Dynamic Load Modelling Within Combined Transport Trains During Transportation on a Railway Ferry

applied sciences

Article Dynamic Load Modelling within Combined Transport Trains during Transportation on a Railway Ferry

Alyona Lovska 1, Oleksij Fomin 2 ,Václav Píštˇek 3,* and Pavel Kuˇcera 3

1 Department of Wagons, Ukrainian State University of Railway Transport, Feuerbach sq., 7, 61050 Kharkiv, Ukraine; [email protected] 2 Department of Cars and Carriage Facilities, State University of Infrastructure and Technologies, Kyrylivska str., 9, 04071 Kyiv, Ukraine; [email protected] 3 Institute of Automotive Engineering, Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic; [email protected] * Correspondence: [email protected]; Tel.: +420-541-142-271

Received: 2 July 2020; Accepted: 13 August 2020; Published: 18 August 2020

Abstract: The development of foreign economic activity of the Eurasian states led to the introduction of rail and ferry transportation. It is important to note that the current normative documentation does not fully cover the issues of transporting combined trains by sea. This can lead to a violation of the traffic safety of both the railway ferry and the transport of containers as part of combined trains by sea. In this connection, we investigated the dynamic loading of a container as part of a combined train when transported by a railway ferry. To ensure the stability of the container relative to the frame, we suggested an improvement of the load-bearing structure of a flat wagon. Additionally, we suggested the use of a viscous linkage between containers with the aim of reducing their dynamic load. To justify the suggested solutions, we carried out a mathematical modelling of the container dynamic load. The calculation was performed in MathCad. Due to the fact that the container has its own degree of freedom when transported by sea, the accelerations were separately determined for the supporting structure of the flat wagon and for the container. We found that the total amount of acceleration that acted on the container was 3.57 m/s2 (0.36 g) and on the load-bearing structure of the wagon was 2.47 m/s2 (0.25 g) which were, respectively, 38% and 23% less than the acceleration values in the typical scheme of their interaction. To determine the fields of acceleration distribution relative to the load-bearing structure of a flat wagon with containers, we carried out computer modelling of their dynamic load. The maximum percentage of discrepancy between the accelerations obtained by mathematical and computer modelling was 17.7%. The study will contribute to the creation of recommendations for the safe transport of combined trains by sea, as well as to increasing the efficiency of combined transport through international transport corridors.

Keywords: wagon; carrying structure; combined transportation; dynamics; strength

1. Introduction In the context of modern development of the transport industry, it is necessary to put into operation the combination of transport systems in order to maintain the leading positions of railway transport. In fact, container transportation is one of the most successful and widespread among combined transport systems. A signiﬁcant segment of this transport is carried out by sea transport. At the same time, the peculiarities of loading and transporting containers by sea are highlighted in research works [1–6]. To improve the eﬃciency of this type of transport, container trains are being transported by sea (see Figure1).

Appl. Sci. 2020, 10, 5710; doi:10.3390/app10165710 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 5710 2 of 15

According to the United Nations, the global maritime traffic is projected to grow by 3.8% in 2018–2023 [7]. Traffic is expected to increase across all sectors, with the fastest growing traffic being container and dry bulk traffic. In this connection, the issues of transporting trains of combined transport by sea are relevant. Transportation of container trains by sea is accompanied by loads on them that are not inherent in the operating conditions for the tracks. The typical scheme of interaction between a container and a flat wagon (fittings, fitting stops) in the conditions of fluctuations of the railway ferry does not provide stability of balance. This situation may contribute to violation of combined transport traffic safety [8]. The main causes of ship sinking are technical failures, human factors, route conditions, delivery factors, as well as factors associated with the transported cargo [9]. Natural factors—wind, waves, and sea currents—also have significant impacts on the safety of sea traffic. These reasons often cause a violation of the stability of the vessel and its sinking [10]. The consequences of the sinking of sea vessels, including rail ferries, can be associated with financial losses, loss of life, as well as environmental aspects [11,12]. It is known that ship accidents cause 14% of oil pollution of the environment. The duration of the existence of an oil slick and slick on the sea surface can reach several months. In addition, oil spills tend to move over considerable distances under the influence of wind and sea currents. Bulk cargo transported by sea is no less dangerous. In case of ship accidents, heavy metals are released into the environment, as well as other materials that negatively affect the ecology of the water area [13]. The study of the causes of the sinking of sea vessels for the transport of vehicles has shown that the main reason for the loss of stability is the displacement of the cargo. For example, in 2002, the rail ferry Mercury-2 sank in the Caspian Sea due to violation of the stability of tank wagons relative to the deck. On board of the vessel were 16 tank wagons with oil products, 1 wagon with consumer cargo, 8 passengers, and 42 crew members. The tank wagons fell off the mountings from the impact of the wave, slid in the direction of the ship’s tilt, and caused the ship to sink [14]. Of the people present on board, only nine were rescued and only four bodies of victims of the disaster were found. After 5 days of almost continuous patrolling of the tragedy from the air and at sea, the search activity was stopped by a decision of a specially created government commission. On 5 June 2009, off the coast of the island of Tonga (Indonesia), the cargo–passenger ferry Princess Ashika was lost. The reason for the overturning of the ferry was the shift of the cargo to one side or its incorrect loading while still in the port. On the deck of the ship there were 117 people and cargo (equipment, several ambulances, and trucks) [15]. There is a known case when, as a result of an unreliable anchorage in the Mediterranean Sea during a storm on 8 December 1966, on the Greek ferry ship “Heraklion”, a refrigerated trailer fell off the attachment and damaged the ferry gate through which water entered the cargo deck. As a result, the ship lost stability, threw on board, and sank [16]. Earlier, on 26 September 1954, during Typhoon Maria (Japan), five ferry ships of the Seikan N.R. company were lost, in chronological order: Hidaka Maru, Kitami Maru, No. 11 Seikan Maru, Tokachi Maru, and Toya Maru. The first four of them are railway ships, which were able to take on board 44 railway wagons [17]. The reason for the accidents of ferry ships is also the unreliable fastening of wagons on the decks. For example, on 8 September 1966, in the Skagerrak Strait (Norway), due to damage to the cargo gate, the Norwegian ferry Skagerrak lost its stability and turned over on board [18]. Therefore, the issues of transportation of railway vehicles by sea require special attention, as they concern both operational safety and environmental aspects. A study on dynamic load of the load-bearing structure of the wagon body during transportations on a railway ferry was given in [19,20]. There was a mathematical model describing the fluctuations of a wagon during the transportation on a railway ferry, taking into account the rigid interaction relative to the deck. The mathematical modelling results were confirmed by computer modelling. However, Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 14 Appl. Sci. 2020, 10, 5710 3 of 15 the fluctuations of a wagon during the transportation on a railway ferry, taking into account the rigid interaction relative to the deck. The mathematical modelling results were confirmed by the issue of container dynamic load within combined transport trains during transportation on a computer modelling. However, the issue of container dynamic load within combined transport railway ferry was not addressed in these works. trains during transportation on a railway ferry was not addressed in these works.

