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Review on rail corrugation studies
Wear 253 (2002) 130–139
Review on rail corrugation studies Yoshihiko Sato a,∗ , Akira Matsumoto b , Klaus Knothe c b
a Railway Track System Institute, 1-11-8, Kurosunadai, Inageku, Chiba-shi, Chiba-ken 263-0041, Japan National Traffic Safety and Environment Laboratory, 7-42-17, Jindaiji-Higashimacht, Chofu-shi, Tokyo 182-0012, Japan c Sekr. F5, Institut für Luft- und Raumfahrt, Berlin Technische Universtät, Marchstr. 12, D-10587, Berlin, Germany
Abstract In Japan, rail corrugations had not been so serious formerly, but it began to be prevailing in recent years. In order to prevent the generation of rail corrugation, many studies have been reported in the world since the end of 19th century, but theories on them have not explained the formation mechanism perfectly and no perfect countermeasures have been established so far. Thus, the studies on corrugation are getting more important, because generation of corrugation shows a tendency to increase due to the speed-up of trains, to the introduction of new vehicles, etc. In such a situation, three authors review the studies on them in the past and those carried out now in the world and more precisely in Japan. The review is on bibliographies, attempts in the 1970s, classification of rail corrugation, short-pitch corrugation and studies in Japan in recent years. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Rail corrugation; Wheel/rail contact; Contact stress; Wear
1. Introduction In recent years, corrugation of rails has been a serious problem in Japan. Formerly, it was noticed just on the wooden ties directly fastened to steel bridge, in the tunnel and on the track firmly set on solid bed before the development of modern slab track or in the sections of braking and acceleration near stations, but not so on ordinary tangent tracks. It is true on Shinkansens even now. The general situation on rail corrugation was surveyed on existing lines in Japan in 1953 (Shinkansens did not yet exist). The situation in the world was discussed on a conference of the International Railway Congress Association (IRCA) in 1958. In the same year, possible causes of corrugation were investigated by Birmann. For approximately 15 years after those, there was nearly a standstill in research, which was also confirmed by the ORE questionnaire 1977. In the 1970s in parallel, several new activities started. In a paper of Johnson and Gray in 1975, it was shown, that a certain type of corrugation on disc machines could be explained theoretically and validated by experiments; in 1977 Mair in Australia investigated the cause of special long-wavelength corrugation; in 1978, Eisenmann published a study on short-pitch corrugation; in 1979, Daniels et al.
∗ Corresponding author. Tel.: +81-43-246-3883; fax: +81-43-246-3922. E-mail address: [email protected] (Y. Sato).
began their experimental investigation on the track of FAST in Pueblo. In 1983, two symposia on rail corrugation took place at The Berlin Technical University and in London, where papers of Frederick and Budgen, Clark and Kalker were presented. The first idea of a new theory was presented by Frederick on the Second International Conference on Contact Mechanics and Wear of Rail/Wheel Systems in 1986 and in the Ph.D. thesis of Valdivia (1987/1988). Within the next 10 years, a fruitful cooperation took place between The Technical University of Berlin (TUB) (Valdivia, Knothe and Hempelmann) and BR Research (Frederick and Sinclair) which brought the problem of short-pitch corrugation closer to a solution. The cause of the corrugation on the Vancouver Skytrain was pursued in 1992 by Kalousek. One year later, Grassie and Kalousek presented a classification of corrugation with their characteristics, causes and treatments. In Europe, the investigations were continued with the Ph.D. theses of Ilias (1996, Berlin), Igeland (1997, Goteborg) and Müller (1998, Berlin). In Japan, the rail corrugation and its related matters have been noticed and studied. Especially, the studies have been getting active in these 10 years. Most of these studies started in order to solve the problems of rail corrugation due to the speed-up of trains, to the introduction of new vehicles such as tilting trains, linear-motor-driven subway, to the unification of vehicle types, etc. Leading studies of corrugation in these 10 years are the studies by Suda and Matsumoto and
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their colleagues. These studies were brought together in the research project of The Japan Subway Association (JSA). The formation mechanism and countermeasures of corrugation on sharp curve were specially noticed in the project. The outcomes of these studies are reflected to the following studies by Railway Technical Research Institute (RTRI) and JR East, etc. In the Fifth Conference on Contact Mechanics and Wear of Rail/Wheel Systems, the presentation on this theme was given by first and second authors separately as parts I and II. In compiling it to Wear, the editor recommended us to revise it mainly supplementing the studies in Australia and UK through the indication of a referee and fusing parts I and II to one. To realize it, the paper has been revised totally with the assistance of third author.
2. Bibliographies, review and survey on studies in early days in Japan and in other parts of the world 2.1. Preliminary comments Between 1950 and 1980, several survey and review papers as well as bibliographies were published. Though not all of them are readily available, those which are known to the authors are mentioned briefly. • In Germany, corrugation had increased since 1895. The first survey study was dated from 1925. In 1953, Fink in Germany published a review-paper on rail corrugations, mainly considering short-wavelength rail corrugations (Riffeln in German) up to 5 cm. More than 50 papers, the first one from 1898, were discussed and a new tribochemical theory was presented. • In 1954, 1961 and 1977, British Rail (BR) Research Library presented bibliographies on rail corrugation [1], which were mainly used in the UK. • In 1958, Birmann [2] published his survey paper to be discussed in more detail in Section 2.2. The paper was summarized and introduced to Japanese people by Satoh [3]. • In the same year on the 17th Congress of the IRCA, two reports on rail corrugation were presented, reporting on rail corrugations at the NSW Government Railway and at RENFE in Spain [4,5], which both were summarized and introduced to Japanese people by Miyahara [6]. • The next survey paper, containing the most extensive survey up to that time, was presented by Krabbendam from The Netherland Railways NS [7] in 1961. In 1977, an ORE report on rail/wheel wear and corrugatory wear appeared [8]. • A more recent survey can be found in Hempelmann’s thesis [9]. Four of these papers shall be discussed in some more detail.
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2.2. Review by Birmann Mostly experimental, but some theoretical papers were reviewed by Birmann [2] all together 107 references. Birmann’s paper was summarized and introduced to Japanese people by Satoh [3]. In the first part, Birmann included the results of experimental studies on a test section in Germany, vibrational behavior of rail and wheel-set and statistical analyses. In the second part of the paper, mainly aspects of rail materials were considered. First results of a German test track to investigate influences of rail material on the formation of corrugation were presented; the effect of segregation was discussed in some detail as well as physical–chemical influences on friction (Fink’s theory) and the effect of corrosion. Finally, the prevention of corrugation growth was discussed considering materials, track structure and vehicle structure. The effect of tempering and heating after grinding was also analyzed. Finally, the increase of corrugated rail due to the continuous development of railway system was mentioned. In Birmann’s paper, mechanical aspects and aspects of rail material were separated and consistent mathematical theories were not yet appeared. 2.3. Questionnaire by IRCA In the IRCA 17th session in 1958, the surveys on undulatory wear of rail were presented by two reporters, Vogan (NSW Government Railway) [4] and Delgado (RENFE) [5]. It was summarized and introduced to Japanese people by Miyahara [6]. It includes the following items: • actuality of corrugation including its kinds, wavelength and amplitude, cause and growth and effect of rail hardness; • effect of material including production and quality, physical property, premium rail, sleeper, ballast and subgrade and rail joint; • other factors than track, including traction and rolling stock, frequency of operation and speed, environment, operation, tyre and rail; • effects of rail corrugation; • prevention and mitigation of corrugation growth; • corrugation grinding machines; • experimental studies; • theories on corrugations due to material and production, wheel pressure and kinematics of wheel, rail vibration, rail residual stress, interaction between wheel and rail and oxidization; • preventing method proposed by theorists. 2.4. Earlier surveys in Japan To respond to the questionnaire on corrugation for the 17th Conference of IRCA in 1958, the survey on corrugation in JNR of 1953 was supplemented with the data from
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the Teito Rapid Transit Authority (TRTA), Transport Department of Osaka-Shi (TDOS) and Kinki Nippon Railway Co. Ltd. (KNR) in 1958. It explained the actuality of corrugation in Japan in these days, the effect of materials and that of other items than track [10]. Corrugation was caused at about 800 sites over a length of 22 000 track-km, 48% of corrugations had wavelengths of 500 and 1500 mm, 30.6% between 200 and 500 mm and 12% of <100 mm. So, most of the corrugations had a wavelength of >200 mm. (In Germany, however, most corrugation had a wavelength of approximately 50 mm and in France, <120 mm in that time.) In Japan, 67% of corrugation were caused by wear, but 33% showed an undulatorily bent rail (may be, caused during rectification in the rail rolling factory with wavelength of about 1 m). The classification of corrugated rails according to curve radii was as follows: 5 sites per 100 track-km on curves of >800 m radius and in tangent track, 3.6 sites in curves of 600–800 m radius, 3.0 sites in curves of 400–600 m radius and 1.6 sites in curves of 200–400 m. Corrugations therefore could be found more often on tangent track and on slack curves than on sharp curves with radii <500 m. 2.5. Questionnaire from ORE ORE sent a questionnaire on corrugation study to member administrations and analyzed the responses in 1977 [8]. The administrations were interested in the problems, but their replies did not introduce many new elements of information with respect to existing knowledge. Taking into account, the complexity of the phenomena concerned, the more or less successful studies already made and the fact that the adopted empirical solutions reduced the economic importance of the phenomena, it was considered that the carrying out of new systematic studies would be superfluous. A permanent exchange of information was nevertheless recommended. 2.6. Intermediate summary Most of these papers concentrated on the presentation of phenomenological observations and tried to explain them. Probably in none of them a consistent mathematical model was formulated and validated in order to explain what had been observed. A second disadvantage was that the distinction between different types of corrugations was insufficient. The reason is quite clear: theories were not sufficiently developed in order to classify rail corrugation. Birmann and Krabbendam at least distinguished the difference between short-wavelength corrugation (German: Riffeln) and long wavelength corrugation (German: Wellen, i.e. waves). Looking at these papers again from the present point of view, they contain valuable phenomenological information which can be partially explained by present theories. A classification was only possible 20 years later.
