浮环密封端面分形磨损预估模型及数值分析

doi:10.11949/0438-1157.20221175

摘要/Abstract

摘要：

针对航空发动机石墨浮环密封端面磨损问题，基于修正的分形接触理论及Archard磨损理论，从微观角度推导出石墨浮环密封端面的分形磨损预估模型，并采用文献实验数据验证模型的合理性。最后通过数值仿真方法分析研究表面形貌参数及工况参数对浮环密封端面磨损率的影响规律。研究结果表明：石墨浮环密封端面磨损率随着分形维数的增加，先增大后减小，当分形维数处于1.45~1.65时存在最小磨损率；当分形维数一定时，石墨浮环密封端面的磨损率随表面特征尺度、摩擦因数及浮环滑移速度的增大而增大；石墨浮环密封端面的磨损率主要与频率指数最小等级及后续的7个等级微凸体相关，其余微凸体对整个浮环密封端面的磨损率影响可忽略不计。

关键词: 分形, 浮环密封, 磨损, 接触模型, 数值分析

Abstract:

Aiming at the end face wear of graphite floating ring seal of aero-engine, based on the modified fractal contact theory and Archard wear theory, the fractal wear prediction model of graphite floating ring seal end face is derived from the microscopic point of view, and the test data of literature is used to verify the rationality of the model. Next, numerical simulations were then adopted to analytically study the influence of surface contour parameters and working conditions on the rate of surface wear. The results show that the rate of surface wear first increased before decreasing with fractal dimension, reaching its minimum when the fractal dimension lies between 1.45 and 1.65. Moreover, keeping the fractal dimension constant proves to raise the rate of surface wear with increasing magnitudes of surface feature parameters, friction coefficient and sliding speed of floating ring. The rate of surface wear is mainly related to the smallest level of the frequency component and the seven successive levels of asperities thereafter. By contrast, the influence of the remaining asperities on the overall surface wear rate is negligible.

Key words: fractal, floating ring seal, attrition, contact model, numerical analysis

中图分类号:

TH 113.2

张志敏, 丁雪兴, 张兰霞, 力宁, 司佳鑫. 浮环密封端面分形磨损预估模型及数值分析[J]. 化工学报, 2022, 73(12): 5526-5536.

Zhimin ZHANG, Xuexing DING, Lanxia ZHANG, Ning LI, Jiaxin SI. Fractal wear prediction model and numerical analysis of floating ring seal face[J]. CIESC Journal, 2022, 73(12): 5526-5536.

图/表 13

图1 石墨浮环密封结构示意图

Fig.1 Schematic diagram of graphite floating ring seal structure

图2 石墨浮环表面采样图

Fig.2 Surface sampling diagram of graphite floating ring

图3 浮环密封端面接触示意图

Fig.3 Schematic diagram of floating ring seal end face contact

图4 单个微凸体与刚性平面接触示意图

Fig.4 Schematic diagram of contact between asperity and smooth rigid surface

表1 文献实验参数［29］

Table 1 Literature test parameter［29］

模型参数	参数值
钢销弹性模量E₁/ GPa	116.5
摩擦因数f	0.058
特征尺度G/ m	$10 - 9$
钢销屈服应力σ_y/MPa	300
弹性变形磨损系数K_e1	$2 × 10 - 6$
塑性变形磨损系数K_e3	$1 × 10 - 7$
平均滑移速度v/(m/s)	0.69
法向接触载荷P /MPa	0.42
名义接触面积A_a / m²	$4 π × 10 - 6$

表1 文献实验参数［29］

Table 1 Literature test parameter［29］

模型参数	参数值
钢销弹性模量E₁/ GPa	116.5
摩擦因数f	0.058
特征尺度G/ m	$10 - 9$
钢销屈服应力σ_y/MPa	300
弹性变形磨损系数K_e1	$2 × 10 - 6$
塑性变形磨损系数K_e3	$1 × 10 - 7$
平均滑移速度v/(m/s)	0.69
法向接触载荷P /MPa	0.42
名义接触面积A_a / m²	$4 π × 10 - 6$

图5 文献实验数据及本文模型对比

Fig.5 Comparison between experimental data in literature and this model

表2 浮环形貌参数、材料参数及工况参数［14，30］

Table 2 Floating ring shape parameters， material parameters and working condition parameters［14，30］

