Sadiq T JERA.26. 11. pdf
International Journal of Engineering Research in Africa
ISSN: 1663-4144, Vol. 26, pp 11-29
doi:10.4028/www.scientific.net/JERA.26.11
© 2016 Trans Tech Publications, Switzerland
Submitted: 2016-04-05
Revised: 2016-07-04
Accepted: 2016-07-11
Online: 2016-10-07
Numerical Estimation of Rolling Load and Torque for Hot Flat Rolling of
Hcss316 at Low Strain Rates Based on Mean Temperature
1
1
Sadiq, T O, a Fadara T G, b Aiyedun, P. O and *Idris, J
Manufacturing Department, Engineering Materials Development Institute
KM4, Ondo Road, P.M.B 611, Akure, Ondo State, Nigeria
a
Department of Mechanical Engineering, College of Engineering
Federal Polytechnic, Ede, Osun State, Nigeria
b
Department of Mechanical Engineering, College of Engineering
Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
*
Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia, UTM, Skudai 81310, Johor Bahru, Malaysia
*
Corresponding Author: +6075534659
E-mail addresses: adisaolohunde@yahoo.com (T.O. Sadiq), Jamaliah@fkm.utm.my (J. Idris)
Keywords: Rolling Process, Numerical Estimation, Rolling Load, Torque, Strain Rates, Yield
Stress, Zener–Hollomon Parameter.
ABSTRACT. Numerical estimation of rolling load and torque often showed large discrepancies
when compared with experimental values. This was attributed to difficulty in estimating the mean
rolling temperature from the available data. This work is thus directed at obtaining a good estimate
for the mean rolling temperature which can effectively be used for load and torque estimates. Hot
flat rolling stimulation by use of the Bland and Ford’s cold rolling (HRBF) theory confirmed the
reverse sandwich effect in selected carbon steels at low strain rates. In this work, the effect of pass
reduction on rolling temperature distribution, yield stress and rolling load were studied for AISI
Type 316 stainless steel (HSCSS316). For this new simulation, at low and high strain rates, results
showed that the ratio of experimental to calculated rolling load and torque were higher at lower
reduction than at higher reduction. These results confirmed excess load and torque in the hot rolling
of HSCSS316 low reductions. The results obtained from Hot Rolling Bland and Ford’s Theory
based on Root Mean Square rolling temperature were in good agreement with values obtained using
Reverse Sandwich Model and the Reverse Sandwich- Hot Rolling Bland and Ford’s Program under
the same rolling conditions.
1.
INTRODUCTION
It was discovered that measured load and torque were excessive when compared with calculated
values using Simple Rolling Theories such as Sims, Bland and Ford, and a simple rolling
temperature based on the mean entry temperature into the roll gap [2], for hot flat rolling at low
strain rates and low reduction. These Theories all gave correct results for high strain rates range
regarded as normal rolling conditions.
The strength of a material is dependent on its microstructure and the condition during testing of
which temperature and strain rate are very important. The structure of the material is equally very
much dependent on temperature. For hot rolling at low strain rates, the contact times with the rolls
become increasingly large and the effect of this is manifested in pronounced temperature variations
as slab is being rolled. It can then be concluded that temperature effects are the most important
factors during hot rolling at low strain rates. From previously conducted investigations, the cause
was traced to the fact that hot rolling at low strain rates actually occur at a temperature much lower
than the mean entry temperature into the roll gap.
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International Journal of Engineering Research in Africa Vol. 26
These low mean rolling temperatures lead to higher stress in materials since the strength of the
material is dependent on temperature. Consequently, higher load and torque were experienced in
material since they are also dependent on the yield stresses. The key to unravelling the mystery is
then left to be found in the determination of the correct mean rolling temperature. In this work,
efforts are aimed at using a suitable method in summarising the set of temperatures encountered
during roll contact time into a single one. This single one is used to obtain the correct flow stress
and hence correct load and torque. In clearer language, the best average temperature is desired. This
will be done by considering various methods of obtaining averages and using each to ascertain the
mean rolling temperature which is most suitable for the computation of loads and torques.
