Strength characteristic determination of a flat wagon carrying structure with a lower centre of gravity

ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 99 S eng h cha ac e is ic de e mina ion o a la wagon ca ying s uc u e wi h a lowe cen e o g a i y Oleksij Fomin 1 , Alyona Lo ska 2 , Václa Píš ěk 3 , Pa el Kuče a 4 1 Depa men o Ca s and Ca iage Facili ies, S a e Uni e si y o In as uc u e and Technologies, Kyi , Uk aine 2 Depa men o Wagons, Uk ainian S a e Uni e si y о Railway T anspo , Kha ki , Uk aine 3, 4 Ins i u e o Au omo i e Enginee ing, B no Uni e si y o Technology, B no, Czech Republic 1 Co esponding au ho E-mail: 1 ominaleksej ik o o[email p o ec ed], 2 [email p o ec ed]m, 3 [email p o ec ed].cz, 4 [email p o ec ed].cz R ecei ed 11 June 2020; accep ed 22 June 2020 D OI h p s://doi.o g /10.21595/ p .2020.21533 Copy igh © 2020 Oleksij Fomin, e al. This is an open access a icle dis ibu ed unde he C ea i e Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. Abs ac . The s udy deals wi h applica ion o la wagons wi h lowe cen e o g a i y o anspo a ion o hea y con aine s and mili a y equipmen . A special ea u e o he wagon s uc u e is he p esence o swi el sec o s, which a e made o composi e ma e ial. The wagon s uc u e makes i possible o conduc i e by mili a y equipmen in mo ion. The esul s o de e mina ion o he dynamic load o a la wagon in shun ing impac s a e p esen ed. The au ho s de ined he basic s eng h cha ac e is ics o he ca ying s uc u e o a la wagon. The calcula ion was conduc ed wi h he ini e elemen me hod in CosmosWo ks so wa e. The esul s o he calcula ion p o ed he e iciency o he solu ions aken. The s udy also p esen s he a igue calcula ion o he ca ying s uc u e o a la wagon designed. The esea ch may encou age enginee s o design he uni ied ca ying s uc u es o la wagons, and imp o e he ail anspo e iciency. Keywo ds: la wagon, ca ying s uc u e, combined anspo a ion, dynamics, s eng h. 1. In oduc ion The de elopmen o economic ela ions be ween indi idual coun ies mos ly depends on he anspo in as uc u e e iciency. As is well known, he ail anspo accoun s o he basic segmen in anspo a ion. In o de o main ain he leading posi ion he in he ail indus y, he e is a need o ha e compe i i e olling s ock. A he p esen s age o he ail indus y de elopmen in oduc ion o he uni ied olling s ock, which can anspo a ious ypes o eigh and be adap able o a ious ope a ional condi ions, is o p ima y impo ance. The ail anspo a ion o o e size eigh can be ul illed by la wagons o lowe cen e o g a i y. Such la wagon s uc u es a e well-es ablished in ope a ions, as hey can anspo bo h o e size eigh and, pa icula ly, mili a y equipmen . The e o e, de elopmen and implemen a ion o la wagons o lowe cen e o g a i y will make i possible o imp o e he ope a ional e iciency o he olling s ock and main ain a leade ’s posi ion in he anspo a ion ma ke . The s uc u al peculia i ies o a new-gene a ion la wagon a e s udied in [1]. The ca ying s uc u e o a la wagon consis s o se e al modules. Such an enginee ing solu ion allows egula ing a use ul leng h acco ding o he o e all dimensions o he eigh anspo ed. The s uc u al ea u es o a la wagon o in e modal anspo a ion a e conside ed in [2]. The s udy gi es he gene al echnological equi emen s o he o ganiza ion o in e modal anspo a ion and de ines hei ad an ages. Howe e , he au ho s do no conside a possibili y o anspo hea y eigh , pa icula ly, mili a y equipmen , on la wagons. The ma hema ic modelling o he dynamic loads o a la wagon a ope a ional loads is gi en in [3]. The s udy de ines he na u al equencies and mode shapes o he ca ying s uc u e o a la wagon. Howe e , de e mina ion o he s eng h cha ac e is ics o he ca ying s uc u e o a STRENGTH CHARACTERISTIC DETERMINATION