Research Into the Strength of an Open Wagon with Double Sidewalls Filled with Aluminium Foam

materials

Article Research into the Strength of an Open Wagon with Double Sidewalls Filled with Aluminium Foam

Oleksij Fomin 1 , Mykola Gorbunov 2, Juraj Gerlici 3 , Glib Vatulia 4, Alyona Lovska 5 and Kateryna Kravchenko 3,*

1 Department of Cars and Carriage Facilities, State University of Infrastructure and Technologies, Kyrylivska Str., 9, 04071 Kyiv, Ukraine; [email protected] 2 Department of Railway, Automobile Transport and Handling Machines, Volodymyr Dahl East Ukrainian National University, Central Avenue 59a, 93400 Sewerodonetsk, Ukraine; [email protected] 3 Department of Transport and Handling Machines, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovakia; [email protected] 4 Department of Structural Mechanics and Hydraulics, Ukrainian State University of Railway Transport, Feuerbach Square 7, 61050 Kharkiv, Ukraine; [email protected] 5 Department of Wagon Engineering and Product Quality, Ukrainian State University of Railway Transport, Feuerbach Square 7, 61050 Kharkiv, Ukraine; [email protected] * Correspondence: [email protected]; Tel.: +421-944-100-382

Abstract: The research is concerned with the use of double walls ﬁlled with aluminium foam for an open wagon in order to decrease the dynamic stresses during the operational modes. The research presents the strength calculation for the bearing structure of an open wagon with consideration of the engineering solutions proposed. It was found that the maximum equivalent stresses appeared in the bottom section of the centre sill behind the back support; they amounted to about 315 MPa and did not exceed the allowable values. The maximum displacements were detected in the middle Citation: Fomin, O.; Gorbunov, M.; section of the centre sill and amounted to 9.6 mm. The maximum deformations were 1.17 × 10−2. Gerlici, J.; Vatulia, G.; Lovska, A.; Kravchenko, K. Research into the The research also presents the strength calculation for a weld joint in the maximum loaded zones Strength of an Open Wagon with of the bearing structure of an open wagon and gives the results of a modal analysis of the bearing Double Sidewalls Filled with structure of the improved open wagon. It was found that the critical oscillation frequencies did Aluminium Foam. Materials 2021, 14, not exceed the allowable values. The results of the research may be useful for those who are 3420. https://doi.org/10.3390/ concerned about designing innovative rolling stock units and improving the operational efﬁciency of ma14123420 railway transport.

Academic Editor: Haim Abramovich Keywords: open wagon with double sidewalls; bearing structure; dynamic stresses; strength; transport mechanics Received: 4 May 2021 Accepted: 18 June 2021 Published: 20 June 2021 1. Introduction Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Higher operational efficiency of transportation can be ensured by introducing innova- published maps and institutional affil- tive design solutions for modern transportation facilities [1]. One of the most promising iations. industries is railway transport which requires introduction of new engineering solutions for the bearing structure of a rail car in order to maintain a leading place in the transportation market. These solutions will reduce the material capacity of freight wagons, increase the loading capacity and the average speeds of both loaded and empty freight wagons, improve anticorrosion and antifriction properties of the construction materials, prolong the service Copyright: © 2021 by the authors. life, and decrease the total production costs and operational expenditures. All of these may Licensee MDPI, Basel, Switzerland. This article is an open access article increase the operational efficiency of railway transport and improve its competitiveness distributed under the terms and both nationally and internationally. conditions of the Creative Commons 2. Analysis of Recent Research and Publications Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ The research into the fatigue strength of an open wagon body during operational 4.0/). loading modes is presented in [2,3]. The research was made for an open wagon C80B. The

