Page 24 - 《摩擦学学报》2020年第6期

第 40 卷 第 6 期 摩 擦 学 学 报 Vol 40 No 6
2020 年 11 月 Tribology Nov, 2020

DOI: 10.16078/j.tribology.2020029

不同压力角下自由端面对渐开线

直齿轮弹流润滑性能的影响

*
郭曼利, 王文中 , 张海波
(北京理工大学 机械与车辆学院，北京 100081)

摘 要: 区别于基于半空间理论的传统直齿轮弹流润滑模型，本文基于有限长空间解建立考虑轮齿自由端面影响的
渐开线直齿轮有限长弹流润滑模型. 采用叠加法构造自由端面，矩阵法和半解析法求解自由端面的影响，快速傅里
叶变换算法加速齿面弹性变形计算；采用统一Reynolds方程法求解油膜压力和油膜厚度. 以啮合节点为特征位置，
分析比较不同压力角下自由端面对直齿轮弹流润滑的影响. 结果表明：与半空间模型比较，考虑自由端面后端面峰
值压力降低，压力分布更均匀，最小油膜厚度增大；增大轮齿压力角，节点压力水平减小，油膜厚度增大；当压力角
不同时，自由端面对齿轮弹流润滑压力峰值的影响基本相当，对最小膜厚的影响较大.
关键词: 渐开线直齿轮; 自由端面; 压力角; 弹流润滑
中图分类号: TH117.2 文献标志码: A 文章编号: 1004-0595(2020)06–0707–09

The Influence of Free End Surfaces on Elastohydrodynamic
Lubrication of Involute Spur Gears with

Different Pressure Angles

*
GUO Manli, WANG Wenzhong , ZHANG Haibo

(School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China)
Abstract: A finite-length elastohydrodynamic lubrication (EHL) model of involute spur gears with consideration of free
end surfaces was established based on the solution to the finite-length space, which was different from the conventional
EHL model of spur gears based on half-space theory. The overlapping method was used to construct the free end
surfaces. Matrix formulation and semi-analytical method were utilized to solve the effect of free end surfaces and FFT
algorithm was utilized to speed up the calculation of the elastic deformation. The unified Reynolds equation method was
used to obtain the oil film pressure and thickness. The effect of free end surfaces on EHL of involute spur gears with
different pressure angles was analyzed and compared at the pitch point. The results showed that, compared with the
conventional half-space model, the free end surfaces reduced the peak pressure, homogenized the distribution of pressure
and increased the minimum oil film thickness. The level of pressure decreased and the film thickness increased as the
pressure angle increased. When different pressure angles were adopted, the influence of free end surfaces on the peak
pressure of the EHL of involute spur gears was approximately identical and that on the minimum film thickness was
significant.
Key words: involute spur gear; free end surface; pressure angle; elastohydrodynamic lubrication

Received 20 February 2020, revised 29 May 2020, accepted 9 June 2020, available online 28 November 2020.
*Corresponding author. E-mail: wangwzhong@bit.edu.cn, Tel: +86-13801271138.
The project was supported by the National Key R&D Program of China (2018YFB2000604) and the National Natural Science
Foundation of China (51675046).
国家重点研发计划(2018YFB2000604)和国家自然科学基金项目(51675046)资助.