OF A FLAT WAGON CARRYING STRUCTURE WITH A LOWER CENTRE OF GRAVITY. OLEKSIJ FOMIN, ALYONA LOVSKA, VÁCLAV PÍŠTĚK, PAV E L KUČERA 100 VIBROENGINEERING PROCEDIA. JUNE 2020, VOLUME 32 la wagon is no conside ed. The s eng h cha ac e is ics o a la wagon du ing anspo a ion o con aine s and he loading/unloading wi h he ACTS sys em a e de ined in [4]. The s eng h calcula ion is conduc ed in he s a ic se ing in Nas an so wa e. The nume ical alues o he designed loads on a la wagon a e aken in acco dance wi h he PNEN12663 and BN-77/3532-40 s anda ds. Howe e , he dynamic load o he ca ying s uc u e o he la wagon is no s udied. Resea ch in o dynamic peculia i ies o he olling s ock unde i s in e ac ion wi h he ack is gi en in [5, 6]. The ma hema ical models p esen ed make i possible o ob ain he basic dynamic cha ac e is ics o he olling s ock. The s udies do no conside de e mina ion o he dynamic cha ac e is ics o he olling s ock unde anspo a ion o mili a y equipmen . Resea ch in o he dynamics and s eng h o he ca ying s uc u es o la wagons a he mos un a ou able ope a ional loading is gi en in [7, 8]. The esul s o ma hema ical modelling a e used in de e mina ion o he s eng h cha ac e is ics o he ca ying s uc u es o la wagons. The dynamics and s eng h o a la wagon o lowe cen e o g a i y unde anspo a ion o hea y eigh a e no conside ed in he s udies. The analysis o li e a y sou ces allows o conclude ha ques ions o he s udy o he dynamic loading and s eng h o la wagons wi h a educed cen e o g a i y ha e no ye been p ope ly cla i ied. The e o e, he esea ch p esen ed in his wo k is ele an and has a scien i ic no el y. 2. C ea ing a compu a ional model The s udy deals wi h a new ca ying s uc u e o a la wagon o anspo a ion o hea y con aine s and mili a y equipmen . A 13-401 la wagon was chosen as he p o o ype model. In o de o anspo mili a y equipmen , he middle pa o he ame was lowe ed in compa ison wi h ha o he p o o ype (Fig. 1). I allows anspo a ion o mili a y equipmen wi hin he es ablished o e all dimensions. The mili a y equipmen was loca ed on he o a ing sec o s made o composi e ma e ial. Be ween a o a ing sec o and he ame, a iscous ma e ial was placed which p o ides he kine ic ene gy abso p ion unde conduc ing i e by he mili a y equipmen . The wagon s uc u e enables o conduc i e by he mili a y equipmen in mo ion. Fo anspo a ion o hea y con aine s i ing ou igge s we e ins alled in he ex ension pa s o he ca ying s uc u es. a) b) Fig. 1. The la wagon o anspo a ion o mili a y equipmen and hea y con aine s a) in emp y s a e, b) in loaded s a e Ma hema ical modelling was conduc ed o he dynamic load de e mina ion o he la wagon ca ying s uc u e. The calcula ion conside ed shun ing impac s and he esea ch was made in he plane coo dina es. I was aken in o accoun ha an impac load o 3.5 MN a ec ed he ea s op o he au oma ic couple . The s udy used he ma hema ical model gi en in [9]. This model conside ed displacemen s o a long-base la wagon loaded wi h h ee ank con aine s. The e o e, he model was imp o ed. Pa icula ly, he model conside ed displacemen s o he ca ying s uc u e o he la wagon wi hou displacemen s o he eigh anspo ed. Thus, he eigh anspo ed was aken as a cap i e mass which comple ely epea ed he ajec o y o he ca ying s uc u e o he la wagon. Besides, he model did no conside displacemen s o he ca ying STRENGTH CHARACTERISTIC DETERMINATION OF A FLAT WAGON CARRYING STRUCTURE WITH A LOWER CENTRE OF GRAVITY. OLEKSIJ FOMIN, ALYONA LOVSKA, VÁCLAV PÍŠTĚK, PAV E L KUČERA ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 101 s uc u e o he la wagon as he basic model was sho e unlike he model conside ed in [9]. The ma hema ic model has he o m: 𝑀 󰆒∙𝑥 󰇘 +𝑀󰆒∙𝜑 󰇘 =𝑆, (1) 𝐼∙𝜑 󰇘 +𝑀󰆒∙𝑥 󰇘 −𝑔∙𝜑 ∙𝑀 󰆒=𝑙∙𝐹   sign∆󰇗−sign∆󰇗  +𝑙󰇛𝐶−𝐶 