Railway Transportation Systems Behaviour of Rolling Stock on Track

Home , Bogie

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Railway Transportation Systems

Christos N. Pyrgidis

Behaviour of rolling stock on track

Publication details https://www.routledgehandbooks.com/doi/10.1201/b19472-4 Christos N. Pyrgidis Published online on: 25 Feb 2016

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The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 increase of the length of the railway wheelset 2e wheelset railway of the length of the increase wheels will be will wheels equal to π αequal yand parameters Behaviour of rolling ontrack stock Chapter equilibrium, the axle is displaced by y displaced is axle the equilibrium, to achieve trying and track the layout 1.12. the consider entering Upon us of Figure Let 3.1.2 ‘ angle by an rotated and by ‘y’ displaced it laterally is time, moment in at arandom time, same at the while axis track of the direction the Vin speed at aconstant 1935). and Rocard, in (Julien 1883Klingel by studied 3.1 was first ) and (Figure motion or hunting asinusoidal as known (isolated) is movement single of wheelset railway The aconventional 3.1.1 3.1

(Esveld, 2001). (Esveld, of a whole body (car vehicle particularly and way wheelset the motion of a rail In reality, contact. flange without and damping without motion ous axle. of the accelerations lateral the reduce and motion The red The Klingel proved that the bicone motion is sinusoidal with a difference of phase of the of the of phase adifference with sinusoidal is bicone motion proved the that Klingel Let us calculate the displacement y displacement the calculate us Let moved axle the that assumed He abicone. with wheelset railway the simulated Klingel Klingel presented a pure kinematic analysis of the phenomenon assuming aharmoni phenomenon of assuming the analysis kinematic apure presented Klingel

Wave amplit Maximum lat Maximum Frequency: Wavelengt BEHAVIOUR OF A SINGLE RAILWAY ASINGLE WHEELSET OF BEHAVIOUR

Movement on straight path straight on Movement Movement in curves uction of conicity γ of conicity uction 3 h: h:

f ude: y ude: L = eral acceleration: acceleration: eral w 2 V = π w 2

π ta γ⋅ oo n ta re oo γ e o n /2 with the following characteristics: following the with /2 o ⋅ of the wheels, the increase of the rolling radius r radius rolling of the increase the wheels, of the γ

yy ′′ ma o o for the above position. The rolling radii of the two two of the radii rolling above The for the position. with regard to the curve’s outer curve’s face. to the regard with xw =⋅ 4 π 2 o increase the wavelength of the sinusoidal sinusoidal of the wavelength the increase ⋅ L V 2 w 2

bogies) is is bogies) much more complex α ’. o and the the and (3.2) (3.3) (3.4) (3.1) 77 - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4

to the equivalent conicity γ conicity equivalent to the 3.2 cleara 78 to the total of ‘secondary suspension – bogie frame and primary suspension –wheelsets’. suspension primary and frame –bogie suspension of ‘secondary total to the refers term the definition, correct the usually is However, this and wheelsets. the including ter The 3.2.1.1 3.2.1 3.1 Figure y displacement of the increase to lead an diameter wheel of the increase the gauge and track t, we havet, o . For y

Let Let and Acc S S

1 2 Railway Transportation Systems Transportation Railway ⇒= and rr rr BEHAVI

S S 1 = 2 = 2 1

nce. ording to the mathematical equation (3.7) the displacement y (3.7) equation displacement the mathematical to the ording us consider S consider us

=+ V V m bogie sometimes simply denotes a construction that supports the car body without without body car the supports that a construction simply denotes sometimes m bogie =− Operational and technical characteristics of bogies of characteristics technical and Operational

S S == Object and purposes of bogies of purposes and Object o 1 2 Sinusoidal motion of a railway wheelset. arailway of motion Sinusoidal 2 1

= oe ⋅ ⋅ oe

t t is the flange way flange the where σis the outer rail, with flange ofσ we the have acontact 2 1 V γ V γ OUR OF A WHOLE VEHICLE AWHOLE OF OUR 2 1 y y () () o o Re Re =

1 co co and S and ω ω +⋅ −⋅ r r y 2 1 x → y

x 1 o 2 2 e as the paths covered by the two wheels during the time interval interval time the during wheels covered two by the paths the as G ξ ξ and the radius of curvature R of radius curvature the and S p = ωγ ωγ V T ⋅+ ⋅− (2) () () 2 ry ry oe oe α (1) G → y o ⋅ ⋅ T o 1 o → x o ⇒= y o (r (1) c e . On the contrary, the increase of increase the contrary, the . On 1 ee )( ooo ⋅γ ⋅ R r

o (2) is in reverse proportion proportion reverse in is r 2 ) (3.5) (3.6) (3.7) Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 namely primary suspension: wheelset–bogie suspension (usually materialised by coil springs springs by coil materialised (usually suspension wheelset–bogie suspension: primary namely levels suspension two with vehicle the providing dampers and elements of elastic by means 2a wheelsets. single of the technique the using no attained longer could be of vehicles inscription the circumstances, these Under length. vehicles’ the in increase the dictated ity, which afact capac transport vehicles’ the in increase the with hand in went hand of transport means body. evolution car to The the of a as railway directly linked wheelsets single or three two through was achieved alignment horizontal of the sections curved in inscription their were relatively and vehicles short trailer railway Initially, vehicle. of the length Figure 3.2 Figure the and body car to the connected is frame bogie wheelsets). The (classical velocity angular same at the axle the and wheels of rotation the the in resulting axle to the linked rigidly are of which the wheels wheelsets, with fitted are bogies the technology, this In power vehicles. and trailer in broadly used are Nowadays, ‘conventional’ bogies or ‘classic’ 3.2.1.2.1 3.2.1.2 Using the bogies, the inscription is achieved essentially via the bogies (wheelbase length (wheelbase length bogies the via essentially achieved is inscription the bogies, the Using on the directly depends curves of in vehicle arailway inscription of the ability The The bogies must bogies The

• • • • • <

4.0 Have rel Provid Provid t Assist th Allow

Conven m) while t m) while in cur in bogies 3-axle two, of (b) Inscription inscription. – ideal curves in bogie a 2-axle of (a) Inscription Descri (a) e dynamic comfort to passengers in three directions three in to passengers comfort e dynamic (development path speeds) of on straight high vehicles of the e stability he optimum transfer of loads from the car body to the rails to the body car of the loads from transfer he optimum K atively low construction and maintenance cost maintenance and atively low construction ves. e smooth inscription of the wheelsets in curves in wheelsets of the inscription e smooth y ption and operation and ption K tional bogies y K he car body follows the movement of the bogies (Figure 3.2). (Figure movement follows bogies the of body the he car x K x Whe Bo R c el gi e base K x K x K y K y Behaviour of rolling stock on track on stock rolling of Behaviour (b ) wheels

79 et et - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 80 dynamic behaviour of the vehicles are (Joly, are 1983) vehicles of the behaviour dynamic stages: main involves following the to commissioning design from bogie arailway Developing of importance. is equivalent stock rolling of the construction and design performances; desired of the achievement the and ride train asmooth own on its not guarantee does superstructure track of the construction Good 3.2.1.2.2 no date). Rail, Jeumont (Schneider on. run will they track of the characteristics geometrical on the on and mounted be will they to which vehicles of the functionality on the directly suspensio body bogie–car suspension: [chevrons]) elements or rubber secondary and dampers and 3.3 Figure

The geometrical and technical characteristics of the bogies that substantially affect the the affect substantially that bogies of the characteristics technical and geometrical The power bogie aconventional form which parts individual the all 3.4 detail shows in Figure depends them among design and choice the bogies; of conventional types various are There • • • • • • •

Railway Transportation Systems Transportation Railway The longitu The Commissio Testing con and Design Theoretica o Conception The bogie wheel bogie The

Conventional n (materialised by air suspension or coil springs and dampers) (Figure 3.3). (Figure dampers) and springs or coil suspension by air n (materialised Design of the b the of Design l study and modelling of its dynamic behaviour using simulation models simulation using behaviour of dynamic its modelling and l study ning and entering into operation into entering and ning dinal (K dinal f the bogie technology and physical explanation of the bogie behaviour bogie of the explanation physical and technology bogie f the bogie wheelsets. classical with struction base (2a) (Figure 3.3) (2a)base (Figure ogies a x a ) and lateral (K lateral ) and K K y x y d ) stiffness of the primary suspension springs suspension primary of the ) stiffness e o e o d Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 as well as well as of curves negotiation good the and paths on straight vehicles of motion the steady the mine deter that bogies of the behaviour lateral to related the directly above are the elements All Figure 3.4 Figure in curves. in of wheelsets negotiation good and paths on straight speeds high both to guarantee possible passengers. of the comfort dynamic the characterise Indicatively it is noted that (Pyrgidis, 1990) (Pyrgidis, that it noted is Indicatively it not is equipment, track the and stock rolling for the advances technological the Despite that bogies of the behaviour vertical to related the directly are features three last The • • • • • • • •