3. New attempts in 1970s Despite of the reserve of ORE several new attempts were made in the 1970s to clarify corrugation phenomena. We restrict to the work of Carson, Johnson and Gray, to Mair’s investigations (including some comments on track dynamics), to the investigations of Eisenmann and finally to the experiments at FAST. 3.1. Carson, Johnson, and Gray: contact resonance and plastic deformation The paper of Carson and Johnson [11] in 1971 and Johnson’s and Gray’s [12] extended version of Gray’s Ph.D. thesis from 1972 considered the contact resonance and plastic deformations on discs. Experiments were performed with a disc machine and the corrugations which had appeared where explained by a new theory. Excited by irregularities, the system vibrates on the contact resonance mode. If the damping is low and the load is high, then vibrations may be severe enough to cause the incremental plastic indentation which then amplifies the vibration in the next revolution. Johnson and Gray distinguished clearly between two aspects: the wavelength is determined by the frequency of the contact resonance; the formation and amplification of quasi-periodic pattern is due to plastic deformation. This seemed to be the first time that a distinction was made between a wavelengths fixing mechanism and a damage mechanism. 3.2. Mair: resonance of unsprung mass and track and gross plastic deformation Long-pitch rail corrugations with wavelength in the range of 200–300 mm were a common occurrence for tracks with high axle loads. To understand how the wavelength was fixed, a basic understanding of track dynamics was necessary. Though already Timoshenko had analyzed the dynamic behavior of wheels moving on tracks, the models, which are used today in analyzing different types of rail corrugation, go back to the 1970s. Mair from Australia in 1977 [13,14] analyzed the vertical dynamic behavior of unsprung mass on a continuously supported track and assumed this to be the wavelength-fixing mechanism for heavy haul corrugation. As with Johnson and Gray, the formation of corrugations was due to gross plastic deformation. The simple type of track model which has been used by Mair was also sufficient for some other type of corrugation. For short-wavelength corrugations, however, more sophisticated track models had to be used. Most of the work, theoretically as well as experimentally, had been performed by Grassie et al. [15]. Considering these papers, validated dynamic track models were now available. Ten years later, a more general theoretical model for discretely supported tracks has been developed and used intensively by Ripke and Knothe [16].
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3.3. Eisenmann: work hardening and residual stress In 1978, Eisenmann proposed a new theory [17]. It explained short-pitch corrugation as caused by the residual stresses in rail head, which were activated during manufacturing of the rail and which vary with the time of operation “it is generally known that under working pressure, the rails near the contact area of the wheel will have hardened by 6–8 mm. This hardening can be explained by bending compressive stresses and activated compressive stresses, especially those which occur directly under the wheel . . . ,” which finally lead “to compressive residual stresses under repeated weight influence in the cant area in the longitudinal as well as in the transverse direction of the railhead . . . ”. Eisenmann then mentioned the so-called Bauschinger effect and postulated that these effects all together finally are responsible for short-pitch rail corrugation. Eisenmann seemed to have got his idea from metallurgical investigations. It is very recent that mathematical models were used to study the influence of work hardening and residual stresses on corrugation [18]. 3.4. Experiments on FAST track in Pueblo In 1979, FAST technical personnel were directed to establish a test with the objective of providing operating railroads with better methods to treat corrugations. An experiment was designed which would first provide an understanding of corrugation growth and then based on that data establish an investigation of corrugating mechanisms [19]. The paper presents the layout, measurement and conduct of the FAST Rail Corrugation Experiment. Corrugation growth rates were presented. Factors affecting corrugation growth were then evaluated and discussed. The effects of corrugations on track maintenance were presented. Rail grinding was then discussed. Current theories on corrugating mechanisms were reviewed. Finally, the paper’s conclusions were summarized with recommendations for revenue service application and recommendations for additional research. 4. Classification of rail corrugation by Grassie and Kalousek In 1993, Grassie and Kalousek reviewed 42 references and published a paper entitled “rail corrugation: characteristics, causes and treatments” [20] which is helpful to understand the work which has been performed within the 1970–1990. Based on their far reaching experience, they classified corrugation into six groups which they called (1) heavy haul corrugation (200–300 mm), (2) light rail corrugation (500–1500 mm), (3) booted sleepers type corrugation (45–60 mm), (4) contact fatigue corrugation (150–450 mm), (5) rutting corrugation (50 mm (trams), 150–450 mm), and (6) roaring rail corrugation (25–80 mm). Most of the rutting-type corrugations are called in Germany
Fig. 1. Feed-back loop of structural dynamics and contact mechanics (wavelength-fixing mechanism) and damage mechanism [20,21].
Wellen (long wavelengths corrugation), whereas, the roaring rail corrugation is called Riffeln (short-wavelength corrugation). Though the authors do not agree completely with Grassie and Kalousek’s classification, the basic idea, namely the introduction of a wavelength-fixing mechanism and a damage mechanism in order to categorize corrugation in Fig. 1 is completely convincing. The basic idea of two different mechanisms can already be found in Johnson’s and Gray’s paper as well as in Frederick’s papers, in Valdivia’s Ph.D. thesis (Section 5.1) and in Suda’s paper (Section 6.1). Wavelengths-fixing mechanisms result from the dynamic interaction of wheel-set and track; it is therefore necessary to have available track and wheel-set models in the whole frequency range of interest. Damage mechanisms are either plastic deformation (plastic bending or plastic flow), rolling contact fatigue, or wear. The diagram of Fig. 1 helped to solve the conflict (especially in Germany) whether structural dynamics or material behavior are mainly responsible for the formation of rail corrugation. Both aspects are integrated in a feedback loop. Grassie and Kalousek’s paper indicates that most types of corrugations were understood. In chapter 5, we therefore concentrate on short-pitch corrugations of the “roaring rail” type, which according to [20] indicated as not to have been understood. 4.1. Clark: self-excited rutting-type corrugation A special version of “rutting-type corrugations” was probably investigated first by Clark and Foster [22]and Clark et al. [23]. Self-excited vibrations of a flexible wheel-set and a discretely supported track system under high creepage conditions were investigated; Mathieu vibrations excited by track stiffness variations and roll-slip vibrations excited by wheel-rail creep forces were also considered: these two mechanisms might exist separately or in combination to
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provide possible explanations for the formation of long- and short-wavelength corrugations on the running surface of railway rails. To get negative damping, which is necessary to cause self-excited vibrations, the creep-force/creep characteristic must decrease after a maximum has been reached and large creepage must be available. This is the case on sharp curve, but not on tangent track. 4.2. Sumi in Japan: rutting-type corrugation in Japan Sumi et al. proposed a theory for the cause of corrugation on curve in Japan in 1991 [24]. “As having been said, the corrugations are caused everywhere due to the combination of various factors. In the curve, as there is a large possibility of irregular slip between inner and outer rails, it is enough to cause the torsional vibration of wheel-set. As the vibrational velocity of wheel-set determined the volume of wear, it could cause the corrugation. It explains the dependency of the wavelength of corrugation on the train speed. With the coefficient of friction for rolling and sliding obtained in the laboratory, the diversion or the continuation (limit cycle) of torsional vibration is caused in more limited conditions than in those causing actual corrugation. It means that finding the actual coefficients of roll and slippage between wheel and rail is important. For the torsional vibration of wheel-set, the effects of brake, motor and track are to be in consideration.” 5. Short-pitch corrugation Short-pitch corrugation mainly occurs on tangent track (or on curves with large radius) of high speed lines. The wavelength of the quasi-periodic pattern is between 2 and 8–10 cm. Since 1980, increasing attention has been paid to them. Most of the work has been done at BR, at The Cambridge University and at The TUB. 5.1. Research on short-pitch rail corrugation at British Rail, at The Cambridge University and at TU Berlin before 1994 Most of the experimental investigations which had been performed at BR, partially together with The Cambridge University, can be found in papers of Frederick and Bugden [25] and Bugden [26] which had been presented at a Symposium on Rail Corrugation Problems in Berlin (June 1983) and at a seminar on the same subject in London (September 1983). A survey of the problem including the influence of steel grade is given. The metallurgical structure of corrugations as well as the effects of grinding and initial rail roughness is discussed in detail. Both symposia provided a good chance to initiate renewed studies on corrugation. Independently at BR and at TU Berlin, the theoretical work was intensified. The paper by Frederick in 1986 [27] showed how measured receptances to quantify the dynamic response of the wheel and rail to vertical, lateral and longitudinal forces could be combined with creep/force-creep
laws and with formulae for rail wear, in order to predict whether or not periodic pattern of certain wavelength in the surface of the rail would be deepened or erased by passing axles. At wave passing frequencies, where the phase of the periodic wear was such as to deepen the initial irregularity, initial rail roughness could develop to corrugation. It was shown that this hypothesis was able to explain observations of short-pitch corrugations on tangent track of BR lines. At The TUB Valdivia pursued the same though it was from a purely analytical point of view [21,28]. Wheel and rail receptances were calculated and combined with normal and tangential contact mechanical equations and finally with a wear analysis. The corrugation formation is described as a feedback loop between structural dynamics and contact mechanics on the one hand and a long-term wear process on the other hand (Fig. 1). “Corrugation growth rates” (real parts of wear eigenvalues) indicate whether the rail roughness of certain wavelength at certain positions in the sleeper bay either increases or decreases. The work of Valdivia in Berlin was continued by Hempelmann [9] and Hempelmann and Knothe [29]. Hempelmann had reviewed 128 papers and described the development of complete wear pattern in the sleeper bay and performed a large number of parametric investigations in order to identify critical parameters. Frederick and Valdivia as well as Hempelmann pointed out that the anti-resonance at the pinned–pinned-mode frequency is the most probable cause for the formation of short-pitch rail corrugation. Especially at BR, several cases forming short-pitch rail corrugation above the sleeper were found. Hempelmann also mentioned that high lateral dynamic receptances may result in corrugation growth at corresponding resonance frequencies if the creepage is maximum. In ORE D 185 committee [30], both algorithms were carefully compared theoretically as well as numerically. They were found to provide nearly the same results.
5.2. Tassilly and Vincen: corrugation at RATP The type of corrugation in Tassilly and Vincent’s paper seemed at first sight to be completely different from roaring rail corrugation. Grassie and Kalousek are classifying them as “booted sleeper corrugation”. The track for the former is laid on concrete with a rubber pad between rail and sleeper and that for the latter, with a rubber boots between sleeper and concrete. Corrugation occurred not on tangent track but in curves. Details can be found in [31,32]. Similar to Frederick and Valdivia, a completely linear model has been used in analysis. First the reference state of the bogie in a curve was determined by a nonlinear quasi-static curving analysis. A linear dynamic analysis and then a linear wear analysis were proceeded. The frequency having the maximum corrugation growth rates (cf. chapter 4) corresponds to an antiresonance of the vertical track vibration and to a resonance of the lateral wheel-set vibration having the coincidence of two negative effects.
