基于围道积分的润滑接触齿轮微点蚀损伤特征模拟

doi:10.13229/j.cnki.jdxbgxb20200903

吉林大学学报(工学版) ›› 2022, Vol. 52 ›› Issue (4): 799-810.doi: 10.13229/j.cnki.jdxbgxb20200903

• 车辆工程·机械工程 • 上一篇

基于围道积分的润滑接触齿轮微点蚀损伤特征模拟

赵洋^1,^2,³(),肖洋²,孙皓⁴,霍文浩⁴,冯松²,廖勇¹()

^1.重庆大学电气工程学院，重庆 400044
^2.重庆邮电大学先进制造工程学院，重庆 400065
^3.西安交通大学机械结构强度与振动国家重点实验室，西安 710039
^4.重庆通用工业（集团）有限责任公司，重庆 401336

收稿日期:2020-08-16 出版日期:2022-04-01 发布日期:2022-04-20
通讯作者: 廖勇 E-mail:zhaoyang@cqupt.edu.cn;yongliaocqu@vip.sina.com
作者简介:赵洋（1988-），男，副教授，博士. 研究方向：机械结构动力学，工程力学. E-mail： zhaoyang@cqupt.edu.cn
基金资助:
国家自然科学基金项目(51807019);机械结构强度与振动国家重点实验室开放基金项目(SV2020-KF-15);重庆市教委科学技术研究项目(KJZD-K201900604);重庆市博士后科研项目(XmT2018030)

Numerical simulation of micro pitting damage characteristics of lubricated contact gears based on contour integral

Yang ZHAO^1,^2,³(),Yang XIAO²,Hao SUN⁴,Wen-hao HUO⁴,Song FENG²,Yong LIAO¹()

^1.School of Electrical Engineering，Chongqing University，Chongqing 400044，China
^2.School of Advanced Manufacturing Engineering，Chongqing University of Posts and Telecommunications，Chongqing 400065，China
^3.State Key Laboratory for Strength and Vibration of Mechanical Structures，Xi'an Jiaotong University，Xi’an 710039，China
^4.Chongqing General Industry （Group） Co. ，Ltd. ，Chongqing 401336，China

Received:2020-08-16 Online:2022-04-01 Published:2022-04-20
Contact: Yong LIAO E-mail:zhaoyang@cqupt.edu.cn;yongliaocqu@vip.sina.com

摘要/Abstract

摘要：

基于围道积分的方法提出了一种考虑润滑接触对的齿轮齿面微点蚀模拟方法，通过建立其二维有限元数值模型，研究微点蚀裂纹扩展过程中的损伤特征，即应力强度因子变化规律及最终齿面点蚀形貌。润滑接触对模型考虑了齿轮相互接触载荷、接触关系以及弹流润滑条件。在ABAQUS中计算得到裂纹尖端处的应力强度因子K_I、K_II以及扩展角θ_C，然后根据最大切向应力（MTS）准则计算等效应力强度因子K_σ 并作为裂纹扩展的判别条件，进一步地探讨不同润滑状态对微点蚀的形成影响。结果表明：齿轮间充分润滑时，K_I和K_σ 随着裂纹长度的增加而快速增大，形成的点蚀坑更小；润滑不足时，K_I和K_σ 随着裂纹长度变化缓慢，形成的点蚀区域更大。研究结果可为后续微点蚀齿轮的接触疲劳寿命分析、在线磨损监测以及啮合刚度计算提供理论支持。

关键词: 机械设计及理论, 微点蚀, 围道积分, 损伤特征, 最大切向应力准则, 润滑状态

Abstract:

A method was proposed to simulate the micro pitting on gear tooth surface considering the lubrication contact pair based on the contour integral， and the damage characteristics of micro pitting， i.e.， the variation law of stress intensity factor and the final pitting morphology of tooth surface were studied by establishing its two-dimensional finite element numerical model. The contact loads， interactions and elasto-hydro dynamic lubrication （EHL） conditions of the gears were considered in the lubrication contact model. The stress intensity factors K_I，K_II and the propagation angle θ_C at the crack tip were calculated by ABAQUS. Then the equivalent stress intensity factor K_σ was calculated according to the maximum tangential stress （MTS） criterion and used as the criterion for crack propagation. The influence of different lubrication conditions on the formation of micro pitting was further discussed. The results indicate that K_I and K_σ are increasing rapidly with larger crack length and the size of pitting is smaller when the gears are lubricated adequately. By contrast， K_I and K_σ are changing slowly with crack length and the size of pitting is larger when the gears are sparely lubricated. The research results can provide theoretical support for contact fatigue life analysis， on-line wear monitoring and meshing stiffness calculation of micro-pitting gears.

Key words: mechanical design and theory, micro pitting, contour integral, damage characteristics, maximum tangential stress criterion, lubrication conditions

中图分类号:

TH117.1

赵洋,肖洋,孙皓,霍文浩,冯松,廖勇. 基于围道积分的润滑接触齿轮微点蚀损伤特征模拟[J]. 吉林大学学报(工学版), 2022, 52(4): 799-810.

Yang ZHAO,Yang XIAO,Hao SUN,Wen-hao HUO,Song FENG,Yong LIAO. Numerical simulation of micro pitting damage characteristics of lubricated contact gears based on contour integral[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(4): 799-810.

