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A new model for thermo-mechanical coupled analysis of hot rolling

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Abstract

A new sine velocity field is proposed to analyze total power in the roll gap for rolling in hot strip finishing mill. The field and linear geometric midline yield criteria are used to calculate the plastic deformation power, and the collinear vector inner product method is used to get friction power. Then analytical equation of strip rolling power functional is obtained. Finally, the roll force and torque can be calculated by minimizing the power functional. In the model, average deformation resistance is determined by the thermo-mechanical coupled analysis. The prediction accuracy of the proposed model is examined through comparing with the on-line measured results in a hot strip finishing mill. It shows that the predicted roll forces are in good agreement with the measured ones, and the maximum error is less than 12 %. Moreover, the effects of various rolling conditions, such as thickness reduction, friction factor, and shape factor, on roll force, location of neutral angle, and stress-state coefficient are discussed systematically.

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Abbreviations

b :

Strip width

c s :

Specific heat of the steel

\(D\left( {\dot{\varepsilon }_{ij} } \right)\) :

Power per unit volume

F min :

Minimum value of rolling force

F, dF :

Friction surface area and an infinitesimal area on it

h 0, h 1 :

Half of the initial and final strip thickness at entrance and exit

h m :

Half of the mean strip thickness in the roll gap

h mf, h mb :

The mean thickness of strip in forward and backward slip zones

h x (h α ):

Half of the strip thickness in deformation zone

h x ′:

The first-order derivatives of h x

\(h_{{\alpha_{n} }}\) :

Half of the strip thickness at position of neutral angle

Δh :

Half of the absolute reduction

J*:

Total power

k :

Yield shear stress

k c :

Roll contact heat flow coefficient

k d :

Deformation efficiency coefficient

k f :

Friction efficiency coefficient

l :

Projected length of roll-strip contact arc

m :

Friction factor

M min :

Minimum value of roll torque

n σ :

Stress-state coefficient

N :

The first-order derivative equation of U

\(\bar{p}\) :

Rolling force per unit roll-strip contact area

R :

Radius of work roll

T entrance :

The strip temperature at entrance

T exit :

The strip temperature at exit

T s :

Strip temperature

T r :

Work roll temperature

U :

The flow volume per second

v 0, v 1 :

Velocity of strip at entrance and exit

v x , v y , v z :

Velocity components in x, y, z directions

v R :

Roll circumferential velocity

v Rx , v Rz :

Velocity components of work roll in x, z directions

∆v f :

Discontinuous quantity of tangential velocity

∆v x , ∆v y , ∆v z :

The components of ∆v f in x, y, z directions

x N :

Projected length between neutral point and entrance

\(\dot{W}_{\text{i}}\) :

Deformation power

\(\dot{W}_{\text{f}}\) :

Friction power

\(\dot{W}_{\text{s}}\) :

Shear power

\(\dot{W}_{s0}\) :

Shear power at entrance

α, β, γ :

Direction angles formed by \(\tau_{f}\) and the coordinate axes in x, y, z directions

α n :

Neutral angle

χ :

Lever arm

ɛ :

Equivalent strain

\(\dot{\varepsilon }_{ij}\), \(\dot{\varepsilon }_{\hbox{max} }\), \(\dot{\varepsilon }_{\hbox{min} }\) :

Strain-rate tensor and its maximum and minimum values

\(\dot{\varepsilon },\dot{\varepsilon }_{x} ,\dot{\varepsilon }_{y} ,\dot{\varepsilon }_{z}\) :

Equivalent strain rate and the components of strain rate in x, y, z directions

θ :

Bite angle

ρ s :

Density of the steel

σ s :

Yield stress

τ f :

Frictional stress on the roll-strip contact surface

τ fx , τ fy , τ fz :

Components of \(\tau_{f}\) in x, y, z directions

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Acknowledgments

The authors gratefully express their appreciation to National Nature Science Foundation of China (No.: 51074051), the Fundamental Research Funds for the Central Universities (No.: N140704001), and the PhD Start-up Fund of Natural Science Foundation of Liaoning Province, China (No.: 20131033), for sponsoring this work.

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Authors and Affiliations

  1. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, 110819, Liaoning, China

    Geng-Sheng Ma, Yuan-Ming Liu, Wen Peng, Fang-Chen Yin, **g-Guo Ding, De-Wen Zhao, Hong-Shuang Di & Dian-Hua Zhang

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  1. Geng-Sheng Ma
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  2. Yuan-Ming Liu
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  3. Wen Peng
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  6. De-Wen Zhao
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  7. Hong-Shuang Di
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Correspondence to Geng-Sheng Ma.

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Technical Editor: Alexandre Mendes Abrao.

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Ma, GS., Liu, YM., Peng, W. et al. A new model for thermo-mechanical coupled analysis of hot rolling. J Braz. Soc. Mech. Sci. Eng. 39, 523–530 (2017). https://doi.org/10.1007/s40430-015-0390-9

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