铁路车辆车轮型面优化设计研究
|
摘要
轮轨几何型面匹配关系直接影响铁路车辆的运行性能、运输成本和运行安全,直是国内外铁路工作者的重要研究课题。虽然人们通过对轮轨型面的优化设计取得了非常丰富的成果,但该问题仍未得到很好地解决。随着列车运行速度的提高,轮轨界面动态作用加剧,轮轨磨耗现象变得更为突出。因此,以降低轮轨动态作用力改善轮轨接触状态为目的,结合车辆系统动力学开展轮轨型面优化设计研究,对铁路轮轨损伤综合防治具有重要工程应用价值和理论指导意义。
本文发展了铁路车辆车轮型面的两种设计方法,分别是依据钢轨型面的车轮型面设计方法和车轮型面数值优化模型。依据钢轨型面设计车轮型面的设计方法是发展了Leary等人的钢轨型面扩展法,用解析表达式将反映动力学性能的轮对等效锥度与代表轮轨型面共形度的钢轨型面扩展系数联系起来,并将扩展系数视为设计变量,可以设计不同等效锥度、轮轨间隙并能适合不同轨底坡的多种车轮型面。在Shevtsov、Jahed等人的工作基础上,利用3次样条理论提出了数值优化约束条件,并根据轮轨蠕滑理论提出了目标滚动圆半径差曲线的确定方法。
在论文第4、5和6章中,根据钢轨型面设计了车轮型面,通过轮轨接触特性分析和车辆动力学计算,分别研究了轮对等效锥度、轮轨名义间隙以及钢轨轨底坡对车辆动力学性能和轮轨作用特性的影响。第7章对一个镟修周期内某高速动车组车轮型面磨耗连续跟踪测量结果进行了详细分析,针对测量结果所发现的问题,结合前面章节研究结果提出了车轮型面设计的新建议。
本论文主要结果和结论如下。
(1)在轮对等效锥度与车辆动力学性能的关系方面,车辆临界速度并不严格地与轮对等效锥度平方根成反比。而是存在一个临界速度比较高的小锥度区域,等效锥度在该区域的变化不会引起临界速度明显变化。等效锥度大于该区域时车辆临界速度方与等效锥度的平方根成反比。锥度太小将导致轮对恢复对中位置能力不足,在一定的情况下车辆临界速度随等效锥度的减小而迅速降低。磨耗型车轮型面在上述小等效锥度范围内临界速度与锥形型面几乎相同。等效锥度应随轮对横移量的增大而持续增大,在轮缘接触前形成轮对等效锥度较高的过渡平台,可以提高车辆曲线通过性能,有效地减少轮缘接触。
(2)关于“轮轨名义间隙”对车辆动力学性能及轮轨接触特性影响方面。通过不同轮轨名义间隙车轮型面的设计分析表明,轮轨名义间隙的减小会导致车辆临界速度明显降低,并在轨道不平顺作用下容易发生轮缘接触。但是,若轮对等效锥度设计适当,仍可获得足够高的临界速度,并减小轮缘接触几率。对于采用较小轮轨间隙的锥形车轮型面,车辆临界速度明显降低,并低于磨耗型车轮型面所对应的临界速度。锥形型面轮对在轨道不平顺作用下发生较大横移量时无法提供足够大的轮径差,故不可避免地发生轮缘接触。因此,轮轨名义间隙对车辆动力学性能和轮轨接触状态影响均很大。
(3)关于轨底坡对车辆动力学性能及轮轨作用力的影响方面。轨底坡的变化对锥形车轮轮对等效锥度影响很小,故对车辆临界速度、曲线通过性能、轮轨作用力未构成实质影响。而依据不同轨底坡设计的磨耗型轮对的临界速度有差别,轨底坡越大它们临界速度差异越大,但磨耗型轮对均存在着临界速度较高的小等效锥度工作区域。只是由于设计的磨耗型轮对的等效锥度随着轨底坡的增大而增大,能够兼顾最佳钢轨受力状态的高临界速度等效锥度区域变窄。依据不同轨底坡设计的并具有相同等效锥度的轮对通过曲线性能和轮轨动态作用力无实质差别。因此,轨底坡仅对车辆临界速度有影响。
(4)车轮型面磨耗跟踪测量结果分析可知,车轮踏面和轮缘平均累积磨耗深度变化规律基本一致,表明车轮型面异常磨耗现象得到缓解。跟踪测试结果发现,列车的运用模式对车轮型面磨耗影响很重要。分析还表明,在约4万公里的初始运用期间,车轮踏面和轮缘磨耗量均几乎占一个镟修周期总磨耗量的一半。
Wheel/rail profile geometric matching relationship exerts direct influence on railway vehicle running performance, transportation costs and operation safety. It has always been an important research subject for railways researchers in home and abroad. While very rich results have been obtained by wheel/rail profile optimal design, this problem has not yet been well settled. With the increase of train speed, wheel/rail interface dynamic interaction intensified, and the wheel/rail wear phenomenon becomes more prominent. Therefore, for the purpose of reducing wheel/rail dynamic interaction forces and improving wheel/rail contact status, wheel/rail profile optimal design combined with vehicle system dynamics research has important engineering application value and theoretical meaning for railway wheel/rail damage comprehensive prevention and control.
The2profile design approaches for railway vehicle wheels are developed. One is the designing railway wheel profile based on existing rail profile method, and another is the wheel profile numerical optimal design model.
The wheel profile design based on the rail profile method further improves the rail profile expansion design method originally proposed by Leary et al. The improved design method utilizes the rail profile expansion factor to build an analytical expression for the relationship between wheelset equivalent conicity, characterizing railway vehicle dynamics performance, and rail profile expansion factor, representing wheel/rail contact conformity. Taking the expansion factor as a design variable, can design the wheel profiles with different equivalent conicities matching different rail cants and wheel/rail nominal clearances.
And the numerical optimal design model of wheel profile is based on the works of Shevtsov and Jahed et al. The present paper puts forward the numerical optimization design constrains by exploiting the cubic Spline theory. And it also proposes an objective wheelset rolling radius difference (RRD) design technique according to the wheel/rail creep theory.
The designing wheel profile based on the existing rail profile method is, hereafter, extensively utilized to design railway wheel profiles. Combined with wheel/rail contact characteristic analysis and vehicle dynamics calculation, the effects of wheelset equivalent conicities, wheel/rail nominal clearances and rail cants on the vehicle dynamics performance and wheel/rail interaction features are studied in detail in Chapters4,5, and6, respectively.
Chapter7analyzes the continuously measured wheel profile wear data of a high-speed electric multiple unit (EMU) train in an interval between two wheel reprofilings in detail. A new wheel profile design proposal is put forward, considering the wheel wear problems found in the site measurements and the foregoing research results.
The main results obtained and conclusions reached of this dissertation are as follows.
(1) The railway vehicle critical speed does not strictly in inverse proportion to the square root of wheelset equivalent conicity. There exists a low wheelset equivalent conicity range with relatively high vehicle critical speed. The variation of equivalent conicity within this range would not cause a great change in the vehicle critical speed. The vehicle critical speed does in inverse proportion to the square root of wheelset equivalent conicity, if the wheelset has higher equivalent conicity than this range. A wheelset with very low conicity would cause it insufficiency in the ability of going back to track central position, the vehicle critical speed drops rapidly. The analysis found that a wheelset with worn shape profile can achieve nearly the same vehicle critical speed as the wheelset with conical profile in the above mentioned low equivalent conicity range. A good behavior wheelset should has an important characteristics that its equivalent conicity increase as the wheelset lateral displacement increases, and the wheelset should has a higher equivalent conicity transition region before its flanging action. This would improve the vehicle curving performance and reduce the occurrence of wheel flanging action effectively.
(2) Regarding the influence of wheel/rail nominal clearance on railway vehicle dynamics performance and wheel/rail contact. The analyses of worn shape wheel profile designed with different wheel/rail nominal clearance indicate that, a decrease in wheel/rail nominal clearance would cause the vehicle critical speed drops obviously. And, under track irregularity excitations a profile with smaller nominal clearance is prone to wheelset flange contact. But, if the wheelset equivalent conicity is designed appropriately, the wheelset with worn shape wheel profile can still has sufficiently high critical speed and lower chance of flange contact. For a conical profile wheelset with smaller wheel/rail nominal clearance, the vehicle critical speed drops more quickly than a worn one. As, in case of larger lateral displacement excited by track irregularities, a conical profile wheelset cannot generate enough radius difference, and flange contact becomes inevitable. Hence, the wheel/rail nominal clearance exerts significant effects on both vehicle dynamics performances and wheel/rail contact status.
(3) The rail cant variation has little effect on the equivalent conicity of a wheelset with conical wheel profile. So, the rail cant has no substantial influence on the vehicle critical speed, curving performance, and wheel/rail forces when the vehicle uses conical profile wheelsets. But, there is a significant difference among the equivalent conicities of the worn profile wheelsets designed based on different rail cants, namely, the rail cant has a great influence on the equivalent connicity of the wheelset with worn shape wheel profile. The larger rail cant the larger difference of the equivalent conicities. The wheelsets with worn profiles designed based on small rail cant always have a low equivalent conicity range, in which there is a high critical speed. As the rail cant increases the equivalent conicity of the worn profile wheelset increases, the low equivalent conicity range preserving high critical speed and desirable wheel/rail forces becomes narrower. For wheelsets with the same equivalent conicity designed based on different rail cants, their curving performance and wheel/rail interaction forces exhibit no obvious differences. Therefore, based on different rail cants, wheelsets with designed wheel profiles have difference in vehicle critical speeds.