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5.3. Kalousek and Johnson: corrugation on vancouver skytrain Shortly after the opening, the Vancouver mass transit system experienced severe rail and wheel corrugation problems. Grassie and Kalousek had classified them also as “roaring rail type” corrugation. The poor alignment of wheel-sets in trucks, the generation of ‘roll-slip’ oscillations between wheel and rail and the development of close conformity between wheel-tread and rail were judged to be associated with the development of corrugations. Remedies included reducing the tolerance on wheel-set misalignment to ±10 min of arc, applying a friction modifier to wheels to change the friction characteristic between wheel-tread and rail from negative to positive, regauging the track and grinding the rail to different profiles in each for the four equal sections in length of tangent track. These remedies have virtually eliminated corrugation from the system. It was reported in 1992 by Kalousek and Johnson [33]. 5.4. Müller’s Ph.D. thesis: introduction of a wavelength constant mechanism The models of Frederick, Valdivia and Hempelmann resulted in a frequency-constant mechanism. According to such a mechanism, the wavelength of short-pitch rail corrugation should be proportional to vehicle speed. This seemed to be in contradiction to experimental evidence. In the Ph.D. thesis, Müller showed that besides frequency fixing mechanisms, there was also a wavelength-fixing mechanism for short-pitch corrugations [34]. Müller’s model was linear on the line of the studies by Valdivia, Frederick and Hempelmann. In his study, it was shown that other structural effects could also dominate the profile development, e.g. the high lateral rail receptance between 1600 and 1800 Hz, sometimes, a low vertical rail receptance near 300 Hz or even high lateral receptances of the wheel-set. If, however, structural dynamics are completely suppressed and only contact mechanical effects are considered, then only the initial rail roughness within a fixed wavelength band between 2 and 8–10 mm is found to increase and finally to form corrugations. Müller called this the contact mechanical filter effect. If structural mechanics are additionally included, then, of course, the wavelengths of corrugations have to be determined by dividing the vehicle speed with the frequency of low vertical receptance or high lateral receptance. As several such frequencies related to different effects of structural dynamics exist, those frequencies are favored where the wavelength of corrugation is within the wavelength band where the contact mechanical filter function promotes corrugation. 5.5. Bhaskar, Johnson, and Woodhouse; Müller: stability analysis It is well known that a critical speed due to vehicle and track-interaction in the low frequency range could be
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observed. The wheel-set hunting motion could become unstable. It was an open discussion whether similar instabilities were possible in the high frequency range resulting in self-excited vibrations and finally corrugations or not. In the paper by Gasch et al. [35] such an instability has indeed been observed. As, however, an unrealistic track model had been used, several new attempts were performed. Nearly in parallel to it in a paper of Bhaskar et al. [36] and in Müller’s Ph.D. thesis [34], the problem was re-examined. Both results are the same: using a realistic track model always sufficient damping, e.g. from rail pads is available to counteract self-excited effects due to contact mechanical effects. 5.6. Ilias, Igeland and Bohmer: non-linearities are included In all the investigations which have been discussed in chapter 5, linear models were used and the wear was considered only as the damage mechanism. In the Ph.D. theses of Ilias [37], and Igeland [38] geometrical as well as mechanical non-linearities were introduced, excluding lateral vibrations. It was found that even for comparatively small corrugation depth nonlinear effects can be important. The first attempt to include plastic deformation together with wear as damage mechanism has been tried by Bohmer [87]. The interesting results indicate, that probably the gap between mechanical and metallurgical investigations will be closed in the near future
6. Studies in Japan in recent years Leading studies of corrugation in these 10 years in Japan are the studies by Suda (The University of Tokyo) and Matsumoto and his colleagues (cooperated studies by TSNRI and SMT). These studies were brought together in the research project of The JSA, and the formation mechanism and countermeasures of corrugation on sharp curve were studied from various point of view. The outcomes of these studies are reflected to the following studies by RTRI and JR East, etc. In this way, the studies of corrugation on sharp curve have been progressed in these 10 years in Japan. 6.1. Studies by Suda (Laboratory of The University of Tokyo) Suda studied the mechanism of corrugation by using experimental model stand of rolling surfaces from 1986 to 1991. He explains the mechanism of formatting and growing of corrugation mainly by using a plastic deformation model [39–42]. He considered wheel/rail system as self-exited vibration system where contact vibration and surface deformation happen simultaneously, and introduced the boundary condition of growth or reduction of corrugation from stability condition of feed back loop of repeated contacts.
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From 1991, Suda et al. [43], and Suda and Komine [44] started the study on control of generation of corrugation by using high dumping alloy. He used Fe-5Ni-15Mn alloy, and researched the effect to the reduction of corrugation formation by experiments on model test stand and trial rail made of high dumping alloy. Suda played a part in the research project of The JSA, which is described in Section 6.2, and started the experimental study of corrugation phenomenon on rolling/sliding contact using a scaled roller test stand from 1995 [45–48]. Following it, he made a new one that can control the slip at contact surface. He verified the formation of corrugation generated by longitudinal and lateral creepage. From 1998, JR East started the research of rail corrugation that occurs on low rail of sharp curve of commuter line. Suda et al. took part in this research [49]. In addition to studies of phenomenon of corrugation, Suda et al. study detecting method of corrugation by using wavelet analysis [50]. 6.2. Cooperated studies by TSNRI of The Ministry of Transport and Sumitomo Metal [51] Matsumoto and Sato of Traffic Safety and Nuisance Research Institute (TSNRI) of The Ministry of Transport, Tanimoto and Kang (Oka) of Sumitomo Metal Technology (SMT) started cooperative studies in the spring of 1993. The study was started in order to investigate the generation mechanism of corrugation and to prevent the corrugation on curved track of subway lines. They thought full-scale experiment is important as well as numerical simulation, so they carried out both and compared both results at all the times. Their studies were jointed to JSA’s research project from 1994, just 1 year after, the start of their studies. For basic research they carried out the research on contact characteristics, such as creep force, by using a full-scale bogie rolling test stand equipped in TSNRI, which can simulate curving condition [52,53]. They studied measuring methods and succeeded in the measurements of bogie/track relative position/force and the fluctuation of rail contact force on commercial subway line [54]. They also tried to investigate rail corrugation on commercial line, and carried out 3D measurement of the shape of corrugated rail. From full-scale test stands, commercial line experiments and numerical simulation, they found that rail corrugation on curve section of track is formed by stick-slip vibration between wheel and rail, which is caused by the large creepage (longitudinal or lateral) and vertical force fluctuation on wheel/rail contact surface [55–57]. Some former report said corrugation is caused by stick-slip, but these theories depend upon negative friction characteristics in the range of large creep rate. However, according to Matsumoto’s studies, the change of maximum creep force by wheel load vibration is much larger than the change by negative friction characteristics. From these reasons, Matsumoto and his colleagues
thought that stick-slip which produces rail corrugation is caused mainly by wheel load vibration. At the same time, they tried to find countermeasure of corrugation generation. After train running test on commercial line, it was provided that several methods [58], such as asymmetric grinding of rail (especially low rail), optimizing worn wheel profile, lubrication by solid lubricant, etc. are effective for prevention of corrugation. On the basis of previous studies described earlier, they are analyzing the growing process of corrugation by numerical simulation now [59]. 6.3. Research project by The JSA [60] The JSA carried out the research project of the practical use of linear-motor-driven subway system (“Linear Metro”) from 1985 to 1988, from 1987 train running tests by trial vehicle were carried out on Osaka Nanko test track. At the time of practical use near at hand, they were afraid that linear-motor-driven railway is easily affected by corrugation because the Canadian Sky Train, which is similar in linear-motor drive with steel wheels, was troubled by severe corrugation at that time. In the autumn of 1987, The JSA dispatched an inquiry commission to Canada. The commission consists of Prof. Ieda of The University of Tokyo, Matsumoto of TSNRI and members of The JSA from car manufacturers and track constructors. After investigations, they reported that the cause of corrugation in Canadian linear-motor system is peculiar to Canadian system and Japanese system is safe from it. In the spring of 1990, first Linear Metro was opened in Osaka and second system was opened in the spring of 1991 in Tokyo. Rail corrugation did not occur in Osaka Subway, but in Tokyo Subway corrugation occurred on sharp curve of 160 m radius. Matsumoto and his colleagues started studies of corrugation described earlier in order to resolve the situation. Since The JSA thought Linear Metro is main subway system in next century, it is important to solve corrugation problems. The JSA organized a research committee on the formation mechanism of corrugation in the spring of 1994. The committee consists of Prof. Iguchi as chairman, Prof. Sumi of The Kyushu University, Prof. Suda, Matsumoto of TSNRI and other members from car manufacturers, track constructors and subway operators. In this research, project practical studies were carried out by three groups, that is, the Suda group from The University of Tokyo, Matsumoto group from TSNRI and S. Ishida, who was a former bogie engineer of Hitachi Ltd. Suda studied mainly by model stand experiments and numerical simulation, Matsumoto studied mainly by full-scale stand tests, train running tests and numerical simulation, Ishida and Furuta studied mainly by FEM analysis [61]. The committee completed the final report in the spring of 1996. The results of studies by Suda and Matsumoto were described Sections 6.1 and 6.2.
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Main countermeasures applied to Tokyo Subway are both the optimized worn profile developed by TSNRI and lubrication to low rail by oil. Up to now, severe corrugation does not occur in Tokyo Subway. 6.4. Studies by JR groups The occurrence of rail corrugation, though the categories are not always same, increases also in JR lines in recent years. Kyushu started the studies of corrugation, because rail corrugation occurs on many sharp curve of less than 400 m radius. For countermeasures, they tried expanding of gauge slack, using DHH rail, etc. [62]. In 1998, JR East started the research project of formation mechanism of corrugation generated on low rail of sharp curve of commuter lines. Train running tests on commercial commuter lines were carried out in this project [49]. M. Ishida of RTRI analyzed the situation of the occurrence of rail corrugation in JR lines, and made observation of plastic flow on the surface of corrugated rail [63,64].
