Detection of early squats
by axle box acceleration
Detection of early squats
by axle box acceleration
Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op woensdag 9 january 2013 om 12:30 uur door MARIA MOLODOVA Master of Mechanics, Lobachevsky State University of Nizhny Novgorod, Russia geboren te Nizhny Novgorod, RussiaCopromotor Dr.ir. Z.Li Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. dr.ir. R.P.B.J. Dollevoet, Technische Universiteit Delft, promotor Dr.ir. Z.Li, Technische Universiteit Delft, copromotor Prof.dr.ir. J.G. Rots, Technische Universiteit Delft Prof.dr.ir. B. De Schutter, Technische Universiteit Delft Prof.ir. A.Q.C. van der Horst, Technische Universiteit Delft Ir. T. Sysling, ProRail Prof. N. Bowring, Manchester Metropolitan University Prof. Dr. Ir. L.J. Sluys, Technische Universiteit Delft, reservelid Published and distributed by: Maria Molodova Email: m.molodova@gmail.com Road and Railway Engineering Section Faculty of Civil Engineering and Geosciences Delft University of Technology P.O. Box 5048 2600 GA Delft The Netherlands ISBN 978‐94‐6203‐273‐6 Cover design: Maria Molodova Printing: Wohrmann Print Service, Zutphen, the Netherlands Copyright: © 2012 Maria Molodova All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the proprietor.
I dedicate this dissertation to my parents, Yulia and Vladimir
Acknowledgments
After I have accomplished my PhD research in the Road and Railway Engineering group of the Delft University of Technology (TU Delft) I would like to thank everyone who has been helping me for all this time.
I would like to thank my daily supervisor and co‐promoter, associate professor Zili Li, who gave me the opportunity to come to Delft and guided me through all stages of my PhD. My research benefited a lot from his experience in railway engineering, his critical reviews and valuable suggestions.
I am grateful to my promoter, Professor Rolf Dollevoet, for his cooperation during my research project. I would also like to express my gratitude to Professor André Molenaar, who was my promoter for several years, for sharing with me his academic experience. I am also grateful to Professor Coenraad Esveld for supervising me during the first year of my PhD study.
I would like to acknowledge Ton Weel, Roland Bongenaar, Gert Jansen from Eurailscout; Hans van der Vecht from Cauberg‐Huygen Raadgevende Ingenieurs BV; Robbie Klein Wolterink from Klein Wolterink Automation; and Jan Moraal from TU Delft for their cooperation in collecting the axle box acceleration data for this research.
My special thanks go to Xin Zhao for our insightful discussions on squats and finite element modelling. I would also like to thank Nico Burgelman for translating the summary of this thesis into Dutch.
I am very grateful to the secretary of Road and Railway Engineering group of TU Delft, Jacqueline Barnhoorn for her daily assistance in various issues. I am also grateful to the former secretary Sonja van den Bos and former manager Abdol Miradi.
I would like to thank my colleagues, Valéry, Maider, Nico, Milliyon, Xin, Mingliang, Mohamad, Chang, Mauricio, Shaoguang, and my officemates Pengpeng and Gang, who made my work at TU Delft pleasant. My special gratitude goes to my former colleagues Ivan Shevtsov and Maryam Miradi for their generous support during my first year in the Netherlands.
I owe deep gratitude to my friend Ilia Korjoukov for encouraging me, giving me the inspiration, sharing his ideas on my research and even correcting this manuscript. Without his support I would never have reached this.
I would like to express my sincere gratitude to my parents, Yulia and Vladimir, who encouraged me to follow my PhD study and supported me through all the years I spent in the Netherlands. To them I dedicate this thesis.
Summary
This thesis discusses a new method for detection of short track irregularities, particularly squats, with axle box acceleration (ABA) measurements.
A squat is a surface initiated short track defect, associated with high frequency vibrations of the wheel‐rail system. High stresses in the contact patch at squats cause accumulation of plastic deformation of the rail and growth of cracks. Cracks growing in the subsurface can cause a rail fracture. Light squats can be treated by grinding of the rail surface; while mature squats lead to replacement of the rail section. For cost effective maintenance policy and operational safety squats should be detected at an early stage. Detection of light squats is the main aim of this study.
Till now, ultrasonic measurements have been mainly used for detection of squats. By that method the depth of cracks is measured; hence, it is applicable only to detection of severe squats with sufficiently large cracks. In the present work, ABA measurements were employed. The advantages associated with this method are that ABA measurements can be performed on standard operating vehicles travelling with usual traffic speeds and squats can be detected at their early stage. The first goal of this study was to find a relationship between squats and ABA characteristics, such as magnitude and frequency content, and apply them for detection of squats. To this end, a three‐dimensional finite element (FE) model was applied for dynamic simulations of the wheel‐track interaction in the high frequency range. By parameter variation, the influence of the geometry of squats, speed of the train and location of the squats relative to the sleepers on ABA characteristics was studied. Local frequency characteristics of ABA at squats were obtained and their relation with the severity of squats was established. These frequency characteristics can be applied for detection of squats and their assessment.
The second goal was to improve the signal‐to‐noise ratio of ABA measurements to enable detection of light squats. Several methods to improve signal‐to‐noise ratio of ABA measurements were suggested. These included noise reduction techniques, reduction of disturbances from the wheel defects and signal enhancement by improvement of the measuring system by using longitudinal ABA. Owing to the improvement of the signal‐to‐ noise ratio, the hit rate of moderate squats increased from 60% to 100% and the hit rate of light squats together with trivial defects1 increased from 57% to 85%. Since light squats are 1 Trivial defects are small rail surface defects which are so small that they will be worn away, and will therefore not grow into squats.
larger than trivial defects and, therefore, easier to detect, the hit rate of light squats, which depends on the threshold that separates light squats from trivial defects, is higher.
The third goal was to develop an algorithm for automatic detection of squats, which enables continuous analysis of track. The initial results indicated that 78% of light squats and trivial defects can be detected automatically by ABA. The hit rate of severe squats was 100%.
The presented ABA method enables automatic detection of squats at their earliest stage, when preventive and early corrective actions can be taken. The employment of such method can significantly reduce life cycle costs of a track infected by squats.
Samenvatting
Deze thesis behandeld een nieuwe methode voor de detectie van kleine oneffenheden op de spoorstaaf, in het bijzonder squats, met behulp van metingen van de aspotversnellingen (Axle Box Accelerations, ABA).