(3 The car bo car The The smal The The damp The The wheel diameter (2r diameter wheel The The equi The o mass The The high v high The The vertic The

× Catalogue pieces de rechange de pieces Catalogue Asynchrones, Moteurs Conven

10 5. Primary suspension 5. Primary 4. T 3. Re 2. 1. Whe 7 Bo 7

ransmitte N/m valent conicity of the wheels ( wheels of the valent conicity ducer de g l value of the equivalent conicity of the wheels ( wheels of the conicity equivalent l value of the tional bogie – main parts. (Adapted from Schneider Jeumont Rail. no date, Bogie CL93 à Bogie date, no Rail. Jeumont Schneider from (Adapted parts. –main bogie tional ie frame al stiffness ( stiffness al ing coefficients ( coefficients ing 9 el dy mass ( dy mass f the bogie (M bogie f the alue of the longitudinal stiffness of the bogie – wheelsets connection connection –wheelsets bogie of the stiffness longitudinal ofalue the set

10 ≥ –axle bo –axle

K r vi x 8 ce

≥

10 M x K 7 4 ) N/m) o z ) ) of the secondary suspension springs suspension secondary ) of the 10. Brakepi 9. Brakepa 8. Airbrake 7. Brakelever 6. Se ′ ) and of the wheelsets (m) wheelsets of the ) and CC xy cond ,, 3 ary suspension ary 11 d an pe dC 5 γ e z ) ) of the secondary suspension dampers suspension secondary ) of the 1 5 13. Whe 12. Contactbr 11. Sandandstonescatteringde , Le Creusot, France.) Creusot, , Le Behaviour of rolling stock on track on stock rolling of Behaviour 12 el ﬂ 13 ange lubricator γ e us

< 6 h

0.12) 2 vi ce

81 - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 this effort, many improvements have been made regarding the way in which bogies are are bogies way which the in regarding made improvements have many been effort, this of context the Within system. wheel–rail of the to improve performance the effort ous to acontinu led has of curves negotiation wear-free and asafe with paths on straight track). of the displacement lateral and of derailment risk lower speeds, rail, the and wheels (wear on the of curves negotiation poor expected an general in contact); and (flange forces of guidance appearance the slip and wheel alikely forces, creep in increase an ment ofment t bogies at the vehicle’s critical speed V speed vehicle’s at the critical bogies parameters (y, α parameters 82 lateral displacement ‘y’ and the yaw angle ‘ yaw the angle and ‘y’ displacement lateral the in increase An speeds. higher of achieving possibility the hence path, on astraight ing constructional characteristics relate to characteristics constructional case of curves with a small radius of curvature (R of radius curvature asmall with of curves case the in which forces development and of out wheels guidance of the wearing to fast leading quality at a speed V at aspeed quality of good path on astraight to move vehicle railway safety complete aconventional in allow

The inability of classical bogies to combine the stable motion of vehicles at high speeds speeds at high of motion vehicles stable the to combine bogies of classical inability The Table 3.1 shows the influence of the constructional and geometrical parameters of the of parameters and geometrical Tableconstructional the of 3.1 influence shows the An increase in the critical speed results in an increase in the stability of the vehicle mov vehicle of the stability the in increase an in results speed critical the in increase An • • • Reduction inequivalent Placement ofyaw dampers Increase inmassofthebogies Note: Source: character Constructional andgeometrical Table 3.1 Increase inlongitudinal stiffness Increase inthediameterof Increase ofthewheelbase2a Increase inlateralstiffnessof

conicity γ car body between thebogieand and thewheelsets(M′,m) linkage (K of thebogie–wheelset wheels 2r linkage (K the bogie–wheelsets Railway Transportation Systems Transportation Railway car bod car the and of bogie the of rotation the horizontal restrict which devices of fixing the And Wheel fla Wheel s Wheel

Movement alongstraightpath andincurves. he track. Comparative, Thèse deDoctoratl’, ENPC, Paris. Véhicule Ferroviaire en Alignement etencourbe–Nouvelles Technologies desBogies–Etude de Doctoratd’Etat, Université deParis, Paris; Pyrgidis, C. 1990, EtudedelaStabilité Transversale d’un Adapted from Joly,

istics ofbogies Influence of constructional and geometricalcharacteristics of bogies e o y x ) y (bogie yaw dampers) y (bogie ) lip nge contact with the outer rail the with contact nge ) which determine the positioning of the wheelsets in curves. in wheelsets of the positioning the determine ) which

350 R. 1983, Stabilité Transversale etConfort Vibratoire enDynamiqueFerroviaire, Thèse

km/h. Ho km/h. Movement alongastraight wever, for a radius of curvature R wever, for of aradius curvature path – change of path –change cr (movement along a straight path) as well as on as path) well as (movement astraight along Increase Reduction Increase Increase Increase Increase Increase α ’ of the bogie’s front wheelset is equivalent to equivalent is bogie’s’ of wheelset front the c

V 500

m) can provokem) can displace alateral Movement in curves – change –change Movement incurves Increase Unchanged Unchanged Increase Increase Increase Increase c of y, α

6,000

thes m e - - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 are als are This technology was first proposed by H. Scheffel in South Africa and it was afterwards afterwards and it was Africa South in Scheffel H. by proposed was first technology This way. aradial in curve to the inwardly wheelset the to position cases, most in tends, that (V paths on average straight of values speed time same at the securing while of radius curvature small in results satisfactory very to achieve stiffness lateral the increasing and stiffness angular the technology, by reducing this using it possible, is curves, in of bogies negotiation the ence and the wheelsets depends on the value of the longitudinal stiffness K stiffness longitudinal value of on the the depends wheelsets the and (100 of radius curvature of small curves in of bogies negotiation ideal almost an allows nology rigid. are connections generally,where bogie–wheelset bogies, conventional with not is possible positioning This path. curved the way within radial a in placed are bogie’s improved is wheelsets the when curves in of abogie behaviour The 3.2.1.3 intervals. at frequent reshaped to be needs treads the wheel of profile the performance, To original the designed. regain originally it was for which speed vehicle’s the in critical adecrease in results this conicity; equivalent initial increased and wear wheel to increased translates bogies by the run of kilometres number the in 2010). increase The Bousmalis, and (Pyrgidis bogies of the behaviour lateral of springs with independent lateral and angular stiffness values (the angular stiffness K stiffness (the values angular stiffness angular and lateral independent with of springs λ conicity conicity wheelsets, etc.). bogies, lighter materials, connecting elastic new (new techniques, manufactured and designed Figure 3.5 Figure K role the as same plays the K Scheffel and Tournay, and 1990).Scheffel Joly, 1980; 1988; Pyrgidis,

b < Moreover, this technology seems to provide the wheelsets with a guidance mechanism mechanism aguidance with to wheelsets provide the seems technology Moreover, this The self-steering (or auto-oriented wheelsets or radial wheelsets or steered bogies) tech bogies) or steered wheelsets or radial (or wheelsets auto-oriented self-steering The One parameter that restricts the performance of conventional bogies is the equivalent equivalent the is bogies of conventional performance the restricts that parameter One In the case of conventional bogies, the value of the lateral stiffness K stiffness lateral value of the the bogies, of conventional case the In 1974; ways (Scheffel, different in achieved is connection frame–wheelset bogie The (Figure 3.5), where K where 3.5), (Figure

1). c the On

m o connected to each other by means of elastic connections of defined stiffness K stiffness of defined connections of elastic by means other to each o connected

Bogies w

Bogie with self-steering wheelsets. = R e which characterises the wheel wear. This parameter significantly influences the influences significantly parameter wear. This wheel the characterises which

160–22 c

500 ontrary, the technology of self-steering wheelsets allows the manufacturing manufacturing the allows wheelsets of self-steering technology the ontrary, ith wheelsets self-steering

m). In this technology, the two classical wheelsets of a conventional bogie bogie of aconventional wheelsets classical two technology,the m). this In 0

km/h) ς is the lateral stiffness and K and stiffness lateral the is . a a x - influ not practically does stiffness lateral value of the the ). As dd e o K b K c e b o the angular stiffness. Behaviour of rolling stock on track on stock rolling of Behaviour y between the bogie bogie the between x (K x

