Structural Evaluation of Variable Gauge Railway

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Article Structural Evaluation of Variable Gauge Railway

Rayhan Usamah 1, Donghoon Kang 2, Youn Doh Ha 3 and Bonyong Koo 1,* 1 Department of Mechanical Engineering, Kunsan National University, 558 Daehak-ro, Gunsan 54140, Korea; [email protected] 2 Railroad Safety Research Team, Korea Railroad Research Institute, 176 Railroad Museum St., Uiwang-si 16105, Korea; [email protected] 3 Department of Naval Architecture and Ocean Engineering, Kunsan National University, 558 Daehak-ro, Gunsan 54150, Korea; [email protected] * Correspondence: [email protected]

Received: 13 September 2020; Accepted: 28 September 2020; Published: 1 October 2020

Abstract: In the Eurasian railway network, a different gauge length is used across several countries. A railroad variable gauge allows railway vehicles in rail transport to travel across a gauge break caused by two railway networks with differing track gauges. The variable gauge railway consists of the bogie system to change the length of the wheel shaft and the gauge changing railroad track. Thus, it is important to assess the structural performance of the variable gauge system. In this study, as a performance improvement subject of the variable gauge bogie and railroad, a structural analysis using dynamic finite element calculation was performed to evaluate the reliability and life cycle of the release system and the variable gauge railway. First, the contact pressure and structural stress of the release disk and the release rail were calculated, which provided the wear condition and fatigue life prediction of variable gauge components. Second, a structural analysis of the gauge stabilization rail after the gauge release was executed. The maximum principal stress was evaluated to guarantee the required service life of the stabilization rail section. For the operational safety of the variable gauge system, the operation conditions and maintenance requirements of the variable gauge railway were proposed.

Keywords: railroad variable gauge system; structural analysis; fatigue life; wear condition

1. Introduction A railway network is comprised of several different gauge lengths for historical reasons: narrow gauge, standard gauge, and broad gauge. Due to this difference in gauge length, conventional trains cannot run on the same track, and consequently, passengers are forced to transfer at intermediate junctions [1]. To avoid transportation difficulties and the cost of different gauge tracks on the trains, a variable gauge system is an efficient solution applied in some countries, such as in the Eurasian railroad network [2,3]. This system effectively replaces time-consuming tasks such as transferring freight, replacing individual wheels and axles, truck exchange, transporters, or transporter flatcars because the systems mentioned above are both time consuming and very costly. Kondo [4] introduced a novel traction control system of the gauge changing train, which can run through two different gauge sections. The Spanish Talgo train, which is operating between Spain and France, is known for its variable system, enabling it to switch between broad (1668 mm) and standard European gauges [5]. Recently a variable gauge wheelset system installed in the bogie was developed and the fatigue strength of the system was investigated [6,7]. A life cycle cost model was developed to assess the effectiveness of a variable gauge system [8]. Several factors can influence fatigue life, including loading history, stress state, strain rate, and temperature, and can lead under certain conditions (like low temperature) to brittle fracture [9,10]. Failure of a component can have catastrophic

Infrastructures 2020, 5, 80; doi:10.3390/infrastructures5100080 www.mdpi.com/journal/infrastructures Infrastructures 2020, 5, 80 2 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 2 of 14 consequences; therefore,therefore, the the study study and and prediction prediction of railroad of railroad failure failure can prevent can prevent loss of lifeloss and of propertylife and damageproperty [damage11–13]. Fatigue[11–13]. crackingFatigue cracking is caused is bycaused cyclic by loads, cyclic although loads, although the resultant the resultant stress level stress is substantiallylevel is substantially below the below material’s the material’s yield strength yield [st14rength]. Besides [14]. fatigue Besides analysis, fatigue other analysis, factors other need factors to be consideredneed to be considered to avoid loss to of avoid life and loss property of life and damage, prop sucherty damage, as wear and such friction. as wear Friction and friction. occurs betweenFriction twooccurs contact between surfaces two in contact relative surfaces motion, whereasin relative wear motion, is the phenomenon whereas wear of mechanicalis the phenomenon and chemical of damagemechanical that and aff ectschemical the quality damage of that the materialsaffects the in quality contact of withthe materials each other in [contact15,16]. Wearwith each of system other components[15,16]. Wearis of often system a critical components factor influencingis often a crit theical product factor influencing service life. the In addition,product service the overhead life. In electricaddition, wire the interactionoverhead electric [17] to transmitwire interaction the electricity [17] to totransmit the railway the electricity vehicle and to the the railway vehicle systemvehicle dynamicsand the vehicle [18] to system reduce dynamics longitudinal [18] oscillations to reduce inlong passengeritudinal trainsoscillations need to in be passenger addressed trains in the need design to ofbe theaddressed wheelset in system.the design of the wheelset system. In this paper, to quantitivelyquantitively evaluate the life of the variable gauge railway, dynamic finitefinite element analysis using Abaqus was executed for for the the release release disk disk and and the the release release rail rail in in Section Section 22.. Between contractingcontracting partsparts of of the the disk disk and and the the rail, rail, there there is limiting is limiting criteria criteria for contact for contact pressure pressure to avoid to wearavoid problems wear problems using the using Archard the Archard formula formula [19,20]. [19,20]. Based on Based the finite on the element finite simulationelement simulation and the wear and criteriathe wear of criteria the contacting of the contacting surface, the surface, safe operating the safe velocity operating and velocity the fatigue and issues the fatigue of the release issues dickof the in therelease variable dick gaugein the systemvariable were gauge proposed system withwere an pr emphasisoposed with on thean lubricationemphasis on of the the lubrication contact surface of the to minimizecontact surface friction to andminimize to reduce friction mechanical and to reduce wear. Inmechanical Section3, thewear. fatigue In Section life of 3, the the grooved fatigue raillife inof the grooved variable rail gauge in the railway variable during gauge the railway gauge duri changingng the operation gauge changing is estimated operation from is the estimated load history from ofthe the load multi-body history of dynamicthe multi-body analysis. dynamic Through analysis. fatigue Through life assessment fatigue life by structuralassessment stress by structural analysis, thestress designed analysis, release the designed rail and the release grooved rail railand in the the grooved variable gaugerail in systemthe variable are guaranteed gauge system to be safeare inguaranteed the sense to of be metal safe fatigue in the ifsense continuous of metal maintenance fatigue if continuous procedures maintenance such as surface procedures lubrication such and as inspectionsurface lubrication are applied and adequately. inspection are applied adequately.

