基于最优凸度比的圆柱滚子轴承滚子相切与滚道全凸联合修形方法探究

靳先明; 邱明; 张家铭; 周大威; 毕明龙

doi:10.13224/j.cnki.jasp.20240549

基于最优凸度比的圆柱滚子轴承滚子相切与滚道全凸联合修形方法探究

doi: 10.13224/j.cnki.jasp.20240549

靳先明^1,,
邱明^{1, 2,*, ,},
张家铭¹,
周大威³,
毕明龙³

1.
河南科技大学机电工程学院，河南洛阳 471003
2.
机械装备先进制造河南省协同创新中心，河南洛阳 471003
3.
中国航发哈尔滨轴承有限公司，哈尔滨 150025

基金项目: 国家自然科学基金（52275186）；中原学者资助项目（244000510001）

详细信息

作者简介:
靳先明（1999-），男，硕士，主要从事轴承修形及摩擦特性研究。E-mail：jxm15993998187@163.com

通讯作者:
邱明（1969-），女，教授，博士，主要从事轴承设计及理论研究。E-mail：qiuming@haust.edu.cn

中图分类号: V232；TH133.3
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- 被引次数: 0
出版历程
- 收稿日期: 2024-08-05
- 网络出版日期: 2026-02-13

Combined modification method exploration of roller tangent and raceway full convexity based on optimal convexity ratio for cylindrical roller bearing

1.
School of Mechatronics Engineering，Henan University of Science and Technology，Luoyang Henan 471003，China
2.
Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province，Luoyang Hennan 471003，China
3.
Harbin Bearing Company Limited，Aero Engine Corporation of China，Harbin 150025，China

摘要

摘要:
针对圆柱滚子轴承接触线上应力分布的不均匀问题，提出一种滚子相切与滚道全凸联合修形方法。在建立有限长线接触弹流润滑模型的基础上，探究分析了联合修形方法下的应力分布特点，给出了最优凸度比的计算方法（定义凸度比为滚子-滚道同时修形时滚子凸度量与滚道凸度量的比值）。结果表明：采用联合修形方法时，联合修形曲线存在最优凸度比，由载荷、总凸度量、直母线长度决定，在此最优凸度比下，接触应力存在3个相等的极值，接触应力的分布更加均匀，最大接触应力更小。此外，随着联合修形曲线的直母线长度增大，最大接触应力先减小后趋于稳定。研究成果为滚子-滚道接触副的修形设计提供一种可借鉴的新方法，该方法可以提高圆柱滚子轴承接触应力分布的均匀性。
- 圆柱滚子轴承 /
- 联合修形 /
- 凸度比 /
- 载荷分布均匀度 /
- 接触应力
Abstract:
Aiming at the problem of uneven stress distribution on the contact line of cylindrical roller bearings, a combined modification method of roller tangent and raceway full convexity is proposed. Based on establishing the elastohydrodynamic lubrication model of finite line contact, the stress distribution characteristics under this modification method were explored and analyzed, and the calculation method of optimal convexity ratio was also provided (the convexity ratio is defined as the ratio of roller convexity to raceway convexity when roller-raceway is modified simultaneously). The results show that when using the combined modification method, there is an optimal crown ratio in the joint modification curve. This ratio is determined by the load, total convexity, and the length of the straight busbar. Within this optimal crown ratio, there are three equal extremes of contact stress, and the distribution of contact stress is more uniform. The maximum contact stress is reduced. Furthermore, with the increase of the straight bus length of the joint modification curve, the maximum contact stress initially decreases and then stabilizes. These research findings introduce a new reference method for the modification design of roller-raceway contact pairs, which can improve the uniformity of contact stress distribution of cylindrical roller bearings.
- cylindrical roller bearings /
- joint modification /
- convexity ratio /
- uniformity of load distribution /
- contact stress

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图 1 滚子-滚道接触副模型示意图

Figure 1. Schematic diagram of roller-raceway contact sub-model

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图 2 试验装置

Figure 2. Test apparatus

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图 3 载荷分布对比

Figure 3. Load distribution comparison

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图 4 测试工况的理论计算结果

Figure 4. Theoretical calculation results of test conditions

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图 5 不同凸度比下的接触应力分布

Figure 5. Contact stress distribution under different convexity ratios

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图 6 凸度比与接触应力的拟合曲线

Figure 6. Fitting curve of convexity ratio and contact stress

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图 7 不同修形方法的接触应力分布

Figure 7. Contact stress distribution of different modification methods

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图 8 载荷对最优凸度比的影响

Figure 8. Effect of load on the optimal convexity ratio

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图 9 最优凸度比下载荷对接触应力分布的影响

Figure 9. Effect of load on contact stress distribution under optimal convexity ratio