(4) The analysis on the wheel profile wear tracking measurement results shows that the change of the average accumulated wear depths on both the wheel tread and the wheel flange are close, which indicates that the abnormal wear of wheel profile main working region is alleviated. The tracking measurement results reveal that the train application pattern has a very important influence on wheel profile wear. The analysis also shows that, after the initial operation period of about40,000km, the average accumulated wear depth on both the wheel tread and the flange amounts to nearly half of one turning cycle of the wheel.
本文发展了铁路车辆车轮型面的两种设计方法,分别是依据钢轨型面的车轮型面设计方法和车轮型面数值优化模型。依据钢轨型面设计车轮型面的设计方法是发展了Leary等人的钢轨型面扩展法,用解析表达式将反映动力学性能的轮对等效锥度与代表轮轨型面共形度的钢轨型面扩展系数联系起来,并将扩展系数视为设计变量,可以设计不同等效锥度、轮轨间隙并能适合不同轨底坡的多种车轮型面。在Shevtsov、Jahed等人的工作基础上,利用3次样条理论提出了数值优化约束条件,并根据轮轨蠕滑理论提出了目标滚动圆半径差曲线的确定方法。
在论文第4、5和6章中,根据钢轨型面设计了车轮型面,通过轮轨接触特性分析和车辆动力学计算,分别研究了轮对等效锥度、轮轨名义间隙以及钢轨轨底坡对车辆动力学性能和轮轨作用特性的影响。第7章对一个镟修周期内某高速动车组车轮型面磨耗连续跟踪测量结果进行了详细分析,针对测量结果所发现的问题,结合前面章节研究结果提出了车轮型面设计的新建议。
本论文主要结果和结论如下。
(1)在轮对等效锥度与车辆动力学性能的关系方面,车辆临界速度并不严格地与轮对等效锥度平方根成反比。而是存在一个临界速度比较高的小锥度区域,等效锥度在该区域的变化不会引起临界速度明显变化。等效锥度大于该区域时车辆临界速度方与等效锥度的平方根成反比。锥度太小将导致轮对恢复对中位置能力不足,在一定的情况下车辆临界速度随等效锥度的减小而迅速降低。磨耗型车轮型面在上述小等效锥度范围内临界速度与锥形型面几乎相同。等效锥度应随轮对横移量的增大而持续增大,在轮缘接触前形成轮对等效锥度较高的过渡平台,可以提高车辆曲线通过性能,有效地减少轮缘接触。
(2)关于“轮轨名义间隙”对车辆动力学性能及轮轨接触特性影响方面。通过不同轮轨名义间隙车轮型面的设计分析表明,轮轨名义间隙的减小会导致车辆临界速度明显降低,并在轨道不平顺作用下容易发生轮缘接触。但是,若轮对等效锥度设计适当,仍可获得足够高的临界速度,并减小轮缘接触几率。对于采用较小轮轨间隙的锥形车轮型面,车辆临界速度明显降低,并低于磨耗型车轮型面所对应的临界速度。锥形型面轮对在轨道不平顺作用下发生较大横移量时无法提供足够大的轮径差,故不可避免地发生轮缘接触。因此,轮轨名义间隙对车辆动力学性能和轮轨接触状态影响均很大。
(3)关于轨底坡对车辆动力学性能及轮轨作用力的影响方面。轨底坡的变化对锥形车轮轮对等效锥度影响很小,故对车辆临界速度、曲线通过性能、轮轨作用力未构成实质影响。而依据不同轨底坡设计的磨耗型轮对的临界速度有差别,轨底坡越大它们临界速度差异越大,但磨耗型轮对均存在着临界速度较高的小等效锥度工作区域。只是由于设计的磨耗型轮对的等效锥度随着轨底坡的增大而增大,能够兼顾最佳钢轨受力状态的高临界速度等效锥度区域变窄。依据不同轨底坡设计的并具有相同等效锥度的轮对通过曲线性能和轮轨动态作用力无实质差别。因此,轨底坡仅对车辆临界速度有影响。
(4)车轮型面磨耗跟踪测量结果分析可知,车轮踏面和轮缘平均累积磨耗深度变化规律基本一致,表明车轮型面异常磨耗现象得到缓解。跟踪测试结果发现,列车的运用模式对车轮型面磨耗影响很重要。分析还表明,在约4万公里的初始运用期间,车轮踏面和轮缘磨耗量均几乎占一个镟修周期总磨耗量的一半。
Wheel/rail profile geometric matching relationship exerts direct influence on railway vehicle running performance, transportation costs and operation safety. It has always been an important research subject for railways researchers in home and abroad. While very rich results have been obtained by wheel/rail profile optimal design, this problem has not yet been well settled. With the increase of train speed, wheel/rail interface dynamic interaction intensified, and the wheel/rail wear phenomenon becomes more prominent. Therefore, for the purpose of reducing wheel/rail dynamic interaction forces and improving wheel/rail contact status, wheel/rail profile optimal design combined with vehicle system dynamics research has important engineering application value and theoretical meaning for railway wheel/rail damage comprehensive prevention and control.
The2profile design approaches for railway vehicle wheels are developed. One is the designing railway wheel profile based on existing rail profile method, and another is the wheel profile numerical optimal design model.
The wheel profile design based on the rail profile method further improves the rail profile expansion design method originally proposed by Leary et al. The improved design method utilizes the rail profile expansion factor to build an analytical expression for the relationship between wheelset equivalent conicity, characterizing railway vehicle dynamics performance, and rail profile expansion factor, representing wheel/rail contact conformity. Taking the expansion factor as a design variable, can design the wheel profiles with different equivalent conicities matching different rail cants and wheel/rail nominal clearances.
And the numerical optimal design model of wheel profile is based on the works of Shevtsov and Jahed et al. The present paper puts forward the numerical optimization design constrains by exploiting the cubic Spline theory. And it also proposes an objective wheelset rolling radius difference (RRD) design technique according to the wheel/rail creep theory.
The designing wheel profile based on the existing rail profile method is, hereafter, extensively utilized to design railway wheel profiles. Combined with wheel/rail contact characteristic analysis and vehicle dynamics calculation, the effects of wheelset equivalent conicities, wheel/rail nominal clearances and rail cants on the vehicle dynamics performance and wheel/rail interaction features are studied in detail in Chapters4,5, and6, respectively.
Chapter7analyzes the continuously measured wheel profile wear data of a high-speed electric multiple unit (EMU) train in an interval between two wheel reprofilings in detail. A new wheel profile design proposal is put forward, considering the wheel wear problems found in the site measurements and the foregoing research results.
The main results obtained and conclusions reached of this dissertation are as follows.
(1) The railway vehicle critical speed does not strictly in inverse proportion to the square root of wheelset equivalent conicity. There exists a low wheelset equivalent conicity range with relatively high vehicle critical speed. The variation of equivalent conicity within this range would not cause a great change in the vehicle critical speed. The vehicle critical speed does in inverse proportion to the square root of wheelset equivalent conicity, if the wheelset has higher equivalent conicity than this range. A wheelset with very low conicity would cause it insufficiency in the ability of going back to track central position, the vehicle critical speed drops rapidly. The analysis found that a wheelset with worn shape profile can achieve nearly the same vehicle critical speed as the wheelset with conical profile in the above mentioned low equivalent conicity range. A good behavior wheelset should has an important characteristics that its equivalent conicity increase as the wheelset lateral displacement increases, and the wheelset should has a higher equivalent conicity transition region before its flanging action. This would improve the vehicle curving performance and reduce the occurrence of wheel flanging action effectively.
(2) Regarding the influence of wheel/rail nominal clearance on railway vehicle dynamics performance and wheel/rail contact. The analyses of worn shape wheel profile designed with different wheel/rail nominal clearance indicate that, a decrease in wheel/rail nominal clearance would cause the vehicle critical speed drops obviously. And, under track irregularity excitations a profile with smaller nominal clearance is prone to wheelset flange contact. But, if the wheelset equivalent conicity is designed appropriately, the wheelset with worn shape wheel profile can still has sufficiently high critical speed and lower chance of flange contact. For a conical profile wheelset with smaller wheel/rail nominal clearance, the vehicle critical speed drops more quickly than a worn one. As, in case of larger lateral displacement excited by track irregularities, a conical profile wheelset cannot generate enough radius difference, and flange contact becomes inevitable. Hence, the wheel/rail nominal clearance exerts significant effects on both vehicle dynamics performances and wheel/rail contact status.
