Unified method for typical gear failure modeling and stiffness calculation based on the matrix equation

Abstract

The failure types in gear systems vary, with typical ones mainly including pitting, cracking, wear, and broken teeth. Different modeling and stiffness calculation methods have been developed for various gear failure types. A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness (TVMS) of faulty gears resulting from the use of different methods. Specifically, a gear tooth is discretized into a large number of microelements expressed with a matrix, and unified models of typical gear failures are built by adjusting the values of the matrix microelements. The values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method (PEM), so the matrix-based failure model can be perfectly matched with PEM. Afterward, a unified method for TVMS is established. Modeling of healthy and faulty gears with pitting, wear, crack, and broken tooth is performed with the matrix equation, and the corresponding TVMS values are calculated by incorporating the matrix models with PEM. On the basis of the results, the mechanism of typical fault types that affect TVMS is analyzed, and the conclusions are verified through the finite element method. The developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.

Graphical abstract

Keywords

gears / matrix equation / failure modeling / TVMS calculation / unified method

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