Abstract
The weighted velocity field was simplified for analysis of hot strip roling. Using the field and GM (geometric midline) yield criterion, the deformation power, friction power and shear power were obtained respectively. Summing the partial power contributions, the total deformation power for strip roling was presented. Then, by minimizing the power function, the roling force was obtained; meanwhile, considering the efect of rol elastic flattening, iterative calculation of the rol radius was carried out until the radius was convergent. On-line data were compared with the calculated results to verify the model accuracy. It was indicated that the calculated roling forces were basicaly in agreement with the measured ones since the maximumerror was less than 10? 0%. Moreover, the efects of various roling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral angle, and stress state coeficient were discussed systematicaly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- hx, hm:
-
Half of the plate thickness and half of the average plate thickness in the rol gap
- α, β, γ:
-
Direction angles formed by τf and the coordinate axes in x, y, z directions
- h0, h1:
-
Half of the initial and final plate thickness at entry and exit in deformation zone
- v0, v1:
-
Velocity of plate at entry and exit in deformation zone
- h, Δh:
-
Plate thickness and half of the absolute reduction
- τf:
-
Frictional shear stress on the plate surface
- Δvf:
-
Discontinuous quantity of tangential velocity
- ε:
-
Logarithmic reduction per pass
- ε̇:
-
Strain rate
- αn:
-
Position of neutral angle
- θ:
-
Contact angle
- ε̇x, ε̇y, ε̇z:
-
Strain rate component along x, y, z directions
- R, R′:
-
Radius of work rol, flatening radius
- ε̇min, ε̇max:
-
Minimum and maximum strain rate
- hx′:
-
The first order derivatives of hx
- n σ :
-
Stress state coeficient
- l:
-
Projected length of roll-workpiece-contact arc
- χ:
-
Leverarm ratio
- b:
-
Plate width
- F:
-
Roling force
- Ẇ i :
-
Deformation power
- D(ε̇ij):
-
Plastic specific work rate
- Ẇ f :
-
Friction power
- σ s :
-
Yield stress
- χ:
-
Arm factor
- Ẇ s :
-
Shear power
- k:
-
Yield shear stress
- t:
-
Temperature
- J*:
-
Total power
- J* min:
-
Minimum value of total power
- m:
-
Friction factor
- M min :
-
Minimum value of roling torque
- vx, vy, vz:
-
Velocity components in x, y, z directions
- F min :
-
Minimum value of roling force
- U:
-
Flow volume per second of the deformation part
- v R :
-
Roll circumferential velocity.
References
S. Kobayashi, T. Altan, S. Oh, Metal Forming and the Finite Element Method, Oxford University Press, Oxford, 1989.
S. M. Hwang, M.S. Joun, Int. J. Mech. Sci. 34 (1992) 971–984.
S. W. Xiong, J. M. C. Rodrigues, P. A. F. Martins, Fin. Elem Anal. Des. 32 (1999) 221–233.
W.J. Kwak, Y. H. Kim, H. D. Park, J. H. Lee, S. M. Hwang, ISIJ Int. 40 (2000) 1013G1018.
X. S. Wang, Y. Peng, L.P. Xu, H. M. Liu, J. Iron Steel Res. Int. (2010) No. 9, 36–39.
Y. K. Kim, W. J. Kwak, T. J. Shin, S. M. Hwang, ISIJ Int. 50 (2010) 1644–1652.
T. von Karman, Zeitschriftfur Angewandte Mathematik and Mechanik (1925) No. 5, 139–141.
E. Orowan, Proc. Inst. Mech. Eng. 150 (1943) 140–167.
R. B. Sims, Proc. Inst. Mech. Eng. 168 (1954) 191–200.
W. Johnson, H. Kudo, Int. J. Mech. Sci. 2 (1960) 175–191.
S. I. Oh, S. Kobayashi, Int. J. Mech. Sci. 17 (1975) 293–305.
K. Kato, T. Murota, T. Kumagai, Jap. Soc. Tech. Plasticity 231 (1980) No. 21, 359–369.
Z. F. Wang, Z. Y. Zhao, Iron and Steel 28 (1993) No. 9, 29–33
D. W. Zhao, S. H. Zhang, C. M. Li, H. Y. Song, G. D. Wang, J. Iron Steel Res. Int. 19 (2012) No. 3, 20–24.
S. H. Zhang, D. W. Zhao, C. R. Gao, Int J. Mech. Sci. 57 (2012) 74–78.
Y. K. Sun, Model and the Control of Hot Strip Mill, Metallurgical Industry Press, Beijing, 2007.
W. Deng, D.W. Zhao, X. M. Qin, X. H. Gao, L. X. Dun, X. H. Liu, J. Iron Steel Res. Int. 17 (2010) No. 3, 28–33.
D.W. Zhao, G.J. Wang, X. H. Liu, G. D. Wang, Trans. Nonf. Met. Soci. Ch. 18 (2008) No. 1, 46–52.
G.J. Wang, H. J. Du, D.W. Zhao, X. H. Liu, G. D. Wang, J. Iron Steel Res. Int. 16 (2009) No. 6, 1, 3–17.
S. H. Zhang, D.W. Zhao, C. R. Gao, J. Northeast. Univ. Nat. Sci. 32 (2011) 1570–1573.
D. W. Zhao, J. Z. Xu, H. Yang, Proc. Int. Sym. on Strength Theory, Science Press, New York, 1998.
D. W. Zhao, Y. J. Xie, X. H. Liu, G. D. Wang, J. Northeast. Univ. Nat. Sci. 25 (2004) 121–124.
D. W. Zhao. Mathematical Solution of Continuum Forming Force, Northeastern University Press, Shenyang, 2003.
G. D. Wang, D. W. Zhao, Modern Material Forming Mechanics, Northeastern University Press, Shenyang, 2004.
Z. Y. Zhao, Metal Plastic Deformation and Rolling Theory, Metallurgical Industry Press, Beijing, 1980.
H. J. Li, L. J. Shi, J. Z. Xu, G. D. Wang, J. Northeast. Univ. Nat. Sci. 30 (2009), 369–372.
X. H. Liu, X. L. Hu, L. X. Du, Rolling Parameter Calculation Model and Its Application, Chemistry Industry Press, Beijing, 2007.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Foundation Item: Item Sponsored by National Natural Science Foundation of China (51074052, 50734002)
Rights and permissions
About this article
Cite this article
Zhang, Dh., Cao, Jz., Xu, Jj. et al. Simplified Weighted Velocity Field for Prediction of Hot Strip Rolling Force by Taking into Account Flatening of Rolls. J. Iron Steel Res. Int. 21, 637–643 (2014). https://doi.org/10.1016/S1006-706X(14)60099-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1006-706X(14)60099-6