2. Structural Analysis of Variable Gauge Release Rail To performperform the the gauge gauge transformation transformation from from the the standard-gauge standard-gauge railway railway with with 1435 mm1435 track mm gaugetrack togauge broad to gaugebroad railwaygauge railway with 1520 with mm 1520 track mm gauge, track ga theuge, release the release disk is disk installed is installed on the bogieon the gauge, bogie andgauge, the and locked the statelocked of state the bogieof the axle bogie is releasedaxle is released by the operatingby the operating principle principle that the that release the release disk is pusheddisk is pushed in contact in contact with the with release the release rail when rail when the bogie the bogie is advancing. is advancing. The The variable variable gauge gauge system system of theof the release release rail rail and and the the release release disk disk in in the the unlocking unlocking section section is is illustrated illustrated in in FigureFigure1 1.. The The unlockingunlocking section of the variable gauge railroad ofof 23802380 mmmm lengthlength isis shownshown inin FigureFigure2 2..

Figure 1. VariableVariable gauge system of releaserelease rail and release disk. Infrastructures 2020, 5, x FOR PEER REVIEW 3 of 14 Infrastructures 2020, 5, 80 3 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 3 of 14

Figure 2. Releasing section of the railway track for a variable gauge system. Figure 2. ReleasingReleasing section of the railway track for a variable gauge system. To perform the gauge conversion between standard gauge and broad gauge, a release disk is To perform the gauge conversion between standard gauge and broad gauge, a release disk is installedTo perform on the bogie the gauge axle to conversion unlock the between gauge system. standa rdAs gauge a fixed and part, broad the release gauge, rail a release is installed disk inis installed on the bogie axle to unlock the gauge system. As a fixed part, the release rail is installed in installedthe releasing on the section bogie in axle Figure to unlock 2. The therelease gauge rail system. made of As SS400 a fixed low part, carbon the releasesteel is railshown is installed in Table in1. the releasing section in Figure2. The release rail made of SS400 low carbon steel is shown in Table1. theThe releasing release disk section is made in Figure of STS304 2. The stainless release steelrail made that hasof SS400 a Young’s low carbon modulus steel of is190 shown GPa andin Table tensile 1. The release disk is made of STS304 stainless steel that has a Young’s modulus of 190 GPa and tensile Thestrength release of 520disk MPa, is made as seen of STS304 in Table stainless 2. For dyna steelmic that finite has a element Young’s analysis modulus using of 190 Abaqus, GPa and the tensilemodel strength of 520 MPa, as seen in Table2. For dynamic finite element analysis using Abaqus, the model strengthand mesh of are520 shownMPa, as in seen Figure in Table 3. Each 2. For model dyna wasmic constructedfinite element using analysis a solid using hexahedral Abaqus, element,the model a and mesh are shown in Figure3. Each model was constructed using a solid hexahedral element, a andspring mesh consisting are shown of 16,848 in Figure elemen 3. ts,Each a release model disk was of constructed 23,752 solid using elements, a solid and hexahedral a release rail element, of 62,505 a spring consisting of 16,848 elements, a release disk of 23,752 solid elements, and a release rail of 62,505 springsolid elements. consisting The of 16,848mesh convergence elements, a release was confirmed disk of 23,752 in all solid finite elements, element andcalculations. a release rail of 62,505 solid elements. The mesh convergence was confirmed in all finite element calculations. solid elements. The mesh convergence was confirmed in all finite element calculations. Table 1. Properties of SS400 low carbon steel. Table 1. Properties of SS400 low carbon steel. Table 1. Properties of SS400 low carbon steel. Density (kg/m3) 7680 Density (kg/m3) 7680 Young’sDensity modulus (kg/m (GPa)3) 7680 210 Young’sTensileYoung’s modulusStrength(MPa) (GPa) (GPa) 210 210 510 Tensile Strength (MPa) 510 TensileYield Strength(MPa) Strength(MPa) 510 245 Yield Strength (MPa) 245 YieldPoisson’s Strength(MPa) ratio ratio 0.25 2450.25 Poisson’s ratio 0.25 Table 2.2. Properties ofof STS304STS304 stainlessstainless steel.steel. Table 2. Properties of STS304 stainless steel. Density (kg/m3) 8000 Density (kg/m3) 8000 Young’sDensity modulus(GPa) (kg/m3) 8000 190 Young’s modulus (GPa) 190 Young’sTensile Strength(MPa)modulus(GPa) 190 520 Tensile Strength (MPa) 520 TensileYieldYield StrengthStrength(MPa) Strength(MPa) (MPa) 240 520 240 YieldPoisson’s Strength(MPa) ratio ratio 0.27 2400.27 Poisson’s ratio 0.27

