An Improved Stiffness Model for Spur Gear with Surface Roughness Under Thermal Elastohydrodynamic Lubrication

Shihua Zhou (), Xuan Li, Chao An, Tengyuan Xu, Dongsheng Zhang, Ye Zhang and Zhaohui Ren ()
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Shihua Zhou: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Xuan Li: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Chao An: Marketing Service Center of State Grid Liaoning Electric Power Co., Ltd., Shenyang 110168, China
Tengyuan Xu: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Dongsheng Zhang: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Ye Zhang: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Zhaohui Ren: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China

Mathematics, 2025, vol. 13, issue 20, 1-23

Abstract: To investigate the contact performances and meshing characteristics of gears systematically, an improved comprehensive meshing stiffness model of spur gears with consideration of the tooth surface morphology, lubrication, friction, and thermal effects is presented based on the thermal elastohydrodynamic lubrication (TEHL) theory. The fractal feature of the tooth surface morphology is verified experimentally and characterized by the Weierstrass–Mandelbrot fractal function. Based on this, the rough contact stiffness, oil film stiffness, and thermal stiffness are introduced into the stiffness model. Comparisons between smooth and rough models are carried out, and the maximum temperature rise is increased by 24.7%. Subsequently, the influences of the torque, rotational speed, and fractal parameters on the oil film pressure and thickness, friction and temperature rise, and contact stiffness and comprehensive meshing stiffness are investigated. The results show that the oil film pressure and the maximum temperature rise increase by 125.18% and 69.08%, respectively, with an increasing torque from 20 N·m to 300 N·m. As the rotational speed is increased, the oil film thickness sharply increases, the rough peak contact area and friction reduce, and the stiffness fluctuation weakens. For fractal parameters, the oil film pressure and film thickness, friction, and temperature rise are nonlinear with changes in the fractal dimension D and fractal scale characteristic G . The results reveal that this work provides a more reasonable analysis for understanding the meshing characteristics and the design and processing of gears.

Keywords: stiffness model; TEHL; spur gear; tooth surface morphology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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