An Improved Mesh Stiffness Model for a Gear Tooth With Double Cracks on Both Sides Considering Opened and Closed States

Abstract

Research on the failure mechanisms of gears with multiple cracks has gained widespread attention. Among these, the study of the mesh stiffness characteristics of gears with multiple cracks is crucial for optimizing gear design and improving transmission reliability. However, for the case where cracks exist on both sides of a gear tooth, the impact of multiple cracks on stiffness is currently simplified as a “dead zone,” neglecting the differences in the stress characteristics of opened cracks and closed cracks under the mesh force. This simplification leads to lower accuracy in calculating the mesh stiffness of gears with multiple cracks. In this study, a mesh stiffness calculation model for a gear tooth with double cracks is established. The differences in the stress characteristics of opened cracks and closed cracks on both sides of the gear tooth under the mesh force are considered. Using the concept of microelement integration, the irregular geometrical region formed by the closed crack and the tooth profile is mapped to an equivalent rectangle of equal area. A load model for gear teeth with closed cracks is proposed, and the expressions for bending stiffness, shear stiffness, and mesh stiffness of a gear tooth with double cracks are revised. The mesh stiffness of a gear tooth with closed cracks is measured using the noncontact DIC technique to verify the accuracy of the proposed calculation method. The study shows that the weakening effect of closed cracks on bending stiffness and mesh stiffness is smaller than that of opened cracks, and the difference in their effects on stiffness gradually increases with the crack length and inclination angle. For both single-crack and double-crack cases with closed cracks, the theoretical prediction values based on the proposed mesh stiffness calculation method exhibit an error of less than 10% when compared with experimental measurements.

Keywords

closed crack / digital image correlation measurement / double cracks on a gear tooth / time-varying mesh stiffness

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2025 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.