Track Geometry for High-Speed Railways
TRITA - FKT Report 2001:54 ISSN 1103 - 470X ISRN KTH/FKT/EX--01/54--SE
Track geometry for high-speed railways
A literature survey and simulation of dynamic vehicle responce
by
Martin Lindahl
Stockholm Railway Technology 2001 Department of Vehicle Engineering Royal Institute of Technology Track geometry for high-speed railways
A literature survey and simulation of dynamic vehicle responce
by
Martin Lindahl
TRITA-FKT Report 2001:54 ISSN 1103-470X ISRN KTH/FKT/EX--01/54--SE
Postal Address Visiting address Telephone E-mail Royal Institute of Technology Teknikringen 8 +4687907628 [email protected] Railway Technology Stockholm Fax S-100 44 Stockholm +4687907629 Abstract
The present work consists of two main parts. The first part (Chapter 2 and 3) deals with a literature survey where a short introduction is given for track geometry and track/vehicle interaction. After the introduction, a survey over the present standard in Europe and Japan is made. In particular the recent proposals for a common European Standard (CEN) and TSI (Technical Specification for Interoperability) are reviewed. The second part (Chapter 4, 5 and 6) starts with an attempt to foresee the performance of a train that would be available from the industry around 2010. Furthermore, the second part deals with simulations. Firstly, hunting stability is simulated to establish a vehicle configuration that could deal with higher speeds. Secondly, track shift forces are simulated with Prud´hommes criteria as boundary condition. Thirdly, a risk factor for vehicle overturning was calculated in the most adverse case where the train was running on a curve and the wind was directed outwards. In the simulations, two sets of track irregularities were used. Some consequences of different kinds of freight train operations are discussed in Chapter 7. In short terms, the following conclusions have been drawn: - A cant up to 200 mm is possible if the track is built for dedicated high-speed traffic; in freight train operations some 20-50 mm lower. - A cant deficiency of 225-250 mm could be allowed when using carbody tilt and suitable bogie technology. The tilt is a basic requirement when using such high values of cant deficiency. - The transition curves should be long, i.e. the duration in the transition curve should be in the order of around 4-5 sec, if carbody tilt is anticipated. - It could be concluded that hunting stability can be achieved. - The track quality has too be improved relative to current standards for 200 km/h in order to meet requirements on lateral track shift forces. The degree of improvement should be further investigated. - It is concluded that safety criteria for side-wind exposure can be met, if the trains have favourable, although, realistic, aerodynamic performance. - The maximum gradient shall be chosen according to the type of freight traffic foreseen in the future.
Keywords: track, geometry, high-speed, train, railway, cant, cant deficiency, cant excess, tangent track, transition curve, horizontal curve radius, gradient, vertical curve radius, simulation, hunting stability, track shift force, vehicle overturning, track irregularity, freight trains
i ii Sammanfattning
I Sverige finns behov av spårgeometri för höghastighetsbanor. Bl.a. har frågan aktualiserats i samband med studier av den s.k. Europakorridoren (Stockholm - Jönköping - Köpenhamn/Göteborg). I dessa sammanhang har det framförts önskemål om en hastighetsstandard för 350 km/h, vilket är den standard som åtminstone delvis projekteras och byggs i Mellan- och Sydeuropa. För Sveriges del, som är ett land med långa transportavstånd, finns det behov av korta restider på långa avstånd, vilket talar för hög hastighet. Detta ställer krav på stora kurvradier. Samtidigt finns ett starkt behov av att bygga banorna med relativt låga investeringskostnader samt små intrång i natur och bebyggelse. Detta ställer krav på att inte göra kurvradierna större än absolut nödvändigt och även att kunna tillåta relativt större lutningar i banan. En litteraturgenomgång har utförts där förslagen till europastandard för spårgeometri studerats (CEN och TSI). Dessa förslag till europastandard skapar flera möjligheter att minimera både horisontella och vertikala kurvradier. Det föreslås även vara möjligt att tillåta tåg med korglutning efter särskilt tillstånd av banhållaren. Lutningar i banan upp emot 35 ‰ föreslås även vara tillåtet. Rapporten tar även upp den framtida tågteknologin om vad som är tekniskt möjligt vilket har diskuterats med tekniska experter inom industrin. Optimerad passiv hjulparsstyrning är en del som diskuterats. I detta sammanhang har utvecklingen av aktiv sekundärfjädring nämnts som ett alternativ men dock inte studerats ingående. Den aerodynamiska utformningen har förfinats och senast känd teknologi har används. Simuleringarna har utförts i tre olika steg. Först görs en gångstabilitetssimulering för att fastställa att använd teknik klarar av hastigheterna som eftersträvas. Nästa steg var att beräkna spårförskjutningskrafter med Prud´hommes kriterium som gränsvärde. I denna del simulerades olika fall där spårläget varierades för att ge en uppfattning om vad som krävdes för att klara gränsvärdet. Slutligen simulerades säkerheten mot vältning vid kraftig sidvind enligt föreslagna riktvärden för vilka vindhastigheter som bör klaras. Bland annat har följande slutsatser dragits: - Rälsförhöjning upp mot 200 mm är möjligt vid antagandet av enbart höghastighets- trafik (V ≥ 200 km/h). - Rälsförhöjningsbrist upp mot 250 mm kan tillåtas förutsatt att korglutningsteknik och lämpliga boggier används. - Långa övergångskurvor rekommenderas (en varaktighet om minst ca 4-5 s). - Uppställda gångstabilitetsvillkor uppnås. - Spårläget måste förbättras för att gränsvärdet för de laterala spårförskjutnings- krafterna ska klaras. Graden av förbättring måste studeras vidare. - Villkoren för sidvindsstabilitet klaras om tåget får en god aerodynamisk utformning. - Banans lutningsförhållanden bör väljas med hänsyn till den godstrafik som förutses.
Nyckelord: Spårgeometri, höghastighetsbana, tåg, höghastighetståg, godståg rälsförhöjning, rälsförhöjningsbrist, rälsförhöjningsöverskott, rakspår, övergångskurva, horisontalkurva, lutning, vertikal- kurva, simulering, gångstabilitet, spårförskjutningskraft, vältning, spårlägesfel.
iii iv Preface and acknowledgements
This study has been carried out at the Division of Railway Technology, Department of Vehicle Engineering, Royal Institute of Technology (KTH, Kungliga Tekniska Högskolan), Stockholm, in close cooperation with the Swedish National Rail Administration (Banverket), Europakorridoren AB, Helsingborg, Bombardier Transportation, Västerås, and the Swedish National Road and Transport Research Institute (VTI), Linköping. The bulk of this study constitutes my Master of Science thesis. The financial support from Banverket, Bombardier Transportation and Europakorridoren for the present work is gratefully acknowledged. Thereby it was possible to give an extra-ordinary support and supervision from KTH senior staff. I would like to thank my supervisor Sebastian Stichel and my examiner Professor Evert Andersson for their knowledge and support during the course of this work. There have been four reference group meetings. This reference group consisted of persons from Banverket, Europakorridoren, Bombardier Transportation, VTI and KTH. I would like to state my kind regards to Bertil Eriksson and Per Hurtig from Banverket, Mikael Stamming from Europakorridoren, Olle Ek and Jan Ågren from Bombardier Transportation and Björn Kufver from VTI. The vehicle model used in the simulations have been provided by courtesy of Bombardier Transportation. Thanks are also delivered to Ingemar Persson from DEsolver AB for his support and help during the simulations. Due to the great extent of this work, some contributions have been delivered from Sebastian Stichel and Evert Andersson. Part of Chapter 4 has been written by Sebastian Stichel and the bulk of Chapter 7 has been written by Evert Andersson. Friends, Brothers, Mum and Dad, thank you for patience. At last but not least I would like to thank my girlfriend for her support and encouragement. I should not managed this without you.
Stockholm, December 2001
Martin Lindahl
v vi Table of contents Abstract ...... i Sammanfattning ...... iii Preface and acknowledgements...... v 1 Introduction...... 1 1.1 Background to the present study ...... 1 1.2 Objective and approach of the present study...... 1 1.3 Thesis contribution ...... 2 2 Track geometry and track/vehicle interaction ...... 3 2.1 Design track geometry...... 3 2.1.1 Track gauge...... 3 2.1.2 Track cant...... 3 2.1.3 Horizontal curve...... 4 2.1.4 Transition curve and superelevation ramp...... 5 2.1.5 Gradient...... 6 2.1.6 Vertical curve...... 6 2.2 Track/vehicle interaction ...... 8 2.2.1 Track plane acceleration ...... 8 2.2.2 Equilibrium cant and balanced speed ...... 9 2.2.3 Cant deficiency and cant excess ...... 10 2.2.4 Permissible speed with respect to radius, cant and cant deficiency...... 12 2.2.5 Rate of cant and rate of cant deficiency...... 13 3 Standards, practices and TSI...... 15 3.1 Track gauge ...... 15 3.2 National standards in Sweden...... 15 3.2.1 Track cant and track distance...... 15 3.2.2 Cant deficiency and cant excess ...... 15 3.2.3 Horizontal curve radius...... 16 3.2.4 Transition curve and superelevation ramp...... 18 3.2.5 Gradient...... 19 3.2.6 Vertical curve radius...... 20 3.3 National standards in Germany ...... 22 3.3.1 Track cant...... 23 3.3.2 Cant deficiency ...... 23 3.3.3 Horizontal curve radius...... 24 3.3.4 Transition curve and superelevation ramp...... 26 3.3.5 Gradient...... 26 3.3.6 Vertical curve radius...... 27 3.4 Practices in France...... 28 3.4.1 Cant, cant deficiency and cant excess...... 28 3.5 Practices in Japan...... 29 3.6 Technical Specifications of Interoperability and CEN proposal ...... 30 3.6.1 Track cant and track distance...... 30 3.6.2 Cant deficiency and cant excess ...... 31
vii 3.6.3 Horizontal curve radius...... 34 3.6.4 Transition curve and superelevation ramp...... 35 3.6.5 Gradient...... 37 3.6.6 Vertical curve radius...... 37 3.7 Comparison between different projects and standards ...... 39 3.7.1 Horizontal curve radius...... 39 3.8 Recent resarch on nominal track geometry ...... 41 3.8.1 Optimisation of horizontal alignments for railways ...... 41 3.8.2 Ride comfort and motion sickness in tilting trains ...... 41 3.9 Summary and conclusions ...... 43 4 High-speed train technology year 2010...... 45 4.1 Maximum train speed ...... 45 4.2 Train configuration ...... 45 4.3 Tilt technology...... 46 4.3.1 General...... 46 4.3.2 Possible overspeed with tilt technology...... 46 4.4 Running gear design ...... 47 4.5 Aerodynamic shape ...... 48 4.6 Track irregularities ...... 48 5 Track/vehicle dynamic simulations - models, conditions and criteria ...... 49 5.1 Simulation strategy ...... 49 5.2 Simulation software...... 49 5.3 Test speed ...... 49 5.4 Hunting stability ...... 50 5.5 Track shift forces ...... 51 5.6 Vehicle overturning at strongly side-wind ...... 52 5.6.1 General...... 52 5.6.2 Tolerable wind velocities...... 52 5.6.3 Intercept method risk factor ...... 53 5.6.4 Disadvantages with intercept method ...... 55 5.6.5 Aerodynamic train design...... 55 5.7 Rails, wheels and equivalent conicity...... 56 5.8 Track irregularities ...... 57 5.8.1 Classification of track irregularities...... 57 5.8.2 Track irregularities for dynamics analysis...... 58 5.8.3 Peak values of track irregularities...... 62 5.9 Model of the EMU coach ...... 65 5.9.1 Three different vehicle configurations...... 65 5.9.2 Hold-off-device...... 68 6 Dynamic analysis of simulated vehicle response...... 69 6.1 Hunting stability on tangent track and on curve...... 69 6.1.1 Conditions...... 69 6.1.2 Track irregularities...... 70 6.1.3 Criteria for hunting stability...... 70 6.1.4 Hunting stability on tangent track...... 70 6.1.5 Hunting stability on large radius curves ...... 72
viii 6.2 Evaluation of track shift forces...... 74 6.2.1 Conditions...... 74 6.2.2 Track irregularities...... 75 6.2.3 Track shift forces variation along the track ...... 76 6.2.4 Track shift forces for different cant ...... 76 6.2.5 Comparisons between different track irregularities...... 78 6.2.6 Improvements of track irregularities...... 80 6.3 Evaluation of vehicle overturning ...... 84 6.3.1 Conditions...... 84 6.3.2 Track irregularities...... 85 6.3.3 Safety against vehicle overturning at different conditions ...... 85 6.3.4 Conclusions...... 88 7 Consequences of freight trains operations...... 89 7.1 Different categories of freight trains ...... 89 7.2 Permissible axle load and track loadings...... 91 7.3 Track cant and cant excess ...... 93 7.4 Gradients versus train mass ...... 96 7.4.1 Freight trains category I - heavy freight trains...... 97 7.4.2 Freight trains category II - fast trains for unit-loads and heavy express..97 7.4.3 Freight trains category III - high-speed for light express or mail...... 99 8 Possible track geometry...... 101 8.1 Horizontal curve radius ...... 101 8.2 Vertical curve radius...... 108 9 Conclusions and further research ...... 109 9.1 Conclusions on the literature study ...... 109 9.2 Conclusions on dynamic analysis of simulated vehicle response ...... 109 9.3 Conclusions on horizontal and vertical curve radii ...... 110 9.4 Conclusions on freight train operations...... 111 9.5 Further research ...... 111 References...... 113
Appendix A - Notations...... 117 Appendix B - Abbreviations ...... 121 Appendix C - Further diagrams on track shift forces...... 123 Appendix D - Further diagrams on vehicle overturning ...... 131 Appendix E - Overturning due to side-wind...... 133 Appendix F - Train mass versus gradient ...... 139 Appendix G - General Description of the GENSYS Software Package ...... 145
ix x Track geometry for high-speed railways
1 Introduction
1.1 Background to the present study
In Sweden the high-speed line ‘Botniabanan’ (250 km/h) is currently in the design phase. There are also feasibility studies concerning ‘Europabanan’ and ‘Götalandsbanan’, a high-speed line intended to connect Stockholm with Gothenburg and Copenhagen. The objective for these railways is to manage speeds above 300 km/h, maybe up to 350 km/h. These railways require a high standard and high performance. With conventional (non-tilting) passenger trains running at 350 km/h, horizontal curve radii tend to be large (6000 m according to Banverket). In some cases it is also recommended to have a margin for future improvement in speed and passenger comfort, which will further increase required radii. In such a case the radius tend to be 10000 m. In addition, heavy freight trains require modest gradients (10 à 12 ‰) if ordinary locomotives are to be used. Altogether, this would cause a very rigid and non-flexible alignment, both horizontally and vertically. There would be a substantial need for bridges, high embankments and tunnels, depending on the topography of the landscape. The cost may increase so much that the project would be unprofitable from the social-economics point of view. Due to the rigid alignment the project would also run the risk to cause excessively large infringements in nature and culture environments. The project could therefore be politically questioned. The present Swedish standards and recommendations are principally the same as for lower speeds. A separate standard for high-speed railways in Sweden does not exist at the moment. The standard for higher speeds have the same margin for future higher speed as for the lower speeds, i.e. speeds less than or equal to 200 km/h. In some feasibility studies there have been attempts to copy standards prepared for the first generation German high-speed railways, which give very large curve radii and modest gradients.
1.2 Objective and approach of the present study
The aim with this work is to investigate what track standards could be allowed in order to achieve high-speed performance. One important boundary condition is the use of latest known train technology, which can be assumed to be a standard within about 10 years. The study has the following approaches: - Make a literature survey of approved and forthcoming standards and practises for high-speed railways in Japan and Europe including the TSI (Technical Specification for Interoperability). It covers horizontal curve radius, transition curve length, appropriate cant, gradient, vertical curve radius etc.
1 Introduction
- Describe a possible train vehicle which might run on the designed high-speed lines. What is today known technology, which could be commercially available within 10 years? The problem should especially focus on tilting technology and modern running gear, track forces, aerodynamics, on side-wind stability etc. Among other things results from present research and experience at Bombardier Transportation, KTH and VTI will be used. - Vehicle dynamic simulations will be performed to investigate possible limits within which modern technology probably can be possible to accomplish. Three kinds of different conditions will be looked at: 1. Track for all types of trains, including heavy freight trains 2. Track for high-speed trains and light freight trains (unit-loads and heavy mail) 3. Track for high-speed trains only (passenger, light express goods and light mail) High-speed trains and heavy freight trains have different demands on track standard concerning horizontal alignment, cant, gradients and vertical curves.
1.3 Thesis contribution
This thesis is believed to make contributions to the following areas: - Give examples of what track geometry parameters that could be managed when taken different train categories into account. - In particular, give examples of horizontal curve radius and cant deficiency that could be allowed for high-speed trains when safety related factors like hunting stability, track shift forces and vehicle overturning are taken into consideration. - Foresee, and discuss the performance of a train that would be available from the industry around 2010.
2 Track geometry for high-speed railways
2 Track geometry and track/vehicle interaction
2.1 Design track geometry
Track geometry is very important for the behaviour of vehicles. In this section an introduction to the most common quantities of track geometry will be presented. These quantities are - Track gauge - Track cant - Transition curve and superelevation ramp - Horizontal curve radius - Vertical curve radius and gradient
2.1.1 Track gauge
The definition of track gauge is shown in Figure 2-1. Standard track gauge is 1435 mm.
Figure 2-1 The definition of track gauge.
2.1.2 Track cant
The difference between the level of the two rails in a curve is called cant ht (also called superelevation) and is arranged to compensate part of the lateral acceleration, see Figure 2-2. A cant angle arise where a cant is arranged. The angle can be determined by h ϕ t t = asin------(2-1) 2bo where 2bo = 1.500 m on standard track gauge.
3 Track geometry and track/vehicle interaction
The cant is maximized with respect to stationary conditions and slowly running trains. A maximum value is set for cant because of the following problems which arise if a train is forced to stop or run slowly in a curve: - passenger discomfort at standstill or low speed; -riskofderailment of freight trains in sharp curves due to the combined effect of high lateral and low vertical load on the outer wheel at low speed; - possible displacement of wagon loads;
ϕ Figure 2-2 Cant ht and cant angle t.
2.1.3 Horizontal curve
The most distinguished parameter for a circular curve is the radius, R = constant, which is inverse proportional to curvature,k = 1 ⁄ R . The radius is related to the centre of the track. Esveld says [11]: “it is a known fact that a vehicle running at a speed v in a curve with a radius R undergoes a centrifugal lateral acceleration a=v2/R which results in a number of undesirable effects”. These effects can be: - possible passenger discomfort; - possible displacement of wagon loads, - risk of vehicle overturning in combination with strong side winds; - risk of derailment caused by flange climbing of a wheel on the outer rail or by loosening of rail fastenings; - high lateral forces on the track.
4 Track geometry for high-speed railways
Figure 2-3 The definition of horizontal circular curve radius R.
2.1.4 Transition curve and superelevation ramp
A transition curve with a linear variation of curvature is called clothoid. Transition curves are used between tangent track and circular curves or between two adjacent curves to allow a gradual change in curvature and lateral acceleration. The centre line of a transition curve has the same tangent at the connecting points as the adjacent part, whereas the curvature changes gradually from the value of one connection point to the value of the other [11]. Transition curves also introduce cant via superelevation ramps. A superelevation ramp is a section of the track where the cant changes gradually. The clothoid type of transition curve has a linear function of chainages, i.e. of the longitudinal coordinate [16]
() s ks = k0 + ------(2-2) A2 if s=s0 =0at the start of the transition curve where k is the curvature and A is the clothoid parameter.
If the clothoid starts from a straight line (k0 =0), has the length Lt and ends at a circle with the radius R, we obtain the following relation:
2 ⋅ A = Lt R (2-3)
5 Track geometry and track/vehicle interaction
2.1.5 Gradient
The topographical conditions usually require some kind of vertical-longitudinal gradients, along the way. Building bridges and tunnels is a very expensive way to manage the topography constraints. In particular heavy railway traffic has problems to overcome large longitudinal gradients. Therefore restrictions for the amount of gradient are needed. The following requirements need to be considered because they have an affect on railway traffic: - The power supply and energy consumption will increase with large gradients. - Heavy freight trains with an ordinary locomotive may have problems to climb up the gradient. - Braking distances increase for high-speed and freight trains in an ascending gradient Thus, large gradients result, principally, in heavier locomotives, increased locomotive power, and/or less freight train weight, and/or reduced speed and line capacity, and/or requirement of higher braking capacity, and/or larger signalling distances.
2.1.6 Vertical curve
A vertical curve provides a smooth transition between successive tangent gradients in the railway profile. In changes of gradients a suitable radius must be used. If the vertical acceleration on a crest is too great, the loads on the vehicle wheels can cause the wheels to climb the rail and thus cause a derailment. Furthermore, the resistance against vehicle overturning at side-winds will be lower It is also important that passenger comfort is being ensured. How two adjacent gradients are related to the vertical curve radius and the profile elevation is shown in Figure 2-4.
6 Track geometry for high-speed railways
Figure 2-4 Conditions for vertical geometry between two adjacent gradients
With the simple parabola in Figure 2-4, using small-angle approximations, the vertical offset at any given longitudinal coordinate x, is given by:
()ab– 2 Ax2 zx()==– ------x ------– (2-4) 2000L 2000L where A is the algebraic difference between two gradients with grades a and b (expressed in ‰, positive uphill) and L is the length of the curve between the tangent points ta and tb. (Note that negative z coordinates are measured downwards from the tangents for a crest and positive z coordinates are measured upwards for a hallow). The maximum z for x=L/2,is given by
æöL L z --- ==eab–()– ------(2-5) èø2 8000
Given values of a, b and Rv gives the following condition R ()ab– L = ------v - (2-6) 1000
()2 æöL ⋅ ab– zèø--- = –Rv ------(2-7) 2 810⋅ 6
7 Track geometry and track/vehicle interaction
2.2 Track/vehicle interaction
This section is believed to present quantities that are significant in track/vehicle interaction.
2.2.1 Track plane acceleration
In case of quasistatic curving (i.e. curving at constant speed, radius and cant on perfect track geometry) the vehicle is exposed to two accelerations: horizontal centrifugal acceleration and gravitational acceleration, see Figure 2-5(a). The resultant of the acceleration vector can be split up into two composants;ay is parallel to the track plane andaz is perpendicular to the track plane, see Figure 2-5(b).
Φ. Figure 2-5 Definition of track plane acceleration ay and lateral force angle
The accelerationay is called track plane acceleration or, simply, lateral acceleration. The equations can be written as follows [1]:
2 2 h v ⋅ ϕ ⋅ ϕ v ⋅ ϕ ⋅ t ay = ----- cos t – g sin t = ----- cos t – g ------(2-8) R R 2bo
v2 a = ----- ⋅ sinϕ + g ⋅ cosϕ (2-9) z R t t
8 Track geometry for high-speed railways
ϕ ≤ 0.15 ) Assuming small angels ( t rad the equations can be approximated by: 2 2 h ≈ v ⋅ ϕ v ⋅ t ay ----- – g sin t = ----- – g ------(2-10) R R 2bo
≈ az g (2-11) Φ The lateral force angle in Figure 2-5 are related to the acceleration ay and az in accordance to the following equation a Φ = atan-----y (2-12) az
2.2.2 Equilibrium cant and balanced speed
The cant which gives ay = 0. for a given radius and given vehicle speed is called equilibrium cant, heq. The equilibrium cant is thus
2b v2 h ≈ ------0 ⋅ ----- (2-13) eq g R Equation (2-13) are based on SI-units. In practice it is useful to express speed V in [km/h] and cant in [mm] shown in Equation (2-14)
2b 2 ≈ omm, ⋅ V heq, mm ------(2-14) g 3.62 ⋅ R
The equation can be simplified further if the values 2bo for standard track gauge and the gravitational acceleration g are used
2 2 ≈ 1500 ⋅ V ≈ ⋅ V heq, mm ------11.8 ------(2-15) 9.81 3.62 ⋅ R R It is very common to write the formula in the way shown in Equation (2-15), but it is important to be careful with the units.