Een squat is een gebrek aan de spoorstaaf dat ontstaat in het spoorstaafoppervlak, het wordt gelinkt met hoogfrequente trillingen in het wiel/spoor systeem. De hoge spanningen in het contactoppervlak tussen wiel en spoorstaaf ter hoogte van de squats, veroorzaken een accumulatie van plastische vervorming en scheurgroei in de spoorstaaf. Lichte squats kunnen weggewerkt worden door het spoorstaafoppervlak te slijpen, bij volgroeide squats moet een stuk spoorstaaf vervangen worden. Om een kostenefficiënte politiek te voeren en de operationele veiligheid te garanderen moeten squats op tijd gedetecteerd worden. De detectie van lichte squats is het belangrijkste doel van deze studie.
Tot nog toe werden vooral ultrasone metingen gebruikt voor de detectie van squats. Die methode meet de diepte van de scheuren, daarom is deze methode alleen geschikt voor volgroeide squats die voldoende grote scheuren bevatten. In deze studie worden ABA metingen gebruikt. Het voordeel is dat de ABA kunnen gemeten worden op gewone diensttreinen aan normale snelheid, zo kunnen squats gedetecteerd worden hun een vroeg stadium.
De eerste stap was om een relatie te vinden tussen de squats en de gemeten ABA karakteristieken, zoals amplitude en frequentie‐inhoud, deze relatie kan dan aangewend worden voor de detectie van squats. Hiervoor werd een driedimensionaal eindige elementen (Finite Elements, FE) model ontwikkeld, dat kan gebruikt worden om de interactie tussen wiel en spoorstaaf te simuleren in het hoogfrequente gebied. De invloed op de ABA karakteristieken van de geometrie van de squats, de snelheid van de trein en de positie van de squats ten opzichte van de dwarsliggers, werd bestudeerd. De lokale karakteristieken van de ABA rond de squats werden gerelateerd aan de ernst van de squats. Deze frequentiekarakteristieken kunnen dan aangewend worden om squats te detecteren en hun ernst te bepalen.
De tweede stap was om de signaal‐ruisverhouding van het ABA signaal te verbeteren zodat ook lichte squats gedetecteerd kunnen worden. Er werden verschillende methodes gesuggereerd om de signaal‐ruis verhouding te verbeteren: ruisreductie technieken, reductie van storingen door wielgebreken, verbetering van het meetsysteem en signaal opwaardering door het gebruik van longitudinale ABA. Door deze verbeteringen in de signaal‐ruisverhouding is het percentage middelmatige squats dat gedetecteerd kan worden
gestegen van 60 tot 100%. Het trefpercentage voor lichte squats samen met onschuldige gebreken1 is gestegen van 57 tot 85%. Lichte squats zijn groter dan onschuldige gebreken en daardoor gemakkelijker te detecteren, daarom is het trefpercentage voor lichte squats hoger. Dit trefpercentage is afhankelijk van de drempel die gehanteerd wordt om licht squats van onschuldige gebreken te onderscheiden.
De derde stap was een algoritme te ontwikkelen dat die automatische detectie van squats mogelijk maakt, dat maakt doorlopende analyse van het spoor mogelijk. De eerste resultaten wijzen erop dat 78% van de lichte squats en onschuldige gebreken automatisch kunnen opgespoord worden. Het trefpercentage voor zware squats is 100%. De gepresenteerde methode laat toe squats te detecteren in hun vroegste stadium, op tijd om preventieve en correctieve maatregelen te nemen. De toepassing van deze methode kan totale levenskosten van een spoor met squats significant verlagen. 1 Onschuldige gebreken zijn gebreken op het spoorstaafoppervlak, die zo klein zijn dat ze zullen wegslijten en dus niet tot squats zullen uitgroeien
Abbreviations
ABA axle box acceleration RCF rolling contact fatigue FE finite element 3D three‐dimensional STFT short time Fourier transform CWT continuous Fourier transform PSD power spectral density WPS wavelet power spectrum SAWP scale averaged wavelet power RMS root mean square error
Table of contents
ACKNOWLEDGMENTS ...I SUMMARY ... III SAMENVATTING ... V ABBREVIATIONS ... VII 1. INTRODUCTION ... 1 1.1. Track defects ... 1 1.2. Squats ... 2 1.2.1. Characteristics of squats ... 2 1.2.2. Historical background ... 3 1.2.3. Initiation of squats ... 4 1.2.4. Growth of squats ... 5 1.3. Detection and assessment of short track irregularities ... 6 1.3.1. Feasibility of track inspection methods for early detection of squats... 6 1.3.2. Novelty of the current research ... 8 1.3.2.1 Periodic or isolated defects ... 8 1.3.2.2 Frequency range ... 8 1.3.2.3 Local characteristics of short irregularities ... 10 1.4. Research approach ... 10 1.5. Chapter outline ... 12 2. FEASIBILITY STUDY OF ABA MEASUREMENTS FOR EARLY DETECTION OF SQUATS 13 2.1. Introduction ... 13 2.2. Trial measurements ... 13 2.2.1. Instrumentation setup ... 13 2.2.2. Track defects ... 14 2.2.2.1 IRIS ... 14 2.2.2.2 Monitoring ... 142.2.3. Measurements in Zuid Holland ... 16 2.2.4. Measurements in Weert ... 17 2.3. Detection of squats ... 17 2.4. Relation between ABA and size of a squat ... 19 2.5. Time‐frequency techniques ... 20 2.6. Conclusions ... 22 3. FE MODELLING OF ABA AND VALIDATION ... 24 3.1. Introduction ... 24 3.2. FE model ... 25 3.2.1. Geometry... 25 3.2.2. Solution procedure ... 27 3.2.3. Length of the modelled track ... 28 3.3. Simulation of a rail surface defect with uniform lateral profile ... 28 3.3.1. Artificial defect ... 28 3.3.2. Dependence of ABA on vertical‐longitudinal profile of defect ... 30 3.3.3. Comparison with measured ABA ... 31 3.3.4. Frequency content of ABA at the defect ... 33 3.4. Simulation of a class C squat ... 35 3.4.1. Geometry of a squat ... 35 3.4.2. Comparison with measured ABA ... 36 3.4.3. Influence of the vertical‐longitudinal profile of the squat to ABA ... 37 3.4.4. Frequency content of ABA at the squat ... 39 3.5. Conclusions ... 41 4. SIGNATURE TUNES OF SQUATS ... 43 4.1. Introduction ... 43 4.2. Variation of defect’s geometry ... 43 4.2.1. Modelling of defects ... 43 4.2.2. ABA at varied geometry of short track defects ... 46
