Review on basic characteristics, formation mechanisms, and treatment measures of rail corrugation in metro systems
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摘要: 对世界各国地铁钢轨波磨的基本特征进行了系统梳理，总结了其普遍性与时间集中性，及其与曲线、轨道结构、车辆及其他因素相关性等典型特征，并对其分类方法、形成机理和治理措施进行了综合评述。研究结果表明：钢轨波磨普遍存在于地铁与有轨电车线路中，在新线开通初期与线路改造初期最为严重；一般而言，相对于直线和大半径曲线，小半径曲线的钢轨波磨最为普遍，低轨侧波磨波长短，幅值大，但也有例外，部分大半径曲线及直线上也有分布；波磨的波长特征和发展速度与轨道结构密切相关，轨道结构及部件不匹配时，易出现快速发展的波磨；车轮踏面廓形、轮对定位、悬挂刚度与簧下质量等车辆结构参数会对波磨萌生、发展与表现特征产生影响；波磨的产生还可能与钢轨材质、牵引和制动、运行环境、湿度及摩擦因数有关。地铁钢轨波磨的形成机理主要基于轮轨系统共振、轮轨黏滑(摩擦自激)振动、钢轨振动波反射等理论，对波磨形成过程的纵向动力学影响与系统非线性因素考虑不完善，关于黏滑自激振动与轮轨负摩擦特性对波磨影响的认识还不统一，难以解释直线以及曲线高低轨波磨特征的差异等，对波磨的形成和发展缺乏理论上的主动预测和试验验证；各国主要以钢轨打磨来控制波磨发展，通过调节轨道结构、运行环境，采用钢轨吸振器和轮轨摩擦调节装置，以及优化车辆设计等主动措施来控制波磨的研究仍需进一步开展；未来应针对车辆-轨道系统的动态特性以及实际运行工况下的轮轨微观接触行为和黏滑自激振动特性，开展车辆-轨道系统的轮轨动态磨耗演化仿真，掌握地铁钢轨波磨形成机理和关键因素影响规律，提出控制地铁钢轨波磨的主动措施和轮轨匹配优化设计原则。Abstract: The basic characteristics of rail corrugations in metro systems worldwide were systematically reviewed, including their typical properties such as universality, time concentration, and the correlation between the corrugations and curve parameters, track structure, vehicle characteristics, and other related factors. The classification methods, formation mechanisms, and treatment measures of rail corrugation in metro were comprehensively evaluated. Research results show that rail corrugation is common in metro and tram lines, particularly in the initial stage of new line opening and line reconstruction. Generally, the rail corrugation of small radius curve is more common than that of straight line and large radius curve, and the wavelength is relatively shorter and the amplitude is larger in low-rail side than that in high-rail side. However, there are still exceptions, that is, rail corrugations are also distributed on some large radius curves and straight lines.The wavelength and growth rate of corrugation are closely related to the track structure. Rail corrugation grows rapidly when the track structure and its components are not compatible. Vehicle structural parameters such as the wheel tread, wheelset alignment, suspension stiffness, and unsprung mass, will affect the generation, growth, and characteristics of rail corrugation. The rail material, traction and braking, operation environment, humidity, and friction coefficient may also influence the generation of rail corrugation. The formation mechanism of metro rail corrugation is mainly based on the resonance of wheel-rail system, stick-slip (friction-induced self-excitation) vibration of wheel-rail, and the reflection of rail vibration wave. The effects of longitudinal dynamics on the rail corrugation formation and nonlinear factors in the wheel-rail system are not thoroughly explored. The understanding about the effects of self-excited stick-slip vibration and negative friction characteristics on the corrugation are not unified. Therefore, it is difficult to explain the differences in corrugation characteristics among the low curve rail, high curve rail, and straight line rail. The prediction theory and experimental validation in the formation and growth of rail corrugation are not sufficient. Currently, rail grinding is widely adopted to control the development of corrugation in various countries worldwide. The research on active methods to control corrugation, such as adjusting track structure, operation condition, adopting rail vibration absorbers, applying wheel-rail friction modifiers, and optimizing vehicle design optimizations, are still need to develop further. According to the dynamic characteristics of vehicle-track system and the micro contact behavior and self-excited stick-slip vibration of wheel-rail in real operation conditions, the wheel-rail dynamic wear evolution simulation of vehicle-track system should be carried out, the formation mechanisms and the key factors influencing the laws of metro rail corrugation should be mastered, and the active measures to control metro rail corrugation and the optimal design principles of wheel-rail compatibility should be developed. 5 figs, 132 refs.