7. Concluding remarks To understand the formation of corrugation, a systematic study of the phenomena including experimental as well as theoretical investigations is essential. The papers referred by Birmann were 107 in 1958 and those reviewed by Hemplemann, 118 in 1994. However, those reviewed by Krabbendam in 1961, all dealing with some kind of corrugation, between 900 and 1000! Thus, more than 1500 papers on rail corrugation may be in the world. The classification which was presented by Grassie and Kalousek in 1993, based on the authors’ experience, is helpful for future investigations. For five out of six categories of it, not only characteristics, but also causes and even treatments of them are identified in it. To their opinion for the sixth category (roaring rail type corrugation), a wavelength-fixing mechanism yet had to be pursued. From the interpretation in Section 5.4, it is evident, that there is a “contact filter”, which only allows corrugations to grow in a wavelength range between 2 and 8–10 cm. “Booted-sleeper” type corrugation and “pinned–pinned-mode” type corrugation are probably only two possible types. The existence of a pinned–pinned-mode type corrugation is confirmed by an investigation of Hiensch et al. [65]. This paper, however, also indicates, that the problem is not solved at all. It could not be explained, why on the same line under the same nominal loading significant differences in corrugation growth were observed. Only the rail material seemed to be different. Improved material and wear models are therefore necessary. Probably the wear as damage mechanism alone is not sufficient to explain why some rails develop corrugation faster than others. Further, the development of friction modifier changing the friction characteristic between wheel-tread and rail from
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negative to positive and applied to the Vancouver Skytrain is noticed. In recent study in Japan, Suda et al. began the theoretical and experimental study on rail corrugation in 1986 and presented it internationally in 1988 [39]. It depends on the stability of the system in Fig. 1. Continuing the study, a corrugation simulator was developed [48]. From 1993, Matsumoto and his colleagues started the study on corrugation on sharp curve in order to prevent the corrugation generated mainly on linear-motor-driven subway. Matsumoto, Suda, Ishida and Sumi joined in the research project in The JSA, and carried out full-scale stand tests, model stand tests, train running tests, field researches and numerical simulations and successfully investigated the formation mechanism and countermeasures of corrugation produced on low rail of sharp curved track [60]. According to the conclusion by Matsumoto, such type of rail corrugation is formed by stick-slip vibration between wheel and rail, which is caused by large creepages (longitudinal or lateral) and vertical force fluctuation on wheel/rail contact surface [55–57]. The output of these studies reflected to other groups, such as RTRI, JR east, etc. because this type of corrugation is the most typical in Japanese railway except Shinkansen where the corrugation has not nearly been noticed so far. The rail corrugations appeared in Japan in recent years are mostly divided into three types: (1) on low rail of sharp curves with short-pitch, (2) on tangent or on slack curve with short-pitch, and (3) on high rail on sharp curve with intermediate wavelength. First one is the major type in Japanese railway described earlier and may be in the third category in Grassie–Kalousek classification. Second one is probably in the sixth category and is accelerated by the speed-up of trains. And the last one is in the first category in the same and appeared by the introduction of tilt trains on sharp curve with much insufficient cant for these trains. The studies on type (1) are advanced in Japan as in chapter 6 in recent years, those on (3) are fairly well known, but those on type (2) did not yet got a convincing explanation as mentioned previously. Authors are grateful for the sincere advices of editor and referees for their cordial propositions. References [1] Bibliography on Corrugation of Rails, Research Deptartment Library, Derby, 1954, 1961, 1977. [2] M. Birmann, Schienenriffeln, ihre Erforschung und Verhütung, Neueres aus der Riffelforschung der Deutschen Bundesbahn, Teil I. Schwingungsuntersuchungen, Teil II. Werkstoffuntersuchungen (English title: Rail Corrugation, Research and Preventive Measures: new results from corrugation research at DB, Part I. Vibrational Investigations, Part II. Material investigations), VDI Z. 26 (1958.9) and 30 (1958.10). [3] Y. Satoh, Study on Rail Corrugation, Tetsudo Senro 9–4 (5) (1961) (in Japanese). [4] N.C. Vogan, Question 9, Experience Obtained Concerning the Undulatory Wear of Rails, Monthly Bulletin of the International Railway Congress Association, Bulletin of IRCA (1958.5).
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[5] L.P. Delgado, Question 9, Experience Obtained Concerning the Undulatory Wear of Rails, Bulletin of IRCA (1958.6). [6] K. Miyahara, Document from Countries on Rail Corrugation, Tetsudo Senro 7–2 (1959.2) (in Japanese). [7] G. Krabbendam, Internationales Schrifttumverzeichnis über die Riffel- und Wellenbildung auf Eisenbahn- und Strassenbahnschienen (English title: International Literature on the Formation of Short and Long Wavelengths Corrugations on Tracks of Main Lines and of Trams), Forschungsdienst der niederändischen Eisenbahnen, 1961. [8] ORE S 1012 Formation of Corrugation and Waves on the Rail and Mutual Wear of Wheel and Rail, RP 1, Mutual Rail/Wheel Wear and Corrugatory Wear, ORE, Utrecht (1977.4). [9] K. Hempelmann, Short-pitch Corrugation on Railway Rails: A Linear Model for Prediction, VDI Fortschritt-Berichte (also Dissertation, TU Berlin), 12–231, VDI-Verlag, Düsseldorf, 1994. [10] Y. Kato, On Rail Corrugation, Tetsudo Senro 6–2 (1958.2) (in Japanese). [11] R.M. Carson, K.L. Johnson, Surface corrugations spontaneously generated in a rolling contact disc, Wear 17 (1971) 59–72. [12] K.L. Johnson, G.G. Gray, Development of corrugations on surfaces in rolling contact, Proc. Inst. Mech. Eng. 189 (1975) 45–58. [13] R.I. Mair, Natural Frequency of Rail Track and its Relationship to Rail Corrugation, Civil Engineering Transportation, The Institution of Engineers, Paper 3494, Australia, 1977. [14] R.I. Mair, Track design to prevent long-pitch rail corrugation, Bulletin 692 (84) (1983) 289–300. [15] S.L. Grassie, R.W. Gregory, D. Harrison, K.L. Johnson, The dynamic response of railway track to high frequency vertical/lateral/longitudinal excitation, J. Mech. Eng. Sci. 24–2 (1982) pp. 77–90, 91–96, 97–102. [16] B. Ripke, K. Knothe, Die unendlich lange Schiene auf diskreten Schwellen bei harmonischer Einzellasterregung (English title: Infinitely Long Rail Discretely Supported by Sleepers under Harmonic Excitation), No. 11-155, VDI Fortschritt-Berichte, VDI-Verlag, Düsseldorf, 1991. [17] J. Eisenmann, Riffelbildung bei Schienen (English title: Corrugation Formation on Rails), Eisenbahningenieur 29–3 (1978). [18] A. Böhmer, T. Klimpel, Plastic deformation of corrugated rails: a numerical approach using material data of rail steel, in: Proceedings of the Presentation at The Fifth International Conference on Contact Mechanics and Wear of Rail/Wheel Systems (Fifth CM), Tokyo, Japan, 2000, WEAR (2001), in press. [19] L.E. Daniels, N. Blume, Real corrugation growth performance, in: Proceedings of The Second International Heavy Haul Railway Conference 28 (82-HH28), (1982.9). [20] S.L. Grassie, J. Kalousek, Rail Corrugation: Characteristics, Causes and Treatments, IMechE 207(F) (1993). [21] A. Valdivia, Die Wechselwirkung zwischen hochfrequenter Rad– Schiene–Dynamik und ungleichförmigem Schienenverschleiss— Ein lineares Modell (English title: The Interaction between High-Frequency Wheel-Rail Dynamics and Irregular Rail Wear—A Linear Model), Fortschritt-Berichte VDI 12–93 (also Dissertation, TU Berlin, 1987), 1988. [22] R.A. Clark, P. Foster, On the Mechanics of Rail Corrugation Formation, Proc. 8th IAVSD-Symp. Cambridge, MA (1983.8), Swets Zeitlinger (Amsterdam/Lisse) (1984) 72–85. [23] R.A. Clark, G.A. Scott, W. Poole, Short Wave Corrugations - An explanation based on stick-slip vibrations, Applied Mechanics Rail Transportation Symposium, Vol. 96 (AMD), Vol. 2 (RTD), ASME (1988) 141–148. [24] T. Sumi, Y. Matsumoto, M. Murao, H. Sasaki, Generation Mechanism of Rail Corrugation at Curved Tracks Having Short Radius, Trans. JSCE 426/IV-14 (1991) (in Japanese). [25] C.O. Frederick, W.G. Bugden, Corrugation Research on British Rail, in: K. Knothe, R. Gasch (Eds.), Proceedings of the Presentation of the Rail Corrugations at the Symposium on Rail Corrugation Problems, Vol. 56, Berlin (1983.6), ILR-Bericht, Berlin, 1983, pp. 7–33.
[26] W.G. Bugden, Characteristics of short-wavelength corrugation on rails, in: Proceedings of the Presentation of Seminar on Rail Corrugation (1983.9), Institution of the Mechanical Engineers, London, 1983. [27] C.O. Frederick, A rail corrugation theory, in: Proceedings of the Second Conference on the Contact Mechanics and Wear of Rail/Wheel Systems, 1986. [28] A. Valdivia, A Linear Dynamic Wear Model to Explain the Initiating Mechanism of Corrugation, in: M. Apetaur (Ed.), The Dynamics of Vehicles on Roads and on Tracks, Proceedings of the Tenth IAVSD-Symposium, Prague, 1987, Swets Zeitlinger (Amsterdam/Lisse) (1988) 493–496. [29] K. Hempelmann, K. Knothe, An extended linear model for the prediction of short-pitch corrugation, Wear 191 (1996) 161–169. [30] ERRI D185, Rail Corrugation Models, Comparison of results obtained using The Berlin Technical University and the British Rail methods, RP 1, D185: Reduction in Corrugation of Rails, European Rail Research Institute (ERRI), Utrecht, 1993. [31] E. Tassilly, N. Vincent, A linear model for the corrugation of rails, J. Sound Vibrat. 150 (1) (1991) 25–45. [32] E. Tassilly, N. Vincent, Rail corrugations: analytical models and field tests, Wear (1991) 163–178. [33] J. Kalousek, K.L. Johnson, An investigation of short-pitch wheel and rail corrugations on the Vancouver mass transit system, IMechE 206 F (1992) 127–135. [34] S. Müller, Linearized Wheel-Rail Dynamics—Stability and Corrugation, Fortschritt-Berichte VDI (also Dissertation, TU Berlin), No. 12-369, VDI-Verlag, Dusseldorf, 1998. [35] R. Gasch, A. Gross-Thebing, K. Knothe, A. Valdivia, Linear, Self-excited vibrations as initiating mechanism of corrugation, in: K. Knothe, R. Gasch (Eds.), Proceedings of the Presentation of the Symposium on Rail Corrugation Problems, Berlin (1983.6), ILR-Bericht 56, TU Berlin, Institut für Luft- und Raumfahrt, Berlin, 1983, pp. 207–230. [36] A. Bhaskar, K.L. Johnson, G.D. Wood, J. Woodhouse, Wheel-rail dynamics with closely conformal contact. Part 1. Dynamic modeling and stability analysis, Proc. Instn. Mech. Eng. 211 (F) (1997) 11–26. [37] H. Ilias, Nichtlinear Wechselwirkungen von Radsatz und Gleis beim Überrollen von Profilstörungen (English title: Nonlinear Interactions of Wheel-set and Track when Rolling over Profile Irregularities), VDI Fortschritt—Berichte (also Dissertation, TU Berlin), No. 12-297, VDI-Verlag, Düsseldorf, 1996. [38] A. Igeland, Dynamic train/track-interaction: simulation of railhead corrugation growth under a moving bogie using mathematical models combined with full-scale measurements, Dissertation, Division of Solid Mechanics, The Chalmers University of Technology, Göteborg, Sweden, 1997. [39] Y. Suda, M. Iguchi, H. Imaizumi, The mechanism of corrugation phenomenon on rolling surface, in: Proceedings of the Symposium on the Applied Mechanics Rail Transportation, Vol. 96 (ASME, AMD), Vol. 2 (RTD), 1988, pp. 29–36. [40] Y. Suda, M. Iguchi, Basic study of Corrugation Mechanism on Rolling Contact in Order to Control Rail Surfaces in: Proceedings of the 11th IAVSD Symposium (1989-8), pp. 566–577. [41] Y. Suda, Effects of vibration system and condition on the development of corrugations, WEAR 144 (1991) 227–242. [42] Y. Suda, The mechanics for self-generation of corrugations, Jpn. J. Tribol. 38-12 (1993) 1553–1563. [43] Y. Suda, I. Nakagami, T. Ueno, S. Watanabe, Corrugation control by vibration damping with high damping alloy, Proc. Asia-Pacific Vibrat. Conf. 91 (3) (1991) 98–103. [44] Y. Suda, H. Komine, Contact vibration with high damping alloy, WEAR 191 (1996) 72–77. [45] Y. Suda, T. Nishigaito, K. Okamoto, H. Komine, Creep characteristics with high damping alloy for corrugation phenomenon, in: Proceedings of the Second Mini Conference on CM (1996.7), pp. 325–332.
