Abstract：[Objective] Rail corrugation is a problem that needs to be addressed urgently and is one of the common technical issues limiting the development of contemporary rail transit. This study uses the finite element method to analyze the formation process of rail corrugation from the wheel-rail transient contact stick-slip vibration to provide new insights into the mechanism of rail corrugation and to understand the phenomenon of rail corrugation on the metro line. [Methods] This study examines the formation mechanism of rail corrugation using field measurements and numerical simulation. First, according to the on-site corrugation situation, a three-dimensional wheel-rail rolling contact model is developed using the finite element software ABAQUS, and its effectiveness is established. The contact stick-slip state is then analyzed during the wheel operation, and the influence of the rail surface and no rail surface defect on it is discussed. Furthermore, the relationship between stick-slip characteristics and corrugation formation is examined. Finally, the inherent characteristics of the wheel-track system and longitudinal wear characteristics of rail are analyzed using the complex modal theory and the Archard wear model to explain the formation mechanism of rail corrugation. [Results] The results revealed that when the wheel rolled over the smooth rail, the adhesion area was at the front edge of the contact area, and the middle and rear edges were the slip area, which was closer to the steady state dynamic calculation results, verifying that the established finite element model was effective. Moreover, the wheel-rail contact was always in a stable rolling state, indicating that the wheel-track system was not easily unstable, consequently making corrugation generation difficult. When the wheel rolled through the squat defect, the contact area was shown as two slip areas surrounding the squat; after the wheel rolled through the squat defect, the area of the wheel-rail contact patch decreased, and almost all of it showed slip. The squat defect changed the stick-slip state of wheel-rail rolling contact and promoted the slip of the wheel-rail interface, which induced the instability of the wheel-track system and caused the wear of the rail surface material; this might eventually form rail corrugation. The complex modal analysis showed that the rail surface defect exacerbated the inherent unstable vibration characteristics of the wheel-track system, and the unstable vibration frequencies fell within the measured corrugation passing frequency range. [Conclusions] The analysis results of wheel-rail contact stick-slip and complex modal reveal that the formation mechanism of rail corrugation can be attributed to the inherent unstable vibration of the wheel-track system caused by the excitation of the rail surface defect, and the unstable vibration is represented by the vertical bending vibration of the rail relative to the track slab. Thus, when the wheel passes through the squat defect, it will stimulate the transient fluctuation wear, which results in wavy wear on the rail surface. The characteristic wavelength of the longitudinal wear on the rail surface is 40～50 mm, which is consistent with the corrugation wavelength on the actual line; thus, the formation mechanism of rail corrugation is further validated in the process of quantifying rail corrugation formation.
王志强, 雷震宇. 基于瞬态接触特性的科隆蛋扣件轨道波磨形成机理[J]. 清华大学学报（自然科学版）, 2023, 63(11): 1844-1855.
WANG Zhiqiang, LEI Zhenyu. Mechanism of corrugation on the track with Cologne egg fasteners based on transient contact characteristics. Journal of Tsinghua University(Science and Technology), 2023, 63(11): 1844-1855.