Figure 3. The ﬁnite elements of the whole geometry. Figure 3. The finite elements of the whole geometry. 2.1. Stress History of ReleaseFigure Rail 3. The finite elements of the whole geometry. 2.1. Stress History of Release Rail 2.1. StressThe contactHistory pressureof Release wasRail calculated, and is shown in Figure4, when the release ﬁrstly comes into contactThe contact with thepressure release was rail calculated, at a velocity and of 5is km show/h andn in a Figure pressure 4, valuewhen ofthe initial release contact firstly of comes about 18.7into MPacontactThe contact at 5with km / pressureh.the It release takes was about rail calculated, at 1.7 a velocity s for theand of release 5is km/h show disk andn in to aFigurereach pressure the 4, horizontalwhenvalue theof initial release section contact firstly of the of releasecomes about into18.7 contactMPa at 5with km/h. the It release takes about rail at 1.7 a velocity s for the of release 5 km/h disk and to a reach pressure the horizontalvalue of initial section contact of the of release about 18.7 MPa at 5 km/h. It takes about 1.7 s for the release disk to reach the horizontal section of the release Infrastructures 2020, 5, 80 4 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 4 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 4 of 14 rail. The contactcontact pressurepressure of of the the impact impact area area is greateris greater than than the yieldthe yield strength strength and isand presented is presented in detail. in detail.rail. The For contact the bogie pressure traveling of theat a impactspeed of area 5 km/h, is gr theeater contact than thepressures yield strength at three positionsand is presented exceed the in Fordetail. the For bogie the travelingbogie traveling at a speed at a speed of 5 km of/h, 5 km/h, the contact the contact pressures pressures at three at positionsthree positions exceed exceed the yield the yieldstrength strength as high as ashigh 350 as MPa, 350 andMPa, their and locationstheir locati areons shown are shown in Figure in Figure5a. For 5a. the For 10 kmthe /10h bogiekm/h speed,bogie speed,yield strength the contact as high pressure as 350 locations MPa, and and their histories locati onsare areshown shown in Figure in Figure 5b. 5a. For the 10 km/h bogie thespeed, contact the contact pressure pressure locations locations and histories and histories are shown are inshown Figure in5 Figureb. 5b.

Figure 4. Contact pressure on the initial impact (5 km/h). Figure 4. ContactContact pressure on the initial impact (5 kmkm/h)./h).

Figure 5. Locations of excessive contact pressure and time history: (a) 5 km/h and (b) 10 km/h. Figure 5. Locations of excessive contact pressure and time history: (a) 5 km/h and (b) 10 km/h. JustFigure because 5. Locations the contact of excessive pressure contact of the pressure impactor and is time greater history: than (a) the5 km/h yield and strength, (b) 10 km/h. it does not meanJust immediate because damagethe contact to thepressure contact of location,the impactor but it is means greater that than there the isyield the possibilitystrength, itof does fatigue not Just because the contact pressure of the impactor is greater than the yield strength, it does not meandamage immediate such as local damage plastic to deformation the contact location, or long-term but wearit means of cracks. that there When is thethe bogie possibility moves of at fatigue 5 km/h mean immediate damage to the contact location, but it means that there is the possibility of fatigue damageand 10 km such/h, as other local high-stress plastic deformation locations are or identiﬁed;long-term theirwear stressof cracks. histories When are the shown bogie inmoves Figures at 65 damage such as local plastic deformation or long-term wear of cracks. When the bogie moves at 5 km/hand7, and respectively. 10 km/h, Fromother the high-stress stress histories, locations the are maximum identified; von their Mises stress stress histories is 20 MPa are for shown 5 km in/h km/h and 10 km/h, other high-stress locations are identified; their stress histories are shown in Figuresbogie speed 6 and and 7, respectively. 160 MPa for 10kmFrom/ hthe bogie stress speed. histories, the maximum von Mises stress is 20 MPa for 5Figures km/h bogie 6 and speed 7, respectively. and 160 MPa From for the 10km/h stress bogie histories, speed. the maximum von Mises stress is 20 MPa for 5 km/h bogie speed and 160 MPa for 10km/h bogie speed. Infrastructures 2020, 5, 80 5 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 5 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 5 of 14

FigureFigure 6. HistoriesHistories of of maximum maximum von von Mises Mises stress stress at at 5 5 km/h km/h bogie’s speed. Figure 6. Histories of maximum von Mises stress at 5 km/h bogie’s speed.