Y. Sato et al. / Wear 253 (2002) 130–139 [46] Y. Suda, T. Nishigaito, H. Komine, K. Okamoto, Study of corrugation phenomenon on rolling/sliding contact using a corrugation simulator, in: Proceedings of the Conference (IMechE) RAILTECH’96, Vol. 16, C511 (1996.2.16). [47] Y. Suda, H. Komine, T. Iwasa, Y. Terumichi, Study on Mechanism of Corrugation Phenomenon with Longitudinal Slips, in: Proceedings of the Asia-Pacific Vibration Conf.’99 (1999), Vol. 2, pp. 660–665. [48] Y. Suda, H. Komine, T. Iwasa, Y. Terumichi, in: Proceedungs of the Fifth CM on the Experimental Study on Mechanism of Rail Corrugation Using Corrugation Simulator(2000), pp. 66–73. [49] Y. Suda, M. Hanawa, M. Okumura, T. Iwasa, in: Proceedings of the Fifth CM on the Study on Rail Corrugation in Sharp Curves of Commuter Line (2000), pp. 171–176. [50] Y. Suda, M. Okumura, B. Qian, T. Iwasa, H. Komine, Y. Terumichi, A New Detecting Method for Rail Corrugation by Using Wavelet Analysis, WCRR’99 179 (1999). [51] A. Matsumoto, Y. Sato, H. Ohno, M. Tanimoto, Y. Oka, E. Miyauchi, Formation Mechanism and Countermeasures of Rail Corrugation on Curved Track, in: Proceedings of the 5th CM (2000). [52] A. Matsumoto, Y. Sato, M. Tanimoto, Q. Kang T. Amano, M. Chishima, Experimental Study on Wheel/Rail Contact Mechanism on Curved Track (first and second reports), in: Proceedings of the Conference of the Japan Society of Mechanical Engineers (JSME), No. 940-26I (1994) No. 95-1 (1995) (in Japanese). [53] A. Matsumoto, Y. Sato, M. Nakata, M. Tanimoto, Wheel/rail contact mechanics at full-scale on the test stand, WEAR 191 (1996). [54] A. Matsumoto, Y. Sato, M. Fujii, M. Tanimoto, Q. Kang, E. Miyauchi, M. Furuta, Characteristics of Bogie and Track on Sharp Curve and Their Effects to Formation of Corrugation (from first to fifth reports), in: Proceedings of the Conference of the JSME No. 95-10, No. 95-44 (1995), No. 96-1, 96-5 I, 96-51 (1996) (in Japanese). [55] A. Matsumoto, Y. Sato, M. Fujii, M. Tanimoto, Y. Oka, E. Miyauchi, The formation mechanism of rail corrugation on curved track
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(first report), longitudinal stick-slip vibration model considering contact stiffness, Trans. JSME 62c-597 (1996) 49–57 (in Japanese). A. Matsumoto, Y. Sato, M. Tanimoto, Y. Oka, E. Miyauchi, The formation mechanism of rail corrugation on curved track (second report), Basic Formation Mech., Trans. JSME 64c-623 (1998) 315–322 (in Japanese). A. Matsumoto, Y. Sato, M. Tanimoto, Q. Kang, Study on the formation mechanism of rail corrugation on curved track, Vehicle Syst. Dynam. 25 (1996). A. Matsumoto, Y. Sato, M. Tanimoto, Y. Oka, Improvement of curving performance of steerable bogie in urban railway, STECH’96, IMechE, b514/19 (1996.9). A. Matsumoto, Y. Oka, Y. Sato, T. Nakagawa, K. Tsida, H. Komatsu, S. Shiozaki, Consideration on Growing Process of Rail Corrugation (from first to third reports), in: Proceedings of the Conference of JSME No. 98-1, No. 98-8, No. 98-37, 1999 (in Japanese) Japan Subway Association, Report on the Analysis of the Formation Mechanism of Rail Corrugation (1996.3) (in Japanese). S. Ishida, M. Furuta, The Effect of Lateral Vibration of Wheel-Track System on the Rail Corrugation, Proc. J-Rail’96 (1996) (in Japanese). K. Date, S. Kai, H. Shibata, Y. Matsumoto, N. Konnya, Countermeasure of Rail Corrugation of Kyusyu Railway Company, in: Proceedings of the 53th Annual Conference of JSCE IV 1998 (in Japanese). M. Ishida, K. Matsuo, Plastic Flow on the Surface of Corrugated Rail in a Sharp Curve, in: Proceedings of the J-Rail’97 on the Plastic Flow, 1997 (in Japanese). M. Ishida, T. Moto, M. Takikawa, The Effect of Lateral Creepage Force on Rail corrugation on Low Rail at Sharp Curves, in: Proceedings of the Fifth CM (200.7), pp. 177–182. M. Hiensch, J. Nielsen, E. Verheijen, Rail Corrugation in The Netherlands—Measurements and numerical Simulation, Proceedings of the Fifth CM, Tokyo, July 2000, pp. 81–88.
Review on rail corrugation studies Yoshihiko Sato a,∗ , Akira Matsumoto b , Klaus Knothe c b
a Railway Track System Institute, 1-11-8, Kurosunadai, Inageku, Chiba-shi, Chiba-ken 263-0041, Japan National Traffic Safety and Environment Laboratory, 7-42-17, Jindaiji-Higashimacht, Chofu-shi, Tokyo 182-0012, Japan c Sekr. F5, Institut für Luft- und Raumfahrt, Berlin Technische Universtät, Marchstr. 12, D-10587, Berlin, Germany
Abstract In Japan, rail corrugations had not been so serious formerly, but it began to be prevailing in recent years. In order to prevent the generation of rail corrugation, many studies have been reported in the world since the end of 19th century, but theories on them have not explained the formation mechanism perfectly and no perfect countermeasures have been established so far. Thus, the studies on corrugation are getting more important, because generation of corrugation shows a tendency to increase due to the speed-up of trains, to the introduction of new vehicles, etc. In such a situation, three authors review the studies on them in the past and those carried out now in the world and more precisely in Japan. The review is on bibliographies, attempts in the 1970s, classification of rail corrugation, short-pitch corrugation and studies in Japan in recent years. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Rail corrugation; Wheel/rail contact; Contact stress; Wear
1. Introduction In recent years, corrugation of rails has been a serious problem in Japan. Formerly, it was noticed just on the wooden ties directly fastened to steel bridge, in the tunnel and on the track firmly set on solid bed before the development of modern slab track or in the sections of braking and acceleration near stations, but not so on ordinary tangent tracks. It is true on Shinkansens even now. The general situation on rail corrugation was surveyed on existing lines in Japan in 1953 (Shinkansens did not yet exist). The situation in the world was discussed on a conference of the International Railway Congress Association (IRCA) in 1958. In the same year, possible causes of corrugation were investigated by Birmann. For approximately 15 years after those, there was nearly a standstill in research, which was also confirmed by the ORE questionnaire 1977. In the 1970s in parallel, several new activities started. In a paper of Johnson and Gray in 1975, it was shown, that a certain type of corrugation on disc machines could be explained theoretically and validated by experiments; in 1977 Mair in Australia investigated the cause of special long-wavelength corrugation; in 1978, Eisenmann published a study on short-pitch corrugation; in 1979, Daniels et al.
∗ Corresponding author. Tel.: +81-43-246-3883; fax: +81-43-246-3922. E-mail address: [email protected] (Y. Sato).
began their experimental investigation on the track of FAST in Pueblo. In 1983, two symposia on rail corrugation took place at The Berlin Technical University and in London, where papers of Frederick and Budgen, Clark and Kalker were presented. The first idea of a new theory was presented by Frederick on the Second International Conference on Contact Mechanics and Wear of Rail/Wheel Systems in 1986 and in the Ph.D. thesis of Valdivia (1987/1988). Within the next 10 years, a fruitful cooperation took place between The Technical University of Berlin (TUB) (Valdivia, Knothe and Hempelmann) and BR Research (Frederick and Sinclair) which brought the problem of short-pitch corrugation closer to a solution. The cause of the corrugation on the Vancouver Skytrain was pursued in 1992 by Kalousek. One year later, Grassie and Kalousek presented a classification of corrugation with their characteristics, causes and treatments. In Europe, the investigations were continued with the Ph.D. theses of Ilias (1996, Berlin), Igeland (1997, Goteborg) and Müller (1998, Berlin). In Japan, the rail corrugation and its related matters have been noticed and studied. Especially, the studies have been getting active in these 10 years. Most of these studies started in order to solve the problems of rail corrugation due to the speed-up of trains, to the introduction of new vehicles such as tilting trains, linear-motor-driven subway, to the unification of vehicle types, etc. Leading studies of corrugation in these 10 years are the studies by Suda and Matsumoto and
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their colleagues. These studies were brought together in the research project of The Japan Subway Association (JSA). The formation mechanism and countermeasures of corrugation on sharp curve were specially noticed in the project. The outcomes of these studies are reflected to the following studies by Railway Technical Research Institute (RTRI) and JR East, etc. In the Fifth Conference on Contact Mechanics and Wear of Rail/Wheel Systems, the presentation on this theme was given by first and second authors separately as parts I and II. In compiling it to Wear, the editor recommended us to revise it mainly supplementing the studies in Australia and UK through the indication of a referee and fusing parts I and II to one. To realize it, the paper has been revised totally with the assistance of third author.