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Key words:
- metro /
- rail corrugation /
- basic characteristic /
- formation mechanism /
- treatment measures
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图 3 温哥华直线电机地铁线路的变轨距铺设
Figure 3. Variable gauge laying of Vancouver linear motor metro lines
图 4 直线及大半径曲线的钢轨对称打磨
Figure 4. Symmetric grindings of rails on straight lines and large radius curves
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[1] 城市轨道交通协会. 2020年上半年中国内地城轨交通线路概况[R]. 北京: 城市轨道交通协会, 2020.China Association of Metros. Overview of urban rail transit lines in Mainland China in the first half year of 2020[R]. Beijing: China Association of Metros, 2020. (in Chinese) [2] OOSTERMEIJER K H. Review on short pitch rail corrugation studies[J]. Wear, 2008, 265(9/10): 1231-1237. http://www.sciencedirect.com/science/article/pii/S0043164808001439 [3] AHLBECK D R, DANIELS L E. A review of rail corrugation processes under different operating modes[C]//IEEE. 1990 ASME/IEEE Joint Railroad Conference. New York: IEEE, 1990: 13-17. [4] 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. doi: 10.1243/PIME_PROC_1993_207_227_02 [5] SATO Y, MATSUMOTO A, KNOTHE K. Review on rail corrugation studies[J]. Wear, 2002, 253(1/2): 130-139. http://www.researchgate.net/publication/221984904_Review_on_rail_corrugation_studies/download [6] NIELSEN J C O, LUNDÉN R, JOHANSSON A, et al. Train-track interaction and mechanisms of irregular wear on wheel and rail surfaces[J]. Vehicle System Dynamics, 2003, 40(1-3): 3-54. doi: 10.1076/vesd.40.1.3.15874 [7] GRASSIE S L. Rail corrugation: advances in measurement, understanding and treatment[J]. Wear, 2005, 258(7/8): 1224-1234. http://www.sciencedirect.com/science/article/pii/S004316480400290X [8] 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. doi: 10.1243/09544097JRRT264 [9] 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. doi: 10.3969/j.issn.0258-2724.2016.02.006JIN Xue-song, LI Xia, LI Wei, et al. Review of rail corrugation progress[J]. Journal of Southwest Jiaotong University, 2016, 51(2): 264-273. (in Chinese) doi: 10.3969/j.issn.0258-2724.2016.02.006 [10] 刘学毅. 钢轨波形磨耗成因研究[D]. 成都: 西南交通大学, 1996.LIU Xue-yi. Study on the formation mechanism of rail corrugations[D]. Chengdu: Southwest Jiaotong University, 1996. (in Chinese) [11] 温泽峰. 钢轨波浪形磨损研究[D]. 成都: 西南交通大学, 2006.WEN Ze-feng. Study on rail corrugation[D]. Chengdu: Southwest Jiaotong University, 2006. (in Chinese) [12] 李霞. 地铁钢轨波磨形成机理研究[D]. 成都: 西南交通大学, 2012.LI Xia. Study on the mechanism of rail corrugation on subway track[D]. Chengdu: Southwest Jiaotong University, 2012. (in Chinese) [13] 李伟. 地铁钢轨波磨成因及其对车辆/轨道行为的影响[D]. 成都: 西南交通大学, 2015.LI Wei. Study on root cause of metro rail corrugation and its influence on behavior vehicle/track system[D]. Chengdu: Southwest Jiaotong University, 2015. (in Chinese) [14] 张厚贵. 北京地铁钢轨波磨的机理及整治方案研究[D]. 北京: 北京交通大学, 2015.ZHANG Hou-gui. Mechanisms and treatment solutions for rail corrugation on Beijing Metro[D]. Beijing: Beijing Jiaotong University, 2015. (in Chinese) [15] 崔晓璐. 地铁线路钢轨波磨现象发生机理研究[D]. 成都: 西南交通大学, 2017.CUI Xiao-lu. Research on occurrence mechanisms of rail corrugation phenomena in metros[D]. Chengdu: Southwest Jiaotong University, 2017. (in Chinese) [16] SAULOT A. Analyse tribologique du contact roue-rail Modélisation et experimentations[D]. Lyon: L'Institut National des Sciences Appliquées de Lyon, 2005. [17] TORSTENSSON P T. Rail corrugation growth on curves[D]. Göteborg: Chalmers University of Technology, 2012. [18] TORTOSA P V. Modelado del crecimiento del desgaste ondulatorio en carriles ferroviarios[D]. Valencia: Universitat Politècnica de València, 2015. [19] HAMPTON R D. Rail corrugation— experience of U.S. transit properties[J]. Transportation Research Record, 1986, 1071: 16-18. http://trid.trb.org/view/288427 [20] AHLBECK D R, DANIELS L E. Investigation of rail corrugations on the Baltimore Metro[J]. Wear, 1991, 144(1/2): 197-210. http://www.sciencedirect.com/science/article/pii/004316489190015M [21] DANIELS L E. Rail transit corrugations[R]. Washington DC: Federal Transit Administration, 1993. [22] BRICKLE B, ELKINS J A, GRASSIE S L, et al. Rail corrugation mitigation in transit[R]. Washington DC: Federal Transit Administration, 1998. [23] GRASSIE S L, ELKINS J A. Rail corrugation on north American transit systems[J]. Vehicle System Dynamics, 1998, 29(S1): 5-17. [24] KALOUSEK J, JOHNSON K L. An investigation of short pitch wheel and rail corrugations on the Vancouver mass transit system[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 1992, 206(2): 127-135. doi: 10.1243/PIME_PROC_1992_206_226_02 [25] WU W X. The corrugation of railway track[D]. London: South Bank University, 1997. [26] GRASSIE S L, EDWARDS J W. Development of corrugation as a result