The vehicle speed giving ay = 0 for a given radius and a given cant is called the equilibrium speed or balanced speed, veq and is defined as ⋅⋅ Rght veq = ------. (2-16) 2bo
Thus, at equilibrium speed the lateral acceleration in the track plane, ay, is zero. With speed expressed in [km/h] and cant in [mm] this equation transforms to (for standard gauge):
9 Track geometry and track/vehicle interaction
Rh⋅ , V = ------tmm (2-17) eq 11.8
2.2.3 Cant deficiency and cant excess
For several reasons, fully compensated track plane acceleration can not be achieved in all cases according to [3]: - It is a possibility that a train stops or runs slowly in a curve. Therefore, the maximum cant has to be limited. Other reasons to limit the cant have been discussed earlier in Section 2.1.2. It is then desirable to allow a cant deficiency, i.e. a certain amount of uncompensated lateral acceleration ay remains in the track plane. - Not all trains have the same speed. Therefore, it would not be possible to achieve fully compensated lateral acceleration for all trains anyway.
Cant deficiency
When the cant is less than the equilibrium cant a so called cant deficiency arises. The cant deficiency is the additional cant that is needed to achieve equilibrium cant. Cant deficiency hd is the difference between equilibrium cant heq and actual cant ht and is thus determined by the following equation:
hd = heq – ht (2-18) With Equation (2-13) substituted into (2-18) we get in SI-units:
2b v2 h = ------0 ⋅ ----- – h (2-19) d g R t A common way to write the formula is shown in Equation (2-20). The speed V is expressed in km/h and cant and cant deficiency is expressed in [mm].
V2 h = 11,8 ⋅ ------– h (2-20) dmm, R tmm, An additional way to express cant deficiency is to solve Equation (2-10) for v2/R and substitute the expression into Equation (2-19) and relate cant deficiency to the track plane acceleration which gives (in SI-units) [1] 2b h = ------o ⋅ a (2-21) d g y where ay >0
10 Track geometry for high-speed railways
In Table 2-1 some examples of the relationship between track plane acceleration, side force angle and cant deficiency are given. Table 2-1 The relationship between track plane acceleration, side force angle and cant deficiency
Track plane acceleration Lateral force angle Cant deficiency 2 Φ (°) ay (m/s ) hd (m) 0.654 3.81 0.100 0.981 5.71 0.150 1.176 6.84 0.180 1.307 7.61 0.200 1.471 8.53 0.225 1.634 9.51 0.250 1.797 10.46 0.275
The cant deficiency allowed in real train operations is determined by the following factors according to [3], [11]: - track construction (with respect to its ability to resist high forces); - state of track components; - track alignment (i.e. magnitude and shape of geometrical irregularities); - type of vehicle and running gear1; - axle loads and unsprung masses; - state of maintenance of the rolling stock; - passenger comfort. If high values are allowed for cant deficiency (track plane acceleration) the track components must be designed accordingly and there must be no risk of exceeding the lateral track resistance immediately after tamping.
1. In particular suspension, centre of gravity and side-wind sensitivity.
11 Track geometry and track/vehicle interaction
Cant excess
If the actual cant is higher than the equilibrium cant something called cant excess will be introduced. Cant excess is the difference between actual cant and equilibrium cant and is defined as:
he = ht – heq (2-22) Cant excess is achieved when the vehicle is running at a lower speed than the design speed of the track. Cant excess can be related to lateral acceleration in the same way as cant deficiency shown in Equation (2-21) 2b h = –------o ⋅ a (2-23) e g y where ay <0andhe >0.
2.2.4 Permissible speed with respect to radius, cant and cant deficiency
With a given horizontal curve radius and permissible lateral acceleration, ay,lim,or permissible cant deficiency, hd,lim, an expression for permissible speed, vlim, can be expressed in many different ways [1]:
h ⋅ æö⋅ t Rg() vlim ==Raèøylim, + g ------hdlim, + ht (2-24) 2bo 2bo SI-units is used in Equation (2-24). Alternatively, in Equation (2-25) permissible speed, Vlim, is given in [km/h] while cant ht and permissible cant deficiency hd,lim are given in [mm]. Radius is always given in metres. Standard gauge is assumed.
Rh()+ h ()⋅ 12.96g ≈ dlim, t Vlim = Rhdlim, + ht ------(2-25) 2bo 11.8
12 Track geometry for high-speed railways
2.2.5 Rate of cant and rate of cant deficiency
Rate of cant (cant gradient) as a function of time
The following relationship are used for cant gradients with linear superelevation ramps, ∆ where ht is the cant variation over the transition length Lt: [3], [7] dh ∆h ⋅ v ------t = ------t max (2-26) dt Lt
Rate of cant deficiency as a function of time
Rate of cant deficiency describes the change of lateral acceleration (in the track plane) as a function of time. Another word for rate of cant deficiency is lateral jerk. For transition curves with a linear change of curvature and superelevation ramps with ∆ linear variation of cant, the following relationship is derived, where hd is the cant deficiency variation: [3], [7] dh ∆h ⋅ v ------d = ------d max (2-27) dt Lt
13 Track geometry and track/vehicle interaction
14 Track geometry for high-speed railways
3 Standards, practices and TSI
In this Chapter standards and practices according to Sweden, Germany, France and Japan are being presented. The proposal from the European Association for Railway Interoperability (AEIF), Technical Specifications of Interoperability (TSI) [12] is also demonstrated. TSI do often refer to the European (CEN) provisional standard [7]. This report will also refer to the European provisional standard.
3.1 Track gauge
Every high-speed rail system in the world have 1435 mm in designed track gauge. All content in the following Sections and Chapters refers to this standard gauge.
3.2 National standards in Sweden
In Sweden does exists a regulation BVF 586.41 [5] and a handbook, BVH 586.40 [4] concerning track geometry parameters. The regulations is mandatory while the handbook is informative. In the following text the regulation is called BVF while the handbook is called BVH.
3.2.1 Track cant and track distance
According to Banverket cant shall not exceed 150 mm. Track distance most frequently used in Sweden is 4.5 metres, although there are exceptions in both directions.
3.2.2 Cant deficiency and cant excess
Cant deficiency
The uncompensated lateral acceleration, which is proportional to cant deficiency, should not be too large. Table 3-1 shows the permissible cant deficiency and its corresponding lateral acceleration for three different categories of rolling stock according to Banverket.
15 Standards, practices and TSI
Table 3-1 Permissible cant deficiency and the corresponding lateral acceleration. Track without turnouts. Source: Banverket [4].
Permissible cant Lateral acceleration, ay Train category deficiency (mm) (m/s2) A 100 0.65 B 150 0.98 S 245 1.60
The different train categories in Table 3-1 have the following meaning: - Category A conventional vehicles with older running gear and freight trains; - Category B vehicles with improved running gear, according to approval; - Category S vehicles with improved running gear and carbody tilt system.
Cant excess
According to Banverket cant excess should not be larger than 100 mm on tracks with radius larger than 1000 m. On tracks with radius less than 1000 m cant excess should not exceed 70 mm.
3.2.3 Horizontal curve radius
The recommended horizontal curve radius in Banverket handbook BVH 586.40 is a value calculated with cant ht = 150 mm and cant deficiency hd = 100 mm in the formula for equilibrium cant, i.e. Category A trains. For new lines it is recommended that the dimensional speed is multiplied with a speed factor γ = 1.3 This factor is used to get a margin with respect to ride comfort and increased speed in the future.
()⋅ 2 ⋅ 1.3 Vdim 11.8 R , = ------(3-1) rec min 250
Table 3-2 Recommended horizontal curve radius. Source: Banverket [4].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Recommended 3200 5000 6300 7200 8700 9800 radius [m]
16 Track geometry for high-speed railways
Minimum value of the horizontal radius according to Banverket can be expressed as
V 2 ⋅ 11.8 R = ------dim - (3-2) min 250
Corresponding radii, as a function of target speed, are shown in Table 3-3. There is an inherent assumption that trains of category A will be used. Table 3-3 Minimum horizontal curve radius. Source: Banverket [4], [5].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Minimum radius [m] 1888 2950 3700 4248 5140 5782
Limit values of horizontal curve radius according to Swedish standard is presented in Figure 3-1 below.
11000 Recommended radius according to BVH 586.40 10000 9000 Minimum radius according to BVF 586.41 and BVH 586.40 8000 7000 6000 5000 4000 3000 2000 1000
Horizontal curve radius [m] 0 100 150 200 250 300 350 Speed [km/h]
Figure 3-1 Recommended and minimum horizontal curve radius as a function of speed. Source: Banverket [4].
In reality, however, it is often difficult to meet these recommendations. On several newly built lines compromises have been made, of economic and other reasons. For example, this is the case for many sections on the West Coast Main Line (Göteborg - Malmö) and the Mälar Line (Stockholm - Örebro), where no margin exists for future improvement in speed or comfort, if trains Category A are used. On the newly started project Botnia- banan ((Sundsvall -) Nyland - Umeå) the target speed is 250 km/h. For large sections of this line such a speed will only be achieved by using tilting trains (Category S).
17 Standards, practices and TSI
3.2.4 Transition curve and superelevation ramp
According to Banverket [4] transition curves should be arranged with linear curvature changes (clothoids) and superelevation ramps should be arranged with linear changes of cant. The transition curve shall coincide with the superelevation ramp in both shape and position. Generally, the length of transition curves depends, among others, on the permitted gradient of cant, which is an important safety aspects because of wheel unloading and thus the risk of derailment. However, in long transition curves, which is the case in high-speed operations, ride comfort aspects usually determine the minimum length of transition curves. The change of lateral acceleration with respect to time is called jerk. The jerk can also be described as a change of cant deficiency with respect to time, as mentioned in Chapter 2. Thus, the length of transition curve is dependent of the allowed amount of jerk. The allowed rate of cant deficiency is a question of comfort. In Sweden used values for maximum rate of cant and rate of cant deficiency is shown in Table 3-4. Table 3-4 Maximum rate of cant and rate of cant deficiency Source: Banverket [4].
Train category Maximum rate of cant Maximum rate of cant deficiency A 46 mm/s 46 mm/s B 55 mm/s 55 mm/s S 70 mm/s 79 mm/s
In a superelevation ramp the cant changes linearly. The twist 1:n states the change of rate of cant per unit length. n is called ramp number.
∆h , --1- = ------tmm- (3-3) ⋅ n 1000 Lt where Lt = length of linear superelevation ramp in metres. ∆ ht,mm = cant difference in [mm]. It is normally the S-train requirements that determines the length of the transition curve. The length of the transition curve should be adjusted to the maximum speed of trains category S that the curve radius allows. The recommended transition curve length according to Banverket [4] is: ⋅ Lt = 5 R (3-4) ≤ for R Rrec and
V3 L = ------dim- (3-5) t 9 ⋅ R for R > Rrec.
18 Track geometry for high-speed railways
There are other formulas used by Banverket that state the permitted speed in transition curves. According to Banverket BVF 586.41 [5] the length of superelevation ramp, Lt [m], and permissible speed, Vlim [km/h], should be calculated with the following statements: ≥ ⋅ ∆ Lt 0.4 htmm, (3-6) L ⋅ 1000 ≤ ------t - Vdim ⋅ ∆ (3-7) qt htmm, L ⋅ 1000 ≤ ------t - Vdim ⋅ ∆ (3-8) qd hdmm,
∆ ∆ Here ht and hd are the changes of cant and cant deficiency, respectively, over the transition curve. The constants qt and qd can be found in Table 3-5 and are depending on train category.
Table 3-5 Constants qt and qd for each train category. Source: Banverket [5].
Train category qt qd A66 B55 S 4 3.5
3.2.5 Gradient
Banverket prescribes in their handbook BVH 586.40 [4] a largest permissible gradient of 10 ‰ on track with heavy freight trains. 12.5 ‰ can be permitted if the mean value does not exceed 10 ‰ over each kilometre. On tracks with only passenger trains and light freight trains higher values may be allowed.
19 Standards, practices and TSI
3.2.6 Vertical curve radius
In Banverket regulation BVF 586.41 [5] the vertical curve radius shall be in accordance to permissible speed as shown in Equation (3-9):
2 Vdim 2 R , ≥ ------0.16= ⋅ V (3-9) vmin 6.25 dim
Equation (3-9) leads to vertical curve radii shown in Table 3-6. Table 3-6 Minimum vertical curve radius. Source: Banverket [5].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Minimum vertical radius [m] 6400 10000 12544 14400 17424 19600
Banverket prescribes in their handbook BVH 586.40 [4] a recommended vertical curve radius:
≥ ⋅ ()⋅ 2 Rvrecmin, , 0.25 1.3 Vdim (3-10)
Some recommended vertical curve radii are shown in Table 3-7. Table 3-7 Recommended vertical curve radius. Source: Banverket [4].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Recommended vertical curve 16900 26500 33200 38100 46100 51800 radius [m]
The minimum vertical curve radius is calculated according to BVH 586.40 [4] with respect to the overspeed of 25% of category S-train (1.252 = 1.5625; 0.16*1.5625 = 0.25).
≥ ⋅ 2 Rvmin, 0.25 Vdim (3-11)
20 Track geometry for high-speed railways
Minimum values of vertical curve radius are shown in Table 3-8. Table 3-8 Minimum vertical curve radius. Source: Banverket [4].
Vertical curve radius 200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Minimum vertical radius [m] 10000 15625 16900 22500 27225 30625
In Figure 3-2 shows the relations between recommended and minimum vertical curve radius according to Banverket.
60000 Minimum vertical radius according to BVF 586.41 Minimum vertical radius according to BVH 586.40 50000 Recommended vertical radius according to BVH 586.40
40000
30000
20000
10000 Vertical curve radius [m] 0 100 150 200 250 300 350 Speed [km/h]
Figure 3-2 Limit value of vertical curve radius as a function of speed. Source: Banverket [4], [5].
21 Standards, practices and TSI
3.3 National standards in Germany
In Germany different train categories are not used in the same manner as in Sweden. A classification is used where values are prescribed with or without permission. Design values for equilibrium cant according to German standards, 800.0110 [9], are shown in Table 3-9. Table 3-9 Design values of equilibrium cant. Source: Deutsche Bahn [9].
Without permission Equilibrium cant
Recommended heq = 170 mm
Limit heq = 290 mm Permission necessary
Permission heq = ht + hd (values are shown in Table 3-10 and Table 3-11)
Exception heq = ht + hd (values are shown in Table 3-10 and Table 3-11)
22 Track geometry for high-speed railways
3.3.1 Track cant
Values for cant according to [9] are shown in Table 3-10. The recommended value for cant is 100 mm and the maximum value with permission is 180 mm. Table 3-10 Design values of cant. Source: Deutsche Bahn [9]
Without permission
Recommended ht = 100 mm
Limit ht = 160 mm (Ballast track) ht = 170 mm (Ballastless track) Permission necessary Permission < ≤ 160 ht 180 mm (Ballast track) < ≤ 170 ht 180 mm (Ballastless track)
Exception ht > 180 mm
There is a recommended value of cant depending on the speed of the fastest trains and the horizontal curve radius.
⋅ 2 7.1 Vdim h , = ------(3-12) trec R
There is also a minimum value of cant which has to be arranged according to Equation (3-13)
11.8 ⋅ V2 h = ------dim – h (3-13) tmin, R dlim, hd,lim, See 3.3.2 “Cant deficiency” Examples of horizontal curve radius according to German standard are shown in section 3.3.3.
3.3.2 Cant deficiency
Table 3-11 shows values for permitted cant deficiency on plain track according to [9].
23 Standards, practices and TSI
Table 3-11 Design value of cant deficiency Source: Deutsche Bahn [9]
Without permission
Recommended hd =70mm
Limit hd = 130 mm Permission necessary
Permission hd = 150 mm
3.3.3 Horizontal curve radius
The recommended horizontal curve radius according to DB is derived from the following formula and some examples are shown in Table 3-12.
2 ⋅ 2 ⋅ Vdim 11.8 Vdim 11.8 Rrec ==------(3-14) heq 170 This recommendation is based on an equilibrium cant of 170 mm, i.e. 100 mm of cant and 70 mm of cant deficiency. Table 3-12 Recommended horizontal curve radius. Source: Deutsche Bahn [9].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Recommended radius [m] 2776 4338 5542 6247 7559 8503
The limit of horizontal curve radius (without permission) can be described of Equation (3-15) and some examples are shown in Table 3-13.
2 V ⋅ 11.8 R = ------dim - (3-15) lim 290 This limit value is based on an equilibrium cant of 290 mm. Table 3-13 Limit value of horizontal curve radius. Source: Deutsche Bahn [9].
200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Limit radius [m] 1628 2543 3190 3662 4431 4984
24 Track geometry for high-speed railways
A value of horizontal curve radius were permission is needed can be described by Equation (3-16) according to DB.
2 V ⋅ 11.8 R = ------dim - (3-16) permission 330 This permission value is based on an equilibrium cant of 330 mm with a cant of 180 mm and a cant deficiency of 150 mm. Some examples are shown in Table 3-14. Table 3-14 Permission value of horizontal curve radius. Source: Deutsche Bahn [9].
Horizontal curve radius 200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Permission value [m] 1430 2234 2803 3218 3894 4380
Figure 3-3 shows the horizontal curve radius as a function of speed for three different levels according to German standard. Table 3-9 to 3-11 described the levels which German standard is based upon.
9000 Recommended minimum value according to DB 8000 Limit value (without permission) according to DB Permission value according to DB 7000 6000 5000 4000 3000 2000
Horizontal curve radius [m] 1000 0 100 150 200 250 300 350 Speed [km/h]
Figure 3-3 Horizontal curve radius as a function of speed. Source: Deutsche Bahn [9].
25 Standards, practices and TSI
3.3.4 Transition curve and superelevation ramp
Transition curvature shall coincide with superelevation ramps in both shape and position. The regulations for the design of transition curves, due to maximum cant gradient, are the same as Equation (3-6) [10], [15]: ≥ ⋅ ∆ Lt 0.4 htmm, (3-17)
The lower permissible limit of Lt according to this formula is applied on low speed track only; for high-speed lines the transition length is determined by the rate of change in cant deficiency according to Equation (3-20). The permitted speed in transition curves with linear change of cant, however, is partly different from Sweden. In Germany the maximum speed for non-tilting trains is according to [10], [15] L ⋅ 1000 ≤ ------t - Vdim ⋅ ∆ (3-18) 8 htmm, L ⋅ 1000 ≤ ------t - Vdim ⋅ ∆ (3-19) 4 hdmm, The minimum length of clothoid type of transition curves is according to DB [9] in accordance with Equation (3-19) which after rewriting can be obtained as follows 4 ⋅⋅V ∆h L ≥ ------dim d (3-20) tmin, 1000 For tilting trains the following formula is valid for transition curves with linear change of curvature and cant, respectively [10] [15]: L ⋅ 1000 ≤ ------t - Vdim ⋅ ∆ (3-21) 6 htmm,
3.3.5 Gradient
DB have prescribed [10] a largest permissible gradient of 12.5 ‰ for mixed traffic main lines (Hauptbahnen). For commuter lines (S-Bahnen) and secondary lines (Nebenbahnen) the maximum gradient is 40 ‰. Also, in the new-build high-speed lines the higher gradient (40 ‰) is used.
26 Track geometry for high-speed railways
3.3.6 Vertical curve radius
Minimum permissible vertical curve radius is shown in Table 3-15. Table 3-15 Design value for vertical curve radius
Without permission
Recommended 2 R = 0.4 ⋅ V minimum value v dim
Limit value ⋅ 2 Rv= 0.25 Vdim Permission necessary
Permission ⋅ 2 Rv= 0.16 Vdim on a crest ⋅ 2 Rv= 0.13 Vdim in a hallow ≥ Rv 2000m Exception value -
Some examples are shown in the following table. Table 3-16 Recommended minimum value for vertical curve radius Source: Deutsche Bahn [9].
Vertical curve radius 200 250 280 300 330 350 km/h km/h km/h km/h km/h km/h Recommended minimum 16000 25000 31360 36000 43560 49000 Limit 10000 15625 16900 22500 27225 30625 Permission value on a crest 6400 10000 12544 14400 17424 19600 Permission value in a hallow 5200 8125 10192 11700 14157 15925
27 Standards, practices and TSI
3.4 Practices in France
3.4.1 Cant, cant deficiency and cant excess
Recent information regarding France is scarce. The following was found in [18]. Experiment shows that the non compensated lateral acceleration should not exceed 0.10 à0.15g(1.0à1.5m/s2) according to comfort requirements. SNCF allows a cant deficiency of 150 mm (exceptional value 160 mm)1 and a cant excess of 70 to 100 mm (exceptional values between 105 and 135 mm, in dedicated high-speed operations, without freight trains). At SNCF the limiting value of cant is about 160 mm and exceptionally 180 mm. A cant of 180 mm was utilized as limiting value at the high-speed line Paris-Sud Est. The cant is given to respect the limiting values of cant deficiency (150 mm) and cant excess (100 mm).
1. The ‘Grande Vitesse Paris-Sud-Est’ line limited the value of cant deficiency to 100 mm [15].
28 Track geometry for high-speed railways
3.5 Practices in Japan
A specified track geometry standard for the Japan railway has not been found in English but a Data Book 2000 for the Central Japan Railway Company [19] was found. In the book a compilation over the structural specifications was arranged, see Table 3-17 Table 3-17 Structural specifications for the Central Japan Railway Company.
Tokaido Sanyo Tohoku-Joetsu Shinkansen Shinkansen Shinkansen Start of operations 1964 1972 1982
Maximum operating speed [km/h] 270 300a 275 Maximum gradient [‰] 20 15 15 Minimum curve radius [m] 2500 4000 4000 Minimum vertical curve radius [m] 10000 15000 15000 Cant [mm] 200 180 180 Distance between track centres 4.24 4.3 4.3
a. Planned speed
29 Standards, practices and TSI
3.6 Technical Specifications of Interoperability and CEN proposal
The purposes of the Technical Specifications of Interoperability (TSI) [12] are according to Article 5(3) of Directive 96/48/EC (among other things): - specify the essential requirements for the subsystems and their interfaces; - establish the basic parameters that are necessary to meet essential requirements; - establish the conditions to be compiled with, to achieve the specified performances for each of the following categories: - lines specially built for high-speed, - lines specially upgraded for high-speed, - lines specially built or upgraded for high-speed, which have special features as a result of topographical, relief or town-planning constraints; - establish possible implementing provisions in certain specific cases; - determine the interoperability constituents and interfaces which must be covered by European specifications, including European standards which are needed to achieve interoperability within the trans-European high-speed rail system while meeting the essential requirements; Furthermore, according to TSI, the performance levels of high-speed trains can also be enhanced by adopting specific systems, such as vehicle body tilting. The TSI is yet not completed; the above mentioned version [12] is a draft.
3.6.1 Track cant and track distance
According to the draft TSI the cant for new high-speed lines in the design phase shall be limited to 180 mm to agree with the specifications set out by CEN/TC 256/WG15, Track alignment design parameters, a provisional European norm, prENV 13803-1 [7]. Further the TSI says that for tracks in operation, a maintenance tolerance of 20 mm is allowed, without trespassing a maximum cant of 190 mm. This value may be raised to 200 mm maximum on tracks reserved for passenger traffic alone in accordance with the specifications in the CEN provisional standard on maximum limiting values. The minimum track distance between main track centres on lines specially built for high- speed is 4.5 m according to TSI. This value could be decreased and adapted according to the performance levels and could be 4.20 m if 250 < V ≤ 300 km/h and 4.0 m if speed V ≤ 250 km/h.
30 Track geometry for high-speed railways
Table 3-18 shows values of cant according to CEN provisional standard, currently prENV 13803-1, final draft, February 2001. Table 3-18 Limiting values of cant Source: CEN provisional standard, prENV 13803-1 [7].
Mixed traffic lines with passenger train Mixed traffic lines V ≤ 230 (or 250 High-speed lines designed for with dedicated Traffic categories on upgraded lines) passenger train with vehicles passenger traffic 200 < V ≤ 300 incorporating 250 ≤≤V 300 special technical design characteristics
Recommended 160 160 160 limiting value [mm] Maximum 180 180 200 limiting value [mm]
3.6.2 Cant deficiency and cant excess
Cant deficiency
Table 3-19 to Table 3-21 show the limit values of cant deficiency on plain track according to TSI. Table 3-19 Cant deficiency for lines specially built for high-speed. Conventional trains without tilt. Source: TSI [12].