4.2.3. PSD of ABA at a range of defect sizes ... 48 4.3. Variation of train speed ... 50 4.3.1. Geometry of the modelled defect ... 50 4.3.2. ABA with varied speed ... 51 4.3.2.3 ABA wavelength ... 51 4.3.2.4 ABA magnitude ... 52 4.3.3. PSD of ABA with varied speed ... 53 4.4. Variation of location of a squat ... 53 4.5. Track parameters ... 56 4.5.1. Frequency response function of the track ... 56 4.5.1.1 FE model ... 56 4.5.1.2 Classification of the track vibration modes ... 57 4.5.1.3 Modes of vibrations ... 58 4.5.1.4 Validation of the frequency response function ... 60 4.5.2. Relation between signature tunes of squats and track parameters... 61 4.6. Conclusions ... 62 5. ASSESSMENT OF SEVERITY OF SQUATS BY ABA ... 64 5.1. Introduction ... 64 5.2. Regression analysis ... 64 5.3. Data ... 65 5.4. Relation between the squat and ABA magnitude ... 67 5.4.1. Defects with battered edges ... 67 5.4.2. All defects ... 69 5.4.3. Reduced model... 70 5.5. Relation between the squat and the power spectrum of ABA ... 71 5.5.1. Defects with battered edges ... 72 5.5.2. All defects ... 72 5.6. Validation of the Regression Models ... 74 5.6.1. Validation of relation between ABA magnitude and squats ... 75
5.6.2. Validation of relation between PSD300Hz and squats ... 77 5.7. Conclusions ... 78 6. IMPROVEMENTS OF THE ABA MEASURING SYSTEM ... 79 6.1. Introduction ... 79 6.2. Wheel vibrations ... 79 6.2.1. Modes of vibration of the wheel ... 79 6.2.2. Transfer function ... 81 6.3. ABA measurements with improved instrumentation ... 83 6.4. Improvement of signal processing of ABA ... 84 6.4.1. Noise reduction ... 84 6.4.2. Effect of noise reduction on the detection of light squats ... 85 6.4.3. Reduction of the influence of wheels’ defect on ABA ... 87 6.5. Hit rate of light squats ... 90 6.6. Conclusions ... 90 7. AUTOMATIC DETECTION OF SQUATS ... 91 7.1. Introduction ... 91 7.2. Validation of signature tunes of squats ... 91 7.2.1. Small rail surface defects ... 91 7.2.2. Light squats ... 92 7.2.3. Moderate and severe squats ... 93 7.3. Signature tunes of other short track irregularities ... 95 7.3.1. Insulated joints ... 95 7.3.2. Thermite welds ... 96 7.4. Automatic detection ... 97 7.4.1. Scale averaged wavelet power ... 97 7.4.2. Evaluation of prediction ... 98 7.4.3. Detection procedure ... 98 7.4.4. Prediction ... 101
7.4.4.1 Detection of light squats ... 101 7.4.4.2 Severe squats ... 102 7.5. Conclusions ... 104 8. CONCLUSIONS AND RECOMMENDATIONS ... 105 8.1. Conclusions ... 105 8.1.1. Frequency characteristics of squats ... 105 8.1.2. Assessment of severity of squats ... 105 8.1.3. Speed dependency ... 106 8.1.4. Wheel state ... 106 8.1.5. Track parameters ... 106 8.1.6. Improvement of signal‐to‐noise ratio ... 107 8.1.6.1 Instrumentation ... 107 8.1.6.2 Signal processing ... 107 8.1.7. Automatic detection of squats ... 107 8.2. Recommendations ... 108 9. REFERENCES ... 109 CURRICULUM VITAE ... 116 RELEVANT PUBLICATIONS ... 117
1. I
NTRODUCTIONCondition monitoring of the railway track is very important for timely maintenance. Therefore, many methods for detection of track irregularities have been developed. The objective of this research is to investigate the possibility of early and automatic detection of local isolated short track irregularities. The study is focused on detection of squats. This chapter reviews the main studies on squats that have been made so far. Then, an overview of methods for detection and assessment of short track irregularities is made.
1.1. TRACK DEFECTS
In recent years railways have experienced significant changes in the vehicle‐track interaction, caused by the increase in axle load and operational speed. The consequences of these changes are higher stresses at the wheel‐rail interface. The situation is aggravated by track irregularities.
Track irregularities associated with low frequency vibrations may cause discomfort to passengers and damages to cargo. Such irregularities, which normally have a length longer than 3 meters are often called long track irregularities. Examples of long track irregularities include poor track alignments, switches, level crossings and bridges.
Track irregularities shorter than about 3 m are often referred to as short track irregularities. Examples of short track irregularities include squats, corrugation, thermite welds with poor finishing quality, insulated joints, blades and frogs of switches and crossings (Figure 1.1). They can cause large dynamic contact forces and wheel‐rail vibrations in the mid‐ and high frequency ranges. According to [1] the mid‐frequency range is 40‐400 Hz and the high frequency range is 400‐2000 Hz or even higher.
Short track irregularities are detrimental to the wheel‐rail interface and the track infrastructure due to the impacting nature of the interaction. Excessive contact forces cause increase of stresses in the contact patch and accumulation of plastic deformation of the rail. Moreover, they lead to initiation and propagation of cracks, damages in the track infrastructure such as fastening and sleepers, fast deterioration of the track and rolling noise emission. Deterioration of the track influences the operational safety, since the growth of cracks, if not controlled, may cause rail fracture.
When damage of the rail exceeds a certain value, the rail should be replaced, which involves high maintenance costs and reduces the availability of the network. However, if damage is detected at a proper time, low cost preventive maintenance actions, like grinding of the rail,
may be taken. Hence, measurements which are appropriate for diagnosis of the track technical state are needed. (a) – Squat (b) – Corrugation (c) – Insulated joint (d) – Two squats initiated at a thermite weld Figure 1.1 Short track irregularities. 1.2. SQUATS A squat is one of the most dangerous short track irregularities. At an early stage squats can be treated by grinding of a thin layer from the rail surface. At the late stage squats always lead to rail replacement. If not treated in time, the cracks may grow in the subsurface and cause rail break. Therefore, for cost effective maintenance policy squats should be detected at an early stage. Early detection of squats is the focus of this study. 1.2.1. Characteristics of squats Squats are generally considered as surface initiated defects [2]. Squats can be classified as being light, moderate and severe, or class A, B, and C correspondingly [3], see Figure 1.2. Light squats are also called early squats, initiating squats, or squats seeds.