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authors found that it is possible to predict the strength capacity of a body with the hybrid dynamic modelling and analysis by means of the finite element method. The theoretical and experimental research into the strength capacity of a freight wagon is given in [4]. The study included the normative operational loads on the wagon relative to the rail tracks. However, the authors did not study the issue of how to decrease the material capacity and dynamic loads on the bearing structure of an open wagon in operation. At the same time, tests were carried out for vertical loading and horizontal compression. The test results made it possible to determine the localisation of stress distribution zones in the load-bearing structure of the wagon. However, the research does not consider the prospects for improving the load-bearing structure of the wagon to increase the efficiency of its operation. However, the authors did not study the issue of how to decrease the material capacity and dynamic loads on the bearing structure of an open wagon in operation. The peculiarities of the structural and parametrical optimization of a wagon are studied in [5]. The evolutionary optimisation diagram of stem, plate, and plate–stem elements was conducted by the algorithm which selected variants of the bearing system by means of the target function criteria. Additionally, the authors considered random changes in the parameters and an exchange of parameters in the variant pairs for the bearing structure. Along with this, the authors do not conduct a study of the dynamic stresses of the proposed car design, and when compiling the design schemes, the standard values of the loads are taken into account. In addition, the paper does not consider the possibility of using materials with damping properties to reduce the dynamic stresses of the wagon in operation. The optimization of open-type freight wagon bodies with the bearing floor is given in [6]. The authors developed a combined algorithm of structural and parametrical optimisation for the side wall and the frame of an open wagon with the bearing floor intended for an axial load on 25 t/axle. However, the main design loads were taken as a quasi-static load in accordance with the normative documentations. Therefore, the authors did not determine the actual dynamic loads on the optimised wagon structure. At the same time, an increase in the axle load entails an increase in the dynamic stresses of the bearing structure, which necessitates the use of draft gear with increased energy consumption or the introduction of damping materials into the bearing structure. However, such studies are absent in this work. Computational modelling and simulations are nowadays widely used for design of railway vehicles, analysis and assessment of their dynamic properties, and also for detection and prediction of the mechanism of deterioration and sources of damages. In [7] (p. 1), the process of computational modelling of a freight wagon multibody system is outlined. The results of the dynamic stresses modelling of a wagon during movement are presented. The actual values of the dynamic loads acting on the bearing structure of the wagon were determined. The results obtained made it possible to formulate the requirements for the design of the modern rolling stock. However, the authors of the article did not carry out studies aimed at reducing the dynamic stresses of the bearing structure under operating conditions. The concept of designing a car body of aluminium panels is considered in [8]. A special feature of such panels is their sandwich-type structure. The characteristic search function for the optimal combination is based on the maximum stresses and displacements. However, the authors did not investigate the possibility of using damping material for the frame and beam elements of a wagon, as the most loaded elements of the carriage supporting structure. The special aspects of modernization for freight wagon bodies are considered in [9]. The authors proposed some measures for prolonging the service life of a wagon and improving the diagnostic systems for the technical state of the modernized wagon bodies. To increase the time between repairs of the wagon, the authors proposed strengthening Materials 2021, 14, x FOR PEER REVIEW 3 of 10 Materials 2021, 14, 3420 3 of 10

ening the structure in the interaction zones of the constituent elements, as well as the use theof anti structure-corrosion in the coatings. interaction However, zones this of the modernization constituent elements, is aimed as at well strengthening as the use the of anti-corrosionload-bearing structure coatings. of However, the wagons. this At modernization the same time, is the aimed possibility at strengthening of using materials the load- bearingwith damping structure properties of the wagons.to reduce Atthe the dynamic same time,stresses the of possibility the wagon ofin usingoperation materials is not withconsidered. damping properties to reduce the dynamic stresses of the wagon in operation is not considered.Study [10] deals with the topological optimization of a wagon body on the basis of the finiteStudy element [10] deals method. with the The topological results of optimization the research of a confirme wagon bodyd the on efficiency the basis of of the finitetechnique element proposed method. for The a wagon results body. of the It research was found confirmed that the the considered efficiency technique of the technique turned proposedout to be an for effective a wagon tool body. for It obtaining was found an that optimal the considered thin-walled technique structure. turned However, out to the be anauthors effective did toolnot forstudy obtaining the dynamic an optimal stresses thin-walled of the bearin structure.g structure. However, Due theto the authors fact that did notthe study optimized the dynamic design has stresses a lower of the mass, bearing then structure. in operation, Due to it the will fact experience that the optimized a greater designdynamic has load. a lower This mass, can influence then in operation, its strength. it will In experiencethis connection, a greater it is dynamic advisable load. to Thiscon- can influence its strength. In this connection, it is advisable to consider issues aimed at sider issues aimed at reducing the dynamic stresses of the bearing structure in operation. reducing the dynamic stresses of the bearing structure in operation. However, the authors However, the authors of the article did not pay attention to this. of the article did not pay attention to this.