Speed range (km/h) Limiting value (mm)
250 ≤≤V 300 100
V > 300 80
Higher values of cant deficiency than shown in Table 3-19 may be allowed for lines whose construction involves very tough topographical constraints, see Table 3-20.
31 Standards, practices and TSI
Table 3-20 Cant deficiency for lines specially upgraded for high-speed and connecting lines. Lines whose construction involves very tough topographical constraints. Conventional trains without tilt. Source: TSI [12].
Speed range (km/h) Limiting value (mm)
V ≤ 160 160
160 < V ≤ 200 150
200 < V ≤ 230 140
230 < V ≤ 250 130
Higher values of cant deficiency than shown in Table 3-20 may be allowed for lines whose construction involves very strict topographical constraints, see Table 3-21.
Table 3-21 Cant deficiency for lines specially built or upgraded for high-speed having special features. Lines whose construction involves very strict topographical constraints. Conventional trains without tilt. Source: TSI [12].
Cant deficiency range for Maximum limiting which the length of curves is Speed range (km/h) value (mm) limited to 20% of the total curve length (mm) ≤ 180 < ≤ V 160 160 hd 180 < ≤ 165 < ≤ 160 V 230 150 hd 165 < ≤ 150 < ≤ 230 V 250 130 hd 150 < ≤ 130 < ≤ 250 V 300 100 hd 130
However, on lines the radii of which have been defined on the basis of the cant deficiency values in the above tables, interoperable high-speed trains equipped with tilt technology may be admitted to run with higher cant deficiency values, provided that adopting such values for those trains does not bring about restrictions for other interoperable trains [12].
32 Track geometry for high-speed railways
According to the CEN provisional standard the values of cant deficiency and its corresponding lateral acceleration are based on the following considerations: - Track forces and safety; - Economic aspects of track maintenance; - Ride comfort and roll flexibility coefficients of the vehicles. Table 3-22 below lists the limiting values of cant deficiency in accordance to CEN provisional standard [7]. Table 3-22 Limiting values of cant deficiency. Conventional trains without tilt. Source: CEN provisional standard, [7].
Recommended Maximum limiting Traffic categories limiting value [mm] value [mm] Freight Passenger Freight Passenger
Mixed traffic lines 200 < V ≤ 250 100 100 150 150 designed for passenger trains 80 80 130 130 250 < V ≤ 300 200 < V ≤ 300 Mixed traffic lines 110 160 160 180 V ≤ 160 with passenger train V ≤ 230 x 140 x 160 160 < V ≤ 200 (or 250 km/ on upgraded lines) x 120 x 160 200 < V ≤ 230 with vehicles incorpo- rating special techni- < ≤ x 100 x 150 cal design 230 V 250 characteristics High-speed lines with x 100 x 150 V = 250 dedicated passenger traffic x 80 x 130 V > 250 250 ≤≤V 300
Cant excess
The TSI does not discuss cant excess. However, CEN provisional standard gives as guidance, the following limiting values for cant excess: - 110 mm as recommended limiting value; - 130 mm is a maximum limiting value.
33 Standards, practices and TSI
3.6.3 Horizontal curve radius
The parameters that shall be considered in the determination of the minimum curve radius according to CEN provisional standard [7] are: - The maximum and minimum operating speeds; - The applied cant; - The limiting values for cant deficiency and cant excess. The minimum allowable curve radius for the maximum operating speed shall be calculated using the following equation:
11.8 ⋅ 2 R = ------Vmax (3-22) ht + hd The minimum allowable curve radius for the minimum operating speed shall be calculated using the following equation:
11.8 ⋅ 2 R = ------Vmin (3-23) ht – he The minimum curve radius should be optimised so that the values of cant, cant deficiency and cant excess comply with the limits specified in [7] and satisfy the following condition:
11.8 ⋅ V2 11.8 ⋅ V2 ------min- ≥≥R ------max- (3-24) ht – he ht + hd
Table 3-23 gives some examples of the usage of Equation (3-22) - (3-24). Table 3-23 Examples of optimised cant and optimised horizontal curve radius. Calculations are made with both high-speed trains (conventional trains without tilt) and slowly running freight trains. Values of cant deficiency and cant excess are recommended values according to TSI [12].
Vmax Vmin hd he ht R [km/h] [km/h] [mm] [mm] [mm] [m] 300 80 100 110 126 4696 300 120 100 110 150 4247 300 160 100 110 193 3618 350 80 80 110 120 7209 350 120 80 110 135 6713 350 160 80 110 160 6017
34 Track geometry for high-speed railways
For lines specially built or upgraded for high-speed having special features a cant deficiency of 130 mm can be applied for speed up to 300 km/h. Still no tilt system is in use. Table 3-24 give some examples. Table 3-24 Examples of horizontal curve radius with a cant deficiency of 130 mm for 250 km/h and 300 km/h with different values of cant. Conventional trains without tilt.
Vmax hd ht R [km/h] [mm] [mm] [m] 250 130 160 2543 300 130 160 3662 250 130 180 2379 300 130 180 3425 250 130 200 2235 300 130 200 3218
3.6.4 Transition curve and superelevation ramp
Rate of cant
∆ For cant gradients with uniform slope, the following relationship with ht being the cant variation is desired according to CEN provisional standard [7]:
dh ∆h ⋅ V æödh t ------t max ≤ ------t ------= ⋅ èø (3-25) dt 3.6 Lt dt lim
The limiting value of rate of cant as a function of time (dht/dt)lim is shown in Table 3-25.
Table 3-25 Limiting values of rate of cant as a function of time (dht/dt)lim. The values apply to cant gradient with uniform slope. Conventional trains without tilt. Source: CEN provisional standard, [7].
Mixed traffic lines Mixed traffic lines High-speed lines designed for with passenger with dedicated Traffic categories passenger trains train speeds passenger traffic 200 < v ≤ 300 v ≤ 230 250 < v ≤ 300
Recommended 50 50 50 limiting values [mm/s] Maximum limiting 60 60 60 values [mm/s]
35 Standards, practices and TSI
Limiting values of rate of cant as a function of length (dht/dx)lim shall apply to the following values, although not critical at high-speed operations: Recommended limiting value: 2.25 mm/m Maximum limiting value: 2.5 mm/m
Rate of cant deficiency
For transition curves with a uniform variation of curvature and a uniform variation of ∆ cant, the following relationship is derived, hd is the variation of cant deficiency:
dh ∆h ⋅ V dh d ------d max ≤ æö------d ------= ⋅ èø (3-26) dt 3.6 Lt dt lim
The limiting value of rate of cant deficiency as a function of time (dhd/dt)lim is shown in Table 3-26. Table 3-26 Limiting values of rate of cant deficiency as a function of time (dhd/dt)lim. The values shown apply to all forms of transition curves. Conventional trains without tilt. Source: CEN provisional standard, [7].
Mixed traffic lines Mixed traffic lines High-speed lines designed for with passenger with dedicated Traffic categories passenger trains train speeds passenger traffic 200 < V ≤ 300 V ≤ 230 250 < V ≤ 300
Recommended 50 50 50 limiting values [mm/s] Maximum limiting 75 90 75 values [mm/s]
Length of transition curves in the horizontal plane
The length of transition curves in the horizontal plane should, according to European provisional standard [7], be determined by the limiting values of rate of cant deficiency as a function of time, dhd/dt and rate of cant as a function of length, dht/dx. V dh –1 ≥ max ⋅ ∆ æöd Lt ------hdèø------(3-27) 3.6 dt lim dh –1 ≥ ∆ ⋅ æöt Lt ht èø------(3-28) dx lim The length of transition curve shall be the longest value derived from the above formula for the selected values of dhd/dt and dht/dx.
36 Track geometry for high-speed railways
3.6.5 Gradient
According to TSI, gradients as steep as 35 ‰ shall be allowed for main tracks at the design phase, provided the following requirements are met: - The slope of the sliding average profile over 10 km is less than or equal to 25 ‰; - The maximum length of continuous 35 ‰ gradient does not exceed 6 km. Those recommended limiting values shown above apply only to high-speed lines dedicated to passenger traffic. Exceptions are made for France, which already has gradients up to 40 ‰ on one line (Paris-Sud-Est). Furthermore, the new line between Cologne and Frankfurt is also using gradients as high as 40 ‰. Other restrictions are valid for freight trains.
3.6.6 Vertical curve radius
The vertical curve radius shall be designed using the following formula
V2 ------max ≥ Rv = ⋅ Rvlim, (3-29) 12.96 av
The vertical acceleration, av, used in Equation (3-29) shall be selected taking into consideration ride comfort where there is a possibility of a non optimal track bed. In addition, consideration shall be given to safety to guard against derailment due to wheel unloading when running over humps (crests). However, this safety limit is not considered unless the maximum limiting values for av are exceeded. The limit values of vertical acceleration are shown in Table 3-27.
Table 3-27 Limit values of vertical acceleration, av,lim. Source: CEN provisional standard [7].
Mixed traffic lines Mixed traffic lines High-speed lines designed for with passenger with dedicated Traffic categories passenger trains train passenger traffic 200 < V ≤ 300 V ≤ 230 250 < V ≤ 300
Recommended limiting values 0.22 0.22 0.22 [m/s2]
Maximum limiting 0.44a 0.31 0.44a values [m/s2]
a. With a tolerance of +10% on a crest, +30% in a hallow
37 Standards, practices and TSI
Equation (3-29) and the limit values of vertical accelerations in Table 3-27 yield limiting values of vertical curve radius.
Table 3-28 Limit values of vertical curve radius, Rv,lim. Source: CEN provisional standard [7].
Mixed traffic lines Mixed traffic lines High-speed lines designed for with passenger with dedicated Traffic categories passenger train train passenger traffic 200 < V ≤ 300 V ≤ 230 250 < V ≤ 300
Recommended 2 2 2 0.35V 0.35V 0.35V limiting values [m] max max max
Minimum limiting 2 2 2 0.175V 0.25V 0.175V values [m] max max max
38 Track geometry for high-speed railways
3.7 Comparison between different projects and standards
3.7.1 Horizontal curve radius
Table 3-29 “Planned alignment and track parameters of new lines of the second generation high-speed railways.” Source: Compilation made of E. Hohnecker [20].
Line Vlim Rmin ht,max hd,max ay [km/h] [m] [mm] [mm] [m/s2]
DBa 300 3200 200 130 0.85
JRb 350 4000 200 160 1.05
SNCFa 350 4000 200 160 1.05
a. Ballast track b. Ballastless track
39 Standards, practices and TSI / b a 250 2000 (partly) 200 11000 Botniabanan TGV Atlantique Sud Est 14000 TGV Paris- Mann Köln-Rhein/ Würzburg Hannover- Joetsu Tokyo- Shinkansen Sanyo Shinkansen Tokaido Shinkansen [m][m] 10000 15000 15000 22000 5100 3425 12000 4000 6020 2950/ Exceptional values not considered. Organisation TSI/CEN JR JR JR DB DB SNCF SNCF BV Item Track distanceMinimum vertical curve radius Maximum gradient [m] [‰] 4.5 35 4.24 4.3 20 4.3 15 15 12.5 40 4.2 35 4.2 25 4.5 10 Maximum design speedMaximum service speed [km/h] [km/h]CantCant deficiencyCant excessMinimum 270 curve radiusMinimum [mm] radius of design 300 speed [m] [mm] 100 [mm] 275 180 100 110 250 200 100 2500 280 180 4000 100 300 4000 180 270 80 300 7000 65 300 150 3350 350 160 4000 85 250 50 180 6250 60 3200 180 100/220 150 100 a. Category A trains b. Category S trains (tilt technology) Table 3-30 Comparison between different quantities on different railway companies throughout the world.
40 Track geometry for high-speed railways
3.8 Recent resarch on nominal track geometry
3.8.1 Optimisation of horizontal alignments for railways
In Kufvers doctoral thesis [16] the focus was on optimal alignment and cant on single horizontal curves. He made, for example, studies on the following track quantities: radius, cant and lenghts of transition curves and corresponding superelevation ramps. The objective of his study was to develop methods for comparing and optimising of horizontal alignments when building new lines and improving existing ones. In short terms some of Kufvers conclusions will now be presented. A single curve consists of a transition curve, a circular curve and transition curve, placed between two tangent tracks. If a lengthening of the transition curves is wanted then it will require a reduction of the radius in the circular part of the curve. This is valid for a single curve between two fixed straight lines. The present study does not bring up passenger comfort as an object function. According to Kufver the PCT functions are the most reasonable overall comfort functions because PCT includes the lateral acceleration, lateral jerk and roll velocity. These physical quantities are the most basic ones when calculating alignment and cant. Kufver came to the conclusion that S-shaped ramps and corresponding types of transition curves have no substantial advantages compared to transition curves with linear change of curvature (clothoids). The optimal lenghts of the clothoids depend on the limit for cant, the roll coefficient of the vehicle and the degree of compensation in the body tilt system. One of the most important findings is that a tilt system with a large degree of compensation for lateral acceleration favours long transition curves (clothoids). Thereby the roll velocities are reduced. Within an alignment restricted by existing obstacles longer transition curves will in many cases lead to less radius in the circular curve and thus a higher lateral acceleration. However, the latter problem will to a large extent be compensated by means of the carbody tilt, which reduces the lateral acceleration on passengers. However, the curve radius must always be sufficiently large in order to cope with the desired speed for conventional (non-tilting) trains. For more detailed descriptions, see Kufver [16].
3.8.2 Ride comfort and motion sickness in tilting trains
Förstberg [14] made two kinds of tests when determining ride comfort and motion sickness. Firstly, in the tilting tests, the concept of symptoms of motion sickness incidence (SMSI) was used. Those tests utilised different strategies for active tilt of the carbody to reduce lateral acceleration during curving. For example, when using a lower ratio of tilt compensation a reduction of reported symptoms of motion sickness was found.
41 Standards, practices and TSI
Secondly, when evaluating the simulator tests, the evaluation variable nausea rating (NR) was used. Förstberg found that it was likely that lower compensation and limited tilt velocity are favourable in a everyday population of passengers. The main conclusions drawn by Förstberg are: - Roll motions presented alone are not very nauseogenic and only small differences were found between gender. - Lateral accelerations alone seem to be medium challenging. - Combinations of high roll and high lateral accelerations seem to be highly provocative for motion sickness. However, it is necessarily not nauseogenic with high compensation ratios alone. For example, low roll velocity and low lateral acceleration with a compensation rate of 75%, show low nausea ratings. - Both high lateral acceleration and high roll velocity have negative effects on the ability to work and/or read as well as the ride comfort. One consequence of Förstberg’s research is that long transition curves would be desirable from a motion point of view. This is essentially the same conclusions as made by Kufver described in the previous Section. For more detailed descriptions, see Förstberg [14].
42 Track geometry for high-speed railways
3.9 Summary and conclusions
In Europe it is a clear trend to make specifications for high-speed track geometry less strict, i.e. to allow tighter horizontal curves and steeper gradients for a given speed. The most obvious case may be Germany, where the first generation of ‘Neubau-Strecken’ (for example Hannover - Würzburg) was built with curve radii of 5100 - 7000 m and a gradient of 12 ‰ at 250 - 280 km/h. The second generation ‘Neubau-Strecken’ (Köln - Frankfurt for example) allows a curve radius of 3350 m and a gradient of 40 ‰ for operation at 300 km/h. The CEN provisional standard and the newly drafted TSI confirm this trend. This is along the same line as part of the Japanese Shinkansen, where a horizontal curve radius of 2500 m is allowed at 270 km/h. Partly this trend is due to the fact that most of the new lines are built exclusively for high-speed passenger trains, not mixed traffic including heavy freight trains. Quite light passenger trains with high traction forces and power (per tonne of train) are able to climb much steeper grades than locomotive-hauled heavy freight trains. Also, for passenger trains a higher track cant can be arranged, in some cases up to 200 mm, because there is no risk of danger if a passenger train stops at a section with high cant - in an ordinary freight train there is risk for load displacement in wagons. The higher cant on high-speed lines allows somewhat reduced horizontal curve radius for the same cant deficiency and speed. However, this seems not to be the main reason for the smaller horizontal curve radius. In the new practice and proposed European standards a quite high cant is allowed also on lines with mixed traffic (normally 160 mm, exceptionally 180 mm). The earlier requirements on (a low) cant excess for slowly running freight trains had typical limit values of just 50 - 70 mm in, for example, Germany and Sweden. This, in turn, required low cant to be arranged on high-speed lines with mixed traffic and slowly running freight trains. In the final draft of the CEN proposal (prENV 13803-1) it is now recommended to have a limit value of 110 mm (maximum 130 mm) for cant excess. The suitability of such a change is also confirmed by recent Swedish research [25]. This produces much better conditions for increasing the cant while reducing curve radius on high-speed lines. Similar trends are obvious also for the maximum allowed cant deficiency (lateral acceleration in the track plane). For conventional trains (without carbody tilt) on lines specially built for high-speed a limit value of 100 mm is recommended (80 mm for speeds above 300 km/h). However, in cases of very strict topological constraints a limit value of 130 mm is allowed. Another important feature of the drafted TSI is the allowance for rising speeds by using tilt technology, or inversely, to reduce the necessary horizontal curve radius for a given speed. Such measures are allowed as long as operations of conventional (non-tilting) high-speed trains are not restricted. It is left to the Infrastructure Manager to take decisions on tilting trains running at a higher cant deficiency than conventional trains. Regarding length of transition curves, recent Swedish research [16] allows optimisation of transition lengths within a defined terrain corridor with a number of obstacles. The optimisation has passenger comfort as an object function. According to this research the optimum transitions lengths are depending on (among others) the position of obstacles and also on whether carbody tilt is applied or not. There is a clear tendency that the
43 Standards, practices and TSI introduction of carbody tilt favours longer transition curves in relation to cases where tilt is not applied. This is mainly due to the additional roll velocity introduced on tilting trains. Longer transition curves reduce the roll velocity, which is favourable from a comfort point of view. In this context, recent Swedish research [14] also shows that lower roll velocity is very favourable also with respect to the provocation of motion sickness, which is shown to be a certain problem on tilting trains. All this is in accordance with CEN proposed standard, which limit the rate of change in cant and cant deficiency. It should be pointed out, however, that for tilting trains the optimum rate of change in cant and cant deficiency are normally lower than the limit values in CEN, transition curves and superelevation ramps are longer. Finally,therecommendedvaluesforverticalcurveradiusarenormally2–3times larger than the minimum limiting radius. This is the case in most standards. The minimum requirements are quite similar to each other, including Banverket standard. Normally, the required vertical radius is somewhat larger on crests than in hallows. This is due to the risk of wheel unloading on crests. Some of the above mentioned design parameters are believed to have significant influence in the average construction cost of newly built high-speed railways, namely horizontal curve radius, vertical curve radius and gradient. The technical feasibility of using tilting trains in very high-speed operations is investigated in Chapter 4 - 6 in the present study. This would reduce the necessary horizontal curve radius. In Chapter 7 a brief investigation is made on the permissible gradient and cant for various types of freight trains.
44 Track geometry for high-speed railways
4 High-speed train technology year 2010
To be able to make realistic suggestions regarding track lay-out for high-speed lines, it is important to reflect upon the trains which are going to run on these lines. Possible maximum train speed without hunting problems or possible cant deficiency in curves without exceeding limits for track shift forces, are strongly depending on design and performance of the running gear. The aerodynamic shape of the train plays an important role not only for running resistance but also for side-wind stability of trains. The aim of this chapter is to foresee the performance of a train, which would be available from industry around 2010, i.e. at the earliest time regular traffic on e.g. The European Corridor (Europakorridoren) or other high-speed lines in Sweden is about to start. This is important for the investigation and proposal of an optimum track geometry for the future, which is the main object of this study. The assumptions on the technology and performance of future high-speed trains are made in close co-operation between the author and a number of experts from KTH and industry (Bombardier Transportation, Västerås, Sweden). Among these experts are Mr. Jan Ågren (Lead engineer, Centre of Competence Vehicle Dynamics, Bombardier), Mr. Mikael Sima (Expert in Aerodynamics, Bombardier) and Prof. Evert Andersson (KTH Railway Technology, as well as Company Senior Specialist in Vehicle Technology, Bombardier). It is aimed that assumptions on possible future vehicle technology should not be too optimistic, but rather be at the safe side. The assumed future technology should be known today, although not always implemented in commercial high-speed trains of today. It should be noted that the technology is judged as possible to implement, although there is yet no decision to fully make these implementations in commercial trains. It is mainly a question whether such trains will be demanded on the European market.
4.1 Maximum train speed
To our opinion it is realistic to achieve maximum train speeds of 350 km/h within ten years. Today there are already trains operating with a design speed of 300 - 330 km/h (France, Germany). In Spain there are trains ordered for a maximum speed of 350 km/h.
4.2 Train configuration
Future high-speed trains will probably mostly be electrical multiple units (EMU) where many axles in the train are driven. Advantages compared to loco-hauled trains are mainly higher possible acceleration and lower maximum axle load. Therefore an EMU unit was chosen for the simulations.
45 High-speed train technology year 2010
4.3 Tilt technology
4.3.1 General
Several trains with tilt technology are today operating in large scale at maximum speeds 200 - 250 km/h (Italy, Sweden, Finland, Germany and also in the UK in the near future). Up to now there are no tilting trains operating at speeds above 250 km/h. The hypothesis is that it may be possible to operate tilting trains also at speeds of 300-350 km/h in the future. This study is an attempt to test this hypothesis.
4.3.2 Possible overspeed with tilt technology
Trains with tilt technology have the opportunity to operate at a higher cant deficiency and hence at higher speeds in curves. The possible percentage of overspeed is, among other things, limited by: - Possible lateral accelerations and roll motions with respect to passenger comfort. This is an issue of suspension and carbody tilt control - Possible tilt angle within the vehicle (in particular between bogie and carbody. - Permissible track forces. This is mainly an issue of track design and maintenance, as well as suspension in the running gear. For vertical track forces also the unsprung mass, axle load and the location of centre of gravity are important factors. Examples of permitted overspeed in circular curves as a function of cant are shown is the following figure.
46 Track geometry for high-speed railways
70% 60% Cant deficiency hd=150mm 50% Cant deficiency hd=250 mm 40% 30% 20% 10% Permitted overspeed [%] 0% 0 50 100 150 200 Cant [mm]
Figure 4-1 Permitted overspeed in a circular curve as a function of cant. The permitted overspeed in relation to conventional trains with an allowed cant deficiency of 100 mm (recommended value according to TSI for the speed range up to 300 km/h). Note: For a cant deficiency of 150 mm is no tilt needed.
Note that length of transition curves and superelevation ramps may also limit the (over-) speed.
4.4 Running gear design
Maximum train speed and maximum overspeed in curves are strongly depending on the design of the running gear, especially the suspension. A train with a maximum speed of 350 km/h on tangent track and with up to 250 mm of cant deficiency in curves has to be equipped with well designed running gear. Using the experience from the Swedish running gear design, this study will test if this is possible or not. In principle, an optimised combination of wheelset guidance and damping has to be applied. A very flexible wheelset steering will likely lead to problems with the hunting stability, while a very stiff guidance would produce high lateral track forces. In the future, active technology might be introduced to even better solve this problem. There are, however, still many uncertainties combined with active technology for steering wheelsets. Therefore a decision was made not to take such possibilities into consideration in the present study. One of the developments which will likely be introduced on a larger scale during the next 5-10 year is the so-called Hold-of-device (HOD). It is added in order to center the
47 High-speed train technology year 2010 carbody in curves. This will make it possible to negotiate curves with high cant deficiency without worsening passenger comfort by hitting the lateral bump stops in the suspension, thus producing less dynamic forces on track and passengers. Also, if the carbody were cantered by means of the HOD, the risk of overturning in strong side- winds would be reduced State of the art technology has been supplied by Bombardier Transportation (Sweden) although this is partly proprietary information. This technology has been further investigated and developed in this study.
4.5 Aerodynamic shape
The aerodynamic shape of a high-speed train is important for the running resistance and energy consumption of the train. Furthermore, side-wind stability (i.e. the ability to be safe against overturning in strong side winds) has become a more and more important issue to study in combination with high-speed train operation. There are at least three reasons for this: Speeds are getting higher, vehicles are getting lighter and high-speed lines are often exposed to wind because of frequent use of high embankments and bridges. In this study an aerodynamic shape representative for the best trains existing today is assumed. The aerodynamic coefficients for the used vehicle model are revealed in Appendix E. In comparison, such a train would generate about 20% less overturning moment than the present Swedish X 2000 (at the same roof height).
