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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 (OTE), 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 OTE 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. (2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior.

High-cycle gear tooth bending fatigue lives of spur gears under fully reversed and fully released loading conditions are compared in this experimental study. The experimental methodology described in an earlier publication, (Hong et al. 2020, “A Rotating Gear Test Methodology for Evaluation of High-Cycle Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions,” Int. J. Fatigue, 133, p. 105432. 10.1016/j.ijfatigue.2019.105432), is employed to perform two sets of rotating, gear tooth bending fatigue tests. Statistical analyses are performed to regress stress versus life (S–N) curves under both loading conditions. These curves indicate that a gear under fully reversed loads has a shorter bending life at the same maximum tooth root stress as a gear under fully released loads. Various planetary gear set kinematic conditions with different stationary members are considered to determine the equivalent number of tooth loading cycles per revolution of the sun gear. They are combined with established S–N curves under both loading conditions to determine the ratios of allowable maximum tooth root stresses amongst the gear components of a P-planet gear set such that each gear in the set has the same bending fatigue life. A “stress-balanced” gear set designed to these stress ratios is expected to have the same bending fatigue life for its sun, ring, and planet gears, ensuring that the planetary gear set life is the longest.