of varying normal load[J]. Wear, 2008, 265(9/10): 1150-1155. http://www.sciencedirect.com/science/article/pii/S0043164808001464 [27] TASSILLY E, VINCENT N. Rail corrugations: analytical model and field tests[J]. Wear, 1991, 144(1/2): 163-178. http://www.sciencedirect.com/science/article/pii/004316489190013K [28] TASSILLY E, VINCENT N. A linear model for the corrugation of rails[J]. Journal of Sound and Vibration, 1991, 150(1): 25-45. doi: 10.1016/0022-460X(91)90400-E [29] SAULOT A, DESCARTES S, DESMYTER D, et al. A tribological characterization of "damage mechanism" of low rail corrugation on sharp curved track[J]. Wear, 2006, 260(9/10): 984-995. http://www.sciencedirect.com/science/article/pii/S004316480500390X [30] SAULOT A, DESCARTES S, BERTHIER Y. Sharp curved track corrugation: from corrugation observed on-site, to corrugation reproduced on simulators[J]. Tribology International, 2009, 42(11/12): 1691-1705. http://www.sciencedirect.com/science/article/pii/S0301679X0900108X [31] COLLETTE C, VANHONACKER P, BASTAITS R, et al. Comparison between time and frequency studies of a corrugated curve of RER Paris network[J]. Wear, 2008, 265(9/10): 1249-1258. http://www.sciencedirect.com/science/article/pii/S0043164808001488 [32] VADILLO E G, TÁRRAGO J A, ZUBIAURRE G G, et al. Effect of sleeper distance on rail corrugation[J]. Wear, 1998, 217(1): 140-145. doi: 10.1016/S0043-1648(97)00239-1 [33] EGANA J I, VINOLAS J, SECO M. Investigation of the influence of rail pad stiffness on rail corrugation on a transit system[J]. Wear, 2006, 261(2): 216-224. doi: 10.1016/j.wear.2005.10.004 [34] DIANA G, CHELI F, BRUNI S, et al. Experimental and numerical investigation on subway short pitch corrugation[J]. Vehicle System Dynamics, 1998, 29(S1): 234-245. [35] BIONDA S, BOCCIOLONE M, COLLINA A, et al. Rail corrugation growth on sharp curves negotiated by a vehicle equipped with resilient wheels[C]//ZOBORY I. Proceedings of the 10th International Conference on Railway Bogies and Running Gears. Budapest: Hungarian Scientific Society of Mechanical Engineers, 2016: 119-126. [36] BRACCIALI A. Rail corrugation growth in a metro curve[C]// Materials Australia. 7th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems (CM2006), Melbourne: Materials Australia, 2006: 207-216. [37] CHIACCHIARI L, THOMPSON D J, SQUICCIARINI G, et al. Rail roughness and rolling noise in tramways[J]. Journal of Physics: Conference Series, 2016, 744: 1-11. http://adsabs.harvard.edu/abs/2016JPhCS.744a2147C [38] TORSTENSSON P T, NIELSEN J C O. Monitoring of rail corrugation growth due to irregular wear on a railway metro curve[J]. Wear, 2009, 267(1-4): 556-561. doi: 10.1016/j.wear.2009.01.046 [39] TORSTENSSON P T, SCHILKE M. Rail corrugation growth on small radius curves-measurements and validation of a numerical prediction model[J]. Wear, 2013, 303(1/2): 381-396. http://www.sciencedirect.com/science/article/pii/S0043164813002184 [40] COLLETTE C. Rail corrugation mitigation via a dynamic vibration absorber mounted on driven wheel sets of metro vehicles[C]//DICK E, VIERENDEELS J, DUPRE L, et al. Proceedings of the 3rd International Conference on Advanced Computational Methods in Engineering. Ghent: Ghent University, 2005: 1-10. [41] VANHONACKER T. Accurate quantification and follow up of rail corrugation on several rail transit networks[C]//American Public Transportation Association. 2007 Proceedings Rail Conference. New York: American Public Transportation Association, 2007: 1-7. [42] KURZECK B. Combined friction induced oscillations of wheelset and track during the curving of metros and their influence on corrugation[J]. Wear, 2011, 271(1/2): 299-310. http://www.sciencedirect.com/science/article/pii/S0043164810003832 [43] HIENSCH M, NIELSEN J C O, VERHEIJEN E. Rail corrugation in the Netherlands—measurements and simulations[J]. Wear, 2002, 253(1/2): 140-149. http://www.sciencedirect.com/science/article/pii/S0043164802000935 [44] MEEHAN P A, BELLETTE P A, BATTEN R D, et al. A case study of wear-type rail corrugation prediction and control using speed variation[J]. Journal of Sound and Vibration, 2009, 325(1/2): 85-105. [45] BATTEN R D, BELLETTE P A, MEEHAN P A, et al. Field and theoretical investigation of the mechanism of corrugation wavelength fixation under speed variation[J]. Wear, 2011, 271(1/2): 278-286. http://www.sciencedirect.com/science/article/pii/S0043164810003613 [46] SUDA Y, HANAWA M, OKUMURA M, et al. Study on rail corrugation in sharp curves of commuter line[J]. Wear, 2002, 253(1/2): 193-198. http://www.sciencedirect.com/science/article/pii/S0043164802000996 [47] SUMI T, MATSUMOTO Y, MURAO M, et al. Generation mechanism of rail corrugation at curved tracks having short radius[J]. Doboku Gakkai Ronbunshu, 1991(425): 99-106. (in