3. Purpose and Tasks ofof thethe ResearchResearch The purpose of the research was to demonstrate demonstrate special features of the the strength strength calculation for the bearing structure of an open wagon with double sidewallssidewalls with fillerfiller during operational loading modes. To achieveachieve thethe objectiveobjective thethe followingfollowing taskstasks werewere set:set: − TToo design the bearing structure of an open wagonwagon with doubledouble sidewalls with fillerfiller (e.g.(e.g.,, aluminium foam) in the program software; − TToo calculate the dynamic stresses of the openopen wagonwagon bearingbearing structurestructure withwith doubledouble sidewalls filled filled with aluminium foam; − TToo calculate the strength of the bearing structure of an an open open wagon wagon with with double double sidewalls with filler; filler; − TToo calculatecalculate the strength of a weld joint in the contact area between the intermediate post and the cross bearer of an open wagon; and − TToo conduct a modal analysis of the bearing structure of an open wagon with double sidewalls with filler. filler.

4. Presentation of the Main Content of the Article The authors proposed the use of circular pipes for the bearing structure in order toto decrease the material material capacity capacity of of an an open open wagon. wagon. A A12 12-757-757 open open wagon wagon manufactured manufactured by byKryukovsky Kryukovsky Railway Railway Car Car Building Building Works Works (Ukraine) (Ukraine) was was taken taken as as the the prototype. The The authors explored explored the the possibility possibility to to achieve achieve a ahigher higher rigidity rigidity of ofthe the bearing bearing structure structure of an of anopen open wagon wagon of circular of circular pipes pipes filled filled with with aluminium aluminium foam foam (Figure (Figure 1). 1The). The sidewalls sidewalls and andthe end the doors end doors were were doubled doubled (Figure (Figure 2). This2). This solution solution is proposed is proposed at the at theconcept concept level, level, i.e., i.e.,scientific scientific idea idea in order in order to to consider consider the the feasibility feasibility of of using using aluminium aluminium foam foam in wagon wagon structures. Therefore, the issues of determining the optimal pore size and the technology of fillingfilling pipes with aluminium foam are notnot consideredconsidered inin thethe work.work.

Figure 1. Bearing structure of an open wagon of circular pipes ﬁlledfilled withwith aluminiumaluminium foam.foam.

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(a) (b)

FigureFigure 2. Components 2. Components of the of thebearing bearing structure structure of an of open an open wagon wagon of double of double walls walls (a) side (a) side wall; wall; (b) (b) endend wall. wall.

To Tosubstantiate substantiate the the proposed proposed solution, solution, the the dynamic dynamic stresses stresses of of the the open open wagon wagon with with a a fillerﬁller was was determined. determined. At At the the same same time, time, a amathematical mathematical model model was was formed formed (1) (1)–(3).–(3).