[1] 周志军,李伟,温泽峰,等.采用GJ-Ⅲ型扣件地铁轨道的钢轨波磨形成机理[J].中国铁道科学, 2022, 43(3):37-49. ZHOU Z J, LI W, WEN Z F, et al. Formation mechanism of rail corrugation on metro track with GJ-Ⅲ fastener[J]. China Railway Science, 2022, 43(3):37-49.(in Chinese) [2] 刘卫丰,张厚贵,陈嘉梁,等.北京地铁采用调频式钢轨减振器治理钢轨波磨的试验研究[J].振动工程学报, 2019, 32(4):695-700. LIU W F, ZHANG H G, CHEN J L, et al. A test of treating rail corrugation by tuned rail damper for Beijing metro[J]. Journal of Vibration Engineering, 2019, 32(4):695-700.(in Chinese) [3] ZHANG H G, LIU W N, LIU W F, et al. Study on the cause and treatment of rail corrugation for Beijing metro[J]. Wear, 2014, 317(1-2):120-128. [4] 吴宗臻,刘维宁,张厚贵.剪切型减振器扣件工作性能及改进[J].中南大学学报(自然科学版), 2016, 47(9):3258-3263. WU Z Z, LIU W N, ZHANG H G. Performance and improvement of shear-type damper fastener[J]. Journal of Central South University (Science and Technology), 2016, 47(9):3258-3263.(in Chinese) [5] 佘才高,张伯林,刘铁旭,等.南京地铁1号线珠江路站振动及二次结构噪声整治研究[J].都市快轨交通, 2021, 34(4):113-118. SHE C G, ZHANG B L, LIU T X, et al. Vibration and secondary structure noise control of Zhujiang Road Station of Nanjing Metro Line 1[J]. Urban Rapid Rail Transit, 2021, 34(4):113-118.(in Chinese) [6] 王志强,王安斌,白健,等.成都地铁轨道GJ-Ⅲ型减振扣件振动控制效果分析[J].噪声与振动控制, 2014, 34(3):190-194. WANG Z Q, WANG A B, BAI J, et al. Experimental study on track vibration control using GJ-Ⅲ rail fastening system in Chengdu metro[J]. Noise and Vibration Control, 2014, 34(3):190-194.(in Chinese) [7] 刘卫丰,刘维宁,吴宗臻,等.北京地铁剪切型减振器扣件钢轨波磨治理的试验研究[J].机械工程学报, 2015, 51(21):73-79. LIU W F, LIU W N, WU Z Z, et al. Test study on treating rail corrugation for egg fastener in Beijing metro[J]. Journal of Mechanical Engineering, 2015, 51(21):73-79.(in Chinese) [8] 王志强,雷震宇.科隆蛋扣件段钢轨波磨产生机理及发展特性[J].振动、测试与诊断, 2021, 41(4):688-694, 829. WANG Z Q, LEI Z Y. Formation mechanism and development properties of rail corrugation of Cologne egg fastener section[J]. Journal of Vibration, Measurement&Diagnosis, 2021, 41(4):688-694, 829.(in Chinese) [9] LIU W F, ZHANG H G, LIU W N, et al. Experimental study of the treatment measures for rail corrugation on tracks with egg fasteners in the Beijing metro[J]. Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit, 2018, 232(5):1360-1374. [10] 崔晓璐,钱韦吉,张青,等.直线线路科隆蛋扣件地段钢轨波磨成因的理论研究[J].振动与冲击, 2016, 35(13):114-118, 152. CUI X L, QIAN W J, ZHANG Q, et al. Forming mechanism of rail corrugation of a straight track section supported by Cologne-egg fasteners[J]. Journal of Vibration and Shock, 2016, 35(13):114-118, 152.(in Chinese) [11] GRASSIE S L, KALOUSEK J. Rail corrugation:Characteristics, causes and treatments[J]. Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit, 1993, 207(1):57-68. [12] GRASSIE S L. Rail corrugation:Characteristics, causes, and treatments[J]. Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit, 2009, 223(6):581-596. [13] SATO Y, MATSUMOTO A, KNOTHE K. Review on rail corrugation studies[J]. Wear, 2002, 253(1-2):130-139. [14] OOSTERMEIJER K H. Review on short pitch rail corrugation studies[J]. Wear, 2008, 265(9-10):1231-1237. [15] 金学松,李霞,李伟,等.铁路钢轨波浪形磨损研究进展[J].西南交通大学学报, 2016, 51(2):264-273. JIN X S, LI X, LI W, et al. Review of rail corrugation progress[J]. Journal of Southwest Jiaotong University, 2016, 51(2):264-273.(in Chinese) [16] SUDA Y. Effects of vibration system and rolling conditions on the development of corrugations[J]. Wear, 1991, 144(1-2):227-242. [17] CHEN G X, ZHOU Z R, OUYANG H, et al. A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system[J]. Journal of Sound and Vibration, 2010, 329(22):4643-4655. [18] CLARK R, SCOTT G, POOLE W. Short wave corrugations:An explanation based on stick-slip vibrations[J]. Proceedings of the Symposium on the Applied Mechanics Rail Transportation, 1998, 92(2):141-148. [19] HEMPELMANN K, KNOTHE K. An extended linear model for the prediction of short pitch corrugation[J]. Wear, 1996, 191(1-2):161-169. [20] DANIEL W J T, HORWOOD R J, MEEHAN P A, et al. Analysis of rail corrugation in cornering[J]. Wear, 2008, 265(9-10):1183-1192. [21] MVLLER S. A linear wheel-rail model to investigate stability and corrugation on straight track[J]. Wear, 2000, 