An analytical-finite-element method for calculating mesh stiffness of spur gear pairs with complicated foundation and crack

Gear weight optimization is mainly through thin-web and hole in gear foundation. In this paper, an analytical-finite-element model for calculating time-varying mesh stiffness of spur gear pairs with complicated foundation (thin-web and holes) and crack is developed. The pinion and gear foundations are simulated as cylinders and modeled by three-dimensional finite element. The tooth pair is equivalent to a spring and mesh stiffness of a tooth pair is obtained by potential energy method. The spring is rigidly coupled with the pinion and gear foundations. Then, three type examples are presented to verify the model. The first type example is three spur gear pairs with solid foundation. The second type example is gear pairs with thin-web and web holes. And the third example is a gear pair with the cracked foundation. The analysis results show that the model proposed in this paper is applicable and efficient for spur gears with complicated foundation and crack. Finally, the time-varying mesh stiffness is also studied to reveal the effects of web widths, web hole radii and crack lengths.