∙ + 2 ∙ + n·IWS ∙ ̈ ..+ ∙ ℎ ∙ ̈ .. = − ∙ ̇ . , (1) M + 2·m + ·x +M ·h·ϕ = P − c·x , (1) W b r2 W W W W ̇ ̇ ∙ ̈ + ∙ ̈ − ∙ ∙ = ∙ ∆ − ∆ + .( ∙ ∆ −. ∙ ∆); (2) .. 0 .. 0 IW ·ϕW + M ·xW − g·ϕW ·M = l·FFR sign∆1 − sign∆2 + l(k1·∆1 − k2·∆2); (2) ̇ ̇ ∙ ̈.. = ∙ ∆ + ∙ ∆ − ∆. − ∆.; (3) MW ·zW = k1·∆1 + k2·∆2 − FFR sign∆1 − sign∆2 ; (3) ∆= − ∙ ; ∆= + ∙ ; ∆1 = zW − l·ϕW; ∆2 = zW + l·ϕW; —mass of carrying structure of the wagon; —inertia moment of wagon rela- tiveM toW the—mass longitudinal of carrying axle; structure p—value of of the longitudinal wagon; IW impact—inertia force moment to automatic of wagon coupler; relative —tostiffness the longitudinal of the aluminium axle; p —valuefoam, of— longitudinalbogie mass; impact—inertia force moment to automatic of a wheel- coupler; set;c —stiffness—radius of the mean aluminium worn- foam,out wheel;mb—bogie —number mass; IofWS bogie’s—inertia axles; moment —half of a-base wheelset; of wagon;r—radius — ofabsolute the mean value worn-out of dry wheel; frictionn—number force in springof bogie’s group; axles; l—half-base, —rigidities of wagon; of springsFFR—absolute in bogie’s valuesuspension; of dry x friction, , force—coordinates in spring group; correspondingk1, k2—rigidities to longitudinal, of springs angularin bogie’s around suspension; longitudinal,xW, andϕW, verticalzW—coordinates displacements corresponding of the wagon, to longitudinal, respectively. angular aroundThe studies longitudinal, were carried and vertical out in displacementsa flat coordinate of system. the wagon, The respectively.case of a shunting col- lision wasThe taken studies into were account. carried At the out same in a flattime, coordinate it was taken system. into account The case that of a aforce shunting of 3.5 collisionMN acts wason the taken end into stop account. of the automatic At the same coupler. time, it When was taken solving into E accountquations that (1)– a(3), force it of was3.5 assumed MN acts that on the endwagon stop was of thebased automatic on a bogie coupler. type When18–100. solving The starting Equations conditions (1)–(3), it werewas taken assumed to be that zero. the Differential wagon was based equations on a werebogie solved type 18–100. in the The MathCad starting software conditions package,were taken which to implements be zero. Differential the Runge equations–Kutta method. were solved in the MathCad software package, whichIt was implements found that thethe Runge–Kuttamaximum acceleration method. of the open wagon bearing structure at It was found that the maximum2 acceleration of the open wagon bearing structure at the centre of mass was 34.6 m/s , which2 was 3% lower than the accelerations obtained for thethe structure centre of of mass round was tubes 34.6 without m/s , which filler and was 6% 3% lower lower than than the accelerations obtainedin the for the structure of round tubes without filler and 6% lower than the accelerations in the standard wagon design. standard wagon design. The strength of the bearing structure of an open wagon with consideration of the The strength of the bearing structure of an open wagon with consideration of the proposed engineering solutions was determined in the CosmosWorks software [11–15] proposed engineering solutions was determined in the CosmosWorks software [11–15] by means of the finite element method. The optimal number of elements in a mesh was by means of the finite element method. The optimal number of elements in a mesh was determined with the graphic analytical method [16–21]. Spatial isoparametric tetrahe- determined with the graphic analytical method [16–21]. Spatial isoparametric tetrahedrons drons were used as the finite elements; the optimal number of the elements was defined were used as the finite elements; the optimal number of the elements was defined with the with the graphic analytical method. The number of units in the mesh was 266,693, and graphic analytical method. The number of units in the mesh was 266,693, and the number the number of elements was 1,173,216. The maximum element size equalled 70 mm; the of elements was 1,173,216. The maximum element size equalled 70 mm; the minimal minimal element size was 14 mm. The minimum number of elements in a circle was 13; element size was 14 mm. The minimum number of elements in a circle was 13; the element the element size gain ratio in the mesh was 1.8. The maximum side ratio was 596.61; the size gain ratio in the mesh was 1.8. The maximum side ratio was 596.61; the percentage of elements with a side ratio of less than three was 61.4 and more than ten was 8.13.

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Materials 2021, 14, 3420 percentage of elements with a side ratio of less than three was 61.4 and more than5 ten of 10 was 8.13. st The design diagram included the vertical static load Pv on the bearing structure of st The design diagram included the vertical static load Pv on the bearing structure of an an open wagon, the longitudinal force Pl on the back support of an automatic coupler, open wagon, the longitudinal force Pl on the back support of an automatic coupler, and the

andpressure the pressure from the from bulk freightthe bulkPb freighton the sidePb andon the end side walls and (Figure end 3walls). The ( lateralFigure pressure 3). The lat- eralfrom pressure the bulk from freight the was bulk calculated freight was by calculated the technique by giventhe technique in [22]. Mineral given in carbon [22]. Mineral was taken as the bulk freight. carbon was taken as the bulk freight.