2. Bibliographies, review and survey on studies in early days in Japan and in other parts of the world 2.1. Preliminary comments Between 1950 and 1980, several survey and review papers as well as bibliographies were published. Though not all of them are readily available, those which are known to the authors are mentioned briefly. • In Germany, corrugation had increased since 1895. The first survey study was dated from 1925. In 1953, Fink in Germany published a review-paper on rail corrugations, mainly considering short-wavelength rail corrugations (Riffeln in German) up to 5 cm. More than 50 papers, the first one from 1898, were discussed and a new tribochemical theory was presented. • In 1954, 1961 and 1977, British Rail (BR) Research Library presented bibliographies on rail corrugation [1], which were mainly used in the UK. • In 1958, Birmann [2] published his survey paper to be discussed in more detail in Section 2.2. The paper was summarized and introduced to Japanese people by Satoh [3]. • In the same year on the 17th Congress of the IRCA, two reports on rail corrugation were presented, reporting on rail corrugations at the NSW Government Railway and at RENFE in Spain [4,5], which both were summarized and introduced to Japanese people by Miyahara [6]. • The next survey paper, containing the most extensive survey up to that time, was presented by Krabbendam from The Netherland Railways NS [7] in 1961. In 1977, an ORE report on rail/wheel wear and corrugatory wear appeared [8]. • A more recent survey can be found in Hempelmann’s thesis [9]. Four of these papers shall be discussed in some more detail.
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2.2. Review by Birmann Mostly experimental, but some theoretical papers were reviewed by Birmann [2] all together 107 references. Birmann’s paper was summarized and introduced to Japanese people by Satoh [3]. In the first part, Birmann included the results of experimental studies on a test section in Germany, vibrational behavior of rail and wheel-set and statistical analyses. In the second part of the paper, mainly aspects of rail materials were considered. First results of a German test track to investigate influences of rail material on the formation of corrugation were presented; the effect of segregation was discussed in some detail as well as physical–chemical influences on friction (Fink’s theory) and the effect of corrosion. Finally, the prevention of corrugation growth was discussed considering materials, track structure and vehicle structure. The effect of tempering and heating after grinding was also analyzed. Finally, the increase of corrugated rail due to the continuous development of railway system was mentioned. In Birmann’s paper, mechanical aspects and aspects of rail material were separated and consistent mathematical theories were not yet appeared. 2.3. Questionnaire by IRCA In the IRCA 17th session in 1958, the surveys on undulatory wear of rail were presented by two reporters, Vogan (NSW Government Railway) [4] and Delgado (RENFE) [5]. It was summarized and introduced to Japanese people by Miyahara [6]. It includes the following items: • actuality of corrugation including its kinds, wavelength and amplitude, cause and growth and effect of rail hardness; • effect of material including production and quality, physical property, premium rail, sleeper, ballast and subgrade and rail joint; • other factors than track, including traction and rolling stock, frequency of operation and speed, environment, operation, tyre and rail; • effects of rail corrugation; • prevention and mitigation of corrugation growth; • corrugation grinding machines; • experimental studies; • theories on corrugations due to material and production, wheel pressure and kinematics of wheel, rail vibration, rail residual stress, interaction between wheel and rail and oxidization; • preventing method proposed by theorists. 2.4. Earlier surveys in Japan To respond to the questionnaire on corrugation for the 17th Conference of IRCA in 1958, the survey on corrugation in JNR of 1953 was supplemented with the data from
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the Teito Rapid Transit Authority (TRTA), Transport Department of Osaka-Shi (TDOS) and Kinki Nippon Railway Co. Ltd. (KNR) in 1958. It explained the actuality of corrugation in Japan in these days, the effect of materials and that of other items than track [10]. Corrugation was caused at about 800 sites over a length of 22 000 track-km, 48% of corrugations had wavelengths of 500 and 1500 mm, 30.6% between 200 and 500 mm and 12% of <100 mm. So, most of the corrugations had a wavelength of >200 mm. (In Germany, however, most corrugation had a wavelength of approximately 50 mm and in France, <120 mm in that time.) In Japan, 67% of corrugation were caused by wear, but 33% showed an undulatorily bent rail (may be, caused during rectification in the rail rolling factory with wavelength of about 1 m). The classification of corrugated rails according to curve radii was as follows: 5 sites per 100 track-km on curves of >800 m radius and in tangent track, 3.6 sites in curves of 600–800 m radius, 3.0 sites in curves of 400–600 m radius and 1.6 sites in curves of 200–400 m. Corrugations therefore could be found more often on tangent track and on slack curves than on sharp curves with radii <500 m. 2.5. Questionnaire from ORE ORE sent a questionnaire on corrugation study to member administrations and analyzed the responses in 1977 [8]. The administrations were interested in the problems, but their replies did not introduce many new elements of information with respect to existing knowledge. Taking into account, the complexity of the phenomena concerned, the more or less successful studies already made and the fact that the adopted empirical solutions reduced the economic importance of the phenomena, it was considered that the carrying out of new systematic studies would be superfluous. A permanent exchange of information was nevertheless recommended. 2.6. Intermediate summary Most of these papers concentrated on the presentation of phenomenological observations and tried to explain them. Probably in none of them a consistent mathematical model was formulated and validated in order to explain what had been observed. A second disadvantage was that the distinction between different types of corrugations was insufficient. The reason is quite clear: theories were not sufficiently developed in order to classify rail corrugation. Birmann and Krabbendam at least distinguished the difference between short-wavelength corrugation (German: Riffeln) and long wavelength corrugation (German: Wellen, i.e. waves). Looking at these papers again from the present point of view, they contain valuable phenomenological information which can be partially explained by present theories. A classification was only possible 20 years later.
3. New attempts in 1970s Despite of the reserve of ORE several new attempts were made in the 1970s to clarify corrugation phenomena. We restrict to the work of Carson, Johnson and Gray, to Mair’s investigations (including some comments on track dynamics), to the investigations of Eisenmann and finally to the experiments at FAST. 3.1. Carson, Johnson, and Gray: contact resonance and plastic deformation The paper of Carson and Johnson [11] in 1971 and Johnson’s and Gray’s [12] extended version of Gray’s Ph.D. thesis from 1972 considered the contact resonance and plastic deformations on discs. Experiments were performed with a disc machine and the corrugations which had appeared where explained by a new theory. Excited by irregularities, the system vibrates on the contact resonance mode. If the damping is low and the load is high, then vibrations may be severe enough to cause the incremental plastic indentation which then amplifies the vibration in the next revolution. Johnson and Gray distinguished clearly between two aspects: the wavelength is determined by the frequency of the contact resonance; the formation and amplification of quasi-periodic pattern is due to plastic deformation. This seemed to be the first time that a distinction was made between a wavelengths fixing mechanism and a damage mechanism. 3.2. Mair: resonance of unsprung mass and track and gross plastic deformation Long-pitch rail corrugations with wavelength in the range of 200–300 mm were a common occurrence for tracks with high axle loads. To understand how the wavelength was fixed, a basic understanding of track dynamics was necessary. Though already Timoshenko had analyzed the dynamic behavior of wheels moving on tracks, the models, which are used today in analyzing different types of rail corrugation, go back to the 1970s. Mair from Australia in 1977 [13,14] analyzed the vertical dynamic behavior of unsprung mass on a continuously supported track and assumed this to be the wavelength-fixing mechanism for heavy haul corrugation. As with Johnson and Gray, the formation of corrugations was due to gross plastic deformation. The simple type of track model which has been used by Mair was also sufficient for some other type of corrugation. For short-wavelength corrugations, however, more sophisticated track models had to be used. Most of the work, theoretically as well as experimentally, had been performed by Grassie et al. [15]. Considering these papers, validated dynamic track models were now available. Ten years later, a more general theoretical model for discretely supported tracks has been developed and used intensively by Ripke and Knothe [16].
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3.3. Eisenmann: work hardening and residual stress In 1978, Eisenmann proposed a new theory [17]. It explained short-pitch corrugation as caused by the residual stresses in rail head, which were activated during manufacturing of the rail and which vary with the time of operation “it is generally known that under working pressure, the rails near the contact area of the wheel will have hardened by 6–8 mm. This hardening can be explained by bending compressive stresses and activated compressive stresses, especially those which occur directly under the wheel . . . ,” which finally lead “to compressive residual stresses under repeated weight influence in the cant area in the longitudinal as well as in the transverse direction of the railhead . . . ”. Eisenmann then mentioned the so-called Bauschinger effect and postulated that these effects all together finally are responsible for short-pitch rail corrugation. Eisenmann seemed to have got his idea from metallurgical investigations. It is very recent that mathematical models were used to study the influence of work hardening and residual stresses on corrugation [18]. 3.4. Experiments on FAST track in Pueblo In 1979, FAST technical personnel were directed to establish a test with the objective of providing operating railroads with better methods to treat corrugations. An experiment was designed which would first provide an understanding of corrugation growth and then based on that data establish an investigation of corrugating mechanisms [19]. The paper presents the layout, measurement and conduct of the FAST Rail Corrugation Experiment. Corrugation growth rates were presented. Factors affecting corrugation growth were then evaluated and discussed. The effects of corrugations on track maintenance were presented. Rail grinding was then discussed. Current theories on corrugating mechanisms were reviewed. Finally, the paper’s conclusions were summarized with recommendations for revenue service application and recommendations for additional research. 4. Classification of rail corrugation by Grassie and Kalousek In 1993, Grassie and Kalousek reviewed 42 references and published a paper entitled “rail corrugation: characteristics, causes and treatments” [20] which is helpful to understand the work which has been performed within the 1970–1990. Based on their far reaching experience, they classified corrugation into six groups which they called (1) heavy haul corrugation (200–300 mm), (2) light rail corrugation (500–1500 mm), (3) booted sleepers type corrugation (45–60 mm), (4) contact fatigue corrugation (150–450 mm), (5) rutting corrugation (50 mm (trams), 150–450 mm), and (6) roaring rail corrugation (25–80 mm). Most of the rutting-type corrugations are called in Germany
Fig. 1. Feed-back loop of structural dynamics and contact mechanics (wavelength-fixing mechanism) and damage mechanism [20,21].