模型参数	参数值
合金钢弹性模量E₂/ GPa	365
石墨弹性模量E₃/ GPa	20
石墨屈服应力σ_y/ MPa	50
合金钢泊松比ν₁	0.24
石墨泊松比ν₂	0.29
弹性变形磨损系数K_e1	$2 × 10 - 7$
弹塑性变形磨损系数K_e2	$1 × 10 - 7$
塑性变形磨损系数 K_e3	$1 × 10 - 8$
平均滑移速度 v/(m/s)	0.176×10^-3
石墨浮环密封端面内径d₁/m	0.0832
石墨浮环密封端面外径d₂ $/ m$	0.0898
石墨浮环端面载荷P /MPa	0.28

表2 浮环形貌参数、材料参数及工况参数［14，30］

Table 2 Floating ring shape parameters， material parameters and working condition parameters［14，30］

模型参数	参数值
合金钢弹性模量E₂/ GPa	365
石墨弹性模量E₃/ GPa	20
石墨屈服应力σ_y/ MPa	50
合金钢泊松比ν₁	0.24
石墨泊松比ν₂	0.29
弹性变形磨损系数K_e1	$2 × 10 - 7$
弹塑性变形磨损系数K_e2	$1 × 10 - 7$
塑性变形磨损系数 K_e3	$1 × 10 - 8$
平均滑移速度 v/(m/s)	0.176×10^-3
石墨浮环密封端面内径d₁/m	0.0832
石墨浮环密封端面外径d₂ $/ m$	0.0898
石墨浮环端面载荷P /MPa	0.28

图6 D-G-h关系

Fig.6 Relationship of D-h-G

图7 最优分形维数

Fig.7 The diagram of optimal fractal dimension

图8 摩擦因数-磨损率关系

Fig.8 Relationship of friction coefficient and wear rate

表3 微凸体临界频率指数

Table 3 The critical frequency index of asperities

D	G/m	n_ec	n_epc	n_pc
1.5	$1 × 10 - 9$	20	25	32
1.6	$1 × 10 - 9$	25	29	35
1.7	$1 × 10 - 9$	29	32	37

表3 微凸体临界频率指数

Table 3 The critical frequency index of asperities

D	G/m	n_ec	n_epc	n_pc
1.5	$1 × 10 - 9$	20	25	32
1.6	$1 × 10 - 9$	25	29	35
1.7	$1 × 10 - 9$	29	32	37