4.6 Track irregularities
A track which is suitable for trains at a speed of 350 km/h must have a good standard regarding track irregularities. It should be possible on future built high-speed lines to achieve and maintain a track quality better than current Swedish main lines standards, without increasing maintenance costs to an unrealistic level. This assumption has been confirmed by personal communications with specialists from Banverket. One of the aims with this study is to estimate the amount of improvements which would be necessary. These issues will be further investigated and discussed in Sections 5.8, 6.2.5 and 6.2.6.
48 Track geometry for high-speed railways
5 Track/vehicle dynamic simulations - models, conditions and criteria
5.1 Simulation strategy
The simulations have been carried out in three different parts. Firstly, simulations of hunting stability is performed to appoint that used technology can be managed in such high speed as 350 km/h. Secondly, the track shift forces will be calculated according to Prud´hommes criteria. Thirdly, vehicle overturning was simulated.
5.2 Simulation software
GENSYS multibody computer code was used in the track/vehicle dynamic simulations. GENSYS calculates the behaviour of a railway vehicle accurately and is one of the oldest and largest packages currently in use. There are more than a few options regarding the number of degrees of freedom for the individual bodies such as wheels, bogies, carbody etc. For further information about the simulation tool, please see Appendix G.
5.3 Test speed
In simulations is it easy to control the speed of the train, compared with full scale testings where the actual train speed might be difficult to control. According to CEN TC 256 WG 10 [8] and UIC 518 [24], safety-related quantities must be evaluated at a slightly higher speed then the intended permissible speed. CEN stated that the test speed should be the lower of 110% of permissible speed and the speed which corresponds to 110% of permissible cant deficiency. Kufver [16] says that it would be relevant in certain studies to compare alignments with different radii. Kufver suggested that it would be reasonable to use the same test speed in all alternatives and hence a different cant deficiency. In simulations concerning hunting stability a test speed of 385 km/h was chosen. This speed corresponds to 110% of the intended permissible speed (350km/h). When evaluating track shift forces a test speed of 360 km/h was regarded to approximately fulfil the condition of 110% of permissible cant deficiency. The horizontal curve radius at a cant of 180 mm, cant deficiency of 250 mm and speed of 350 km/h is equal to the horizontal curve radius at a cant of 180 mm, cant deficiency of 275 mm and speed of 360 km/h (R=3361m in both cases). 110% of 250 mm is equal to 275 mm. A cant deficiency of 275 mm was chosen as boundary condition. In the simulations concerning vehicle overturning it was judged to be adequate to choose a test speed of 350 km/h (100% of permissible speed) and radii that correspond to cant
49 Track/vehicle dynamic simulations - models, conditions and criteria deficiencies of 100% of permissible cant deficiency. This is because very strong side- winds and the risk of overturning is a very unlikely event, two unlikely events - too high cant deficiency and strong side-winds - is still more unlikely to happen and should therefore not be considered as a realistic case.
5.4 Hunting stability
Two types of instabilities will be studied in the present work. High frequency instability occurs at high-speeds and high equivalent conicity. Low frequency instability tends to occur if the wheelset hunting frequency and a natural frequency of the vehicle on its suspension are rather similar. Thus, low frequency instability is more or less similar to a resonance phenomenon. The matter of equivalent conicity is explained in detail in the course books [2], Chapter 4, and [3], Chapter 7 and 8. Two requirements must be fulfilled in the simulations: - The hunting frequency should not exceed 10 Hz because of the risk of resonance with the lateral bending mode of the carbody. Wheelset steering will be chosen to fulfill this requirement. - The decay of the hunting amplitude must be at least 60% in two cycles after a sudden disturbance. In addition, no significant sustained vibration shall be visible after 200- 400 metres. The hunting stability is tested by simulation on both tangent and curved track, at speed according to Section 5.3. The equivalent conicity is varied according to Section 5.7.
50 Track geometry for high-speed railways
5.5 Track shift forces
The track shift force is represented by ΣYinFigure5-1.
Figure 5-1 Track forces where Ql and Qr are the vertical forces and Yl and Yr are the lateral forces. The track shift force is represented by ΣY.
The safety-critical limit for track shifting according to Prud’homme criterion is
æö2Q ΣY =10S = k ⋅ k ⋅ + ------0- [kN] (5-1) lim lim s 1 èø3 where ks = 0.85 in the simplified statistical analysis in this study. 2Q0 is the static vertical axle load and k1 is a factor usually set to 1 for passenger vehicles, according to CEN and UIC 518 [8], [24]. The value of ks = 0.85 was chosen because track shift forces usually are evaluated statistically. This usually results in a spread of track shift forces of about ±15% around the mean value. Therefore we decided to apply the safety margin to “be on the conservative side”. Further, the track shift forces are filtered before evaluation. The mean value over 2 metres is compared with Prud’hommes limit. The limit refers to 46 kg/metre rails in ballasted track with a maximum timber sleepers spacing of 650 mm. Today’s track with concrete sleepers, 60 kg/metre rails with welded joints and ballasted track gives also a certain safety margin, see further CEN [8].
51 Track/vehicle dynamic simulations - models, conditions and criteria
5.6 Vehicle overturning at strongly side-wind
5.6.1 General
For trains, which are exposed to strong side-winds pointing outwards in the curve there exists a risk for vehicle overturning around the outer rail. This is particularly true if they are running through curves at high-speed, high cant deficiency and track irregularities. The overturning risk is increased if the centre of gravity is moved outwards in the curve. Thus, large lateral spring travels due to suspension flexibility usually increase the risk of overturning. A tight lateral bump stop, or a Hold-off-Device (HOD), both limiting the lateral offset of the centre of gravity, will help to reduce the risk of overturning. In this Section a method to quantify the risk of vehicle overturning is presented.
5.6.2 Tolerable wind velocities
The environment in which a train operates may be very different from place to place, especially regarding the probability of being exposed to strong side winds. In Sweden, side winds velocities up to 30 à 40 m/s may be found on selected open locations without any shielding trees, buildings, hills or similar. The strongest winds usually occur in vicinity of the sea, especially at the West Coast. The wind velocity increases at higher height above ground. The wind velocity also increases above high embankments, because the wind hitting the embankment side is usually forced to run over it. Also, the wind varies over time and occurs as “wind gales”. It is usually very difficult to summarise these complex phenomena into a limited number of simple load cases for each newly built train. Furthermore, different types of trains can also be more or less sensitive to side winds. The aerodynamic properties, especially the cross section shape and height are decisive for the aerodynamic forces acting on the train. In particular, the lateral force and the roll moment are important aerodynamic characteristics with respect to overturning; for example a higher roof height of the train will usually increase the risk. Also the height of centre of gravity is important for the risk of overturning. See further Appendix E and Lippert [21] for details. Another factor increasing the risk of overturning is the lateral deflection of the centre of gravity, i.e. how much the c.g. is moved outwards in the curve under influence of the centrifugal forces and the side wind forces. Thus a large lateral spring travel due to suspension flexibility is not desirable from this point of view (although improving the ride quality). Therefore, a tight lateral bump stop or a so-called Hold-off-Device (HOD), both limiting the lateral offset of the c.g., will help to reduce the risk of overturning. Several procedures have been used to cope with the side wind issue. In Sweden a comprehensive effort was made in the 1980´s, related to the design of X 2000.Large efforts have recently been made in Germany and France.
52 Track geometry for high-speed railways
The European standard for evaluating safety against vehicle overturning at strong side winds is under development within the framework of TSI [12] [13]. In this study the preliminary requirements according to a “Working proposal”, June 2001, [26] are used. The idea is firstly that the train must have a basic resistance against overturning at strong side winds. Although the exact level of side wind velocity is yet not settled, a level around 23 m/s of tolerable side wind from the most adverse direction is discussed. This level is related to the “Vector intercept” criterion presented in the next Section 5.6.3. The level 23 m/s is quite equivalent to the safety level set down for X 2000, although the overturning risk criteria were formulated in another way [28]. Secondly, if there is an unacceptable risk that the wind velocity on specific locations will be higher than the basic level mentioned above, the infrastructure manager is responsible for taking adequate measures to maintain the level of traffic safety [12]. This can be made by temporary speed restrictions at strong side winds (which requires an appropriate wind reporting system and traffic management). The infrastructure manager may also install protective equipment such as wind barriers. In this study the strategy is to investigate whether the high-speed train meets the appropriate overturning criteria (see Section 5.6.3), with a constant side wind velocity of 23 m/s applied to the train from the most adverse direction, when the train is running at its maximum admissible cant deficiency at the maximum operating speed.
5.6.3 Intercept method risk factor
The method for determining the risk of vehicle overturning used in the present study is the intercept method, which is based on the vertical track forces of the vehicle. The intercept method calculates a resulting force as a result of all wheel forces. Figure 5-2 and Table 5-1 show the definition of quantities for calculation of the risk of vehicle overturn with the intercept method.
Figure 5-2 Definition of quantities for calculation of risk of vehicle overturn with the intercept method.
53 Track/vehicle dynamic simulations - models, conditions and criteria
bt is a measure for the risk of the vehicle turn-over and describes the distance between the centre of the track plane and the point where the resultant force is acting. bt can be calculated by replacing the wheel forces with a resultant force under the restriction that the resultant force causes the same forces and moments as the wheel forces. Table 5-1 Quantities for the calculation of the overturning risk according to the intercept method Σ Ql Sum of the vertical wheel forces, left wheel [kN] Σ Qr Sum of the vertical wheel forces, right wheel [kN] R Resulting force [kN]
bt SeeFigure5-2 [m]
bo Half lateral distance between the contact points of [m] left and right wheel
The forces in the left and right parts of Figure 5-2 are equivalent to each other, the two force components in the right figure are the vector sums of the Y- and Q-forces in the left figure. The resultant R of the two forces in the right figure cuts the track plane at a distance bt from the track centre line. The roll moments in the two parts of Figure 5-2 are the same if the following is valid:
ΣQ ΣQ l – r b ------⋅ b t = Σ Σ o (5-2) Ql + Qr The absolute value in the nominator is needed to consider overturning to both the left and right side. When the wheels on one side are totally unloaded, bt has got the value bo and stays constant. The permissible value for bt can be defined as ⋅ bt ==btlim, Ebo (5-3) Put Equation (5-3) into Equation (5-2) and solve E in the new equation. We get a ratio of bt and bo that defines a risk factor according to Equation (5-4):
ΣQ ΣQ l – r ------⋅ b o ΣQ ΣQ b ΣQ + ΣQ l – r E ==-----t ------l r - =------(5-4) bo bo Σ Σ Ql + Qr Typical values for E are between 0.8-1. In the present study a limit value of 0.9 has been used. With the intercept method risk factor, E can be calculated for one wheelset, one bogie or the whole vehicle. In this study, E is calculated for the whole vehicle, considering the forces of all wheels.
54 Track geometry for high-speed railways
The quantity E from the simulations has been low-pass filtered with the frequency f =1.5 Hz (the reason is given below).
5.6.4 Disadvantages with intercept method
According to Lippert [21] the intercept method has two disadvantages. Firstly, the vector intercept is calculated by using the wheel forces which are - due to fast dynamic variations - a conservative criterion to show side-wind stability, especially when real track with track irregularities is simulated. As commented above, the signals must be low-pass filtered to be appropriate to a quite slow process like overturning. Secondly, bt of the intercept method can not become larger than bo. This means that as soon as all wheels on one side loose contact, bt stays constant, independent from changes in the force acting on the train. Although losing contact with all wheels at the same time is a critical situation, it must not necessarily immediately overturn the vehicle due to the vehicle’s inertia. A low-pass filtering of 1.5 Hz is considered as slightly conservative. It has been used for overturning investigations of the Swedish X 2000 train and has been used in the preliminary outline of the future Rolling stock TSI [13]. However, it is yet (Dec. 2001) not finally decided exactly how to make a realistic specification of safety against vehicle overturning.
5.6.5 Aerodynamic train design
A good aerodynamic shape, according to Section 4.5 is assumed. In combination with a roof height limited to 3.6 m the lateral forces and the overturning moments due to side- wind is on the low side, although considered to be realistic.
55 Track/vehicle dynamic simulations - models, conditions and criteria
5.7 Rails, wheels and equivalent conicity
Equivalent conicity is a geometrical property between wheels and rails, describing the magnitude of rolling radius difference (between right and left wheel) when the wheelset is displaced laterally relative to a tangent track (where the wheelset is nominally at its centre position). For exact definitions and many other details, see course books [2], Chapter 4, and [3], Chapter 7 and 8. The equivalent conicity is very dependent on the actual wheel and rail profiles (at the rail head) as well as on the rail inclination in the track and on the track gauge. It is also dependent on built-in geometrical tolerances and on the actual wear shapes of both wheels and rails. In the TSI and CEN specifications the maximum equivalent conicity shall apply for different maximum speeds V (km/h) corresponding to Table 5-2: Table 5-2 Maximum equivalent conicity at different maximum speed. All according to CEN and TSI.
Design value In service, taking into Speed (km/h) (maximum) account wheel and rail wear 230 < V ≤ 250 0.25 0.30 250 < V ≤ 280 0.20 0.25 V > 280 0.10 0.15
Thus, on tracks and vehicles for these speeds the rails and wheels shall be obtained and maintained that the above shown equivalent conicity can be achieved. As one of several measures to meet these conicity requirements, the track gauge must be in the range of 1434 - 1440 mm in all speeds above 250 km/h, according to TSI [12]. The strategy in this study is to select a suitable combination of rail and wheel profiles in order to arrive at the desired equivalent conicity on tangent track. Variations of conicity (for given rail and wheel profiles) are made by varying the track gauge within certain limits. Two kinds of rail profiles have been used in the present study; UIC 60 rail profile and a BV 50 rail profile, both with the Swedish rail inclination of 1:30. The UIC 60 rail profile is standardised by the UIC and is used on many lines and new-built lines in Europe. This rail profile has been used in the simulations of track forces and vehicle overturn. A worn BV 50 rail has been used for stability simulations on tangent track thus leading to a higher value of equivalent conicity than new nominal rail head shapes. For stability simulations on curves the UIC 60 rail profile is used. The above-mentioned rail profiles are combined with wheel profiles type UIC/ORE S1002, see Section 5.9. In this procedure the equivalent conicity can be varied up to a value of at least 0.40, which can be used in the stability simulations.
56 Track geometry for high-speed railways
5.8 Track irregularities
5.8.1 Classification of track irregularities
Most railway companies classify their tracks with regard to the level of permissible track irregularities. On main lines, in particular on high-speed lines, less irregularities are permitted than on lines for lower speeds. This section refers to the classification in the CEN/TC 256 WG 10 [8] as well as Banverket BVF 587.02 [6]. Three classes of track qualities are defined with regard to the necessity of maintenance and to the applicability for acceptance of vehicles. The three levels used by the CEN are described below. - QN1 refers to the value which necessitates observing the condition of the track or taking maintenance measures as part of regularly planned maintenance operations. - QN2 refers to the value which requires short term maintenance action. - QN3 refers to the value which, if exceeded, leads to the track section being excluded from the analysis because the track quality encountered is not representative of usual quality standards. Banverket uses the following levels: - A. New-built or recently adjusted track. - B. Lower quality limit. States target value of maintenance actions. The track irregularities should normally be adjusted before this level attains. This limit is often related to comfort aspects. - C. This limit should not be exceeded. The track irregularity must be corrected as soon as possible. Reduced speed limits should be taken into consideration until the irregularities have been corrected. Each level refer to a certain quality class, K0 - K5, depending on the permitted speed on that particular track [6].
57 Track/vehicle dynamic simulations - models, conditions and criteria
5.8.2 Track irregularities for dynamics analysis
As input data for analysis of vehicle dynamics the absolute irregularities as function of distance have to be known or assumed. Track irregularities can be represented by the following description: - Vertical irregularity, deviation from the designed vertical alignment (centre line). - Lateral irregularity, deviation from the designed lateral alignment (centre line). - Gauge irregularity, deviation from nominal gauge. - Cant irregularity, deviation from designed cant. The four different irregularity types are illustrated in Figure 5-3.
Figure 5-3 Track irregularities described by four different quantities
In the present study two sets of track irregularities with quite different characteristics were used. The first set of irregularities originals from a curve between Simonstorp and Katrineholm recorded by a Mauzin track recording coach. The track is denoted S221. The other track irregularity is measured on a tangent track between Åby and Nyköping. Both tracks are regarded as “median standard” track. The aim of the simulations performed in this study is to find out what amplitude of irregularities can be permitted, without exceeding the safety-critical limit of track shift forces at 275 mm cant deficiency (i.e. 110% of the cant deficiency 250 mm. The amplitude of the described track irregularities are varied by multiplication with different factors. The other characteristics (wavelengths etc.) remain the same.
1. S22: BV50 rails, continuous welded rails (CWR) and concrete sleepers spacing of 650 mm. It was orig- inally defined for the specification of the track forces and ride qualities for the high-speed tilting train X 2000.
58 Track geometry for high-speed railways
To make a quality control of the track irregularities a methodology was set out in this study. The so-called Q-values [6] of the reference irregularities were calculated. The Q- value is a measure of the average standard deviations with respect to the comfort limits of Banverket’s standard classification. A Q-value of 80 means the standard deviations are 0.7 times the limit. A Q-value of 100 means that the standard deviations are 0.5 times the limit value of the current quality class. Thus, the aim of this part of the study was to find the Q-value and relative amplitude that meets the regarded levels of track forces. To get a track classified in a special quality class a Q-value of 80 is necessary to be achieved. If the Q-value is equal to 80 it meets the quality requirements stated for Ban- verket quality classification level B. The Q-values in this study refer to Banverket quality class K0. This is the quality class defined for speeds in the range of 200 km/h (above 145 km/h for conventional trains and above 185 km/h for tilting high-speed trains). The different combinations of track irregu- larities are shown in Table 5-3 and Table 5-4. Table 5-3 Track irregularities based on the irregularity S22 (curved track).
Q-value Lateral Vertical Gauge Cant Multiplication Track (class K0) factor factor factor factor factor Track 2 (S22) 65 0.650 0.800 0.650 0.800 1.0 Track 3 82 0.520 0.640 0.520 0.640 0.8 Track 4 90 0.455 0.560 0.455 0.560 0.7 Track 5 99 0.390 0.480 0.390 0.480 0.6 Track 6 107 0.325 0.400 0.325 0.400 0.5
Table 5-4 Track irregularities based on the irregularity between Åby and Nyköping (tangent track).
Q-value Lateral Vertical Gauge Cant Multiplication Track (class K0) factor factor factor factor factor Track 7 89 0.650 0.800 0.650 0.800 1.0 Track 8 107 0.455 0.560 0.455 0.560 0.7 Track 9 114 0.390 0.480 0.390 0.480 0.6 Track 10 99 0.533 0.680 0.533 0.680 0.85
The characteristics of Track 5 and Track 10 are shown in Figure 5-4 and Figure 5-5, respectively.
59 Track/vehicle dynamic simulations - models, conditions and criteria
15 10 5 0 -5
Vertical [mm] -10 -15 600 700 800 900 1000 1100 Distance [m]
15 10 5 0 -5 Lateral [mm] -10 -15 600 700 800 900 1000 1100 Distance [m]
15 10 5 0 -5 Cant [mm] -10 -15 600 700 800 900 1000 1100 Distance [m]
1445
1440
1435
Gauge [mm] 1430
1425 600 700 800 900 1000 1100 Distance [m]
Figure 5-4 Track irregularity characteristics of Track 5.
60 Track geometry for high-speed railways
15 10 5 0 -5
Vertical [mm] -10 -15 600 800 1000 1200 1400 Distance [m]
15 10 5 0 -5 Lateral [mm] -10 -15 600 800 1000 1200 1400 Distance [m]
15 10 5 0 -5 Cant [mm] -10 -15 600 800 1000 1200 1400 Distance [m]
1445
1440
1435
1430 Gauge [mm]
1425 600 800 1000 1200 1400 Distance [m]
Figure 5-5 Track irregularity characteristics of Track 10.
61 Track/vehicle dynamic simulations - models, conditions and criteria
5.8.3 Peak values of track irregularities
Another check of track irregularities is to look at peak values. The quality standard according to Banverket is measured with the testing and track recording coach called STRIX [6] and are shown in Table 5-5. Table 5-5 Track geometry quality of longitudinal level (vertical irregularity). Peak values according to Banverket [6].
Deviation from base value [mm]
Longitudinal level Cant Speed limit Speed limit Long Quality conventional high-speed Short wave wave Deviation Class train train fault 1-25 m fault (km/h) (km/h) ABCABABC K0 145 - 185 - 2 6 9 7 15 2 4 6
Table 5-6 Track geometry quality of alignment (lateral irregularity). Peak values according to Banverket [6].
Deviation from base value [mm]
Alignment Gauge
Speed limit Speed limit Short wave Long Quality conventional high-speed fault wave Deviation class train train wavelength fault (km/h) (km/h) 1-25 m
ABCABA B C K0 145 - 185 - 2 3 5 5 10 ±2 ±5 +15,-5
The track quality values according to CEN/TC 256 WG 10 [8] have been obtained from measurements with the NS measuring vehicle and are shown in Table 5-7. CEN/TC 256 WG 10 says among others that a transfer function of the measuring system may be used to obtain absolute values of measured track geometry. Note that quantities in Table 5-7 are not directly comparable with quantities in Table 5-5 and Table 5-6, as the measuring system has different transfer functions from real to recorded irregularities.
62 Track geometry for high-speed railways
Table 5-7 Track geometry quality values. Source: CEN/TC 256 WG 10 [8].
Alignment Longitudinal level Permissible local speed in Values of quality level in mm km/h QN1 QN2 QN1 QN2
Absolute maximum value of lateral and vertical irregularity (mean to peak) 200 < v ≤ 3004648
The STRIX values of Track 5 are plotted against distance along the track and are illustrated in Figure 5-6. The maximum peak value of vertical irregularity of left and right rail for Track 5 are 3.64 mm and 3.6 mm, respectively. The maximum peak value of lateral irregularity for the left rail is 1.21 mm.
5 5
0 0 peak value [mm] peak value [mm]
vertical irregularity, left rail, -5 -5 vertical irregularity, right rail, 600 700 800 900 1000 1100 600 700 800 900 1000 1100 distance [m] distance [m]
5
0 peak value [mm]
lateral irregularity, left rail, -5 600 700 800 900 1000 1100 distance [m]
Figure 5-6 Track irregularities as a function of distance. Longitudinal level (vertical irregularity) and alignment (lateral irregularity) of Track 5.
63 Track/vehicle dynamic simulations - models, conditions and criteria
In Figure 5-7 the STRIX values of Track 10 are shown. The maximum peak values of vertical irregularity for left and right rail for Track 10 are 3.91 mm and 4.13 mm, respectively. The maximum peak value of lateral irregularity for the left (outer rail in the curve) rail is 2.25 mm.
5 5
0 0 peak value [mm] peak value [mm] vertical irregularity, left rail, -5 vertical right irregularity, rail, -5 600 800 1000 1200 1400 600 800 1000 1200 1400 distance [m] distance [m]
5
0 peak value [mm] lateral left irregularity, rail, -5 600 800 1000 1200 1400 distance [m]
Figure 5-7 Track irregularities as a function of distance. Longitudinal level (vertical irregularity) and alignment (lateral irregularity) of Track 10.
In Section 6.2.4 - 6.2.6 further studies on the effect of different track irregularities will be presented.
64 Track geometry for high-speed railways
5.9 Model of the EMU coach
One electric multiple unit (EMU), a four-axled bogie vehicle (axle arrangement Bo’Bo’), will be used in the simulations. This is a simplification, because the different vehicles in a train will interact. However, the results will most likely be on the conservative and safe side, because the interaction between coaches rather improves the running behaviour than worsens it. Especially, this is true with respect to low-frequency dynamics (0.5-2 Hz) due to long-waved track irregularities, low frequency instability and vehicle overturning. As mentioned in Section 5.7, in the stability simulations a worn UIC/ORE S1002 wheel profile have been used in order to achieve the desired equivalent conicity of at least 0.15, preferably up to 0.3 á 0.4. In the simulations of track shift forces and vehicle overturn a theoretical UIC/ORE S1002 wheel profile have been used.