1.2
OBJECTIVES
To estimate the Mean Rolling Temperatures using the different averaging methods and to use these
results obtained in estimating Yield Stresses which will be subsequently used in calculating the
Rolling Load and Torque. Also, to make comparison between the Rolling Load and Torque with
results obtained by other Researchers.
2.
METHODOLOGY
2.1
Hot Rolling Bland and Ford’s Theory
The Bland and Ford’s Theory (HRBF) is a cold rolling theory, where sliding takes place throughout
the arc of contact. It has however been found to be applicable to a hot rolling situation where sliding
exists throughout the roll gap. This is the situation for hot rolling of HCSS316 at 9000C – 12000C;
reductions of 0 -15%; strain rates of 0.07 -1.5 ; and geometrical factor of 4.0 – 20.00 as reported
in the literatures [2, 3, 4].
Rolling Load (P) and rolling torque (T) are respectively given by equation (1) and (2);
∅
=
+
1
∅
2
=
Where:
=
=
. .
. .
.
3
.
4
.
=
=
.
=
.
+
.
5
6
+
−
7
International Journal of Engineering Research in Africa Vol. 26
Where;
Α
K
θ
∅
R’
R0
S
h1,2
N
μ
13
Angle of entry i.e. maximum value of θ in radians
Instantaneous yield stress (N/m2)
Angle subtended by a point on roll surface w.r.t. line joining roll centres in radians.
Neutral angles in radians
Deformed roll radius (mm)
Undeformed roll radius in mm
Normal roll pressure (N/mm2)
Entry and exit height (mm)
Number of measured values
Fractional coefficient
In rolling processes generally, it is vital to know the temperature distribution within the slab. The
literatures of previous researchers showed that temperature is the dominant parameter controlling
the kinetics of metallurgical transformations and the flow stress of the rolled metal. The mean
temperature used by Aiyedun (1984) in Hot Rolling Bland and Ford’s Theory is given in the
equation 8
=
+
Where: T1 and T2 are entry and exit temperatures.
8
The true yield stresses for load and torque calculation are respectively given as equations (9) and
(10);
=
9
=
Where:
=
10
=
r = reduction
The percentage rolling reduction is given as:
2.2
=
×
%
11
The Reverse Sandwich Model (RSM)
The reverse sandwich model predicts the rolling reduction, rolling temperatures and temperature
distribution along the through thickness of HCSS316. Detailed theoretical analyses of the model
have been reported [7, 8, 13].
With the specimen partitioned into 17 zones (n = 1 – 17), the model’s prediction of rolling
temperature follows equation (12) to (15).
The temperature at the specimen’s core is given as:
=
+
12)
14
International Journal of Engineering Research in Africa Vol. 26
Where:
TF
TM
TS
Furnace temperature,
The mean rolling temperature
Exist or entry temperature
=
13
+
=
K Reverse Sandwich Model constant, values of which are functions of the rolling speed.
1≤
≤4
8<
< 9,
5≤
15 ≥
≤7
≥ 12,
=
11 ≥
=
+
.
.
=
9,
≤
Where:
V
=
≤
≤
≤
≤
≤
,
≤ 10,
+
.
=
=
,
=
,
15
15
The rolling speed is related to the reverse sandwich model constant as follow:
9 ≤
14
1.59
.
.
=
15
16
16
16
.
16
Peripheral velocity of rolls (mm-1)
The approximate empirical equation of Farag and Sellars [9] was used in the model for
determination of mean strain rate thus:
δ
=
=
.
.
[
reduction (mm)
]
.