st st Figure 3. Design diagram of an open wagon: Pl—the longitudinal force, Pv —the vertical static load, Figure 3. Design diagram of an open wagon: Pl —the longitudinal force, Pv —the vertical static Pb—the bulk freight. load, Pb —the bulk freight. Steel 09G2S was taken as the material for the bearing structure of a wagon. The model wasSteel secured 09G2S in the was areas taken of support as the on material the gear for parts. the bearing structure of a wagon. The modelThe was maximum secured in equivalent the areas stressesof support appeared on the ingear the parts. bottom section of the centre sill behindThe the maximum back support; equivalent they amounted stresses to appeared about 315 in MPa the and bottom did not section exceed of the the allowable centre sill values [23–25]. The maximum displacements were detected in the middle part of the centre behind the back support; they amounted to about 315 МPа and did not exceed the al- sill; they amounted to 9.6 mm. The maximum deformations were 1.17 × 10−2. lowable values [23–25]. The maximum displacements were detected in the middle part of The calculation demonstrated that when aluminium foam was used as filler for the −2 thecentre centre sill, sill; the they maximum amounted equivalent to 9.6 mm. stresses The in maximum the bearing deformations structure of were an open 1.17 wagon × 10 . decreasedThe calculation by about 8%, demonstrated and displacements that wh decreaseden aluminium by 9% in foam comparison was used with as the filler similar for the centrevalues sill, for the circular-pipedmaximum equivalent bearing structure stresses ofin anthe open bearing wagon structure without of filler. an open The mass wagon decreasedof the bearing by aboutstructure 8%, of andan open displacements wagon increased decreased by 24% by in comparison 9% in comparison with that with of the the similarfiller-free values structure for the (at ancircular aluminium-piped foam bearin densityg structure of 300 kg/mof an 3open). wagon without filler. The massIn order of the to reduce bearing the structure sprung mass of an of open the wagons, wagon it increased is advisable by to 24% use in aluminium comparison withfoam that in the of the most filler loaded-free areas structure of the (at supporting an aluminium structure—namely, foam density the of centre300 kg/m beam,3). end beam,In andorder pinching to reduce nodes the ofsprung vertical mass struts of withthe wagons, cross beams it is ofadvisable the frame. to use At thealuminium same foamtime, in the the bearing most loaded structure areas mass of ofthe the supporting wagon will structure increase— bynamely, 3.4% in the comparison centre beam, with end beam,the structure and pinching of pipes nodes without of vertical filler. It isstruts important with cross to say beams that the of introduction the frame. At of roundthe same time,pipes the as load-bearingbearing structure elements mass of of the the open wagon wagon will provides increase aby 6% 3.4% reduction in comparison in material with theconsumption structure of compared pipes without with a filler. prototype It is important wagon. Consequently, to say that the taking introduction into account of theround use of aluminium foam, the mass of the wagon’s load-bearing structure is 2.6% lower than pipes as load-bearing elements of the open wagon provides a 6% reduction in material the standard one. In addition, the advisability of using aluminium foam is to reduce the consumption compared with a prototype wagon. Consequently, taking into account the dynamic stresses of the bearing structure due to the damping properties of the filler. use ofFigure aluminium4 demonstrates foam, the the mass comparative of the analysiswagon’s of load the stresses-bearing in structure the bearing is structure2.6% lower thanof an the open standard wagon one. of circular In addition, pipes (I), the of advisability circular pipes of with using filler aluminium (II), and of foam circular is to pipes reduce theand dynamic the double stresses side and of the end bea wallsring with structure filler (III). due to the damping properties of the filler. FigureThe data 4 demonstrates presented in Figure the comparative4 demonstrate analysis that the of minimum the stresses stresses in the on thebearing bearing structurestructure of an ofopen an openwagon car of were circular detected pipes for (І), variant of circular III. The pipes research with shows filler (ІІ) that, and the applica-of circular pipestion ofand filler the for do theuble circular-piped side and end bearing walls with structure filler decreases (ІІІ). the operational loading. TheThe data strength presented of the improvedin Figure bearing4 demonstrate structure that of anthe open minimum wagon stresses body was on studied the bear- ingthrough structure determination of an open of car the were strength detected of a weldfor variant joint in III. the The contact research areas shows of the mostthat the applicationloaded elements. of filler The for stress the strain circular state-piped calculation bearing for structure the bearing decreases structure the of aoperational wagon loading.body demonstrated that one of the most loaded areas is the contact assembly between the intermediate vertical brace and the cross bearer welded to each other (Figure5).