5.9.1 Three different vehicle configurations
A baseline vehicle (vehicle configuration A) was firstly defined. This vehicle has the following data: Table 5-8 Data of the vehicle configuration A.
Carbody length [m] 25 Carbody height [m] 3.6 Bogie centre distance [m] 18 Bogie wheelbase [m] 2.7 Total vehicle mass [t] 51.4 Mass distribution See Table 5-9
65 Track/vehicle dynamic simulations - models, conditions and criteria
Table 5-9 Rigid bodies in the model of the EMU, vehicle configuration A
Height of mass centre Mass Mass moments of inertia above track plane
M Jxx Jyy Jzz (m) (kg) (kgm2) (kgm2) (kgm2) Carbody 33 000 50 600 1 800 300 1 800 300 1.55
Bogie framea 6 000 1 590 5 300 8 500 0.70
Wheelsetb 1 600 960 300 960 0.42
a. Including frame-mounted traction motors. b. Including traction gear and bearings.
The static axle loads are 126 kN for all wheelsets, which is a very low axle load for a motored coach of full length. The vehicle data used for the simulations are not taken from any real rail vehicle, but are reasonable extracts from today´s vehicle technology. Despite of this, detailed suspension data are proprietary. When evaluating the risk of vehicle overturning also two other configurations were used, in order to investigate the sensitivity for vehicle mass and the location of the centre of gravity (c.g.). The first simulations on side-wind stability showed that vehicle configuration A was not stable enough. Therefore a vehicle configuration B was defined, having an extra mass of 4000 kg, with its centre located 3 metres behind the leading bogie centre and 0.4 m above the track plane. This was judged to be a realistic approach to be used in the leading vehicle (and in the vehicle at the opposite end if necessary). Normally just the leading vehicle is being critical with respect to side-wind stability [21] [2]. Apart from the additional mass, vehicle configuration B is the same as configuration A. Mass distribution data for vehicle configuration B are shown in Table 5-10. Table 5-10 Rigid bodies in the model of the EMU, vehicle configuration B
Height of mass centre Mass Mass moments of inertia above track plane
M Jxx Jyy Jzz (m) (kg) (kgm2) (kgm2) (kgm2) Carbody 37 000 55 800 1 950 000 1 950 000 1.426
Bogie framea 6 000 1 590 5 300 8 500 0.70
Wheelsetb 1 600 960 300 960 0.42
a. Including frame mounted traction motors. b. Including traction gear and bearings.
66 Track geometry for high-speed railways
The static axle loads for vehicle configuration B (in empty condition) are 142.4 kN for the wheelsets in the leading bogie and 129.3 kN for the trailing bogie. The higher axle loads (142.4 kN) in the leading bogie is believed to meet the requirements of TSI [13], specifying a maximum axle load of 167 kN in fully loaded condition. Finally, to further investigate the influence of the centre of gravity with respect to strong side-winds a third vehicle configuration C was defined. This vehicle has the carbody centre of gravity located 0.10 m above that of configuration B. Otherwise, configuration C is identical to configuration B. See Table 5-11. Table 5-11 Rigid bodies in the model of the EMU, vehicle configuration C
Height of mass centre Mass Mass moments of inertia above track plane
M Jxx Jyy Jzz (m) (kg) (kgm2) (kgm2) (kgm2) Carbody 37 000 55 800 1 950 000 1 950 000 1.526
Bogie framea 6 000 1 590 5 300 8 500 0.70
Wheelsetb 1 600 960 300 960 0.42
a. Including frame mounted traction motors. b. Including traction gear and bearings.
Vehicle configurations B and C are considered as being realistic for future high-speed EMUs. It should be pointed out that the “extra mass” located behind the leading bogie in reality may be part of ordinary vehicle equipment, such as heavy electrical transformers or similar. It may not be necessary to put in additional “ballast mass”, but rather to consider the desired mass and mass distribution when the ordinary equipment is located in future vehicles. The resulting total mass and axle loads of configurations B and C are quite normal according to recent vehicle technology; compare for example with the German ICE 3 and the Swedish Öresund Train. As said above, configurations B and C have been used only for side-wind stability evaluations, although they are considered as the most realistic for future high-speed trains. Only configuration A has been used in the hunting stability and track shift analysis. The reason is that the investigations started with hunting stability and track shift forces, while the problem related to side-wind stability was experienced on a later stage. It was not judged as necessary to rework hunting stability and track shift forces with the new configurations B and C. The carbody mass and centre of gravity normally have no significant influence on hunting stability or the risk of exceeding the track shift force limit, all this according to Prof. Andersson´s experience.
67 Track/vehicle dynamic simulations - models, conditions and criteria
5.9.2 Hold-off-device
A future train designed for a high-speed line like in the present study would be equipped with a so-called hold-off-device (HOD) as described before. The HOD is not taken into full consideration in the present simulation model. This leads to hits in the bumpstops in curves with high cant deficiencies. This can be regarded as the “worst case” corresponding to a malfunction of the HOD. The dynamic performance would be better if the HOD is used and is working properly. Thus the conditions investigated in this study are conservative. Therefore we judged to make this simplification. However, one aspect of HOD is considered, namely that the lateral suspension travel in the secondary suspension is limited to ± 30 mm. This assumption will reduce the risk of vehicle overturning at strong winds, compared to the case with an ordinary passive suspension having 60 - 90 mm of lateral travel.
68 Track geometry for high-speed railways
6 Dynamic analysis of simulated vehicle response
This chapter deals with the simulation results. Firstly, an exposition of the simulation results from the hunting stability point of view is made. Secondly a presentation is made of the track shift forces simulations. Finally the evaluation of vehicle overturning is presented.
6.1 Hunting stability on tangent track and on curve
6.1.1 Conditions
Hunting stability was evaluated on tangent track and in curves with different radius, in the latter cant deficiency was varied in order to use the same test speed. A test speed of 385 km/h was chosen to fulfil the condition of 110% of the desirable top speed 350 km/h, in accordance with UIC 518 requirements. In order to use the same test speed on tangent track and in different curve combinations this condition satisfies the intention. This also corresponds to the other condition stated of CEN and UIC. This condition says that the test speed must be evaluated at 110% of permissible cant deficiency. For example: Speed V = 350 km/h,cantht = 180 mm and cant deficiency hd = 250 mm give a radius of R= 3361 m. Speed V = 385 km/h, cant ht = 180 mm and radius R = 3361 give a cant deficiency hd = 340 mm. This results in 136% of permissible cant deficiency. This is more than 110% of permissible cant deficiency and the condition is fulfilled. Table 6-1 and 6-2 show the simulation conditions for hunting stability in curves. Table 6-1 Simulation conditions for hunting stability in curves. Speed V = 385 km/h and cant ht = 180 mm.
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m]
385 180 50 7604 385 180 100 6246 385 180 150 5299 385 180 200 4602 385 180 250 4067 385 180 300 3643
69 Dynamic analysis of simulated vehicle response
Table 6-2 Simulation conditions for hunting stability in curves. Speed V = 385 km/h and cant ht = 200 mm.
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m] 385 200 50 6995 385 200 100 5829 385 200 150 4997 385 200 200 4372 385 200 250 3886 385 200 300 3498
6.1.2 Track irregularities
In the hunting stability simulations the track is without irregularities except a single lateral disturbance (i.e about the same amplitude as the lateral wheel/rail clearance) have been used in the stability simulations. The irregularity used will excite a lateral motion of the wheelsets and bogies. The wheel flanges will hit the rails. Thus also high wheel/rail contact angles are taken into account, not limiting the hunting investigations to small motions around the centre position. The wavelength and the amplitude of the single lateral disturbance is 20 m and ± 3 mm, respectively.
6.1.3 Criteria for hunting stability
To be considered as “fully stable” without undesired “hunting”, the lateral accelerations in the carbody shall have a decay of at least 60% in the first two cycles from the highest peak. I addition, no sustained vibration shall be visible after 200 – 400 m. Finally, the frequency of vibration should not be higher than 10 Hz, in order to limit the risk of exciting the carbody vibration modes in lateral bending.
6.1.4 Hunting stability on tangent track
With the wheel and rail profiles chosen according to Section 5.7 equivalent conicity up to about 0.3 has been investigated. This is very much above the required conicity according to TSI, which is 0.15 including tolerances for wheel and rail wear. A minor and brief optimisation was firstly made on suitable parameters in the bogie, such as wheelset guidance stiffness (longitudinal and lateral), primary damping (between wheelsets and bogie frame) and yaw damping (between bogie frame and carbody). It was found that an intermediate stiffness in the wheelset guidance was near optimum with
70 Track geometry for high-speed railways respect to hunting stability. This intermediate stiffness is something in between the quite flexible guidance stiffness on X 2000 (for 200 - 210 km/h) and the traditional stiff guidance normally used in Continental Europe. It is believed (although not proved in this study) that certain flexibility is favourable also with respect to lateral track shift forces. With the “optimised” parameters as mentioned above, stability on tangent track – at 385 km/h - can be achieved at an equivalent conicity of 0.20 – 0.25, according to the simulations. This is above the required value of 0.15, but it should be noted that stability should also be achieved with some adverse change in stiffness or damping in the bogie. That matter has not been further investigated in this study. For evaluation of the stability, the lateral acceleration in the carbody was calculated at three different locations in the simulations. The three locations on the floor was above each bogie and in the middle of the carbody. In Figure 6-1 to 6-3 an example of the lateral accelerations is shown for these three locations. In this case the vehicle is fully stable without any hunting motion, according to the criteria defined in Section 6.1.3. A lot of other cases, with different equivalent conicity, have been simulated, but are not shownindetail.
Lateral acceleration in the carbody above 1st bogie
] 2,00 2 1,00 0,00 [m/s
yc -1,00 a -2,00 500 600 700 800 900 1000 Distance [m]
Figure 6-1 Lateral acceleration (m/s2) in the carbody above 1st bogie. Tangent track with initial disturbance. Speed V = 385 km/h.
Lateral acceleration in the middle of the carbody
] 2,00 2 1,00 0,00 [m/s
yc -1,00 a -2,00 500 600 700 800 900 1000 Distance [m]
Figure 6-2 Lateral acceleration (m/s2) in the middle of the carbody. Tangent track with initial disturbance. Speed V = 385 km/h.
71 Dynamic analysis of simulated vehicle response
Lateral acceleration in the carbody above 2nd bogie
] 2,00 2 1,00 0,00 [m/s
yc -1,00 a -2,00 500 600 700 800 900 1000 Distance [m]
Figure 6-3 Lateral acceleration (m/s2) in the carbody above 2nd bogie. Tangent track with initial disturbance. Speed V = 385 km/h.
6.1.5 Hunting stability on large radius curves
In curves the lateral acceleration is much larger. There is not only a contribution from the dynamic behaviour but also a quasi-static contribution which occurs when a vehicle runs with constant speed on ideal track with a constant curve radius, cant and wheel-rail friction. The quasistatic contribution to the carbody lateral acceleration in a curve with a cant deficiency of 250 mm is in the order of 2 m/s2. This is under assumption that the carbody is not tilted. The lateral accelerations in the carbody for a case where the radius is 4067, cant is 180 mm and cant deficiency is 250 mm are presented in Figure 6-4 to 6-6
Lateral acceleration in the carbody above 1st bogie 5.00 ]
2 4.00 3.00 2.00 [m/s 1.00 yc
a 0.00 -1.00 500 600 700 800 900 1000 distance [m]
Figure 6-4 Lateral acceleration (m/s2) in the carbody above 1st bogie. A curve with initial disturbance where radius is 4067 m, cant is 180 mm and cant deficiency is 250 mm. Speed V = 385 km/h.
72 Track geometry for high-speed railways
Lateral acceleration in the middle of the carbody 5.00 ]
2 4.00 3.00
[m/s 2.00 1.00 yc
a 0.00 -1.00 500 600 700 800 900 1000 distance [m]
Figure 6-5 Lateral acceleration (m/s2) in the middle of the carbody. A curve with initial disturbance where radius is 4067 m, cant is 180 mm and cant deficiency is 250 mm. Speed V = 385 km/h.
Lateral acceleration in the carbody above 2nd bogie 5.00 ]
2 4.00 3.00
[m/s 2.00
yc 1.00
a 0.00 -1.00 500 600 700 800 900 1000 distance [m]
Figure 6-6 Lateral acceleration (m/s2) in the carbody above 2nd bogie. A curve with initial disturbance where radius is 4067 m, cant is 180 mm and cant deficiency is 250 mm. Speed V = 385 km/h.
From the figures it is concluded that the vehicle is stable without hunting. This is the case also for all the other cases according to Table 6-1 and 6-2. The criteria of reducing the oscillation within two cycles is also fulfilled in the large horizontal curves with a high cant deficiency. The hunting frequency is much lower than the stated condition of 10 Hz.
73 Dynamic analysis of simulated vehicle response
6.2 Evaluation of track shift forces
6.2.1 Conditions
Track shift forces can be critical when high lateral forces shift the track, which might, as a final consequence, lead to a derailment of the following vehicle. The limit value according to CEN/TC 256 WG 10 depends on axle load and is calculated using the Prud’homme formula (see Section 5.5). The limit value for the used vehicle configuration A in the present study is 44.2 kN which allows an extra margin of 15% for statistical scatter. According to CEN TC 256 WG 10 and UIC 518, track shift forces must be evaluated at a slightly higher speed then the intended permissible speed. CEN stated that the vehicle must be evaluated at 110% of permissible cant deficiency in curves. Kufver [16] came to the conclusion that it may be reasonable to modify this condition slightly when alignment alternatives with different radii are being evaluated, in order to use the same test speed in all alternatives. This principle will be used here. The investigations has been performed for cant deficiencies of adequately 100, 150, 200, 250, 275 and 300 mm and the curve radii will be varied in accordance. Note that these cant deficiencies correspond to 110% of admissible cant deficiency, as earlier discussed in Section 5.3. These relations are shown in shown in Table 6-3. The corresponding test speed is 360 km/h in these investigations. Table 6-3 Used values of cant deficiency and admissible cant deficiency according to European standards.
Cant deficiency used in simulation [mm] 100 150 200 250 275 300 Admissible cant deficiency [mm] 91 136 182 227 250 273
Table 6-4 to 6-6 show simulation conditions for the evaluation of track shift forces.
Table 6-4 Simulation conditions for track shift forces. Cant ht = 160 mm, speed V = 360 km/h.
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m] 360 160 100 5881 360 160 150 4933 360 160 200 4248 360 160 250 3730 360 160 275 3516 360 160 300 3325
74 Track geometry for high-speed railways
Table 6-5 Simulation conditions for track shift forces. Cant ht = 180 mm, speed V = 360 km/h
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m] 360 180 100 5462 360 180 150 4634 360 180 200 4024 360 180 250 3556 360 180 275 3361 360 180 300 3186
Table 6-6 Simulation conditions for track shift forces. Cant ht = 200 mm, speed V = 360 km/h.
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m] 360 200 100 5098 360 200 150 4369 360 200 200 3823 360 200 250 3398 360 200 275 3220 360 200 300 3059
6.2.2 Track irregularities
Nine sets of track irregularities were used in the present study for simulations of track shift forces, denoted Track 2 to Track 10, c.f. Section 5.8.
75 Dynamic analysis of simulated vehicle response
6.2.3 Track shift forces variation along the track
A study of the track shift forces as a function of distance confirm the substantial dynamic contribution of track irregularities which starts at 600 metres. Figure 6-7 shows the whole simulated track including the transition curve. Note that these simulations are made under the conditions of a lateral bumpstop between carbody and bogie. With a smother suspension, i.e. a Hold-off-Device (HOD) or a tilting bogie bolster below the secondary suspension, the dynamic peaks of the track shift forces would have been reduced. The peak values of the track shift forces would have been much less with a Hold-off-device in operation.
Track shift force 1st bogie, 2nd wheelset
50000
Start of the horizontal 40000 curve radius (360 m) 30000
S[N] 20000
10000
0 0 200 400 600 800 1000 1200 1400 Distance [m]
Figure 6-7 Example of track shift force S as a function of distance on Track 5. Transition curve have a length of 360 m, radius is 3361 m, cant is 180 mm and cant deficiency is 275 mm. Speed V = 360 km/h. The slight disturbance from the transition curve is almost damped out when the track irregularity starts (at the distance of 600 m).
6.2.4 Track shift forces for different cant
An example of the resulting track shift force for Track 5 and Track 10, where cant is varied from 160 mm to 200 mm at a vehicle speed of 360 km/h, are shown in Figure 6-8 to Figure 6-9. The simulation results for other tracks are shown in Appendix C. No significant differences between different cant values can be observed. The limit value is reached at a cant deficiency of 275 mm on both tracks.
Note that the track shift forces are evaluated as the average over 2 m, denoted S2m.
76 Track geometry for high-speed railways
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 55 50 45 40 [kN]
max 35 S 30 25 20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure 6-8 Track shift force S as a function of cant deficiency hd on Track 5. Three different values of cant are shown. 1st bogie, 2nd wheelset.
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 50 45 40 35 [kN] 30 max S 25 20 15 50 75 100 125 150 175 200 225 250 275 300 325 350
Cant deficiency [mm]
Figure 6-9 Track shift force S as a function of cant deficiency hd on Track 10. Three different values of cant are shown. 1st bogie, 2nd wheelset.
77 Dynamic analysis of simulated vehicle response
6.2.5 Comparisons between different track irregularities
In this section comparisons between different track irregularities are presented. In Figure 6-10 and Figure 6-11 the track shift forces in relation to limit value (Smax/Slim)are shown for cant ht = 180 mm. A comparison with a simulation without irregularities shows the dynamic contribution.
It can be observed in Figure 6-11 that the maximum peak forces Smax in relation to the limit Slim are not always increasing monotonously with increasing cant deficiency or increasing magnitude of track irregularities. This is mainly due to non-linearity in the wheel-rail contact or in the lateral bump-stop suspension. It is quite typical for cases where just an occasional peak is registered and evaluated for each simulated case, which leads to results with a limited statistical significance. Within the scope of this study it has not been judged as possible to perform a full set of simulation on different tracks to gain a full statistical significance. Instead, we have chosen the approximate approach to have a margin of 15% in the limit value of track-shift forces, to allow for typical statistical scatter; c.f. Section 5.5.
Track 2 Track 3 Track 4 Track 5 Track 6 No irregularities 1,5
lim 1 /S max
S 0,5
ht=180 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350
Cant deficiency [mm]
Figure 6-10 Track shift force S (in relation to limit value) as a function of cant deficiency hd forTrack2-Track6,aswellastrackwithno irregularities. Cant ht = 180 mm. 1st bogie, 2nd wheelset.
78 Track geometry for high-speed railways
Track 7 Track 8 Track 9 Track 10 No irregularities 1,5
1 lim /S max
S 0,5
ht=180 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure 6-11 Track shift force S (in relation to limit) as a function of cant deficiency hd for Track 7 - Track 10, as well as track with no irregularities. Cant ht = 180 mm. 1st bogie, 2nd wheelset.
It is interesting to note that the two cases in Figure 6-10 and 6-11, differing in the sources of track irregularities, produce approximately the same results if the Q-values are the same. Both Track 5 and Track 10 has Q-values of 99 and they both produce Smax =Slim at a cant deficiency of 275 mm. However, these results should not be generalised, because just two different tracks irregularities have been investigated.
79 Dynamic analysis of simulated vehicle response
6.2.6 Improvements of track irregularities
As mentioned earlier, a full study on the effect of track irregularities for different operational cases, including sets of different high-speed rail vehicle configurations in various conditions, is outside the scope and possibilities of this study. Therefore a simplified procedure has been applied, just to give an indication whether lateral track forces and track quality would be in the right order of magnitude. As described in Section 5.8 the simulated tracks are evaluated according to Banverket Q- number definition, taking the standard deviations of vertical, lateral and cant irregularities into account. There is no statistical analysis on different types and amplitudes of occasional irregularities, to be evaluated according to quality level C (c.f. Section 5.8). This is to be done in further investigations. From this point of view this study would produce somewhat optimistic results. Also from the vehicle point of view there are simplifications, mainly due to the assumption of a lateral bump stop in the suspension between bogie and carbody, instead of having a Hold-off-Device (HOD) or a tilting bolster below the secondary suspension, both cases allowing a more flexible suspension. Such implementations would produce a better ride and likely somewhat reduced peak lateral track forces. From this point of view this study would produce somewhat conservative results. With the above mentioned in mind some preliminary results and indications will be shown and discussed below.
80 Track geometry for high-speed railways
Figure 6-12 shows necessary improvement of the relative magnitude of the track irregularities, compared to a track with Q-number of 80 for class K0 according to Banverket. Preliminary, this improvement of track irregularities is needed to get a suitable track quality for high-speed operations. The necessary improvement of the track bed to allow a cant deficiency of 275 mm is approximately 25% in relation to a track with quality class K0 according to Banverket. In this context it should be repeated that a cant deficiency of 275 mm is necessary at tests, in order to have an admissible cant deficiency of 250 mm in operation.
150
125 ht = 180 mm 100
75 [%] 50
25
0 Track irregularity relative K0 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure 6-12 Necessary improvements of track irregularities as a function of cant deficiency. Track 2 - 6. The results are presented relative quality class K0 according to Banverket based on the track irregularities measured on a curve between Simonstorp and Katrineholm.
81 Dynamic analysis of simulated vehicle response
The corresponding necessary improvement with respect to quality class K0 according to Banverket for track irregularity measured between Åby and Nyköping to be allowed for a cant deficiency of 275 mm are shown in Figure 6-13. Also in this track the necessary improvements would be approximately 25% in relation to current quality class K0.
100
ht = 180 mm 75
50 [%]
25
0 Track irregularity relative K0 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure 6-13 Necessary improvements of track irregularities as a function of cant deficiency. Track 7 - 10. The results are presented relative quality class K0 according to Banverket based on the track irregularities measured on tangent track between Åby and Nyköping.
82 Track geometry for high-speed railways
Figure 6-14 gives a hint of the necessary improvement of track irregularities to get a suitable track for high-speed operations at different cant deficiencies.
Cant = 180 mm, 1st bogie, 2nd wheelset 60 55 S2m,till 50 45 40 Track 3 35 (K0) 30 25 Track 5 20 15 No track
Track shift force10 [kN] 5 irregularities 0 50 100 150 200 250 300 350 Cant deficiency [mm]
Figure 6-14 Comparison of the track shift forces between different tracks. The figure gives a indication of the necessary improvements of track irregularities.
83 Dynamic analysis of simulated vehicle response
6.3 Evaluation of vehicle overturning
6.3.1 Conditions
In Section 5.6.3 a description of the intercept method was given. As mentioned before, the intercept method evaluates the risk of overturning by calculating a so-called vector intercept of all wheel forces. The distance of the intercept vector from the middle of the track plane can be determined by only knowing the vertical wheel forces. This distance in relation to half the distance between contact points (bo) will lead to the intercept risk factor E. The vehicle will run safe for E < 1 and begin to turn over for the value of 1. It will become 1, when all windward wheels are unloaded. The value of E can not exceed the value 1. In this study the intercept method risk factor E is calculated for the whole vehicle, i.e all vertical forces for one side of the vehicle are summarized. Before evaluation, E is filtered by a low pass filter at 1.5 Hz limit frequency. Cant deficiency was adequately chosen to 150, 200, 250 and 275 mm, and the curve radii were varied in accordance. After a few preliminary simulations where both a cant of 180 mm and 200 mm were used, a difference between these two values of cant were hard to discern when evaluating the risk of vehicle overturning. As a result, only simulations with a cant of 180 mm are presented here.
In such a case the vector intercept E must not exceed 0.9, i.e. the vector intercept bt shall not reach more than 0.9 x 0.75 m from the track centre towards the outer rail. In this criterion there is a margin before the train really turns over. According to simulations this margin is typically 3 – 5 m/s of wind velocity above the stated wind velocity of 23 m/s.