17
The Zener-Hollomon parameter was determined for each of the seventeen (17) zones along
thickness (Z1 – Z17) using the proposition of Zener and Hollomon equation [2, 3] written as;
=
Where:
R
T
Z
Q
=
=
=
=
=
Universal constant (8.314Jkg-1/ K)
Absolute temperature (0C)
Zener-Hollomon parameter
Thermal energy
18
International Journal of Engineering Research in Africa Vol. 26
15
The Z-values are uniquely related to the stress, and, hence the deformation of the material. For
HCSS316 specimen under the prevailing rolling condition, Q = 460 KJ/mol. [2, 3, 4]
2.3
Choice of Averaging Method for obtaining Mean Rolling Temperature.
Based on comparison of the results obtained with experimental values for the four averaging
methods of harmonic mean method, geometric mean method, arithmetic mean method and root
mean square method, the root square method gave the lowest error percentage. Hence was used in
Bland and Ford’s Theory to estimate the yield stresses for load and torque and hence rolling load
and torque for the various specimens.
2.4
Simulation of the Model
Simulation of the model was carried out using FORTRAN 77. The required input data are rolling
speed, roll radius, furnace temperature, initial and final height of the specimen, and specimen width.
From the output of the program, the temperature distribution, yield stress validation, rolling load
and torque distribution across the thickness of the rolled specimen at different pass reduction are
evident.
2.5
Experimental
Data used in validating the new hot rolling simulation was obtained through preliminary
metallographic, hot torsion tests, and hot rolling experiments performed on the as-received wrought
AISI316 with inclusions of Nb, V and Ti in the temperature range (600 – 1200) 0C and strain rate
range of 3.6 X 10-3s-1 to 1.4s-1. The wrought material was High Carbon Stainless Steel; ASME SA240 from Heat 38256-2C, product of G.O. Carlson Inc., P.A., and U.S.A. The material was cut into
slabs of small sizes and hot rolled. The hot rolling experiments were performed on two laboratory
mills; a 1000KN, 2-high, single stand, reversible mill with rolls of 254.0mm diameter by 266.0mm
barrel length and 50T (498KN) capacity, 2-high reversible, Hille 50T rolling mill with rolls of
diameter 139,7mm.
3.0
DISCUSSION OF RESULTS
The analyses presented above were used to write a Computer program which gave hot rolling load
and torque to a reasonable accuracy. The program made use of experimental and theoretical data
from a study of loads and torques for light reduction in hot flat rolling at strain rates carried out by
[2] and the results from the reverse sandwich effects in HCSS316 hot flat rolled at low strain rates
and low reductions investigated by [13] as input data.
In estimating the correct mean rolling temperature, four averaging methods of harmonic means,
geometric mean, arithmetic mean and root mean square were used to calculate mean rolling
temperature from the measured temperatures of various specimens of steels during roll contact. Due
to the least error involved when compared with experimental values, the root square method was
used in Bland and Ford’s Theory to calculate yield stresses and hence rolling loads and torques for
the various specimens.
The results presented in Table1 will be discussed under the following headings:
•
Rolling Load Estimation
•
Rolling Torque estimation
•
Results for different Rolling Conditions
•
Results of Comparison of the results obtained with other Researchers.
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International Journal of Engineering Research in Africa Vol. 26
3.1
Rolling Load Estimation
With reference toTable2, the results obtained for rolling load at different hot rolling conditions
using the Hot Rolling Bland and Ford’s Theory (based on RMS mean rolling temperature) are in
very good agreement with experimental values obtained for the same rolling condition [2]. The
results gave a maximum and minimum error of 20.19% and .42% respectively.
3.2
Rolling Torque Estimation
The results obtained for rolling torque estimation at different hot rolling condition using the Hot
Rolling Bland and Ford’s Theory (based on RMS mean rolling temperature) are in good agreement
with the experimental results obtained [2] under the same rolling condition. The results gave a
minimum error of 0.41% and a maximum error of 22.54% (see Table 3).