(a) (b)

Figure 1. Combined transport trains ( a) rolling of combined trains onto a rail ferry;ferry; (b) fastening a container train on the deck of a railway ferry.ferry.

Analysis of the load load-bearing-bearing structure of the new new-generation-generation flat flat wagon was was carried carried out out in in [ [2121].]. The paperpaper presentspresents thethe results results of of static static calculations calculations prepared prepared in in accordance accordance with with relevant relevant standards standards for thisfor this type type of construction. of construction Structural. Structural features features of a long of a baselong flatbase wagon flat wagon were covered were covered in [22]. in The [22 special]. The featurespecial offeature the wagon of the waswagon the was absence the ofabsence a spinal of beama spinal along beam the along length the of length the frame. of the The frame. results The of strengthresults of calculations strength calculations of the flat wagon of the load-bearing flat wagon load structure-bearing were structure given, which were weregiven, realized which inwere an ANSYSrealized finite in an elementANSYS software.finite element It is importantsoftware. toIt is note important that these to structures note that these of flat structures wagons did of notflat providewagons fordid thenot stability provide offor containers the stability when of containers transported when on a transported railway ferry. on a railway ferry. Forces acting on wagons during their transportation on a railway ferry by sea were determined in [23]. Investigations were carried out on anan open top wagon loaded with bulkbulk cargo.cargo. The definingdefining of container load load within within combined combined transport transport trains trains during during transportation transportation on onrailway railway ferries ferries has hasnot notbeen been paid paidattention attention to up to to up now. to now.Stress– Stress–strainstrain state of state a container of a container body, while body, lifting while it lifting by a crane it by aand crane dragging, and dragging, was analyzed was analyzed in [24]. Definition in [24]. Definition of strength of indicators strength indicators was carried was out carried in the out APM in theMachine APM package. Machine Experimental package. Experimental research of strength research was of strengthconducted was with conducted the help of with electrical the help strain of electricalgauging method. strain gauging Peculiarities method. of building Peculiarities a container of building for fruit a container and vegetable for fruit produce and vegetable transportation produce transportationwere highlighted were in highlighted [25]. The article in [25 included]. The article requirements included for requirements a container for body, a container provided body, its providedsuggested its structure suggested, as structure, well as illustrated as well as strengthillustrated calculations strength calculations on the basis on ofthe the basis finite ofthe element finite elementmethod. method.Significantly, Significantly, the study the of studycontainer of container dynamic dynamic load has load not hasbeen not conducted been conducted in the works in the worksmentioned mentioned above, above,but the butdefinition the definition of strength of strength indicators indicators has been has carried been out carried, taking out, into taking account into accountnormative normative values of values loads. of loads. Dynamic load load of of a container a container under under operational operational load modes load modes was determined was determined in [26]. The in [ obtained26]. The valuesobtained of values dynamic of dynamic loads were loads taken were intotaken account into account during during container container strength strength calculations calculations in anin ANSYSan ANSYS environment. environment. Peculiarities Peculiarities of floorof floor strength strength calculations calculations for for a 40-feet a 40-feet container container conducted conducted in Abaqusin Abaqus/CAE/CAE v 6.1v 6.1 complex complex were were outlined outlined in in [27 [27].]. Recommendations Recommendations werewere oofferedffered inin termsterms ofof safe operation of of this this type type of of container. container. Measures Measures aimed aimed at reduction at reduction of the of container the container dynamic dynamic load during load combinedduring combined transportation transportation have not have been not off beenered inoffered the works in the considered works considered above. above. The methodology for determining the forces acting on a wagon during transportation by a railway ferry is presented in [28]. A A brief brief outline outline of of the the development of of ferry ferry services services is is provided. provided. TheThe technology of fixingfixing wagons on the decks of railway ferries is considered. The main forces acting on the wagon during the ferry rolling are determined. In this case, the dynamic load on the wagon is determined by didifferentiatingfferentiating the law of motion of the seasea wave.wave. Moreover,Moreover, the paper considers the issues of carriage stability on deck in conditionsconditions ofof seasea waves.waves. At the same time, the author does not propose measures to improve the wagon’s supporting structure in order to adapt to safe transportation on a railway ferry. Appl. Sci. 2020, 10, 5710 4 of 15 propose measures to improve the wagon’s supporting structure in order to adapt to safe transportation on a railway ferry. In the study by [29], design features and the interaction of means for securing wagons on the decks of railway ferries that are operated in the Caspian Sea are considered. Moreover, special ship devices that are used on railway ferries serving the main world ferry routes are considered in the work. The issues of carriage fastening on railway ferries are regulated [30]. Recommendations on the use of removable fasteners and wagon location on a ship as well as safety requirements for mounting wagons on decks are given. There are also other analogues of this document [31,32]. It is important to note that the removable fasteners (chain ties with lashings) have a rigid interaction with the supporting structure of the wagons and do not provide the possibility of reducing their dynamic load. Therefore, the goal of this article was to study the dynamic load of a container placed on a flat wagon, taking into account their viscous interaction during transportation on a railway ferry. To achieve this goal, the following tasks are defined:

- To improve the load-bearing structure of the flat wagon in order to ensure the stability of containers during transportation by a railway ferry. This is done by placing removable superstructures on the wagon-supporting structure. At the same time, on the inner surface of the superstructures, there is a material with viscous energy-absorbing properties - To conduct mathematical modelling of the dynamic load of containers, taking into account the new scheme of interaction with the flat wagon. The simulation results will make it possible to determine the more precise definition of the dynamic load, which acts on the supporting structure of the flat wagon during transportation by sea - To conduct a computer simulation of the dynamic load of containers, taking into account the new scheme of interaction with the flat wagon. The results of computational modelling will make it possible to determine the numerical values of accelerations and their dislocation fields on the supporting structure of a flat wagon with containers, as well as to check the adequacy of the developed mathematical model.

2. Improvement of the Load-Bearing Structure of the Flat Wagon The purpose of this section is to highlight the features of improving the supporting structure of a flat wagon for the safe transportation of containers on a rail ferry by sea. Research conducted by the authors of the article has established that the typical scheme of interaction between the wagon and the container does not ensure the stability of the container during sea transportation [8]. In this regard, it is advisable to use wagons of model 13-9744 (TU 3182-002-47766175-2004) with special superstructures for transporting containers as part of combined trains. It is also possible to install such removable superstructures on the supporting structures of other models of wagons that are used for railway and ferry transport. Since the fleet of universal flat wagons has a larger number of units than a specialized one, such a solution will allow for the adaptation of universal flat wagons for the carriage of containers by sea on railway ferries. As part of this study, the model 13-401 wagon was selected as a prototype. This model of a flat wagon was chosen as a prototype because there is a project of its modernization for container transportation, developed by the Research and Development Centre “Wagons” (Russia). This modernization consists of placing fitting stops on the supporting structure for fastening and transporting containers. However, the authors of the article propose further improvement of this wagon for the possibility of safe transportation of containers by sea. The load-bearing structure of the wagons, in view of the installation of removable superstructures, is shown in Figure2. Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 14

Appl.Appl. Sci. 20202020,, 1010,, 5710x FOR PEER REVIEW 55 ofof 1514

(a) (b) Figure 2. Flat wagon of model(a) 13-401: (a) typical design of a flat wagon;( b(b) ) improved flat wagon design. FigureFigure 2.2.Flat Flat wagon wagon of of model model 13-401: 13-401 (a:) ( typicala) typical design design of a flatof a wagon; flat wagon; (b) improved (b) improved flat wagon flat design.wagon designFor fastening. containers on the main longitudinal beams of the frame, hinged fitting stops are installed,For fastening which containers makes it possibleon the main to longitudinal transport containers beams of the of differentframe, hinged standard fitting sizes. stops Theare For fastening containers on the main longitudinal beams of the frame, hinged fitting stops are installed,superstructures which makes interact it possible with the to supporting transport containers structure ofby di welding.fferent standard The load sizes.-bearing The superstructureselements of the installed, which makes it possible to transport containers of different standard sizes. The interactsuperstructures with the supporting are made of structure the same by profiles welding. as The on load-bearing the 13-9744 elementsflat wagon. of theThe superstructures installing of a superstructures interact with the supporting structure by welding. The load-bearing elements of the arematerial made with of the viscous same profiles properties as on on the the 13-9744 internal flat surfaces wagon. of The superstructures installing of a materialhas been withproposed viscous to superstructures are made of the same profiles as on the 13-9744 flat wagon. The installing of a propertiesreduce the on dynamic the internal load surfaces of containers of superstructures. Elastomer is has one been option. proposed When to the reduce supporti the dynamicng structure load ofof material with viscous properties on the internal surfaces of superstructures has been proposed to containers.the container Elastomer interacts iswith one such option. material, When partial the supporting damping structureof natural of vibrations the container occurs, interacts which withtakes reduce the dynamic load of containers. Elastomer is one option. When the supporting structure of suchplace material, during the partial roll dampingof the ship. of It natural is possible vibrations to use occurs, other materials which takes with place similar during energy the- rollabsorbing of the the container interacts with such material, partial damping of natural vibrations occurs, which takes ship.properties. It is possible to use other materials with similar energy-absorbing properties. place during the roll of the ship. It is possible to use other materials with similar energy-absorbing 3.properties. Mathematical Modelling of the Dynamic Load of Containers 3. Mathematical Modelling of the Dynamic Load of Containers To determine the dynamic loads that act on the supporting structure of the flat wagon and 3. MathematicalTo determine Modelli the dynamicng of the loads Dynamic that actLoad on of the Containers supporting structure of the flat wagon and container, we carried out mathematical modelling. The calculation scheme is shown in Figure3, container, we carried out mathematical modelling. The calculation scheme is shown in Figure 3, whereinTo determinethe angular the movements dynamic loadsof the thatrailway act ferryon the relative supporting to the structure longitudinal of the axis, flat which wagon passes and wherein the angular movements of the railway ferry relative to the longitudinal axis, which passes throughcontainer, its centerwe carried of gravity, out mathematical are taken into account.modelling This. The type calculation of oscillation scheme in seafaring is shown practice in Figure is called 3, through its center of gravity, are taken into account. This type of oscillation in seafaring practice is rolling.wherein In the the angular “dynamics movements of wagons”, of the such railway vibrations ferry relative are called to lateralthe longitudinal pitching. Whenaxis, which transporting passes called rolling. In the “dynamics of wagons”, such vibrations are called lateral pitching. When wagonsthrough byits sea,center the of lateral gravity, rolling are taken of a railwayinto account. ferry hasThis the type greatest of oscillation impact in on seafaring their stability practice with is transporting wagons by sea, the lateral rolling of a railway ferry has the greatest impact on their respectcalled rolling. to decks. In the “dynamics of wagons”, such vibrations are called lateral pitching. When stability with respect to decks. transporting wagons by sea, the lateral rolling of a railway ferry has the greatest impact on their stability with respect to decks.

