blackmetИзвестия высших учебных заведений. Черная МеталлургияIzvestiya. Ferrous Metallurgy0368-07972410-2091National University of Science and Technology "MISIS"10.17073/0368-0797-2018-3-194-200blackmet-1269Research ArticleМЕТАЛЛУРГИЧЕСКИЕ ТЕХНОЛОГИИMETALLURGICAL TECHNOLOGIESУПРУГОПЛАСТИЧЕСКИЙ ИЗГИБ КРУГЛОГО СТАЛЬНОГО БРУСА. СООБЩЕНИЕ 1. КОЭФФИЦИЕНТ ПРУЖИНЕНИЯELASTOPLASTIC BEND OF ROUND STEEL BEAM. REPORT 1. SPRINGBACK COEFFICIENTШинкинВ. Н.ShinkinV. N.

д.ф.-м.н., профессор

кафедра физики 

119049, Москва, Ленинский пр., 4

Dr. Sci. (Phys.-Math.), Professor of the Chair of Physics

shinkin-korolev@yandex.ruНациональный исследовательский технологический университет «МИСиС»РоссияNational University of Science and Technology “MISIS” (MISIS)Russian Federation201808042018613194200Copyright © Шинкин В.Н., 20182018Шинкин В.Н.Shinkin V.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://fermet.misis.ru/jour/article/view/1269

Круглый стальной брус широко применяется в металлургии, машиностроении, строительстве и является одним из главных игроков в машинной индустрии. Обладая отличными антикоррозийными свойствами, в сочетании с недюжинной прочностью, круглый стальной брус часто оказывается незаменим при производстве всевозможных механических машин и приспособлений. Цилиндрические рессоры для железнодорожного и автомобильного транспорта изготавливаются из круглого бруса с помощью специальных гибочных машин. Заготовка из круглого бруса также используется в металлургии при производстве бесшовных труб для газонефтяной промышленности. Валки прокатных и листоправильных станов в металлургии имеют форму ступенчатого круглого бруса. Стальная строительная арматура изготавливается из круглого бруса и близка к нему по геометрическим размерам. Основными зарубежными производителями машин непрерывного литья заготовок для производства заготовок круглого сечения являются SMS-Demag (Германия), Danieli (Италия), SMS  Concast (Швецария) и Siemens VAI (Австрия). Современное производство круглого стального бруса имеется на многих российских металлургических заводах, например, на АО «Чусовской металлургический завод», ПАО «Челябинский металлургический комбинат», АО  «Волжский трубный завод», ОАО «Нижнесергинский метизно-металлургический завод», АО «Чепецкий механический завод», ПАО  «Северский трубный завод» и ПАО «Таганрогский металлургический завод». При изготовлении изделий из круглого бруса и их эксплуатации они часто испытывают упругую или упругопластическую деформацию изгиба или сложную деформацию кручения с изгибом. В данной работе предложен аналитический метод расчета остаточной кривизны круглого стального бруса при упругопластическом изгибе. Расчеты позволяют определить остаточную кривизну бруса после изгиба и изгибающие моменты поперечного сечения бруса при изгибе в зависимости от радиуса бруса, модуля Юнга, предела текучести и модуля упрочнения металла бруса. Результаты исследований могут быть широко использованы на машиностроительных и металлургических заводах.

