A non‐circular arc roll force model for gold rolling

Abstract

SUMMARYA long established approximation, normally invoked in the development of classical rolling theory, is that the work roll-strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper formulates the analysis of non-circular arc rolling conditions, and describes a new iterative procedure for computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional analysis. The algorithm is of the 'hill climbing' variety, involving the calculation of suitable gradients.One notable feature is that the gradients have to be carefully defined with respect to the correct 'space', in order that physically inadmissible discontinuities are not introduced during the hill-climbing.Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this feature.

Numerical Modeling Rolling Contact Problem and Elasticity Deformation of Rolling Die under Hot Milling

“…where T is the temperature, given here in • C and V r is given in m/s. For steel rolling, the relevant formula for µ in Equation (36) is developed by Geleji in [27] and even cited by different researchers. In the same way, Equations (38) and (37) are given in [28] and [29], respectively.…”

Numerical Treatments of Slipping/No-Slip Zones in Cold Rolling of Thin Sheets with Heavy Roll Deformation

“…The iterative process described above often fails to converge if no precautions are taken. This is why alternatives have been proposed, based on conjugate gradient [10] or one-domain FEM computation with internal discontinuity-the roll-strip interface [11]. However the fixed point iterative technique remains the only one in use.…”

Experimental and theoretical analysis of roll flattening in the deformation zone for ultra-thin strip rolling

“…Hitchcock [3] considers the elastic deformation of the rolls but assumes that the deformed profile remains a circular arc of increased radius. During the rolling and temper rolling process of an ultra-thin strip, the contact arc length is much larger than the thickness of the strip, resulting in a non-circular roll shape in the deformation zone [4][5][6][7]. Consequently, the conventional theory is not suitable for ultra-thin strip rolling and skin pass rolling.…”

“…Accordingly, they consider there to be a minimum rolling gauge in the rolling process. For the non-circular rolling condition, Grimble et al [5] provide a new iterative algorithm. Fleck et al [6,7] propose a new roll flattening model based on Johnson's theory [8].…”