Wellen (long wavelengths corrugation), whereas, the roaring rail corrugation is called Riffeln (short-wavelength corrugation). Though the authors do not agree completely with Grassie and Kalousek’s classification, the basic idea, namely the introduction of a wavelength-fixing mechanism and a damage mechanism in order to categorize corrugation in Fig. 1 is completely convincing. The basic idea of two different mechanisms can already be found in Johnson’s and Gray’s paper as well as in Frederick’s papers, in Valdivia’s Ph.D. thesis (Section 5.1) and in Suda’s paper (Section 6.1). Wavelengths-fixing mechanisms result from the dynamic interaction of wheel-set and track; it is therefore necessary to have available track and wheel-set models in the whole frequency range of interest. Damage mechanisms are either plastic deformation (plastic bending or plastic flow), rolling contact fatigue, or wear. The diagram of Fig. 1 helped to solve the conflict (especially in Germany) whether structural dynamics or material behavior are mainly responsible for the formation of rail corrugation. Both aspects are integrated in a feedback loop. Grassie and Kalousek’s paper indicates that most types of corrugations were understood. In chapter 5, we therefore concentrate on short-pitch corrugations of the “roaring rail” type, which according to [20] indicated as not to have been understood. 4.1. Clark: self-excited rutting-type corrugation A special version of “rutting-type corrugations” was probably investigated first by Clark and Foster [22]and Clark et al. [23]. Self-excited vibrations of a flexible wheel-set and a discretely supported track system under high creepage conditions were investigated; Mathieu vibrations excited by track stiffness variations and roll-slip vibrations excited by wheel-rail creep forces were also considered: these two mechanisms might exist separately or in combination to
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provide possible explanations for the formation of long- and short-wavelength corrugations on the running surface of railway rails. To get negative damping, which is necessary to cause self-excited vibrations, the creep-force/creep characteristic must decrease after a maximum has been reached and large creepage must be available. This is the case on sharp curve, but not on tangent track. 4.2. Sumi in Japan: rutting-type corrugation in Japan Sumi et al. proposed a theory for the cause of corrugation on curve in Japan in 1991 [24]. “As having been said, the corrugations are caused everywhere due to the combination of various factors. In the curve, as there is a large possibility of irregular slip between inner and outer rails, it is enough to cause the torsional vibration of wheel-set. As the vibrational velocity of wheel-set determined the volume of wear, it could cause the corrugation. It explains the dependency of the wavelength of corrugation on the train speed. With the coefficient of friction for rolling and sliding obtained in the laboratory, the diversion or the continuation (limit cycle) of torsional vibration is caused in more limited conditions than in those causing actual corrugation. It means that finding the actual coefficients of roll and slippage between wheel and rail is important. For the torsional vibration of wheel-set, the effects of brake, motor and track are to be in consideration.” 5. Short-pitch corrugation Short-pitch corrugation mainly occurs on tangent track (or on curves with large radius) of high speed lines. The wavelength of the quasi-periodic pattern is between 2 and 8–10 cm. Since 1980, increasing attention has been paid to them. Most of the work has been done at BR, at The Cambridge University and at The TUB. 5.1. Research on short-pitch rail corrugation at British Rail, at The Cambridge University and at TU Berlin before 1994 Most of the experimental investigations which had been performed at BR, partially together with The Cambridge University, can be found in papers of Frederick and Bugden [25] and Bugden [26] which had been presented at a Symposium on Rail Corrugation Problems in Berlin (June 1983) and at a seminar on the same subject in London (September 1983). A survey of the problem including the influence of steel grade is given. The metallurgical structure of corrugations as well as the effects of grinding and initial rail roughness is discussed in detail. Both symposia provided a good chance to initiate renewed studies on corrugation. Independently at BR and at TU Berlin, the theoretical work was intensified. The paper by Frederick in 1986 [27] showed how measured receptances to quantify the dynamic response of the wheel and rail to vertical, lateral and longitudinal forces could be combined with creep/force-creep
laws and with formulae for rail wear, in order to predict whether or not periodic pattern of certain wavelength in the surface of the rail would be deepened or erased by passing axles. At wave passing frequencies, where the phase of the periodic wear was such as to deepen the initial irregularity, initial rail roughness could develop to corrugation. It was shown that this hypothesis was able to explain observations of short-pitch corrugations on tangent track of BR lines. At The TUB Valdivia pursued the same though it was from a purely analytical point of view [21,28]. Wheel and rail receptances were calculated and combined with normal and tangential contact mechanical equations and finally with a wear analysis. The corrugation formation is described as a feedback loop between structural dynamics and contact mechanics on the one hand and a long-term wear process on the other hand (Fig. 1). “Corrugation growth rates” (real parts of wear eigenvalues) indicate whether the rail roughness of certain wavelength at certain positions in the sleeper bay either increases or decreases. The work of Valdivia in Berlin was continued by Hempelmann [9] and Hempelmann and Knothe [29]. Hempelmann had reviewed 128 papers and described the development of complete wear pattern in the sleeper bay and performed a large number of parametric investigations in order to identify critical parameters. Frederick and Valdivia as well as Hempelmann pointed out that the anti-resonance at the pinned–pinned-mode frequency is the most probable cause for the formation of short-pitch rail corrugation. Especially at BR, several cases forming short-pitch rail corrugation above the sleeper were found. Hempelmann also mentioned that high lateral dynamic receptances may result in corrugation growth at corresponding resonance frequencies if the creepage is maximum. In ORE D 185 committee [30], both algorithms were carefully compared theoretically as well as numerically. They were found to provide nearly the same results.
5.2. Tassilly and Vincen: corrugation at RATP The type of corrugation in Tassilly and Vincent’s paper seemed at first sight to be completely different from roaring rail corrugation. Grassie and Kalousek are classifying them as “booted sleeper corrugation”. The track for the former is laid on concrete with a rubber pad between rail and sleeper and that for the latter, with a rubber boots between sleeper and concrete. Corrugation occurred not on tangent track but in curves. Details can be found in [31,32]. Similar to Frederick and Valdivia, a completely linear model has been used in analysis. First the reference state of the bogie in a curve was determined by a nonlinear quasi-static curving analysis. A linear dynamic analysis and then a linear wear analysis were proceeded. The frequency having the maximum corrugation growth rates (cf. chapter 4) corresponds to an antiresonance of the vertical track vibration and to a resonance of the lateral wheel-set vibration having the coincidence of two negative effects.
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5.3. Kalousek and Johnson: corrugation on vancouver skytrain Shortly after the opening, the Vancouver mass transit system experienced severe rail and wheel corrugation problems. Grassie and Kalousek had classified them also as “roaring rail type” corrugation. The poor alignment of wheel-sets in trucks, the generation of ‘roll-slip’ oscillations between wheel and rail and the development of close conformity between wheel-tread and rail were judged to be associated with the development of corrugations. Remedies included reducing the tolerance on wheel-set misalignment to ±10 min of arc, applying a friction modifier to wheels to change the friction characteristic between wheel-tread and rail from negative to positive, regauging the track and grinding the rail to different profiles in each for the four equal sections in length of tangent track. These remedies have virtually eliminated corrugation from the system. It was reported in 1992 by Kalousek and Johnson [33]. 5.4. Müller’s Ph.D. thesis: introduction of a wavelength constant mechanism The models of Frederick, Valdivia and Hempelmann resulted in a frequency-constant mechanism. According to such a mechanism, the wavelength of short-pitch rail corrugation should be proportional to vehicle speed. This seemed to be in contradiction to experimental evidence. In the Ph.D. thesis, Müller showed that besides frequency fixing mechanisms, there was also a wavelength-fixing mechanism for short-pitch corrugations [34]. Müller’s model was linear on the line of the studies by Valdivia, Frederick and Hempelmann. In his study, it was shown that other structural effects could also dominate the profile development, e.g. the high lateral rail receptance between 1600 and 1800 Hz, sometimes, a low vertical rail receptance near 300 Hz or even high lateral receptances of the wheel-set. If, however, structural dynamics are completely suppressed and only contact mechanical effects are considered, then only the initial rail roughness within a fixed wavelength band between 2 and 8–10 mm is found to increase and finally to form corrugations. Müller called this the contact mechanical filter effect. If structural mechanics are additionally included, then, of course, the wavelengths of corrugations have to be determined by dividing the vehicle speed with the frequency of low vertical receptance or high lateral receptance. As several such frequencies related to different effects of structural dynamics exist, those frequencies are favored where the wavelength of corrugation is within the wavelength band where the contact mechanical filter function promotes corrugation. 5.5. Bhaskar, Johnson, and Woodhouse; Müller: stability analysis It is well known that a critical speed due to vehicle and track-interaction in the low frequency range could be
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observed. The wheel-set hunting motion could become unstable. It was an open discussion whether similar instabilities were possible in the high frequency range resulting in self-excited vibrations and finally corrugations or not. In the paper by Gasch et al. [35] such an instability has indeed been observed. As, however, an unrealistic track model had been used, several new attempts were performed. Nearly in parallel to it in a paper of Bhaskar et al. [36] and in Müller’s Ph.D. thesis [34], the problem was re-examined. Both results are the same: using a realistic track model always sufficient damping, e.g. from rail pads is available to counteract self-excited effects due to contact mechanical effects. 5.6. Ilias, Igeland and Bohmer: non-linearities are included In all the investigations which have been discussed in chapter 5, linear models were used and the wear was considered only as the damage mechanism. In the Ph.D. theses of Ilias [37], and Igeland [38] geometrical as well as mechanical non-linearities were introduced, excluding lateral vibrations. It was found that even for comparatively small corrugation depth nonlinear effects can be important. The first attempt to include plastic deformation together with wear as damage mechanism has been tried by Bohmer [87]. The interesting results indicate, that probably the gap between mechanical and metallurgical investigations will be closed in the near future
6. Studies in Japan in recent years Leading studies of corrugation in these 10 years in Japan are the studies by Suda (The University of Tokyo) and Matsumoto and his colleagues (cooperated studies by TSNRI and SMT). These studies were brought together in the research project of The JSA, and the formation mechanism and countermeasures of corrugation on sharp curve were studied from various point of view. The outcomes of these studies are reflected to the following studies by RTRI and JR East, etc. In this way, the studies of corrugation on sharp curve have been progressed in these 10 years in Japan. 6.1. Studies by Suda (Laboratory of The University of Tokyo) Suda studied the mechanism of corrugation by using experimental model stand of rolling surfaces from 1986 to 1991. He explains the mechanism of formatting and growing of corrugation mainly by using a plastic deformation model [39–42]. He considered wheel/rail system as self-exited vibration system where contact vibration and surface deformation happen simultaneously, and introduced the boundary condition of growth or reduction of corrugation from stability condition of feed back loop of repeated contacts.