The round steel beam is widely used in metallurgy, mechanical engineering, construction and is one of the major players in the engine industry. Having the excellent anti-corrosion properties, combined with a remarkable strength, the round steel beam is often indispensable in the production of the various mechanical machines and devices. The cylindrical springs for the railway and motor transport are made from the round beam with the help of the special bending machines. Billets from the round beam are also used in the metallurgy at the manufacture of seamless pipes for the oil and gas industry. The rollers of the sheet-straightening machines and rolling mills in metallurgy have the form of stepped round beam. The steel construction armature is made from the round beam and is close to it by geometric dimensions. The main foreign producers of continuous-casting-billets machines for production of round-cross-section blanks are SMS-Demag (Germany), Danieli (Italy), SMS Concast (Switzerland) and Siemens VAI (Austria). The modern production of round steel beam has place on many Russian metallurgical plants, for example, on JSC “Chusovskoy metallurgical plant”, PJSC “Chelyabinsk metallurgical plant”, JSC “Volzhsky pipe plant”, OJSC “Nizhneserginsky metizno-metallurgical plant”, JSC “Chepetsky mechanical plant”, PJSC “Seversky pipe plant” and PJSC “Taganrog metallurgical plant”. In manufacture of articles from round beam and under their exploitation, they often have an elastic or elastoplastic deformation of bending or have a complex deformation of torsion with bending. The analytical method for determining residual curvature of round steel beam under elastoplastic bend is proposed in this paper. The calculations allow us to determine residual curvature of round beam after bending and the bending moments of beam’s cross section at bending depending on the beam’ radius, elastic modulus, yield stress and hardening modulus of beam’s metal. The research results can be widely used at engineering and metallurgical plants.