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Figure 4. Stresses on components of the bearing structure of a circular-piped wagon.

The strength of the improved bearing structure of an open wagon body was studied through determination of the strength of a weld joint in the contact areas of the most loaded elements. The stress strain state calculation for the bearing structure of a wagon

body demonstrated that one of the most loaded areas is the contact assembly between the FigureFigureintermediate 4. 4.Stresses Stresses vertical on on components components brace and of of the thethe bearing bearing cross structure bearer structure welded of of a circular-piped a circular to each-piped other wagon. wagon. (Figure 5). The strength of the improved bearing structure of an open wagon body was studied through determination of the strength of a weld joint in the contact areas of the most loaded elements. The stress strain state calculation for the bearing structure of a wagon body demonstrated that one of the most loaded areas is the contact assembly between the intermediate vertical brace and the cross bearer welded to each other (Figure 5).

FigureFigure 5. 5.Contact Contact assembly assembly between between the the intermediate intermediate vertical vertical post post and theand cross the cross bearer bearer of an openof an open wagon frame. wagon frame.

SinceSince the the proposed proposed bearing bearing structure structure of the ofopen the wagon open consists wagon of consists circular cross-of circular sectioncross-secti pipes,on thenpipes, when then calculating when calculating the welding the welding seams in seams the most in the loaded most zones, loaded the zones, technique given in [26,27] was used. In addition, this method was chosen due to the Figurethe technique 5. Contact given assembly in [26,27 between] was the used.intermediate In addition, vertical thispost methodand the crosswas bearerchosen of due an open to the factwagonfact that that frame. standard standard regulatory regulatory documents documents for thefor designthe design and and calculation calculation of wagons of wagons do not do not regulateregulate such such loading loading modes, modes, since since specialized specialized proﬁles profiles areused are used as load-bearing as load-bearing elements elements ofof the theSince bodies. bodies. the proposed bearing structure of the open wagon consists of circular The strength of the bearing structure of an open wagon body was calculated through cross-Thesecti strengthon pipes, of then the bearingwhen calculating structure theof an welding open wagon seams body in the was most calculated loaded zones, through the strength of a weld joint in the contact area between the intermediate vertical post and thethe technique strength ofgiven a weld in [26,27joint in] was the used.contact In area addition, between this the method intermediat was chosene vertical due postto the and the cross bearer of an open wagon. factthe thatcross standard bearer of regulatory an open wagon. documents for the design and calculation of wagons do not In operation, this assembly suffers the following deformations: tension/compression, regulateIn such operation loading, modes,this since assembly specialized suffers profiles the are following used as load deformations:-bearing elements ten- bending, and shearing. ofsion/compression, theAccording bodies. to [26 ,bending,27], the butt and joints shearing. of piped elements for the central tension/compression were calculatedTheAccording strength by of tothe the[26,27 formula: bearing], the structure butt joints of an open of piped wagon elements body was forcalculated the central through ten- thesion/compression strength of a weld were joint calculated in the contact by the area formula: between the intermediate vertical post and the cross bearer of an open wagon. N ≤ Rwy · γwc, (4) In operation, this assemblyπ · Dm · t suffers the following deformations: tension/compression, bending, and shearing. where D —average diameter of a pipe with a less wall thickness, mm; t—least wall thick- Accordingm to [26,27], the butt joints of piped elements for the central ten- ness of pipes connected, mm; Rwy—design resistance of a weld joint, kPa; γwc—coefﬁcient sion/compression were calculated by the formula: of the condition load effect for a weld joint.