(3) The rail cant variation has little effect on the equivalent conicity of a wheelset with conical wheel profile. So, the rail cant has no substantial influence on the vehicle critical speed, curving performance, and wheel/rail forces when the vehicle uses conical profile wheelsets. But, there is a significant difference among the equivalent conicities of the worn profile wheelsets designed based on different rail cants, namely, the rail cant has a great influence on the equivalent connicity of the wheelset with worn shape wheel profile. The larger rail cant the larger difference of the equivalent conicities. The wheelsets with worn profiles designed based on small rail cant always have a low equivalent conicity range, in which there is a high critical speed. As the rail cant increases the equivalent conicity of the worn profile wheelset increases, the low equivalent conicity range preserving high critical speed and desirable wheel/rail forces becomes narrower. For wheelsets with the same equivalent conicity designed based on different rail cants, their curving performance and wheel/rail interaction forces exhibit no obvious differences. Therefore, based on different rail cants, wheelsets with designed wheel profiles have difference in vehicle critical speeds.
(4) The analysis on the wheel profile wear tracking measurement results shows that the change of the average accumulated wear depths on both the wheel tread and the wheel flange are close, which indicates that the abnormal wear of wheel profile main working region is alleviated. The tracking measurement results reveal that the train application pattern has a very important influence on wheel profile wear. The analysis also shows that, after the initial operation period of about40,000km, the average accumulated wear depth on both the wheel tread and the flange amounts to nearly half of one turning cycle of the wheel.
引文
1 沈志云.关于高速铁路及高速列车的研究[J].振动、测试与诊断,1998,18(1)：1-7.
2 国际重载协会.国际重载铁路最佳应用指南——轮轨关系[M].郭俊,温泽峰,王文健,陈光雄,曾京,刘启跃,译.北京：中国铁道出版社,2009：116-181
3 铁路大事记(1997-2011年)[J].中国投资,2011,(12)：74-75.
4 铁正轩.全面实施第六次大面积提速调图促进经济社会又好又快发展[J].中国铁路,2007,(5)：7-13.
5 SMITH R A. The wheel-rail interface—some recent accidents [J]. Fatigue Fract Eng Mater Struct,2003,26(10):901-907.
6 金学松,沈志云.轮轨滚动接触疲劳研究的最新进展[J].铁道学报,2001,23(2)：92-108.
7 金学松,张继业,温泽峰,李芾.轮轨滚动接触疲劳现象分析[J].机械强度,2002,24(2)：250-257
8 金学松,沈志云.轮轨滚动接触力学的发展.力学进展[J],2001,31(1)：33-46.
9 SMALLWOOD R, SINCLAIR J C, SAWLEY K J. An optimization technique to minimize rail contact stresses[J]. Wear,1991,144(1-2):373-384.
10 MAGEL E E, KALOUSEK J. The application of contact mechanics to rail profile design and rail grinding[J]. Wear,2002(253):308-316.
11 UEDA M, UCHINO K, KAGEYAMA H, et al. Development of bainitic steel rail with excellent surface damage resistance[C]. Proceeding of IHHA'99, Moscow, Russia, 1999,259-266.
12 MARICH S. Major advances in rail technologies achieved in the past 10-20 years[C]. In:Proceedings of the 8th International Heavy Haul Conference, Brazil,2005, 747-760.
13 MAGEL E, RONEY M, KALOUSEK J, et al. The blending of theory and practice in modern rail grinding[J]. Fatigue Fract Eng Mater Struct,2003,26(10):921-929.
14 WICKENS A H. Dynamics of railway vehicles-from Stephenson to Carter[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,1998,212(3):209-217.
15 WICKENS A H. Fundamentals of rail vehicle dynamics:guidance and stability[M]. Netherlands:Swets & Zeitlinger Publishers,2003,1-18.
16 严隽耄,傅茂海.车辆工程[M].第3版.北京：中国铁道出版社,2011：43-44.
17 杨国桢.车轮踏面形状的初步研究(上)[J],铁道车辆,1978,(11)：1-6.
18 杨国桢.车轮踏面形状的初步研究(下)[J].铁道车辆,1978,(12)：1-17.
19 汤村光造,芦淑嫒译.车辆与轨道的关系——存在的问题及其重要性[J].国外铁道车辆,1983,(3)：42-46.
20 MARCOTTE P P,陈明资译.加拿大国营铁路的新型车轮踏面[J].国外铁道车辆,1982,(1)：2-10.
21 柳拥军.高速轮轨接触几何学及高速轮轨几何型面优化的研究[D].铁道部科学研究院博士学位论文,1999.
22 HELLER R, LAW E H. Optimizing the wheel profile to improve rail vehicle dynamic performance[J]. Vehicle system dynamics,1979,15(Suppl):179-197.
23 李立,崔大宾,金学松.车轮型面优化的研究进展[J].西南交通大学学报,2009,44(1)：13-19.
24 HAQUE I, LATIMER D A, LAW E H. Computer-aided wheel profile design for railway vehicles[J]. ASME Journal of Engineering for Industry,1989, (111):288-291.
25 SMITH R E, KALOUSEK J. A design methodology for wheel and rail profiles for use on steered railway vehicles[J]. Wear,1991,144(1-2):329-342.
26 成棣,王成国,刘金朝.车轮踏面多目标优化设计研究进展[J].铁道机车车辆,2010,30(4)：5-11.
27 CHOROMANSKI W, ZBOINSKI K. Optimization of wheel and rail profiles for various conditions of vehicle motion[J]. Vehicle system dynamics,1991, 20(Suppl):84-98.
28 LEARY J F, HANDAL S N, RAJKUMAR B. Development of freight car wheel profile-a case study [J]. Wear,1991,144(1-2):353-362.
29 WU H. Effects of wheel and rail profiles on vehicle performance [J]. Vehicle System Dynamics,2006,44(Suppl):541-550.
30 WILSON N, WU H, TOURNAY H, URBAN C. Effects of wheel rail contact patterns and vehicle parameters on lateral stability [J]. Vehicle System Dynamics,2010, 48(Suppl):487-503.
31 WU H. Investigation of wheel rail interaction on wheel flange climb derailment and wheel rail profile compatibility[D]. Illinois Institute of Technology,2000.
32 佐藤荣作,叶娟译.车轮踏面形状设计的科学化[J].国外内燃机车,2000,(3)：39-43.
33 真野辰哉,彭惠民译.既有线车轮踏面形状的优化研究[J].国外机车车辆工艺,2007,(4)：14-17.
34 藤本裕,蒋立忱译.车轮踏面形状对高速动车运动特性的影响——通过相对于圆 弧、圆锥踏面形状的输入能量和几何蛇行运动波长进行评价[J].国外内燃机车,1999,(2)：22-29.
35 YAMADA K, HAYASHI T, NAKATA M, ISA M. New profiled tread design method and it's applied tread named "CS Tread"[C]//5th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Tokyo,2000,259-264
36 SASAKI K, KAGEYAMA T, ASANO K, OKUMURA M:Development of the wheel tread profile for commuter train[C]//5th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Tokyo,2000.
37 MIYAMOTO M, SUDA Y. Recent research and development on advanced technologies of high-speed railways in Japan[J]. Vehicle System Dynamics,2003, 40(1-3):55-99.
38 SATO Y. Historical study on designing Japanese rail profiles[J]. Wear,2005,258(7-8): 1064-1070.
39 SHEVTSOV I Y, MARKINE V L, ESVELD C. Optimal design of wheel profile for railway vehicles[J]. Wear,2005,258(7-8):1022-1030.
40 MARKINE V L, SHEVTSOV I Y, ESVELD C. An inverse shape design method for railway wheel profiles[J]. Struct Multidisc Optim,2007,33(2):243-253.
41 SHEVTSOV I Y, MARKINE V L, ESVELD C. Design of railway wheel profile taking into account rolling contact fatigue and wear[J]. Wear,2008,265(9-10):1273-1282.
42 MARKINE V L, SHEVTSOV I Y. Optimization of a wheel profile accounting for design robustness [J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,2011, 225(5):433-441.
43 JAHED H, FARSHI B, ESHRAGHI M A, NASR A. A numerical optimization technique for design of wheel profiles[J]. Wear,2008,264(1-2):1-10.
44 Hamid Jahed等,李艳译.车轮外形设计的数值优化方法[J].国外铁道车辆,2009,46(2)：20-27.
45 POLACH O. Wheel profile design for target conicity and wide tread wear spreading[J].Wear,2011,271(1-2):195-202.
46 POLACH O. Wheel profile design for the target conicity and a wide contact spreading[C]//8th International conference on contact mechanics and wear of rail/wheel systems, Firenze,2009,809-816.
47 GERLICI J, LACK T. Railway wheel and rail head profiles development based on the geometric characteristics shapes [J]. Wear,2011,271(1-2):246-258.
48 PERSSON I, IWNICKI S D. Optimisation of railway wheel profiles using a genetic algorithm[J].Vehicle system dynamics,2004,41(Suppl)：517-526.
49 NOVALES M,ORRO A,BUGARIN M R.Use of a genetic algorithm to optimizewheel profile geometry[J].Proc Inst Mech Eng Part F J Rail Rapid Transit,2007,221(4)：467-476.
50 PERSSON I,NILSSON R,BIK U,LUNDGREN M,IWNICKI S.Use of a geneticalgorithm to improve the rail profile on Stockholm underground[J].Vehicle SystemDynamics,2010,48(Suppl)：89-104.
51 杨国桢,张孝珂.对磨耗形踏面的研究[J].铁道学报,1983,(2):9.19.
52 张孝坷,刘新明,刘煌,任玉君.LM型车辆车轮磨耗形踏面[J].铁道车辆,1984, (11):1-7.