󰇜, (2) 𝑀∙𝑧 󰇘 =𝐶+𝐶−𝐹   sign∆󰇗−sign∆󰇗  , (3) whe e 𝑀 󰆒=𝑀+2𝑚+∙ , 𝑀󰆒=𝑀∙ℎ, 𝐶=𝑘∙∆ , 𝐶=𝑘∙∆ , ∆=𝑧−𝑙∙𝜑 , ∆=𝑧+𝑙∙𝜑 , 𝑀 – mass o he ca ying s uc u e o a la wagon; 𝐼 – ine ia momen o he ca ying s uc u e o a la wagon ela i e o he longi udinal axle; 𝑆 – alue o he longi udinal impac o he au oma ic couple ; 𝑚 – bogie mass; 𝐼 – ine ia momen o a wheelse ; 𝑟 – adius o a mean wo n-ou wheel; 𝑛 – numbe o bogie axles; 𝑙 – hal -base o a la wagon; 𝐹 – absolu e alue o he d y ic ion o ce in a sp ing g oup; 𝑘, 𝑘 – igidi ies o he sp ings in he bogie suspension; 𝑥, 𝜑, 𝑧 – coo dina es co esponding o he longi udinal, angula a ound longi udinal, and e ical displacemen s o a la wagon, espec i ely. Sys em o equa ions Eq. (1-3) we e sol ed in Ma hCad so wa e using s anda d algo i hms [10-15]. The ini ial displacemen s and speeds we e aken equal o ze o. The inpu pa ame e s o he ma hema ical model we e he echnical cha ac e is ics o he la wagon, pa ame e s o a sp ing suspension and alues o a longi udinal impac in o he au oma ic couple . I was conside ed ha he la wagon was loaded wi h condi ional eigh unde he comple e wagon load consignmen . Fig. 2 shows ha he maximum accele a ion alue on he ca ying s uc u e o he la wagon was abou 40 m/s2 (0.4 g). The accele a ion alue ob ained did no exceed he no ma i e alue es ablished in [16, 17]. The s eng h o he ca ying s uc u e o a la wagon was s udied wi h a spa ial model in SolidWo ks so wa e [18]. The s eng h calcula ion was made by he ini e elemen me hod [19-21]. The ini e elemen model o he ca ying s uc u e o he la wagon is gi en in Fig. 3. Fig. 2. The accele a ions on he ca ying s uc u e o a la wagon a shun ing impac s Fig. 3. The ini e elemen model o he ca ying s uc u e o a la wagon The model used isopa ame ic e ahed ons. The model consis ed o 225669 nodes and 679072 elemen s. The maximum size o an elemen was 105 mm, he minimum one 21 mm. The elemen size expansion a io was 1.6. The minimum numbe o he elemen s in a ci cle was 8. The model was ixed in he suppo ing a eas on he bogies. The s uc u al ma e ial was he s eel 09G2S. Two loading diag ams o he ca ying s uc u e o he la wagon we e conside ed: – anspo a ion o mili a y equipmen , see Fig. 4(a) and – anspo a ion o a hea y con aine , see Fig. 4(b). The design diag am conside ed he ca ying s uc u e elemen s which we e in igid in e ac ion by welding o i e ing. Thus, a o a ing sec o was neglec ed. I was conside ed ha he ca ying s uc u e o he la wagon was unde he e ical load 𝑃 , and he longi udinal load on he ea s op o he au oma ic couple 𝑃. STRENGTH CHARACTERISTIC DETERMINATION OF A FLAT WAGON CARRYING STRUCTURE WITH A LOWER CENTRE OF GRAVITY. OLEKSIJ FOMIN, ALYONA LOVSKA, VÁCLAV PÍŠTĚK, PAV E L KUČERA 102 VIBROENGINEERING PROCEDIA. JUNE 2020, VOLUME 32 a ) b) Fig. 4. The design diag am o he ca ying s uc u e o he la wagon a) anspo a ion o mili a y equipmen , b) anspo a ion o a hea y con aine The design diag am o he ca ying s uc u e o he la wagon conside ed he e ical s a ic load, dis ibu ed as a dis ance load, and he loca ion o he con aine cen e o g a i y unde he loading o a hea y con aine . On he basis o he calcula ion he au ho s de ined he basic s eng h pa ame e s o he ca ying s uc u e o a la wagon. The esul s o he calcula ion a e gi en in Figs. 5-6. Fig. 5. The s ess s a e o he ca ying s uc u e o a la wagon unde anspo a ion o mili a y e q ui p men Fig. 6. The s ess s a e o he ca ying s uc u e o a la wagon unde anspo a ion o a con aine In he i s design diag am he maximum equi alen s ess was 337 MPа, displacemen in s uc u al uni s was 4.8mm, and s ain was 4.35×10-3. The second design diag am demons a es he maximum equi alen s ess 324 МPа, displacemen o 4.4 mm, and s ain o 1.13×10-3. Thus, he maximum equi alen s esses we e wi hin