A severe squat is normally characterized by localized depression of the contact surface of the rail head that can have a shape of two lungs, accompanied by a dark spot with V, U, Y or circular shaped cracks [4]. It is believed that the cracks are initiated in the surface [4]. These cracks propagate inside the rail head at a shallow angle to the surface, and grow till about 3– 6 mm deep in the subsurface, before they branch downward transversely [5]. Another characteristic is widening of the running band, as a result of plastic deformation caused by the impact wheel‐rail interaction.
At the light stage squats usually do not bear these characteristics that are typical of moderate and severe squats. At the last stage the lung shape might become less obvious, but the nearly circular boundary due to the widening of the running band can still be seen [4]. The cracks may become more visible in the surface.
(a) – Light (b) – Moderate (c) – Severe Figure 1.2 Squats: class A – light, class B – moderate, and class C – severe.
1.2.2. Historical background
A squat is a type of rolling contact fatigue (RCF) damage. It was first reported in Japan in the 1950s [4],[6]. In the 1970s squats became known in the UK [7]. In France they were reported in the early eighties [8].
To understand the squats’ phenomena, research on squats has been carried out over the past decades in several countries. In Japan, Masumoto et al. [9] attempted to reproduce squats through RCF tests. The test setup consisted of two discs rotating in the opposite direction. Slipping on the contact surfaces was generated by a difference in circumferential speed. A normal load was applied to represent the wheel load. The resulting defects (squats and head checks) were similar to those found on the running surface. The defects initiated on the contact surface; for their initiation tangential component of the load was necessary in addition to the normal load. The effect of microstructure of rail steels on the initiation and propagation of cracks was also investigated.
Kondo et al. [5] discussed hypotheses for causes of the Shinkansen rail surface shelling, which was similar to squats. They mentioned the following causes of such phenomenon: dents due to entrapped solids between wheel and rail, deformation of the rail top due to rolling of the wheels, high dynamic load from wheel flats and increased wheel torque. The formation and growth of the cracks was also considered.
Ishida et al. [10] studied the effect of preventive grinding on reduction of the number of squats. The study combined theoretical modelling, laboratory experiments with twin disc machine and field tests. They observed that the number of squats was decreasing as a result of grinding. class A Wave pattern class B Cracks class C Crack Wave pattern
In the UK, Clayton and Hill [11] investigated RCF behaviour under water‐lubricated condition through a laboratory test. The results of the test showed plastic deformation on the surface and surface‐initiated cracks in the specimen, similar to the ones at squats. Bold et al. [12] studied the surface‐initiated cracks growing at a shallow angle to the surface which appear at squats. The loading, experienced by RCF cracks and the growth rate of the cracks were calculated.
Cannon and Pradier [13] presented a review of an RCF research program of the European Rail Research Institute started in 1987. The purpose of the program was to understand the RCF problem and develop means to control or eliminate it. The program involved theoretical analyses, laboratory and field tests. The authors indicated factors significant for RCF, such as: head hardened rails showed improved fatigue resistance, while lubrication of the rails encouraged the development of cracks.
Bogdanski et al. in [14] introduced 2D modelling of a squat‐type crack, where the influence of crack inclination angle, residual stresses, traction load and the liquid trapped in the crack were studied. In [15] Bogdanski et al. presented a 3D finite element model of a squat‐type crack. The stress state in the vicinity of the crack front was determined and the values and ranges of the stress intensity factors at the crack front were calculated. In his later paper Bogdanski et al. [16] studied the liquid entrapment mechanism for a squat‐type crack through 3D finite element modelling.
Squats are also an important RCF problem for the Dutch Railways (ProRail) [3], [17]. Therefore, ProRail have launched a project which aimed at the causes of squats, their initiation and early detection. Some results of the study on squats that have been reported by Li et al. in [4], [17], [18], and [19] are summarized below. 1.2.3. Initiation of squats Squats mainly occur on tangent tracks, shallow curves, at switches and crossings. They may appear as individual isolated defects or as closely spaced multiple defects. Multiple defects are more dangerous, because multiple rail fractures may occur, causing significant gaps in a rail.
A squat may initiate at any geometrical deviation which can cause sufficiently large stress and strain, resulting in localized deformation [17], [20]. Indentation by hard objects in the wheel–rail contact is one of the sources of squat’s initiation [3], [4], [5], [17]. The indentations can be caused by ballast stones [5]. Indentations may also be caused by other hard objects, such as balls from roller bearings or from aerosol paint [4], indented in wheels
and brought forward. In this case multiple indentations with a periodicity equal to the wheel’s circumference (about 3 m) can often be observed.
Another source of initiation of squats is differential wear and differential plastic deformation [17], [19]. Normally, both wear and plastic deformation are uniform along the rails. However, if large contact forces are excited at a certain place at each wheel passage, differential wear and/or deformation will occur at that place. Such wear and deformation, when it is accumulated to certain amount, may become a source of squat’s initiation. Sometimes short wave defects in rail, rail pads, fastening, and sleepers may excite the large dynamic contact force that is necessary for squat’s initiation and growth, repeatedly at the same location so that differential wear and plastic deformation occur.
Short pitch corrugation is the consequence of periodic differential wear or plastic deformation which is related to the occurrence of squats. In [4] it was reported that 33% of squats initiated from the corrugation and another 41% had corrugation‐like wave pattern after them. That suggests that development of corrugation and squats may be related to the same local natural characteristics of the track. A corrugation‐related squat is counted as a squat only when a locally dented rail surface is observed.
Thermite welds and flash butt welds often have differential wear and deformation, due to material inhomogeneity at the heat affected zone. Figure 1.1(d) shows two squats initiated at a thermite weld. Spin and sliding damages by wheels during traction and braking is a frequent initiation source of squats [4]. Some wheel slide protection systems allow large wheel slip accompanied by large tangential contact force. Hence, they may promote squat initiation and growth.
Rail surface defects which were not removed completely by grinding (like previous squats or head checks) may also cause squats.