84 Track geometry for high-speed railways
According to the above mentioned requirements the simulated speed is 350 km/h, i.e. the tested maximum speed of the trains. Cant deficiency is varied in intervals up to 275 mm. Because the cant itself has obviously just an insignificant influence, a “standard” cant of 180 mm is chosen. The horizontal curve radius is chosen to suit speed and cant deficiency, according to Table 6-7 below. Table 6-7 Simulation conditions for vehicle overturning. Speed V = 350 km/h and cant ht = 180 mm
Train speed Cant Cant deficiency Horizontal curve radius [km/h] [mm] [mm] [m] 350 180 150 4380 350 180 200 3804 350 180 250 3362 350 180 275 3177
6.3.2 Track irregularities
The track irregularities that were used in the present study for simulations of vehicle overturning are Track 5 and Track 10. The reason for not using other tracks in the simulations were that it is important to have a suitable and adapted track standard when evaluating vehicle overturning. If several very unlikely events are combined the resulting worst case would be too unrealistic.
6.3.3 Safety against vehicle overturning at different conditions
In Figure 6-15 the maximum value of the intercept method risk factor E is shown as a function of wind velocity for vehicle configuration B. Vehicle speed V = 350 km/h and cant ht = 180 mm. The results are shown at four different values of cant deficiencies and their corresponding radius.
85 Dynamic analysis of simulated vehicle response
Intercept method risk factor, Intercept method risk factor, R=4380 m, hd=150 mm R=3804 m, hd=200 mm 1,00 1,00
0,90 0,90
0,80 0,80 [-] [-] int int E E 0,70 0,70
0,60 0,60
0,50 0,50 20 22 24 26 28 30 20 22 24 26 28 30 Wind velocity [m/s] Wind velocity [m/s]
Intercept method risk factor, Intercept method risk factor, R=3362 m, hd=250 mm R=3177 m, hd=275 mm 1,00 1,00
0,90 0,90
0,80 0,80 [-] [-] int int E E 0,70 0,70
0,60 0,60
0,50 0,50 20 22 24 26 28 30 20 22 24 26 28 30 Wind velocity [m/s] Wind velocity [m/s]
Figure 6-15 Maximum value of the intercept method risk factor E at different wind velocities for vehicle configuration B. Speed V = 350 km/h and cant ht = 180 mm. Values are shown at four different values of cant deficiencies from 150 mm to 275 mm.
Permissible wind velocity from the most unfavourable direction for three different train configurations are presented in Figure 6-16. Train configuration B has 4000 kg more weight in the carbody behind the leading bogie. This condition must be taken into consideration when evaluating safety against vehicle overturning. The permissible wind velocity according to the intercept method risk factor for vehicle configuration B at a cant deficiency of 250 mm is 23.4 m/s. In vehicle configuration C the permissible wind velocity is calculated to 22.5 m/s. The difference between configuration B and C is the height of c.g. for the carbody, c.f. Section 5.9.1. These
86 Track geometry for high-speed railways vehicle configurations are considered to be technically achieveable and realistic for future high-speed EMUs.
Permissible wind speed according to intercept method risk factor 28 27 Train configuration A 26 Train configuration B [m/s] 25 Train configuration C
wind 24 23 22 21 ht = 180 mm 20
Wind velocity, v 19 18 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 6-16 Permissible wind velocity as a function of cant deficiency according to intercept method risk factor. Speed V = 350 km/h and cant ht = 180 mm.
87 Dynamic analysis of simulated vehicle response
The significant difference between allowed wind velocity with respect to E =0.9and critical wind velocity at simulated vehicle overturning is presented in Figure 6-17. The lines are not parallel and the cap of wind velocity is diverted at higher value of cant deficiency.
Intercept method risk factor Vehicle overturning 30
ht = 180 mm
[m/s] 28
wind 26
24
22 Wind velocity, v 20 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 6-17 Allowed wind velocity as a function of cant deficiency. According to intercept method risk factor at simulated vehicle overturning. Speed V = 350 km/h and cant ht = 180 mm.
6.3.4 Conclusions
As a result of simulations on vehicle overturning it seems to be realistic to run at about 350 km/h at cant deficiencies around 250 mm with state-of-the-art vehicle technology. However, the final TSI criteria for evaluation of overturning was not laid down at the time of this study. Therefore, there is some incertainty on this matter.
88 Track geometry for high-speed railways
7 Consequences of freight trains operations
This chapter will discuss some consequences of different kinds of freight train operations from a track geometry point of view. In order to do this, it is initially necessary to identify the different categories of future freight trains that are likely to occur, with speeds, total train mass, axle loads and other characteristics. The main issue is how steep gradients that can be allowed with respect to possible train mass hauled by different sizes of locomotives. Also other aspects will be discussed, such as the influence of gradients with respect to braking performance, as well as possible track cant and cant excess. Very briefly also the issue of permissible axle load will be discussed.
7.1 Different categories of freight trains
Principally three principal categories of freight trains, I, II and III according to below, have been identified and considered for future rail operations in general:
I. Freight trains for heavy mass goods, such as bulk, steel, paper, timber, chemicals, heavy machinery and other finished heavy goods in large quantities. Trains for unit-load carriers such as containers and swap bodies, with open flat wagons, also containing a various amount of road vehicle semitrailers are included in this category. The unit-loads are loaded and unloaded at large-scale terminals on non-electrified track, with cranes or heavy mobile lifts. Sometimes the wagons of such trains have long-stroke end buffers to limit the impact on sensible goods at wagon shunting operations. It is quite common that wagons for heavy mass goods are mixed with container and swap bodies in the same train. This category of trains is typical for today's rail freight traffic. They have usually an axle load of up to 22.5 tonnes and a maximum speed of 90 - 100 km/h, in some special cases up to 120 km/h. Freight wagons have a traditional design with standardised components and subsystems for international cross-border exchange. In the future a great part of these trains are assumed to have an axle load of 25 tonnes, in some cases likely up to 28 - 30 tons. In some cases they will have a wider and higher loading gauge (height 4.8 m), at least in Swedish domestic traffic, than today's internationally exchangeable wagons (maximum height 4.3 - 4.6 m). Train length is believed to stay within the internationally standardised 750 m, although longer trains may be considered in special cases. Train mass may in most cases stay within about 2000 - 2500 tonnes, which is 30 - 50% higher than today's ordinary trains. If high-strength automatic couplers are introduced in the future, train mass may be further increased on certain trains. Speeds will be maintained in the present range: around 90 - 120 km/h, possibly with an increased amount of traffic in the higher range. However, the use of tarpaulin covers on many loads, semi-trailers and swap bodies may prevent higher speeds than about 100 km/h. A possible trend is that transport of containers and swap bodies
89 Consequences of freight trains operations
may - to a large extent - be transferred to lighter and faster trains according to category II.
II. Fast freight trains for unit-loads, heavy express goods and heavy mail. This is a fairly new category of freight trains, which may be an important category in the future. The Swedish trains for heavy mail (called B-mail), in service from 2001, is an example of such trains. Such operations are run also in France and Germany. In the future, transport of containers and swap bodies (with stiff covers) may be transferred from category I trains to category II trains. The characteristics of category II trains are: - Maximum speed 160 - 180 km/h, average speed in the range 120 - 150 km/h, on suitable track. - Trains just make short underway stops for fast loading and unloading (5 - 15 min) at small-scale terminals, on electrified track sidings, with small-scale or automatic load transfer equipment. - Goods and pallets are in many cases loaded directly on the floor, thus goods is in many cases not secured from sliding on the floor or ‘moving around’ to some extent in the wagon or in the container. - Trains are believed to be hauled by ordinary locomotives in most cases, principally similar to modern passenger train locomotives. Another option may be self-propelled multiple-unit freight trains, with traction equipment in the wagons. - Locomotives and loaded wagons have a total centre of gravity lower than 2 m above rail level, in most cases lower than 1.8 m. - Brake systems have high performance disc brakes with 2 - 4 brake discs per axle. Brake control and actuation is of the electro-pneumatic type, with a proper electronic wheel skid protection. - Trains have a limited mass and length, for quick acceleration, short stops and suitability for fast loading/unloading at small-scale terminals. - Due to the high average speed and short stops this type of trains will be able to follow - or almost follow - the speed pattern of fast regional and inter-regional passenger trains. This will increase the capacity on lines with a great share of fast passenger traffic. It will also enhance the productivity of such trains, making it possible to run 1000 - 1500 km per day, also under day-time, with an average annual performance of at least 200 - 300 kkm.
90 Track geometry for high-speed railways
III. Freight trains for light express goods or mail, with high punctuality and service level. In principal, category III is made up by trains which are, technically similar to high- speed passenger trains. They also have similar speed and braking performance as such trains. The French TGV trains for ordinary mail are of this category. It has been discussed also to introduce similar fast mail trains in Sweden, but limited line capacity in mixed heavy freight operation makes it inconvenient. The possible introduction of future dedicated high-speed lines would make such trains more convenient. The characteristics of category III trains are: - Maximum speed 200 - 300 km/h, average speed in the range 160 - 250 km/h, on suitable track. Due to a good traction performance these trains will also be able to climb the same gradients as high-speed trains. - Trains just make very short underway stops for fast loading and unloading (3 - 10 min), on electrified track sidings with loading platforms. - Goods are loaded in small containers or ‘baskets’ on board the train, thus preventing the goods to slip on the floor and move around. - Due to the high average speed and short stops this type of trains will be able to follow approximately the same speed pattern as high-speed passenger trains. They will be able to run at night- or daytime, likely without special restrictions due to limited capacity. They will have a high productivity, in most cases in the order of 300 - 500 kkm per year.
7.2 Permissible axle load and track loadings
Most high-speed lines in Europe and Japan are dedicated high-speed lines for high-speed passenger (or mail) trains only. As far as known there are two exceptions: (1) the first generation of the German high-speed lines (Neubaustrecken) and (2) the North East Corridor (New York - Washington DC) in the USA, in both cases with heavy freight mixed with high-speed passenger operations. It is reported that some extra wear and track maintenance has occurred. In Germany, axle loads up to 22.5 tonnes are allowed; in the USA freight train axle loads up to at least 30 tonnes is usual. There are at least two problems associated with mixed operations with heavy freight trains on the same track as lighter high-speed passenger trains: 1. Line capacity. Due to the different average speeds the two types of trains reduces the line capacity, although these problems can be reduced with proper infrastructure facilities (possibilities of quick overtaking) and a high time precision. 2. Dynamic track loadings and track maintenance. Freight trains with heavy axle loads and simple suspensions may likely cause high dynamic track loadings and a quite high rate of track deterioration. A poor track standard with significant geometrical
91 Consequences of freight trains operations
irregularities would then cause problems for the lighter high-speed trains. Alternatively, the track maintenance and renewal would be excessive and expensive. It is anticipated that future high-speed lines for speeds above 250 km/h would normally not allow heavy freight trains, i.e. trains of category I. In most cases other parallel lines are available, otherwise it is anticipated either that speed is kept at 250 km/h as a maximum, or that special measures are taken to maintain the track properly. As a third alternative it would be possible to improve the rail vehicles in order to reduce their sensitivity to track irregularities (active suspensions etc.). For trains of category II amaximumaxle load in the range of 20 - 22.5 tonnes is foreseen. This is the range which is used for passenger trains on modern track in some countries. In Germany, France and USA such passenger trains are run with ordinary modern locomotives at axle loads between 20 and 23 tonnes. In the latter case - 23 tonnes in the USA, with a maximum speed of 200 km/h - the track is built up by 68 kg/m rails. In Germany and France axle loads of locomotives in passenger trains are 20 - 21 tonnes at speeds around 200 km/h. In this case the track is built up by 60 kg/m rails, normally with a sleeper spacing of 0.6 m. In Sweden and the UK axle loads of about 18 tonnes is used on locomotives in speeds around 200 km/h. In Sweden this track loading was originally accepted for the older 50 kg/m rails and quite weak concrete sleepers (types 101 and S2) at a spacing of 0.65 m. In Sweden, modern high-performance track is built up by UIC 60 kg/m rails on elastic rubber pads laid on concrete sleepers (type S3) with a spacing of 0.6 - 0.65 m. The elastic rubber pads (thickness ca 10 mm) are believed to reduce the dynamic vertical high- frequency forces (30 - 150 Hz) compared to stiffer pads which has earlier being used and is still used on several railways. To further increase the resistance against track deterioration concrete sleepers with a larger support area may be considered in the future [25] [27]. All the three major European rail vehicle suppliers - Alstom, Bombardier (former Adtranz) and Siemens - offer passenger locomotives for around 200 km/h with an axle load of 20 - 21 tonnes. They typically have a maximum tractive power of 6000 - 6500 kW (at the wheel periphery) and would be suitable for category II freight operations. It is assumed that the Swedish authorities (mainly Banverket) will put relevant requirements on freight wagons for speeds in the range of 160 - 180 km/h, i.e. not only accepting the poor dynamic performance of ordinary freight wagons at these speeds. It would at least be possible to apply the minimum requirements according to UIC 518 [24]. A further possibility may be to give incentives for improved dynamic performance (low dynamic track forces) by differentiated track fees. This possibility is also applicable to the locomotives. For freight trains of category III, i.e. high-speed trains, axle loads are assumed to be within the range as defined in TSI; i.e. generally a maximum of 167 kN, although driven axles are allowed to have static axle loads up to 177 kN at speeds not exceding 250 km/h.
92 Track geometry for high-speed railways
In any case the general requirements according to CEN and UIC must be considered, i.e. the dynamic maximum vertical wheel loads should meet the following limit values: ≤ for speeds up to 160 km/h Qmax,lim 200 kN ≤ ≤ 160 km/h < Vlim 200 km/h Qmax,lim 190 kN ≤ ≤ 200 km/h < Vlim 250 km/h Qmax,lim 180 kN ≤ ≤ 250 km/h < Vlim 300 km/h Qmax,lim 170 kN ≤ 300 km/h and above Qmax,lim 160 kN Note that it would be possible - also in this case - to give incentives for a good dynamic performance by differentiated track fees.
7.3 Track cant and cant excess
Track cant - or superelevation - is currently limited to 150 mm in Sweden. This is a normal cant on lines with ordinary freight traffic. Similar cant is used in many other countries, although up to 160 mm is applied in a few cases. There are at least two reasons for limiting track cant: 1. A very high track cant leads to high lateral accelerations parallel to the wagon floor, if the train is running very slowly. In ordinary freight wagons where goods and pallets may be loaded directly on the floor and is secured from moving around just by friction, it seems important not to have too large track cant if the trains are stopped or is moving slowly on a canted curve. Because of the generally good track standard on high-speed tracks, with small anticipated dynamic lateral accelerations at low speeds, it would be possible to increase the track cant without infringing the safety against ‘moving around’. From this point of view it would likely be possible to increase the maximum cant to 160 or 170 mm. This is also the limit values of cant in the newly proposed CEN provisional standard on track for mixed freight and passenger traffic [7]. 2. Cant excess should not be too high for slow trains. On high cant, the low wheels and rails would be highly loaded, possibly causing track deterioration. In the popular railway engineering traditions it is also said that high cant excess leads to excessive wear and damage on the low rail, due to the higher vertical force. According to investigations made by KTH in co-operation with Banverket [25] the latter problem is obviously overstated, at least in larger curve radii (R > 800 m). In larger curves (R > 2000 m) the wear problem is negligible, because the attack angles between wheels and rail are very small. Also from the track deterioration point of view it is very likely that a cant excess of 110 - 130 mm is acceptable occasionally, at least for vehicles with an axle load limited to 22 tonnes and a centre of gravity at maximum 2 m above rail level (1.8 m for locomotives); i.e. freight trains category II. At a cant excess of 120 mm the quasistatic vertical wheel-rail force is calculated to approx. 140 kN in this case, which is below the permissible vertical quasistatic force according to UIC 518.
93 Consequences of freight trains operations
These principles and conclusions are also reflected in the newly proposed CEN provisional standard [7], which states that a cant excess of 110 mm would be acceptable, with 130 mm as a maximum limit value. In case of freight trains without goods and pallets loaded directly on the floor,for example mail trains, it may be possible to have a larger track cant, i.e 180 - 200 mm. This is also in line with the newly proposed CEN and TSI standards. Example:Afreight train of category II runs at 120 km/h in a curve radius of 3525 m and a track cant of 160 mm. The cant excess at this speed is 112 mm. At 140 km/h the cant excess is 94 mm. More examples: Let us consider a case were heavy freight train (category I) is allowed to run at 90 km/h. This is combined with conventional high-speed trains where the permissible cant deficiency is maximised to 80 mm according to TSI for speeds over 300 km/h. At a top speed of 350 km/h for the high-speed train the corresponding cant is 123 mm and the smallest possible horizontal curve radius is 7120 m. This pertains to a cant excess of 110 mm for a heavy freight train at 90 km/h, which is in accordance to TSI. With a tilting train the possible cant deficiency would be as much as 250 mm according to the preliminary conclusions of this study. Thus, the permissible cant is 135 mm and the horizontal curve radius is 3755 m. Even this would be valid with a cant excess of 110 mm. This reduces the horizontal curve radius with 47%. The results are presented in Table 7-1. Table 7-1 Optimised horizontal curve radius and optimised cant for all kind of operations, trains for heavy mass goods, category I, are included. Vmin =90km/h.
Conventional Train with tilt train technology Speed of high-speed trains km/h 350 350 Speed of heavy freight trains km/h 90 90
Cant deficiencya mm 80b 250
Cant excess mm 110b 110b Cant (optimised) mm 123 135 Horizontal curve radius (optimised) m 7121 3755
a. Valid for high-speed passenger train b. Recommended value according to CEN and TSI
However, as pointed out earlier it is questionable whether heavy freight trains of category I should be allowed on high-speed lines with maximum speeds above 250 km/h.
94 Track geometry for high-speed railways
In Table 7-2 further results are presented with speed of 120 km/h for freight trains of category II. Table 7-2 Optimised horizontal curve radius and optimised cant for high-speed trains and freight trains of category II. Vmin = 120 km/h.
Conventional Train with tilt train technology Speed of high-speed trains km/h 350 350 Speed of freight train of category II km/h 120 120
Cant deficiencya mm 80b 250
Cant excess mm 110b 110b Cant (optimised) mm 135 158 Horizontal curve radius (optimised) m 6723 3543
a. Valid for high-speed passenger train b. Recommended value according to CEN and TSI
95 Consequences of freight trains operations
If the permissible speed for freight trains of category II increases to 160 km/h the conditions become more favourable concerning maximised cant and optimised horizontal curve radius. According to TSI a cant of 160 mm is allowed for mixed traffic lines. For a conventional high-speed train the permissible cant deficiency is 80 mm at speeds above 300 km/h. The optimised horizontal curve radius in this case is 6023 m. The cant excess becomes exactly 110 mm. With a cant deficiency of 250 mm for the tilting train a calculation gives a horizontal curve radius of 3526 m. The cant excess is for this case only 74 mm, which is significantly lower than the permissible value. The results are shown in Figure 7-3. Table 7-3 Optimised horizontal curve radius for high-speed lines with fast freight trains of category II. Vmin = 160 km/h.
Conventional Train with tilting train technologya Speed of high-speed passenger trains km/h 350 350 Speed of freight trains of category II km/h 160 160
Cant deficiency mm 80b 250
Cant excess mm 110b 74 Cant mm 160 160 Horizontal curve radius (optimised) m 6023 3526
a. High-speed passenger train b. Recommended value according to CEN and TSI
7.4 Gradients versus train mass
In this section we will investigate the ability to run freight trains as function of gradients. Firstly the locomotive must be able to bring the train in motion also on an uphill gradient, if the train has been stopped. Secondly the train must be able to accelerate after it has been brought into motion. The desired amount of acceleration, however, is dependent on the performance requirements of the trains and on the desired capacity of the line - a slow acceleration of a freight train will block the line for a long time, thus reducing the line capacity. Thirdly the trains must be able to brake on the prescribed braking distance also on downhill gradients. This is a question of braking capacity of the trains and also of signalling distances. We will briefly investigate these issues for the three train categories defined in 7.1.
96 Track geometry for high-speed railways
7.4.1 Freight trains category I - heavy freight trains
If ordinary heavy freight trains are to be run on the high-speed line, the gradients must be built to the usual national standard. In Sweden this means a gradient of maximum 10 ‰. This is the standard for main lines in southern Sweden and will also be built on the new ‘Botniabanan’ Sundsvall - Umeå, where a maximum speed of 250 km/h is foreseen for high-speed passenger trains. With the current four-axled locomotives, class Rc (mass 78 tonnes), a maximum trainload of 1400 tonnes can be hauled in gradients of 10 ‰. With this train load the locomotive is able to bring the train in motion, with an available adhesion α =0.25and running resistance as defined in Appendix F in a 400 m radius curve. The acceleration of such heavy trains in the above mentioned gradients will, however, be very slow. In cases where the adhesion is just 0.25 all the time, it will not be able to reach the normal maximum speed of the train (usually 90 - 100 km/h) in that gradient. In short gradients, however, this limitation may not be severe, because the train will accelerate as soon as the train has left the steep gradient. The required signalling distance is dependent on the gradient: a long downhill gradient will usually increase the required signalling distance in order to stop the train with normal brakes. In some cases the maximum speed will be reduced. As briefly discussed in Section 7.2 it is believed that heavy freight trains will normally not be allowed on high-speed lines with a maximum speed of more than 250 km/h. It is also believed that many lines for the speed range 200 - 250 km/h will not either be designed for heavy freight trains, if gradients are considered. In many cases there are parallel lines for heavy freight traffic. A limited number of lighter category I freight trains are able to run on steeper gradients at suitable speed anyway.
7.4.2 Freight trains category II - fast trains for unit-loads and heavy express
This category of trains would, under certain conditions, be allowed on high-speed lines for speeds above 250 km/h. Some of these technical conditions have been briefly discussed in Section 7.2 (axle load) and 7.3 (cant and cant excess). In this section, the gradients will be discussed. The first requirement is that the gradient is limited in order to assure that the train can be brought in motion with the available tractive force of the locomotive and the available wheel-rail adhesion. Or inversely: the train mass must be limited depending on the gradient. As for trains in category I the tractive force with an available adhesion of 0.25 must balance the running resistance at starting, according to the equations in Appendix F. However, in the case of high-speed lines the curves radii are much larger - in the order of 3000 - 5000 m instead of down to 300 á 400 m. Therefore, in this case the curve radius is assumed to be 3000 m. This will reduce the running resistance at starting, thus allowing some more train mass in the same gradient.
97 Consequences of freight trains operations
Using the equations and assumptions in Appendix F the permissible train mass for different gradients is calculated and shown in Table 7-4. Table 7-4 Permissible train mass in order to bring the train in motion on gradients. One or two locomotives á 84 tonnes. Container train, 50 axles (one loco), 100 axles (two locos) Curve radius: min 3000 m
Gradient Number Train mass Wagon mass (‰) of locos (tonnes) (tonnes) 15 1 1242 1158 20 1 950 866 25 1 770 686 30 1 647 563 20 2 1900 1732 25 2 1540 1372 30 2 1294 1126 40 2 980 812
The trains are assumed to contain 50 axles in the case of one locomotive and 100 axles in the case of two locomotives. This is simple stepwise assumptions. However, a sensitivity analysis has been made, showing that variation of the number of axles with 40% in the case of one locomotive, changes the permissible train mass by just approx. 6 tonnes in a 25 ‰ gradient, which is not considered as significant. Thus, the number of axles in the train is not critical as long as the total train mass is the same. The calculations shown in Table 7-4 are just considering what is required in order to bring the train in motion, according to traditional rules for conventional freight trains. The acceleration of the freight train will be very slow as long as the whole train remains in the gradient. This may not be acceptable in long gradients, if high train performance and/or capacity of the line are required. As a rough limit of what is considered as a long gradient, the maximum train length may be used, say in the order of 400 - 750 m. Therefore, in long gradients it is recommended that the gradients be reduced below what is indicated in Table 7-4. This is particularly important if the uphill gradient is located immediately after a station or a signal, where freight trains stop frequently. These issues have not been investigated in detail in this study. However, it is recommended to make proper investigations in each real case of a high-speed line, provided that category II freight trains are planned to be run on the actual line. Traffic simulations must be done with a proper simulation model. It should be noted that the braking performance of category II freight trains must be higher than for ordinary category I freight trains, due to the higher speeds. The gradients, the signalling distances and the maximum axle load has to be considered. It is believed
98 Track geometry for high-speed railways that electro-pneumatic disc brakes will be used, with two or three discs per axle. These mechanical brakes will be supplemented by regenerative electrical brakes on the locomotive, which is used as the first option for braking in normal operation. In principal, this is the same braking technology as on passenger trains.