3.3
Results for Different Rolling Conditions
The results for hot flat rolling of HCSS316 (with Nb, V and Ti inclusions) at low strain rates (0.08 –
1.5) s-1 and low reductions (r ≈10%) on Mills A and B for varying parameters (Appendix A) are
sub-divided into the following headings:
• Effect of Variation of Reduction at Low and High Strain Rates
•
Effect of Variation of Strain Rates and Furnace Temperature
•
Effect of Varying Geometry (W1/h1) at Low and High Strain Rates.
•
Effect of Shot Blasted and Smooth Specimen Rolling on Mills A and B at Varying Strain
Rates.
3.3.1
Effect of Variation of Strain Rates and Furnace Temperature
For varying strain rates and furnace temperature (TF) values, specimen H20 – H24, H30-H31 and
H32 – H36 in that order, the Table 4&5 plotted as Figs. 3.1 to 3.3, show that as the strain rates
increases, the ratio of experimental to calculated load decreases on Mill A.
The output also shows that as the furnace temperature increased from 10500C at lowest strain rates
i.e. specimen H20 to approximately 12000C (SpecimenH32), the ratio of experimental to calculated
to load and torque increased from 1.02 to 1.05 and 0.99 t0 1.18 respectively. (See Tables 4&5).
However, the results from rolling on Mill B show no significant variation of the ratio of
experimental to calculated load at highest and lowest strain rates (See Table 4).
3.3.2
Effect of Variation of Reduction at Low and High Strain Rates
With reference to Table4 and the plot of Fig. 3.4, the ratio of experimental to calculated load
decreases from 1.03 to 0.93 with increase in rolling reduction (specimen H37 – H43) (6.29% –
23.27%) for rolling on Mill A at low strain rates.
Also, at high strain rates, the ratio of experimental load to calculated load decreases from 0.92 to
0.76 as rolling reduction increases (Specimen H38 – H44).
From Table5 plotted as Fig. 3.5 shows that the ratio of experimental torque to calculated torque
decreases from 1.17 to 0.90 with increase in rolling reduction (6.87 %– 24.53%) for rolling at low
strain rates (Specimen H38 – H44) on Mill A.
For rolling on mill B, the results in Table4 and Fig. 3.4 reveal that the ratio of experimental to
calculated load increases with rolling reduction at low strain rates (Specimen P55 – P50) and high
strain rates (Specimen P47- P53).
International Journal of Engineering Research in Africa Vol. 26
17
3.3.3. Effect of Varying Geometry (W/H0) at Low and High Strain Rates
At a reduction of about 10%, furnace temperature Tf = 11250C at low and high strain rates, the
following results were obtained:
From Table4 plotted as Fig.3.6 for specimens H50 - H53, H54 - H57 on Mill A as well as P58 –
P61, P62 – P65 on mill B, the average of the ratio of experimental to calculated rolling load is about
1.0 for hot rolling on both Mills at low and high strain rates with geometry (W/H0) varied between
5.0 and 10.00; an indication that there is no systematic effect of geometry variation on the ratio of
experimental to calculated load obtained using the Hot Rolling Bland and Ford’s approach.
3.3.4 Effect of Shot-blasted and Smooth Specimen Rolling on Mills A and B at Varying
Strain Rates, r ≈ 10%, Tf ≈ 10500C
Results showing the effect of rolling rough and smooth specimen on both Mills at varying strain
rates, reduction of about 10% and furnace temperature 10500C are reflected in Table 4 &Table 5.
For smooth specimen on mill A (Specimen H01H – H06H), the ratio of experimental to calculated
load and torque are higher (average of 1.138 and 1.208 respectively) than the values obtained for
rough specimen (Specimen H20 – H24) on the same mill (average of 0.974 and 0.948)
respectively).
However, on mill B, Table 4 shows that rough specimens (P30 – P31) have higher experimental to
calculated load ratio (average of 1.064) than smooth specimens (P21 – P19) with average value of
0.964.
