet load sharing on the gear set transmission error is quantified. Gear manufacturing imperfections such as run-out errors at their relative angles are introduced to observe their signatures on the resultant transmission error. Simplified formulations are presented to combine individual gear mesh transmission error functions with required modifications in order to obtain the overall transmission error. The predicted transmission error time histories are examined in the frequency domain to explore their diagnostic value in determining what errors the gear set possesses.

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This study presents, a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely planet load sharing, overall transmission error, and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High precision optical encoders were used to measure the overall transmission error of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system's response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. [1] to not only validate the model but also comprehend the measured behavior.

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