Figure 7. Histories of maximum von Mises stress at 10 km/h bogie’s speed. Figure 7. Histories of maximum von Mises stress at 10 km/h bogie’s speed. Figure 7. Histories of maximum von Mises stress at 10 km/h bogie’s speed. 2.2. Life Cycle Prediction 2.2. Life Cycle Prediction 2.2. LifeThe Cycle wear Prediction of the contact area may be indicated by a value of contact pressure and the slip velocity, The wear of the contact area may be indicated by a value of contact pressure and the slip velocity, as shownThe wear in Table of the3. contact This data area refers may tobe the indicated information by a value and indicationof contact pressure of the wear and of the railway slip velocity, tracks as shown in Table 3. This data refers to the information and indication of the wear of railway tracks ascarried shown out in byTable the 3. Bombardier This data refers company, to the which information quantitatively and indication evaluates of thethe valuewear ofof therailway wear tracks factor carried out by the Bombardier company, which quantitatively evaluates the value of the wear factor carriedusing the out Archard by the Bombardier wear formula company, [18]. In which the performed quantitatively analysis, evaluates the contact the value pressure of the betweenwear factor the using the Archard wear formula [18]. In the performed analysis, the contact pressure between the usingrelease the disk Archard and the wear release formula rail is considered[18]. In the toperformed be a mild analysis, wear condition the contact for the pressure 350 MPa between at the speed the release disk and the release rail is considered to be a mild wear condition for the 350 MPa at the speed releaseof 5 km disk/h (1.39 and the m/s), release which rail does is considered not cause anyto be particular a mild wear problems condition in for the the area 350 of MPa operation at the speed of the of 5 km/h (1.39 m/s), which does not cause any particular problems in the area of operation of the ofvariable 5 km/h track (1.39 gauge m/s), system.which does not cause any particular problems in the area of operation of the variable track gauge system. variableSince track the gauge wear is system. related to uncertainties such as the shape of the contact surface and the lubrication Since the wear is related to uncertainties such as the shape of the contact surface and the conditions,Since the then wear applying is related a lubricant to uncertainties between the such release as disk the andshape the of release the contact rail can preventsurface problemsand the lubrication conditions, then applying a lubricant between the release disk and the release rail can lubricationrelated to wear.conditions, Therefore, then applying referring toa lubricant [21] we stressbetween the the importance release disk of applying and the therelease appropriate rail can prevent problems related to wear. Therefore, referring to [21] we stress the importance2 of applying preventlubricant problems for the release related rail. to wear. In the Therefore, dry case, the referr wearing rate to [21] is higher we stress than 8.0the µimportanceg/m/mm but of applying decreases the appropriate lubricant for the release2 rail. In the dry case, the wear rate is higher than 8.0 theto aappropriate value smaller lubricant than 1.0 forµg/ mthe/mm releasewhen rail. lubricated. In the dry Performed case, the numerical wear rate calculations is higher indicatedthan 8.0 µg/m/mm2 but decreases to a value smaller than 1.0 µg/m/mm2 when lubricated. Performed µg/m/mmonly mild2 wear but happensdecreases between to a value the release smaller rail andthan the 1.0 release µg/m/mm disk;2 the when application lubricated. of lubricants Performed will numerical calculations indicated only mild wear happens between the release rail and the release numerical calculations indicated only mild wear happens between the release rail and the release disk; the application of lubricants will minimize the uncertainties in real engineering applications. disk; the application of lubricants will minimize the uncertainties in real engineering applications. Infrastructures 2020, 5, x FOR PEER REVIEW 6 of 14

Infrastructures 2020, 5, 80 6 of 14 The applying schedule of lubricants is another subject to be addressed by the real maintenance and inspection of rail conditions. minimize the uncertainties in real engineering applications. The applying schedule of lubricants is another subject to be addressedTable 3. Wear by the factor real by maintenance contact pressure and inspectionand slip velocity. of rail conditions.

