板带轧制过程考虑滑动与粘着摩擦的轧制力模型

摘要

将轧制变形区分为滑动摩擦区和粘着摩擦区，得到适用于带钢热轧过程的改进卡尔曼(KARMAN)微分方程，给出轧制力数值计算公式。结合变形区入口与出口的边界条件，采用龙格−库塔(Runge−Kutta)法交替求解前滑区与后滑区的单位压力分布，2个接触弧角相交处就是中性点，通过对单位压力与摩擦应力进行数值积分得到轧件的轧制力，再根据希齐柯克(Hitchcock)公式迭代计算多次得到最终轧制力。最后，分析新型轧制力模型应用于热连轧机组面临的问题，给出热轧过程摩擦因数对单位压力分布与轧制力的影响规律，并通过布伦特(Brent)方法实现对热轧过程摩擦因数的软测量，指出摩擦因数在1个轧制周期内的演变规律，为热连轧过程摩擦因素在线模型的建立与新型数值轧制力模型的在线应用提供参考。%An improved KARMAN equation for hot rolling process was deduced in consideration of slipping and sticking friction in the roll-bite, and the numerical formula of roll force calculation was given. Combined with boundary condition of inlet and outlet in the roll bite, the Runge−Kutta method was adopted to alternately solve the distribution of normal pressure in the forward and backward slip zones. The intersection of contact angle was just the neutral point. The roll force could be calculated by integrating the normal pressure and friction shear stress in the roll bite, and then the final roll force was obtained by repeated iteration calculation in the use of Hitchcock formula. Finally, the problem in the application of the numerical roll force model to hot strip mill was analyzed, and the influence of friction coefficient on the normal pressure distribution and roll force during hot rolling was shown. The soft measurement of friction coefficient during hot rolling process was carried out by Brent method, and evolution rule of friction coefficient in a rolling recycle was pointed out, which provides references for the establishment of online mathematical model of friction coefficient and the application of the proposed numerical roll force model in online process control of hot strip mill.