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图 10 总凸度量对最优凸度比的影响

Figure 10. Effect of total convexity on the optimal convexity ratio

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图 11 最优凸度比下总凸度量对接触应力分布的影响

Figure 11. Effect of total convexity on contact stress distribution under optimal convexity ratio

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图 12 直母线长度对最优凸度比的影响

Figure 12. Effect of straight bus length on the optimal convexity ratio

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图 13 最优凸度比下直母线长度对接触应力分布的影响

Figure 13. Effect of the straight bus length on the contact stress distribution under the optimal convexity ratio

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图 14 轴系模型

Figure 14. Shafting model

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图 15 修形方法的仿真对比验证

Figure 15. Simulation and comparison verification of shaping methods

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表 1 最小膜厚的计算值与文献值对比

Table 1. Calculated value of minimum film thickness is compared with the literature value

项目		轴承载荷/kN
项目		0.5	1	2	3
最小膜厚/µm	文献值	0.250	0.193	0.136	0.125
最小膜厚/µm	计算值	0.204	0.167	0.130	0.122
相对误差/%		−18.4	−11.5	−4.41	−2.4

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表 2 轴承及润滑油相关参数

Table 2. Bearing and lubricating oil related parameters

参数名称	数值
内径d/mm	35
外径D/mm	62
节圆直径d_m/mm	48.5
滚子直径D_w/mm	6.5
滚子长度l/mm	6.5
综合弹性弹性模量E′/GPa	225.3
Barus黏压系数α/GPa⁻¹	22
大气压下润滑油黏度η/（Pa·s）	0.08
大气压下润滑油密度ρ/（kg·m³）	875

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表 3 不同修形方法的最大接触应力对比

Table 3. Comparison of the maximum contact stress of different modification methods

常规修形方法	最大接触应力/GPa	联合修形的最大接触应力/GPa	减小百分比/%
滚子相交修形	1.69	1.48	12.43
滚子全凸修形	1.62	1.48	8.64
滚子相切修形	1.56	1.48	5.13

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表 4 不同修形方法的载荷分布均匀度对比

Table 4. Comparison of load distribution uniformity of different modification methods

常规修形方法	载荷分布均匀度	联合修形的载荷分布均匀度	减小百分比/%
滚子相交修形	1.37	1.15	16.06
滚子全凸修形	1.35	1.15	14.81
滚子相切修形	1.21	1.15	4.96

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表 5 不同修形方法的最大接触应力对比

Table 5. Comparison of the maximum contact stress of different modification methods

常规修形方法	最大接触应力/GPa	联合修形的最大接触应力/GPa	减小百分比/%
滚子相切修形	1.55	1.50	3.23
滚子相交修形	1.86	1.50	19.35
滚子全凸修形	1.68	1.50	10.71

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表 6 不同修形方法的载荷分布均匀度对比

Table 6. Comparison of load distribution uniformity of different modification methods

修形方法	载荷分布均匀度	联合修形的载荷分布均匀度	减小百分比/%
滚子相切修形	1.14	1.10	3.50
滚子相交修形	1.38	1.10	20.29
滚子全凸修形	1.27	1.10	13.39

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参考文献(24)

