机车车辆/轨道系统垂耦合动力学有限元分析的研究
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摘要
众所周知，近几十年来，有限元法的发展堪称是突飞猛进的。它以方便、快捷、高
精度、适应性广等优点在工程中得到了越来越广泛的应用。尤其是随着近年来计算机技术
的飞速发展，有限元法更是倍受青睐。然而，有限元法在机车车辆_—轨道耦合动力学中
的应用仍处于起步阶段。其巨大的优越性虽己为人们所关注，但却未能得到充分发挥。本
文通过利用有限元法求解机车车辆／轨道系统会向耦合振动问题，试图将其先进技术广泛、
深入地引入到机车车辆—轨道大系统的耦合动力学中，从而克服传统多刚体系统动力学研
究方法在建模及计算方面的局限性，探讨一些传统研究方法难以解决的问题。
轮／轨关系是联系机车车辆系统与轨道系统的关键环节，属于空间接触问题。大量实
际工程应用已充分证实参数二次规划法是解决空间接触问题的一种先进的、行之有效的方
法。本文对轮对／轨道系统建立了详细的三维实体有限元模型，并采用参数二次规划法来
求解轮对／轨道系统的弹性／弹塑性接触问题，同时归纳出轮／轨法向等效接触刚度与接触
力、接触位置的关系。
本文对机车车辆／轨道大系统建立了由空间梁、杆等单元组成的三维有限元模型，利
用轮对／轨道系统弹性／弹塑性计算结果，对在几种轨面不平顺（单一谐波型、连续谐波型、
钢轨接头等）及激振力作用下机车车辆／轨道大系统的垂向耦合振动进行了研究。其中振动
方程的求解采用大连理工大学钟万勰教授开发的精细时程积分法。该算法的时间步长选取
与结构自振频率无关，且具有无条件稳定性及可比拟于计算机精度的高精度解等优点。
轨下结构在机车车辆／轨道大系统中扮演着举足轻重的角色。轨下结构的变形、受力
情况对于列车运行的安全性、平稳性、线路的使用寿命均起着至关重要的作用。为了能真
实地反映各组成部件间的相互作用关系，本文对轮对／轨道系统按五体接触问题建立了详
细的三维接触有限元实体模型，并对受载时轨道结构的变形及应力分布做了详细的研究。
本文的研究表明，将有限元法及其先进技术应用到机车车辆一轨道耦合动力学研究
中是可行的，不仅如此，它还具有其它传统方法无可比拟的优越性，并具有非常广阔的发
展前景。
As we all known, FEM (Ftoite Element Method) has been developing very rapidly in the
past few decades. Convenient, fast, accurate and broadly suitable, it is being used more and
more extensively Combined with computer science, FEM has acquired an extrinary favor
However the application in SCDOV/T (System Coupling Dynamics of Vehicle/Track) is still at
its initial stage. It is true that the great advantages of FEM have been come into attention. but
they have not been brought into full play To break the limitation of the conventional multi-
rigid system dynamics in modeling and calculation and to solve some difficult problems faced
by traditional methods, in this paper, I try to solve such problems as Vertical coupling vibration
of Locomotive & Vehicle/Track with the help of FEM and to introduce the advanced
techniques of FEM more extensively and deeply into SCDOV/T.
Whee/Rail relationship, actually a space contact problem, is crucial in studying the
relatonship between vehicle and track system. The advancedness and effectiveness of the PQP
(Parametric Quadratic Programming) in solving space contac problem are amply proved in
pracical engineering applications. In this paper a detailed 3D entity Finite Element model is
established, by means of PQP, the elastic/plastoelastic contac calculations of Wheel/Rail
system are worked out and the relations in between the Wheeel/Rail normal equivalent contact
stiffness, the contact forces and the contact point positions are generalized.
Based on the 3D FE model of Vehicle/Track whole system which composed of space beam
elements, rod elements, etc., and by use of the elastic/plastoelastic calculating results of
Wheel/Rail system, the vertical coupling vibrations of Vehicle/Track whole system are studied
under a several of track boularities and exciting forees such as, the single harmonic
irregularity the continuous harmonic irregularity and the rail joint, etc. The vibration
equations are solved with PCMOTA (Precise Computation Method of Transient Analysis)
developed by Prof Zhong Wanxie in Dalian University of Technology PCMOTA has many
merits, for example, the choice of time step has nothing to do with the natural frequencies of
structure vibration, the stability is unconditional and the calculation precision is comparable to
the computor precision.
