Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation

In an n planet epicyclic gear set, under ideal conditions, each path will carry an equal amount of torque and therefore can be designed to transmit only 1/n of the input torque. However, earlier works have shown that such equal sharing of the input torque between the parallel paths is not realized in practical applications, due to the presence of manufacturing errors. While various aspects of the load sharing behaviors have been shown both through computational models and experiments, a physical understanding of the true nature of the load sharing behavior is still lacking. In this paper, a physical explanation will be provided for the basic mechanism causing the unequal load sharing phenomenon. Both floating (system with clearances) and non-floating systems will be treated. On the basis of the physical explanation, closed form non-dimensional equations that predict the planet to planet load sharing behavior in the presence of positional errors will be derived. Epicyclic systems having 3–6 planets will be specifically treated and generalized equations for systems having an arbitrary number of planets will be presented. The developed expressions will be validated by comparing their predictions with previously published predictions from a computational model and experimental data.