53 刘新民.机车车辆弧形踏面外形研制[J].铁道车辆,2000,38(2):24-28.
54 张孝珂,任玉君.轮轨磨耗损伤及对策[J].内燃机车,1991,(7):1-4.
55 四方车辆研究所踏面形状研究课题组.SY-50型机车车轮磨耗形踏面[J].铁道车辆, 1987,(4):1-10.
56 杨艳丽,孙传喜,张军,徐永绥,张迎洲.我国机车车辆车轮磨耗型踏面外形及设 计方法[J].内燃机车,2011,(1):6-9.
57 鲍维千,金鼎昌.对机车磨耗形踏面定型的一些看法[J].西南交通大学学报,1984, (4):44-52.
58 金鼎昌.磨耗形踏面研究[J].西南交通大学学报,1984,(1):81.88.
59 罗赞,金鼎昌.高速动力车轮轨几何参数设计[J].铁道学报,1994,16(增刊):24-30.
60 龚积球.机车磨耗形踏面研制应用的回顾及展望[J].上海铁道科技,2004, (1):10-11.
61 张定贤,沈钢,洪晓频,傅佩喜.轮对与轨道接触几何学的研究[J].中国铁道科学, 1990,11(2):44-61.
62 龚积球,陆冠东,余业宏,郑平,沈海元,李羽荷.ND2型机车应用凹形踏面的试 验研究[J].内燃机车,1985,(10):13-16.
63 龚积球,沈海元.凹形踏面与轮箍剥离的改善[J].内燃机车,1991,(4):17-19.
64 龚积球,张定贤,陈惠良,江纪松,王业发.改善ND5型机车轮箍踏面磨耗的试验 研究[J].内燃机车,1989,(5):24-27.
65 龚积球,陈石华,夏建新,王金琪,李长生.25t轴重机车磨耗形踏面的研究[J].内 燃机车,2000,(8):7-10.
66 夏建新,龚积球,陈石华,俞国伟,金文浩,倪新诚.ST2型踏面车轮在DF11型机 车上的应用[J].内燃机车,2004,(1):6-9.
67 夏建新,龚积球,陈石华,王金琪,李长生.减缓25t轴重DF8B型机车车轮磨耗 的试验研究[J].内燃机车,2004,(4)：7-9.
68 任玉君.DJNJ型轮缘踏面外形及运用限度的设计计算[J].铁道车辆,1994,(8)：17-22.
69 文志举,孙强.DJND型轮缘踏面在东风5型机车上的应用[J].内燃机车,2001,(2)：42-46.
70 中华人民共和国铁道部.TB/T 499—2003机车车辆车轮轮缘踏面外形[S].北京：中国铁道出版社,2003.
71 王家玉,王顺福.机车轮对JM、JM2、JM3磨耗型踏面及其剥离[J].内燃机车,2009,(5)：34-37.
72 刘新明.LMA系列轮缘踏面外形简介[J].铁道车辆,2008,46(6)：26.
73 臧其吉,黄成荣,范钦海.高速动力车磨耗型车轮踏面的参数研究[J].中国铁道科学,1994,15(4)：1-7.
74 沈钢,叶志森.用接触角曲线反推法设计铁路车轮踏面外形[J].同济大学学报,2002,30(9)：1095-1098.
75 SHEN G, AYASSE J B, CHOLLET H, PRATT I. A unique design method for wheel profiles by considering the contact angle function[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,2003,217(1):25-30.
76 沈钢,CHOLLET H,叶志森.轮轨外形及接触问题的进一步研究[J].铁道学报,2005,27(4)：25-29.
77 沈钢,钟晓波.铁路车轮踏面外形的逆向设计方法[J].机械工程学报,2010,46(16)：41-47.
78 SHEN G,ZHONG X.A design method for wheel profiles according to the rollingradius difference function[J].Proc Inst Mech Eng Part F J Rail Rapid Transit,2011,225(5)：457-462.
79 钟晓波,沈钢.高速列车车轮踏面外形优化设计[J].同济大学学报,2011,39(5)：710-715.
80 成棣,王成国,刘金朝,陈波.2种响应面方法在车轮踏面优化中的应用分析比较[J].中国铁道科学,2010,31(3)：64-69.
81 成棣,王成国,刘金朝.客车车轮型面的多目标优化设计模型研究[J].中国铁道科学,2011,32(2)：77-84.
82 成棣,王成国,刘金朝,李海涛.以圆弧参数为设计变量的车轮型面优化数学模型研究[J].中国铁道科学,2011,32(6)：107-113.
83 崔大宾,李立,金学松,肖广文.基于轮轨法向间隙的车轮踏面优化方法[J].机械工程学报,2009,45(12)：205-211.
84 DABIN CUI, LI LI, XUESONG JIN, XIA LI. Optimal design of wheel profiles based on weighed wheel/rail gap[C].8th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems (CM2009), Firenze,2009,927-934.
85 CUI DABIN, LI LI, JIN XUESONG, Li Xia. Optimal design of wheel profiles based on weighed wheel/rail gap[J]. Wear,2011,271(1-2):218-226.
86 CUI DABIN, LI LI, JIN XUESONG, LI LING. Wheel-rail profiles matching design considering railway track parameters [J]. Chinese Journal of Mechanical Engineering, 2010,23(4):410-417.
87 崔大宾,李立,金学松.重载货车车轮踏面优化研究[J].铁道学报,2011,33(5)：31-37.
88 崔大宾,李立,金学松,周亮节.铁路钢轨打磨目标型面研究[J].工程力学,2011,28(4)：178-184.
89 张剑,温泽峰,孙丽萍,金学松.基于钢轨型面扩展法的车轮型面设计[J].机械工程学报,2008,44(3)：44-49
90 张剑,王玉艳,金学松,崔大宾.改善轮轨接触状态的车轮型面几何设计方法[J].交通运输工程学报,2011,11(1)：36-42.
91 张剑,金学松,孙丽萍,张军.车轮型面数值优化技术[J].机械工程学报,2011,47(2)：115-122.
92 李庆升.基于基因遗传算法的车轮踏面优化[J].铁道车辆,2011,49(5)：7-11.
93 温泽峰,金学松,刘兴奇.两种型面轮轨滚动接触蠕滑率和摩擦功[J].摩擦学学报,2001,21(4)：288-292.
94 温泽峰,金学松.两种型面轮轨滚动接触蠕滑率/力的比较[J].工程力学,2002,19(3)：82-89.
95 王开云,翟婉明,蔡成标.两种类型踏面的车辆与轨道耦合动力学性能比较[J].西南交通大学学报,2002,37(3)：260-264.
96 王开云,翟婉明,蔡成标.轮轨型面及系统参数对轮轨空间接触几何关系的影响[J].铁道车辆,2002,40(2)：14-18.
97 王开云,翟婉明,蔡成标.轮轨结构参数对列车运动稳定性的影响[J].中国铁道科学,2003,24(1)：43-48.
98 金学松,温泽峰,张卫华.两种型面轮轨滚动接触应力分析[J].机械工程学报,2004,40(2)：5-11.
99 张剑,孙丽萍.车轮型面动态高速曲线通过性比较[J].交通运输工程学报,2007,7(6)：6-11.
100张剑,肖新标,王玉艳,金学松.三种高速轮对型面的性能比较[J].铁道学报, 2009,31(2)：23-31.
101周新建,王琦,王成国,张海.不同车轮踏面对高速轮轨关系的影响研究[J].华东交通大学学报,2011,28(2)：14-18.
102沈宏峻,徐博铭.上海地铁车辆轮对内侧距对安全性的影响分析[J].铁道车辆,1993,(7)：28-32.
103刘新明.关于引进高速车轮对内侧距之我见[J].铁道车辆,2006,44(6)：37-38.
104陈厚嫦,黄体忠,王群伟,黄成荣.轮对内侧距对机车车辆动力学性能影响的试验研究[J].中国铁道科学,2006,27(5)：99-103.
105孙善超,王成国,李海涛,曾树谷.轮/轨接触几何参数对高速客车动力学性能的影响[J].中国铁道科学,2006,27(5)：93-98.
106 肖广文,肖新标,温泽峰,金学松.高速客车轮对动力学性能的比较[J].铁道学报,2008,30(6)：29-35.
107陈厚嫦,王群伟,黄体忠,黄成荣.客运专线列车轮对内侧距选择的研究[J].铁道机车车辆,2008,28(1)：4-8.
108罗仁,曾京,邬平波,戴焕云.高速列车轮轨参数对车轮踏面磨耗的影响[J].交通运输工程学报,2009,9(6)：47-53.
109罗仁,曾京,戴焕云,滕万秀.高速动车组线路运行适应性[J].交通运输工程学报,2011,11(6)：37-43.
110梁树林,朴明伟,张祥杰,兆文忠.高速车辆横向稳定性的非线性影响因素研究[J].铁道学报,2009,31(5)：23-30.
111李霞,温泽峰,金学松.钢轨轨底坡对LM和LMA两种轮对接触行为的影响[J].机械工程学报,2008,44(3)：64-69
112李霞,温泽峰,张剑,金学松.轨底坡对轮轨滚动接触行为的影响[J].机械强度,2009,31(3)：475-480
113张剑,金学松,孙丽萍,张军.基于CRH5高速动车组车辆的轮对动态特性与等效锥度关系初探[J].铁道学报,2010,32(3)：20-27.
