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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。张力是连轧过程的纽带,由动平衡条件建立了张力微分方程: (dσi/dt)=(E/l)[V′_(i+1)-V_i][1+(σ_i)/E] 利用生产实践和实验研究中认识的物理规律,如体积不变定律、前滑与张力成线性关系,推导得到连轧状态方程: σ=-τ~(-1)Aσ+(E/l)BU 动态张力公式: σ(t)=e~(-τ~(-1))At σ_0+A~(-1)[I-e~(-τ~(-1))At]W~(-1)ΔV 稳态张力公式: σ=A~(-1)m~(-1)q 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近稳定的,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 development of computer controlled tandem rolling process calls for a mathematical expression to represent the condition of inequality of mass flow constant. From the condition of dynamic equilibrium, a differential equation of tension is given as:dσ_i/dt=E/l[V′_(i+1)-V_i][1+σ_i/E]Based upon the physical rules in industrial practice and in experiments, for example, the law of volume constancy, the linear relation between forward slip and tension, the following equations are derived.The equation of the state of tandem rolling:(?)=-τ~(-1)Aσ+E/lBUThe equation of the dynamic state of tension:σ(t)=e~(-~(r-1))Atσ_0+A~(-1)[I-e~(-~(r-1))At]W~(-1)△VThe equation of the static state of tension:σ=A~(-1)m~(-1)qThe equation of tension represents the relation between tension, thickness, velocity of roll and time of the tandem rolling process. It implies that the tandem rolling process is an asymtotically stable, controllable and measurable dynamic system.