2500 Wagon mass, one loco Wagon mass, two locos Train mass, one loco Train mass, two locos 2000
2 locos á 84 ton 1500
1locoá84ton 1000
500 Possible train mass [tonne]
0 0 1020304050 Gradient [‰ ]
Figure 7-1 Possible train mass due to starting in gradients
7.4.3 Freight trains category III - high-speed for light express or mail
As category III freight trains are intended to have similar performance as the high-speed passenger trains, i.e. with good traction performance, these trains will also be able to climb the same gradients as passenger high-speed trains. Also the braking performance must be equipped accordingly, to match the signalling system. Hence, if only category III freight trains will be allowed on the line, the gradients are in this case not restricted by the freight trains. The gradients may be as high as 35 ‰ according to TSI.
99 Consequences of freight trains operations
100 Track geometry for high-speed railways
8 Possible track geometry
In this chapter possible track geometry is presented. Tables and figures show a proposal of possible values of cant and cant deficiency and their corresponding horizontal curve radius at different target speeds. Examples of possible vertical curve radius are given as well.
8.1 Horizontal curve radius
Examples of possible horizontal curve radius are given in the following tables and figures. Tables 8-1 to 8-4 show examples of horizontal curve radius at different values of cant deficiencies. The applied cant will be varied from 150 mm to 200 mm at different speeds from 200 km/h to 350 km/h. the relations are also shown in Figures 8-1 to 8-4. Further, the same relations are shown in Figures 8-5 to 8-8 changing the independent variables and parameters. Note that the cant, and consequently also the curve radius, may be limited if freight trains of category I or II are to be run on the high-speed track. This issue has been dealt with in Section 7.3.
101 Possible track geometry
Table 8-1 Examples of horizontal curve radius at four different values of cant deficiencies. Speeds varied from 200 km/h to 350 km/h. Cant ht = 150 mm.
Speed [km/h] 200 250 280 300 330 350 Cant deficiency [mm] 100 1888 2950 3700 4248 5140 5782 150 1573 2458 3084 3540 4283 4818 200 1349 2107 2643 3034 3671 4130 250 1180 1844 2313 2655 3213 3614
V=200 km/h V=280 km/h V=350 km/h 6000
5000 ht = 150 mm 4000
3000
2000
1000
Horizontal curve radius [m] 0 100 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 8-1 Horizontal curve radius R as a function of cant deficiency hd. Curves are shown at speeds of 200, 280 and 350 km/h. Cant ht = 150 mm.
102 Track geometry for high-speed railways
Table 8-2 Examples of horizontal curve radius at four different values of cant deficiencies. Speeds varied from 200 km/h to 350 km/h. Cant ht = 160 mm.
Speed [km/h] 200 250 280 300 330 350 Cant deficiency [mm] 100 1816 2837 3558 4085 4942 5560 150 1523 2379 2984 3426 4145 4663 200 1312 2049 2570 2950 3570 4015 250 1152 1799 2257 2590 3134 3526
V=200 km/h V=280 km/h V=350 km/h 6000
5000 ht = 160 mm 4000
3000
2000
1000
Horizontal curve radius [m] 0 100 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 8-2 Horizontal curve radius R as a function of cant deficiency hd. Curves are shown at speeds of 200, 280 and 350 km/h. Cant ht = 160 mm.
103 Possible track geometry
Table 8-3 Examples of horizontal curve radius at four different values of cant deficiencies. Speeds varied from 200 km/h to 350 km/h. Cant ht = 180 mm.
Speed [km/h] 200 250 280 300 330 350 Cant deficiency [mm] 100 1686 2634 3304 3793 4589 5162 150 1431 2236 2803 3218 3894 4380 200 1242 1941 2435 2795 3382 3804 250 1098 1715 2152 2740 2988 3362
V=200 km/h V=280 km/h V=350 km/h 6000
5000 ht =180mm 4000
3000
2000
1000
Horizontal curve radius [m] 0 100 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 8-3 Horizontal curve radius R as a function of cant deficiency hd. Curves are shown at speeds of 200, 280 and 350 km/h. Cant ht = 180 mm.
104 Track geometry for high-speed railways
Table 8-4 Examples of horizontal curve radius at four different values of cant deficiencies. Speeds varied from 200 km/h to 350 km/h. Cant ht = 200 mm.
Speed [km/h] 200 250 280 300 330 350 Cant deficiency [mm] 100 1574 2458 3084 3540 4283 4818 150 1349 2107 2643 3034 3671 4130 200 1180 1844 2313 2655 3213 3614 250 1049 1639 2056 2360 2856 3212
V=200 km/h V=280 km/h V=350 km/h 6000
5000 ht =200mm 4000
3000
2000 1000
Horizontal curve radius [m] 0 100 125 150 175 200 225 250 275 300 Cant deficiency [mm]
Figure 8-4 Horizontal curve radius R as a function of cant deficiency hd. Curves are shown at speeds of 200, 280 and 350 km/h. Cant ht = 200 mm.
105 Possible track geometry
Cant deficiency, hd=100 Cant deficiency, hd=150 Cant deficiency, hd=200 Cant deficiency, hd=250 6000
5000
4000
3000
2000 h = 150 mm 1000 t
Horizontal curve radius [m] 0 100 150 200 250 300 350 Speed [km/h]
Figure 8-5 Horizontal curve radius R as a function of speed V. The different curves show conceivable values of cant deficiency hd. Cant ht = 150 mm.
Cant deficiency, hd=100 Cant deficiency, hd=150 Cant deficiency, hd=200 Cant deficiency, hd=250 6000
5000
4000
3000
2000
ht = 160 mm 1000
Horizontal curve radius [m] 0 100 150 200 250 300 350 Speed [km/h]
Figure 8-6 Horizontal curve radius R as a function of speed V. The different curves show conceivable values of cant deficiency hd. Cant ht = 160 mm.
106 Track geometry for high-speed railways
Cant deficiency, hd=100 Cant deficiency, hd=150 Cant deficiency, hd=200 Cant deficiency, hd=250 6000 5000 4000 3000 2000
1000 ht = 180 mm 0 Horizontal curve radius [m] 100 150 200 250 300 350 Speed [km/h]
Figure 8-7 Horizontal curve radius R as a function of speed V. The different curves show conceivable values of cant deficiency hd. Cant ht = 180 mm.
Cant deficiency, hd=100 Cant deficiency, hd=150 Cant deficiency, hd=200 Cant deficiency, hd=250 6000 5000 4000 3000 2000
1000 ht = 200 mm 0 Horizontal curve radius [m] 100 150 200 250 300 350 Speed [km/h]
Figure 8-8 Horizontal curve radius R as a function of speed V. The different curves show conceivable values of cant deficiency hd. Cant ht = 200 mm.
107 Possible track geometry
8.2 Vertical curve radius
Possible vertical curve radii with limiting values according to CEN provisional standard [7] are shown in Table 8-5. In Figure 8-9 the vertical curve radius as a function of speed is presented. The values have been rounded up to nearest 100 m. There are different minimum values of vertical curve radius dependent of different requirements of limiting values on a crest or in a hallow. The limited vertical accelerations have been presented in Section 3.6.6. Table 8-5 Limiting values on vertical curve radius Source: CEN provisional standard [7].
Speed [km/h] 200 250 280 300 330 350 Vertical curve radius [m] [km/h] [km/h] [km/h] [km/h] [km/h] [km/h] Recommended value 14100 22000 27500 31600 38200 43000 Minimum value 7100 11000 13800 15800 19100 21500 without tolerance Minimum value on a crest 6400 10000 12500 14400 17400 19600 Minimum value in a hallow 5400 8500 10600 12200 15000 16600
Recommended minimum value according to CEN/TC 60000 Minimum value without tolerance according to CEN/TC Minimum value with tolerance (on a crest) according to CEN/TC 50000 Minimum value with tolerance (in a hallow) according to CEN/TC 40000
30000
20000
10000 Vertical curve radius [m] 0 200 250 300 350 Speed [km/h]
Figure 8-9 Vertical curve radius as a function of speed. Curves are shown for four different limiting values. Source: CEN provisional standard [7].
108 Track geometry for high-speed railways
9 Conclusions and further research
9.1 Conclusions on the literature study
Track cant in the range of 160-200 mm are possible to achieve. The higher values (180- 200 mm) can be allowed where only high-speed passenger trains are intended to operate. However, when mixed traffic with freight trains would come into question, the lower value must be considered. This is mainly due to the risk of loads “moving around” on the floor of the wagon. Hence, higher values of cant than 160 mm should not normally be chosen in such cases. The literature study also made a compilation over different worldwide projects and their used values of track cant, cant deficiency, horizontal curve radius, gradients and vertical curve radius. The recommended value of cant deficiency according to TSI is 100 mm (for conventional trains up to 300 km/h) but higher values may be allowed for lines with tough topographical constrains. Also, as described in Section 3.6.2, interoperable high- speed trains equipped with tilt technology may be admitted to run with higher cant deficiency values. To further investigate this issue is one of the main contributions of this study. Transition curves should be long if tilting trains are considered. The duration in the transition curves should at least be around 4-5 sec (i.e. 390 - 485 m for 350 km/h). Kufver says [16]: “A higher limit for cant, a lower roll coefficient and a higher degree of compensation in the body tilt system favour longer clothoids”. This proposal corresponds also to the rate of cant and the rate of cant deficiency recommendations according to TSI.
9.2 Conclusions on dynamic analysis of simulated vehicle response
According to hunting stability the following conclusions have been drawn: The hunting stability simulations have given an insight on the hunting stability problem. It can be established that it is likely possible to run a properly designed train at a speed of 350 km/h with the stability criteria being considered. In other words, it could be concluded that the vehicle configuration has the required properties that was foreseen before the simulations started. The simulated wheelset quidance is stiffer than on current Swedish self-steering bogie designs, but is more flexible than traditional quite stiff design from continental Europe. These characteristics of the vehicles have been studied before but not simulated for speeds in this range. It is important, however, that wheels and rails have suitable shapes in the wheel-rail interface, in order to limit the equivalent conicity to appropriate levels (e.g. 0.2 - 0.25, which is anyhow more liberal than TSI requirements of maximum 0.15).
109 Conclusions and further research
Concerning track shift forces the following conclusions have been drawn: With properly designed vehicles this study shows that it would be possible to maintain the European lateral track shift criteria at 350 km/h and at a cant deficiency in the order of 250 mm. However, it is likely impossible to get required performance without improving the track quality compared to current Swedish standards for 200 km/h. In order to achieve a top-speed of 350 km/h and a cant deficiency of 250 mm it seems necessary to improve the track quality with at least 25%, i.e. track irregularities should be at least 25% less in magnitude. This conclusion is, however, just an indication based on simplified assumptions. It is outside the scope and possibilities of this study to make a detailed complete investigation on this issue. Following conclusions on vehicle overturning have been drawn: With a modern high-speed train having a state-of-the-art aerodynamic performance, and a roof height in the order of 3.6 m, it is technically possible to make a train design for appropriate safety at strong side-wind at a cant deficiency up to 250 mm. In addition to the aerodynamic requirements, also the mass and mass distribution of the leading car have to be considered. The simulated case with a leading car mass around 55 tonnes (empty), the mass centre somewhat displaced towards the leading end, seems to be appropriate. The height of the c.g. should preferably be low. For motor-coaches with traction equipment in bogies and underneath the floor, these properties are most likely realistic.
9.3 Conclusions on horizontal and vertical curve radii
The horizontal curve radius is a function of allowed cant, cant deficiency and speed. The curve radius must be sufficiently large to cope with the desired speed for both conventional and tilting trains respectively. For example, if conventional high-speed trains are to be run at 280 km/h and and tilting trains at 350 km/h, the horizontal curve radius should be at least in the order of 3200 m. This requires a track cant of 200 mm and a cant deficiency of 100 mm for the conventional train and 250 mm for the tilting train. Such a geometry requires that no freight trains of category I or II are allowed. To be more conservative, if the track cant is limited to 160 mm and the cant deficiency for tilting trains to 225 mm, a minimum curve radius of 3750 m is needed for tilting trains at 350 km/h. In this case it would be possible to accomodate also freight trains category II (lighter freight trains for containers, swap bodies etc.). It should be kept in mind, however, that such speeds are not necessary or possible at all sections of the line. For example, in the vincinity of stations where most trains are stopping, the speed will be lower and the curve radius can be accordingly less. The standards of Banverket concerning vertical curve radius are quite conventional in relation to the proposals from TSI. These standards are, in turn, close to the standards of DB and several other railways. The minimum curve radius is 0.175 times the square of speed (in km/h), with tolerances 0.16 times the square of speed on a crest and 0.135 times the square of speed in a hallow. This requires a minimum vertical radius of 21500 m at 350 km/h (19600 and 16500 m with tolerances on a crest and in a hallow, respectively).
110 Track geometry for high-speed railways
9.4 Conclusions on freight train operations
It is anticipated that heavy freight trains should normally not be allowed on high-speed lines for speeds above 250 km/h. If only high-speed freight trains (category III, for express goods or mail) without goods and pallets loaded directly on the floor are operated, it may be possible to have a quite large track cant in the range of 180 - 200 mm. If freight trains category II with containers and swap bodies) are allowed, a maximum cant of 160 mm is recommended. A maximum allowed cant excess of around 120 mm seems to be acceptable for a category II freight trains (containers and swap bodies) running at a modest speed of 120 km/h. If only freight trains category III - high-speed for light express or mail - are allowed the gradients may be as high as 35 ‰ (this is in accordance with TSI). If freight trains category II are allowed, gradients up to 20 á 30 ‰ seems to be realistic. For example, at a gradient of 25 ‰ a total wagon mass of 650 - 700 tonnes can be halued by one four-axled locomotive.
9.5 Further research
This study primary deals with track geometry, having vehicle dynamics as a secondary issue. It is important to include passenger comfort in further studies. Also hunting stability simulations have to be done under a more complete set of conditions. A full study on the effect of track irregularities for different operational cases, including sets of different high-speed rail vehicle configurations in various conditions, is outside the scope and possibilities of this study. A simplified procedure has been applied, just to give an indication whether lateral track forces and track quality would be in the right order of magnitude. Future studies should penetrate this issue in more detail. In this connection, also the issue of track maintenance requirements should be penetrated comprehensively. It should be further investigated (in each individual case) whether the recommended gradients are appropriate with respect to the train´s ability to accelerate quickly on a line with dence traffic and limited capacity. Finally, an optimisation of track geometry with respect to required train performance (travel time etc.) and the cost of removing different topographical or other obstacles should be done. Such optimisation studies must be done for each individual section of proposed high-speed line.
111 Conclusions and further research
112 Track geometry for high-speed railways
References
[1] Andersson E. and Berg M.: Järnvägssystem och spårfordon (Railway systems and Rail vehicles), Kompendium, Del 1 - Järnvägssystem, KTH Järnvägsteknik, 1999.
[2] Andersson E. and Berg M.: Järnvägssystem och spårfordon (Railway systems and Rail vehicles), Kompendium, Del 2 - Spårfordon, KTH Järnvägsteknik, 1999.
[3] Andersson E., Berg M. and Stichel S.: Spårfordons dynamik (Rail vehicle dynamics), Kompendium, KTH Järnvägsteknik, 1999.
[4] Banverket: Spårgeometrihandboken (Track geometry handbook), BVH 586.40, Banverket, Borlänge, 1996.
[5] Banverket: Tillåten hastighet mht spårets geometriska form (Permissible speed with respect to track geometry), BVF 586.41, Banverket, Borlänge, 1996.
[6] Banverket: Spårlägeskontroll och Kvalitetsnormer - Central mätvagn Strix (Control and quality standards of track geometried irregularities), BVF 587.02, Banverket, Borlänge, 1997.
[7] CEN: Railway application - Track alignment design parameters - Track gauges 1435 and wider - Part 1: Plain line, prENV 13803-1:2001, CEN/TC256/WG15.
[8] CEN: Railway application - Testing for acceptance of the running characteristics of railway vehicles - Part 1: Testing of running behaviour, CEN/ TC 256 WG 10; Draft September 1999.
[9] Deutsche Bahn, DB: Netzinfrastruktur Technik entwerfen; Linienführung (Net Infrastructure Technical Draft; Alignment), 800.0110, DB, Germany, 1999.
[10] Deutsche Bahn, DB: Bahnanlagen entwerfen - allgemeine Entwurfsgrundlagen, Druckschrift DS 800.01.
[11] Esveld, C.: Modern railway track, NS Permanent Way Department, 1989.
[12] European Association for Railway Interoperability (AEIF): Trans-European High-Speed Rail system, Technical Specification for Interoperability (TSI), “Infrastructure” Subsystem, Version A, April 2000.
[13] European Association for Railway Interoperability (AEIF): Trans-European High-Speed Rail system, Technical Specification for Interoperability (TSI), “Rolling stock” Subsystem, Version A, Dec 5, 2000.
113 References
[14] Förstberg, J.: Ride comfort and motion sickness in tilting trains,Human responses to motion environments in train and simulator experiments, Doctoral thesis, TRITA-FKT Report 2000:28, KTH Railway Technology, 2000.
[15] Hecke A.: Effects of future mixed traffic on track deterioration,Masterof Science thesis, TRITA-FKT Report 1998:30, KTH Railway Technology, 1998.
[16] Kufver, B.: Optimisation of horizontal alignments for railways, Procedures involving evaluation of dynamic vehicle response, Doctoral thesis, TRITA-FKT Report 2000:47, KTH Railway Technology, 2000.
[17] Rail International: Planning and building of the German Federal Railway´s new lines and their consequences. W. Blind and M. Wölbing. Article in Rail International - May 1985.
[18] S.N.C.F: La voie Ferrée, Techniques de construction et D’entretien. Alias, J et al, Paris, 1984.
[19] Central Japan Railway Company: Data Book 2000.
[20] Hohnecker, E.: Zukunftssichere Trassierung von Eisenbahn- Hochgeschwindigkeit-strecken. Forschungsarbeiten des Verkehrswissenschaftlichen Instituts an der Universität Stuttgart, 1993.
[21] Lippert, S.: On side-wind stability of trains, Master of science thesis, TRITA- FKT Report 1999:38, KTH Railway Technology, 2000.
[22] Krieg R.: Extreme wind statistics for Säve and Arlanda. Reportet by order of ABB Traction AB, Sweden, April 1993.
[23] Lukascewicz, P.; Energy Consumption and Running Time for Trains - Modelling of running resistance and driver behaviour based on full-scale testing.TRITA- FKT 2001:25. Doctoral thesis, KTH Railway Technology, Stockholm 2001.
[24] UIC: Test and acceptance of railway vehicles from the points of view of dynamic behaviour, safety, track fatigue and quality of ride, Code 518 OR, Draft, January 1999.
[25] Andersson, E.: The influence on cant excess on track deterioration – Simulations and field measurements. TRITA FKT Report 2002:03.
[26] Tengstrand, H.: Personal communication with Mr. Henrik Tengstrand, Bombardier Transportation, chairman of the TSI technical committee on the side-wind issue.
[27] Sima, M.: Personal communication with Mr. Mikael Sima, one of the areodynamic experts at Bombardier Transportation, Västerås.
114 Track geometry for high-speed railways
[28] Andersson, E. : Personal communication with prof. Evert Andersson, KTH Railway Technology, also Company Senior Specialist in Vehicle Engineering at Bombardier Transportation, Västerås.
[29] DEsolver: GENSYS user´s manual. Release 0003, Östersund 2000.
115 References
116 Track geometry for high-speed railways
Appendix A - Notations
A.1 Latin letters
2 ay track plane acceleration [m/s ] 2 ay,lim permissible track plane acceleration [m/s ] 2 ayc carbody plane acceleration [m/s ] A clothoid parameter [m] bt distance between middle of track plane and origin of resulting force[m] b0 semi-span of wheelset-to-rail contact points [m] c curve cant [mm] CD aerodynamic drag coefficient [-] CL aerodynamic lift coefficient [-] CP aerodynamic pitch coefficient [-] CR aerodynamic roll coefficient [-] CS aerodynamic side coefficient [-] CY aerodynamic yaw coefficient [-] d distance between wind force origin and vehicle front [m] e exposition length of vehicle [m] f aerodynamic rolling coefficient factor [-] F force [N] g acceleration of gravity [m/s2] G track gauge [m] h height [m] heq quilibrium cant [m] ht track cant [m, mm] hd cant deficiency [m, mm] hd,lim permissible cant deficiency [m] he cant excess [m] heq,mm quilibrium cant [mm] ht,mm track cant [mm] hd,mm cant deficiency [mm] he,mm cant excess [mm] Jxx mass moment of inertia with respect to its centre of gravity and around the x-axis [kgm2]
Jyy mass moment of inertia with respect to its centre of gravity and around the y-axis [kgm2]
Jzz mass moment of inertia with respect to its centre of gravity and around the z-axis [kgm2]
117 Notations
k curvature [m-1] KL topographical factor [-] KN probability factor [-] KS surface roughness factor [-] KT time-averaging factor [-] KZ height factor [-] l length [m] L length of alignment element [m] Lt length of transition curve [m] m mass [kg] M moment [Nm] Eint intercept method overturning risk factor [-] P0 static axle load of stillstanding vehicle [N] q wheel unloading ratio [-] Q vertical wheel force [N] Q0 static vertical wheel force of stillstanding vehicle [N] R horizontal curve radius [m] Rrec,min recommended minimum value of horizontal curve radius [m] Rmin minimum value of horizontal curve radius [m] Rv vertical curve radius [m] Rv,rec,min recommended minimum value of vertical curve radius [m] Rv,min minimum value of vertical curve radius [m] Rf resulting force [N] S track shift force [N] Σ S2m track shift force (sum of guiding forces over 2 m track) [N] t time [s] td duration time of gale [s] tg gradient time of wind velocity [s] vres resulting wind velocity [m/s] v train speed [m/s] veq quilibrium train speed [m/s] V train speed [km/h] Vlim Operating speed limit [km/h]
Vdim dimensional train speed, design speed [km/h] vwind constant wind velocity [m/s] vgale gale wind velocity [m/s] vW side wind velocity [m/s] v10' average wind velocity mean-hourly value at height 10 m [m/s] w width [m] x longitudinal coordinate [m] y lateral coordinate [m] ÿ dynamic track plane acceleration [m/s2]
118 Track geometry for high-speed railways
∆y lateral shift [m] Y lateral wheel force [N] ΣY track shift force [N] Y/Q flange climbing ratio [-] z vertical coordinate [m]
A.2 Greek letters
µ friction coefficient [-] ρ density of air [kg/m3] Ψ yaw angle [rad] ϕ t cant angle, roll angle [rad] Φ lateral force angle [rad]
A.3 Indices b bogie c contact cg centre of gravity C carbody l left max maximum min minimum r right start start wwind ww windward x longitudinal direction y lateral direction z vertical direction
119 Notations
120 Track geometry for high-speed railways
Appendix B - Abbreviations
APT Advanced Passenger Train BV (=Banverket) Swedish National Rail Administration BVF Banverket regulation (standard) BVH Banverket handbook CEN Comité Européen de Normalisation (Committé for European Standardisation) DB German National Railways DS German Railways standard EMU Electrical Multiple Unit EN European Norm (Standards) ESDU Engineering Science Data Unit EU European Union GENSYS Multibody dynamics program ICE InterCityExpress, German high-speed train ICT Tilting ICE ORE Office for Research and Experiments of UIC, now ERRI SJ Swedish State Railways S1002 Standard wheel profile SNCF French National Railways TGV Train a Grande Vitesse, french high-speed train TSI Technical Specification for Interoperability (of European high- speed trains) UIC International Union of Railways UIC 60 Standard rail profile X 2000 Swedish high-speed train with tilting technology
121 Abbreviations
122 Track geometry for high-speed railways
Appendix C - Further diagrams on track shift forces
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 60
55
50
[kN] 45 max
S 40
35
30 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-1 Track shift force S as a function of cant deficiency hd. Track 2. 2nd wheelset, 1st bogie.
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 55
50
45
[kN] 40 max
S 35
30
25 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-2 Track shift force S as a function of cant deficiency hd. Track 3. 2nd wheelset, 1st bogie.
123 Further diagrams on track shift forces
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 55 50 45 40 [kN]
max 35 S 30 25 20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-3 Track shift force S as a function of cant deficiency hd. Track 4. 2nd wheelset, 1st bogie.