图9 频率指数-磨损率关系

Fig.9 Relationship of frequency index and wear rate

图10 滑移速度-磨损率关系

Fig.10 Relationship of slip velocity and wear rate

参考文献 30

1	胡广阳. 航空发动机密封技术应用研究[J]. 航空发动机, 2012, 38(3): 1-4.
	Hu G Y. Application research of seal technologies for aeroengine[J]. Aeroengine, 2012, 38(3): 1-4.
2	苏呈龙, 陈美军, 黄俊. 某型航空发动机石墨密封环应用与失效分析[J]. 成都航空职业技术学院学报, 2021, 37(2): 60-62, 88.
	Su C L, Chen M J, Huang J. Application and failure analysis of graphite seal ring on an aero engine[J]. Journal of Chengdu Aeronautic Polytechnic, 2021, 37(2): 60-62, 88.
3	陈涛, 刘美红. 柱面气膜密封研究进展及发展趋势[J]. 新技术新工艺, 2014(6): 78-81.
	Chen T, Liu M H. Research progress and development trend of cylindrical gas film seal[J]. New Technology ＆ New Process, 2014(6): 78-81.
4	郑娆, 陈潇竹, 李双喜, 等. 高速气膜镶装式浮环密封的开启特性[J]. 北京航空航天大学学报, 2022(11): 2111-2120.
	Zheng R, Chen X Z, Li S X, et al. Study on opening characteristics of high speed gas film inlaid floating ring seal[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022(11): 2111-2120.
5	何强, 黄伟峰, 胡广阳, 等. 航空发动机气膜密封技术的发展[J]. 航空发动机, 2021, 47(4):106-113.
	He Q, Huang W F, Hu G Y, et al. Research status of the film-riding gas seal technologies in aeroengine[J]. Aeroengine, 2021, 47(4): 106-113.
6	力宁, 江平, 翁泽文, 等. 航空发动机浮环密封上浮性能试验研究[J]. 润滑与密封, 2020, 45(11): 143-148.
	Li N, Jiang P, Weng Z W, et al. Experimental study on floating performance of floating ring seals used in aero engine[J]. Lubrication Engineering, 2020, 45(11): 143-148.
7	马也, 王庆锋, 施任杰, 等. 航空发动机气膜浮环密封上浮性能研究[J]. 润滑与密封, 2021, 46(1): 38-44, 50.
	Ma Y, Wang Q F, Shi R J, et al. Research on floating performance of aeroengine air film floating ring seal[J]. Lubrication Engineering, 2021, 46(1): 38-44, 50.
8	俞树荣, 丁俊华, 王世鹏, 等. 柱面密封气膜动压效应模拟及试验[J]. 化工学报, 2020, 71(7): 3220-3228.
	Yu S R, Ding J H, Wang S P, et al. Simulation and analysis of dynamic pressure effect of gas film on cylinder seal[J]. CIESC Journal, 2020, 71(7): 3220-3228.
9	陆俊杰, 张炜, 马浩. 基于F-K滑移流模型的柱面微槽气浮密封浮升能力分析[J]. 化工学报, 2021, 72(8): 4267-4278.
	Lu J J, Zhang W, Ma H. Floating performance of cylindrical microgroove gas floating seal based on F-K slip flow model[J]. CIESC Journal, 2021, 72(8): 4267-4278.
10	丁雪兴, 贺振泓, 张伟政, 等. 柱面螺旋槽气膜密封微尺度流动场稳态特性分析[J]. 化工学报, 2018, 69(4): 1537-1546.
	Ding X X, He Z H, Zhang W Z, et al. Parameters analysis of steady micro-scale flow of cylindrical spiral groove dry gas seal[J]. CIESC Journal, 2018, 69(4): 1537-1546.
11	Zhou G Y, Leu M C, Blackmore D. Fractal geometry model for wear prediction[J]. Wear, 1993, 170(1): 1-14.
12	Ge S R, Chen G A. Fractal prediction models of sliding wear during the running-in process[J]. Wear, 1999, 231(2): 249-255.
13	房桂芳, 滕文锐, 刘其和, 等. 机械密封端面黏着磨损分形模型[J]. 流体机械, 2013, 41(1): 35-40.
	Fang G F, Teng W R, Liu Q H, et al. Adhesive wear fractal model for end face of mechanical seals[J]. Fluid Machinery, 2013, 41(1): 35-40.
14	魏龙, 顾伯勤, 张鹏高. 接触式机械密封端面磨损预测[J]. 南京工业大学学报(自然科学版), 2012, 34(4): 16-21.
	Wei L, Gu B Q, Zhang P G. Wear prediction for end face of contact mechanical seals[J]. Journal of Nanjing University of Technology (Natural Science Edition), 2012, 34(4): 16-21.
15	魏龙, 顾伯勤, 张鹏高, 等. 机械密封磨合过程端面接触特性[J]. 化工学报, 2012, 63(10): 3202-3207.
	Wei L, Gu B Q, Zhang P G, et al. Contact characterizations of end faces in mechanical seals running-in[J]. CIESC Journal, 2012, 63(10): 3202-3207.
16	Kim Y W, Kim J H, Seo B H, et al. Mathematical model to evaluate wear rate of graphite as sealing materials[J]. Advanced Materials Research, 2013, 871: 200-205.
17	李小彭, 杨泽敏, 潘五九, 等. 接触式机械密封端面的分形磨损模型[J]. 振动·测试与诊断, 2020, 40(5): 841-846, 1017.
	Li X P, Yang Z M, Pan W J, et al. Fractal wear model of contact mechanical seal[J]. Journal of Vibration, Measurement ＆ Diagnosis, 2020, 40(5): 841-846, 1017.
18	惠玉祥, 刘莹, 王悦昶, 等. 考虑磨损的接触式端面密封模型及试验[J]. 摩擦学学报, 2021, 41(3): 316-324.
	Hui Y X, Liu Y, Wang Y C, et al. Contact end face seals considering wear: modelling and experiments[J]. Tribology, 2021, 41(3): 316-324.
19	Majumdar A, Tien C L. Fractal characterization and simulation of rough surfaces[J]. Wear, 1990, 136(2): 313-327.
20	Yuan Y, Cheng Y, Liu K, et al. A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces[J]. Applied Surface Science, 2017, 425: 1138-1157.
21	Kogut L, Etsion I. Elastic-plastic contact analysis of a sphere and a rigid flat[J]. Journal of Applied Mechanics, 2002, 69(5): 657-662.
22	Wang S, Komvopoulos K. Closure to “discussion of ‘A fractal theory of the interfacial temperature distribution in the slow sliding regime(part Ⅰ): Elastic contact and heat transfer analysis’” (1994, ASME J. Tribol., 116, p. 822)[J]. Journal of Tribology, 1994, 116(4): 822-823.
23	Wang S, Komvopoulos K. A fractal theory of the interfacial temperature distribution in the slow sliding regime(part Ⅱ): Multiple domains, elastoplastic contacts and applications[J]. Journal of Tribology, 1994, 116(4): 824-832.
24	Whitehouse D J. Surface topography and quality and its relevance to wear[J]. Fundamentals of Tribology, 1980: 17-50.
25	温诗铸, 黄平. 摩擦学原理[M]. 北京: 清华大学出版社, 2012.
	Wen S Z, Huang P. Principles of Tribology[M]. Beijing: Tsinghua University Press, 2012.
26	王松年, 苏诒福. 摩擦学原理及应用[M]. 北京: 中国铁道出版社, 1990: 95-96, 103-106.
	Wang S N, Su Y F. Tribology Principle Application[M]. Beijing: China Railway Publishing House, 1990: 95-96, 103-106.
27	Halling J. Principles of Tribology[M]. London: Macmillan Education UK, 1978: 81-83.
28	Archard J F. Wear theory and mechanisms[J]. Wear Control Handbook, 1980, 58: 35-80.
29	葛世荣, 朱华. 摩擦学的分形[M]. 北京: 机械工业出版社, 2005: 260-261.
	Ge S R, Zhu H. Friction and Wear of the Fractal[M]. Beijing: China Machine Press, 2005: 260-261.
30	孙见君. 机械密封泄漏预测理论及其应用[M]. 北京:中国电力出版社, 2011: 93-103.
	Sun J J. Prediction Theory and Its Application of Mechanical Seal Leakage[M]. Beijing: China Electric Power Press, 2011: 93-103.

