DYNAMICS OF PLANETARY GEAR TRAINS.

This investigation has developed a comprehensive method for analyzing the static and dynamic loads in a planetary gear train. A variable-variable mesh stiffness (VVMS) model was used to simulate the external and internal spur gear mesh behavior, and an equivalent conventional gear train concept was adapted for the dynamic studies. With this technique, the design and analysis of planetary gearing is based on an engineering rather than an empirical approach. The analysis is applicable for either involute or noninvolute, i. e. , modified, spur gearing. By utilizing the equivalent gear train concept, the developed method may be extended for use for all types of epicyclic gearing. This method is incorporated into a computer program so that the static and dynamic behavior of individual components can be examined. A mathematical model consisting of power source, load, and planetary transmission is used to determine the instantaneous loads to which the components are subjected. It is capable of considering fluctuating output torque, elastic behavior in the system, and loss of contact between gear teeth. The dynamic model has nine degrees of freedom, resulting in a set of simultaneous second-order differential equations with time-varying coefficients, which are solved by numerical methods.