东北大学学报(自然科学版) ›› 2007, Vol. 28 ›› Issue (4): 514-517.DOI: -

• 论著 • 上一篇    下一篇

扁带拉拔挤压柱坐标应变速率矢量内积

赵德文;王根矶;刘相华;王国栋;   

  1. 东北大学轧制技术及连轧自动化国家重点实验室;东北大学轧制技术及连轧自动化国家重点实验室;东北大学轧制技术及连轧自动化国家重点实验室;东北大学轧制技术及连轧自动化国家重点实验室 辽宁沈阳110004;辽宁沈阳110004;辽宁沈阳110004;辽宁沈阳110004
  • 收稿日期:2013-06-24 修回日期:2013-06-24 出版日期:2007-04-15 发布日期:2013-06-24
  • 通讯作者: Zhao, D.-W.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(50474015)

Strain rate vector inner-product during strip drawing or extrusion in cylindrical coordinate system

Zhao, De-Wen (1); Wang, Gen-Ji (1); Liu, Xiang-Hua (1); Wang, Guo-Dong (1)   

  1. (1) State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, China
  • Received:2013-06-24 Revised:2013-06-24 Online:2007-04-15 Published:2013-06-24
  • Contact: Zhao, D.-W.
  • About author:-
  • Supported by:
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摘要: 提出以积分中值定理简化应变速率矢量内积的积分方法.将楔形模平面变形拉拔和挤压的等效应变速率表示成二维的应变速率矢量,再用积分中值定理确定应变速率比值函数及该矢量的方向余弦,最后对其内积进行逐项积分并求和,得到了应力状态系数nσ和最佳模角αopt的解析解.通过算例将不同α与m条件下计算的应力状态系数与Avitzur椭圆积分的数值解进行了比较,结果表明:当α=15°,不同摩擦因子m条件下,以该解析解计算的拉拔力与椭圆积分的数值结果相对误差不超过0.05%;ξ(α)值相差不大于0.002;极限道次加工率ε随αopt增大及m减小而增加.

关键词: 扁带拉拔, 柱坐标, 应变速率矢量, 内积, 逐项积分, 解析解

Abstract: A new integration method is proposed to simplify the strain rate vector inner product by the mean value theorem in a cylindrical coordinate system. The equivalent strain rate of the strip passing through a wedge-shaped die during drawing/extrusion for plane deformation is first expressed in terms of two-dimensional vector. Then, the strain rate ratio function and direction cosine of the vector are determined by the integral mean value theorem. Finally, the termwise integration and summation of the inner product are done to give an upper-bound analytical solution to the stress state factor nσ and optimal die angle αopt. An example is given to compare the stress state factors thus solved under conditions of different α and m values with those by Avitzur's elliptic integral. The results show that if α = 15° and the friction factor m varies, the error of the value of drawing force by this analytical solution relative to that by the numerical solution resulting from elliptic integral isn't higher than 0.05%, and the absolute error of the stress state factor resulting from elliptic integral ξ(α) isn't higher than 0.002. In addition, the ultimate pass reduction Ε increases with increasing αopt and decreasing m.

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