Pressure (GPa) SlipTable Velocity 3. Wear [m/s] factor Wear by contact Coefficient, pressure k [10 and4] slip velocity.Wear Condition 4 Pressure0–2 (GPa) Slip Velocity0–0.2 [m/s] Wear Coeﬃ1–10cient, k [10 ] MildWear wear Condition (oxide) 0–2 0–0.2 1–10 Mild wear (oxide) 0–2 0.2–0.7 30–40 Severe wear 0–2 0.2–0.7 30–40 Severe wear 0–20–2 0.8–1 1–10 MildMild wear wear (high (high oxidation oxidation rate) rate) 2–3 0–1 300–400 Seizure 2–3 0–1 300–400 Seizure The results of the analysis were used to assess fatigue loads and predict the life cycle of the The results of the analysis were used to assess fatigue loads and predict the life cycle of the release rail. Morishita et al. [12] represented the fatigue line by the correlation of the equivalent stress release rail. Morishita et al. [12] represented the fatigue line by the correlation of the equivalent stress amplitude vs. the number of fatigue cycles. For SS400 low-carbon steel, which is the material of the amplitude vs. the number of fatigue cycles. For SS400 low-carbon steel, which is the material of the release rail, the fatigue endurance limit, σe, was about 175 MPa. If the yield strength, σy, is 245 MPa release rail, the fatigue endurance limit, σe, was about 175 MPa. If the yield strength, σy, is 245 MPa for SS400, the Soderberg fatigue criteria in Equation (1) is considered conservatively. for SS400, the Soderberg fatigue criteria in Equation (1) is considered conservatively. σσm σa + =1= 1 (1) σy σe (1) σ σ where σm andand σσaa areare the the mean mean stress stress and and the the alternating alternating stress stress amplitude, amplitude, respectively. When calculating the fatigue life using the SoderbergSoderberg criteria, it is common to use the principal stresses. Alternatively, Alternatively, a a signed signed von Mises theory can be utilized for fatigue evaluation under the condition that the the biaxiality biaxiality ratio, ratio, σσ2/2σ/σ1 1isis less less than than zero zero [22]. [22 ].Given Given the the von von Mises Mises stress stress level level of 20 of 20MPa MPa at a at velocity a velocity of 5 ofkm/h, 5 km it/ canh, it be can confirmed be conﬁrmed that the that variable the variable gauge gaugerelease release rail is free rail from is free fatigue from fatiguedamage damage when the when bogie the is bogie traveling is traveling at 5 km/h at 5in km the/h variable in the variable gauge section, gauge section, as the stress as the level stress is level much is muchlower lowerthan the than fatigue the fatigue endurance endurance limit limit of 175 of 175MPa. MPa. To Tominimize minimize uncertainties uncertainties in in fatigue fatigue life, life, it it is recommended to reinforce the area at the neck of the release rail, shown in Figure 88,, wherewhere aa largelarge stress concentration occurs.

Figure 8. Stress concentration at release rail neck.

3. Structural Analysis and Fatigue Life Prediction of the Rail in the Stabilization Section After the variable gauge system in the bogie releases,releases, it passes through the stabilization track section of 12,260 mm, which changes the wheel distan distancece of the bogie from standard gauge railway to broad gauge. The The floor ﬂoor plan of this variable gauge railway is as follows.follows. The variable gauge rail is made of a groove-shaped section that is different diﬀerent in shape from the normal rail to support the wheel when the gauge widens, andand itsits cross-sectioncross-section isis shownshown inin FigureFigure9 9.. InfrastructuresInfrastructures 20202020,, 55,, 80x FOR PEER REVIEW 7 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 7 of 14

Figure 9. View of release and stabilization section and track cross-section. Figure 9. View of release and stabilization section and track cross-section. The railwayrailway tracktrack in in the the release release section section and and the the stabilization stabilization section section uses uses the samethe same material material of UIC of The railway track in the release section and the stabilization section uses the same material of 60UIC rail. 60 rail. It has It highhas high strength strength steel st properties:eel properties: a tensile a tensile strength strength of 880of 880 MPa MPa and and an an yield yield strength strength of UIC 60 rail. It has high strength steel properties: a tensile strength of 880 MPa and an yield strength 580of 580 MPa. MPa. For For the the ﬁnite finite element element analysis analysis in in the the stabilization stabilization rail rail section, section, thethe wheelwheel andand thethe variablevariable of 580 MPa. For the finite element analysis in the stabilization rail section, the wheel and the variable gauge track of aa groovegroove sectionsection werewere modeled.modeled. The generated mesh used a solid hexagonal element gauge track of a groove section were modeled. The generated mesh used a solid hexagonal element withwith 53,87953,879 elementselements appliedapplied for wheels and 180,600 elements for the stabilization rail, as shown in with 53,879 elements applied for wheels and 180,600 elements for the stabilization rail, as shown in Figure 1010.. Figure 10.

Figure 10. A finite ﬁnite element model of bogie wheel and stabilization railroad. Figure 10. A finite element model of bogie wheel and stabilization railroad. 3.1. Input Loads by Multi-Body Dynamics 3.1. Input Loads by Multi-Body Dynamics 3.1. Input Loads by Multi-Body Dynamics The multi-body dynamic analysis is carried out when the bogie passed the overall gauge changing The multi-body dynamic analysis is carried out when the bogie passed the overall gauge section,The shown multi-body in Figure dynamic9, at a speedanalysis of 5is kmcarried/h. The out acting when and the reactingbogie passed force results the overall between gauge the changing section, shown in Figure 9, at a speed of 5 km/h. The acting and reacting force results wheelchanging and section, the rail shown obtained in fromFigure the 9, multi-bodyat a speed dynamicof 5 km/h. analysis The acting of the and bogie reacting and the force track results were between the wheel and the rail obtained from the multi-body dynamic analysis of the bogie and the betweenused as input the wheel loads and for the the analysis rail obtained of the groovedfrom the railmu inlti-body the stabilization dynamic analysis track. The of three-dimensionalthe bogie and the track were used as input loads for the analysis of the grooved rail in the stabilization track. The three- trackmodel were and used numbering as input of loads the multi-body for the analysis dynamics of the model grooved are shownrail in the in Figure stabilization 11, and track. the time The history three- dimensional model and numbering of the multi-body dynamics model are shown in Figure 11, and dimensionalof contact forces model applied and numbering to each wheel of the is shown multi-bod in Figurey dynamics 12. model are shown in Figure 11, and the time history of contact forces applied to each wheel is shown in Figure 12. the time history of contact forces applied to each wheel is shown in Figure 12. InfrastructuresInfrastructures2020 2020, ,5 5,, 80 x FOR PEER REVIEW 88 of of 14 14 Infrastructures 2020, 5, x FOR PEER REVIEW 8 of 14