Japanese) http://ci.nii.ac.jp/naid/130003981312 [48] MATSUURA A, UCHIDA T, FUKUDA T. Formation and growth mechanism of inner rail corrugation on steep-curved track[J]. Doboku Gakkai Ronbunshu, 2004(773): 125-135. (in Japanese) http://ci.nii.ac.jp/naid/130003984875 [49] MATSUMOTO A, SATO Y, TANIMOTO M, et al. Study on the formation mechanism of rail corrugation on curved track[J]. Vehicle System Dynamics, 1996, 25(1): 450-465. [50] TANAKA H, HAGA A. The on-vehicle supervision method for rail corrugation[J]. RRR, 2011(4): 10-13. (in Japanese) http://en.cnki.com.cn/Article_en/CJFDTotal-GWTD201701006.htm [51] TANAKA H, MIWA M. Modeling the development of rail corrugation to schedule a more economical rail grinding[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2020, 234(4): 370-380. doi: 10.1177/0954409719894833 [52] ARAI I, KAWANO Y, WATANABE S, et al. Observation of inner rail characteristics in terms of corrugation focused on rail fastening device of the track structure[C]//LI Zi-li, NÚÑEZ A. 11th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems(CM2018), Delft: Delft University of Technology, 2018: 50-55. [53] WATANABE N. Current statue of linear induction motor metro-problems and countermeasures of Oedo line[J]. Rolling Stock and Machinery, 2006, 14(3): 34-37. (in Japanese) [54] 阳建鸣. 日本直线电机牵引地铁钢轨波形磨耗的对策[J]. 现代城市轨道交通, 2007(2): 57-62. doi: 10.3969/j.issn.1672-7533.2007.02.021YANG Jian-ming. Countermeasures to rail corrugations of the linear metro in Japan[J]. Modern Urban Transit, 2007(2): 57-62. (in Chinese) doi: 10.3969/j.issn.1672-7533.2007.02.021 [55] 张学华, 宗清泉, 郭满鸿, 等. 轮轨异常磨耗成因分析[J]. 现代城市轨道交通, 2006(4): 56-58. doi: 10.3969/j.issn.1672-7533.2006.04.020ZHANG Xue-hua, ZONG Qing-quan, GUO Man-hong, et al. Analysis on the formation of abnormal wear of wheel and rail[J]. Modern Urban Transit, 2006(4): 56-58. (in Chinese) doi: 10.3969/j.issn.1672-7533.2006.04.020 [56] 张学华. 城市轨道钢轨波浪形磨耗的产生和预防[J]. 上海铁道科技, 2008(1): 100-101. doi: 10.3969/j.issn.1673-7652.2008.01.047ZHANG Xue-hua. Generation and prevention of rail corrugations in rail transit[J]. Shanghai Railway Science and Technology, 2008(1): 100-101. (in Chinese) doi: 10.3969/j.issn.1673-7652.2008.01.047 [57] 郭满鸿, 张学华, 沈钢. 南京地铁曲线波浪型磨耗研究[J]. 都市快轨交通, 2010, 23(4): 1-3. doi: 10.3969/j.issn.1672-6073.2010.04.001GUO Man-hong, ZHANG Xue-hua, SHEN Gang. Study on the rail corrugation on curved tracks of Nanjing metro[J]. Urban Rapid Rail Transit, 2010, 23(4): 1-3. (in Chinese) doi: 10.3969/j.issn.1672-6073.2010.04.001 [58] 乔小雷. 南京地铁钢轨使用状况及换轨方式分析[J]. 都市快轨交通, 2014, 27(3): 88-93. doi: 10.3969/j.issn.1672-6073.2014.03.021QIAO Xiao-lei. Application status of steel rail and rail exchanging modes in Nanjing Metro[J]. Urban Rapid Rail Transit, 2014, 27(3): 88-93. (in Chinese) doi: 10.3969/j.issn.1672-6073.2014.03.021 [59] 杜茂金. 南京地铁DTⅥ2型扣件弹条折断原因分析[J]. 城市轨道交通研究, 2009(7): 40-42. doi: 10.3969/j.issn.1007-869X.2009.07.013DU Mao-jin. Analysis of DTⅥ 2 type fastener broken shells in Nanjing Metro[J]. Urban Mass Transit, 2009(7): 40-42. (in Chinese) doi: 10.3969/j.issn.1007-869X.2009.07.013 [60] 曹亮, 许玉德, 周宇, 等. 城市轨道交通钢轨波浪形磨耗特征分析[J]. 城市轨道交通研究, 2010(2): 46-48, 52. doi: 10.3969/j.issn.1007-869X.2010.02.012CAO Liang, XU Yu-de, ZHOU Yu, et al. Characteristics of rail corrugation in urban mass transit[J]. Urban Mass Transit, 2010(2): 46-48, 52. (in Chinese) doi: 10.3969/j.issn.1007-869X.2010.02.012 [61] 王少锋, 许玉德, 周宇, 等. 城市轨道交通曲线钢轨波磨检测与评价方法研究[J]. 城市轨道交通研究, 2011, 14(10): 56-60. doi: 10.3969/j.issn.1007-869X.2011.10.015WANG Shao-feng, XU Yu-de, ZHOU Yu, et al. Detection and evaluation of curve corrugation of urban mass transit[J]. Urban Mass Transit, 2011, 14(10): 56-60. (in Chinese) doi: 10.3969/j.issn.1007-869X.2011.10.015 [62] 姚湘静. 上海轨道交通2号线钢轨波磨分布及其打磨作业效果分析[J]. 城市轨道交通研究, 2014, 17(8): 78-82. doi: 10.3969/j.issn.1007-869X.2014.08.019YAO Xiang-jing. Distribution of rail corrugation and effectiveness of rail grinding on Shanghai Metro Line 2[J]. Urban Mass Transit, 2014, 17(8): 78-82. (in Chinese) doi: 10.3969/j.issn.1007-869X.2014.08.019 [63] 瞿锋. 城市轨道交通曲线钢轨短波不平顺分析[J]. 城市轨道交通研究, 2011, 14(8): 65-68. doi: 10.3969/j.issn.1007-869X.2011.08.017QU Feng. Analysis of short wavelength irregularity of rail surface in curve of urban mass transit[J]. Urban Mass Transit, 2011, 14(8): 65-68. (in Chinese) doi: 10.3969/j.issn.1007-869X.2011.08.017 [64] 雷震宇, 王志强, 李莉, 等. 地铁普通扣件钢轨波磨特性[J]. 同济大学学报(自然科学版), 2019, 47(9): 1334-1340. doi: 10.11908/j.issn.0253-374x.2019.09.014LEI Zhen-yu, WANG Zhi-qiang, LI Li, et al. Rail corrugation characteristics of the common fastener track in metro[J]. Journal of Tongji University (Natural Science), 2019, 47(9): 1334-1340. (in Chinese) doi: 10.11908/j.issn.0253-374x.2019.09.014 [65] 方格. 高弹轨道短波磨形成机理及钢轨不平顺检测方法研究[D]. 