Abstract
The mesh stiffness of gear teeth is one of the major sources of excitation in gear systems. Many analytical and finite element methods have been proposed in order to determine the mesh stiffness of gears especially parallel axis spur gears. Most of these methods are not trivial because they involve complicated analyses which incorporate parameters like gear tooth error, gear spalling sizes and shapes, nonlinear contact stiffness and sliding friction before mesh stiffness can be determined. In this work, a method is proposed to determine the sun-planet and ring-planet mesh stiffnesses of a planetary gear system. This approach involves fitting a relationship between the measured natural frequencies from an experimental modal test and natural frequencies predicted using an analytical model of a planetary gear. This method is relatively easier compared to the existing methods which involve complicated analyses. For this study, the average mesh stiffness estimated is 12.5 MN/m.
Highlights
The determination of the mesh stiffness of planetary gear systems is critical to prediction of their dynamic responses
The red line denotes the error function when four natural frequencies were chosen from Table II while the black is for the error function when three natural frequencies were chosen
The minimum value in the error function corresponds to an estimated mesh stiffness of 1.0 × 107 N/m and this was taken as the sun-planet mesh stiffness in the analytical model
Summary
The determination of the mesh stiffness of planetary gear systems is critical to prediction of their dynamic responses. Zaigang and Yimin proposed a general analytical model for calculating the mesh stiffness of spur gears [16] They incorporated in the model, the effect of tooth errors which is as a result of tooth profile modifications, manufacturing errors or assembly errors. Fitting method in this study involves minimisation of error in the squared difference between the predicted and measured natural frequencies as a function of mesh stiffness This method which is relatively easier than the existing ones has not been used before to determine the mesh stiffness of a planetary gear. This was done by fitting a relationship between the natural frequencies measured from the experiment and those predicted by the analytical model. The natural frequencies are determined for a linear timeinvariant case
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