FigureFigure 11.11.Multi-body Multi-body dynamicdynamic analysisanalysis ofof thethe variablevariable gaugegauge bogiebogie andand thethe rail. rail. Figure 11. Multi-body dynamic analysis of the variable gauge bogie and the rail.

Railroad contact force Railroad contact force 1.50E+05 1.50E+05

1.00E+05 Max. lateral force in rear wheel : 35 kN 1.00E+05 Max. lateral force in rear wheel : 35 kN

5.00E+04 5.00E+04

0.00E+00 0.00E+00 0 5 10 15 20 25 30

Force (N) 0 5 10 15 20 25 30 Force (N) -5.00E+04 -5.00E+04

-1.00E+05 -1.00E+05 Max. lateral force in front wheel : 122 kN -1.50E+05 Max. lateral force in front wheel : 122 kN -1.50E+05 Time (s) Time (s) Lateral_force_front Vertical_force_front Lateral_force_rear Vertical_force_rear Lateral_force_front Vertical_force_front Lateral_force_rear Vertical_force_rear

FigureFigure 12. 12.Contact Contact force–timeforce–time historyhistory variable.variable. Figure 12. Contact force–time history variable. FromFrom thethe contactcontact force histories shown shown in in Figure Figure 12, 12 ,a avertical vertical load load of of85 85 kN kN by bythe the weight weight of the of From the contact force histories shown in Figure 12, a vertical load of 85 kN by the weight of the thecargo cargo train train is applied. is applied. In the In front the frontwheel, wheel, the maximum the maximum lateral lateral forces forcesare 35 arekN 35and kN 122 and kN 122 for kNthe cargo train is applied. In the front wheel, the maximum lateral forces are 35 kN and 122 kN for the forfront the wheel front and wheel the and rear the wheel, rear respectively. wheel, respectively. These lateral These forces lateral occur forces due occur to the due lateral to the imbalance lateral front wheel and the rear wheel, respectively. These lateral forces occur due to the lateral imbalance imbalancein the stabilization in the stabilization section. From section. the contact From the force contact history, force the history, rear wheel the rear hits wheel the track hits thefirst, track the front ﬁrst, in the stabilization section. From the contact force history, the rear wheel hits the track first, the front thewheel front reacts, wheel and reacts, finally and the ﬁnally motion the of motionthe bogie of is the stabilized. bogie is stabilized.For the structural For the analysis structural of the analysis track, wheel reacts, and finally the motion of the bogie is stabilized. For the structural analysis of the track, ofthe the maximum track, the lateral maximum loadslateral are taken loads from are the taken contac fromt force thecontact history forceand 110 history kN vertical and 110 force kN verticalin KRL- the maximum lateral loads are taken from the contact force history and 110 kN vertical force in KRL- force2012 instandard KRL-2012 design standard load design for loadthe forconservati the conservativeve assessment. assessment. The Theapplied applied load load condition condition isis 2012 standard design load for the conservative assessment. The applied load condition is summarizedsummarized in in Figure Figure 13 13.. summarized in Figure 13. Infrastructures 2020, 5, x FOR PEER REVIEW 9 of 14 Infrastructures 2020,, 5,, 80x FOR PEER REVIEW 9 of 14

Figure 13. Analysis model of bogie wheels and stabilization track and load application. Figure 13. Analysis model of bogie wheels and stab stabilizationilization track and load application. 3.2. Structural Analysis of the Rail in the Stabilization Section 3.2. Structural Analysis of th thee Rail in the Stabilization Section To verify the effect of the railroad tie as boundary conditions, the quasi-static analysis was To verifyverify the the e ﬀeffectect of of the the railroad railroad tie astie boundary as boundary conditions, conditions, the quasi-static the quasi-static analysis analysis was carried was carried out for two cases; the first was when the front and rear wheels were located between the outcarried for twoout cases;for two the cases; ﬁrst wasthe whenfirst was the frontwhen and the rearfront wheels and rear were wheels located were between located the between railroad ties,the railroad ties, and the second was when the wheels were placed on the railroad tie. Due to the slow andrailroad the secondties, and was the when second the was wheels when were the placedwheels on we there railroadplaced on tie. the Due railroad to the tie. slow Due change to the rate slow of change rate of contact forces shown in Figure 12, dynamic analysis was not considered here. contactchange rate forces of showncontact in forces Figure shown 12, dynamic in Figure analysis 12, dynamic was not analysis considered was not here. considered here. 1. When both wheels are placed between the railroad ties. 1. WhenWhen both both wheels wheels are are placed placed between between the the railroad railroad ties. ties. Figure 14 shows the analysis results, in terms of the von Mises stress resulting from the contact Figure 14 shows the analysis results, in terms of the von Mises stress resulting from the contact between the wheel and the grooved rail. The stress at the contact position by the front wheel and by between the wheel and the grooved rail. The stress at the contact position by the front wheel and by the rear wheel was 357 MPa and 682 MPa, respectively. The contour plot of von Mises stress by the the rear wheel was 357 MPa and 682 MPa, respectively.respectively. The contour plot of von Mises stress by the wheel contract is shown in Figure 14 in detail. wheel contract is shown inin FigureFigure 1414 inin detail.detail.