It has been mentioned above that severe squats are characterized by cracks. However, initiating squats are usually free from cracks, since indentations, corrugation, welds, differential wear and differential plastic deformation usually do not contain cracks.
1.2.4. Growth of squats
Observations of rail surface defects have shown that not all of them can grow into squats [18]. According to [2], rail surface defects can be divided by their mechanisms of initiation and growth into two categories: the passive and the active types. The active type, like corrugation, differential wear and differential deformation, are self‐initiated. The passive type, like the ones caused by wheel slip or indentations, can be smoothed out by wear and/or plastic deformation, if they are small enough.
If the size of a rail surface defect exceeds a critical size, it may grow into a squat. In [18] the critical size has been found to be 6–8 mm for both the rolling and the transverse directions in the case the traction and braking efforts are maximal for the Dutch railways. The rail surface defects that exceed the critical size are considered in this thesis as light squats. Defects those are below this threshold are considered as trivial. In [17] a squats’ growth process has been postulated based on numerical simulation of a rail surface defect without cracks. The postulation has been validated in [4]. A small rail surface defect (like the one in Figure 1.2(a)) excites a dynamic contact force of a certain wavelength with a series of peaks. These contact force peaks are repeated at every wheel passage at the same location, causing localized differential wear and differential plastic deformation. After many wheel passages, the deformation caused by the contact force peaks forms the specific lung‐like shape of a mature squat and the wave pattern that follows it (see Figure 1.2(c)). 1.3. DETECTION AND ASSESSMENT OF SHORT TRACK IRREGULARITIES
Current methods for track inspection may be divided into several groups: ultrasonic and eddy current measurements, visual methods, strain gauge instrumented wheelsets and accelerometer‐based methods. Feasibility of these methods for early detection of squats is discussed below.
1.3.1. Feasibility of track inspection methods for early detection of squats
Ultrasonic test vehicles for inspection of a railway track were introduced in Germany about 50 years ago [21]. Kondo et al. [5] reported that ultrasonic measurements and visual inspection for detection of the shelling, which is similar to squats, had been performed in Japan since 1971. However, ultrasonic measurements may be applied only for detection of squats with cracks, which mainly appear at the late stage of squat and it is reliable only when the cracks are deeper than 5 mm. Therefore, this method is inappropriate for early detection of squats. Visual inspections are subjective to the experience of the inspectors. Besides, they are unsafe for the inspectors and are labour intensive. Thomas et al. [21] discussed a combination of ultrasonic and eddy current measurements for track inspection. It was reported that such combination can improve detection and classification of welds, rail joints, and head checks, compared to results of only one test method. However, the authors admitted that determination of depth of squats was problematic with both inspection techniques.
Strain gauge instrumented wheelsets can be used for measurements of vertical, longitudinal and lateral forces. Magel et al. [22] utilized instrumented wheelsets to evaluate adhesion, peak curving tractions, wheel climb index and RCF damage. The standard method of
measuring wheel‐rail contact forces by instrumented wheelsets includes frequencies up to 90 Hz [23]. However, detection of squats requires higher frequency signals to be measured and analysed [17]. Gullers et al. [23] and Nielsen [24] discussed a method to measure the high‐frequency contents (up to 2 kHz) of the contact force using instrumented wheelsets. A new method of signal processing including suppression of disturbing wheel resonances was introduced. The method showed a correlation between high values of the contact forces and several types of track irregularities, such as bad rail joints, indentations from damaged wheel, corrugations, and stiff rail pads. Although an instrumented wheelset is capable to measure wheel‐rail contact forces, it might be sensitive to damage of the wheel tread; it is also an expensive tool which is not available to most researchers and daily operation of infra managers.
Berry et al. [25] presented an image‐based visual inspection system that can detect the cracks in fishplates of rail joints. This system was developed and tested to capture high quality digital video images of fishplates from a moving vehicle. A similar system can also be applied to inspection of the rail surface. However, it can be difficult in distinguishing between squats and contaminations; further, an image does not reflect the dynamic wheel‐ rail interaction, therefore, it cannot predict the growth rate of squats.
Delprete and Rosso [26] developed a transducer for measuring vertical, lateral and longitudinal contact forces. Since the transducer is installed on the rail web, by this method only the local forces can be measured. This method, as well as other wayside measurements, is not applicable for continuous monitoring along the track.
Grassie [27] introduced a trolley profilometer to measure the vertical‐longitudinal profile of the rail at short pitch corrugation. The profile was measured using an accelerometer mounted in a resilient suspension relative to the trolley at a speed of about 0.7 m/s. Double integration was used to get vertical‐longitudinal profile of the rail. In [28] Grassie concluded that the advantage of the axle box acceleration (ABA) measuring technique compared to other methods of measurement of railhead vertical‐longitudinal profile is the ability to measure the irregularities of the rail at line speeds.
Since accelerometer‐based methods are feasible for measuring the rail irregularities, and besides, have the advantages of being simple and cheap compared to most of other methods, further literature study was made on such methods, which is presented below.
1.3.2. Novelty of the current research 1.3.2.1 Periodic or isolated defects Lewis [29] ‐ [30] presented an inertial measuring system for monitoring of track quality from standard track inspection vehicles at high speed, which had been in use on British Rail since 1982. The system included accelerometers, rate gyroscopes and displacement transducers. Double integration of acceleration was used to calculate the vertical profile of the running surface. In [29] the wavelength range of measured track irregularities was from 0.5 to 50 m. In [30] a method of determining short wave (50‐80 mm) rail head corrugations based on the processing of ABA was described. Bocciolone et al. [31] discussed a track maintenance strategy using ABA measurements. The paper was focused on short‐pitch corrugation. The study showed correlation between ABA and corrugation level. Caprioli et al. [32] analysed the possibilities of the wavelet techniques for detection of short pitch corrugation from axle box acceleration.
Matsumoto et al. [33] developed a portable on‐board detection system for passenger service vehicles to enable detection of rail corrugation on a commercial line. They proposed two methods to detect corrugation: by wavelet‐based multi‐resolution analysis of the measured acceleration on the cabin floor; and by the spectra which were obtained by using a windowed Fourier transform of cabin noise data, recorded with a microphone. They concluded that both methods were able to detect the occurrences of rail corrugation at early stage. Tsunashima and Mori [34] summarized the development of this system.
Remennikov and Kaewunruen [35] discussed the application of ABA to estimation of the contact forces at both corrugation and wheel flats.
