柱坐标应变矢量内积解析模拔圆棒线材

Analysis of Die Drawing of Round Bar and Wire in Cylindrical Coordinate by Inner-Product of Strain Rate Vector

建立了棒线材拉拔的柱坐标系速度场,提出了一种应变速率内积积分方法,并获得了解析解.分析了摩擦因子对最佳模角和应力状态系数的影响规律.结果发现:最佳模角αopt和nσ均随着m的增大而增大;当m一定时,最佳模角αopt对应nσ的最小值.为了验证柱坐标内积解析圆棒拉拔结果,将该方法同Avitzur提出的方法进行了比较.结果表明,该方法和Avitzur提出的方法结果趋于一致.最后讨论了摩擦因子对极限加工率的影响规律.

A cylindrical coordinate velocity field for round bar and wire drawing was established.A new integration method of strain rate inner-product was proposed,and then an analytical solution was obtained.The effects of friction factor on optimal die angle and stress state coefficient were also discussed.The results showed that the optimal die angel αopt and stress state coefficient nσ increase with the m increasing,the nσ obtains its minimum value at αopt.In order to validate the accuracy of the calculated result,it is compared with that of Avitzur.It showed that the proposed solution obtained by the inner-product method is in good agreement with Avitzur solution.Besides,the effect of friction factor on the limit deformation ratio is also discussed.