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Permissible Minimum Thickness in Asymmetrical Cold Rolling

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Abstract

The minimum rolling thickness in asymmetrical rolling was analyzed compared with that in symmetrical rolling. The differential equilibrium equations on forces were established to calculate the asymmetrical rolling force equation by slab method. An implicit expression of the minimum rolling thickness was then derived from the rolling force equation and Hitchcock equation. The results show that permissible minimum rolling thickness of asymmetrical rolling only exists within a specific range of cross-shear ratio, which is termed the cross-shear zone proportion of the whole deformation zone. Numerical computation was carried out to obtain a discrete solution of the minimum rolling thickness. Experiments were designed to investigate the influence factors on cross-shear ratio. Finally, experimental results prove the correctness of the improved formula given.

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Abbreviations

C 0 :

Constant

E 1 :

Elastic modulus of work piece

E 2 :

Elastic modulus of work roller

f:

Friction coefficient

Δh:

Thickness difference of entrance and exit

h̄:

Average thickness of entrance and exit

h:

Thickness in exit of deformation region

H:

Thickness in entrance of deformation region

h min :

Permissible minimum thickness

i:

Asymmetrical ratio

K:

Plane deformation resistance

l:

Arc length of contact

l′:

Arc length of contact considering elastic deformation of rolling piece and rollers

P:

Rolling force

p̄:

Average unit rolling force

p b :

Average unit rolling force in backward-slip zone

p f :

Average unit rolling force in forward-slip zone

p r :

Average unit rolling force in cross-shear zone

p x :

Average unit rolling force in whole deformation region

R:

Diameter of work roller

v:

Linear velocity of rollers in symmetrical rolling

v s :

Linear velocity of slow rollers in asymmetrical rolling

v f :

Linear velocity of fast rollers in asymmetrical rolling

x:

Horizontal displacement

ε:

Percentage of cross-shear zone in whole deformation region

τ f :

Frictional force

γ 1 :

Poison ratio of work piece

γ 2 :

Poison ratio of work roller

η c :

Limiting value of η.

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Authors and Affiliations

  1. State Key Laboratory of Rolling and Automation Laboratory, Northeastern University, Shenyang, Liaoning, 110004, China

    De-lin Tang (Doctor Candidate), Xiang-hua Liu, Xiang-yu Li & Liang-gui Peng

Authors
  1. De-lin Tang
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  2. Xiang-hua Liu
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  3. Xiang-yu Li
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  4. Liang-gui Peng
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Corresponding author

Correspondence to De-lin Tang.

Additional information

Foundation Item: Item Sponsored by National Natural Science Foundation of China (50974039)

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Tang, Dl., Liu, Xh., Li, Xy. et al. Permissible Minimum Thickness in Asymmetrical Cold Rolling. J. Iron Steel Res. Int. 20, 21–26 (2013). https://doi.org/10.1016/S1006-706X(13)60191-0

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  • DOI: https://doi.org/10.1016/S1006-706X(13)60191-0

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