Journal of Jilin University(Engineering and Technology Edition) ›› 2020, Vol. 50 ›› Issue (2): 494-503.doi: 10.13229/j.cnki.jdxbgxb20181131

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Gear contact stiffness under mixed lubrication status

Gong CHENG1(),Ke XIAO1(),Jia-xu WANG1,2,Wei PU2,Yan-feng HAN1   

  1. 1.College of Mechanical Engineering，Chongqing University, Chongqing 400044，China
    2.School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
  • Received:2018-11-13 Online:2020-03-01 Published:2020-03-08
  • Contact: Ke XIAO E-mail:chenggong@cqu.edu.cn;470567110@qq.com

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Abstract:

In gear transmission mechanism, stiffness is undoubtedly an important parameter, and considering the ubiquitous lubricant in mechanical system, it is necessary to study the contact stiffness under the condition of mixed lubrication. It is certain that the gear contact stiffness considering lubrication is the result of a multi-factor combination. In real working conditions, the gear contact stiffness is time-varying due to the variation of meshing force，the influence of rough interface and the presence of lubricant. In fact, the mixed lubrication solution is crucial. Once the film thickness and pressure distribution under mixed lubrication are known, the final result can be obtained by substituting the obtained results into the calculation expression. In order to study the contact stiffness of gears under mixed lubrication conditions, a calculation method is proposed. First, the motion parameters and normal contact force during the gear meshing process are determined. Second, the mixed elastohydrodynamic lubrication method is used to obtain the film thickness and pressure distribution on the meshing rough tooth surface at different moment. Finally, the obtained film thickness and pressure distribution are brought into the contact stiffness calculation formula to get the contact stiffness of gear at different times. The influence of different working conditions on the contact stiffness of gear is further discussed, and the contact stiffness of smooth surface is compared with that of rough surface. The results show that the speed and load have obvious influences on the contact stiffness. The higher the gear speed, the smaller the contact stiffness, and the smaller the applied load, the greater the contact stiffness of the gear.

Key words: mechanical design, mixed lubrication, contact stiffness, rough surface, gear mesh

CLC Number: 

  • TH117.2

Fig.1

Basic geometric parameters of a gear pair"

Table 1

Parameters of gears"

参数齿轮1齿轮2
齿数2520
模数44
压力角/(°)2020
基圆半径/mm91.83478.934
转速/(r·min -1) 1 0001 250

Fig.2

Curvature radius and speed during gear meshing"

Fig.3

Variation of meshing load with roll angle"

Fig.4

Diagram of rough surface contact model"

Fig.5

Rough surface morphology and corresponding film thickness and asperity contact ratio when speed is 2 000 r/min and load is 100 N·m"

Fig.6

Comparison of film thickness and pressure distribution along x-axis, and that of contact stiffness of smooth and rough surfaces when speed is 2 000 r/min and load is 50 N·m "

Fig.7

Film thickness and pressure distribution at different meshing points when speed is 2 000 r/min and load is 100 N·m"

Fig.8

Film thickness and contact stiffness change with rolling angle at different speeds when load is 100 N·m"

Fig.9

Film thickness and pressure distribution at same meshing point for different loads when speed is 2 000 r/min"

Fig.10

Film thickness and contact stiffness change with rolling angle under different loads when speed is 2 000 r/min"