上海: 上海交通大学, 2017.FANG Ge. The generation mechanism of short pitch corrugation on high resilient rail and the measurement of rail unevenness[D]. Shanghai: Shanghai Jiaotong University, 2017. (in Chinese) [66] FANG G, WANG Y, PENG Z, et al. Theoretical investigation into the formation mechanism and mitigation measures of short pitch rail corrugation in resilient tracks of metros[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2018, 232(9): 2260-2271. doi: 10.1177/0954409718769750 [67] WANG Y, WU T X. The growth and mitigation of rail corrugation due to vibrational interference between moving wheels and resilient track[J]. Vehicle System Dynamics, 2020, 58(8): 1257-1284. doi: 10.1080/00423114.2019.1616099 [68] 刘维宁, 任静, 刘卫丰, 等. 北京地铁钢轨波磨测试分析[J]. 都市快轨交通2011, 24(3): 6-9. doi: 10.3969/j.issn.1672-6073.2011.03.003LIU Wei-ning, REN Jing, LIU Wei-feng, et al. In-situ tests and analysis on rail corrugation of Beijing Metro[J]. Urban Rapid Rail Transit, 2011, 24(3): 6-9. (in Chinese) doi: 10.3969/j.issn.1672-6073.2011.03.003 [69] 郭建平, 刘维宁, 雷黔湘, 等. 北京地铁4号线钢轨异常波磨调查及整治措施[J]. 都市快轨交通, 2011, 24(3): 10-13. doi: 10.3969/j.issn.1672-6073.2011.03.004GUO Jian-ping, LIU Wei-ning, LEI Qian-xiang, et al. Survey on and solutions to abnormal rail corrugation problem of Beijing Metro Line 4[J]. Urban Rapid Rail Transit, 2011, 24(3): 10-13. (in Chinese) doi: 10.3969/j.issn.1672-6073.2011.03.004 [70] 张厚贵, 刘维宁, 吴宗臻, 等. 地铁剪切型减振扣件地段钢轨波磨成因与治理措施[J]. 中国铁道科学, 2014, 35(4): 22-28. doi: 10.3969/j.issn.1001-4632.2014.04.04ZHANG Hou-gui, LIU Wei-ning, WU Zong-zhen, et al. Case and treatment for rail corrugation developed on egg fastening system section of metro line[J]. China Railway Science, 2014, 35(4): 22-28. (in Chinese) doi: 10.3969/j.issn.1001-4632.2014.04.04 [71] YAN Z, MARKINE V, GU A, et al. Optimization of the dynamic properties of the ladder track system to control rail vibration using the multipoint approximation method[J]. Journal of Vibration and Control, 2014, 20(13): 1967-1984. doi: 10.1177/1077546313480539 [72] YAN Z, MARKINE V, GU A, et al. Optimisation of the dynamic properties of ladder track to minimise the chance of rail corrugation[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2014, 228(3): 285-297. doi: 10.1177/0954409712472329 [73] 闫子权. 控制梯型轨道钢轨波磨的动力性能优化研究[D]. 北京: 北京交通大学, 2014.YAN Zi-quan. Optimization study of the dynamic properties of ladder track to minimize the probability of rail corrugation[D]. Beijing: Beijing Jiaotong University, 2014. (in Chinese) [74] 杨松. 基于轮轨振动特性的地铁钢轨波磨产生及发展机理研究[D]. 北京: 北京交通大学, 2015.YANG Song. Generation and development mechanisms of rail corrugation on subway track based on wheel/rail vibration characteristics[D]. Beijing: Beijing Jiaotong University, 2015. (in Chinese) [75] XIAO H, YANG S, WANG H, et al. Initiation and development of rail corrugation based on track vibration in metro systems[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2018, 232(9): 2228-2243. doi: 10.1177/0954409718768956 [76] 刘慧慧. 曲线参数对钢轨波磨及车辆系统振动影响研究[D]. 北京: 北京交通大学, 2015.LIU Hui-hui. Research on the effect of curve parameters on rail corrugation and vehicle system vibration[D]. Beijing: Beijing Jiaotong University, 2015. (in Chinese) [77] 李响. 地铁减振轨道结构振动及钢轨波磨研究[D]. 北京: 北京交通大学, 2018.LI Xiang. Study on vibration and rail corrugation of subway vibration-reduction track structure[D]. Beijing: Beijing Jiaotong University, 2018. (in Chinese) [78] 李响, 任尊松, 徐宁. 地铁小半径曲线段钢弹簧浮置板轨道的钢轨波磨研究[J]. 铁道学报, 2017, 39(8): 70-76. doi: 10.3969/j.issn.1001-8360.2017.08.010LI Xiang, REN Zun-song, XU Ning. Study on rail corrugation of steel spring floating slab track[J]. Journal of the China Railway Society, 2017, 39(8): 70-76. (in Chinese) doi: 10.3969/j.issn.1001-8360.2017.08.010 [79] 李响, 任尊松. 地铁钢弹簧浮置板轨道垂向振动特性研究[J]. 华南理工大学学报(自然科学版), 2018, 46(12): 103-110, 120. https://www.cnki.com.cn/Article/CJFDTOTAL-HNLG201812014.htmLI Xiang, REN Zun-song. Study on vertical vibration characteristics of steel spring floating slab track in subway[J]. Journal of South China University of Technology (Natural Science Edition), 2018, 46(12): 103-110, 120. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HNLG201812014.htm [80] 陈嘉梁, 刘维宁, 刘卫丰, 等. 北京地铁DTVI2扣件钢轨波磨整治措施的试验研究[J]. 机械工程学报, 2018, 54(4): 64-69. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201804011.htmCHEN Jia-liang, LIU Wei-ning, LIU Wei-feng, et al. Demonstration test on treatment solution against rail corrugation occurs at DTVI2 fastener track sections in Beijing metro[J]. Journal of Mechanical Engineering, 2018, 54(4): 64-69. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201804011.htm [81] 黑勇进. 地铁钢轨波磨引起的扣件病害分析与治理[J]. 铁道建筑, 2019, 59(8): 150-153. doi: 10.3969/j.issn.1003-1995.2019.08.35HEI Yong-jin. Analysis and treatment of fastener defects caused by metro rail corrugation[J]. Railway Engineering, 2019, 59(8): 150-153. (in Chinese) doi: 10.3969/j.issn.1003-1995.2019.08.35 [82] 李霞, 李伟, 温泽峰, 等. 