{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T14:19:34Z","timestamp":1792937974225,"version":"4.5.0"},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100006109","name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","doi-asserted-by":"publisher","award":["1\/0325\/14"],"award-info":[{"award-number":["1\/0325\/14"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"crossref","award":["1\/0325\/14"],"award-info":[{"award-number":["1\/0325\/14"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.<\/jats:p>","DOI":"10.1155\/2015\/843720","type":"journal-article","created":{"date-parts":[[2015,9,30]],"date-time":"2015-09-30T21:27:44Z","timestamp":1443648464000},"page":"1-20","source":"Crossref","is-referenced-by-count":10,"title":["New Numerical Solution of von Karman Equation of Lengthwise Rolling"],"prefix":"10.1155","volume":"2015","author":[{"given":"Rudolf","family":"Pernis","sequence":"first","affiliation":[{"name":"Alexander Dub\u010dek University of Tren\u010d\u00edn, Pri Parku 19, 911 06 Tren\u010d\u00edn-Z\u00e1blatie, Slovakia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tibor","family":"Kvackaj","sequence":"additional","affiliation":[{"name":"Technical University of Ko\u0161ice, Faculty of Metallurgy, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"issue":"2","key":"1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1002\/zamm.19250050213","volume":"5","year":"1925","journal-title":"Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik"},{"key":"2","year":"1968"},{"key":"3"},{"key":"4","year":"1991"},{"key":"5"},{"key":"6"},{"issue":"4","key":"7","first-page":"610","volume":"13","year":"2007","journal-title":"Acta Metallurgica Slovaca"},{"issue":"1","key":"8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.4149\/km_2010_1_41","volume":"48","year":"2010","journal-title":"Kovov\u00e9 Materi\u00e1ly\u2014Metallic Materials"},{"issue":"3","key":"9","first-page":"242","volume":"6","year":"2000","journal-title":"Acta Metallurgica Slovaca"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1243\/PIME_PROC_1943_150_025_02"},{"key":"11","series-title":"Hybrid Computer, Technical Information Series No. 8","year":"1968"},{"issue":"1","key":"12","first-page":"34","volume":"9","year":"2003","journal-title":"Acta Metallurgica Slovaca"},{"key":"13"},{"issue":"17","key":"14","first-page":"s822","volume":"105","year":"2011","journal-title":"Chemicke Listy"},{"key":"15"},{"key":"16","year":"1981"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1243\/PIME_PROC_1948_159_015_02"},{"issue":"6","key":"18","first-page":"191","volume":"168","year":"1954","journal-title":"Proceedings of the Institution of Mechanical Engineers"},{"key":"19"},{"issue":"2","key":"20","first-page":"68","volume":"17","year":"2011","journal-title":"Acta Metallurgica Slovaca"},{"issue":"3, article 75","key":"21","volume":"9","year":"2008","journal-title":"Journal of Inequalities in Pure and Applied Mathematics"},{"key":"22","year":"2007"},{"issue":"1","key":"23","first-page":"91","volume":"45","year":"1995","journal-title":"Mathematica Slovaca"},{"key":"24","year":"1957"},{"key":"25","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1098\/rspa.1972.0025","volume":"326","year":"1972","journal-title":"Proceedings of the Royal Society of London A"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/843720.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/843720.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/843720.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T22:54:47Z","timestamp":1589583287000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/843720\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":25,"alternative-id":["843720","843720"],"URL":"https:\/\/doi.org\/10.1155\/2015\/843720","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}