λ K y where where ς and and

83 b -

Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 where appearance of longitudinal creep forces of equal value and opposite direction (X opposite direction value and of equal forces creep of longitudinal appearance the in results This profile. conical due to their radii rolling at rotate different axle of each wheels two the track, on the movement alateral of awheelset during bogies, conventional In 3.2.1.4 2006). Demiridis, and (Pyrgidis trains of tilting bogies the applied in also is 1974). technology (Scheffel, This of radius curvature small with curves of percentage asignificant comprising networks railway with countries in developed 84 Figure 3.6 Figure equation (2.32) equation movement mathematical the their during maintaining thus velocities, angular at different able to be to wheels rotate order two for in the axle the with wheels of the connection wheel. each

ties (freely).ties 1990). Pyrgidis, 1988; 1985, Frederich, 1984; et al., 1978; Frullini (Panagin, 3.6) (Figure wheels rotating independently with bogies of to develop technology the researchers led reasoning simple This forces. creep longitudinal

To avoid the sinusoidal movement of a wheelset, it is necessary to dispense of the rigid rigid of the to dispense To it necessary is movement avoid of awheelset, sinusoidal the Two techniques of implementation of this technology are distinguished are technology Two of this of implementation techniques veloci angular at rotate different which wheels, four has bogie each technology this Using of nullification slip and without rolling wheel guarantees equation mathematical This • •

r ω V: forward wheelset speed V: wheelset forward Railway Transportation Systems Transportation Railway ωω 1 Bogies w Bogies w Bogies 1 , r 11 , ω

⋅= 2

Bogies : rolling radii of the two wheels two of the radii : rolling rr Bogies with independently rotating wheels. (a) Bogies with wheelsets and (b) bogies without without (b) bogies and wheelsets with (a) Bogies wheels. rotating independently with Bogies rail-roue, rail-roue, wheel 2 : angular velocities of the two wheels two of the velocities : angular sets. (Adapted from Frederich, F. 1985, Possibilités inconnues et inutilisées du contact contact du inutilisées et inconnues F. Possibilités 1985, Frederich, from (Adapted sets. ithout wheelsets (Figure 3.6b) (Figure ithout wheelsets 3.6a) (Figure wheelsets ith 22 with rotating independently wheels ⋅= , Brussels, Novembre, 33–40.) Novembre, , Brussels, International Rail V 1

− X 2 ) on - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 wheels (Geuenich et al., 1985): al., et (Geuenich wheels two of the velocities angular of the difference to the proportional is value ofthe which not apply. (2.32) does equation mathematical the case, this in hence velocities; angular at different rotating wheels four bears bogie technology,each this In 3.2.1.5 2012). Panagiotopoulos, and Pyrgidis 2004; (Pyrgidis, gravitational forces increases. value of stabilising the time, same at the movement mitigated), while is wheelset sinusoidal (since paths problems on straight not cause does choice This used. be conicity equivalent position. aradial in track on the placed be independently, rotate cannot which wheels, with wheelsets 2012). curves, in Converselyand Panagiotopoulos, (Pyrgidis profile wheel conical variable due to the wheelset of the displacement lateral at each activated is which track, force on the apply only gravitational it the can since displacement to lateral vulnerable very is However, wheelset paths. the on straight speeds critical development high of very Figure 3.7 Figure where C connection. bogie–wheelset the simplifying significantly thus dampers, of bogie–yaw use the without paths on straight speeds high for very allows It Germany. and States United but much smaller. φ A magnetic coupling of the two wheels (Figure 3.7) generates a damping torsional torque, torsional adamping 3.7) generates (Figure wheels two of the coupling A magnetic tramways in implemented extensively is wheels rotating of independently technology The value of should ahigh curves in wheelsets of the to improve possible positioning is It the for the allows theoretically technology this implementation, technical of the Irrespective The torqueThe C The performance of this technology can be optimised by varying the damping coefficient coefficient damping the by varying optimised be can technology of this performance The the in developed was mainly technology creeping controlled with wheelset bogie The as a function of the vehicle forward speed V. speed forward vehicle of the afunction as C C CC φ ρ ρϕ : damping torsional torque torsional : damping : damping coefficient : damping

=− Bogies w Bogies Creep- April, 279–281.) International Gazette Railway wheelsets, controlled creep has bogies composite Fibre 1985, R. Leo, and W., C. Cunther, Geuenich, Paris; ENPC, l’ de Doctorat de Thèse Comparative, Etude – Bogies des Technologies –Nouvelles courbe en et Alignement en Ferroviaire d’un Véhicule () ωω controlled wheelset. (Adapted from Pyrgidis, C. 1990, Etude de la Stabilité Transversale Transversale Stabilité la de Etude 1990, C. Pyrgidis, from (Adapted wheelset. controlled 12 ρ is of the same nature as the one that causes the pair of lateral creep forces, forces, creep of lateral pair the causes one that the as nature same of is the ith creep-controlled wheelsets creep-controlled ith 2d 2e o Behaviour of rolling stock on track on stock rolling of Behaviour

85 , Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4

2004). (Pyrgidis, vehicles tramway applied in is technology This curves. in wheels dently rotating indepen with bogies to behave like and track, of the sections on straight bogies ventional con to behave like them allows that mechanism aspecial with equipped are bogies These 3.2.1.6 cost. implementation duewas abandoned increased to its 86 considered: may be cases positioning bogie–wheelsets and rolling wheel following the curves In 3.2.2

In spite of its positive impact on vehicle behaviour, the development of this technology technology development the of behaviour, this on vehicle spite impact of positive its In

2. 1. Railway Transportation Systems Transportation Railway

F σ and emission). low-level and noise fatigue material (minimal considerably is minimised track on the and stock rolling on the impact negative where the conditions service real under met may be and ideal considered is case This forces. creep the are wheels applied on the Rollin Rollin X where y stock or the track. or the stock rolling on the either noticed is no wear of forces, absence due to the since perfect be to considered is and theoretical purely is case This rolling). (pure forces ofment creep XT yF

i ij : flange way clearance : flange : lateral displacements of the two wheelsets of a bogie (i of abogie wheelsets two of the displacements : lateral

XT ii ij behav inscription bogies and conditions rolling Wheel jij ij : guidance forces exerted from the four wheels of a 2-axle bogie to the rails (i rails to the bogie of a 2-axle wheels four the from exerted forces : guidance , T In this ca this In In this ca this In Bogies w Bogies <= jij ij 2 == +< ij set, respectively) set, bogie (i bogie fro wheel, respectively, in the direction of movement) direction the respectively, in wheel, in the direction of movement) direction the in σ g of all bogie wheels without flange contact and without slip. The only forces forces The only without slip.and contact flange without wheels bogie g of all : longitudinal and transversal creep forces exerted on the four wheels of a 2-axle of a2-axle wheels four on the exerted forces creep transversal and : longitudinal g of all bogie wheels without flange contact, without slip and withoutdevelop and without slip contact, flange without wheels bogie g of all nt and rear wheelset, respectively and j and respectively wheelset, rear nt and 2 iour in curves () j 0 se, the following mathematical expression applies: expression mathematical following the se, se, the following mathematical expression applies: expression mathematical following the se, ith wheels with mixed behaviour mixed with wheels ith

µ = Q 0

1,2 fron 1,2 o

t and rear wheelset, respectively and j and respectively wheelset, rear t and

1, 2 left and r and 1, 2left

1,2 fron 1,2 ight wheel, respectively, wheel, ight

1,2 left an left 1,2 t and rear wheel rear t and d right d right

= (3.8)

1, 2 1, - - - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4

Figure 3.8 Figure

3. 4.

provided that the value of the exerted guidance force F guidance exerted value of the the provided that however, not is desirable; acceptable it considered is of inscription case This materials. of contact fatigue and noise rolling outer rail, of the mainly and wheel contact of the provided that derailment and track lateral shift are within the set limits. set the within are shift lateral track and derailment provided that acceptable may be case However, this increased. is adverse impact the aresult as and the rail with flange) (via the contact in come wheels four of the two 3as case than may or may not 3.8). slip) (Figure wheelset rear (the wheelset bogie the rear of contact accordingly, no and, flange) wheel fea Rolling flanges) (b flanges) outer wheel (via their outer rail the with contact in wheelsets bogie of both Rolling and ously, it is lower than the limits set by derailment and track lateral shift criteria. shift lateral track and by derailment set ously, limits the it lower is than μ where Q || F yF yF yF 11 11 : wheel–r 22 ii o This case is fr is case This In this case, t case, this In In this case, t case, this In