круглый стальной брускривизна брусаизгибающий момент поперечного сечения брусакоэффициент пружинения брусаостаточная деформациянормальное напряжениеотносительное удлинениемодуль упругостимодуль упрочненияупругопластическая среда с линейным упрочнениемround steel beamcurvature of beambending moment of beam’s cross sectionresidual deformationnormal stressrelative elongationelastic modulushardening moduluselastoplastic continuous medium with linear hardeningReferencesBanabic D. Multiscale modeling in sheet metal forming. – Springer, 2016. – 405 p.Banabic D. Multiscale modeling in sheet metal forming. Springer, 2016, 405 p.Banabic D. Sheet metal forming processes. Constitutive modelling and numerical simulation. – Springer, 2010. – 301 p.Banabic D. Sheet metal forming processes. Constitutive modelling and numerical simulation. Springer, 2010, 301 p.Belskiy S.M., Yankova S., Chuprov V.B. etc. Temperature field of stripes under hot rolling // Journal of Chemical Technology and Metallurgy. 2015. Vol. 50. No. 6. P. 613 – 616.Belskiy S.M., Yankova S., Chuprov V.B., Bakhaev K.V., StoyakinA.O. Temperature field of stripes under hot rolling. Journal of Chemical Technology and Metallurgy. 2015, vol. 50, no. 6, pp. 613–616.Belskiy S., Mazur I., Lezhnev S., Panin E. Distribution of linear pressure ofthin-sheetrolling acrossstrip width //Journal ofChemical Technology and Metallurgy. 2016. Vol. 51. No. 4. P. 371 – 378.Belskiy S., Mazur I., Lezhnev S., Panin E. Distribution of linear pressure of thin-sheet rolling across strip width. Journal of Chemical Technology and Metallurgy. 2016, vol. 51, no. 4, pp. 371–378.Belskiy S.M., Yankova S., Mazur I.P., Stoyakin A.O. Influence of the transversal displacements of metal on the camber formation of hot-rolled strip // Journal of Chemical Technology and Metallurgy. 2017. Vol. 52. No. 4. P. 672 – 678.Belskiy S.M., Yankova S., Mazur I.P., Stoyakin A.O. Influence of the transversal displacements of metal on the camber formation of hot-rolled strip. Journal of Chemical Technology and Metallurgy. 2017, vol. 52, no. 4, pp. 672–678.Belskiy S.M. Parameters of evaluation of shape cross section of hot-rolled steel strips. Message 1. The determination coefficient // Chernye Metally. 2017. No. 10. P. 65 – 70.Belskiy S.M. Parameters of evaluation of shape cross section of hot-rolled steel strips. Message 1. The determination coefficient. Chernye Metally. 2017, no. 10, pp. 65–70.Bhattacharyya D. Composite sheet forming. Vol. 11. – Elsevier Science, 1997. – 530 p.Bhattacharyya D. Composite sheet forming. Vol. 11. Elsevier Science, 1997, 530 p.Calladine C.R. Plasticity for engineers. Theory and applications. – Woodhead Publishing, 2000. – 328 p.Calladine C.R. Plasticity for engineers. Theory and applications. Woodhead Publishing, 2000, 328 p.Chakrabarty J. Theory of plasticity. – Butterworth-Heinemann, 2006. – 896 p.Chakrabarty J. Theory of plasticity. Butterworth-Heinemann, 2006, 896 p.Chakrabarty J. Applied plasticity. – Springer, 2010. – 758 p.Chakrabarty J. Applied plasticity. Springer, 2010, 758 p.Davim J.P. Tribology in manufacturing technology. – Springer, 2013. – 198 p.Davim J.P. Tribology in manufacturing technology. Springer, 2013, 198 p.Davim J.P. Materials Forming and Machining. Research and Development. – Woodhead Publishing, 2015. – 202 p.Davim J.P. Materials Forming and Machining. Research and Development. Woodhead Publishing, 2015, 202 p.Dixit U.S., Hazarika M., Davim J.P. A brief history of mechanical engineering. – Springer, 2017. – 178 p.Dixit U.S., Hazarika M., Davim J.P. A brief history of mechanical engineering. Springer, 2017, 178 p.Dixit P.M., Dixit U.S. Modeling of metal forming and machining processes by finite element and soft computing methods. – Springer, 2008. – 590 p.Dixit P.M., Dixit U.S. Modeling of metal forming and machining processes by finite element and soft computing methods. Springer, 2008, 590 p.Shinkin V.N. Calculation of steel sheet’s curvature for its flattening in the eight-roller straightening machine // Chernye Metally. 2017. No. 2. P. 46 – 50.Shinkin V.N. Calculation of steel sheet’s curvature for its flattening in the eight-roller straightening machine. Chernye Metally. 2017, no. 2, pp. 46–50.Shinkin V.N. Calculation of bending moments of steel sheet and support reactions under flattening on the eight-roller straightening machine // Chernye Metally. 