FigureFigure 3.3. DiagramDiagram ofof aa ﬂatflat wagonwagon withwith aa container.container. Figure 3. Diagram of a flat wagon with a container. Appl. Sci. 2020, 10, 5710 6 of 15

At the same time, we considered that fixing the wagon relative to the deck of the railway ferry should be carried out according to a standard scheme. In other words, to de-load the spring suspension of the flat wagon, we used four mechanical stop-jacks, which were installed under the pivot beams of the frame. Eight chain binders were also used, which were attached to the supporting structure of the wagon at one end, and to the deck eye at the other. We also installed break shoes under the end wagons in the couplings. The end wagons in the couplings also interact with dead-end stops. A mathematical model developed by the authors that describes the movement of the supporting structure of a flat wagon with containers during oscillations of a railway ferry is given below:

.. . .  Iθ q + Λ B q = p h + Λ B F(t),  S · 1 θ· 2 1 w0 · 2 θ· 2 ·  θ .. hw c h  Iwag q = pwag0 + Mwag + Mwag,  (1) · 2 · 2  θ .. hc . wag  I q = p β hc q + M ,  c · 3 c0· 2 − · · 3 c where q θn—generalized coordinate that corresponds to the angular movement around the 1 ≈ longitudinal axis of a railway ferry; q θw—generalized coordinate, which corresponds to the 2 ≈ angular movement around the longitudinal axis of the flat wagon; q3 θc—generalized coordinate that ≈ θ corresponds to the angular movement around the longitudinal axis of the container; IS —moment of inertia; B—width; h—depth; Λθ—coefficient of resistance to vibrations; pw0 —wind load on the surface projection; F(t)—law of action of the effort that causes the movement of a railway ferry with wagons θ placed on its decks; Iw—moment of inertia of the flat wagon; hw—height of the side surface of the flat c wagon; pwag0 —wind load on the side surface of the flat wagon; Mwag—moment of forces that occurs between the flat wagon and the deck of a railway ferry during angular movements relative to the h longitudinal axis; Mwag—moment of forces that occurs between the flat wagon and containers during θ angular movements relative to the longitudinal axis; Ic —moment of inertia of a container; hc—height wag of the side surface of the container; pc0—wind load on the side surface of the container; Mc —moment of forces that occurs between the container and the flat wagon during angular movements relative to the longitudinal axis; β—coefficient of viscous resistance between the load-bearing structure of the flat wagon and the container. It is important to note that this mathematical model has no analogues, since the proposed technical solutions were developed by the authors of the article. Previously, the issues of transporting combined trains by sea, as well as the improvement of the supporting structures of flat wagons for safe transportation by sea, were not considered. The moment of inertia of a vessel was determined according to the classical formula [33]

D Iθ = B2 + 4z2 , (2) s 12g g where D is ship displacement, and zg is coordinate of the center of gravity. The coordinate of the center of gravity of a vessel with cargo on board is determined by [33]

1 X zg = D zc + m1z1 + m2z2 + + mnzn, (3) D + m + m + + mn · ··· 1 2 ··· where m1, m2, ... , mn are cargo masses, and z1, z2, ... , zn are distances of the center of gravity of the cargo from the main plane (keel). The distance of the center of gravity of the vessel above-water surface from the current waterline is given by S1zc + m1z01 + m2z02 + + mnz0n zc = ··· , (4) S + S + + Sn 1 2 ··· where S1, S2, ... , Sn are areas of ﬁgures into which the side projection of the surface of the ship is divided, and z01, z02, ... , z0n are distances of the center of gravity of areas S1, S2, ... , Sn from the current waterline. Appl. Sci. 2020, 10, 5710 7 of 15