: wheel load. wheel : =+ =+ Third special rolling condition. Left-wheel flange of front wheelset–outer rail contact – rolling of rolling – contact rail wheelset–outer front of flange Left-wheel condition. rolling special Third rear wheel rear <= ≠= σ 00 σ σ ,, F () 12 12 22 21 oth wheelsets may or may not slip) wheelsets ( oth ail friction coefficient friction ail turing contact of the front bogie wheelset with the outer rail (via their outer (via their outer rail the with wheelset bogie front of the contact turing j 11 set without wheel flange–rail contact. flange–rail wheel without set 12 F ≠= ≠= 0 he following mathematical expressions pertain: expressions mathematical he following he following mathematical expressions pertain: expressions mathematical he following ,, equently encountered in small radii curves. It results in wearing out wearing in results It curves. radii small in encountered equently F F 00 Fy 00 , , Rear wh 2 2 ee 12 lset +≠± =+ σσ Whee , y lset center Fr ont whe Figure 3.9 Figure Behaviour of rolling stock on track on stock rolling of Behaviour G F y el y 11 1 1 1 set =±σ ≠0 11 ). This case is more adverse is case ). This is not very high and, obvi and, high not is very V Tr ack center (+)

87 - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4

88 Figure 3.10Figure 3.9 Figure

In this case, the following mathematical expressions pertain: expressions mathematical following the case, this In 5. Railway Transportation Systems Transportation Railway yF yF

(Figu flange) outer wheel (via the contact rail wheelset–outer bogie front with Rolling suspension is particularly rigid and the radius of curvature is small. is of radius curvature the and rigid particularly is suspension primary the when observed is case This hindered. is displacement its and track on the ‘locked’ is bogie the stock, rolling and track on the adverse impact the from apart as, 11 22 =+ =−

Fourth special rolling condition. Left-wheel flange of front and rear wheelset–outer rail contact. rail wheelset–outer rear and front of flange Left-wheel condition. rolling special Fourth Fifth sp Fifth contact. Right-wheel flange of rear wheelset–inner rail contact. rail wheelset–inner rear of flange Right-wheel contact. re 3.10). This case, known as ‘crabbing’, is the most averse and should be avoided ‘crabbing’, as should be averse and most known re 3.10). the is case, This σ σ ecial rolling condition. ‘Crabbing rolling’: left-wheel flange of front wheelset–outer rail rail wheelset–outer front of flange left-wheel rolling’: ‘Crabbing condition. rolling ecial 11 12 ≠= =≠ Rear whe 00 00 , , y 2 y F =–σ 2 21 =+σ F F ≠0 Rear wh 2 2 el y G G 2 set 2 2 ee y F 2 lset 22 ≠0 Whee Whee lset lset center center Fr Fr ont whe ont whe y 1 G F G y y el el y 11 1 1 1 1 F 1 set set =+σ =+σ ≠0 11 ≠0 V V Tr Tr ack center ack center Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 behaviour): mixed with bogies and wheelsets creep-controlled with bogies wheels, rotating dently - indepen with bogies wheelsets, self-steering with bogies (conventional bogies, of bogies technologies different for five features following the to study it possible is models these Joly, and 1993). Pyrgidis With 2004; 1990, Pyrgidis, 1996; 1990, Joly Pyrgidis, and market. the in found be cannot and use, own for groups their or research researchers by individual oped devel have been that models some are there calculator) contact (wheel to use rail free are forces). the calculate (some only models line on the wheelsets of the positioning geometric the and area surface contact the applied forces/stresses, the calculate they curves in and speeds) calculate only (some accelerations models and speeds calculate models these segments straight In wheels. the of conditions and rolling defects track geometric the profile, wheel real the account into take models these All MEDYNA. and GENSYS NUCARS, Vampire Adams/Rail, Pro, stock. rolling and infrastructure of track maintenance lower for the cost and a cost a and lowerto construction achieve vehicle levels, all at safety to improve traffic helping evolving constantly are models approach. These mathematical their as well as ment develop for made their hypotheses the and assumptions on the depends to what extent and approach models reality these Whether institutes. research in also and academia, in and try forces). of guidance absence of slipping, (avoidance track of the sections curved in wheelsets of the inscription and conditions rolling acceptable ensures which alignment, horizontal the in of radius curvature minimum the characteristics, construction for bogie given and for speed agiven to determine, and vehicle of the behaviour ‘geometric’ on the bogies of the characteristics construction of the ence influ the to study it possible is models of aid these the With curves. in and paths on straight of vehicle arailway behaviour lateral the simulating models development of mathematical wheelset. railway of asingle that more complex than 3.1.1, Section movement in the mentioned of awhole body (car As vehicle 3.2.3 alignment. track the or outer rail). (inner face rail inner the with wheel Remark A group of such models are described in the literature references (Joly, references 1983, 1988; literature the in described are ofA group models such that models other some and market the available in are above that the models from Apart UMLAB, SIMPACK, are: market the from acquired be can that models simulation The indus the in both used are models These market. the available in models many are There the allows sector, applied engineering of the adivision engineering, railway Dynamic of curvatures horizontal movement the along during observed 5are 4and 3, Conditions • •

slipping). of of appearance verification forces, contact wheel–rail of the (calculation conditions rolling wheel the and of wheelsets) yaw and (displacements angles behaviour vehicle ‘geometric’ on the bogies of the features main of the effect the and behaviour vehicle In the cas the In cas the In construction features of the bogies on the ‘critical’ vehicle speed. vehicle ‘critical’ on the bogies of the features construction

Lateral behaviour of a whole vehicle awhole of behaviour Lateral : The wheel slip of a wheelset is always accompanied by contact of the flange of one flange of the by contact always is accompanied slip of wheel a wheelset : The e of tangent track, the lateral vehicle stability and the influence of the main main the of influence the and stability vehicle lateral the track, e of tangent e of curved segments of the horizontal alignment, the semi-static lateral lateral semi-static the alignment, horizontal of the segments e of curved Behaviour of rolling stock on track on stock rolling of Behaviour

bogies ) is much ) is

89 - - - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 shows the variation in the vehicle critical speed V speed 3.11 critical vehicle the Figure in variation shows the longitudinal bogie–wheelsets stiffness K stiffness bogie–wheelsets longitudinal and in curves. in and of curves. negotiation facilitates which it relatively is small hand, other nal stiffness (K type. dampers. 2vertical and damper 1longitudinal damper, 1lateral springs, dampers. 2vertical and damper 1longitudinal damper, 1 lateral 4wheelsets. and 2 bogies body, 1car undeformable: and rigid considered are that bodies solid seven following of the (Joly,contact) circle to circle 1983). profile (i.e. by acircle simulated both are rail of the surface contact the as well as wheel the contact of the geometry the study To defects. tack geometric without and gradient longitudinal the without track a railway 90 ness. On the o the On ness. V speed reac speed Figure 3.11 Figure in . illustrated vehicle of the characteristics constructional for the paths on straight of vehicles stability the regards as margin’ ‘safety greatest the being as seen is ues 3.2.3.1 cr

shows the performances of vehicles with conventional bogies on straight paths paths on straight bogies conventional with of vehicles Table performances shows the 3.2 Additionally, the following key assumptions/assumptions are made: are key assumptions/assumptions following Additionally, the ‘Corail’ of the vehicles French passenger the fact in illustrates system mechanical This 2 bogie: per were considered following the suspension level secondary of the the At 4springs, bogie: per were considered following the suspension level primary of the the At consists system mechanical the bogies conventional with of equipped avehicle case the In on movement its Vand occurs speed moves vehicle at aconstant the models For these There is azon is There For K values The value of K The • • • curves In • At straight segments straight At •

Railway Transportation Systems Transportation Railway

450 For the calcul For the lo vertical The of th study The ignored. is links, elastic vehicle’s of the stiffness the than bigger is which stiffness, lateral their time same the level. At contact wheel–rail on the exerted are that forces creep the and wheels the of conicity equivalent of the action combined by the movement ensured the is during n are rails The coefficients C coefficients The creep for creep The adopted (Vermeulen and Johnson, 1964). Johnson, and adopted (Vermeulen

