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Stresses and Defects in Roll Products: A Review of Stress Models and Control Techniques

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Abstract

Coiling is a method used to store long and thin products, such as a wire or film, made out of steel, plastic, or rubber, in a volumeefficient manner, and is the final phase of most roll product manufacturing systems. Internal stress in a roll product is exerted during this process, and can decrease the productivity by causing buckling or telescoping. Therefore, this issue has warranted interest in the roll-to-roll manufacturing process, and significant effort has gone into improving the internal stress while avoiding the loosening and slippage between adjacent coiled layers. In this paper, we review various studies on the dynamics of internal stresses, as well as the control techniques used to improve the stress and quality of a roll product. Initially, the various defects occurring in roll products and a radial stress generating such defects are introduced, and mathematical models applied to analyze the dynamics of stress with respect to the characteristics of the coiled materials and the coiling process conditions are compared. In addition, techniques to control the internal stress are introduced. Finally, tension profiles used in the coiled tension control technique are introduced and compared. This review will be useful for understanding the defects that occur in roll products due to internal stress, as well as alternative methods to improve the quality of a coiled roll.

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Abbreviations

εh :

hoop strain

εr :

radial strain

u:

radial displacement

r:

ratio radius of wound roll to core radius

R:

outside radius of fully wound roll

σr :

radial stress

σh :

hoop stress

Er :

modulus of elasticity of the roll in the radial direction

Eh :

modulus of elasticity of the roll in the hoop direction

μr :

Poisson’s ratio in the radial direction

μh :

Poisson’s ratio in the hoop direction

Tw :

winding tension

σw :

winding stress

I(r, p):

winding integrals in terms of hypergeometric functions in Yagoda model

a:

non-dimensional constant related to elastic material properties of roll in Yagoda model

δ:

non-dimensional constant related to elastic material properties of core in Yagoda model

μ:

coefficient of friction

N:

nip load

h:

thickness of film

s:

radial location of the current outer wrap of the winding roll

Γ:

constant related to boundary conditions of radial stress of roll in Lee model

sij :

compliance of film

σg * :

effective residual stress considering gravity force of film

β:

non-dimensional constant related to elastic material properties of roll in Lee model

ρ:

density of film

g:

gravitational acceleration

εθ,b :

bending stress in wound layer

εw :

strain of film in winding section

εu:

strain of film in upstream of winding section

Vw :

film velocity in winding section

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  1. School of Mechanical Engineering, Changwon National University, 20, Changwondaehak-ro, Uichang-gu, Changwon-si, Gyeongsangnam-do, 51140, Republic of Korea

    Changwoo Lee

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Lee, C. Stresses and Defects in Roll Products: A Review of Stress Models and Control Techniques. Int. J. Precis. Eng. Manuf. 19, 781–789 (2018). https://doi.org/10.1007/s12541-018-0094-z

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