Determination of the coeﬃcient of resistance to vibrations of a railway ferry was carried out according to the method given in [33,34]. When determining the accelerations that act on the ﬂat wagon with containers, the course angles of the wave in relation to the body of the railway ferry are taken into account

χ = kλ L cos(α), (5) · · where kλ is a coefficient that depends on the shape of the vessel contours, L is length of the vessel, and α is the angle of the wave relative to the body. During the model building process, the impact action of sea waves was not taken into account. The motion of the wave was described as a trochoidal law. When determining the moments of forces arising between the flat wagon and the deck, as well as between the flat wagon and the container, we took into account the horizontal components of the gross weight of the flat wagon and the container, respectively. Since container trains are placed on the decks of a railway ferry and repeat its trajectory during oscillations, we took into account the technical characteristics of the vessel when creating and solving the mathematical model (1). Accelerations that act directly on the railway ferry and on container trains placed on decks depend on these characteristics. Calculations were made for the railway ferry “Heroes of Shipka”, running in the Black Sea waters. The main technical characteristics of the railway ferry are given in Table1[35].

Table 1. Main technical characteristics of the ship ferry “Heroes of Shipka”.

Parameter Name Value Length, m: Maximum 184.25 Between perpendiculars 170 Width 26 Height, m: To the upper deck 15.2 To the main deck 9 Draft, m 6.5 Deadweight, t 12,889 Displacement, t 23,744 Speed, knots 18.6 Wagon capacity, pcs. 108

The parameters of the disturbing eﬀect (sea waves) were determined on the basis of the reference literature (Table2)[36].

Table 2. Parameters of sea waves used in mathematical modelling.

Parameter Name Numerical Value Sea wave height, m 8 Sea wave period, s 9 Heading angle of a wave, degree 0–180 Wind pressure on the surface projection of the vessel, kPa 1.47

The solution of the system of differential Equation (1) was performed using the Runge–Kutta method in the MathCad environment [37–43]. For this purpose, the transition was made from systems of second-order differential equations to systems of first-order differential equations, followed by the use of standard algorithms for solving systems using the rkfixed function of Mathcad. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14

That is, when 푦1 = 휃1, 푦2 = 휃̇1, 푦3 = 휃2, 푦4 = 휃̇2, 푦5 = 휃3, 푦6 = 휃̇3, it follows that

푦2 푦4 | 푦6 | ′ ℎ 퐵 퐵 푝푤 ∙ + 훬휃 ∙ ∙ 퐹̇ (푡) − (훬휃 ∙ ) 푦2 | 2 2 2 | 퐼휃 푄(푡, 푦) = 푆 , ℎ 푝′ ∙ 푤 + 푀푐 + 푀ℎ (6) | 푤푎𝑔 2 푤푎𝑔 푤푎𝑔 | 휃 퐼푤푎𝑔 ℎ | 푝′ ∙ 푐 − 훽 ∙ ℎ ∙ 푞̇ + 푀푤푎𝑔 | 푐 2 푐 3 푐 휃 퐼푐 ′ 푍 = 푟푘푓𝑖푥푒푑(푌0, 푡푛, 푡푘, 푛 , 푄), where Y0 is a vector containing the initial conditions, tn and tk are values that define the initial and final integrationAppl. Sci. 2020, 10variable,, 5710 n’ is fixed number of steps, and Q is character vector. 8 of 15 The initial displacements and velocities were assumed to be zero. The coefficient of viscous resistance should be in this case in. the range 0.5. –1.2 kN∙s/m. On. the basis of the calculations, we That is, when y1 = θ1, y2 = θ1, y3 = θ2, y4 = θ2, y5 = θ3, y6 = θ3, it follows that found that the greatest acceleration values occurred when the course angles of the wave in relation

y to the body of the railway ferry were χ = 60° and2 χ = 120°. At the same time, the maximum y acceleration of the container was about 1.5 m/s2 (see4 Figure 4) of the flat wagon 0.4 m/s2 (see Figure y6 . 5). The numerical values of accelerations wereh givenB withoutB taking into account the component of pw0 +Λθ F(t) (Λθ )y2 · 2 · 2 · − · 2 gravitational acceleration. Q(t, y) = Iθ , S (6) p hw +Mc +Mh The total amount of acceleration can be determined:wag0 · 2 wag wag θ Iwag . wag p hc β h q +M 휃̈ =c0 휃2̈ +c 3푔 ∙ csin휃, (7) 푡 · 푝푟푡− · θ· Ic Z = rk f ixed(Y0, tn, tk, n0, Q), where 휃̈푝푟푡 is acceleration, which applies to the regular position of the flat wagon with containers on the deckwhere; g isY 0gravitationalis a vector containing acceleration the initial; and conditions, θ is rolltn angleand tk ofare the values railway that define ferry. the initial and Consideringfinal integration the variable, hydrometeorological n’ is fixed number of characteristics steps, and Q is character of the vector. Black Sea area and the surface projection Theof a initial railway displacements ferry of the and “Heroes velocities of were Shipka assumed” type, to be we zero. obtained The coe affi valuecient ofof viscous θ = 12.2° for the resistance should be in this case in the range 0.5–1.2 kN s/m. On the basis of the calculations, we found roll angle of a railway ferry. The roll value was calculated· for the case of static wind action on the that the greatest acceleration values occurred when the course angles of the wave in relation to the body surface projection of a railway ferry [33]. Then, the total amount of acceleration that acts on the of the railway ferry were χ = 60◦ and χ = 120◦. At the same time, the maximum acceleration of the containercontainer was was3.57 about m/s 1.52 (0.36 m/s2 (seeg), Figureand on4) of the the flatload wagon-bearing 0.4 m /structures2 (see Figure of5 ).the The flat numerical wagon values was 2.47 m/s2 (0.25 g).of accelerations were given without taking into account the component of gravitational acceleration.