Vehicles with c

km/h. The absence of bogie–yaw dampers reduces the critical speed by about 20%.speed critical the reduces dampers of bogie–yaw absence The km/h. hes its highest values (V values highest its hes : ne hand, this specific value is within the 7 within is value specific this ne hand, x o

> = e of of values K x

3.5 3

ces are expressed on the basis of the linear theory of Kalker and the creep creep the and of Kalker theory linear of the basis on the expressed are ces = ij ation of the creep forces the nonlinear theory of Johnson–Vermeulen was of Johnson–Vermeulen theory nonlinear the forces creep ation of the

ot taken into consideration, and as a result the guidance of the wheelsets wheelsets of the guidance the aresult as and consideration, into ot taken are considered to be reduced by 33%. reduced to be considered are ads are distributed equally on both wheels of the axles. of the wheels on both equally distributed are ads

× 8 e lateral vehicle behaviour refers to the circular segment of the curve. of the segment circular to the refers behaviour vehicle e lateral

× ×

10 10 onventional bogies 6

N/m and K and N/m 7 6

N/m approximately, the critical speed remains roughly equal to equal roughly remains speed approximately,N/m critical the N/m is considered as the optimum value for longitudinal stiff value for longitudinal optimum the as considered is N/m x cr between 7 between

= o

465–495 =

0). x for both values of bogie–yaw dampers longitudi dampers of values bogie–yaw for both

× km/h) (Pyrg km/h)

10 6 and 1.5 and

10 idis, 1990). This area of K area 1990). This idis,

× cr 6 –1.5

is given as a function of the of the afunction as given is 10 7

N/m, where the critical critical where the N/m, ×

10 7 limits and, on the on the and, limits x val - - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 γ at speeds V at speeds quality ride of good path on astraight to run vehicle railway allow, theory, aclassical in Figure 3.11Figure e

= K dutbecaatrsisStr Adjustable characteristics K K Table 3.2 Indicatively, that it noted is Source: γ γ γ K K • • • e e e

y x o o o

0.10 K and

= = =

= = = = =

K yaw dampers) fixin The The high v high The The smal The

0.05 0.20 0.10

10 8 3 3 3 x

× × × ×

≥ N/m

en courbe–Nouvelles Technologies desBogies–EtudeComparative, Thèse deDoctorat del’ENPC, Paris. Adapted from Pyrgidis, C. 1990, 10 Technologies des Bogies – Etude Comparative, Thèse de Doctorat de l’, ENPC, Paris.) l’, de ENPC, Doctorat de Thèse Comparative, –Etude Bogies des Technologies –Nouvelles courbe en et Alignement en Ferroviaire d’un Véhicule Transversale Stabilité la de Conven 10 10 10

7 Performances of vehicles with conventional bogies – running on straight path and in curves in and path straight on –running bogies conventional with vehicles of Performances

6 6 6 6

> N/m

× N/m N/m N/m

Vcr (km/h)

600 600 100 200 300 400 500 10 g of devices that limit the horizontal rotation of bogies and car body (bogie– body car and of rotation bogies horizontal the limit that g of devices l value of the wheel equivalent conicity ( conicity equivalent wheel l value of the x

0 = tional bogies – variation of V of –variation bogies tional 6

8 6 alue of the bogie–wheelset longitudinal stiffness (3.5 stiffness longitudinal bogie–wheelset ofalue the N/m) km/h. Ho km/h. Kx = 10

10 6

6 N/m), we observe (Pyrgidis, 1990) (Pyrgidis, N/m), we observe K = 2.5×10 658 320 482 2r x aight path(V 2a wever, with such properties, in case of radii R of radii case in properties, wever, such with o

= km/h km/h km/h

0.90 3.0 EtudedelaStabilité Transversale d’un Véhicule Ferroviaire en Alignement et K = 5.0×106 x m

m cr ) Curves (occurrence of slip) Curves (R Curves (occurrence ofslip) Curves )

cr 6 as a function of K of afunction as Kx = 7.5×10 K x (N/m) R R R V 2e (contact) c c c Q

7 cr = = =

o K = 10 o x =f(K

= 4,800 6,300 4,300 =

1.50 7.03 t 7.03 x γ

) Behaviour of rolling stock on track on stock rolling of Behaviour m m m

e 7 m

x K = 2.5×10 ≤

. (Adapted from Pyrgidis, C. 1990, Etude Etude 1990, C. Pyrgidis, from . (Adapted x

0.10) Legend

7 Kx = 5.0×10 K 2a =3.0m K K Q γ e o y o =0.10 o =10 =0N/m =3×10 =7.03t 7

7 N/m F F F K = 7.5×10 σ 11 11 11 x γ 6 c

= N/m = = = =

±10 20.7 35.1 0 (slip) 0

500

< 0.02

4,800

× 8

mm K = 10 m) (K m) kN kN x

10 g 7

o N/m m (for m

0) 91

≥

Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 3.2.3.2 forces. development the of guidance in and wear wheel increased an in resulting

where springs of stiffness K of stiffness springs nected to the bogie using springs of stiffness K of stiffness springs using bogie to the nected con are of abogie wheelsets where both 3.5 Figure in system mechanical the we consider If 92 and in curves. Compared with conventional bogies, a smaller value of the total longitudinal longitudinal total value of the asmaller bogies, conventional with Compared curves. in and for K and 1990):

From th For d shows the performance of bogies with self-steering wheelsets on straight paths paths on straight wheelsets self-steering with of bogies Table performance shows the 3.3 • • • • •

K 2a: bogie wheelbase bogie 2a: K Railway Transportation Systems Transportation Railway KK K KK KK KK KK as much on K as The total la total The Contact of th Contact slip Wheel Stiffnesses The angular s angular The K bt st bt st bt s st bt s st : overall lateral stiffness of the mechanical system mechanical of the stiffness lateral : overall : overall longitudinal stiffness of the mechanical system mechanical of the stiffness longitudinal : overall x

of a conventional bogie of aconventional = = =+ =+ Vehicles with b = =+ =+

s 1.0

e above relations, the following may be concluded: may be following the e above relations, = KK

K bx bx xy x

m and 2a and m

b + KK

= K dK KK xy Kd K 22

teral stiffness of the primary suspension of a conventional bogie depends depends bogie of a conventional suspension primary of the stiffness teral 0 relations (3.11)0 relations (3.12) and become 2 xy s dK and K and e wheel flange with the outer rail with flange e wheel tiffness K tiffness ⋅+ x

+ 5. ⋅ KK 2 as on K as b (angular) K ⋅⋅ xy 22 x 2

xy ogies with wheelsets self-steering

5. b 3.0 aK increase the total stiffness (lateral and longitudinal) of the system of the longitudinal) and (lateral stiffness total the increase 2 K y b ⋅

m relations ( m relations plays the same role (for same plays the d

αι K s (lateral), then the following relations apply (Pyrgidis, apply relations (Pyrgidis, following (lateral), the then 3.9) (3.10) and become x and K and

y = and connected to each other using using other to each connected and

1.0

m) as the longi m) the as tudinal stiffness stiffness tudinal (3.12) (3.10) (3.13) (3.14) (3.11) (3.9) - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 paths and in curves (Pyrgidis, 1990; Pyrgidis and Joly, 1993; Joly and Pyrgidis, 1996). Joly, and 1993; Joly Pyrgidis, Pyrgidis and 1990; (Pyrgidis, curves in and paths on straight wheels rotating independently with of bogies Table performances the 3.4 presents (K stiffness (K 3.2.3.3 paths. straight on value of speed a fair with curves radius small very and of small negotiation good very bine Indicatively, that it noted is Indica st • • •

radii, while the forces exerted in very small radius curves are much smaller. are curves radius small very in exerted forces the while radii, curvature comparatively much smaller in observed slip is awheel bogies, conventional For whee track. on the wheelset the to centre tends force that gravitational value of the the it as increases paths on straight motion the and va A great displacements. to lateral sensitive forces). very creep is However, wheelset the (absence of longitudinal of wheelsets ing hunt the eliminating while paths on straight speeds critical development high of very tec This 1.3

tively, it is noted that bogies with self-steering wheelsets make it to com possible make wheelsets self-steering with tively, bogies that it noted is Vehicle K V Source: K Table 3.4 Vulnerability inlateral (V Straight path K K Table 3.3 Source: γ K γ K K characteristics Adjustable

× displacements e e y x cr s x b o o

= = =

= = = ) bt 10 = = ≈

0.20 0.10 10

10 K 10 = 0 3 ∞ hnology allows theoretically, without the fixing of bogie–yaw dampers, the dampers, bogie–yaw of fixing the without theoretically, allows hnology 6 y

lbase and wheel diameter values, which are the same as those of high-speed of high-speed those as same the are which values, diameter wheel and lbase N/m × 6

