In this paper, an analytical solution on the dynamic mesh forces of planetary gear trains (PGTs) is proposed by investigating a lumped-parameter model. By using the method of multiple-scales (MMS), closed-form expressions of mesh force under the effects of manufacturing and assembly errors are obtained. From these expressions, the effects of several key factors such as the tooth thickness error, pin position error, applied torque, support stiffness of sun gear, and tooth profile modifications (TPM) on dynamic load sharing behaviours are explored. Numerical integration is carried out to verify the validation of the proposed method, and the developed expressions are also validated by comparing the results with previously published predictions. The results for several examined PGT systems show that the key factors abovementioned affect the dynamic load sharing behaviours as both static and dynamic factors. An important new conclusion obtained by this work is that proper tooth profile modifications keep the dynamic load sharing factors almost equal to the results obtained under static conditions. This conclusion provides the possibility to simplify the dynamic analysis to the static analysis on the dynamic load sharing problems.
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