[1]	余永健, 李济顺, 陈国定, 等. 基于内圈滚道廓形的圆柱滚子轴承旋转精度[J]. 航空动力学报, 2017, 32(1): 155-161. YU Yongjian, LI Jishun, CHEN Guoding, et al. Rotational accuracy of the cylindrical roller bearing based on inner raceway profile[J]. Journal of Aerospace Power, 2017, 32(1): 155-161. (in Chinese YU Yongjian, LI Jishun, CHEN Guoding, et al. Rotational accuracy of the cylindrical roller bearing based on inner raceway profile[J]. Journal of Aerospace Power, 2017, 32(1): 155-161. (in Chinese)
[2]	邓四二, 滕弘飞, 周彦伟, 等. 航空发动机主轴轴承滚道表面光饰强化处理[J]. 航空动力学报, 2006, 21(3): 545-549. DENG Sier, TENG Hongfei, ZHOU Yanwei, et al. Luster Polish strengthening for race surface of the mainshaft bearings of aeroengine[J]. Journal of Aerospace Power, 2006, 21(3): 545-549. (in Chinese doi: 10.3969/j.issn.1000-8055.2006.03.020 DENG Sier, TENG Hongfei, ZHOU Yanwei, et al. Luster Polish strengthening for race surface of the mainshaft bearings of aeroengine[J]. Journal of Aerospace Power, 2006, 21(3): 545-549. (in Chinese) doi: 10.3969/j.issn.1000-8055.2006.03.020
[3]	李伟伟, 陈晓阳, 沈雪瑾, 等. 歪斜状况下滚子轴承的接触应力求解与分析[J]. 中国机械工程, 2011, 22(17): 2034-2039. LI Weiwei, CHEN Xiaoyang, SHEN Xuejin, et al. Contact pressure calculation and analysis of roller bearings in skewing condition[J]. China Mechanical Engineering, 2011, 22(17): 2034-2039. (in Chinese LI Weiwei, CHEN Xiaoyang, SHEN Xuejin, et al. Contact pressure calculation and analysis of roller bearings in skewing condition[J]. China Mechanical Engineering, 2011, 22(17): 2034-2039. (in Chinese)
[4]	LUNDBERG G. Elastische beruehrung zweier halbraeume[J]. Forschung aufdem Gebiet des Ingenieurwesens A, 1939, 10(5): 201-211.
[5]	POPLAWSKI J V, PETERS S M, ZARETSKY E V. Effect of roller profile on cylindrical roller bearing life prediction: Part Ⅱ comparison of roller profiles[J]. Tribology Transactions, 2001, 44(3): 417-427. doi: 10.1080/10402000108982476
[6]	OSWALD F B, ZARETSKY E V, POPLAWSKI J V. Effect of roller geometry on roller bearing load-life relation[J]. Tribology Transactions, 2014, 57(5): 928-938. doi: 10.1080/10402004.2014.927545
[7]	FUJIWARA H, KOBAYASHI T, KAWASE T, et al. Optimized logarithmic roller crowning design of cylindrical roller bearings and its experimental demonstration[J]. Tribology Transactions, 2010, 53(6): 909-916. doi: 10.1080/10402004.2010.510619
[8]	陈志. 不确定因素下圆柱滚子轴承多目标稳健性设计[D]. 大连: 大连理工大学, 2022. CHEN Zhi. Multi-objective robust design of cylindrical roller bearings with uncertain factors[D]. Dalian: Dalian University of Technology, 2022. (in Chinese CHEN Zhi. Multi-objective robust design of cylindrical roller bearings with uncertain factors[D]. Dalian: Dalian University of Technology, 2022. (in Chinese)
[9]	DUAN Hongyu, SONG Jiawei, WANG Zhijian. Lubrication and fatigue life evaluation of high-speed cylindrical roller bearing under misalignment[J]. Mathematical Problems in Engineering, 2020, 2020(1): 2068924. doi: 10.1155/2020/2068924
[10]	LIU Xiaoling, LI Shuyi, YANG Ping, et al. On the lubricating mechanism of roller skew in cylindrical roller bearings[J]. Tribology Transactions, 2013, 56(6): 929-942. doi: 10.1080/10402004.2013.812760
[11]	QIU Liangwei, LIU Shuangbiao, CHEN Xiaoyang, et al. Lubrication and loading characteristics of cylindrical roller bearings with misalignment and roller modifications[J]. Tribology International, 2022, 165: 107291. doi: 10.1016/j.triboint.2021.107291
[12]	ZHU Dong, WANG Jiaxu, REN Ning, et al. Mixed elastohydrodynamic lubrication in finite roller contacts involving realistic geometry and surface roughness[J]. Journal of Tribology, 2012, 134: 011504. doi: 10.1115/1.4005952
[13]	吴继强, 王黎钦, 陆宇帆, 等. 几何修形对低速圆柱滚子轴承混合润滑性能的影响研究[J]. 摩擦学学报, 2019, 39(4): 470-478. WU Jiqiang, WANG Liqin, LU Yufan, et al. Geometric modification on mixed lubrication performance of low-speed cylindrical roller bearing[J]. Tribology, 2019, 39(4): 470-478. (in Chinese WU Jiqiang, WANG Liqin, LU Yufan, et al. Geometric modification on mixed lubrication performance of low-speed cylindrical roller bearing[J]. Tribology, 2019, 39(4): 470-478. (in Chinese)
