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Asymptotic analysis of asymmetric thin sheet rolling

机译:不对称薄板轧制的渐近分析

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摘要

An analytical model for asymmetric rolling is presented, which includes asymmetry in roll friction, roll size and roll speed, for a rigid, perfectly plastic thin sheet deformed with Coulomb friction. This model is solved asymptotically, based on the systematic assumptions that both the roll gap aspect ratio and the friction coefficient are small. While the leading order solution is shown to be consistent with an existing slab model, we are able to derive additional detail by looking to higher orders. We compare our higher order solution and the leading order solution with finite element simulations, and use the results to determine the practical range of validity of our analytical model. Within this region, it gives reasonable quantitative predictions of the force and torque results from finite element simulations and approximates through thickness variation of stress and strain with orders of magnitude shorter computation times. A MATLAB implementation of this solution is included in the supplementary material. (C) 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license.
机译:提出了一种不对称轧制的分析模型,该模型包括轧辊摩擦力,轧辊尺寸和轧辊速度的不对称性,用于因库仑摩擦而变形的刚性,完美塑性薄膜。基于轧辊间隙纵横比和摩擦系数均较小的系统假设,渐近求解该模型。虽然领先的订单解决方案已证明与现有的平板模型一致,但我们可以通过查找更高的订单来得出更多详细信息。我们将我们的高阶解和前阶解与有限元模拟进行比较,并使用结果确定分析模型有效性的实际范围。在此区域内,它可以对有限元模拟中的力和扭矩结果进行合理的定量预测,并通过应力和应变的厚度变化来近似估算,而计算时间要短几个数量级。该解决方案的MATLAB实现包含在补充材料中。 (C)2016作者。由Elsevier Ltd.发行。这是CC BY许可下的开放访问文章。

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