FigureFigure 4. Accelerations 4. Accelerations acting acting on on the the load-bearingload-bearing structure structure of the of ﬂat the wagon flat wagon when transported when transported on a on a railway ferry. railway ferry. Appl. Sci. 2020, 10, 5710 9 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 14

FigureFigure 5. Accelerations 5. Accelerations applied applied to thethe container container during during transportation transportation on a railway on a ferry.railway ferry.

The total amount of acceleration can be determined: Therefore, the introduction of a viscous connection between the load-bearing structure of the .. .. flat wagon and the containers made itθ t possible= θprt + g tosin reduceθ, the dynamic load by 38% (7) and 23%, · respectively,.. compared to the typical interaction scheme. Dynamic load is the main factor that affects the stabilitywhere θofprt ais flat acceleration, wagon whichwith containers applies to the when regular transported position of the on flat a wagonrail ferry. with Consequently, containers on due to the deck; g is gravitational acceleration; and θ is roll angle of the railway ferry. the decreaseConsidering in the dynamic the hydrometeorological load that acts characteristics on the container of the Black placed Sea area on and the the flat surface wagon, projection its stability is also improvedof a railway during ferry of oscillations the “Heroes of of Shipka” the railway type, we ferry. obtained a value of θ = 12.2◦ for the roll angle of a railway ferry. The roll value was calculated for the case of static wind action on the surface projection 4. Resultsof a railway ferry [33]. Then, the total amount of acceleration that acts on the container was 3.57 m/s2 (0.36 g), and on the load-bearing structure of the flat wagon was 2.47 m/s2 (0.25 g). To checkTherefore, the adequacy the introduction of the of mathematical a viscous connection model between (1), we the load-bearingcarried out structurea computer of the simulation flat of the dynamicwagon and load the of containers a container made itplaced possible on to reducea flat wagon. the dynamic For load computer by 38% and simulation 23%, respectively, of the dynamic load ofcompared a flat wagon to the typical with interactioncontainers scheme. based Dynamic on the load suggested is the main solution, factor that we affects used the stabilitythe CosmosWorks of packagea flat [44 wagon–47]. withThe containers calculation when was transported done using on a rail the ferry. finite Consequently, element duemethod. to thedecrease Spatial in isoparametric the dynamic load that acts on the container placed on the flat wagon, its stability is also improved during tetrahedraoscillations were ofused the railwayto build ferry. the finite element model. The optimal number of finite elements was determined by the graphical and analytical method [48–51]. The number of nodes was 302,512 and the number4. Results of elements was 883,801. The maximum element size was 100 mm, the minimum size was 20 mm.To checkThe design the adequacy scheme of the considered mathematical that model the (1),carrying we carried structure out a computer was affected simulation by ofthe vertical load ofthe the dynamic container load gross of a container weight placedPgw, the on tension a flat wagon. of chain For binders computer P simulationf, the wind of load the dynamic Pw, as well as the load of a flat wagon with containers based on the suggested solution, we used the CosmosWorks horizontal load of the container on superstructure Ph, due to fluctuations of the flat wagon (see package [44–47]. The calculation was done using the finite element method. Spatial isoparametric Figuretetrahedra 6). Since were the used chain to build coupler the finite has element certain model. angles The of optimal inclination number relative of finite elements to the waswagon when securing,determined when creating by the graphical the computational and analytical method scheme, [48 –the51]. load The number that is of transmitted nodes was 302,512 to the and supporting structurethe numberof the flat of elements wagon wasthrough 883,801. the The chain maximum coupler element is laid size out was in 100 three mm, thecomponents. minimum size At the same time, thewas angle 20 mm. ofThe inclination design scheme of the considered chain coupler that the was carrying taken structure into account: was affected in the by theplane vertical YZ, the angle of inclinationload of the was container 30°, for gross XY weightand XZPgw it, thewas tension 60°. of chain binders Pf, the wind load Pw, as well as the horizontal load of the container on superstructure Ph, due to fluctuations푐 of the flat wagon (see The container was subjected to the vertical static load 푃푣 , the horizontal load in the areas of 푐 푐 interaction with superstructures 푃ℎ , as well as the wind load on the side surface 푃푤. Fixing the model was carried out in the areas where it rests on the bogies as well as the working surfaces of mechanical stop-jacks. To do this, the model was fitted with pads, the area of which was equal to the area of the working surfaces of the stop-jacks. The carrying structure material was 09G2S [52–54]. Between the interaction zones of the container and the superstructures of the flat wagon, we established a viscous linkage with a coefficient of viscous resistance 1.2 kN∙s/m. The results of calculating the acceleration of a container placed on a flat wagon, taking into account different roll angles of a railway ferry, are shown in Figure 7. The maximum acceleration in this case affected the upper part of the containers along the central axis of the symmetry of the load-bearing structure of the flat wagon and was about 2.6 m/s2. Appl. Sci. 2020, 10, 5710 10 of 15

Figure6). Since the chain coupler has certain angles of inclination relative to the wagon when securing, when creating the computational scheme, the load that is transmitted to the supporting structure of the ﬂat wagon through the chain coupler is laid out in three components. At the same time, the angle of inclination of the chain coupler was taken into account: in the plane YZ, the angle of inclination was 30Appl.◦, forSci. 20 XY20 and, 10, x XZ FOR it PEER was REVIEW 60◦. 10 of 14

Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 14

Figure 6. Design scheme of the load load-bearing-bearing structure of the ﬂatflat wagon with a container.container.