114池茂儒,张卫华,曾京,金学松,朱昊.轮径差对车辆系统稳定性的影响[J].中国铁道科学,2008,29(6)：65-70.
115池茂儒,张卫华,曾京,金学松,朱昊.轮径差对行车安全性的影响[J].交通运输工程学报,2009,8(5)：19-22.
116池茂儒,张卫华,金学松,朱旻昊.轮对安装形位偏差对车辆系统稳定性的影响[J].西南交通大学学报,2008,43(5)：621-625.
117金学松.轮轨蠕滑理论及其试验研究[D].成都：西南交通大学博士学位论文,1999.
118孙效杰,周文祥.踏面磨耗及其对轮轨接触几何关系的影响[J].铁道车辆,2010, 48(7)：1-4.
119李艳,张卫华,池茂儒,周文祥.车轮踏面外形及轮径差对车辆动力学性能的影响[J].铁道学报,2010,32(1)：104-108.
120李艳,张卫华,周文祥.车轮型面磨耗对车辆服役性能的影响[J].西南交通大学学报,2010,45(4)：549-554.
121中华人民共和国铁道部.TB/T 2344-200343kg/m-75kg/m热轧钢轨订货技术条件[S].北京：中国铁道出版社,2003.
122 GB 2585-2007铁路用热轧钢轨[S].北京：中国标准出版社,2007.
123 BS EN 13674-1-2003+Al-2007 Railway applications-Track-Rail-Part 1:Vignole railway rails 46 kg/m and above[S]. London:British Standards Institution,2007.
124 JIS E 1101-2001 Flat bottom railway rails and special rails for switches and crossings of non-treated steel[S]. Japan:Japanese Standards Association,2001.
125 BS EN 13715 Railway applications-Wheelsets and bogies-Wheels-Wheels tread[S]. London:British Standards Institution,2006.
126 UIC 502-2 Trailing stock:wheels and wheelsets. Conditions concerning the use of wheels of various diameters[S]. Paris:International Union of Railways,2004.
127陈海.日本E2系-1000型新干线电动车组[J].国外铁道车辆,2005,42(5)：1-7.
128 PASCAL J P, SAUVAGE G. The available methods to calculate the wheel/rail forces in non Hertzian contact patches and rail damaging[J]. Vehicle System Dynamics,1993, 22:263-275.
129 PASCAL J P. About multi-Hertzian-contact hypothesis and equivalent conicity in the case of S1002 and UIC60 analytical wheel/rail profiles[J]. Vehicle System Dynamics, 1993,22(2):57-78.
130 SHACKLETON P, IWNICKI S. Comparison of wheel-rail contact codes for railway vehicle simulation:An introduction to the Manchester Contact Benchmark and initial results[J]. Vehicle System Dynamics,2008,46(1-2):129-149.
131王成国,王永菲,李海涛,李兰.高速轮轨接触几何关系的比较分析[J].铁道机车车辆,2006,26(4)：1-5.
132陈波,王成国,孙善超,李兰.轮轨接触几何关系对高速客车稳定性的影响[J].铁道机车车辆,2008,28(增刊)：189-192.
133金学松,刘启跃.轮轨摩擦学[M].北京：中国铁道出版社,2004,28-107.
134 JIN X S, WEN Z F, ZHANG W H, SHEN Z Y. Numerical simulation of rail corrugation on a curved track[J]. Comput Struct,2005,83(25-26):2052-2065.
135陈泽深,王成国.铁道车辆动力学与控制[M].北京：中国铁道出版社,2004,10-16.
136 KALKER J J. Three-dimensional elastic bodies in rolling contact[M]. The Netherlands: Kluwer Academic Publishers,1990.
137翟婉明.车辆轨道耦合动力学[M].第3版.北京：科学出版社,2007,12-87.
138王福天.车辆系统动力学[M].北京：中国铁道出版社,1994,24-58.
139 JOHNSON K. L. Contact mechanics[M]. United Kingdom:Cambridge University Press,1987,1-10.
140 REN Z, SUN S, XIE G. A method to determine the two-point contact zone and transfer of wheel-rail forces in a turnout [J]. Vehicle system dynamics,2010,48(10):1115-1133.
141张曙光.高速列车设计方法研究[M].北京：中国铁道出版社,2009,77-94.
142 ZAKHAROV S,GORYACHEVA I,BOGDANOV V,POGORELOV D,ZHAROV I,YAZYKOV V, TORSKAYA E, SOSHENKOV S. Problems with wheel and rail profiles selection and optimization[J]. Wear,2008,265(9-10):1266-1272.
143 LEARY J F,张云昌,杨瑛译.美国铁路采用磨耗形踏面[J].国外铁道车辆,1991,(2)：39-42.
144 UIC518-2005. Testing and approval of railway vehicles from the point of view of their dynamic behaviour-Safety-Track fatigue-Ride quality [S].3rd edition, Paris: International Union of Railways.
145 CARL DE B. A practical guide to splines[M]. Revised Ed. New York:Springer-Verlag, 2001,39-47.
146 CURTIS F G, PATRICK O W. Applied numerical analysis [M].7th Ed. Massachusetts: Addison-Wesley,2004,138-142.
147 IWNICKI S. Handbook of Railway Vehicle Dynamics[M]. New York:CRC Press, Taylor & Francis Group,2006,86-120.
148 POPP K, SCHIEHLEN W. Ground vehicle dynamics[M]. Berlin:Springer-Verlag, 2010,11-95.
149 SHABANA A A, ZAAZAA K E, SUGIYAMA H. Railroad vehicle dynamics, a computational approach[M]. New York:CRC Press, Taylor & Francis Group,2008, 35-159.
150 GARG V K, DUKKIPATI R V. Dynamics of railway vehicle systems [M]. Toronto:Academic Press,1984.
151 MAZZOLA L, ALFI S, BRAGHIN F, BRUNI S. Limit wheel profile for hunting instability of railway vehicles[C]. THOMSEN P G, TRUE H (eds.), Non-smooth Problems in Vehicle Systems Dynamics, Berlin Heidelberg:Springer-Verlag,2010,41-52.
152任利惠,谢纲,沈钢,伍智敏,孙继武,漆晖.踏面等效斜率计算方法的比较[J].城市轨道交通研究,2011,(6)：9-13.
153 GOOD ALL R M, IWNICKI S D. Non-linear dynamic techniques v. equivalent conicity methods for rail vehicle stability assessment[J]. Vehicle System Dynamics, 2004,41(Suppl):791-799.
154 PEARCE T G. Wheelset guidance-conicity, wheel wear and safety[J]. Proc. Instn Mech. Engrs, Part F:J. Rail and Rapid Transit,1996,210(4):1-9.
155 CUI DABIN, LI LI, JIN XUESONG, XIAO XINBIAO, DING JUNJUN. Influence of vehicle parameters on critical hunting speed based on ruzicka model[J]. Chinese Journal of Mechanical Engineering,2012,25(3):536-542.
156郭陕云.应该采用什么样的轨底坡[J].铁道建筑,1980,7：24-25.
157戴光辉.关于直线地段轨底坡标准的探讨[J].铁道标准设计通讯,1989,2：7-10.
158赵镜荣.恢复1：20轨底坡[J].铁道建筑,1990,3：27-29.
159司道林,王继军,孟宏.钢轨轨底坡对重载铁路轮轨关系影响的研究[J].铁道建筑,2010,5：108-110.
160沈钢,张定贤.轨底坡对曲线钢轨侧磨影响的研究[J].铁道学报,1994,16(3)：95：99.
161张宏海,李培楠,刘信立.轨底坡对钢轨横向变形及扭转变形的影响[J].四川建筑,2009,29(5)：70-73.
162王开文,严隽耄.机车车辆广义轮轨重力效应分析[J].铁道学报,1996,18(3)：37-43.
163 SAWLEY K, WU H. The formation of hollow-worn wheels and their effect on wheel/rail interaction[J]. Wear,2005,258(7-8):1179-1186.
164 SAWLEY K, URBAN C, WALKER R. The effect of hollow-worn wheels on vehicle stability in straight track [J]. Wear,2005,258(7-8):1100-1108.
165 REZVANI M A, OWHADI A, NIKSAI F. The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks[J]. Vehicle System Dynamics,2009, 47(3):325-342.
166罗仁,曾京,戴焕云,邬平波.高速列车车轮磨耗预测仿真[J].摩擦学报,2009,29(6)：551-558.
167 POMBO J,AMBROSIO J,PEREIRA M,LEWIS R,DWYER-JOYCE R,ARIAUDOC, KUKA N. Development of a wear prediction tool for steel railway wheels using three alternative wear functions[J]. Wear,2011,271(1-2):238-245.
168 LI XIA,JIN XUESONG,WEN ZEFENG,CUI DABIN,ZHANG WEIHUA.A new integrated model to predict wheel profile evolution due to wear[J]. Wear,2011, 271(1-2):227-237.
169 CHANG CHONGYI, WANG CHENGGUO, JIN YING. Study on numerical method to predict wheel/rail profile evolution due to wear[J]. Wear,2010,269(3-4):167-173.
170李霞,金学松,胡东.车轮磨耗计算模型及其数值方法[J].机械工程学报,2009,45(9)：193-200.
