MATHEMATICAL TREATMENT OF TENSION IN TANDEM ROLLING
Zhang Jin-zhi (Beijing Institute of Iron and Steel Research)
Cite this article:
Zhang Jin-zhi (Beijing Institute of Iron and Steel Research). MATHEMATICAL TREATMENT OF TENSION IN TANDEM ROLLING. Acta Metall Sin, 1978, 14(2): 127-138.
Abstract 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.
[1] Hessenberg, W. C. and Jenkins, W. N., Proc. Inst. Mech. Eng., 169 (1955) , 1051. [2] Lianis, G. and Ford, H., Proc. Inst. Mech. Eng., 171 (1957) , 757. [3] Sekulic, M. R. and Alexander, J. M., J. Mech. Eng, Sci., 4 (1962) , 301. [4] #12 [5] 美坂佳助,塑性と加工,8(1967) ,№ 75,188. [6] Bryant, G. F., Automation of Tandem Mills, The Iron & Steel Institute, London, 1973. [7] 田沼正也,大成干彦,塑性と加工,13(1972) ,№ 133,122. [8] 小西正躬,鈴木 弘,塑性と加工,13(1972) ,№ 140,689. [9] #12 [10] #12 [11] #12 [12] Ford, H. and Bland, D. R., J. Iron Steel Inst., 168 (1951) , 57. [13] 北京钢铁研究院,待发表的工作,(1974年).$