Pc The container was subjected to the vertical static load v, the horizontalAX (m/s2) load in the areas of interaction with superstructures Pc , as well as the wind load on the side surface Pc . h 2.617 w Fixing the model was carried out in the areas where it rests on the bogies as well as the working surfaces of mechanical stop-jacks. To do this, the model was fitted2.347 with pads, the area of which was equal to the area of the working surfaces of the stop-jacks. The carrying2.077 structure material was 09G2S [52–54]. Between the interaction zones of the container and the1.806 superstructures of the flat wagon, we established a viscous linkage with a coefficient of viscous resistance 1.2 kN s/m. The results 1.536 · of calculating the acceleration of a container placed on a flat wagon, taking into account different roll 1.266 angles of a railway ferry, are shown in Figure7. The maximum acceleration in this case a ffected the upper part of the containers along the central axis of the symmetry of the9.962 load-bearing×10−1 structure of the flat wagon and wasFigure about 6. 2.6 Design m/s scheme2. of the load-bearing structure of the flat7.260 wagon×10 with−1 a container. 4.559×10−1 AX (m/s2) 1.858×10−1 2.617 –8.428×10−2 2.347 –3.544×10−2 2.077 −2 –6.2451.806×10 1.536 1.266 Figure 7. Distribution of acceleration fields relative to the load-bearing structure9.962 of×10 a −flat1 wagon with containers. 7.260×10−1 4.559×10−1 The accelerations acting on the container obtained by theoretical and computer modelling are × −1 shown in Figure 8, which shows that the maximum percentage of discrepancy1.858 between10 accelerations −2 was 17.7% at the roll angle 10°. –8.428×10 Thus, given the viscous connection between the flat wagon and–3.544 the×10 −2 container during transportation on a railway ferry, it becomes possible to reduce the dynamic–6.245 ×load10−2 of the container supporting structure and improve the safety of sea transport. FigureThe F- 7.criterionDistribution was usedof acceleration to check fields the adequacy relative to ofthe the load-bearing mathematical structure and of computer a flat wagon models with containers. developed by theFigure authors. 7. Distribution The roll of acceleration angle of thefields railway relative toferry the load was-bearing taken structure into account of a flat wagonas a variation with parameter (5°containers.–30°). If the value of the dispersion adequacy Sa = 6.0 and the dispersion reproducibility Sy = 4.21, the calculated value of the criterion was Fp = 1.41, which was less than The accelerations acting on the container obtained by theoretical and computer modelling are tabular Ft = 4.53. Hence the hypothesis of adequacy was not rejected. shown in Figure 8, which shows that the maximum percentage of discrepancy between accelerations was 17.7% at the roll angle 10°. Thus, given the viscous connection between the flat wagon and the container during transportation on a railway ferry, it becomes possible to reduce the dynamic load of the container supporting structure and improve the safety of sea transport. The F-criterion was used to check the adequacy of the mathematical and computer models developed by the authors. The roll angle of the railway ferry was taken into account as a variation parameter (5°–30°). If the value of the dispersion adequacy Sa = 6.0 and the dispersion reproducibility Sy = 4.21, the calculated value of the criterion was Fp = 1.41, which was less than tabular Ft = 4.53. Hence the hypothesis of adequacy was not rejected. Appl. Sci. 2020, 10, 5710 11 of 15

The accelerations acting on the container obtained by theoretical and computer modelling are shown in Figure8, which shows that the maximum percentage of discrepancy between accelerations Appl.was Sci. 17.7% 2020, at10,the x FOR roll PEER angle REVIEW 10◦. 11 of 14