3.4
COMPARISON OF THE RESULTS BASED ON THE RATIO OF EXPERIMENTAL
TO CALCULATED ROLLING LOAD AND TORQUE [HRBF] WITH RESULTS OF
REVERSE SANDWICH MODEL [SHOBOWALE] AND RSM-HRBF [ALAMU]
The accuracy or applicability of the Hot Rolling Bland and Ford’s Theory (based on RMS mean
rolling temperature) used in this work was investigated through comparison with results obtained
from the Reverse Sandwich Model [13] and RSM-HRBF Theory [7]. The comparison showed that
the results obtained were in good agreement.
3.4.1
Ratio of Experimental to Calculated Rolling Load and Torque
The following observations were made from the results presented in Table 7 and 8 plotted as Figs.
3.8, 3.9 and 3.10:
• The ratio of experimental load to calculated load (Pexp/Pcal) values obtained from HRBF
Theory (based on RMS mean rolling temperature) was lower than results obtained using
RSM-HRBF Theory [7] and Reverse Sandwich Model [13] for all rolling conditions
investigated on Mill A and Mill B, see Figs. 3.8 and 3.10. The results obtained from HRBF
Theory (based on RMS mean rolling temperature) usually fall below similar lines for the
RMS-HRBF Theory [7] and Reverse Sandwich Model [13].
• Also, the ratio of experimental to calculated torque (Gexp/Gcal) values was generally lower
using HRBF Theory (based on RMS mean rolling temperature) compared to ratio of
experimental to calculated torque (Gexp/Gcal) values using RMS-HRBF Theory [7] and
Reverse Sandwich Model [13] for all rolling conditions investigated on mill A, see Figs.3.9.
• Figures 3.8 and 3.10 revealed that the values of load obtained using HRBF Theory (based on
RMS mean rolling temperature) compared to RMS-HRBF Theory [7] and Reverse
Sandwich Model [13] values are closer to experimental values.
The points listed above show that the results obtained using HRBF Theory (based on RMS mean
rolling temperature) were in good agreement on both mills. This confirmed the applicability of the
HRBF Theory for estimating the Load and Torque in hot flat rolling of the HCSS316 based on
RSM Mean Rolling Temperature.
18
International Journal of Engineering Research in Africa Vol. 26
4.0
CONCLUSION
From the results obtained from the Hot Rolling Bland and Ford’s Theory based on RMS mean
rolling temperature, it can be concluded that:
• The mean rolling temperatures obtained were in very good agreement with experimental
values with a mean error of 3.60%.
•
The mean yield stress (for both Load and Torque calculations) obtained from the Hot
Rolling Bland and Ford’s Theory based on RMS mean rolling temperature was in very
good agreement with experimental values with a mean error of 10.14% and 7.13% for Load
and Torque calculations, respectively.
•
For varying reductions at low and high strain rates, furnace temperature of 11250C. The
following conclusions can be drawn.
(a) The ratio of experimental to calculated Load and Torque based on RMS mean rolling
temperature was higher at lower reduction of 5% than at higher reductions of 25% on
both mills.
(b) For 5% reduction on mill B, the ratio of experimental to calculated Load based on RMS
mean rolling temperature was about 1.03 at low strain rates and 0.93 at high strain rate.
(c) The ratio of experimental to calculated Torque based on RMS mean rolling temperature
on mill A was high about 1.17 at low reductions (5%) and low about 0.91 at higher
reduction.
•
For a furnace temperature of 11250C, 10% reductions at low and high strain rates for
varying geometry (W/H1), this conclusion can be drawn.
(a) The geometry (W/H1) varied between 5.0 and 10.0 has no systematic effect on the ratio
of experimental to calculated Load
(b) based on RMS mean rolling temperature on both mills but has a marked effect on the
ratio of experimental to calculated Torque based on RMS mean rolling temperature. It
increased from 0.99 to 1.05 on mill A.
•
Comparing smooth and rough specimens at a reduction of ̴ 10%, Tf ̴ 1050 0C and varying
strain rates, it can be concluded that:
(a) The ratio of experimental to calculated Load and Torque based on RMS mean rolling
temperature was both higher for smooth specimens than for rough specimens on mill A.