普通短轨枕轨道结构钢轨波磨初步研究[J]. 机械工程学报. 2013, 49(2): 109-115. doi: 10.3969/j.issn.1674-8530.2013.02.004LI Xia, LI Wei, WEN Ze-feng, et al. Preliminary study on the rail corrugation of the fixed-dual short sleeper track[J]. Journal of Mechanical Engineering, 2013, 49(2): 109-115. (in Chinese) doi: 10.3969/j.issn.1674-8530.2013.02.004 [83] 李伟, 杜星, 王衡禹, 等. 地铁钢轨一种波磨机理的调查分析[J]. 机械工程学报, 2013, 49(16): 26-32. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201316005.htmLI Wei, DU Xing, WANG Heng-yu, et al. Investigation into the mechanism of type of rail corrugation of metro[J]. Journal of Mechanical Engineering, 2013, 49(16): 26-32. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201316005.htm [84] 李霞, 李伟, 吴磊, 等. 套靴轨枕轨道钢轨波磨初步研究[J]. 铁道学报, 2014, 36(11): 80-85. doi: 10.3969/j.issn.1001-8360.2014.11.016LI Xia, LI Wei, WU Lei, et al. Preliminary study on the rail corrugation of rubber booted short sleeper track[J]. Journal of the China Railway Society, 2014, 36(11): 80-85. (in Chinese) doi: 10.3969/j.issn.1001-8360.2014.11.016 [85] 李霞, 李伟, 申莹莹, 等. 基于轨道振动理论的梯形轨枕轨道钢轨波磨研究[J]. 机械工程学报, 2016, 52(22): 121-128. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201622016.htmLI Xia, LI Wei, SHEN Ying-ying, et al. Study on the rail corrugation of the ladder-type sleepers track based on the track vibration theory[J]. Journal of Mechanical Engineering, 2016, 52(22): 121-128. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201622016.htm [86] LI W, WANG H, WEN Z, et al. An investigation into the mechanism of metro rail corrugation using experimental and theoretical methods[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2016, 230(4): 1025-1039. doi: 10.1177/0954409715596182 [87] 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. doi: 10.1177/0954409719877318 [88] 王华川, 王仲林. 打磨技术在地铁轨道养护中的实践探讨[J]. 甘肃科技, 2006, 22(1): 51-53. https://www.cnki.com.cn/Article/CJFDTOTAL-GSKJ200601021.htmWANG Hua-chuan, WANG Zhong-lin. Discussion on the practice of grinding technology on metro track maintenance[J]. Gansu Science and Technology, 2006, 22(1): 51-53. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GSKJ200601021.htm [89] 李伟, 曾全君, 朱士友, 等. 地铁钢轨波磨对车辆和轨道动态行为的影响[J]. 交通运输工程学报, 2015, 15(1): 34-42. doi: 10.3969/j.issn.1671-1637.2015.01.005LI Wei, ZENG Quan-jun, ZHU Shi-you, et al. Effect of metro rail corrugation on dynamic behaviors of vehicle and track[J]. Journal of Traffic and Transportation Engineering, 2015, 15(1): 34-42. (in Chinese) doi: 10.3969/j.issn.1671-1637.2015.01.005 [90] 李伟, 温泽峰, 王衡禹, 等. 地铁钢轨波磨演化过程中的特性分析[J]. 机械工程学报, 2018, 54(4): 70-78. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201804012.htmLI Wei, WEN Ze-feng, WANG Heng-yu, et al. Analysis on the evolution characteristics of rail corrugation on a metro[J]. Journal of Mechanical Engineering, 2018, 54(4): 70-78. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201804012.htm [91] 朱强强. 地铁先锋扣件轨道钢轨波磨形成机理初探[D]. 成都: 西南交通大学, 2018.ZHU Qiang-qiang. A preliminary investigation into the causes of rail corrugation on subway track with Vanguard fasteners[D]. Chengdu: Southwest Jiaotong University, 2018. [92] 黄学翾. 直线电机运载系统轮轨病害整治[J]. 都市快轨交通, 2016, 29(4): 64-66. doi: 10.3969/j.issn.1672-6073.2016.04.014HUANG Xue-xuan. Wheel and rail disease control of linear motor propulsion system[J]. Urban Rapid Rail Transit, 2016, 29(4): 64-66. (in Chinese) doi: 10.3969/j.issn.1672-6073.2016.04.014 [93] QIAN W J, WU Y F, CHEN G X, et al. Experimental and numerical studies of the effects of a rail vibration absorber on suppressing short pitch rail corrugation[J]. Journal of Vibroengineering, 2016, 18(2): 1133-1144. http://www.researchgate.net/publication/301727104_Experimental_and_numerical_studies_of_the_effects_of_a_rail_vibration_absorber_on_suppressing_short_pitch_rail_corrugation [94] 秦艳. 浅述城市轨道交通钢轨波磨的成因及防治措施[J]. 科学时代, 2014(4): 1-3.QIN Yan. Brief talk on cause and treatment of rail corrugation in rail urban transit[J]. Science Times, 2014(4): 1-3. (in Chinese) [95] 刘石清. 地铁线路钢轨异常波磨的分析与解决措施[J]. 铁道通信信号, 2014, 50(5): 18-19. https://www.cnki.com.cn/Article/CJFDTOTAL-TDTH201405008.htmLIU Shi-qing. Analysis and treatment on the rail abnormal corrugation in metros[J]. Railway Signalling and Communication, 2014, 50(5): 18-19. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDTH201405008.htm [96] ZHAO Cai-you, WANG Ping, SHENG Xi, et al. Theoretical simulation and experimental investigation of a rail damper to minimize short-pitch rail corrugation[J]. Mathematical Problems in Engineering, 2017, 2017: 1-15. http://downloads.hindawi.com/journals/mpe/2017/2359404.xml [97] 仲莹涵, 关庆华, 温泽峰, 等. 地铁钢轨波磨对轨道结构振动及减振特性影响[J]. 