243(1-2):122-132. [22] GRASSIE S L, ELKINS J A. Rail corrugation on North American transit systems[J]. Vehicle System Dynamics, 1998, 29(S1):5-17. [23] SUN Y Q, SIMSON S. Nonlinear three-dimensional wagon-track model for the investigation of rail corrugation initiation on curved track[J]. Vehicle System Dynamics, 2007, 45(2):113-132. [24] SUN Y Q, SIMSON S. Wagon-track modelling and parametric study on rail corrugation initiation due to wheel stick-slip process on curved track[J]. Wear, 2008, 265(9-10):1193-1201. [25] WANG Z Q, LEI Z Y. Formation mechanism of metro rail corrugation based on wheel-rail stick-slip behaviors[J]. Applied Sciences, 2021, 11(17):8128. [26] 尧辉明,沈钢,高利君.基于试验验证的磨耗型钢轨波磨形成机理[J].同济大学学报(自然科学版), 2018, 46(10):1427-1432. YAO H M, SHEN G, GAO L J. Formation mechanism of worn profile rail corrugation based on experimental verification[J]. Journal of Tongji University (Natural Science), 2018, 46(10):1427-1432.(in Chinese) [27] ZHAO X, WEN Z F, WANG H Y, et al. Modeling of high-speed wheel-rail rolling contact on a corrugated rail and corrugation development[J]. Journal of Zhejiang University Science A, 2014, 15(12):946-963. [28] 赵鑫,温泽峰,王衡禹,等.三维高速轮轨瞬态滚动接触有限元模型及其应用[J].机械工程学报, 2013, 49(18):1-7. ZHAO X, WEN Z F, WANG H Y, et al. 3D transient finite element model for high-speed wheel-rail rolling contact and its application[J]. Journal of Mechanical Engineering, 2013, 49(18):1-7.(in Chinese) [29] LI S G, LI Z L, N AU'GÑEZ A, et al. New insights into the short pitch corrugation enigma based on 3D-FE coupled dynamic vehicle-track modeling of frictional rolling contact[J]. Applied Sciences, 2017, 7(8):807. [30] MOLODOVA M, LI Z L, N AU'GÑEZ A, et al. Validation of a finite element model for axle box acceleration at squats in the high frequency range[J]. Computers&Structures, 2014, 141:84-93. [31] MATSUMOTO K, SUDA Y, KOMINE H, et al. A proposal of wheel/rail contact model for friction control[J]. Journal of Mechanical Science and Technology, 2005, 19(1):437-443. [32] CREMONA M A, LIU B B, HU Y, et al. Predicting railway wheel wear under uncertainty of wear coefficient, using universal kriging[J]. Reliability Engineering&System Safety, 2016, 154:49-59. [33] XI Y H, BJÖRLING M, ALMQVIST A. A numerical model for solving three-dimensional rolling contact problems with elastic coating layers[J]. Tribology Letters, 2021, 69(4):139. [34] JIN X S, WEN Z F, WANG K Y, et al. Effect of a scratch on curved rail on initiation and evolution of rail corrugation[J]. Tribology International, 2004, 37(5):385-394. [35] WEN Z F, JIN X S. Effect of track lateral geometry defects on corrugations of curved rails[J]. Wear, 2005, 259(7-12):1324-1331. [36] JIN X S, WEN Z F, WANG K Y. Effect of track irregularities on initiation and evolution of rail corrugation[J]. Journal of Sound and Vibration, 2005, 285(1-2):121-148. [37] WEN Z F, JIN X S, XIAO X B, et al. Effect of a scratch on curved rail on initiation and evolution of plastic deformation induced rail corrugation[J]. International Journal of Solids and Structures, 2008, 45(7-8):2077-2096. [38] CHEN G X, ZHANG S, WU B W, et al. Field measurement and model prediction of rail corrugation[J]. Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit, 2020, 234(4):381-392. [39] ZHAO X, ZHANG P, WEN Z F. On the coupling of the vertical, lateral and longitudinal wheel-rail interactions at high frequencies and the resulting irregular wear[J]. Wear, 2019, 430-431:317-326. [40] 潘兵,王安斌,高晓刚,等.轮轨耦合系统横向动态响应特性对钢轨波浪磨耗的影响[J].噪声与振动控制, 2020, 40(1):132-137. PAN B, WANG A B, GAO X G, et al. Effects of lateral dynamic response characteristics of wheel-rail coupling systems on rail corrugation[J]. Noise and Vibration Control, 2020, 40(1):132-137.(in Chinese) [41] WANG Z Q, LEI Z Y, ZHAO Y, et al. Rail corrugation characteristics of Cologne egg fastener section in small radius curve[J]. Shock and Vibration, 2020:1827053.
2023, Vol. 63 