171李霞,温泽峰,金学松.重载铁路车轮磨耗和滚动接触疲劳研究[J].铁道学报,2011,33(3)：28-34.
172 JIN Y, ISHIDA M, NAMURA A. Experimental simulation and prediction of wear of wheel flange and rail gauge corner[J]. Wear,2011,271(1-2):259-267.
173胡海滨,吕可维,邵文东,李立东,刘振明.大秦铁路货车车轮磨耗问题的调查与研究[J].铁道学报,2010,32(1)：30-37.
2 国际重载协会.国际重载铁路最佳应用指南——轮轨关系[M].郭俊,温泽峰,王文健,陈光雄,曾京,刘启跃,译.北京：中国铁道出版社,2009：116-181
3 铁路大事记(1997-2011年)[J].中国投资,2011,(12)：74-75.
4 铁正轩.全面实施第六次大面积提速调图促进经济社会又好又快发展[J].中国铁路,2007,(5)：7-13.
5 SMITH R A. The wheel-rail interface—some recent accidents [J]. Fatigue Fract Eng Mater Struct,2003,26(10):901-907.
6 金学松,沈志云.轮轨滚动接触疲劳研究的最新进展[J].铁道学报,2001,23(2)：92-108.
7 金学松,张继业,温泽峰,李芾.轮轨滚动接触疲劳现象分析[J].机械强度,2002,24(2)：250-257
8 金学松,沈志云.轮轨滚动接触力学的发展.力学进展[J],2001,31(1)：33-46.
9 SMALLWOOD R, SINCLAIR J C, SAWLEY K J. An optimization technique to minimize rail contact stresses[J]. Wear,1991,144(1-2):373-384.
10 MAGEL E E, KALOUSEK J. The application of contact mechanics to rail profile design and rail grinding[J]. Wear,2002(253):308-316.
11 UEDA M, UCHINO K, KAGEYAMA H, et al. Development of bainitic steel rail with excellent surface damage resistance[C]. Proceeding of IHHA'99, Moscow, Russia, 1999,259-266.
12 MARICH S. Major advances in rail technologies achieved in the past 10-20 years[C]. In:Proceedings of the 8th International Heavy Haul Conference, Brazil,2005, 747-760.
13 MAGEL E, RONEY M, KALOUSEK J, et al. The blending of theory and practice in modern rail grinding[J]. Fatigue Fract Eng Mater Struct,2003,26(10):921-929.
14 WICKENS A H. Dynamics of railway vehicles-from Stephenson to Carter[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,1998,212(3):209-217.
15 WICKENS A H. Fundamentals of rail vehicle dynamics:guidance and stability[M]. Netherlands:Swets & Zeitlinger Publishers,2003,1-18.
16 严隽耄,傅茂海.车辆工程[M].第3版.北京：中国铁道出版社,2011：43-44.
17 杨国桢.车轮踏面形状的初步研究(上)[J],铁道车辆,1978,(11)：1-6.
18 杨国桢.车轮踏面形状的初步研究(下)[J].铁道车辆,1978,(12)：1-17.
19 汤村光造,芦淑嫒译.车辆与轨道的关系——存在的问题及其重要性[J].国外铁道车辆,1983,(3)：42-46.
20 MARCOTTE P P,陈明资译.加拿大国营铁路的新型车轮踏面[J].国外铁道车辆,1982,(1)：2-10.
21 柳拥军.高速轮轨接触几何学及高速轮轨几何型面优化的研究[D].铁道部科学研究院博士学位论文,1999.
22 HELLER R, LAW E H. Optimizing the wheel profile to improve rail vehicle dynamic performance[J]. Vehicle system dynamics,1979,15(Suppl):179-197.
23 李立,崔大宾,金学松.车轮型面优化的研究进展[J].西南交通大学学报,2009,44(1)：13-19.
24 HAQUE I, LATIMER D A, LAW E H. Computer-aided wheel profile design for railway vehicles[J]. ASME Journal of Engineering for Industry,1989, (111):288-291.
25 SMITH R E, KALOUSEK J. A design methodology for wheel and rail profiles for use on steered railway vehicles[J]. Wear,1991,144(1-2):329-342.
26 成棣,王成国,刘金朝.车轮踏面多目标优化设计研究进展[J].铁道机车车辆,2010,30(4)：5-11.
27 CHOROMANSKI W, ZBOINSKI K. Optimization of wheel and rail profiles for various conditions of vehicle motion[J]. Vehicle system dynamics,1991, 20(Suppl):84-98.
28 LEARY J F, HANDAL S N, RAJKUMAR B. Development of freight car wheel profile-a case study [J]. Wear,1991,144(1-2):353-362.
29 WU H. Effects of wheel and rail profiles on vehicle performance [J]. Vehicle System Dynamics,2006,44(Suppl):541-550.
30 WILSON N, WU H, TOURNAY H, URBAN C. Effects of wheel rail contact patterns and vehicle parameters on lateral stability [J]. Vehicle System Dynamics,2010, 48(Suppl):487-503.
31 WU H. Investigation of wheel rail interaction on wheel flange climb derailment and wheel rail profile compatibility[D]. Illinois Institute of Technology,2000.
32 佐藤荣作,叶娟译.车轮踏面形状设计的科学化[J].国外内燃机车,2000,(3)：39-43.
33 真野辰哉,彭惠民译.既有线车轮踏面形状的优化研究[J].国外机车车辆工艺,2007,(4)：14-17.
34 藤本裕,蒋立忱译.车轮踏面形状对高速动车运动特性的影响——通过相对于圆 弧、圆锥踏面形状的输入能量和几何蛇行运动波长进行评价[J].国外内燃机车,1999,(2)：22-29.
35 YAMADA K, HAYASHI T, NAKATA M, ISA M. New profiled tread design method and it's applied tread named "CS Tread"[C]//5th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Tokyo,2000,259-264
36 SASAKI K, KAGEYAMA T, ASANO K, OKUMURA M:Development of the wheel tread profile for commuter train[C]//5th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Tokyo,2000.
37 MIYAMOTO M, SUDA Y. Recent research and development on advanced technologies of high-speed railways in Japan[J]. Vehicle System Dynamics,2003, 40(1-3):55-99.
38 SATO Y. Historical study on designing Japanese rail profiles[J]. Wear,2005,258(7-8): 1064-1070.
39 SHEVTSOV I Y, MARKINE V L, ESVELD C. Optimal design of wheel profile for railway vehicles[J]. Wear,2005,258(7-8):1022-1030.
40 MARKINE V L, SHEVTSOV I Y, ESVELD C. An inverse shape design method for railway wheel profiles[J]. Struct Multidisc Optim,2007,33(2):243-253.
41 SHEVTSOV I Y, MARKINE V L, ESVELD C. Design of railway wheel profile taking into account rolling contact fatigue and wear[J]. Wear,2008,265(9-10):1273-1282.
42 MARKINE V L, SHEVTSOV I Y. Optimization of a wheel profile accounting for design robustness [J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,2011, 225(5):433-441.
43 JAHED H, FARSHI B, ESHRAGHI M A, NASR A. A numerical optimization technique for design of wheel profiles[J]. Wear,2008,264(1-2):1-10.
44 Hamid Jahed等,李艳译.车轮外形设计的数值优化方法[J].国外铁道车辆,2009,46(2)：20-27.
45 POLACH O. Wheel profile design for target conicity and wide tread wear spreading[J].Wear,2011,271(1-2):195-202.
46 POLACH O. Wheel profile design for the target conicity and a wide contact spreading[C]//8th International conference on contact mechanics and wear of rail/wheel systems, Firenze,2009,809-816.
47 GERLICI J, LACK T. Railway wheel and rail head profiles development based on the geometric characteristics shapes [J]. Wear,2011,271(1-2):246-258.
48 PERSSON I, IWNICKI S D. Optimisation of railway wheel profiles using a genetic algorithm[J].Vehicle system dynamics,2004,41(Suppl)：517-526.
49 NOVALES M,ORRO A,BUGARIN M R.Use of a genetic algorithm to optimizewheel profile geometry[J].Proc Inst Mech Eng Part F J Rail Rapid Transit,2007,221(4)：467-476.
50 PERSSON I,NILSSON R,BIK U,LUNDGREN M,IWNICKI S.Use of a geneticalgorithm to improve the rail profile on Stockholm underground[J].Vehicle SystemDynamics,2010,48(Suppl)：89-104.
51 杨国桢,张孝珂.对磨耗形踏面的研究[J].铁道学报,1983,(2):9.19.
52 张孝坷,刘新明,刘煌,任玉君.LM型车辆车轮磨耗形踏面[J].铁道车辆,1984, (11):1-7.
53 刘新民.机车车辆弧形踏面外形研制[J].铁道车辆,2000,38(2):24-28.
54 张孝珂,任玉君.轮轨磨耗损伤及对策[J].内燃机车,1991,(7):1-4.
55 四方车辆研究所踏面形状研究课题组.SY-50型机车车轮磨耗形踏面[J].铁道车辆, 1987,(4):1-10.
56 杨艳丽,孙传喜,张军,徐永绥,张迎洲.我国机车车辆车轮磨耗型踏面外形及设 计方法[J].内燃机车,2011,(1):6-9.
