Analysis of dynamic behaviour of 2K-H planetary gearing

The dynamic behaviour of gear system in aeroengine has an important influence on the reliability of aircraft. Hidaka and Boyd have solved the equations of motion of planetary gearing by numerical method, but it involves tedious and complicated computation. The load equalization on each branch is another important problem of planetary gearing which has been calculated and experimentally measured by Hayashi and Yanaba, but only for static conditions. Up to now, the two problems just mentioned require separate solutions and separate computer programs. It is believed that this paper succeeds in its attempt to overcome the various shortcomings just mentioned. In this paper, the Fourier method presented by Kubo for a simple gear system has been considerably improved, and used to deal with planetary gear system. The authors have found that proceeding as Kubo did would lead to a criterion for planetary gearing that is too difficult to use to judge a system as complex as planetary gearing. A new method of derivation has been developed to avoid getting something like Kubo's criterion. Then the analytical solution can be obtained conveniently with new derivation, and calculation can be considerably simplified. By using this approach, the vibration and dynamic load distribution on each branch, the floating locus of sun gears, the influences of various kinds of runout errors, and exciting function of tooth errors require just one solution and one computer program.