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Cold rolling mill process: a numerical procedure for industrial applications

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Abstract

The paper proposes a model for a cold rolling mill process in the full-film regime that uses lubricant emulsion sprayed on at the entrance of the strip. The aim of the model is to forecast the reduction of strip thickness versus the flow rate of lubricant given the other operation parameters. The model includes strip plastic deformation, lubricant flow and lubricant viscosity depending on pressure. The mathematical problem is a free boundary one and a numerical procedure, applied to an industrial plant, is presented with some results.

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Abbreviations

h(x):

Lubricant film thickness

h 0 :

Inlet lubricant film thickness

p(x):

Normal pressure of lubricant film acting on the strip surface

R :

Roll radius

S 1 :

Inlet strip thickness

S 2 :

Outlet strip thickness

u 1 :

Horizontal component of the strip speed

u 1,0 :

Horizontal component of the strip speed in the inlet zone

u 1,f :

Horizontal component of the strip speed in the outlet zone

u 2 :

Horizontal component of the roll speed

v 1 :

Vertical component of the strip speed

v 2 :

Vertical component of the roll speed

x :

Generic abscissa

x 1 :

Abscissa of the point in which the plastic deformation takes place

y :

Generic ordinate

y 1,0 :

Strip ordinate in the inlet zone

y 1,f :

Strip ordinate in the outlet zone

y 1(x):

Strip profile ordinate

y 2(x):

Roll profile ordinate

γ :

Viscosity coefficient in Barus law

μ :

Lubricant viscosity

μ 0 :

Lubricant viscosity corresponding to a pressure p=0

σ s :

Material yield stress

σ x :

Normal horizontal stress

σ Y :

Normal vertical stress

τ :

Tangential stress acting on the strip surface

ω :

Angular roll speed

Q :

Lubricant flow rate

P * :

Pressure relative to material yield stress

X * :

Dimensionless abscissa X *=x/x 1

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Authors and Affiliations

  1. Dipartimento di Ingegneria Industriale, Università degli Studi di Perugia, via G. Duranti, 67, 06125, Perugia, Italy

    Maria Cristina Valigi

  2. Dipartimento di Energetica “Sergio Stecco”, Sezione di Meccanica Applicata, Università degli Studi di Firenze, via S.Marta 3, 50139, Firenze, Italy

    Monica Malvezzi

Authors
  1. Maria Cristina Valigi
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  2. Monica Malvezzi
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Correspondence to Maria Cristina Valigi.

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Valigi, M.C., Malvezzi, M. Cold rolling mill process: a numerical procedure for industrial applications. Meccanica 43, 1–9 (2008). https://doi.org/10.1007/s11012-007-9085-3

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  • DOI: https://doi.org/10.1007/s11012-007-9085-3

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