Method for controlling a tension of a metal strip in a heat treatment

Abstract

A method for controlling a tension of a metal strip in a heat treatment furnace, comprising (a) travelling the metal strip through a plurality of tapered rolls; (b) measuring a tension (.sigma.) working on the metal strip through at least one of the tapered rolls; (c) computing a critical tension (.sigma..sub.cr) which generates heat buckle based on a thickness of the metal strip, a width of the metal strip, an elastic modulus of the metal strip, a length of a flat roll portion and a roll taper under a hot state; and (d) controlling the tension measured by the step (b) to be over a tension (.sigma..sub.min) sufficient to prevent transverse displacement but less than the critical tension (.sigma..sub.cr) which generates heat buckle. The critical tension (.sigma..sub.cr) which generates heat buckle is calculated by the equation: .sigma..sub.cr =K.multidot.t.sup.A .multidot.(W-FL).sup.B .multidot..theta..sub.h.sup.c .multidot.E, where t is the thickness of the metal strip (mm), W is the width of the metal strip (mm), FL is the length of a flat roll portion, .theta..sub.h is the roll taper (rad) under a hot state, E is the elastic modulus of the metal strip (kgf/mm.sub.2), and K, A, B, C are constants. The tension (.sigma..sub.min) sufficient to prevent transverse displacement is obtained as a minimum value of the tension (.sigma.) satisfying the following equations: .DELTA.D<(l-W))/2 and .DELTA.D=g(t, W, .mu., LS, E, .theta..sub.h, .sigma., Ra, Ra'), where .DELTA. D is the transverse displacement amount, l is the roll barrel length, .mu. is the coefficient of friction between the metal strip and roll, LS is the line speed, .sigma. is the tension of the metal strip, Ra is the surface roughness of the metal strip, and Ra' is the surface roughness of a roll.