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参数	名称	数值
齿轮材料、结构参数	等效接触模型的半径R^*	10 mm
	最大接触压力p₀	1550 MPa
	接触半长b	0.2 mm
	杨氏模量E	206 GPa
	泊松比μ	0.3
润滑油相关参数	密度ρ	900 kg/m³
	运动粘度v	220 mm²/s
	卷吸速度u	5 m/s
	压力粘度系数α	0.018 mm²/N

	a/μm	K_I /（MPa·m^1/2）	K_II /（MPa·m^1/2）	K_σ /（MPa·m^1/2）	θ_C /（°）	Eq.9 /10^-3
文献值	20	8.85	4.18	11.13	-39	4.08
本文值		8.65	4.04	10.84	-38.74	0.46
误差		2.26%	3.35%	2.61%	0.67%	/
文献值	22	15.67	3.29	16.64	-22	8.78
本文值		15.50	3.25	16.45	-21.95	0.63
误差		1.08%	1.22%	1.14%	0.23%	/
文献值	24	23.19	3.59	23.98	-15	811.01
本文值		26.65	3.64	27.37	-15.01	5.40
误差		14.92%	1.39%	14.14%	0.07%	/
文献值	26	53.32	5.66	54.2	-12	136.91
本文值		57.83	6.52	58.91	-12.56	3.91
误差		8.46%	15.19%	8.69%	4.67%	/

a/μm	工况	K_I /（MPa·m^1/2）	K_II /（MPa·m^1/2）	K_σ 最大值 /（MPa·m^1/2）	θ_C /（°）
20	I	0.16	-0.06	10.27 （工况IV）	-33.88 （工况IV）
	II	0.87	0.24
	III	8.31	3.26
	IV	8.74	3.27
	V	8.72	3.05
	VI	8.11	2.55
	VII	7.35	2.05
22	I	0.12	-0.05	14.70 （工况IV）	-19.35 （工况IV）
	II	1.29	0.15
	III	13.46	2.59
	IV	14.05	2.54
	V	13.84	2.28
	VI	12.67	1.80
	VII	11.28	1.32
24	I	0.14	-0.02	22.67 （工况IV）	-14.66 （工况IV）
	II	1.96	0.19
	III	21.23	3.00
	IV	22.10	2.94
	V	21.76	2.66
	VI	19.81	2.10
	VII	17.58	1.56
26	I	0.25	0.01	41.42 （工况IV）	-13.17 （工况IV）
	II	3.57	0.37
	III	38.99	4.84
	IV	40.59	4.81
	V	39.98	4.46
	VI	36.40	3.70
	VII	32.31	2.93
28	I	0.69	0.07	113.73 （工况IV）	-12.40 （工况IV）
	II	9.85	1.05
	III	107.30	12.23
	IV	111.70	12.43
	V	110.00	11.87
	VI	100.30	10.31
	VII	89.04	8.69

润滑状态	油膜厚度h_c /μm	a /μm	K_I /（MPa·m^1/2）	K_II /（MPa·m^1/2）	K_σ /（MPa·m^1/2）	θ_C /（°）
边界润滑	2	20	8.69	3.23	10.19	-33.71
		22	12.81	2.03	13.27	-17.19
		24	15.38	1.19	15.52	-8.72
		26	16.04	0.36	16.05	-2.58
		28	14.83	-0.65	14.87	4.98
部分弹流润滑	4	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.7	-19.35
		24	20.23	2.61	20.72	-14.25
		26	24.79	1.34	24.9	-6.15
		28	22.86	-0.63	22.89	3.14
部分弹流润滑	6	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.7	-19.35
		24	22.10	2.94	22.67	-14.66
		26	31.65	2.78	32.01	-9.88
		28	29.85	-0.15	29.85	0.58
部分弹流润滑	8	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.7	-19.35
		24	22.10	2.94	22.67	-14.66
		26	37.06	4.00	37.69	-12.05
		28	36.68	0.49	36.69	-1.52
全膜润滑	10	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.7	-19.35
		24	22.10	2.94	22.67	-14.66
		26	40.59	4.81	41.42	-13.17
		28	43.30	1.23	43.35	-3.26
全膜润滑	12	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.7	-19.35
		24	22.10	2.94	22.67	-14.66
		26	40.59	4.81	41.42	-13.17
		28	50.14	2.38	50.31	-5.42
全膜润滑	∞	20	8.74	3.27	10.27	-33.88
		22	14.05	2.54	14.70	-19.35
		24	22.10	2.94	22.67	-14.66
		26	40.59	4.81	41.42	-13.17
		28	111.70	12.43	113.73	-12.40

油膜厚度 h_c/μm	裂纹最终长度a/μm	点蚀长轴尺寸L/μm	点蚀深度D /μm
2	32.50	29.057	6.84
4	30.83	26.744	6.84
6	30.49	26.163	6.84
8	30.33	25.866	6.84
10	30.25	25.694	6.84
12	30.22	25.601	6.84
∞	30.12	25.320	6.84

基于围道积分的润滑接触齿轮微点蚀损伤特征模拟

Numerical simulation of micro pitting damage characteristics of lubricated contact gears based on contour integral

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