57 鲍维千,金鼎昌.对机车磨耗形踏面定型的一些看法[J].西南交通大学学报,1984, (4):44-52.
58 金鼎昌.磨耗形踏面研究[J].西南交通大学学报,1984,(1):81.88.
59 罗赞,金鼎昌.高速动力车轮轨几何参数设计[J].铁道学报,1994,16(增刊):24-30.
60 龚积球.机车磨耗形踏面研制应用的回顾及展望[J].上海铁道科技,2004, (1):10-11.
61 张定贤,沈钢,洪晓频,傅佩喜.轮对与轨道接触几何学的研究[J].中国铁道科学, 1990,11(2):44-61.
62 龚积球,陆冠东,余业宏,郑平,沈海元,李羽荷.ND2型机车应用凹形踏面的试 验研究[J].内燃机车,1985,(10):13-16.
63 龚积球,沈海元.凹形踏面与轮箍剥离的改善[J].内燃机车,1991,(4):17-19.
64 龚积球,张定贤,陈惠良,江纪松,王业发.改善ND5型机车轮箍踏面磨耗的试验 研究[J].内燃机车,1989,(5):24-27.
65 龚积球,陈石华,夏建新,王金琪,李长生.25t轴重机车磨耗形踏面的研究[J].内 燃机车,2000,(8):7-10.
66 夏建新,龚积球,陈石华,俞国伟,金文浩,倪新诚.ST2型踏面车轮在DF11型机 车上的应用[J].内燃机车,2004,(1):6-9.
67 夏建新,龚积球,陈石华,王金琪,李长生.减缓25t轴重DF8B型机车车轮磨耗 的试验研究[J].内燃机车,2004,(4)：7-9.
68 任玉君.DJNJ型轮缘踏面外形及运用限度的设计计算[J].铁道车辆,1994,(8)：17-22.
69 文志举,孙强.DJND型轮缘踏面在东风5型机车上的应用[J].内燃机车,2001,(2)：42-46.
70 中华人民共和国铁道部.TB/T 499—2003机车车辆车轮轮缘踏面外形[S].北京：中国铁道出版社,2003.
71 王家玉,王顺福.机车轮对JM、JM2、JM3磨耗型踏面及其剥离[J].内燃机车,2009,(5)：34-37.
72 刘新明.LMA系列轮缘踏面外形简介[J].铁道车辆,2008,46(6)：26.
73 臧其吉,黄成荣,范钦海.高速动力车磨耗型车轮踏面的参数研究[J].中国铁道科学,1994,15(4)：1-7.
74 沈钢,叶志森.用接触角曲线反推法设计铁路车轮踏面外形[J].同济大学学报,2002,30(9)：1095-1098.
75 SHEN G, AYASSE J B, CHOLLET H, PRATT I. A unique design method for wheel profiles by considering the contact angle function[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit,2003,217(1):25-30.
76 沈钢,CHOLLET H,叶志森.轮轨外形及接触问题的进一步研究[J].铁道学报,2005,27(4)：25-29.
77 沈钢,钟晓波.铁路车轮踏面外形的逆向设计方法[J].机械工程学报,2010,46(16)：41-47.
78 SHEN G,ZHONG X.A design method for wheel profiles according to the rollingradius difference function[J].Proc Inst Mech Eng Part F J Rail Rapid Transit,2011,225(5)：457-462.
79 钟晓波,沈钢.高速列车车轮踏面外形优化设计[J].同济大学学报,2011,39(5)：710-715.
80 成棣,王成国,刘金朝,陈波.2种响应面方法在车轮踏面优化中的应用分析比较[J].中国铁道科学,2010,31(3)：64-69.
81 成棣,王成国,刘金朝.客车车轮型面的多目标优化设计模型研究[J].中国铁道科学,2011,32(2)：77-84.
82 成棣,王成国,刘金朝,李海涛.以圆弧参数为设计变量的车轮型面优化数学模型研究[J].中国铁道科学,2011,32(6)：107-113.
83 崔大宾,李立,金学松,肖广文.基于轮轨法向间隙的车轮踏面优化方法[J].机械工程学报,2009,45(12)：205-211.
84 DABIN CUI, LI LI, XUESONG JIN, XIA LI. Optimal design of wheel profiles based on weighed wheel/rail gap[C].8th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems (CM2009), Firenze,2009,927-934.
85 CUI DABIN, LI LI, JIN XUESONG, Li Xia. Optimal design of wheel profiles based on weighed wheel/rail gap[J]. Wear,2011,271(1-2):218-226.
86 CUI DABIN, LI LI, JIN XUESONG, LI LING. Wheel-rail profiles matching design considering railway track parameters [J]. Chinese Journal of Mechanical Engineering, 2010,23(4):410-417.
87 崔大宾,李立,金学松.重载货车车轮踏面优化研究[J].铁道学报,2011,33(5)：31-37.
88 崔大宾,李立,金学松,周亮节.铁路钢轨打磨目标型面研究[J].工程力学,2011,28(4)：178-184.
89 张剑,温泽峰,孙丽萍,金学松.基于钢轨型面扩展法的车轮型面设计[J].机械工程学报,2008,44(3)：44-49
90 张剑,王玉艳,金学松,崔大宾.改善轮轨接触状态的车轮型面几何设计方法[J].交通运输工程学报,2011,11(1)：36-42.
91 张剑,金学松,孙丽萍,张军.车轮型面数值优化技术[J].机械工程学报,2011,47(2)：115-122.
92 李庆升.基于基因遗传算法的车轮踏面优化[J].铁道车辆,2011,49(5)：7-11.
93 温泽峰,金学松,刘兴奇.两种型面轮轨滚动接触蠕滑率和摩擦功[J].摩擦学学报,2001,21(4)：288-292.
94 温泽峰,金学松.两种型面轮轨滚动接触蠕滑率/力的比较[J].工程力学,2002,19(3)：82-89.
95 王开云,翟婉明,蔡成标.两种类型踏面的车辆与轨道耦合动力学性能比较[J].西南交通大学学报,2002,37(3)：260-264.
96 王开云,翟婉明,蔡成标.轮轨型面及系统参数对轮轨空间接触几何关系的影响[J].铁道车辆,2002,40(2)：14-18.
97 王开云,翟婉明,蔡成标.轮轨结构参数对列车运动稳定性的影响[J].中国铁道科学,2003,24(1)：43-48.
98 金学松,温泽峰,张卫华.两种型面轮轨滚动接触应力分析[J].机械工程学报,2004,40(2)：5-11.
99 张剑,孙丽萍.车轮型面动态高速曲线通过性比较[J].交通运输工程学报,2007,7(6)：6-11.
100张剑,肖新标,王玉艳,金学松.三种高速轮对型面的性能比较[J].铁道学报, 2009,31(2)：23-31.
101周新建,王琦,王成国,张海.不同车轮踏面对高速轮轨关系的影响研究[J].华东交通大学学报,2011,28(2)：14-18.
102沈宏峻,徐博铭.上海地铁车辆轮对内侧距对安全性的影响分析[J].铁道车辆,1993,(7)：28-32.
103刘新明.关于引进高速车轮对内侧距之我见[J].铁道车辆,2006,44(6)：37-38.
104陈厚嫦,黄体忠,王群伟,黄成荣.轮对内侧距对机车车辆动力学性能影响的试验研究[J].中国铁道科学,2006,27(5)：99-103.
105孙善超,王成国,李海涛,曾树谷.轮/轨接触几何参数对高速客车动力学性能的影响[J].中国铁道科学,2006,27(5)：93-98.
106 肖广文,肖新标,温泽峰,金学松.高速客车轮对动力学性能的比较[J].铁道学报,2008,30(6)：29-35.
107陈厚嫦,王群伟,黄体忠,黄成荣.客运专线列车轮对内侧距选择的研究[J].铁道机车车辆,2008,28(1)：4-8.
108罗仁,曾京,邬平波,戴焕云.高速列车轮轨参数对车轮踏面磨耗的影响[J].交通运输工程学报,2009,9(6)：47-53.
109罗仁,曾京,戴焕云,滕万秀.高速动车组线路运行适应性[J].交通运输工程学报,2011,11(6)：37-43.
110梁树林,朴明伟,张祥杰,兆文忠.高速车辆横向稳定性的非线性影响因素研究[J].铁道学报,2009,31(5)：23-30.
111李霞,温泽峰,金学松.钢轨轨底坡对LM和LMA两种轮对接触行为的影响[J].机械工程学报,2008,44(3)：64-69
112李霞,温泽峰,张剑,金学松.轨底坡对轮轨滚动接触行为的影响[J].机械强度,2009,31(3)：475-480
113张剑,金学松,孙丽萍,张军.基于CRH5高速动车组车辆的轮对动态特性与等效锥度关系初探[J].铁道学报,2010,32(3)：20-27.
114池茂儒,张卫华,曾京,金学松,朱昊.轮径差对车辆系统稳定性的影响[J].中国铁道科学,2008,29(6)：65-70.
115池茂儒,张卫华,曾京,金学松,朱昊.轮径差对行车安全性的影响[J].交通运输工程学报,2009,8(5)：19-22.
116池茂儒,张卫华,金学松,朱旻昊.轮对安装形位偏差对车辆系统稳定性的影响[J].西南交通大学学报,2008,43(5)：621-625.