FigureFigure 14. 14.Structural Structural analysis analysis results results (von (von Mises Mises stress) stress) of of the the rail rail when when the the wheels wheels are are placed placed between between Figure 14. Structural analysis results (von Mises stress) of the rail when the wheels are placed between thethe railroad railroad ties. ties. the railroad ties. Infrastructures 2020, 5, 80 10 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 10 of 14

ItIt is is important important to to evaluate evaluate the the contact contact pressure pressure between between the the grooved grooved rail rail and and wheels wheels to to analyze analyze thethe fatigue fatigue failure failure of of the the component component due due to to wear. wear. Fi Figuregure 1515 showsshows that that the the maximum maximum contact contact pressure pressure byby the rear wheelwheel isis largerlarger than than the the maximum maximum contact contac pressuret pressure of of the the front front wheel wheel with with the the values values of 349 of 349MPa MPa and and 580 MPa,580 MPa, respectively. respectively. As seen As inseen Table in 3Table, this level3, this of level contact of contact pressure pressure and the slipand velocitythe slip velocityof 5 km/ hof only 5 km/h result only in result mild wear.in mild wear.

FigureFigure 15. 15. MaximumMaximum contact contact pressure pressure in in the the rail. rail.

TableTable 44 showsshows aa summarysummary ofof thethe structuralstructural analysisanalysis whenwhen thethe wheelswheels areare placedplaced betweenbetween thethe railwayrailway ties. ties.

TableTable 4. 4. VonVon Mises Mises stress, stress, maximum principal stress, and maximum contact pressure in the rail.

StressStress of of Grooved Grooved RailRail Front Front Wheel Wheel Rear Rear Wheel Wheel Max.Max. von von Mises Mises stress stress on on outer groovegroove 33.7 33.7 MPa MPa 15.9 15.9 MPa MPa Max.Max. principal principal stress stress on on outer groovegroove 29.6 29.6 MPa MPa 5.7 5.7 MPa MPa Max. von Mises stress on inner groove 55.1 MPa 80.5 MPa Max. von Mises stress on inner groove 55.1 MPa 80.5 MPa Max. principal stress on inner groove 37.4 MPa 23.8 MPa Max.Max. principal von Mises stress stress onon bottominner groove surface 25 37.4 MPa MPa 25.9 23.8 MPa MPa Max.Max. von principal Mises stress stress on bottombottom surface surface 37.3 25 MPa MPa 28.4 25.9 MPa MPa Max. principalMax. stress contact on pressure bottom surface 349 37.3 MPa MPa 580 28.4 MPa MPa Max. contact pressure 349 MPa 580 MPa

2.2. WhenWhen the the wheels wheels are are on on the the railroad railroad tie tie FigureFigure 1616 shows the the analysis analysis results, results, in in terms terms of of the the von von Mises Mises stress stress resulting resulting from from the the contact contact betweenbetween the wheel and the rail. rail. The The stresses stresses at at the the co contactntact position position by by the the front front wheel wheel and and by by the the rear rear wheel were 357 MPa and 682 MPa, respectively. Th Thee contour contour plot plot of of von Mises stress stress by the wheel contractcontract is shown in Figure 16 in detail. To assess wear possibility by the contract pressure and the slip, the contract pressure at the contract location was evaluated. Figure 17 shows the maximum contact pressure by the rear wheel was larger than the maximum contact pressure of the front wheel with the values of 325 MPa and 535 MPa, respectively. As seen in Table3, this level of contact pressure and the slip velocity of 5 km /h only result in mild wear. Infrastructures 2020, 5, x FOR PEER REVIEW 11 of 14

Infrastructures 2020, 5, 80 11 of 14 Infrastructures 2020, 5, x FOR PEER REVIEW 11 of 14

Figure 16. Structural analysis results (von Mises stress) of the rail when the wheels are placed between the railroad ties.

To assess wear possibility by the contract pressure and the slip, the contract pressure at the contract location was evaluated. Figure 17 shows the maximum contact pressure by the rear wheel was larger than the maximum contact pressure of the front wheel with the values of 325 MPa and 535 MPa, respectively. As seen in Table 3, this level of contact pressure and the slip velocity of 5 km/h FigureFigure 16. 16. StructuralStructural analysis analysis results results (von (von Mises Mises stress) stress) of of the the rail rail when when the the wheels wheels are are placed placed between between only theresultthe railroad railroad in mild ties. ties. wear.

