Ideal tooth profile modifications for improving nonlinear dynamic response of planetary gear trains

Abstract The ultimate goal in this study is to investigate the effects of tooth profile modifications (TPMs) on PGTs by performing parametric studies. For this purpose, firstly a nonlinear planetary gear dynamics model with time-varying stiffness is introduced. A time-varying stiffness function is included into the analysis by using loaded static transmission error (LSTE) for sun-planet and ring-planet gear meshes. In this analysis the computationally calculated values of LSTE are used; however, if an experimentally measured LSTE can be used, it will include all gear errors that exist in the gear pair, as well as time-varying mesh stiffness. Therefore, when this method is used with experimentally measured LSTE for dynamic modeling of planetary gear trains, one does not require any additional computational tool to estimate the time-varying mesh stiffness parameter. A drive-train simulation tool (Transmission3D), which combines analytical contact mechanics solutions with FE effectively, is used for verification purposes. The validity of the proposed model is shown by comparisons of the dynamic response of the proposed model with the response obtained through Transmission3D on an example PGT. A wide frequency range is selected to cover superharmonics of the natural frequencies in order to verify the accuracy of the dynamic model for speed ranges lower than the natural frequencies of the system, which are often encountered in practical applications. Harmonic balance method (HBM) is used to obtain the nonlinear algebraic equations of motion in frequency domain, which are solved by using Newton's method with arc length continuation. Parametric studies are performed by employing the mathematical model suggested important outcomes for application of TPMs in PGTs. The relationships between the distinct modal characteristics of PGTs and effectivity of TPMs are investigated in detail, leading to interesting outcomes. Moreover, different sensitivity characteristics are observed for linear and parabolic modification schemes. These outcomes; along with further evaluations on other aspects of design such as load intervals during operation, manufacturing tolerances, wear on gears, etc.; can be used in design guidelines for PGTs.

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