Journal of Materials Engineering and Performance

, Volume 19, Issue 7, pp 936–941 | Cite as

An Analytical Modified Model of Clad Sheet Bonding by Cold Rolling Using Upper Bond Theorem

Article

Abstract

In this paper, clad sheet bonding by cold rolling was investigated using the upper bond theorem. Plastic deformation behavior of the strip at the roll gap was investigated, unlike previous methods; distinctive angular velocities are used for different zones in roll gap in present model and absolute minimum of rolling power function is achieved. Rolling power, rolling force, and thickness ratio of the rolled product affected by various rolling condition such as flow stress of sheets, initial thickness ratio, roller radius, total thickness reduction, coefficient of friction between rollers and metals and between components layer, roll speed, etc., are discussed. It was found that the theoretical prediction of the thickness ratio of the rolled product, rolling force, and rolling power are in good agreement with the experimental measurement.

Keywords

clad sheet bonding cold rolling cladding modeling of bimetallic strip upper bound theorem 

Nomenclature

V01

initial velocity of upper layer

V02

initial velocity of lower layer

Vf

final velocity of bimetal strip

ΔV

amount of velocity discontinuity on each surface of velocity discontinuity

ωR

rotational velocity of roller

ω

rotational velocity of each rigid zone

U

linear velocity of roll

tsi

initial thickness of upper layer

thi

initial thickness of lower layer

tsf

final thickness of upper layer

thf

final thickness of lower layer

tf

final thickness of strip

R0

roller radius

R

radius of cylindrical surface of velocity discontinuity

r

reduction in area

ma

coefficient of friction between roller and strip

mb

coefficient of friction between layers

\( \Upgamma \)

surface of velocity discontinuity

S

area of the surface of velocity discontinuity

W

shear power of the surface of velocity discontinuity

σs or SS

flow stress of upper layer

σh or Sh

flow stress of lower layer

F

rolling force

L

contact length

J

rolling power

θ

angle between motion direction and X-axis

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Copyright information

© ASM International 2009

Authors and Affiliations

  1. 1.Faculty of Metallurgy and Material Science Engineering, College of EngineeringUniversity of TehranTehranIran

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