[1]	邵远哲, 赵忠盖, 刘飞. 基于共同趋势模型的非平稳过程质量相关故障检测方法[J]. 化工学报, 2023, 74(6): 2522-2537.
[2]	刘道银, 陈柄岐, 张祖扬, 吴琰. 颗粒聚团结构对曳力特性影响的数值模拟[J]. 化工学报, 2023, 74(6): 2351-2362.
[3]	李正涛, 袁志杰, 贺高红, 姜晓滨. 疏水界面上的NaCl液滴蒸发过程内环流调控机制研究[J]. 化工学报, 2023, 74(5): 1904-1913.
[4]	魏琳, 郭剑, 廖梓豪, Dafalla Ahmed Mohmed, 蒋方明. 空气流量对空冷燃料电池电堆性能的影响研究[J]. 化工学报, 2022, 73(7): 3222-3231.
[5]	宋伟, 李万佳, 俞树荣, 马荣荣. 热力耦合下TC4合金微动磨损行为影响的研究[J]. 化工学报, 2022, 73(3): 1324-1334.
[6]	周楠, 王簪, 邵应娟, 钟文琪. 煤沥青球气固流化磨损特性实验研究[J]. 化工学报, 2022, 73(2): 587-594.
[7]	徐祖良, 汪宇昊, 赵辉, 周骛, 蔡小舒, 刘海峰. 同轴四通道喷嘴气流式雾化特性影响因素研究[J]. 化工学报, 2022, 73(2): 604-611.
[8]	龚海峰, 罗鑫, 彭烨, 余保, 杨阳, 张浩华. 工业废油异构旋流三相分离装置去固结构及优化[J]. 化工学报, 2022, 73(11): 5025-5038.
[9]	徐玲玲, 蒲亮. 基于热短路问题的仿生地埋管换热器模拟[J]. 化工学报, 2021, 72(S1): 134-139.
[10]	陈尔健, 代彦军. 使用NH₃-LiNO₃工质对的增压型回热吸收循环性能分析[J]. 化工学报, 2021, 72(S1): 445-452.
[11]	王彦红, 陆英楠, 李素芬, 东明. U形圆管中超临界压力RP-3航空煤油换热数值研究[J]. 化工学报, 2021, 72(9): 4639-4648.
[12]	马玖辰, 易飞羽, 张秋丽, 王宇. 富水型热储层深井套管式换热器传热特性研究[J]. 化工学报, 2021, 72(8): 4134-4145.
[13]	刘庭江, 王静娴, 于洋, 赵一鸣, 胡大鹏. 壁面脉动传热对气波制冷性能影响研究[J]. 化工学报, 2021, 72(8): 4073-4080.
[14]	郭金玉, 李文涛, 李元. 在线压缩KECA的自适应算法在故障检测中的应用[J]. 化工学报, 2021, 72(8): 4227-4238.
[15]	石敦峰, 甘云华, 罗燕来, 江政纬, 周毅. 乙醇浓度和应变率对扩散火焰特性的数值分析[J]. 化工学报, 2021, 72(5): 2801-2809.