The infrastructure of rail plays a very important role in the Vehicle/Track system. The
situations of deformation and force distribution among track infratructure have significant
influence on the running safety and stationarity of train and on the service life of the track. To
ge a trUe inteffiction relationship in bdeeen all componentS, a detailed 3D five-body cohact
FE model is PrOPOsed in this W and the defOnnation and strCss distribution of traCk
strUctUre is researchd deeply
There are various indications that the FEM and itS advanced tecboques to SCDOVrr
research are not only feasible bu also incomparable in itS adVantages over the other
conventional methods. It is opcted to aPply FEM on railway dynamics successfully and tO
gOt it exensive Prospect si~canhy
Ph.D. Candidatof Quan YUy'Un
SuMisorf PrOf Zhan Feisheng
bof wu cnan
精度、适应性广等优点在工程中得到了越来越广泛的应用。尤其是随着近年来计算机技术
的飞速发展，有限元法更是倍受青睐。然而，有限元法在机车车辆_—轨道耦合动力学中
的应用仍处于起步阶段。其巨大的优越性虽己为人们所关注，但却未能得到充分发挥。本
文通过利用有限元法求解机车车辆／轨道系统会向耦合振动问题，试图将其先进技术广泛、
深入地引入到机车车辆—轨道大系统的耦合动力学中，从而克服传统多刚体系统动力学研
究方法在建模及计算方面的局限性，探讨一些传统研究方法难以解决的问题。
轮／轨关系是联系机车车辆系统与轨道系统的关键环节，属于空间接触问题。大量实
际工程应用已充分证实参数二次规划法是解决空间接触问题的一种先进的、行之有效的方
法。本文对轮对／轨道系统建立了详细的三维实体有限元模型，并采用参数二次规划法来
求解轮对／轨道系统的弹性／弹塑性接触问题，同时归纳出轮／轨法向等效接触刚度与接触
力、接触位置的关系。
本文对机车车辆／轨道大系统建立了由空间梁、杆等单元组成的三维有限元模型，利
用轮对／轨道系统弹性／弹塑性计算结果，对在几种轨面不平顺（单一谐波型、连续谐波型、
钢轨接头等）及激振力作用下机车车辆／轨道大系统的垂向耦合振动进行了研究。其中振动
方程的求解采用大连理工大学钟万勰教授开发的精细时程积分法。该算法的时间步长选取
与结构自振频率无关，且具有无条件稳定性及可比拟于计算机精度的高精度解等优点。
轨下结构在机车车辆／轨道大系统中扮演着举足轻重的角色。轨下结构的变形、受力
情况对于列车运行的安全性、平稳性、线路的使用寿命均起着至关重要的作用。为了能真
实地反映各组成部件间的相互作用关系，本文对轮对／轨道系统按五体接触问题建立了详
细的三维接触有限元实体模型，并对受载时轨道结构的变形及应力分布做了详细的研究。
本文的研究表明，将有限元法及其先进技术应用到机车车辆一轨道耦合动力学研究
中是可行的，不仅如此，它还具有其它传统方法无可比拟的优越性，并具有非常广阔的发
展前景。
As we all known, FEM (Ftoite Element Method) has been developing very rapidly in the
past few decades. Convenient, fast, accurate and broadly suitable, it is being used more and
more extensively Combined with computer science, FEM has acquired an extrinary favor
However the application in SCDOV/T (System Coupling Dynamics of Vehicle/Track) is still at
its initial stage. It is true that the great advantages of FEM have been come into attention. but
they have not been brought into full play To break the limitation of the conventional multi-
rigid system dynamics in modeling and calculation and to solve some difficult problems faced
by traditional methods, in this paper, I try to solve such problems as Vertical coupling vibration
of Locomotive & Vehicle/Track with the help of FEM and to introduce the advanced
techniques of FEM more extensively and deeply into SCDOV/T.
Whee/Rail relationship, actually a space contact problem, is crucial in studying the
relatonship between vehicle and track system. The advancedness and effectiveness of the PQP
(Parametric Quadratic Programming) in solving space contac problem are amply proved in
pracical engineering applications. In this paper a detailed 3D entity Finite Element model is
established, by means of PQP, the elastic/plastoelastic contac calculations of Wheel/Rail
system are worked out and the relations in between the Wheeel/Rail normal equivalent contact
stiffness, the contact forces and the contact point positions are generalized.
Based on the 3D FE model of Vehicle/Track whole system which composed of space beam
elements, rod elements, etc., and by use of the elastic/plastoelastic calculating results of
Wheel/Rail system, the vertical coupling vibrations of Vehicle/Track whole system are studied
under a several of track boularities and exciting forees such as, the single harmonic
irregularity the continuous harmonic irregularity and the rail joint, etc. The vibration
equations are solved with PCMOTA (Precise Computation Method of Transient Analysis)
developed by Prof Zhong Wanxie in Dalian University of Technology PCMOTA has many
merits, for example, the choice of time step has nothing to do with the natural frequencies of
structure vibration, the stability is unconditional and the calculation precision is comparable to
the computor precision.
The infrastructure of rail plays a very important role in the Vehicle/Track system. The
situations of deformation and force distribution among track infratructure have significant
influence on the running safety and stationarity of train and on the service life of the track. To
ge a trUe inteffiction relationship in bdeeen all componentS, a detailed 3D five-body cohact
FE model is PrOPOsed in this W and the defOnnation and strCss distribution of traCk
strUctUre is researchd deeply
There are various indications that the FEM and itS advanced tecboques to SCDOVrr
research are not only feasible bu also incomparable in itS adVantages over the other
conventional methods. It is opcted to aPply FEM on railway dynamics successfully and tO
gOt it exensive Prospect si~canhy
Ph.D. Candidatof Quan YUy'Un
SuMisorf PrOf Zhan Feisheng
bof wu cnan
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