8 6 2 = 6 N/m N/m

lue of equivalent conicity facilitates both the negotiation of bogies in curves curves in of bogies negotiation the both facilitates lue of conicity equivalent

Thèse deDoctorat del’ENPC, Paris. en Alignement etencourbe–Nouvelles Technologies desBogies–EtudeComparative, Adapted from Pyrgidis, C. 1990,

N/m Thèse deDoctoratl’, ENPC, Paris. en Alignement etencourbe–Nouvelles Technologies desBogies–EtudeComparative, Adapted from Pyrgidis, C. 1990,

N/m s with rotating independently wheels

N/m

10 × Performances of vehicles with bogies with independently rotating wheels – wheels – rotating independently with bogies with vehicles of Performances motio Performances of vehicles with bogies with self-steering wheelset – running –running wheelset self-steering with bogies with vehicles of Performances on stra on

6 10 6

N/m

N/m < 6

2.62 n on straight path and in curves in and path straight n on N/m ight path and in curves in and path ight 323.5 2r

198 2a × path (V < Straight o

= 8 Curves (occurrence Curves =

km/h

0.90 × 3.0 km/h 6 2e

N/m) are observed. N/m) are 10 cr 1,400 o

)

of slip) Curves (R Curves of slip) K m

= m 6 o

1.50 = N/m) and a smaller value of the total lateral stiffness stiffness lateral total value of the asmaller N/m) and

0 (occurrence ofslip) m EtudedelaStabilité Transversale d’un Véhicule Ferroviaire EtudedelaStabilité Transversale d’un Véhicule Ferroviaire

R m R 2e c Q

c =

o Curves o =

= = 1,200

250

1.50 7.03

σ F m t Q 11

= o

= ±10

1.7 c 7.03 Behaviour of rolling stock on track on stock rolling of Behaviour

= F (R

11 mm 500 kN c (K

= F t Curves = 11

15.4 m)

500

= =

0) 0 σ

γ kN m)

nc = Curves (R Curves

= ±10

F 0.02 11 γ nc F F γ

= e 11 11

= =

15.7 g

(K = = Curves Curves

c = 0.02 0.20

14.8 59.6 o 200

100 =

kN kN m)

93 - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 wheel flange and the inner side of the rail). side of inner the and flange wheel the between contact without occurs rolling when bogie of the wheels level four at of the the 94 Track design speed: V Track speed: design by characterised are These 3.2.4.1 Joly, and 1993). Pyrgidis 2004; 1990, Pyrgidis, 1996; 1990, 1983, 1988; Joly Pyrgidis, and (Joly, by developed Joly Pyrgidis models and mathematical of application the the from obtained are Data network. of the characteristics operational the considering suggested are bogies vehicle for characteristics technical section, this In operate. will trains the which in network of the characteristics operational to related the directly is characteristics design of bogie selection The 3.2.4 (where attempted P is curves in and paths on straight nation TablIn 3.2.3.4 Alig γ K γ γ K K K K K Source: K Conventional bogies bogies Technology/char Table 3.5 2a 2a 2a K Bogies with K Bogies withself e e e wheels independently rotating wheelsets o x o s b x o y x

= = =

======

0.30 0.20 0.10

nment nment layout: Railway Transportation Systems Transportation Railway 10 3.0 3.0 3.0 10 K 10 K 8 0 3 3

y y

× × ×

6 7 6 - exami under technologies bogie three of the performances of the acomparison e 3.5, = =

on oper on based characteristics design bogie of Selection

courbe –Nouvelles Technologies desBogies–EtudeComparative, Thèse deDoctoratl’, ENPC, Paris. Adapted from Pyrgidis, C. 1990, m 2r m 2r m m 2r m N/m N/m 10 N/m 10 10

High-s Comparative assessment 10 10 Performances of examined bogie’s technologies in motion on a straight path and in curves in and path astraight on motion in technologies bogie’s examined of Performances 6 6 6

8 6 N/m N/m N/m

o o o N/m N/m

= = = acteristics of acteristics

0.90 0.90 0.90 - peed networks peed steering ational aspects of networks of aspects ational

m m m Small per Small very large curve radii (for radii V curve large very d

≥

200 Vulnerability in V 226 482 displacements lateral cr centage of curved sections out of total track length. Large and and Large length. track out of total sections of curved centage

Straight path

km/h =

km/h km/h

EtudedelaStabilité Transversale d’un Véhicule Ferroviaire en Alignement eten ∞ R Occurrence ofslip R R c c c

= = =

d 250 4,800 1,400

200

m m

km/h and R and km/h P P F F F 11 11 11 4w 4w 4w

= = = = = is the power that is consumed consumed is power that the is R

c 0 20.7 0 K 1.11 4.3

= Curves o

500

kW =

cmin

kN kW 0

2,000 F F F P 11 11 11 4w

= = =

= R m)

c 14.9 65.9 0 K 12.2

= o

200 =

kN kN kW 0

m Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 Track design speed: 140Track speed: design by characterised are They 3.2.4.2 Bogi Bogie wheelbase: High (e.g., 2a High wheelbase: Bogie Whee Track design speed: V Track speed: design by Characterised Stif Track design speed: V Track speed: design by characterised are These 3.2.4. Bogies: Bogies: Equivalent conicity: Medium (e.g., γ Medium conicity: Equivalent Equivalent conicity: Small (e.g., γ Small conicity: Equivalent Conventional Bogies: Alig Al Tota Total la 3.2.4.3 used. may be trains state) good tilting very in is superstructure track the (assuming track existing on an to improve performance the it desired is : If Remark alignment. geometry track the and speed design track on the depends istics Alig Conv The fo The The following are proposed for the rolling stock: rolling for the proposed are following The ignment ignment layout: fness of the primary suspension: High (e.g., K High suspension: primary of the fness nment nment layout: nment layout: Mainly medium curve radii (R radii curve medium layout:nment Mainly e and wheelset masses: Small masses: wheelset e and l longitudinal stiffness of primary suspension: Small (e.g., K Small suspension: of primary stiffness l longitudinal l diameter: Big (e.g., Big 2r l diameter: 4

entional bogies are proposed. The selection of values of the bogie design character design bogie of of values the selection The proposed. are bogies entional teral stiffness of primary suspension: Small (e.g., K Small suspension: of primary stiffness teral With sel With Metro ne Metro Conven Mountai llowing proposals are made for the rolling stock: rolling for made the are proposals llowing f-steering wheelsets (or wheelsets f-steering tional speed networks speed tional nous networks nous tworks Mainly small curve radii (R radii curve small Mainly Very larg (R radii alignment horizontal small and medium per Large d d

< =

km/h 90–100 140 e percentage of curved sections out of the total track length. length. track out total of the sections of curved e percentage centage of curved sections out of the total track length mainly mainly length track out total of the sections of curved centage o

km/h

= ≤

0.90 = V

km/h 3.0

d =

e 0.05–0.10)

m) 200 = m)

0.20) conven

km/h c tional wheelsets) tional

x c 150–300

= =

500–1,500 8

× Behaviour of rolling stock on track on stock rolling of Behaviour

10 st

6 m) N/m and K and N/m

1.3

m) bt

× =

2 =

× 6 250–750

N/m)

10 =

10 6

N/m) 7 N/m)

95 - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 Lateral stiffness in primary suspension: Small (e.g., K Small suspension: primary in stiffness Lateral effect No suspension: primary in stiffness Longitudinal (e.g., K Small suspension: of primary Stiffness Bogie and w and Bogie w and Bogie 3.3 2012). Panagiotopoulos, and Pyrgidis 2004; (Pyrgidis, curves) in Bogie whe Bogie Track design speed: V Track speed: design by characterised are These 3.2.4.5 Equivalent conicity: High (e.g., γ High conicity: Equivalent Conventional Bogies: 96 Figures 3.12 3.13 and (Figures ). surface rolling head rail the with wheel one vehicle of at least contact of loss definite the to describe used is ‘derailment’ term The 3.3.1 ment ofment ( switches) adjust (incorrect layout) track and or external quality poor stock, of rolling design and tion Alignme Wheel dia Wheel Bogie wheelbase: Small (e.g., 2a Small wheelbase: Bogie Very high conicity: Equivalent wheels rotating independently With Bogies: values (‘smart profile’) profile’) of γ (‘smart values Wheel dia Wheel ogy, a wheel profile with varying conicity is needed to secure small values for γ values small secure to is needed conicity with varying ogy, profile awheel technol of operation this tramway). series correct For the Sirio of the (bogies used be can