All the papers discussed above were focused on detection of defects that produce a periodically repeated dynamic interaction between wheel and rail, such as corrugation and wheel flats. These defects excite vibrations with a certain frequency over a long track section, which facilitate their detection. In contrast, the present study discusses detection and assessment of local isolated short track defects. Their major difference from periodic defects is that the wheel‐rail response at isolated defects has short duration and unpredictable occurrence.
1.3.2.2 Frequency range
Kawasaki and Youcef‐Toumi [36] proposed a method to estimate rail irregularities by measuring passenger car accelerations. Using data obtained by simulations based on a three‐dimensional rail vehicle model with rail irregularities, the inverse problem was solved,
where inputs are accelerations of a vehicle and outputs are rail irregularities. The frequencies considered were up to 70 rad/sec, which is approximately 11Hz.
Reicke and Popp [37] proposed the identification of the running‐state of the wheelset by ABA in longitudinal, transversal and vertical direction. The transient behaviour of structural vibrations of the wheelset was analysed by time‐frequency transforms. The considered frequency range was up to 200 Hz.
Tanaka and Furukawa [38] analysed the relation between the wheel load and the vertical ABA in the frequency range up to 100Hz. Wheel loads were measured by strain gauges attached on the wheel. It was assumed that the large value of the wheel load included an impact component and a quasi‐static component. The quasi‐static components of axle box acceleration and the wheel load were eliminated by applying high pass filter; only variable impact components were analysed. Based on the result of regression analysis, it was found that the relation between the maximum values of wheel load and vertical axle box acceleration could be expressed by linear equation.
Sunaga et al. [39] proposed to use ABA to evaluate wheel load fluctuation at short track irregularities for a cut‐off frequency of up to 300 Hz, to maintain good quality of Shinkansen track. He discussed the possibility to detect welds, corrugations of wavelength between 1.2 and 1.5 m, as well as loose sleepers by axle box acceleration. The method showed good correlation between ABA and dynamic wheel load in the frequency range from 10 to 80 Hz. To distinguish the rail defects from loose sleepers an adaptive filter process was used for analysis of the frequency range of axle box acceleration. Consequently, track maintenance actions were selected with either a rail grinding or ballast tamping.
Real et al. [40] presented a new inertial method to obtain rail vertical‐longitudinal profile by ABA measurements in the frequency range up to 250 Hz. The paper was focused on long rail irregularities. The method was based on a model representing the interaction between the train and the track. The model used the Fourier transform in order to find the transfer function that relates the axles’ vertical displacement to the vertical rail profile and the bogie’s vertical movement. The solution was obtained in the frequency domain and then reverted back into the time domain by applying the inverse Fourier transform. The procedure was employed in order to determine, by measuring accelerations, whether the track has to be maintained or not.
In the papers mentioned above the considered frequency range was below 300 Hz. In a recent study [17] it has been found, that squats are related to the frequency components up to 2 kHz or even higher. The present study therefore investigates the high frequency characteristics of ABA at local isolated short track defects.
1.3.2.3 Local characteristics of short irregularities
Elia et al. [41] presented a research program for condition monitoring of the railway track from standard operation vehicle. One of the points of this research program was detection of long wavelength irregularities by accelerations measured from car bodies, bogies and axle boxes.
Xia et al. [42] used axle box acceleration measurements to study the dynamic response of railway bridges under train loads. The paper was focused on long wave irregularities. The dynamic interaction on railway bridges was simulated to design bridge reinforcement. The axle box acceleration was obtained from the train running at different speeds between 40 and 155 km/h, and integrated twice to calculate the displacement responses. Random excitations were generated by a time series autoregressive model from experimentally obtained displacement. The generated random excitations were used in simulations train running on the bridge.
Dings et al. [43] presented a traffic‐dependent acoustical grinding criterion for the Dutch railway network based on ABA measurements. It was proposed to measure the rail roughness on the entire network, to compare it with the wheel roughness of the trains for each line, and to select the track sections where rail grinding could bring a significant noise reduction. The decisions about grinding were made based on the average roughness for every 25 m track section.
Spanner [44] proposed a new approach of assessing rail roughness, based on signal processing of measured ABA data. The spectrograms, where the rail roughness was presented with both spatial and wavelength resolution, were used to make decisions about grinding. The roughness is assessed for long track sections (≥10m).
The papers mentioned above discuss long track irregularities or roughness characteristics of long track sections, while the present research is focused on local characteristics (length scale is shorter than 1 m) of isolated short track irregularities.
1.4. RESEARCH APPROACH
Based on the literature study presented above, ABA measurements will be employed in this work for early detection of squats. Since the ABA is a measure of the vibrations of the wheel in the vehicle‐track system, excited during the wheel‐rail interaction, it can give an indication of the irregularities at the wheel‐rail interface. There are several advantages associated to this method. Firstly, the presence of cracks is not necessary for detection; therefore, early squats can be detected. Secondly, the method can also give indication of the level of the dynamic contact force. Besides, ABA measurement does not need complicated
instrumentation as accelerometers can easily be mounted on many of the standard operating vehicles. Further, this method may be used for automatic detection of short rail top irregularities.
Some drawbacks of axle box acceleration measuring method have been indicated in [44]. Firstly, the measured ABA signal is influenced by the vibrations of both the track and the wheelset. When the wheel is damaged, the assessment of rail irregularities is affected by vibrations originated from the wheel. It is expected that this problem will be solved by signal processing of the measured data. Since the vibrations excited by a wheel defect have a certain periodicity, it should be possible to distinguish between these vibrations and the ones originated at an isolated track defect. However, the ABA responses at wheel defects have the same periodicity with ABA responses at periodic rail surface defects initiated from a hard object indented into wheel; yet it is expected that they can be distinguished. This question will be further discussed in chapter 6 of this thesis.
Secondly, ABA measurements are speed dependent. To eliminate the influence of the train speed, the measurements should be performed at nearly constant speed, and where not possible, a mapping between ABA measurements and speed is needed. This question will be addressed in chapter 4 of this thesis.
Thirdly, the frequencies of track vibrations are dependent on the stiffness and damping properties of the track. The ABA responses on tracks with different properties can be studied by numerical simulations. Then, the algorithm for detection of squats can be calibrated for each type of track. This question will be investigated in chapter 4 of this thesis.