[14]	吝水林, 孙建亮, 彭艳. 高速板带轧机四列滚动轴承非均匀接触力学性能及修形优化研究[J]. 机械工程学报, 2021, 57(19): 128-137. LIN Shuilin, SUN Jianliang, PENG Yan. Research on non-uniform contact mechanical properties and modification optimization of four-row rolling bearings in high speed strip mill[J]. Journal of Mechanical Engineering, 2021, 57(19): 128-137. (in Chinese LIN Shuilin, SUN Jianliang, PENG Yan. Research on non-uniform contact mechanical properties and modification optimization of four-row rolling bearings in high speed strip mill[J]. Journal of Mechanical Engineering, 2021, 57(19): 128-137. (in Chinese)
[15]	CAO Renshui, BAI Hang, CAO Hui, et al. Mixed lubrication analysis of tapered roller bearings and crowning profile optimization based on numerical running-In method[J]. Lubricants, 2023, 11(3): 97. doi: 10.3390/lubricants11030097
[16]	高泽成. 外圈滚道带凸度的圆柱滚子轴承[J]. 轴承, 1996(10): 14-16. GAO Zecheng. Cylindrical roller bearing with convex outer ring raceway[J]. Bearing, 1996(10): 14-16. (in Chinese GAO Zecheng. Cylindrical roller bearing with convex outer ring raceway[J]. Bearing, 1996(10): 14-16. (in Chinese)
[17]	李广志. 轴承凸度滚道及其电化学机械复合加工方法研究[D]. 山东东营: 中国石油大学(华东), 2012. LI Guangzhi. Study on bearing raceway crown and the method for its electrochemical mechanical machining[D]. Dongying, Shandong: China University of Petroleum (Huadong), 2012. (in Chinese LI Guangzhi. Study on bearing raceway crown and the method for its electrochemical mechanical machining[D]. Dongying, Shandong: China University of Petroleum (Huadong), 2012. (in Chinese)
[18]	ACAR E, ÜSTÜN E E, ALI GÜLER M, et al. Design of an energy efficient cylindrical roller bearing[J]. Mechanics Based Design of Structures and Machines, 2024, 52(2): 826-847. doi: 10.1080/15397734.2022.2124172
[19]	ZHANG Y, BIBOULET N, VENNER C H, et al. Prediction of the stribeck curve under full-film elastohydrodynamic lubrication[J]. Tribology International, 2020, 149: 105569. doi: 10.1016/j.triboint.2019.01.028
[20]	YANG X, LI Y, LIU G, et al. Effect of surface roughness on elastohydrodynamic lubrication performance of cylindrical roller bearing[J]. Tehnički Vjesnik, 2019, 26(3): 710-721. doi: 10.17559/tv-20190104091451
[21]	史修江, 王黎钦. 基于拟动力学的航空发动机主轴滚子轴承热弹流润滑分析[J]. 机械工程学报, 2016, 52(3): 86-92. SHI Xiujiang, WANG Liqin. TEHL analysis of aero-engine mainshaft roller bearing based on quasi-dynamics[J]. Journal of Mechanical Engineering, 2016, 52(3): 86-92. (in Chinese doi: 10.3901/JME.2016.03.086 SHI Xiujiang, WANG Liqin. TEHL analysis of aero-engine mainshaft roller bearing based on quasi-dynamics[J]. Journal of Mechanical Engineering, 2016, 52(3): 86-92. (in Chinese) doi: 10.3901/JME.2016.03.086
[22]	AWATI V B, NAIK S. An Isothermal Elastohydrodynamic lubrication of elliptical contact with Multigrid method[J]. Australian Journal of Mechanical Engineering, 2020, 18(3): 375-384. doi: 10.1080/14484846.2018.1531810
[23]	LI Meng, JING Minqing, CHEN Zengfan, et al. An improved ultrasonic method for lubricant-film thickness measurement in cylindrical roller bearings under light radial load[J]. Tribology International, 2014, 78: 35-40. doi: 10.1016/j.triboint.2014.04.023
[24]	白晓波, 吉晓民, 王毅. 滚针轴承载荷分布影响因素的分析及其优化[J]. 机械科学与技术, 2014, 33(8): 1186-1191. BAI Xiaobo, JI Xiaomin, WANG Yi. Analysis and optimization of load distribution influence factors of needle bearings[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(8): 1186-1191. (in Chinese doi: 10.13433/j.cnki.1003-8728.2014.0815 BAI Xiaobo, JI Xiaomin, WANG Yi. Analysis and optimization of load distribution influence factors of needle bearings[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(8): 1186-1191. (in Chinese) doi: 10.13433/j.cnki.1003-8728.2014.0815