Figure 8. Dependence of container accelerations on the roll angle of a railway ferry and differences in Figure 8. Dependence of container accelerations on the roll angle of a railway ferry and differences in the results of the theoretical and computer solution in percent. the results of the theoretical and computer solution in percent. Thus, given the viscous connection between the flat wagon and the container during transportation In the future, it is planned to conduct a physical experiment aimed at studying the dynamic on a railway ferry, it becomes possible to reduce the dynamic load of the container supporting structure load of a container placed on a flat wagon during transportation by sea. and improve the safety of sea transport. The F-criterion was used to check the adequacy of the mathematical and computer models 5. The Discussion of the Results developed by the authors. The roll angle of the railway ferry was taken into account as a variation parameterTo ensure (5◦–30 the◦ ).safe If thetransportation value of the of dispersion containers adequacy as part of Sa combined= 6.0 and thetrains dispersion on railway reproducibility ferries, we proposedSy = 4.21, the the improve calculatedment value of the of supporting the criterion structure was Fp of= the1.41, flat which wagon. was A less feature than of tabular the flat F wagont = 4.53. isHence the presence the hypothesis of superstructures, of adequacy the was inner not rejected. surface of which is equipped with a viscous material with energyIn the- future,absorbing it is properties. planned to conductTo substantiate a physical the experimentproposed technic aimedal at solution, studying the the authors dynamic have load createdof a container a mathematical placed on model a flat that wagon describes during the transportation process of moving by sea. the supporting structure of a flat wagon with containers during the rolling of a railway ferry. The limitation of the model is that it does5. The not Discussion take into accoun of thet Resultsthe shock effect of sea waves on the hull of the rail ferry. In addition, the modelTo cannot ensure be the used safe to transportationstudy the dynamic of containers loading of as a parttank of container. combined The trains results on railwayof solving ferries, the mathematicalwe proposed the model improvement made it possibleof the supporting to determine structure the of accelerations the flat wagon. as A the feature comp ofonents the flat of wagon the dynamicis the presence loads that of superstructures, act on the supporting the inner structure surface of of the which flat wagon is equipped with withcontainers. a viscous In this material case, withthe accelerationenergy-absorbing to the properties.supporting Tostructure substantiate of the the flat proposed wagon was technical 0.25g solution,(Figure 4), the and authors on the have container created wasa mathematical 0.35g (Figure model 5). that describes the process of moving the supporting structure of a flat wagon withTo containers determine during the fields the rolling of acceleration of a railway distribution, ferry. The limitationas well as of to the check model the is results that it obtained does not takeby mathematicalinto account the modelling, shock effect we of seacarried waves out on the computer hull of the modelling rail ferry. of In addition, the dynamic the model load cannot of the be loadused-bearing to study structure the dynamic of a flat loading wagon of with a tank containers container. (Figure The results 7). of solving the mathematical model madeWe it possibleused the to F determine-criterion in the order accelerations to check as the the adequacy components of of the the mathematical dynamic loads and that computer act on the modelssupporting developed structure by ofthe the authors. flat wagon It was with found containers. that the Inhypothesis this case, of the adequacy acceleration was to not the rejected. supporting In subsequentstructure of studies the flat in wagon this area, was 0.25it is gimportant (Figure4), to and consider on the the container issues wasof the 0.35g stability (Figure of5 the). railway ferry whenTo determine transporting the fields trains of of acceleration combined distribution,transport [55 as], as well well as as to checkissues therelated results to obtainedthe energy by efficiencymathematical of loading modelling, and unloading we carried operations out computer [56]. modelling of the dynamic load of the load-bearing structureIn further of a flatstudies wagon of the with issues containers of dynamic (Figure loading7). of containers in combined trains, we plan to conductWe a used physical the F-criterion experiment. in orderThis experiment to check the will adequacy be carried of the out mathematical using the electrical and computer tensometry models method.developed The by research the authors. is planned It was found to be thatcarried the hypothesisout on the of railway adequacy ferry was “ notHeroes rejected. of Shipki In subsequent” while sailing in the Black Sea. The conducted studies are a useful technical basis in the creation of load-bearing structures of flat wagons and containers of a new generation. Moreover, the results obtained will contribute to the expansion of regulatory documents that cover the issues of rail transport by sea.

Appl. Sci. 2020, 10, 5710 12 of 15 studies in this area, it is important to consider the issues of the stability of the railway ferry when transporting trains of combined transport [55], as well as issues related to the energy eﬃciency of loading and unloading operations [56]. In further studies of the issues of dynamic loading of containers in combined trains, we plan to conduct a physical experiment. This experiment will be carried out using the electrical tensometry method. The research is planned to be carried out on the railway ferry “Heroes of Shipki” while sailing in the Black Sea. The conducted studies are a useful technical basis in the creation of load-bearing structures of ﬂat wagons and containers of a new generation. Moreover, the results obtained will contribute to the expansion of regulatory documents that cover the issues of rail transport by sea.

6. Conclusions The load-bearing structure of the flat wagon was improved in order to ensure the stability of containers during transportation by a railway ferry. We proposed the installation of removable superstructures on the supporting structure of the flat wagon. To reduce the dynamic load of containers, we proposed the installation of a material with viscous properties on the internal surfaces of the flat wagon superstructures. Mathematical modelling of the dynamic load of containers was carried out, considering the new scheme of interaction with the flat wagon. On the basis of the conducted calculations, we found that the greatest acceleration values occurred at the course angles of the wave relative to the body of the railway ferry χ = 60◦ and χ = 120◦. The total amount of acceleration that acted on the container was 3.57 m/s2 (0.36 g) and on the load-bearing structure of the flat wagon was 2.47 m/s2 (0.25 g). The viscous connection between the load-bearing structure of the flat wagon and the containers made it possible to reduce the dynamic load by 38% and 23%, respectively, compared to the typical interaction scheme. Computer simulation of the dynamic load of containers was performed, taking into account the new scheme of interaction with the flat wagon. The maximum acceleration applied to the container was about 2.6 m/s2. The maximum percentage of discrepancy between the accelerations obtained by theoretical and computer modelling was 17.7%. The conducted studies will contribute to improving the efficiency of combined transport and may also be useful developments in the creation of new designs of flat wagons.

Author Contributions: Conceptualization, A.L.; methodology, A.L. and O.F.; software, P.K.; validation, P.K., writing—review and editing, V.P. All authors have read and agreed to the published version of the manuscript. Funding: The authors 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 is funded from the state budget of Ukraine in 2020. The authors also gratefully acknowledge funding from the specific research on BUT FSI-S-20-6267. Acknowledgments: The authors thank to Ukrainian State University of Railway Transport, State University of Infrastructure and Technologies, and Brno University of Technology for support. Conflicts of Interest: The authors declare no conflict of interest.

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