The primary task of this research is to study relationships between ABA and squats. These relationships can be studied with signal processing of measured ABA and with finite element (FE) simulations. Wavelet technique can be applied for analyses of the measured and calculated ABA responses. The established relationships are then used for development of detection procedure. The following measurement data is available for research: recorded ABA, information about positions and severity of squats in the track and rail profiles at these squats.
The advantage of the FE modelling is the ability to establish quantitative relationships between squats and ABA characteristics under controlled parameter conditions. The influence of track parameters on ABA can be examined by parameter variation study. Although it can also be obtained by track or lab tests and measurements, they are much more expensive and time consuming. The track parameters used in this work are those of the Dutch railways, but the approach is applicable to other tracks.
When the relationships between ABA and squats are established and the influence of track parameters is studied, detection criteria may be introduced. Then, the detection procedure can be validated by track inspection.
1.5. CHAPTER OUTLINE
Feasibility study of ABA for early detection of squats is discussed in chapter 2. A pilot analysis of the relationship between ABA and squats demonstrates the need for improvement of instrumentation and signal processing of ABA in order to gain the capability of detection of light squats.
To obtain a quantitative relationship between ABA characteristics and squats, an FE model of the vehicle‐track system is employed for dynamic simulations of a wheel rolling over a rail with surface geometrical irregularity. Chapter 3 is focused on validation of the FE model against ABA measurements.
In chapter 4 the ABA frequencies related to squats (signature tunes) are identified through FE modelling of ABA at a number of squats of different severity. The influence of varied train speed, varied track parameters and location of a squat on ABA is studied.
The relationships between ABA characteristics such as magnitude and frequency contents and severity of squats are established in chapter 5.
Based on the analysis of ABA measurements, FE simulations and hammer tests, a prototype of the improved ABA system for the detection of light squats is developed in chapter 6. Problems with the instrumentation, revealed by trial measurements are treated. The improvement of instrumentation provides better signal‐to‐noise ratio of ABA measurements which facilitated detection of light squats.
Then, employing the signature tunes obtained by FE modelling and confirmed by field measurements, an automatic detection algorithm for squats is developed and validated in chapter 7.
The main conclusions are summarized in Chapter 8. The necessity of further work is also indicated.
2. F
EASIBILITY STUDY OFABA
MEASUREMENTS FOR EARLY DETECTION OF SQUATS2.1. INTRODUCTION
In the previous chapter a literature overview of different methods of track inspection has been presented. It has been indicated that among others, ABA method is the most appropriate for early detection of squats. In this chapter a feasibility study of ABA measurements for early detection of squats, based on field measurements, is presented. This chapter also discussed advanced signal processing techniques for the analysis of ABA.
2.2. TRIAL MEASUREMENTS 2.2.1. Instrumentation setup
Two trial measurement rounds were performed: in Zuid Holland (at the end of 2005 – beginning 2006), and in Weert (in 2007). The instrumentation setup (see Figure 2.1) was similar for both trial measuring rounds. The accelerometers were mounted on the four axles of a bogie. The mounting position of an accelerometer is shown in Figure 2.2. Each data set included four vertical ABA signals, recorded on the axle boxes of one bogie, GPS coordinates for determining the location of the signals, and the train speed. Figure 2.1 Instrumentation setup
The ABA measurements were repeated three times on the same track. That was made because of several reasons. First of all, to examine the repeatability of ABA at short track irregularities: ABA signals measured at a short track irregularity should have similar response for every measurement within one day. The second reason to repeat the measurements is to increase the probability to detect light squats. The wheel‐rail interaction at a squat is influenced by the lateral geometry of the squat. However, during the several measurement runs a wheel might have travelled along different trajectory on the rail because of the hunting oscillation. This factor becomes even more influential when the size of the squat is
Vehicle Accelerometers
smaller than the width of the rolling band, because not every wheel passage will necessarily run over it. The third reason is to check the accuracy of on‐board GPS positioning: the responses measured at one location should have the same GPS. Figure 2.2 Position of accelerometer. 2.2.2. Track defects 2.2.2.1 IRIS Track geometrical irregularity data are obtained by a measuring train running twice a year over the entire Dutch network and collected in a database called IRISsys [17]. IRIS also contains information about locations of squats, their severities, and photos of the rail tops. Locations of joints, switches, bridges, viaducts, level crossing can be also found there.
In this database, the locations of short track irregularities are identified by the GeoCode* of the track and conventional kilometre position. This conventional kilometre position is also used in this work for positioning of ABA responses and identification of locations of squats.
2.2.2.2 Monitoring
For the current research, the most complete and up to date information about the short track irregularities on the track sections, where the ABA was measured, was necessary. Thus, several tracks (Weert, Assen, Schiedam, and Steenwijk) were regularly monitored since 2007.
The monitoring provided the following data for this research: GPS coordinates measured on the ground, photos, vertical‐longitudinal profiles of the rail measured with the RAILPROF device (Figure 2.3, Figure 2.4), and the MINIPROF measurements of the cross‐sectional profile of the rail at short track irregularities, such as squats, welds and insulated joints. The accuracy of the handheld GPS was ±5 m. * GeoCode is a unique code assigned to each track Axle Rail Wheel Accelerometer
Figure 2.3 RAILPROF ‐1.5 ‐1 ‐0.5 0 0.5 ‐500 ‐400 ‐300 ‐200 ‐100 0 100 200 300 400 500 Position, mm Ve rt ic al de vi at io n, mm (a) Insulated joint (b) Rail profile at insulated joint ‐1.5 ‐1 ‐0.5 0 0.5 ‐500 ‐400 ‐300 ‐200 ‐100 0 100 200 300 400 500 Position, mm Ve rt ic al de vi at io n, mm (c) Thermite weld (d) Rail profile at thermite weld ‐0.5 ‐0.3 ‐0.1 0.1 0.3 0.5 ‐500 ‐400 ‐300 ‐200 ‐100 0 100 200 300 400 500 Position, mm Ve rt ic al de vi at io n , mm (e)Severe squat (f) Rail profile at severe squat ‐0.5 ‐0.3 ‐0.1 0.1 0.3 0.5 ‐500 ‐400 ‐300 ‐200 ‐100 0 100 200 300 400 500 Position, mm Ve rt ic al de vi at io n, mm (g)Light squat (h) Rail profile at light squat Figure 2.4 Photos and measurements of vertical‐longitudinal profile of the rail at track irregularities. The travelling direction is from left to right in all the pictures. White line indicates the centre line of the rail, where the measurements were taken.