1 Greenwood J A, Williamson J B P. Contact of nominally flat surfaces[J]. Proceedings of the Royal Society of London, Series A, 1966, 295( 1442): 300- 319.
2 张学良, 黄玉美, 傅卫平, 等. 粗糙表面法向接触刚度的分形模型[J]. 应用力学学报, 2000, 17( 2): 31- 35.
Zhang Xue-liang, Huang Yu-mei, Fu Wei-ping, et al. Fractal model of normal contact stiffness between rough surfaces[J]. Chinese Journal of Applied Mechanics, 2000, 17( 2): 31- 35.
3 Akarapu S, Sharp T, Robbins M O. Stiffness of contacts between rough surfaces[J]. Physical Review Letters, 2011, 106( 20): 204- 301.
4 尤晋闽, 陈天宁. 基于分形接触理论的结合面法向接触参数预估[J]. 上海交通大学学报, 2011, 45( 9): 1275- 1280.
You Jin-min, Chen Tian-ning. Estimation for normal parameters of joint surfaces based on fractal theory[J]. Journal of Shanghai Jiaotong University, 2011, 45( 9): 1275- 1280.
5 Hyun S, Robbins M O. Elastic contact between rough surfaces: effect of roughness at large and small wavelengths[J]. Tribology International, 2007, 40( 10-12): 1413- 1422.
6 李辉光, 刘恒, 虞烈. 粗糙机械结合面的接触刚度研究[J]. 西安交通大学学报, 2011, 45( 6): 69- 74.
Li Hui-guang, Liu Heng, Yu Lie. Contact stiffness of rough mechanical joint surface[J]. Journal of Xi'an Jiaotong University, 2011, 45( 6): 69- 74.
7 Pohrt R, Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces[J]. Physical Review Letters, 2012, 108( 10): 1- 12.
8 Pohrt R, Popov V L. Contact stiffness of randomly rough surfaces[J/OL].[ 2018-11-13].
9 庄艳, 李宝童, 洪军, 等. 一种结合面法向接触刚度计算模型的构建[J]. 上海交通大学学报, 2013, 47( 2): 180- 186.
Zhuang Yan, Li Bao-tong, Hong Jun, et al. A normal contact stiffness model of the interface [J]. Journal of Shanghai Jiaotong University, 2013, 47( 2): 180- 186.
10 田小龙, 王雯, 傅卫平, 等. 考虑微凸体相互作用的机械结合面接触刚度模型[J]. 机械工程学报, 2017, 53( 17): 149- 159.
Tian Xiao-long, Wang Wen, Fu Wei-Ping, et al. Contact stiffness model of mechanical joint surfaces considering the asperity interactions[J]. Journal of Mechanical Engineering, 2017, 53( 17): 149- 159.
11 王雯, 吴洁蓓, 傅卫平, 等. 机械结合面法向动态接触刚度理论模型与试验研究[J]. 机械工程学报, 2016, 52( 13): 123- 130.
Wang Wen, Wu Jie-bei, Fu Wei-ping, et al. Theoretical and experimental research on normal dynamic contact stiffness of machined joint surfaces[J]. Journal of Mechanical Engineering, 2016, 52( 13): 123- 130.
12 傅卫平, 娄雷亭, 高志强, 等. 机械结合面法向接触刚度和阻尼的理论模型[J]. 机械工程学报, 2017, 53( 9): 73- 82.
Fu Wei-ping, Lou Lei-ting, Gao Zhi-qiang， et al. Theoretical model for the contact stiffness and damping of mechanical joint surface[J]. Journal of Mechanical Engineering, 2017, 53( 9): 73- 82.
13 赵韩, 陈奇, 黄康. 两圆柱体结合面的法向接触刚度分形模型[J]. 机械工程学报, 2011, 47( 7): 53- 58.
Zhao Han, Chen Qi, Huang Kang. Fractal model of normal contact stiffness between two cylinders’ joint interfaces[J]. Journal of Mechanical Engineering, 2011, 47( 7): 53- 58.
14 Chen Q， Xu F， Liu P, et al. Research on fractal model of normal contact stiffness between two spheroidal joint surfaces considering friction factor[J]. Tribology International, 2016, 97: 253- 264.
15 刘鹏, 赵韩, 黄康, 等. 线段齿轮法向接触刚度的改进分形模型研究[J]. 机械工程学报, 2018, 54( 7): 114- 122.
Liu Peng, Zhao Han, Huang Kang, et al. Research on normal contact stiffness of micro-segments gear based on improved fractal model[J]. Journal of Mechanical Engineering, 2018, 54( 7): 114- 122.
16 欧阳天成, 陈南, 牛亚峰. 不同粗糙面渐开线齿轮混合弹流润滑[J]. 吉林大学学报: 工学版, 2016, 46( 6): 1933- 1939.
Ouyang Tian-cheng， Chen Nan， Niu Ya-feng. Mixed elastohydrodynamic lubrication for involute gear with different rough surfaces[J]. Journal of Jilin University (Engineering and Technology Edition), 2016, 46( 6): 1933- 1939.
17 张阔, 谭庆昌, 王顺, 等. 表面粗糙度幅值对点接触混合润滑的影响[J]. 吉林大学学报: 工学版, 2012, 42( 2): 377- 381.
Zhang Kuo, Tan Qing-chang, Wang Shun, et al. Effect of surface roughness amplitude on point contact mixed lubrication condition[J]. Journal of Jilin University (Engineering and Technology Edition), 2012, 42( 2): 377- 381.
18 Dwyer-joyce R S, Reddyhoff T, Zhu J. Ultrasonic measurement for film thickness and solid contact in elastohydrodynamic lubrication[J]. Journal of Tribology, 2011, 133( 3): 031501.
19 Xiao H, Sun Y, Xu J. Investigation into the normal contact stiffness of rough surface in line contact mixed elastohydrodynamic lubrication[J]. Tribology Transactions, 2018, 41( 4): 742- 753.
20 Zhou C, Xiao Z, Chen S, et al. Normal and tangential oil film stiffness of modified spur gear with non-Newtonian elastohydrodynamic lubrication[J]. Tribology International, 2017, 109: 319- 327.
21 Zhou C, Xiao Z. Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive[J]. Applied Mathematical Modeling, 2018, 61: 634- 649.
22 Ren N, Zhu D, Chen W W, et al. A three-dimensional deterministic model for rough surface line-contact EHL problems[J]. Journal of Tribology, 2009, 131( 1): 011501.
23 Masjedi M, Khonsari M M. Film thickness and asperity load formulas for line-contact elastohydrodynamic lubrication with provision for surface roughness[J]. Journal of Tribology, 2012, 134( 1): 011503.
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