Apart from th from Apart The following options are proposed for the rolling stock: rolling for the proposed are options following The T of aresult as of may occur vehicle arailway derailment The The follow The • • •

- condi poor speed, excessive forces, exerted (high internal be can of derailment he causes

Railway Transportation Systems Transportation Railway DERAILMEN Wheelclimb Overturnin disp Lateral

Definition

nt layout: Tramway net meter: Small (e.g., 2r Small meter: meter: Small (e.g., 2r Small meter: elbase: Small (e.g., 2a Small elbase: heelset masses: Small masses: heelset Small masses: heel ing options are proposed for the rolling stock: rolling for the proposed are options ing e technology of bogies with independently rotating wheels, a mixed system system amixed wheels, rotating independently with of bogies e technology g/tilting of the vehicle of the g/tilting lacement (shift) of the track of (shift) the lacement Curve radii mainly in the range of R range the in mainly radii Curve Very large perc Very large Figure 3.14Figure T OF RAILWAYT OF VEHICLES d

works =

80–90 e (for the lateral displacements – that is to say during the motion motion the to say is during –that (for displacements lateral the ). o o

km/h = = = = e

= 2.00–2.40 1.80 0.65 0.70–0.75 entage of curved sections out of the total track length. length. track out total of the sections of curved entage

0.30)

m) m)

m) m) x

4.10 y 6

N/m and K and N/m = c

= 10

25–50 5 –10 6

N/m) m y

10 6 N/m) e and high high and - - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 Figure 3.14Figure 3.13Figure 3.12Figure • F • Cr loads wheel • Dynamic force • Guidance forc Applied riction forc ee es p forces s es

Derail Derailm Causes o Causes Ge angle friction • Wheel–rail yaw angle • Whee ment of railway vehicles. (Photo: A. Klonos.) A. (Photo: vehicles. railway of ment ometric dat Dir ent. (Photo: A. Klonos.) (Photo: A. ent. f derailment. ect lset - a g timefor • A forc uidanc pplication Time es e superstr • Po • G alig • Track ge d • Track ge b • L • Staticwh co • Whee sp • Passage st rolling construction ef ogies andcar ateral force Internal cause oc eo eﬃcien or conditiono ects nment dat k dat metric and Indir l–rail frictio ucture ometri omet a ee t ec eed l load t s fro ry a -b c s od f m n y Po area Pa Behaviour of rolling stock on track on stock rolling of Behaviour Pa and crossing Derailment or conditionof ssing through ssage sp swit s ofswitches ch es eed s adjustment of switches Incorre ct Ex ter nal causes Cross winds phenomena Ea Natural rt Flood hquake

97 Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 derailment. vehicle toward the outer toward rail. vehicle the where (rails panel track the case, this In 3.3.2 98 Figure 3.15Figure conditions. certain under may overturn vehicle the alignment, zontal hori of the sections of on curved vehicle arailway movement immobilisation or the During 3.3.3 of significant lateral forces, resulting in the derailment of one or more of the train’s of onethe or more of vehicles. derailment the in resulting forces, lateral of significant

This type of derailment is solely due to internal causes and is the most common type of type common most the is and causes solely is due to internal of derailment type This In the second case (Figure 3.15b) the following reasons may pertain, respectively, 3.15b) may pertain, reasons (Figure following case the second the In the to tend overturn development which the of moments, in result above the reasons All In the first case (Figure 3.15a), the following reasons may pertain (Esveld, 2001): (Esveld, 3.15a),maypertain (Figure case reasons the following first the In curve. of the inside outside toward or the the may occur Overturning Derailment through displacement of the track occurs when occurs track of the displacement through Derailment • • • • • • •

Σ H Railway Transportation Systems Transportation Railway ΣΥ Displa a Small ture, Unequa Immobi Crossw Crosswind force H force Crosswind Signifi (Q Y

R : total lateral force, which is transferred from the vehicle to the rail to the vehicle the from transferred is which force, lateral : total : lateral track resistance track : lateral Derailment through displacement of track of displacement through Derailment Derailment as a result of vehicle overturning vehicle of aresult as Derailment 1 >

> (b) Toward the inside of the curve. the of (b) Toward inside the and curve the of (a) West Germany.): Toward outside the MRT-Productions, edition, 2nd Vehicl

H which tr which Q cant deficiency in relation to the passage speed V speed passage the in relation to deficiency cant cement of wheels loadcement inside toward the R xle load xle ind force H force ind 2 l load distribution on two wheels with lower loading on the inside wheel wheel inside on lower the loading with wheels on two l load distribution lisation of vehicles (V of vehicles lisation )

e overturning mechanism in curves (Adapted from Esveld, C. 2001, Modern 2001, Railway C. Track Esveld, from (Adapted curves in mechanism e overturning U anslates to an increased value of the lateral residual centrifugal force F centrifugal residual value lateral of the increased to an anslates (a) w w directed toward the inside of the curve of the inside toward the directed curve outside toward of the the directed Q δ 1 p F w Q

+ 2

p sleeper

0) on a curved track section with a high cant U cant ahigh with section track 0) on acurved H s) of a track segment is displaced due to the effect effect due to the displaced is s) segment of atrack w (b U ) H w Q 1 δ p Q p 2 and the radius of radius curva the and B ty (3.15) nc - - , Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 via the wheel flange on the rail) are applied on the point of contact I contact point of the are on applied the rail) on flange wheel the via rail may be analysed in two components: two in analysed may be rail 3.3.4.1 3.3.4 derailment. in ultimately develop resulting rail Figure 3.16Figure where t Assuming

(3.17) criterion: expression Nadal the mathematical illustrate the with 3.17 do Figure not. others combination in while aderailment under is that wheelset of the yaw the angle account into take criteria of these Some 1977). (Alias, etc. criterion, Chartet the criterion, Nadal the as such used being are criteria various derailment against For testing 3.3.4.2 over rail. the to climb wheel for the long is enough time application their upwards and directed are force axis) (derailment yy axis applied on the forces oftion all close to a derailment (wheel 1) and the vertical load Q (wheel 1) vertical to aderailment close the and In the case where wheel 1 slips, the force T the 1slips, where wheel case the In Under these circumstances moments which tend to overturn the vehicle toward the inner inner toward vehicle the the to tend overturn which moments circumstances these Under In practice, derailment through wheel climb occurs when the projection of the combina of the projection the when occurs climb wheel through derailment practice, In • •

α C YQ TC The lateral cr lateral The A force N upwards, having a value equal to avalue equal having upwards, at 12 22 11

: angle of attack (wheelset yaw angle when flange contact occurs) ( occurs) contact flange when yaw (wheelset angle of attack : angle

Derailment with wheel climb wheel with Derailment

: lateral creep coefficient creep : lateral == < Description of the phenomenon the of Description Derailment cr

Derailmen (Alias, 1977), for the wheel, which is is 3.13 which wheel, for 3.16 the Figures and 1977), in of rolling (Alias, he case 21 1 αβ εϕ at + 1 that is perpendicular to the level of wheel–rail contact xOy contact level of to the wheel–rail perpendicular is that βµ µεϕβ − eep force T eep t through wheel climb. (Adapted from Alias, J. 1977, J. La Voie Alias, from Ferrée (Adapted climb. wheel t through Ν N 1 ta R

iteria 1 n Y 1 α 1 αt

β 1 which acts on the level of wheel–rail contact, and is directed directed is and contact, level of on the wheel–rail acts which 1 y Q I 1 1 T α 1 y αt 1 is equal to Coulomb’s friction force. to Coulomb’s equal is friction 2α 1 and the force Y the and Behaviour of rolling stock on track on stock rolling of Behaviour I 1 α 1 αt . The reaction R reaction . The 1 (total force exerted (total force exerted Figure 3.16Figure , Eyrolles, Paris.) , Eyrolles, 1 ) of the of the (3.17) (3.16)