Figure 2.4 shows examples of RAILPROF measurements at an insulated joint, a weld, a severe squat and a light squat, with corresponding photos. The horizontal axis is the longitudinal position along the rail in millimetres; the vertical axis is the vertical deviation of the rail surface in millimetres. RAILPROF measures rail profile within 1 meter on the centre line of the rail. If a defect is offset, like the light squat in Figure 2.4(g), the RAILPROF can miss it.
The data obtained by monitoring were used for several purposes:
The GPS coordinates of defects were used to find relation between the ABA peaks and track defects.
The measurements of rail profiles were used as an input to the FE model for numerical simulation of dynamic responses at short track defects.
2.2.3. Measurements in Zuid Holland
The first ABA measurements were performed in Zuid Holland in December 2005 – January 2006. Three different sections of the Dutch Railway track were measured: Delft – Den Haag, Lage Zwaluwe – brug Hollands Diep, and Lage Zwaluwe – Dordrecht. For the reasons explained in section 2.2.1, each track was measured several times.
It was found that insulated joints cause high peaks in ABA signals. Knowing the distances between the insulated joints from IRIS database and comparing to the distances between peaks in ABA signals, the peaks excited by insulated joints were identified. Figure 2.5 shows the ABA signal measured on the track Lage Zwaluwe – Dordrecht. The positions of the insulated joints were taken from IRIS database and marked with red asterisks. The travelling direction is from left to right. The negative values in the abscissa‐axis mean that the train was travelling in the direction of decreasing conventional kilometre position.
Figure 2.5 ABA measured in Lage Zwaluwe – Dordrecht. The measurement was taken on the leading wheelset. The abscissa axis is position along the track in kilometres. Red asterisks indicate positions of
Comparing the GPS coordinates of insulated joints taken during the track monitoring to on‐ board GPS coordinates corresponding to the ABA peaks, it was found that the error of on‐ board GPS coordinates was up to 80 m in longitudinal direction. Because of the large positioning error it was not possible to locate other short track irregularities, such as squats, in these measurements. Another measurement round was needed to find relation between ABA and squats.
2.2.4. Measurements in Weert
Another trial measurement, with improved GPS positioning, was made on the track Eindhoven – Weert in March 2007. The measurements were repeated three times on the same section of track of about 3 km long. The on‐board GPS coordinate recorded at the same short track irregularity were compared, and the calculated positioning error of the on‐ board GPS system was within 1 m. Thus, it was possible to make a correlation analysis to find the relation between ABA and short track irregularities. The kilometre position of joints known from IRIS database was used for cross checking of the positioning of the ABA signals.
The quality of the data was checked by simple repeatability analysis. The ABA signals from different runs measured at a severe squat were overlapped (see Figure 2.6). The characteristics of the signals, such as magnitude and wavelength, were similar in the different runs; thus, the measurements were reliable. ‐150 ‐100 ‐50 0 50 100 150 ‐0.1 ‐0.05 0 0.05 0.1 0.15 0.2 Ac ce le ra ti o n , m/ s 2 Position, m
Measurement 1 Measurement 2 Measurement 3
Figure 2.6 Repeatability of ABA at a severe squat
2.3. DETECTION OF SQUATS
To assess the feasibility to detect squats from ABA, the magnitude of ABA signals at positions, corresponding to squats, were examined. If an outstanding magnitude of ABA was observed at such location, the squat was considered as detectible. The feasibility for detection of squats by ABA was assessed in terms of hit rate, which is the ratio of detected
irregularities over the total number of irregularities. The hit rate presented in Table 2.1 is obtained based only on ABA peaks.
Table 2.1 Hit rate of squats based on statistics of ABA peaks
Squats Total Number Detectable Hit rate, %
Severe 6 6 100
Moderate 15 9 60
Light 21 12 57
The hit rate for severe squats was 100 %. Severe squats can be detected in every measurement run. A severe squat causes peaks in signals measured both at the leading and trailing wheels. The hit rates of moderate and light squats were 60% and 57% respectively. The light squats in Table 2.1 were larger than the critical size of squats, i.e. no trivial defects were included in these statistics. The reason for the low hit rate of light and moderate squats is that such squats do not excite peaks in each measurement run, since the size of these squats may be not large enough and the wheel does not hit these defects in every run. Another reason is that ABA measurements in Weert were low‐pass filtered with a cut‐off frequency of 1 kHz during the measuring process. However, for detection of light and moderate squats, the measured frequency range should be higher, as the excited frequencies lie in the frequency range up to 2 kHz. In [17] it was found that the wavelength of the contact force, determined by the natural frequencies of the system, is between 20mm and 40mm, which corresponds to 950–1900Hz for a rolling speed of 140 km/h, the typical speed of Dutch passenger trains. Since ABA is a measure of vibration of the coupled vehicle‐track system, it should be influenced by the same natural frequencies as the contact force. Because of that, the presented hit rate may be improved by analysis of the high frequency part of ABA. In later measurements attention was paid to ensure that no mechanical filter was applied, so that the measured signals contained higher frequency components.
The hit rate of detection may also be improved by considering the frequency content of ABA. The ABA is a combination of vibrations of the vehicle‐track system excited by short irregularities and long irregularities. Therefore, at the moment of impact at a squat the different resonance characteristics could be seen in the time‐frequency representation of the ABA signal. These characteristics may be used for detection of squats.
Further, on a track with high rail roughness the average amplitude of ABA vibrations is higher than that of recently ground rails. On rough tracks it might be difficult to distinguish squats based only on the magnitude of ABA. Investigating the frequency contents of the signals might be helpful in this case. An overview of time‐frequency techniques is presented below.
2.4. RELATION BETWEEN ABA AND SIZE OF A SQUAT
To get an insight into relation between the ABA and size of squat, ABA responses at a number of squats from the same track were investigated. Figure 2.7 shows three examples of squats, the ABA responses of which were compared. Note that the geometry of these squats was significantly different: squat 1 in Figure 2.7(a) is a moderate squat, while squats 2 and 3 are severe.
(a) Squat 1 (b) Squat 2 (c) Squat 3
Figure 2.7 Squats.
The ABA signals measured at these squats are presented in Figure 2.8. After the excitation point (around position zero meters) the peaks appear at the same positions. This means that the ABA wavelength is mainly determined by the natural frequencies of the wheel‐track system. As it was mentioned earlier, it is also dependent on the train speed, but in these measurements the speed was constant.