(b) The ratio of experimental to calculated Load based on RMS mean rolling temperature
was higher for rough specimens than for smooth specimens on mill B.
•
For varying furnace temperature (Tf) and varying strain rates at low reductions on mill A
and B, it can be concluded that:
(a) As the strain rate increases, the ratio of experimental to calculated Load and Torque
based on RMS mean rolling temperature decreases for a particular furnace temperature.
This confirms the presence of excess Load at low strain rate when greater chilling leads to
higher values of Z.
•
The
calculated
{(EXPT/CALC)LOAD}RMS
&
{(EXPT/CALC)TORQUE}RMS,
{(EXPT/CALC)LOAD}SHOBOWALE
&
{(EXPT/CALC)TORQUE}SHOBOWALE
and
{(EXPT/CALC)LOAD}ALAMU & {(EXPT/CALC)TORQUE}ALAMU were all in agreement,
indicating the applicability of the Hot Rolling Bland and Ford’s Theory based on RMS
mean rolling temperature for calculating Rolling Load and Torque at Low Strain Rates.
International Journal of Engineering Research in Africa Vol. 26
19
Acknowledgments
The Staff Members in the Department of Materials, Manufacturing and Industrial Engineering,
Faculty of Mechanical Engineering and ISI, Universiti Teknologi Malaysia are sincerely
appreciated for their financial and technical support during and after this work. This work was
partially supported by the Ministry of Higher Education of Malaysia (MOHE), Research
Management Centre, Universiti Teknologi Malaysia, through GUP no: 4F577
TABLE 1: VALUES OF YIELD STRESSES, LOADS AND TORQUE OBTANED USING HRBFAND MEAN
TEMPERATURE BY ROOT MEAN SQUARE METHOD
S/N
SP. NO
TM(0C)
LOG(10) Z
KP(N/mm2)
Kg(N/mm2)
P(KN)
G(Nm)
1
2
3
4
5
6
7
8
H20
H25
H22
H23
H24
H31
H27
H28
852.32
894.22
894.22
889.14
971.51
902.76
952.65
952.65
20.66
19.80
19.97
20.28
19.36
19.68
18.82
19.00
212.80
178.65
184.22
193.83
159.77
178.42
145.68
151.29
248.10
206.90
213.64
225.35
183.00
207.09
167.01
173.72
302.25
289.68
265.24
250.97
273.97
261.75
261.38
230.52
4498.58
4632.13
3964.33
3761.39
3797.88
3752.74
3702.52
3359.26
9
10
11
12
H29
H30
H32
H33
951.79
1040.91
954.92
1007.69
19.24
18.35
18.80
17.98
157.69
125.84
149.75
118.35
182.49
141.72
173.32
134.79
190.51
143.86
238.81
140.41
3154.07
3186.61
3447.05
3243.89
13
14
H34
H35
1007.69
1007.69
18.09
18.38
122.65
129.10
140.25
148.25
205.10
185.65
3113.72
2781.55
15
16
H36
H37
1099.48
904.11
17.56
19.73
97.71
173.47
109.99
205.36
188.64
167.25
3206.64
1862.24
17
18
19
H39
H41
H43
901.16
905.17
902.76
19.74
19.71
19.78
162.49
147.42
139.28
198.09
187.79
183.78
375.99
443.78
589.87
6276.27
8745.00
12180.62
20
21
22
23
24
25
H38
H40
H42
H44
H50
H51
1040.91
1045.53
1045.53
1045.53
898.75
904.12
18.32
18.33
18.35
18.31
19.78
19.72
135.95
115.52
108.57
103.42
185.16
183.73
144.57
137.36
135.60
134.44
213.51
211.60
151.03