117金学松.轮轨蠕滑理论及其试验研究[D].成都：西南交通大学博士学位论文,1999.
118孙效杰,周文祥.踏面磨耗及其对轮轨接触几何关系的影响[J].铁道车辆,2010, 48(7)：1-4.
119李艳,张卫华,池茂儒,周文祥.车轮踏面外形及轮径差对车辆动力学性能的影响[J].铁道学报,2010,32(1)：104-108.
120李艳,张卫华,周文祥.车轮型面磨耗对车辆服役性能的影响[J].西南交通大学学报,2010,45(4)：549-554.
121中华人民共和国铁道部.TB/T 2344-200343kg/m-75kg/m热轧钢轨订货技术条件[S].北京：中国铁道出版社,2003.
122 GB 2585-2007铁路用热轧钢轨[S].北京：中国标准出版社,2007.
123 BS EN 13674-1-2003+Al-2007 Railway applications-Track-Rail-Part 1:Vignole railway rails 46 kg/m and above[S]. London:British Standards Institution,2007.
124 JIS E 1101-2001 Flat bottom railway rails and special rails for switches and crossings of non-treated steel[S]. Japan:Japanese Standards Association,2001.
125 BS EN 13715 Railway applications-Wheelsets and bogies-Wheels-Wheels tread[S]. London:British Standards Institution,2006.
126 UIC 502-2 Trailing stock:wheels and wheelsets. Conditions concerning the use of wheels of various diameters[S]. Paris:International Union of Railways,2004.
127陈海.日本E2系-1000型新干线电动车组[J].国外铁道车辆,2005,42(5)：1-7.
128 PASCAL J P, SAUVAGE G. The available methods to calculate the wheel/rail forces in non Hertzian contact patches and rail damaging[J]. Vehicle System Dynamics,1993, 22:263-275.
129 PASCAL J P. About multi-Hertzian-contact hypothesis and equivalent conicity in the case of S1002 and UIC60 analytical wheel/rail profiles[J]. Vehicle System Dynamics, 1993,22(2):57-78.
130 SHACKLETON P, IWNICKI S. Comparison of wheel-rail contact codes for railway vehicle simulation:An introduction to the Manchester Contact Benchmark and initial results[J]. Vehicle System Dynamics,2008,46(1-2):129-149.
131王成国,王永菲,李海涛,李兰.高速轮轨接触几何关系的比较分析[J].铁道机车车辆,2006,26(4)：1-5.
132陈波,王成国,孙善超,李兰.轮轨接触几何关系对高速客车稳定性的影响[J].铁道机车车辆,2008,28(增刊)：189-192.
133金学松,刘启跃.轮轨摩擦学[M].北京：中国铁道出版社,2004,28-107.
134 JIN X S, WEN Z F, ZHANG W H, SHEN Z Y. Numerical simulation of rail corrugation on a curved track[J]. Comput Struct,2005,83(25-26):2052-2065.
135陈泽深,王成国.铁道车辆动力学与控制[M].北京：中国铁道出版社,2004,10-16.
136 KALKER J J. Three-dimensional elastic bodies in rolling contact[M]. The Netherlands: Kluwer Academic Publishers,1990.
137翟婉明.车辆轨道耦合动力学[M].第3版.北京：科学出版社,2007,12-87.
138王福天.车辆系统动力学[M].北京：中国铁道出版社,1994,24-58.
139 JOHNSON K. L. Contact mechanics[M]. United Kingdom:Cambridge University Press,1987,1-10.
140 REN Z, SUN S, XIE G. A method to determine the two-point contact zone and transfer of wheel-rail forces in a turnout [J]. Vehicle system dynamics,2010,48(10):1115-1133.
141张曙光.高速列车设计方法研究[M].北京：中国铁道出版社,2009,77-94.
142 ZAKHAROV S,GORYACHEVA I,BOGDANOV V,POGORELOV D,ZHAROV I,YAZYKOV V, TORSKAYA E, SOSHENKOV S. Problems with wheel and rail profiles selection and optimization[J]. Wear,2008,265(9-10):1266-1272.
143 LEARY J F,张云昌,杨瑛译.美国铁路采用磨耗形踏面[J].国外铁道车辆,1991,(2)：39-42.
144 UIC518-2005. Testing and approval of railway vehicles from the point of view of their dynamic behaviour-Safety-Track fatigue-Ride quality [S].3rd edition, Paris: International Union of Railways.
145 CARL DE B. A practical guide to splines[M]. Revised Ed. New York:Springer-Verlag, 2001,39-47.
146 CURTIS F G, PATRICK O W. Applied numerical analysis [M].7th Ed. Massachusetts: Addison-Wesley,2004,138-142.
147 IWNICKI S. Handbook of Railway Vehicle Dynamics[M]. New York:CRC Press, Taylor & Francis Group,2006,86-120.
148 POPP K, SCHIEHLEN W. Ground vehicle dynamics[M]. Berlin:Springer-Verlag, 2010,11-95.
149 SHABANA A A, ZAAZAA K E, SUGIYAMA H. Railroad vehicle dynamics, a computational approach[M]. New York:CRC Press, Taylor & Francis Group,2008, 35-159.
150 GARG V K, DUKKIPATI R V. Dynamics of railway vehicle systems [M]. Toronto:Academic Press,1984.
151 MAZZOLA L, ALFI S, BRAGHIN F, BRUNI S. Limit wheel profile for hunting instability of railway vehicles[C]. THOMSEN P G, TRUE H (eds.), Non-smooth Problems in Vehicle Systems Dynamics, Berlin Heidelberg:Springer-Verlag,2010,41-52.
152任利惠,谢纲,沈钢,伍智敏,孙继武,漆晖.踏面等效斜率计算方法的比较[J].城市轨道交通研究,2011,(6)：9-13.
153 GOOD ALL R M, IWNICKI S D. Non-linear dynamic techniques v. equivalent conicity methods for rail vehicle stability assessment[J]. Vehicle System Dynamics, 2004,41(Suppl):791-799.
154 PEARCE T G. Wheelset guidance-conicity, wheel wear and safety[J]. Proc. Instn Mech. Engrs, Part F:J. Rail and Rapid Transit,1996,210(4):1-9.
155 CUI DABIN, LI LI, JIN XUESONG, XIAO XINBIAO, DING JUNJUN. Influence of vehicle parameters on critical hunting speed based on ruzicka model[J]. Chinese Journal of Mechanical Engineering,2012,25(3):536-542.
156郭陕云.应该采用什么样的轨底坡[J].铁道建筑,1980,7：24-25.
157戴光辉.关于直线地段轨底坡标准的探讨[J].铁道标准设计通讯,1989,2：7-10.
158赵镜荣.恢复1：20轨底坡[J].铁道建筑,1990,3：27-29.
159司道林,王继军,孟宏.钢轨轨底坡对重载铁路轮轨关系影响的研究[J].铁道建筑,2010,5：108-110.
160沈钢,张定贤.轨底坡对曲线钢轨侧磨影响的研究[J].铁道学报,1994,16(3)：95：99.
161张宏海,李培楠,刘信立.轨底坡对钢轨横向变形及扭转变形的影响[J].四川建筑,2009,29(5)：70-73.
162王开文,严隽耄.机车车辆广义轮轨重力效应分析[J].铁道学报,1996,18(3)：37-43.
163 SAWLEY K, WU H. The formation of hollow-worn wheels and their effect on wheel/rail interaction[J]. Wear,2005,258(7-8):1179-1186.
164 SAWLEY K, URBAN C, WALKER R. The effect of hollow-worn wheels on vehicle stability in straight track [J]. Wear,2005,258(7-8):1100-1108.
165 REZVANI M A, OWHADI A, NIKSAI F. The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks[J]. Vehicle System Dynamics,2009, 47(3):325-342.
166罗仁,曾京,戴焕云,邬平波.高速列车车轮磨耗预测仿真[J].摩擦学报,2009,29(6)：551-558.
167 POMBO J,AMBROSIO J,PEREIRA M,LEWIS R,DWYER-JOYCE R,ARIAUDOC, KUKA N. Development of a wear prediction tool for steel railway wheels using three alternative wear functions[J]. Wear,2011,271(1-2):238-245.
168 LI XIA,JIN XUESONG,WEN ZEFENG,CUI DABIN,ZHANG WEIHUA.A new integrated model to predict wheel profile evolution due to wear[J]. Wear,2011, 271(1-2):227-237.
169 CHANG CHONGYI, WANG CHENGGUO, JIN YING. Study on numerical method to predict wheel/rail profile evolution due to wear[J]. Wear,2010,269(3-4):167-173.
170李霞,金学松,胡东.车轮磨耗计算模型及其数值方法[J].机械工程学报,2009,45(9)：193-200.
171李霞,温泽峰,金学松.重载铁路车轮磨耗和滚动接触疲劳研究[J].铁道学报,2011,33(3)：28-34.
172 JIN Y, ISHIDA M, NAMURA A. Experimental simulation and prediction of wear of wheel flange and rail gauge corner[J]. Wear,2011,271(1-2):259-267.
173胡海滨,吕可维,邵文东,李立东,刘振明.大秦铁路货车车轮磨耗问题的调查与研究[J].铁道学报,2010,32(1)：30-37.