A primary factor in manufacturing high-quality cold-rolled sheet is the ability to accurately predict the required rolling force. Rolling force directly influences roll-stack deflections, which correlate to strip thickness profile and flatness. Accurate rolling force predictions enable assignment of efficient pass schedules and appropriate flatness actuator set-points, thereby reducing rolling time, improving quality, and reducing scrap. Traditionally, force predictions in cold rolling have employed deterministic, two-dimensional analytical models such as those proposed by Roberts and Bland and Ford. These simplified methods are prone to inaccuracy, however, because of several uncertain, yet influential, model parameters that cannot be established deterministically under diverse cold rolling conditions. Typical uncertain model parameters include the material's strength coefficient, strain-hardening exponent, strain-rate dependency, and the roll-bite friction characteristics at low and high mill speeds. Conventionally, such parameters are evaluated deterministically by comparing force predictions to force measurements and employing a best-fit regression approach. In this work, Bayesian inference is applied to identify posterior probability distributions of the uncertain parameters in rolling force models. The aim is to incorporate Bayesian inference into rolling force prediction for cold rolling mills to create a probabilistic modeling approach that learns as new data are added. The rolling data are based on stainless steel types 301 and 304, rolled on a 10-in. wide, 4-high production cold mill. Force data were collected by observing load-cell measurements at steady rolling speeds for four coils. Several studies are performed in this work to investigate the probabilistic learning capability of the Bayesian inference approach. These include studies to examine learning from repeated rolling passes, from passes of diverse coils, and by assuming uniform prior probabilities when changing materials. It is concluded that the Bayesian updating approach is useful for improving rolling force probability estimates as evidence is introduced in the form of additional rolling data. Evaluation of learning behavior implies that data from sequential groups of coils having similar gauge and material is important for practical implementation of Bayesian updating in cold rolling.

References

References
1.
Roberts
,
W. L.
,
1965
, “
A Simplified Cold Rolling Model
,”
Iron Steel Engineer
,
42
(10), pp.75–87.
2.
Bland
,
D. R.
, and
Ford
,
H.
,
1948
, “
The Calculation of Roll Force and Torque in Cold Strip Rolling With Tensions
,”
Proc. Inst. Mech. Eng.
,
159
, pp.
144
153
.10.1243/PIME_PROC_1948_159_015_02
3.
Xie
,
H.
,
Jiang
,
Z.
,
Tieu
,
A.
,
Liu
,
X.
, and
Wang
,
G.
,
2008
, “
Prediction of Rolling Force Using an Adaptive Neural Network Model During Cold Rolling of Thin Strip
,”
Int. J. Modern Phys. B
,
22
(
31-32
), pp.
5723
5727
.10.1142/S0217979208051078
4.
Dixit
,
U. S.
, and
Chandra
,
S.
,
2003
, “
A Neural Network Based Methodology for the Prediction of Roll Force and Roll Torque in Fuzzy Form for Flat Rolling Process
,”
Int. J. Adv. Manuf. Technol.
,
22
(
3
), pp.
883
889
.10.1007/s00170-003-1628-8
5.
Larkiola
,
J.
,
Myllykoski
,
M.
,
Korhonen
,
A. S.
, and
Cser
,
L.
,
1998
, “
The Role of Neural Networks in the Optimization of Rolling Processes
,”
J. Mater. Process. Technol.
,
80-81
, pp.
16
23
.10.1016/S0924-0136(98)00206-4
6.
Bagheripoor
,
M.
, and
Bisadi
,
H.
,
2013
, “
Application of Artificial Neural Networks for the Prediction of Roll Force and Roll Torque in Hot Strip Rolling Process
,”
Appl. Math. Model.
,
37
, pp.
4593
4607
.10.1016/j.apm.2012.09.070
7.
Fleck
,
N. A.
,
Johnson
,
K. L.
,
Mear
,
M. E.
, and
Zhang
,
L. C.
,
1992
, “
Cold Rolling of Foil
,”
Proc. Inst. Mech. Eng.
,
206
, pp.
119
131
.10.1243/PIME_PROC_1992_206_064_02
8.
Dixit
,
U. S.
, and
Dixit
,
P. M.
,
1996
, “
A Finite Element Analysis of Flat Rolling and Application of Fuzzy Set Theory
,”
Int. J. Mach. Tools Manuf.
,
36
(
8
), pp.
947
969
.10.1016/0890-6955(95)00099-2
9.
Syed
,
N. U. A.
,
2012
, “
Bayesian Statistics
,”
AccessScience
,
McGraw-Hill Education
,
New York
.
10.
Karandikar
,
J.
,
Schmitz
,
T.
, and
Abbas
,
A.
,
2012
, “
Spindle Speed Selection for Tool Life Testing Using Bayesian Inference
,”
J. Manuf. Syst.
,
31
(
4
), pp.
403
411
.10.1016/j.jmsy.2012.07.013
11.
Zapata
,
R.
,
Traverso
,
M.
,
Abbas
,
A.
, and
Schmitz
,
T.
,
2008
, “
Bayesian Updating of Stability Beliefs
,”
Proceedings of American Society for Precision Engineering Annual Meeting
, Portland, OR, Oct. 19–24.
12.
Ettler
,
P.
,
Karny
,
M.
, and
Guy
,
T.
,
2005
, “
Bayes for Rolling Mills: From Parameter Estimation to Decision Support
,”
Proceedings of the 16th IFAC World Congress
, Vol. 16, No. 1, pp.
1682
1682
.
13.
Capdevila
,
C.
,
Toda
, I
.
,
Caballero
,
F.
,
Garcia-Mateo
,
C.
, and
de Andres
,
C.
,
2012
, “
Determination of Hot and Cold Rolling Textures of Steels: Combined Bayesian Neural Network Model
,”
Mater. Sci. Technol.
,
28
(
3
), pp.
321
333
.10.1179/1743284711Y.0000000035
14.
Hitchcock
,
J. H.
,
1935
, “
Roll Neck Bearings
,” Report of ASME Special Research Committee on Heavy-duty Anti-friction Bearings, pp. 33–41.
15.
Smith
,
W. F.
, and
Hashemi
,
J.
,
2005
,
Foundations of Materials Science and Engineering
,
McGraw-Hill
,
Boston
, MA.
16.
Orowan
,
E.
,
1943
, “
The Calculation of Roll Pressure in Hot and Cold Flat Rolling
,”
Proc. Inst. Mech. Eng.
,
150
, pp.
140
167
.10.1243/PIME_PROC_1943_150_025_02
17.
Roberts
,
W. L.
,
1978
,
Cold Rolling of Steel
,
Marcel Dekker, Inc.
,
New York
, p.
325
.
18.
Hastings
,
W. K.
,
1970
, “
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
,”
Biometrika
,
57
(
1
), pp.
97
109
.10.1093/biomet/57.1.97
19.
Universal-Cyclops Specialty Steel Division
,
1977
,
Stainless Steels
,
Cyclops Corporation
,
Pittsburgh, PA
, pp.
43
59
.
20.
Malik
,
A. S.
, and
Grandhi
,
R. V.
,
2008
. “
A Computational Method to Predict Strip Profile in Rolling Mills
,”
J. Mater. Process. Technol.
,
206
(
1-3
), pp.
263
274
.10.1016/j.jmatprotec.2007.12.026
21.
Malik
,
A.
, and
Hinton
,
J.
,
2012
, “
Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills
,”
ASME J. Manuf. Sci. Eng.
,
134
(
5
), p.
051009
.10.1115/1.4007185
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