Epicyclic Load Sharing Map — Development and validation

Under ideal conditions, every sun-planet-ring path in an epicyclic gear set transmits the same amount of torque. But, in the presence of certain manufacturing variations, equal load sharing is not achieved. In a companion paper, a physical explanation has been provided for the load sharing behavior observed in epicyclic gears. The explanation of the root cause led to the development of a load sharing formulation for 3, 4, 5, and 6 planet epicyclic systems. In this paper the same approach will be taken to develop the formulation for a seven planet epicyclic gear set. The developed expressions will then be used to develop the concept of an Epicyclic Load Sharing Map. This map describes the load sharing characteristics of every epicyclic gear set at any positional error and torque level. The developed expressions are then expanded to describe the general case when there are arbitrary errors on the position of every planet in the epicyclic gear set. Finally, the developed expressions will be validated by comparing the predicted load sharing behavior with the results from a validated system level computational model.