99 - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 as foras μ and adjustment of switches, etc. of adjustment switches, and twist. and of values cant high and of radius curvature asmall with curves of movement in at case low the speeds in observed be phenomenon can This wheel. non-derailed of the loading simultaneous with wheel derailed track. of the displacement alateral following place of takes avehicle derailment the occasions, most In 3.3. 100 where 3.17Figure shorter this distance is, the faster the derailment will become apparent. become will derailment the faster the is, distance this shorter 2010). The et al., Sandos (Dos 26.6° reaches angle flange contact wheel–rail the on which moment the applied until force is guidance value of the total moment the when the from ered cov distance the as defined is and distance’ ‘flange-climbing called is distance This metres. some usually track, on the covers distance wheel some derailing the thus and required, For For The risk of derailment due to rail climb increases when there is there when increases climb due to rail of derailment risk The crossings. and of switches areas in occur derailments most that noted shouldIt be operation poor is, that causes, external through occurs also climbing by rail Derailment the of unloading a significant is there when only occur can climbing by rail Derailment Rail climb by the wheel does not occur instantaneously. A certain amount of time is is of time amount Acertain instantaneously. not occur does wheel by the climb Rail • • • • •

4.3 Y Q β μ Railway Transportation Systems Transportation Railway : wheel–rail contact flange angle flange contact wheel–rail : : wheel–rail friction coefficient friction : wheel–rail An incre An An incre An increase of the vertical load of the non-derailed wheel load non-derailed of the vertical of the increase A decrea A decrea incre An 1 1 β : the total transversal force exerted on the rail via the wheel flange of the derailing derailing the of flange wheel the via rail on the force exerted transversal total : the : static load of 1 wheel : static

= = Factors a Factors

wheel (wheelwheel 1) Nadal’ 70°, 70°, 0.12 (we ase of the value of the Y value of of the the ase ase in the value of the wheel–rail friction coefficient μ coefficient friction wheel–rail value of the the in ase ase in the application time of Y time application the in ase se in the value of the wheel–rail contact angle β angle contact wheel–rail value of the the in se se in the value of the vertical load on the derailed wheel with a simultaneous asimultaneous with wheel derailed load on the vertical value of the the in se μ s derailment criterion. (Adapted from Alias, J. 1977, J. La Voie Alias, from Ferrée (Adapted criterion. s derailment

0.25 (dr 0.25 t rail) it results Y itt rail) results ffecting derailment ffecting y rail), the mathematical equation (3.17) equation Y mathematical y rail), the results 1 /Q 1 1 force

2.0. Y 1 1 force μN′ Q 1 β β N ′ , Eyrolles, Paris.) , Eyrolles, 1 /Q 1

1.5 while while 1.5 - Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 Pyrgidis, C. and Joly, R. 1993, Forces acting in the guidance of a railway vehicle with conventional conventional with vehicle of a railway guidance the in acting Joly, and 1993, Forces R. C. Pyrgidis, 1st 1st superstructure, track the on trains of tilting effects The 2006, N. Demiridis, and C. Pyrgidis, REFERENCES 2010) et al., slows Sandos down) (Dos when of derailment appearance (and the thus increases distance flange-climbing the have that shown results The modelling. of aid simulation the Pyrgidis, C. and Bousmalis, T. 2010, A design procedure of the optimal wheel profile for railway railway for profile wheel optimal of the T. procedure 2010, Adesign Bousmalis, and C. Pyrgidis, Ingegneria tranviari, veicoli per carrelli dei transversale comportamento Il 2004, C. Pyrgidis, en et alignement en ferroviaire véhicule d’un transversale stabilité la de Etude 1990, C. Pyrgidis, nei laterale l’instabilita eliminare di fine al independenti ruota delle technica La 1978, R. Panagin, locomotives des route de Y. stabilité 1935, Rocard, La and M. Julien, International Rail alignement, en véhicules des transversale Stabilité 1996, C. Joly, Pyrgidis, and R. guidage, de –Efforts courbe en ferroviaire véhicule d’un Circulation 1990, C. Joly, Pyrgidis, and R. conception de rayon –Bogies faible de courbe en ferroviaire véhicule d’un Joly, Circulation 1988, R. Doctorat de Thèse Ferroviaire, Dynamique en vibratoire confort et transversale Joly, Stabilité 1983, R. International Gazette Railway 1990s, the for concept F. A bogie 1988, Frederich, International Rail rail-roue, du contact inutilisées et inconnues F. 1985, Possibilités Frederich, Track Railway Modern 2001, C. Esveld, profile wheel of influence 2010, J. The Tunna, and E.J. Kina, L.A.S., Lopes, G.F.M., Sandos, Dos 1977, Voie J. Ferrée La Alias, Geuenich, W., Cunther, C. and Leo, R. 1985, Fibre composite bogies has creep controlled wheelsets, wheelsets, controlled creep has bogies 1985, composite Fibre R. Leo, and W., C. Cunther, Geuenich, àroues véhicle d’un ligne en du comportement Simulation 1984, Tacci, G. and C. Casini, R., Frullini, The influence of various wheel parameters on the above distance was examined with with examined was the distance above on parameters wheel of various influence The • • •

axles and independently rotating wheels, Ingegneria wheels, rotating Ferroviaria independently and axles pp. 38–43. Proceedings, Conference UK, Birmingham, International Congress International (CD). Proceedings 2010, Congress Volos, 27–28 September vehicles running at conventional speeds, 5 speeds, at conventional running vehicles Ferroviaria Paris. ENPC, l’, de Doctorat de Thèse comparative, – Etude bogies des technologies – Nouvelles courbe 10-79). Ingegneriaveicoli ferroviari, Ferroviaria 25–33. 12, International Rail International Rail auto –orientés, àessieux classique/Bogie Paris. Paris, de Université d’Etat, 11, November, 33–40. Brussels, 429–434. IMechE Proc. index, safety on Railway Gazette International Gazette Railway 84–307). No RATP (translation Rome résultats, avec les comparaison indépendantes, 583–585. limited when the yaw angle is large. is yaw the when angle limited is significantly flange of a high effect positive The increases. climbing for rail required angl The The valu The heig The e of q ht of the wheel flange is increased. When the wheel is worn out the distance distance the is out worn the wheel When increased. is flange wheel ht of the e of attack is smaller. is e of attack , October, Rome, 10, 837–847. Rome, , October, r increases (see Figure 1.8). (see Figure increases , Brussels, 12, 11–28. 12, , Brussels, , , Eyrolles, Paris. Eyrolles, , Railway Conditioning and Monitoring , Vol. 224, Part F: J. Rail and Rapid Transit, Special issue paper, paper, issue Special Transit, Rapid and Rail F: J. , Vol. Part 224, , April, 3, 79–281. 3, , April, , 2nd edition, MRT-Productions, West Germany. MRT-Productions, edition, , 2nd , February, Rome, 2, 143–150 (translation SNCF No No SNCF 143–150 (translation 2, Rome, , February, th International Congress for Transport Research Transport for Congress International th Ingegneria Ferroviaria Behaviour of rolling stock on track on stock rolling of Behaviour , Brussels, April, 3, 31–42. 3, April, , Brussels, , HERMANN et Cie Editeurs, Paris. Editeurs, Cie et , HERMANN 2006, IET, 29–30 November, November, 29–30 IET, 2006, , August, Rome, pp. 511–529. Rome, , August, , January–February, , January–February, , September, 9, , September,

101 , , , Downloaded By: 10.3.98.104 At: 15:12 29 Sep 2021; For: 9781315228945, chapter3, 10.1201/b19472-4 Vermeulen, P.J. and Johnson, K.L. 1964, Contact of non-spherical elastic bodies transmitting tangen transmitting bodies elastic of non-spherical Contact 1964, K.L. P.J.Vermeulen, Johnson, and rechange de pieces Catalogue asynchrones, àmoteurs CL93 Bogie no date, Rail. Jeumont Schneider self-steering for profile wheel optimum of an development The 1980, Tournay, and H. H.M. Scheffel, ferrovi véhicules des suspension de dispositifs aux relatives nouvelles 1974, H. Conceptions Scheffel, Pyrgi 102

dis, C. and Panagiotopoulos, A. 2012, An optimization process of the wheel profile of tramway tramway of profile wheel of the process optimization An 2012, A. Panagiotopoulos, and C. dis, Le Creusot, France. Creusot, Le 1980. June 23 at ASME, received Manuscript IL, Chicago, Meeting Annual Winter load conditions, axle heavy under trucks Journal of Applied Mechanics Applied of Journal forces, tial International Rail aires, Elsevier Procedia Social and Behavioral Sciences Behavioral and Social Procedia Elsevier vehicles, Railway Transportation Systems Transportation Railway , Brussels, December, 801–817. December, , Brussels, , 86, 338–340. , 86, , 48, 1130–1142. 48, , , 16–21 November 1980, 1980, , 16–21 November - - ,