Matrix Methods in Planetary Gear Train Analyses

In the old methods that need the efficiency-calculation formulae for each planetary gearset, there are several problems in the way of calculating the efficiency of the power transmitted and in further applications to practical analyses of complicated planetary gear systems considering the several kinds of friction and to such a multiple-stage train that requires a great deal of labor in calculation. The author examined defects of old calculation technique and investigated a new method to analyze the characteristics of planetary gear trains with matrix methods by applying the same technique that has been used in FEM analyses, that is, constructing the system equations from the element equations. This method makes it possible to give the data that characterize the geometries of gear elements and the efficiencies of meshing areas as input to the computer programs, and to automatically analyze the velocity, the torque, the efficiency and the equivalent inertia moment of the whole system.