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From 1991, Suda et al. [43], and Suda and Komine [44] started the study on control of generation of corrugation by using high dumping alloy. He used Fe-5Ni-15Mn alloy, and researched the effect to the reduction of corrugation formation by experiments on model test stand and trial rail made of high dumping alloy. Suda played a part in the research project of The JSA, which is described in Section 6.2, and started the experimental study of corrugation phenomenon on rolling/sliding contact using a scaled roller test stand from 1995 [45–48]. Following it, he made a new one that can control the slip at contact surface. He verified the formation of corrugation generated by longitudinal and lateral creepage. From 1998, JR East started the research of rail corrugation that occurs on low rail of sharp curve of commuter line. Suda et al. took part in this research [49]. In addition to studies of phenomenon of corrugation, Suda et al. study detecting method of corrugation by using wavelet analysis [50]. 6.2. Cooperated studies by TSNRI of The Ministry of Transport and Sumitomo Metal [51] Matsumoto and Sato of Traffic Safety and Nuisance Research Institute (TSNRI) of The Ministry of Transport, Tanimoto and Kang (Oka) of Sumitomo Metal Technology (SMT) started cooperative studies in the spring of 1993. The study was started in order to investigate the generation mechanism of corrugation and to prevent the corrugation on curved track of subway lines. They thought full-scale experiment is important as well as numerical simulation, so they carried out both and compared both results at all the times. Their studies were jointed to JSA’s research project from 1994, just 1 year after, the start of their studies. For basic research they carried out the research on contact characteristics, such as creep force, by using a full-scale bogie rolling test stand equipped in TSNRI, which can simulate curving condition [52,53]. They studied measuring methods and succeeded in the measurements of bogie/track relative position/force and the fluctuation of rail contact force on commercial subway line [54]. They also tried to investigate rail corrugation on commercial line, and carried out 3D measurement of the shape of corrugated rail. From full-scale test stands, commercial line experiments and numerical simulation, they found that rail corrugation on curve section of track is formed by stick-slip vibration between wheel and rail, which is caused by the large creepage (longitudinal or lateral) and vertical force fluctuation on wheel/rail contact surface [55–57]. Some former report said corrugation is caused by stick-slip, but these theories depend upon negative friction characteristics in the range of large creep rate. However, according to Matsumoto’s studies, the change of maximum creep force by wheel load vibration is much larger than the change by negative friction characteristics. From these reasons, Matsumoto and his colleagues
thought that stick-slip which produces rail corrugation is caused mainly by wheel load vibration. At the same time, they tried to find countermeasure of corrugation generation. After train running test on commercial line, it was provided that several methods [58], such as asymmetric grinding of rail (especially low rail), optimizing worn wheel profile, lubrication by solid lubricant, etc. are effective for prevention of corrugation. On the basis of previous studies described earlier, they are analyzing the growing process of corrugation by numerical simulation now [59]. 6.3. Research project by The JSA [60] The JSA carried out the research project of the practical use of linear-motor-driven subway system (“Linear Metro”) from 1985 to 1988, from 1987 train running tests by trial vehicle were carried out on Osaka Nanko test track. At the time of practical use near at hand, they were afraid that linear-motor-driven railway is easily affected by corrugation because the Canadian Sky Train, which is similar in linear-motor drive with steel wheels, was troubled by severe corrugation at that time. In the autumn of 1987, The JSA dispatched an inquiry commission to Canada. The commission consists of Prof. Ieda of The University of Tokyo, Matsumoto of TSNRI and members of The JSA from car manufacturers and track constructors. After investigations, they reported that the cause of corrugation in Canadian linear-motor system is peculiar to Canadian system and Japanese system is safe from it. In the spring of 1990, first Linear Metro was opened in Osaka and second system was opened in the spring of 1991 in Tokyo. Rail corrugation did not occur in Osaka Subway, but in Tokyo Subway corrugation occurred on sharp curve of 160 m radius. Matsumoto and his colleagues started studies of corrugation described earlier in order to resolve the situation. Since The JSA thought Linear Metro is main subway system in next century, it is important to solve corrugation problems. The JSA organized a research committee on the formation mechanism of corrugation in the spring of 1994. The committee consists of Prof. Iguchi as chairman, Prof. Sumi of The Kyushu University, Prof. Suda, Matsumoto of TSNRI and other members from car manufacturers, track constructors and subway operators. In this research, project practical studies were carried out by three groups, that is, the Suda group from The University of Tokyo, Matsumoto group from TSNRI and S. Ishida, who was a former bogie engineer of Hitachi Ltd. Suda studied mainly by model stand experiments and numerical simulation, Matsumoto studied mainly by full-scale stand tests, train running tests and numerical simulation, Ishida and Furuta studied mainly by FEM analysis [61]. The committee completed the final report in the spring of 1996. The results of studies by Suda and Matsumoto were described Sections 6.1 and 6.2.
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Main countermeasures applied to Tokyo Subway are both the optimized worn profile developed by TSNRI and lubrication to low rail by oil. Up to now, severe corrugation does not occur in Tokyo Subway. 6.4. Studies by JR groups The occurrence of rail corrugation, though the categories are not always same, increases also in JR lines in recent years. Kyushu started the studies of corrugation, because rail corrugation occurs on many sharp curve of less than 400 m radius. For countermeasures, they tried expanding of gauge slack, using DHH rail, etc. [62]. In 1998, JR East started the research project of formation mechanism of corrugation generated on low rail of sharp curve of commuter lines. Train running tests on commercial commuter lines were carried out in this project [49]. M. Ishida of RTRI analyzed the situation of the occurrence of rail corrugation in JR lines, and made observation of plastic flow on the surface of corrugated rail [63,64].
7. Concluding remarks To understand the formation of corrugation, a systematic study of the phenomena including experimental as well as theoretical investigations is essential. The papers referred by Birmann were 107 in 1958 and those reviewed by Hemplemann, 118 in 1994. However, those reviewed by Krabbendam in 1961, all dealing with some kind of corrugation, between 900 and 1000! Thus, more than 1500 papers on rail corrugation may be in the world. The classification which was presented by Grassie and Kalousek in 1993, based on the authors’ experience, is helpful for future investigations. For five out of six categories of it, not only characteristics, but also causes and even treatments of them are identified in it. To their opinion for the sixth category (roaring rail type corrugation), a wavelength-fixing mechanism yet had to be pursued. From the interpretation in Section 5.4, it is evident, that there is a “contact filter”, which only allows corrugations to grow in a wavelength range between 2 and 8–10 cm. “Booted-sleeper” type corrugation and “pinned–pinned-mode” type corrugation are probably only two possible types. The existence of a pinned–pinned-mode type corrugation is confirmed by an investigation of Hiensch et al. [65]. This paper, however, also indicates, that the problem is not solved at all. It could not be explained, why on the same line under the same nominal loading significant differences in corrugation growth were observed. Only the rail material seemed to be different. Improved material and wear models are therefore necessary. Probably the wear as damage mechanism alone is not sufficient to explain why some rails develop corrugation faster than others. Further, the development of friction modifier changing the friction characteristic between wheel-tread and rail from
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negative to positive and applied to the Vancouver Skytrain is noticed. In recent study in Japan, Suda et al. began the theoretical and experimental study on rail corrugation in 1986 and presented it internationally in 1988 [39]. It depends on the stability of the system in Fig. 1. Continuing the study, a corrugation simulator was developed [48]. From 1993, Matsumoto and his colleagues started the study on corrugation on sharp curve in order to prevent the corrugation generated mainly on linear-motor-driven subway. Matsumoto, Suda, Ishida and Sumi joined in the research project in The JSA, and carried out full-scale stand tests, model stand tests, train running tests, field researches and numerical simulations and successfully investigated the formation mechanism and countermeasures of corrugation produced on low rail of sharp curved track [60]. According to the conclusion by Matsumoto, such type of rail corrugation is formed by stick-slip vibration between wheel and rail, which is caused by large creepages (longitudinal or lateral) and vertical force fluctuation on wheel/rail contact surface [55–57]. The output of these studies reflected to other groups, such as RTRI, JR east, etc. because this type of corrugation is the most typical in Japanese railway except Shinkansen where the corrugation has not nearly been noticed so far. The rail corrugations appeared in Japan in recent years are mostly divided into three types: (1) on low rail of sharp curves with short-pitch, (2) on tangent or on slack curve with short-pitch, and (3) on high rail on sharp curve with intermediate wavelength. First one is the major type in Japanese railway described earlier and may be in the third category in Grassie–Kalousek classification. Second one is probably in the sixth category and is accelerated by the speed-up of trains. And the last one is in the first category in the same and appeared by the introduction of tilt trains on sharp curve with much insufficient cant for these trains. The studies on type (1) are advanced in Japan as in chapter 6 in recent years, those on (3) are fairly well known, but those on type (2) did not yet got a convincing explanation as mentioned previously. Authors are grateful for the sincere advices of editor and referees for their cordial propositions. References [1] Bibliography on Corrugation of Rails, Research Deptartment Library, Derby, 1954, 1961, 1977. [2] M. Birmann, Schienenriffeln, ihre Erforschung und Verhütung, Neueres aus der Riffelforschung der Deutschen Bundesbahn, Teil I. Schwingungsuntersuchungen, Teil II. Werkstoffuntersuchungen (English title: Rail Corrugation, Research and Preventive Measures: new results from corrugation research at DB, Part I. Vibrational Investigations, Part II. Material investigations), VDI Z. 26 (1958.9) and 30 (1958.10). [3] Y. Satoh, Study on Rail Corrugation, Tetsudo Senro 9–4 (5) (1961) (in Japanese). [4] N.C. Vogan, Question 9, Experience Obtained Concerning the Undulatory Wear of Rails, Monthly Bulletin of the International Railway Congress Association, Bulletin of IRCA (1958.5).
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