噪声与振动控制, 2017, 37(4): 85-89, 154. doi: 10.3969/j.issn.1006-1355.2017.04.017ZHONG Ying-han, GUAN Qing-hua, WEN Ze-feng, et al. Influence of metro rail corrugation on track system's vibration and mitigation characteristics[J]. Noise and Vibration Control, 2017, 37(4): 85-89, 154. (in Chinese) doi: 10.3969/j.issn.1006-1355.2017.04.017 [98] 李元康, 王安斌, 徐宁, 等. 钢轨波浪磨耗测试分析研究[J]. 材料开发与应用, 2016, 31(4): 7-11. https://www.cnki.com.cn/Article/CJFDTOTAL-CLKY201604002.htmLI Yuan-kang, WANG An-bin, XU Ning, et al. Testing and theoretical exploration on rail corrugation[J]. Development and Application of Materials, 2016, 31(4): 7-11. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CLKY201604002.htm [99] 徐宁, 王岗, 张用兵, 等. 低速工况下浮轨扣件减振降噪及钢轨波磨分析[J]. 噪声与振动控制, 2018, 38(4): 213-216, 236. https://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK201804042.htmXU Ning, WANG Gang, ZHANG Yong-bing, et al. Floating rail fastener vibration noise reduction and rail corrugation analysis in low speed condition[J]. Noise and Vibration Control, 2018, 38(4): 213-216, 236. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK201804042.htm [100] 谷爱军, 刘维宁. 国外城市轨道交通钢轨波浪形磨耗病害研究及治理[J]. 城市轨道交通研究, 2011, 14(12): 51-55. doi: 10.3969/j.issn.1007-869X.2011.12.012GU Ai-jun, LIU Wei-ning. Study and control of rail corrugation defects of urban rail transit in foreign cities[J]. Urban Mass Transit, 2011, 14(12): 51-55. (in Chinese) doi: 10.3969/j.issn.1007-869X.2011.12.012 [101] ISHIDA M, MOTO T, TAKIKAWA M. The effect of lateral creepage force on rail corrugation on low rail at sharp curves[J]. Wear, 2002, 253(1/2): 172-177. http://www.sciencedirect.com/science/article/pii/S0043164802000960 [102] 关庆华, 周业明, 李伟, 等. 车辆轨道系统的P2共振频率研究[J]. 机械工程学报, 2019, 55(8): 118-127. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201908017.htmGUAN Qing-hua, ZHOU Ye-ming, LI Wei, et al. Study on the P2 resonance frequency of vehicle track system[J]. Journal of Mechanical Engineering, 2019, 55(8): 118-127. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201908017.htm [103] MEEHAN P A, BELLETTE P A, HORWOOD R J. "Does god play dice with corrugations?": Environmental effects on growth[J]. Wear, 2014, 314(1/2): 254-260. http://www.sciencedirect.com/science/article/pii/S0043164813005711 [104] ISHIDA M, AOKI F, SONE Y, et al. Rail corrugations caused by low coefficient of friction in submarine railway tunnel[C]//ASME. Proceedings of WTC 2005 World Tribology Congress Ⅲ. Washington DC: ASME, 2002: 1-2. [105] ALIAS J. Characteristics of wave formation in rails[J]. Rail International, 1986, 17(11): 17-23. http://www.researchgate.net/publication/293135273_CHARACTERISTICS_OF_WAVE_FORMATION_IN_RAILS [106] CIAVARELLA M, BARBER J. Influence of longitudinal creepage and wheel inertia on short-pitch corrugation: a resonance-free mechanism to explain the roaring rail phenomenon[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2008, 222(3): 171-181. doi: 10.1243/13506501JET373 [107] AFFERRANTE L, CIAVARELLA M. Short-pitch rail corrugation: a possible resonance-free regime as a step forward to explain "enigma"?[J]. Wear, 2009, 266(9/10): 934-944. http://www.sciencedirect.com/science/article/pii/S0043164808004353 [108] AFFERRANTE L, CIAVARELLA M. Short-pitch corrugation of railway tracks with wooden or concrete sleepers: an enigma solved?[J]. Tribology International, 2010, 43(3): 610-622. doi: 10.1016/j.triboint.2009.09.010 [109] LI S, LI Z, NUNEZ 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): 807-1-23. http://www.researchgate.net/publication/319009674_New_Insights_into_the_Short_Pitch_Corrugation_Enigma_Based_on_3D-FE_Coupled_Dynamic_Vehicle-Track_Modeling_of_Frictional_Rolling_Contact [110] CLARK R A, FOSTER P. On the mechanics of rail corrugation formation[J]. Vehicle System Dynamics, 1983, 12(1): 35-39. [111] MATSUMOTO A, SATO Y, ONO H, et al. Formation mechanism and countermeasures of rail corrugation on curved track[J]. Wear, 2002, 253(1/2): 178-184. http://www.sciencedirect.com/science/article/pii/S0043164802000972 [112] 闫子权, 谷爱军, 黑勇进, 等. 轮对振动对产生钢轨异常波磨的影响[J]. 都市快轨交通, 2011, 24(3): 22-25, 29. doi: 10.3969/j.issn.1672-6073.2011.03.007YAN Zi-quan, GU Ai-jun, HEI Yong-jin, et al. Influences of wheel set vibration on rail abnormal corrugation[J]. Urban Rapid Rail Transit, 2011, 24(3): 22-25, 29. (in Chinese) doi: 10.3969/j.issn.1672-6073.2011.03.007 [113] 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. doi: 10.1016/j.jsv.2010.05.011 [114] 陈光雄, 钱韦吉, 莫继良, 等. 轮轨摩擦自激振动引起小半径曲线钢轨波磨的瞬态动力学[J]. 机械工程学报, 2014, 50(9): 71-76. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201409010.htmCHEN Guang-xiong, QIAN Wei-ji, MO Ji-liang, et al. A transient dynamics study on wear-type rail corrugation on a tight curve due to the friction-induced self-excited vibration of a wheelset-track system[J]. Journal of Mechanical Engineering, 2014, 50(9): 71-76. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201409010.htm [115] CUI X L, CHEN G X, YANG H G, et al. Study on rail corrugation of a metro tangential track with Cologne-egg type fasteners[J]. Vehicle System Dynamics, 2016, 54(3): 353-369. doi: 10.1080/00423114.2015.1137955 [116] CUI X, CHEN G, ZHAO J, et al. Field investigation and numerical study of the rail corrugation caused by frictional self-excited vibration[J]. Wear, 2017, 376/377: 1919-1929. doi: 10.1016/j.wear.2017.01.089 [117] GRASSIE S L, SAXON M J, SMITH J D. Measurement of longitudinal rail irregularities and criteria for acceptable grinding[J]. Journal of Sound and Vibration, 1999, 227 (5): 949-964. doi: 10.1006/jsvi.1999.2980 [118] GRASSIE S L. A practical methodology to prioritise reprofiling sites for corrugation removal[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2020, 234(4): 362-369. doi: 10.1177/0954409719853071 [119] ILIAS H. The influence of railpad stiffness on wheelset/track interaction and corrugation growth[J]. Journal of Sound and Vibration, 1999, 227(5): 935-948. doi: 10.1006/jsvi.1999.2059 [120] JIN X, LI W, WEN Z, et al. An investigation into rail corrugation, its mechanisms and effects on the dynamic behavior of metro trains and tracks in China[J]. International Journal of Railway Technology, 2016, 5(3): 1-29. doi: 10.4203/ijrt.5.3.1 [121] COLLETTE C, HORODINCA M, PREUMONT A. Rotational vibration absorber for the mitigation of rail rutting corrugation[J]. Vehicle System Dynamics, 2009, 47(6): 641-659. doi: 10.1080/00423110802339792 [122] WU T X. Effects on short pitch rail corrugation growth of a rail vibration absorber/damper[J]. Wear, 2011, 271(1/2): 339-348. http://www.sciencedirect.com/science/article/pii/S0043164810003741 [123] 文永蓬, 纪忠辉, 翁琳, 等. 双重钢轨吸振器对轨道系统的振动抑制研究[J]. 机械工程学报, 2020, 56(12): 184-195. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB202012023.htmWEN Yong-peng, JI Zhong-hui, WENG Lin, et al. Study on vibration suppression of track system via double rail vibration absorber[J]. Journal of Mechanical Engineering, 2020, 56(12): 184-195. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB202012023.htm [124] 纪忠辉, 文永蓬, 翁琳, 等. 钢轨横垂双向Pinned-pinned振动抑制研究[J]. 铁道科学与工程学报, 2020, 17(8): 1935-1942. https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD202008007.htmJI Zhong-hui, WEN Yong-peng, WENG Lin, et al. Study on the lateral and vertical two-direction Pinned-pinned vibration suppression of rails[J]. Journal of Railway Science and Engineering, 2020, 17(8): 1935-1942. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD202008007.htm [125] 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. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201904017.htmLIU Wei-feng, ZHANG Hou-gui, CHEN Jia-liang, et al. A test of treating rail vibration by tuned rail damper for Beijing Metro[J]. Journal of Vibration Engineering, 2019, 32(4): 695-700. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201904017.htm [126] 关庆华, 张丹煕, 王鹏, 等. 扣件支撑长度对车轮-轨道耦合振动的影响[J]. 机械工程学报, 2019, 55(16): 159-169. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201916017.htmGUAN Qing-hua, ZHANG Dan-xi, WANG Peng, et al. Influence of pad support length on the vibration of wheel-track[J]. Journal of Mechanical Engineering, 2019, 55(16): 159-169. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201916017.htm [127] 楚永萍. 钢轨波浪型磨耗对地铁车辆振动性能的影响[J]. 城市轨道交通研究, 2009, 12(8): 17-20. doi: 10.3969/j.issn.1007-869X.2009.08.006CHU Yong-ping. Effects of rail undulation wear on vehicle vibration[J]. Urban Mass Transit, 2009, 12(8): 17-20. (in Chinese) doi: 10.3969/j.issn.1007-869X.2009.08.006 [128] CORREA N, VADILLO E G, SANTAMARIA J, et al. A versatile method in the space domain to study short-wave rail undulatory wear caused by rail surface defects[J]. Wear, 2016, 352/353: 196-208. doi: 10.1016/j.wear.2016.02.012 [129] EADIE D T, KALOUSEK J, CHIDDICK K C. The role of high positive friction (HPF) modifier in the control of short pitch corrugations and related phenomena[J]. Wear, 2002, 253(1): 185-192. http://www.sciencedirect.com/science/article/pii/S0043164802000984 [130] EADIE D T, SANTORO M. Top-of-rail friction control for curve noise mitigation and corrugation rate reduction[J]. Journal of Sound and Vibration, 2006, 293(3/5): 747-757. http://www.sciencedirect.com/science/article/pii/S0022460X05007832 [131] EADIE D T, SANTORO M, OLDKNOW K, et al. Field studies of the effect of friction modifiers on short pitch corrugation generation in curves[J]. Wear, 2008, 265(9/10): 1212-1221. http://www.sciencedirect.com/science/article/pii/S0043164808001427 [132] SUDA Y, IWASA T, KOMINE H, et al. Development of onboard friction control[J]. Wear, 2005, 258(7/8): 1109-1114. http://www.sciencedirect.com/science/article/pii/S0043164804003205 -
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