he admissible alues [16, 17, 22]. Fu he he s eng h capaci y o he ca ying s uc u e o a la wagon was ensu ed. The s udy also conce ns wi h he a igue s eng h calcula ion o he la wagon s uc u e. The es base included 107 cycles. The a igue cu e was ob ained by di iding each s ess alue o he cu e SN by he elas ici y modulus o he e e ence ma e ial (ASME) and mul iplying he ob ained alue by he elas ici y modulus o he conside ed ma e ial [18] (see Fig. 7). This cu e was ob ained in he CosmosWo ks so wa e en i onmen o s eel g ade 09G2S. I cha ac e izes he change in s esses o he ma e ial o he suppo ing s uc u e o he pla o m wagon depending on he numbe o loading cycles. The calcula ion o a igue is implemen ed in a linea o m when s ess accumula ion is diagnosed. The heo y o damage accumula ion sugges s ha a s ess cycle wi h an al e na ing s ess abo e he a igue limi causes damage. To al damage is equal o he sum o he damage caused by indi idual s ess cycles. Tha is, a e applying loads o he calcula ion model wi h a loading cycle o 107, no damage was de ec ed. The calcula ions made i possible o conclude ha he a igue s eng h o he ca ying s uc u e o a la wagon was p o ided in ope a ional load modes. STRENGTH CHARACTERISTIC DETERMINATION OF A FLAT WAGON CARRYING STRUCTURE WITH A LOWER CENTRE OF GRAVITY. OLEKSIJ FOMIN, ALYONA LOVSKA, VÁCLAV PÍŠTĚK, PAV E L KUČERA ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 103 Fig. 7. The a igue cu e o he ca ying s uc u e o a la wagon 3. Conclusions The ca ying s uc u e o a la wagon o lowe cen e o g a i y was designed. A 13-401 la wagon was chosen as he p o o ype wagon. In o de o anspo mili a y equipmen , he middle pa o he ame was lowe ed in compa ison wi h ha o he p o o ype (Fig. 1). Mili a y equipmen was placed on he o a ing sec o s made o composi e ma e ial. Fi ing ou igge s we e ins alled in he ex ension pa s o he ca ying s uc u e o a la wagon o anspo a ion o hea y con aine s. The dynamic loading o he ca ying s uc u e o a la wagon o lowe cen e o g a i y was de e mined. The esea ch was made in he plane coo dina es. I was aken ha he ea s op o he au oma ic couple was unde an impac load o 3.5 МN and he maximum accele a ion on he ca ying s uc u e was abou 0.4 g, hus i was wi hin he admissible alues. The basic s eng h cha ac e is ics o he ca ying s uc u e o a la wagon o lowe cen e o g a i y we e de ined. The calcula ion was made wi h he ini e elemen me hod. The s udy conside ed he loading on he ca ying s uc u e o a la wagon unde anspo a ion o mili a y equipmen and a hea y con aine . I was es ablished ha he i s design diag am had he maximum equi alen s ess equal o 337 МPа, maximum displacemen s in he s uc u al uni s we e 4.8 mm, and s ain o 4.35×10-3. The second design diag am had he maximum equi alen s ess equal o 324×МPа, displacemen o 4.4 mm, and s ain o 1.13×10-3. The a igue calcula ions o he ca ying s uc u e o he la wagon made i possible o conclude ha he a igue s eng h was ensu ed a ope a ional loading modes. The esea ch may encou age enginee s o design uni ied ca ying s uc u es o la wagons, and imp o e he ail anspo e iciency. Acknowledgemen s The p esen s udy was conduc ed wi hin he amewo k o he scien i ic opic o young scien is s “Inno a i e P inciples o C ea ion o Resou ce-Sa ing S uc u es o Rail oad Ca s by Taking in o Accoun he Re ined Dynamic Loads and Func ional-Adap i e Flash Concep s”, which is unded by he s a e budge o Uk aine in 2020 and he au ho s g a e ully acknowledge unding om he Speci ic esea ch on BUT FSI-S-20-6267. Re e ences [1] WBN Waggonbau Niesky GmbH: De eloping a Flexible Pla o m o F eigh Wagons. In e na ional Edi ion, No. 1, 2016, p. 46. [2] Nade M., Sala M., Ko zeb J., Kos zewski A. 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