连轧张力公式

Tension calculations in continuous rolling

连轧生产过程电子计算机控制的发展,需要能反映“流量常数”不相等条件的数学表达式.由动平衡条件建立了连轧张力微分方程:dσi/dt=E/l[V′i+1-Vi][1+σi/E].利用生产实践和实验研究中认识的物理规律,如体积不变规律、前滑与张力成线性关系,推导得到连轧状态方程:σ.=-τ-1Aσ+E/lBU,动态张力公式:σ(t)=e-τ-1Atσ0+A-1∟I-e-τ-1At」W-1ΔV;稳态张力公式:σ=A-1m-1q.张力公式反映了连轧过程中张力、厚度、轧辊速度及时间之间的函数关系.证明了连轧工艺过程是渐进稳定的,可控的和可测的动力学系统,并提出张力公式预报钢板厚度的设想.

The computer control of continuous rolling process needs a mathematical treatment that involves unequal constants of mass flow. In light of the dynamic equilibrium condition, a differential equation for tension involved in the continuous rolling was derived as dσi/dt=E/l[Vi＋1-Vi][1＋σi/E] In addition to this equation, three more equations were worked out as well, namely the condition equation for continuous rolling σ（t）=^-τ^-1Atσ0＋A^-1[I-e^-τ^-1At]W^-1ΔV the dynamie tension equation; and the steady tension equation. These tension equations can correlate the tensions with the plate thickness, roller velocity and time of the continuous rolling σ=-τ^-1Aσ＋E/l BU. It was revealed that the continuous rolling process was a gradually stabilized σ=A^-1m^-1q, controllable and measurable dynamic system. These tension equations could be used to predict the plate thickness.