New Numerical Solution of von Karman Equation of Lengthwise Rolling
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...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/843720 |
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| author | Rudolf Pernis Tibor Kvackaj |
| author_facet | Rudolf Pernis Tibor Kvackaj |
| author_sort | Rudolf Pernis |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-56fec8546b6342d68a9ff2be40811f9d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-56fec8546b6342d68a9ff2be40811f9d2025-02-03T06:44:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/843720843720New Numerical Solution of von Karman Equation of Lengthwise RollingRudolf Pernis0Tibor Kvackaj1Alexander Dubček University of Trenčín, Pri Parku 19, 911 06 Trenčín-Záblatie, SlovakiaTechnical University of Košice, Faculty of Metallurgy, 042 00 Košice, SlovakiaThe 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.http://dx.doi.org/10.1155/2015/843720 |
| spellingShingle | Rudolf Pernis Tibor Kvackaj New Numerical Solution of von Karman Equation of Lengthwise Rolling Journal of Applied Mathematics |
| title | New Numerical Solution of von Karman Equation of Lengthwise Rolling |
| title_full | New Numerical Solution of von Karman Equation of Lengthwise Rolling |
| title_fullStr | New Numerical Solution of von Karman Equation of Lengthwise Rolling |
| title_full_unstemmed | New Numerical Solution of von Karman Equation of Lengthwise Rolling |
| title_short | New Numerical Solution of von Karman Equation of Lengthwise Rolling |
| title_sort | new numerical solution of von karman equation of lengthwise rolling |
| url | http://dx.doi.org/10.1155/2015/843720 |
| work_keys_str_mv | AT rudolfpernis newnumericalsolutionofvonkarmanequationoflengthwiserolling AT tiborkvackaj newnumericalsolutionofvonkarmanequationoflengthwiserolling |