FigureFigure 17. 17. MaximumMaximum contact contact pressure pressure in in the the rail. rail.

Table5 shows a summary of the structural analysis when the wheels are placed between the railway ties. From Tables4 and5, it is evaluated that the stabilization rail made of UIC60 is free of

Figure 17. Maximum contact pressure in the rail. Infrastructures 2020, 5, 80 12 of 14 structural failure or fatigue damage from the calculated level of von Mises stress and the maximum principal stress.

Table 5. Von Mises stress, maximum principal stress, and maximum contact pressure in the rail.

Stress of Grooved Rail Front Wheel Rear Wheel Max. von Mises stress on outer groove 69.1 MPa 37.5 MPa Max. principal stress on outer groove 39.1 MPa 28.2 MPa Max. von Mises stress on inner groove 13.9 MPa 45.1 MPa Max. principal stress on inner groove 9.7 MPa 67.3 MPa Max. von Mises stress on bottom surface - 24.4 MPa Max. principal stress on bottom surface 20.4 MPa 27.3 MPa Max. contact pressure 352 MPa 534 MPa

3.3. Life Cycle Prediction We intended to predict the rail fatigue life using the S–N fatigue curve when the load results obtained from the structural analysis are applied to the grooved rail in the stabilization section in the variable gauge railway. The maximum principal stress values of the rails outlined in the preceding section are summarized as follows.

Outer surface on the grooved rail: 39.1 MPa (maximum principal stress) • Inner surface on the grooved rail: 67.4 MPa (maximum principal stress) • Bottom surface of the grooved rail: 37.3 MPa (maximum principal stress) • Maximum contact pressure between railroad wheel: 534 MPa • In reference [23], the S–N fatigue curve of UIC60 rail is given by the following formula:

S = 789.86 96.19logN. (2) − With the estimated endurance limit of about 180 MPa, the maximum principal stress level of 67.3 MPa is not likely to cause fatigue issues. However, the fatigue life assessment using Equation (2) based on the modiﬁed miner’s rule was executed for conservativeness. Utilizing the Soderberg fatigue criteria, the estimated fatigue counts were 39,878,000. With the assumption of 16 cargo trains passing 100 times per day, this is equivalent to an operational life of 34 years. These results are also predictable under load conditions in which the calculated vertical and lateral loads of the dynamic analysis are less than KRL-2012 design load requirements. In particular, the cross-sectional modulus of the grooved rail is greater than the normal rail, indicating that the bending stress caused by the vertical load is negligible. As a calculation result of contact pressure between wheels and railroads, the maximum contact pressure is at the 534 MPa level, and this can be compared with the data in the contact pressure and life in the reference [18], in which the contact pressure vs. cycles curve indicate 104 million cycles at the contract pressure level lower than 1 GPa. Although fatigue failure due to wear is not expected at the contact pressure level of 534 MPa from the data in the reference [18], the fatigue failure at the contact area is highly aﬀected by surface conditions and external environments, and that is why surface lubrication and maintenance need to be carried out regularly.

4. Conclusions and Suggestions The variable gauge railway and the bogie are mainly composed of unlocking parts to initiate the track gauge change, a widening railway track to change the gauge of the actual bogie axle and to stabilize the motion of the bogie. As a performance improvement subject of the release system of the variable gauge components and the gauge changing railroad, a dynamic ﬁnite element analysis was performed to evaluate the reliability and life of the release system and the railroad. Infrastructures 2020, 5, 80 13 of 14

In Section2, the contact that occurs between release disk and release rail on a variable gauge system is analyzed. We evaluated the contact pressure and the von Mises stress on the release rail to examine the life prediction of it. As a result of the structural analysis, the operational conditions and maintenance of the bogie are proposed by reviewing the bogie speed, fatigue life, and railroad lubrication conditions in terms of the stress and contact pressure added between the release disk and release rail. The proposed operation speed of the variable gauge bogie is 5 km/h. Given the stress level of 20 MPa, the release rail is free of fatigue issues. Only mild wear happens between the release rail and the release disk, and the application of lubricants will minimize the uncertainties in real engineering applications. In Section3, we analyzed the maximum principal stress of the stabilization rail considering two railroad-tie passing cases as boundary conditions. The calculated maximum principal stress of 67.4 MPa was analyzed to obtain fatigue life using the modiﬁed miner’s rule; the calculated life of the variable gauge railroad is about 34 years conservatively. Contact pressure generated in the rail in the variable gauge railroad is as low as not to cause a severe wear problem but it is highly aﬀected by surface conditions and external environments. Therefore, continuous maintenance such as surface lubrication and inspection is recommended.

Author Contributions: Conceptualization, D.K. and B.K.; methodology, Y.D.H.; software, Y.D.H.; validation, Y.D.H. and B.K.; formal analysis, B.K.; investigation, R.U.; resources, Y.D.H.; data curation, R.U.; writing—original draft preparation, R.U.; writing—review and editing, B.K.; visualization, R.U.; supervision, B.K.; project administration, B.K.; funding acquisition, D.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by a grant from the R&D Program of the Korea Railroad Research Institute, Korea, and by the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (P0012769, the Competency Development Program for Industry Specialist). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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