2017. No. 4. P. 49 – 53.Shinkin V.N. Calculation of bending moments of steel sheet and support reactions under flattening on the eight-roller straightening machine. Chernye Metally. 2017, no. 4, pp. 49–53.Shinkin V.N. Asymmetric three-roller sheet-bending systems in steel-pipe production // Steel in Translation. 2017. Vol. 47. No. 4. P. 235 – 240.Shinkin V.N. Asymmetric three-roller sheet-bending systems in steel-pipe production. Steel in Translation. 2017, vol. 47, no. 4, pp. 235–240.Shinkin V.N. Failure of large-diameter steel pipe with rolling scabs // Steel in Translation. 2017. Vol. 47. No. 6. P. 363 – 368.Shinkin V.N. Failure of large-diameter steel pipe with rolling scabs. Steel in Translation. 2017, vol. 47, no. 6, pp. 363–368.Shinkin V.N. Simplified calculation of the bending torques of steel sheet and the roller reaction in a straightening machine // Steel in Translation. 2017. Vol. 47. No. 10. P. 639 – 644.Shinkin V.N. Simplified calculation of the bending torques of steel sheet and the roller reaction in a straightening machine. Steel in Translation. 2017, vol. 47, no. 10, pp. 639–644.Frank V. Lecture notes in production engineering. – Springer, 2013. – 211 p.Frank V. Lecture notes in production engineering. Springer, 2013, 211 p.Qin Y. Micromanufacturing engineering and technology. – William Andrew, 2015. – 858 p.Qin Y. Micromanufacturing engineering and technology. William Andrew, 2015, 858 p.Hingole R.S. Advances in metal forming. Expert system for metal forming. – Springer, 2015. – 116 p.Hingole R.S. Advances in metal forming. Expert system for metal forming. Springer, 2015, 116 p.Hu J., Marciniak Z., Duncan J. Mechanics of Sheet Metal Forming. – Butterworth-Heinemann, 2002. – 211 p.Hu J., Marciniak Z., Duncan J. Mechanics of Sheet Metal Forming. Butterworth-Heinemann, 2002, 211 p.Kang S.-J. Sintering. Densification, grain growth and microstructure. – Butterworth-Heinemann, 2004. – 280 p.Kang S.-J. Sintering. Densification, grain growth and microstructure. Butterworth-Heinemann, 2004, 280 p.Muhin U., Belskij S., Makarov E. Simulation of accelerated strip cooling on the hot rolling mill run-out roller table // Frattura ed Integrita Strutturale. 2016. Vol. 37. P. 305 – 311.Muhin U., Belskij S., Makarov E. Simulation of accelerated strip cooling on the hot rolling mill run-out roller table. Frattura ed Integrita Strutturale. 2016, vol. 37, pp. 305–311.Muhin U., Belskij S., Makarov E. Application of between-stand cooling in the production hot-rolled strips // Frattura ed Integrita Strutturale. 2016. Vol. 37. P. 312 – 317.Muhin U., Belskij S., Makarov E. Application of between-stand cooling in the production hot-rolled strips. Frattura ed Integrita Strutturale. 2016, vol. 37, pp. 312–317.Muhin U., Belskij S. Study of the influence between the strength of antibending of working rolls on the widening during hot rolling of thin sheet metal // Frattura ed Integrita Strutturale. 2016. Vol. 37. P. 318 – 324.Muhin U., Belskij S. Study of the influence between the strength of antibending of working rolls on the widening during hot rolling of thin sheet metal. Frattura ed Integrita Strutturale. 2016, vol. 37, pp. 318–324.Shabalov I.P., Solov’ev D.M., Filippov G.A., Livanova O.V. Influence of UO shaping on the mechanical properties of large-diameter electrowelded pipe // Steel in Translation. 2015. Vol. 45. No. 4. P. 287 – 292.Shabalov I.P., Solov’ev D.M., Filippov G.A., Livanova O.V. Influence of UO shaping on the mechanical properties of large-diameter electrowelded pipe. Steel in Translation. 2015, vol. 45, no. 4, pp. 287–292.Lenard J.G. Metal Forming Science and Practice. – Elsevier Science, 2002. – 378 p.Lenard J.G. Metal Forming Science and Practice. Elsevier Science, 2002, 378 p.Lim Y., Venugopal R., Ulsoy A.G. Process control for sheetmetal stamping process modeling, controller design and stop-floor implementation. – Springer, 2014. – 140 p.Lim Y., Venugopal R., Ulsoy A.G. Process control for sheet-metal stamping process modeling, controller design and stop-floor implementation. Springer, 2014, 140 p.Lin J., Balint D., Pietrzyk M. Microstructure evolution in metal forming processes. – Woodhead Publishing, 2012. – 416 p.Lin J., Balint D., Pietrzyk M. Microstructure evolution in metal forming processes. Woodhead Publishing, 2012, 416 p.Shinkin V.N. Calculation of technological parameters of O-forming press for manufacture of large-diameter steel pipes // CIS Iron and Steel Review. 