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The calculation included the following parameters: Dm = 73.25 mm, t = 5.5 mm, Rwy −3 was calculated according to [27] and amounted to 328.57 × 10 MPa, γwc = 0.75. The longitudinal force value was determined with the assumption that the pressure force to the cross bearer of an open wagon body created a static impact and acted as the evenly distributed loading. The value of this loading equalled the maximum pressure loading to the post (the triangle foundation). By taking into account the surface of the post located inside the body, the authors determined the longitudinal force to the weld joint in the contact area between the intermediate post and the cross bearer. The calculation demonstrated that condition (4) was fulﬁlled, and the strength of a weld joint was provided. Additionally, the authors checked the strength of the weld joint when a circular pipe was attached to another detail (a circular pipe) under the action of the longitudinal force:

N ≤ 0.85 · (Swh + Swt), (5)

N ≤ 2 · Swh, (6)

N ≤ 2 · Swt, (7)

where Swh, Swt—bearing capacity of the root of weld and the face of weld deﬁned by the formula: Swh = td · lwah · Rwc · γwc + k f · lw f h · Rwd · γwc, (8)

where Rwd—corresponds to the numerical value Rw f or Rwz, a lower value is taken for calculation: 0.7 · Rw f or Rwz, kPa; Rw f and kwz—design resistance of an angular joint (conditional), respectively, by the weld metal and the weld fusion boundary, kPa; td—thickness of a pipe wall attached, mm; k f —height of an angular weld joint, mm; lwah and lwat—total length of the joint sections taken as butt joints, in the root of weld and the face of weld, respectively, mm; lw f h and lw f t—total length of the joint sections taken as angular joints in the root of weld and the face of weld, respectively, mm. On the basis of the calculation, it was found that the weld joint provided the needed strength. The following data were included in the calculation: td = 5.5 mm, lwah = 1.06 mm, lwat = 1.12 mm, kf = 4.5 mm (with consideration of the thickness of the pipe welded −3 −3 and the welding conditions), Rwd = 150.92 × 10 kPa (at Rwf = 215.6 × 10 kPa and −3 Rwd = 196 × 10 kPa). The research included a modal analysis of the bearing structure of an open wagon with double walls ﬁlled with aluminium foam by means of the design diagram (Figure3) and conducted in the CosmosWorks software. Some forms of the natural oscillations are given in Figure6. The natural oscillations obtained are given in Table1.

Table 1. Natural oscillation frequencies in the bearing structure of an open wagon.

Frequency, Hz Frequency, Hz Form of Oscillations (Filler-Free Construction) (Filled Construction) 1 17.012 16.047 2 17.543 16.661 3 28.567 27.645 4 28.678 28.958 5 30.521 29.738 6 38.654 38.146 7 40.121 39.094 8 42.015 41.921 9 47.656 46.46 10 50.651 49.573 Materials 2021, 14, 3420 8 of 10 Materials 2021, 14, x FOR PEER REVIEW 8 of 10

Figure 6.6. FormsForms ofof thethe oscillations oscillations of of the the bearing bearing structure structure of anof openan open wagon wagon (scale (scale 20:1) 20:1) (a) 1st (a) 1st natural frequency;frequency; ( b(b)) 2nd 2nd natural natural frequency; frequency; (c) ( 3rdc) 3rd natural natural frequency; frequency; (d) 4th(d) natural4th natural frequency. frequency.

