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上界法による角棒の平圧延の解析

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川崎製鉄技報 KAWASAKI STEEL GIHO

Vol.20 (1988) No.1

上界法による角棒の平圧延の解析

Three-dimensional Analysis of Flat Rolling of Rectangular Stock by a Numerical Method Based on Upper Bound Theory

林 宏之(Hiroyuki Hayashi) 磯辺 邦夫(Kunio Isobe) 片岡 健二(Kenji Kataoka) 要旨 : 三次元変形の解析手段のひとつに上界法がある。これは上界定理に基づき,速度場を調節 可能なパラメーターを含む数式で表し,全仕事消散率を極小化して最も正解に近い速度場 を得る近似解法である。本報では,カリバレス圧延として実用化されている角棒の平圧延 を対象に,上界法による幅広がりおよびトルクの解析を行った。ここでは横断面が平面を 保持するという簡単な速度場にしたにもかかわらず,計算結果と鉛を用いたモデル実験結 果はよく一致した。また上界法の計算結果を用いて変形エネルギー効率ηに及ぼす各種圧 延条件の影響を検討し,平均ロール間隙形状比Ld/Hm=1 のときηが最大になるという結果 が得られた。 Synopsis :

Three-dimensional rolling of rectangular bar is analyzed. This analysis is based on the upper bound theorem. The total energy dissipation rate is minimized by the simplex method which is one of the direct methods of nonlinear optimization. It is assumed that kinematically admissible velocity is a cubic function of the distance from the entry plane and the cross section of rolled stock keeps plane in the roll gap. Though the velocity field is simple,the calculation results of the spread and rolling torque agree well with lead-model experiments. From these results, deformation energy efficiency in case of flat rolling of the rectangular bar becomes maximum in the rolling condition of Ld/Hm=1.

(c)JFE Steel Corporation, 2003

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