2017. Vol. 13. P. 33 – 37.Shinkin V.N. Calculation of technological parameters of O-forming press for manufacture of large-diameter steel pipes. CIS Iron and Steel Review. 2017, vol. 13, pp. 33–37.Shinkin V.N. Mathematical model of technological parameters’ calculation of flanging press and the formation criterion of corrugation defect of steel sheet’s edge // CIS Iron and Steel Review. 2017. Vol. 13. P. 44 – 47.Shinkin V.N. Mathematical model of technological parameters’ calculation of flanging press and the formation criterion of corrugation defect of steel sheet’s edge. CIS Iron and Steel Review. 2017, vol. 13, pp. 44–47.Shinkin V.N. Springback coefficient of the main pipelines’ steel large-diameter pipes under elastoplastic bending // CIS Iron and Steel Review. 2017. Vol. 14. P. 28 – 33.Shinkin V.N. Springback coefficient of the main pipelines’ steel large-diameter pipes under elastoplastic bending. CIS Iron and Steel Review. 2017, vol. 14, pp. 28–33.Shinkin V.N. Arithmetical method of calculation of power parameters of 2N-roller straightening machine under flattening of steel sheet // CIS Iron and Steel Review. 2017. Vol. 14. P. 22 – 27.Shinkin V.N. Arithmetical method of calculation of power parameters of 2N-roller straightening machine under flattening of steel sheet. CIS Iron and Steel Review. 2017, vol. 14, pp. 22–27.Klocke F. Manufacturing processes 1. Cutting. – Springer, 2011. – 506 p.Klocke F. Manufacturing processes 1. Cutting. Springer, 2011, 506 p.Klocke F. Manufacturing processes 4. Forming. – Springer, 2013. – 516 p.Klocke F. Manufacturing processes 4. Forming. Springer, 2013, 516 p.Nielsen C.V., Zhang W., Alves L.M. etc. Modeling of thermoelectro-mechanical processes. Applications in metal forming and resistance welding. – Springer, 2013. – 120 p.Nielsen C.V., Zhang W., Alves L.M., Bay N., Martins P. Modeling of thermo-electro-mechanical processes. Applications in metal forming and resistance welding. Springer, 2013, 120 p.Predeleanu M., Gilormini P. Advanced methods in materials processing defects. Vol. 45. – Elsevier Science, 1997. – 422 p.Predeleanu M., Gilormini P. Advanced methods in materials processing defects. Vol. 45. Elsevier Science, 1997, 422 p.Groshkova A.L., Polulyakh L.A., Travyanov A.Ya. etc. Phosphorus distribution between phasesin smelting high-carbon ferromanganese in the blast furnace // Steel in Translation. 2007. Vol. 37. No. 11. P. 904 – 907.Groshkova A.L., Polulyakh L.A., Travyanov A.Ya., Dashevskii V. Ya., Yusfin Yu.S. Phosphorus distribution between phases in smelting high-carbon ferromanganese in the blast furnace. Steel in Translation. 2007, vol. 37, no. 11, pp. 904–907.Podgorodetskii G.S., Yusfin Yu.S., Sazhin A.Yu. etc. Production of generator gas from solid fuels // Steel in Translation. 2015. Vol. 45. No. 6. P. 395 – 402.Podgorodetskii G.S., Yusfin Yu.S., Sazhin A.Yu., Gorbunov V.B., Polulyakh L.A. Production of generator gas from solid fuels. Steel in Translation. 2015, vol. 45, no. 6, pp. 395–402.Orelkina O.A., Petelin A.L., Polulyakh L.A. Distribution of secondary gas emissions around steel plants // Steel in Translation. 2015. Vol. 45. No. 11. P. 811 – 814.Orelkina O.A., Petelin A.L., Polulyakh L.A. Distribution of secondary gas emissions around steel plants. Steel in Translation. 2015, vol. 45, no. 11, pp. 811–814.Polulyakh L.A., Dashevskii V.Ya., Yusfin Yu.S. Manganese-ferroalloy production from Russian manganese ore // Steel in Translation. 2014. Vol. 44. No. 9. P. 617 – 624.Polulyakh L.A., Dashevskii V.Ya., Yusfin Yu.S. Manganese-ferroalloy production from Russian manganese ore. Steel in Translation. 2014, vol. 44, no. 9, pp. 617–624.Predeleanu M., Ghosh S.K. Materials processing defects. Vol. 43. – Elsevier Science, 1995. – 434 p.Predeleanu M., Ghosh S.K. Materials processing defects. Vol. 43. Elsevier Science, 1995, 434 p.Rees D. Basic engineering plasticity. An introduction with engineering and manufacturing applications. – Butterworth-Heinemann, 2006. – 528 p.Rees D. Basic engineering plasticity. An introduction with engineering and manufacturing applications. Butterworth-Heinemann, 2006, 528 p.Wilko C.E. Formability. A review of parameters and processes that control, limit or enhance the formability of sheet metal. – Springer, 2011. – 112 p.Wilko C.E. Formability. A review of parameters and processes that control, limit or enhance the formability of sheet metal. Springer, 2011, 112 p.

The authors declare that there are no conflicts of interest present.