TheThe datanatural presented oscillations in Table obtained1 demonstrate are given that in Table the natural 1. oscillation frequencies are within the allowable values [23,24]. At the same time, taking into account the use of aluminiumTable 1. Natural foam, oscillation the natural frequencies vibration in frequencies the bearing of structure the structure of an changeopen wagon. by 5% compared with the vibration frequencies of the structure without a filler. Frequency, Hz Frequency, Hz Form Of Oscillations 5. Conclusions (Filler-Free Construction) (Filled Construction) 1. The research1 shows the development of17.012 the bearing structure of an open16.047 wagon with double walls2 with filler (e.g., aluminium17.543 foam) in the program software.16.661 This solution will increase3 the rigidity of the bearing28.567 structure of an open wagon27.645 in operation and decrease4 the dynamic stresses and28.678 vulnerability under the most28.958 unfavourable operational5 modes. 30.521 29.738 2. The calculation6 of the dynamic stresses38.654 of the bearing structure of the38.146 open wagon with double7 sidewalls filled with filler was40.121 carried out. It was found that39.094 the maximum acceleration8 of the open wagon bearing42.015 structure at the centre of mass41.921 is 34.6 m/s2, which is 3%9 lower than the accelerations47.656 obtained for the structure of46.46 round tubes without filler10 and 6% lower than the accelerations50.651 in the standard wagon49.573 design. 3. By applying aluminium foam as filler for the centre sill, the maximum equivalent Thestresses data in presented the bearing in structureTable 1 demonstrate of an open wagonthat the decreased natural oscillation by about 8%, frequencies and are withindisplacements the allowable decreased values by 9%[23,24 in comparison]. At the same with time, the similar taking values into account for the bearing the use of aluminiumstructure foam, of circular the natural pipes withoutvibration filler. frequencies The mass ofof thethe bearing structure structure change of by an open5% com- paredwagon with the increased vibration by frequencies 24% in comparison of the structure with that without of the filler-free a filler. structure (at an aluminium foam density of 300 kg/m3). 5. ConclusionsIn order to reduce the sprung mass of the wagons, it is advisable to use aluminium foam in the most loaded areas of the supporting structure—namely, the centre beam, 1. Theend research beam, and shows pinching the development nodes of vertical of the struts bearing with structure cross beams of an of theopen frame. wagon At with doublethe same walls time, with the filler bearing (e.g. structure, aluminium mass foam) of the in wagon the program will increase software. by 3.4% This in solu- tioncomparison will increase with thethe structurerigidity of of the pipes bearing without structure filler. It of is importantan open wagon to say in that operation the andintroduction decrease of the round dynamic pipes as stresses load-bearing and v elementsulnerability of the under open wagonthe most provides unfavourable a 6% operationalreduction in modes. material consumption compared with a prototype wagon. Consequently, 2. Thetaking calculation into account of the usedynamic of aluminium stresses foam, of the the bearing mass of structure the wagon’s of the load-bearing open wagon withstructure double is 2.6% sidewalls lower thanfilled the with standard filler one.was carried out. It was found that the max- 4. imumThe research acceleration presents of thethe strengthopen wagon calculation bearing of structure a weld joint at inthe the centre contact of mass area be-is 34.6 m/stween2, which the intermediate is 3% lower post than and the crossaccelerations bearer of anobtained open wagon for the frame. structure The follow- of round tubesing deformations without filler in such and an6% assembly lower than were the taken accelerations into account: in tension/compression,the standard wagon de- R × −3 R × −3 sign.bending, and shearing. With wd = 150.92 10 kPa (at wf = 215.6 10 kPa × −3 3. Byand applyingRwf = 196 aluminium10 kPa), foam the as strength filler for of the weldcentre joint sill, wasthe providedmaximum at equivalent these deformations. stresses in the bearing structure of an open wagon decreased by about 8%, and displacements decreased by 9% in comparison with the similar values for the bearing structure of circular pipes without filler. The mass of the bearing structure of an

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5. The authors conducted a modal analysis of the bearing structure of an open wagon with double walls with ﬁller and obtained the main forms and the numerical values of the natural oscillation frequencies of the bearing structure of an open wagon. It was found that the natural oscillation frequencies did not exceed the allowable values. The research will be useful for those who are concerned about designing innovative rolling stock units and improving the operational efﬁciency of railway transport.

Author Contributions: Conceptualization, O.F., M.G. and A.L.; methodology, O.F., M.G. and A.L.; software, A.L.; validation, A.L., J.G. and G.V.; investigation, O.F., A.L. and K.K.; resources, O.F., A.L. and K.K.; writing—original draft preparation, O.F., A.L. and K.K.; writing—review and editing, M.G., J.G. and G.V.; visualization, O.F., A.L. and K.K.; supervision, M.G., J.G. and G.V. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the Slovak Research and Development Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic in the Educational Grant Agency of the Ministry of Education of the Slovak Republic in project No. VEGA 1/0558/18: Research of the interaction of a braked railway wheelset and track in simulated operational conditions of a vehicle running in a track on the test bench. The authors also gratefully acknowledge funding from the specific research on “Innovative principles for creating resource-saving structures of railroad cars based on the refined dynamic loads and functionally adaptive flash-concepts”, which was funded from the state budget of Ukraine in 2020. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest.

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