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 55 50 45 40 [kN]
max 35 S 30 25 20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-4 Track shift force S as a function of cant deficiency hd. Track 5. 2nd wheelset, 1st bogie.
124 Track geometry for high-speed railways
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 50
45
40
[kN] 35 max
S 30
25
20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-5 Track shift force S as a function of cant deficiency hd. Track 6. 2nd wheelset, 1st bogie.
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 55 50 45 40 [kN]
max 35 S 30 25 20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-6 Track shift force S as a function of cant deficiency hd. Track 7. 2nd wheelset, 1st bogie.
125 Further diagrams on track shift forces
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 50
45
40
[kN] 35 max
S 30
25
20 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-7 Track shift force S as a function of cant deficiency hd. Track 8. 2nd wheelset, 1st bogie.
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 50 45 40 35 [kN]
max 30 S 25 20 15 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-8 Track shift force S as a function of cant deficiency hd. Track 9. 2nd wheelset, 1st bogie.
126 Track geometry for high-speed railways
S2m (ht=160mm) S2m (ht=180mm) S2m (ht=200mm) S2m,lim 50 45 40 35 [kN]
max 30 S 25 20 15 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-9 Track shift force S as a function of cant deficiency hd. Track 10. 2nd wheelset, 1st bogie.
127 Further diagrams on track shift forces
Track 2 Track 3 Track 4 Track 5 1,5
[-] 1 lim /S
max 0,5 S
ht=160 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-10 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 160 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.
Track 2 Track 3 Track 4 Track 5 Track 6 No irregularities 1,5
[-] 1 lim /S
max 0,5 S
ht=180 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-11 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 180 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.
128 Track geometry for high-speed railways
Track 2 Track 3 Track 4 Track 5 Track 6 No irregularities 1,5
[-] 1 lim /S
max 0,5 S
ht=200 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-12 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 200 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.
Track 7 Track 8 Track 9 Track 10 No irregularities 1,5
[-] 1 lim /S
max 0,5 S ht=160 mm 0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-13 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 160 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.
129 Further diagrams on track shift forces
Track 7 Track 8 Track 9 Track 10 No irregularities 1,5
[-] 1 lim /S
max 0,5 S ht=180 mm
0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-14 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 180 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.
Track 7 Track 8 Track 9 Track 10 No irregularities 1,5
[-] 1 lim /S
max 0,5 S ht=200 mm
0 50 75 100 125 150 175 200 225 250 275 300 325 350 Cant deficiency [mm]
Figure C-15 Track shift force Smax/Slim (-) as a function of cant deficiency hd. Cant ht = 200 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.
130 Track geometry for high-speed railways
Appendix D - Further diagrams on vehicle overturning
Intercept method risk factor, R=4380 m, hd=150 mm 1.00 0.90 0.80 0.70 0.60 [-]
int 0.50
E 0.40 0.30 Overturning 0.20 0.10 0.00 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Wind speed [m/s]
Figure D-1 Intercept method risk factor E as a function of wind velocity where cant deficiency hd = 150 mm. Vehicle speed V = 350 km/h and cant ht = 180 mm.
Intercept method risk factor, R=3804 m, hd=200 mm 1.00 0.90 0.80 0.70 0.60 [-]
int 0.50
E 0.40 0.30 Overturning 0.20 0.10 0.00 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Wind speed [m/s]
Figure D-2 Intercept method risk factor E as a function of wind velocity where cant deficiency hd = 200 mm. Vehicle speed V = 350 km/h and cant ht = 180 mm.
131 Further diagrams on vehicle overturning
Intercept method risk factor, R=3362 m, hd=250 mm 1.00 0.90 0.80 0.70 0.60 [-]
int 0.50
E 0.40 Overturning 0.30 0.20 0.10 0.00 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Wind speed [m/s]
Figure D-3 Intercept method risk factor E as a function of wind velocity where cant deficiency hd = 250 mm. Vehicle speed V = 350 km/h and cant ht = 180 mm.
Intercept method risk factor, R=3177 m, hd=275 mm 1.00 0.90 0.80 0.70 0.60 [-]
int 0.50
E 0.40 Overturning 0.30 0.20 0.10 0.00 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Wind speed [m/s]
Figure D-4 Intercept method risk factor E as a function of wind velocity where cant deficiency hd is 275 mm. Vehicle speed V = 350 km/h and cant ht = 180 mm.
132 Track geometry for high-speed railways
Appendix E - Overturning due to side-wind
The aim of this Appendix is to describe the calculation of the wind-induced forces and moments and provide the reader with a short introduction of how to determine the aerodynamic coefficients and a reference wind velocity. As exact aerodynamic train data as possible and a good knowledge of the wind conditions at the track side are the most important conditions to get accurate values for the forces acting on the train. Up to today it is not easy to get this data - especially the wind data - with a satisfying accuracy. A problem when trying to define side-wind stability is that these two parameters with the highest uncertainty are also the most sensitive ones to the overturning probability.
E.1 Wind-induced forces and moments
Two different wind velocities are acting on a running vehicle. The first is the ambient wind that is blowing at the track side. The speed of this natural wind is in the following named as wind velocity vW. Apart from the natural wind velocity, also the wind caused by the speed of the train has to be considered. This wind velocity has got the same absolute value as the train speed and is in the following called train speed vT. The wind velocity and the train speed can be summarized to a resulting wind velocity vres. The angle between train speed and resulting wind velocity is called yaw angle Ψ. The quantities are shown in Figure E-1.
vT vT Ψ
vres vW
Figure E-1 wind velocity vW andtrainspeedvT, added to resulting wind velocity Ψ vres. Yaw angle between resulting wind velocity and train speed.
To calculate forces and moments on the train from the resulting wind velocity, aerodynamic coefficients are needed, which can be obtained experimentally or numerically (see Section E.2). They are usually assumed to be independent of train speed and density of air, but depend on the flow around the train, i.e. the yaw angle.
133 Overturning due to side-wind
It has been shown that the greatest side-wind forces are induced with a wind velocity approximately normal to the train speed. Now the absolute value of the resulting wind velocity and the yaw angle can be calculate with the Pythagorean formula (Figure E-2):
2 2 vT vres = vW + vT Ψ vT vW v W vres v Ψ = atan------W vT Figure E-2 Calculation of resulting wind velocity and yaw angle for the special case of a wind velocity normal to the train speed.
The coefficients allow - depending on yaw angle and resulting wind velocity - to calculate the forces acting on the train according to Equations (E-1) to (E-6). The density of air ρ is set as constant.
1 ⋅ ()ρΨ ⋅⋅ ⋅ ⋅2 Drag forceFxw, = --- C hC wC vres [N] (E-1) 2 D
1 ⋅ ()ρΨ ⋅⋅ ⋅ ⋅2 Side forceFyw, = --- C hC lC vres [N] (E-2) 2 S
1 ⋅ ()ρΨ ⋅⋅ ⋅ ⋅2 Lift forceFzw, = --- C wC lC vres [N] (E-3) 2 L
1 ⋅ ()ρΨ ⋅⋅2 ⋅ ⋅2 Roll momentMxw, = --- C h C lC vres [N] (E-4) 2 R
1 ⋅ ()ρΨ ⋅⋅ ⋅2 ⋅2 Pitch momentMyw, = --- C wC l C vres [N] (E-5) 2 P
1 ⋅ ()ρΨ ⋅⋅ ⋅2 ⋅2 Yaw momentMzw, = --- C hC l C vres [N] (E-6) 2 Y
CD: Drag coefficient [-]
CS: Side coefficient [-]
CL: Lift coefficient [-]
CR: Roll coefficient [-]
CP: Pitch coefficient [-]
CY: Yaw coefficient [-]
134 Track geometry for high-speed railways
ρ: density of air [kg/m3] hC: height of car body [m] lC: length of car body [m] wC: width of car body [m] vres: resulting wind velocity [m/s] Note that the coefficients in this study are related to the geometrical measures of the car body. Coefficients related to other geometrical parameters, like length over buffers, total height, projected areas etc., can also be found in other studies. This has to be considered when comparing the coefficients from different studies. Secondly, the location of the coordinate system is important when defining the forces and moments. The coefficients used in this study are determined for a coordinate system located in the middle of the two bogie pivots in height of the track plane. The coordinate system is shown in Figure E-3.
g
vT
x
Fx,w
Mx,w F y,w y
My,w Mz,w
Fz,w track plane (top of rail)
Figure E-3 Coordinate system with the three wind-induces forces and moments.
135 Overturning due to side-wind
E.2 Aerodynamic train data
Aerodynamic coefficients can mainly be determined by three different methods: (i) Numerical simulation (ii) Windtunnel test on scale models (iii) Test with full scale models Aerodynamic tests with full scale models are not very practicable. Wind tunnels of the needed size to take full scale models do not exist, and outdoor tests fail – though giving real data - because of the rareness of suitable and well-defined wind conditions. Deutsche Bahn tried within the Transaero project, a project of the European Community dealing i.a. with side-winds, to make full scale tests with trains on real track with wind shielding devices. One of the greatest problems has been that much time got lost by waiting for strong wind conditions. When high wind velocities were reached it was often a problem to arrive without delay at the track sections where the measurements were to be carried out. This because preparing a test train with necessary instrumentation and staff requires some time. The highest wind velocity measured in the tests was 14 m/s. However, the measurements are important to enable a comparison between similar data from wind tunnels and computations, thus to obtain basic data for verifying scaled tests and computer models. Another disadvantage of full scale model tests on real trains is that the train must already exist. Changes in the shape are no longer possible if the coefficients are not sufficient. In the past, wind tunnel tests with scale models have been the best and most common way to obtain accurate coefficients. A good copy not only of the train but also of ground effects (e.g. ground roughness due to trees, houses, etc.), turbulent flow, track (viaducts, embankments), etc. is necessary for good results. For instance, relative velocity between vehicle and track/ground is very important. Scale effects and critical Reynold numbers have also to be considered. With improved computer capacity and falling computer prices the determination of the aerodynamical coefficients by numerical simulation (CFD calculation) is becoming more and more common. To calculate the coefficients, different mathematical models exist. One of the biggest disadvantages of the computer models are the simplifications that have to be made in order to get suitable simulation times. Nevertheless, carefully made CFD calculations are able to give results with a good agreement with wind tunnel tests. A comparison that has been made at Bombardier between wind tunnel and computed forces and moments showed a good agreement of the results. For yaw angles between Ψ
= 10°…30° the computeredCS ,CL andCR values are lower than the wind tunnel data, the maximum error is 20%, so that the wind tunnel aerodynamic coefficients can be regarded as more conservative in this range of these angles. It is very important to point out that only the relative error between wind tunnel and computed results has been determined. Nothing is said about the error relative to the real coefficients of the vehicle. As a conclusion from this report, the computed values are regarded as good as the wind tunnel results.
136 Track geometry for high-speed railways
It can be assumed that with further increased computer performance the results become more and more accurate. A problem for all the three methods is the tilting of the train. The tilting angle of the train is not constant when running on a track. On the one hand the train will be tilted to the leeward side by the wind loads and to the outer side when running in a curve with cant deficiency. On the other hand, tilting to the inner side must be considered due to track cant and a possible tilt system of the train when passing a curve. It is difficult to decide for which tilting angle the coefficients should be determined. A comparison that has been made at Bombardier for the Norwegian airport shuttle between Oslo - Gardermoen showed a difference between tilting 3,5° outwards and 6,5° inwards ofCL and CR values of about 20% at 20° yaw angle [27]. A solution would be to combine the multibody simulation program with a CFD program to determine the aerodynamic coefficients at every time step. However, this would cause unacceptable high computing times. Thus, there is a risk that the overturning wind forces are somewhat underestimated on tilting trains. On the other hand, on a train with active tilt and a self-centering ability (like X 2000) the centre of gravity will move somewhat inwards to the curve centre. This effect will reduce the risk of overturning. According to Prof. E. Andersson experience [28] the two effects of tilting with respect to overturning (one negative and one positive) will to a great extent compensate each other. When determining the coefficients that have been used in this study, track cant has been considered and the tilt has been neglected. To examine an exact way of determining the moments and forces acting on a train would go wide beyond the scope of this work. The aim of this section is to provide the reader with the certainty that there are many things that have to be considered when determining aerodynamic coefficients. The used aerodynamic data in this study is assumed to be appropriate in the range of today’s determination possibilities. Further work on the problem of determining aerodynamic coefficients is an important issue to get even more precise results than today.
E.3 Aerodynamic coefficients for the simulated vehicle
In the following, the aerodynamic coefficients for the simulated vehicle model in this study are listed. The wind is blowing from the right side of the vehicle i.e. the inside of the curve. Notice that the coefficients are related to the geometrical measures of the car body. These measures are listed in Table E-1. The used density of air is ρ = 1.205 kg/m3. In Table E-1, the aerodynamic coefficients for the vehicle used in the present study are shown. They have been calculated by Bombardier Transportation by CFD [27]. They can be seen as typical for state-of-the-art for well designed vehicles (2001).
137 Overturning due to side-wind
Table E-1 Aerodynamic coefficients for simulated vehicle model at different yaw angles [27].
Ψ CD CS CL CR CP CY [degree] [-] [-] [-] [-] [-] [-] 10 0 -0.1278 -0.0534 -0.05921 -0.01598 -0.0343 20 0 -0.3029 -0.211 -0.1446 -0.01196 -0.0592 30 0 -0.5190 -0.416 -0.2534 0.00368 -0.07655 40 0 -0.7251 -0.6042 -0.3598 0.03542 -0.09022
138 Track geometry for high-speed railways
Appendix F - Train mass versus gradient
The locomotive of the freight train must be able to produce sufficient tractive force in order to bring the train into motion and to maintain a certain speed or acceleration. The tractive force has firstly to balance the total running resistance, including gradient resistance, secondly to accelerate the train. The basic requirement is to overcome the resistance at the starting moment and thus bring the train into motion.
F.1 Running resistance
F.1.1 General
The total running resistance FRT of a train can generally be expressed by [2], [23]:
() () ()2 FRT = FMA +++FM v FD v FD v ++FC FG (F-1) where
FMA = Mechanical resistance on straight track, due to wheel rail friction, bearing friction etc., independent of speed.
FM(v) = Mechanical resistance, linearly dependent of speed.
FD(v) = Air drag, linearly dependent of speed. 2 FD(v ) = Air drag, dependent on speed squared.
FC = Additional curving resistance
FG = Gradient resistance. v = Speed (m/s). In the following sections general formulas and experimental results from the above mentioned references are used.
139 Train mass versus gradient
F.1.2 Mechanical resistance
For modern locomotives with three-phase induction motors as traction motors (combination of [2], [23]):
()⋅ ⋅ ⋅ ⋅⋅⋅ FMA = Ks 30 naxl + aQl ml g + 65 naxw + aQw mw g [N] (F-2) where
Ks = 2 at the starting moment;
Ks = 1 otherwise. , ⋅ –3 aQl = aQw =06 10 (assumed that wheelset guidance has about the same flexibility and alignment as ordinary European freight wagons) g = gravitational acceleration = 9.81 m/s2.
ml = mass of locomotive
mw = total mass of all freight wagons
naxl = number of locomotive axles
naxw = number of freight wagon axles. Thus, the mechanical resistance is higher at the starting moment than if the train is in motion, i.e. Ks is 2 instead of 1. If the tractive force of the locomotive is maintained after the starting moment there will be a certain excess in tractive force and therefore an extra push in train acceleration.
F.1.3 Resistance linearly dependent of speed
In this section mechanical resistance and air drag, linearly dependent of speed is considered, i.e. FM(v) + FD(v). In [23] linearly speed dependent mechanical and air resistance is given for ordinary covered freight wagons (type Hbis or similar). This is assumed to be approximately equivalent to container trains or trains transporting swap bodies. This assumption may be conservative, as future high-speed freight trains (140 - 180 km/h) will likely have better aerodynamics than ordinary freight trains of today. However, in relation to other parts of running resistance, these terms are quite small, which reduces the sensitivity for somewhat conservative assumptions. Therefore, experimental results for covered wagons from [23] can be expressed:
() ()≈ ⋅ ≈ ⋅ FM v + FD v –0.622 + LT 0.6 LT [N] (F-3) where LT = total train length, including locomotive (m).
140 Track geometry for high-speed railways
F.1.4 Air drag (air resistance)
Air resistance of container trains and trains with swap bodies are assumed to be approxi- mately equivalent to conventional European freight trains with covered wagons (type Hbis or similar). Air drag of the latter trains is given in [23]. As mentioned in the previous section, these assumptions may be conservative, as future high-speed freight trains (140 - 180 km/h) will likely have better aerodynamics than ordinary freight trains of today. On the other hand, it is assumed that not more than one container location out of eight is empty, i.e. is run as an open wagon, in fully loaded trains. This assumption may be non-conservative or optimistic. Therefore, conservative and non-conservative assumptions are believed to balance each other, which reduces the uncertainties and possible resulting errors. Thus from [23], assuming that the possible influence of ambient wind is negligible:
()2 ()⋅⋅–2 ⋅ 2 FD v = 5.4+ 5.2 10 LT v [N] (F-4) where LT = total train length, including locomotive (m).
F.1.5 Curving resistance
Additional curving resistance FC mainly corresponds to the increased energy dissipation that occurs in the wheel-rail interface, due to sliding motions (creep) and friction phenomena, at curve negotiation. It is dependent on wheel-rail friction and the stiffness and character of the wheelset guidance (radial self-steering or forced radial steering produce lower curving resistance than stiff wheelset guidance). In this context it is assumed that the wheelset guidance of future high-speed freight trains has almost about the same flexibility and alignment as ordinary European freight wagons. This may be an optimistic assumption; however as seen from the example following Equation (F-5), the curving resistance will be low anyhow in great curve radii on high-speed lines. Curving resistance is determined from a corrected formula of Röckl [2], [23]:
K ⋅⋅⋅()m + m g 0.65 F = ------C l w - [N] (F-5) C ()R – 55 where
g = gravitational acceleration = 9.81 m/s2 ≈ KC = correction factor0.7 (for European freight trains)
ml = mass of locomotive
mw = total mass of all freight wagons R = curve radius (formula valid for R ≥ 350 m).
141 Train mass versus gradient
Example: R = 400 m produces an additional curving resistance, according to Equation (5), of approx. 1.3 ‰ of the train load, which is in many cases not negligible (typically some 10 % of total running resistance for a freight train in a 10-‰ gradient) R ≤ 2000 m produces an additional curving resistance of ≤ 0.2 %, which in most cases may be considered as negligible. Even if the real resistance for high-speed freight trains is as much as 30 - 50 % higher, due to a possibly stiffer wheelset guidance, curving resistance is still almost without significance in these large curve radii.
F.1.6 Gradient resistance
Gradient resistance FG is the composant of the train load against the direction of travel. It is positive for uphill gradients and negative for downhill gradients (i.e. pushes the train forward). Thus the gradient resistance is determined by:
()m + m ⋅⋅gG F = ------l w [N] (F-6) C 1000 where G = gradient along the track (‰)
g, ml and mw as in Section F.1.3. This part of the running resistance is mostly dominating for freight trains in gradients (10 - 25 ‰). This is also the main issue in this special investigation.
F.2 Tractive force of the locomotive
F.2.1 Necessary tractive force
The locomotive(s) must be able to produce a tractive force which can balance the running resistance and also give the train the desired acceleration. For ordinary freight trains just a low acceleration is required; the basic requirement is to overcome the starting resistance and the gradient resistance. Thus the total tractive force F from the locomotive(s) must at least satisfy the following condition:
≥ FFRT (F-7) where the extra starting resistance is included in FRT. After the train has been brought into motion (v ≥ 0, a = 1), the train forward acceleration ax is determined by:
142 Track geometry for high-speed railways
FF– RT ax = ------(F-8) me where me is the equivalent mass of the train, including the effect on inertia of rotating masses (me is sometimes called "dynamic mass" and is usually in the order of 2 - 5% higher than the train mass for a freight train).
< IfFFRT the train is subject to a deceleration.
F.2.2 Tractive forces and adhesion
ThetractiveforceF of the locomotive (or the multiple-unit train) is determined and limited either by the traction equipment on board the locomotive - i.e. by the tractive effort -orbytheavailable wheel-rail adhesion α, whatever the lowest. Modern loco- motives are in most cases able to produce more tractive force than the lowest value of available adhesion; this is also the case for locomotives geared for 140 - 180 km/h. Thus the limiting factor is very often the available adhesion. If adhesion is limiting and determining the tractive force:
α ⋅⋅ F = ml g (F-9)
In Equation (F-9) it is assumed that all axles of the locomotive are tractive, i.e. the adhesive load of the locomotive is equal to the total locomotive load on the track. For modern locomotives with sophisticated slip control (for optimum use of available adhesion) and sanding (for improving very low adhesion), an adhesion level α of at least 0.25 can be almost guaranteed under most conditions (excluding leaves on the track during the autumn).
143 Train mass versus gradient
144 Track geometry for high-speed railways
Appendix G - General Description of the GENSYS Software Package
The GENSYS software package consists of 51 programs for the analysis of railway vehicle dynamic behavior. Some of these programs can be used for all kinds of multibody dynamics simulation. The following sections give a brief overview of the package. For more information, see [29]. Other comparable packages are for instance ADAMS, MEDYNA, SIMPACK and VAMPIRE .
G.1 Modelling phase
G.1.1 Local coordinate system
In GENSYS, two types of local Euler coordinate systems can be defined. They can be either fixed systems relative to a fixed global coordinate system or can be guided by the three parameters: design track curvature, design cant and design level of track centre. Another possibility are linear local coordinate systems which have to be related to an Euler coordinate system.
G.1.2 Track geometry
The design track can be assembled with tangent track parts, circular curves and different kinds of transition curves. Transition curves and circular curves are defined by the three track design parameters: curvature, cant and vertical level of the track centre. Track irregularities can be taken over either from library files or be created by functions. It is possible to express the track irregularities in different forms. They can be expressed in cartesian coordinates, Mauzin diagrams, Plasser diagrams, Fourier series and power spectral densities. Routines included in the package interpolate the track irregularity arrays.
G.1.3 Mases and coupling elements
In GENSYS, different types of masses can be created. Possibilities are masses without any degree of freedom or with 6 degrees of freedom. To create a coupling between two masses (bodies), the coupling coordinates and properties have to be defined. Possible options are linear and non-linear properties. Fourteen different types of couplings are available. The three basic elements are a linear spring, a linear viscous damper and a friction damper.
145 General Description of the GENSYS Software Package
G.1.4 Wheel-rail contact
The GENSYS package includes more than 20 modules to create a wheel-rail contact model, in order to simplify the model generation. The one used in the present simulations interpolates the creep forces in a 4-dimensional matrix. The calculation of the matrix elements is performed according to the simplified theory of J.J. Kalker.
G.2 Analysis phase
G.2.1 Quasi static analysis
This analysis is non-linear in every phase of the analyzing process. Element forces balance load and inertial forces. The basic output are quasi-static vehicle displacements. They can be used in a modal analysis or a frequency response analysis. In a time integration analysis they can be used as initial values for the simulations.
G.2.2 Modal analysis
The modal analysis is started with a linearisation of the model. The calculated eigenmodes are, due to normally large damping, complex. The resulting eigenfrequencies are given both as complex roots expressed in [rad/s] and as damped eigenfrequencies expressed in [Hz] and damping as a fraction of critical damping.
G.2.3 Frequency response analysis
As in modal analysis, first a linearisation of the model is started, in order to make a linear analysis possible. The linearization amplitude and the type of spectra can be chosen. Various transfer functions can be calculated in this analysis.
G.2.4 Time integration analysis
This analysis is in general non-linear. Several numerical integration methods are available. Possible are for instance Euler’s method, Heun’s method or the classical method of Runge-Kutta.
146 Track geometry for high-speed railways
G.3 Output phase
G.3.1 Output quantities
The most important railway-specific output quantities from GENSYS are: - body acceleration and jerks - wheel-rail contact forces - track shift forces - derailment ratios - wheel unload ratios - different wheel-rail wear indices
G.3.2 Filtering, statistics, etc.
Resulting time histories can be processed in several ways, for instance: - different orders of low / high pass filtering - Fourier analysis - ride comfort determination (based on accelerations etc.) - statistical analysis of the time histories
G.3.3 Plotting and animation
Time histories, spectra, eigenmodes etc. can be plotted. Vehicle motions can also be animated.
147 General Description of the GENSYS Software Package
148