285.33
366.98
433.27
260.26
251.09
1684.95
4899.38
7172.93
9124.43
3417.21
2385.33
26
27
28
29
30
31
H52
H53
H54
H55
H56
H57
898.03
900.35
1038.13
1039.06
1040.91
1041.83
19.89
19.97
18.43
18.47
18.51
18.58
155.97
156.27
128.81
128.81
133.58
129.73
183.92
197.83
144.82
146.33
149.20
149.46
266.60
233.92
221.08
218.90
201.34
236.80
2902.07
2087.22
2948.46
3331.62
2614.72
2546.28
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
32
P30
892.53
20.06
208.33
230.69
158.17
-
33
P32
888.29
20.57
199.20
233.03
179.67
-
34
P33
965.67
19.29
151.05
177.03
167.69
-
35
P34
967.81
19.45
161.35
186.13
178.04
-
36
P31
971.51
19.57
172.47
195.09
167.63
-
37
P35
944.18
19.24
157.10
182.31
171.63
-
38
P36
1023.23
18.30
123.74
140.04
159.24
-
39
40
41
42
43
44
45
P37
P38
P40
P41
P42
P43
P44
1025.97
1021.40
1034.43
1007.68
1012.77
1084.44
1093.64
18.40
18.64
18.66
18.26
18.56
17.57
17.61
127.32
134.38
140.87
125.04
134.73
100.56
103.81
144.12
153.67
156.36
143.73
155.36
111.60
113.98
153.63
168.56
150.03
135.10
123.33
122.27
122.27
-
20
International Journal of Engineering Research in Africa Vol. 26
TABLE 2: A COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED ROLLING LOAD USING
HOT ROLLING BLAND AND FORD’S THEORY BASED ON RMS MEAN ROLLING TEMPERATURE.
SPEC.
EXPERIMENTAL
CALCULATED
PERCENTAGE
NO
ROLLING LOAD
ROLLING LOAD
ERROR (%)
[KN]
[KN]
AIYEDUN]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
1
H20
300.60
302.25
-0.55
2
H25
271.48
289.68
-6.70
3
H22
251.18
265.24
-5.60
4
5
H23
H24
237.24
241.03
250.97
259.38
-5.79
-7.61
6
H31
257.34
261.75
-1.71
7
H27
232.46
261.38
-12.44
8
H28
227.09
230.52
-1.51
9
H29
197.98
190.51
3.78
10
H30
199.69
143.86
12.22
11
H32
251.18
238.81
4.93
12
H33
215.65
208.55
3.29
13
H34
185.22
205.10
-10.73
14
H35
167.48
185.65
-10.85
15
H36
178.84
188.64
-5.48
16
H37
159.94
167.25
-4.57
17
H39
345.18
375.99
-8.93
18
H41
455.54
443.78
2.58
19
H43
549.43
589.87
-7.36
20
H38
138.28
151.03
-9.22
21
H40
261.33
285.33
-9.18
22
H42
329.00
366.98
-11.54
23
H44
329.49
433.27
-10.09
24
H50
263.90
260.26
1.38
25
H51
225.90
251.09
-11.15
26
H52
265.19
266.60
-0.53
27
H53
208.00
233.92
-12.46
28
H54
202.96
221.08
-8.93
29
H55
209.33
218.90
-4.57
30
H56
215.65
201.34
6.64
31
H57
230.99
236.80
-2.52
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
32
P30
160.34
158.17
1.35
33
P32
180.43
179.67
0.42
34
P33
188.56
167.69
11.07
35
P34
187.03
178.04
4.81
36
P31
173.36
167.63
3.30
37
P35
157.13
171.63
-9.23
38
P36
149.03
159.24
-6.85
39
P37
149.86
153.63
-2.52
40
P38
169.59
168.56
0.61
41
P40
146.34
150.03
-2.52
International Journal of Engineering Research in Africa Vol. 26
21
42
P41
133.08
135.10
-1.52
43
P42
125.84
123.33
1.99
44
P43
121.61
122.27
-0.55
45
P44
128.61
122.27
4.93
46
P45
135.26
134.49
0.57
TABLE 3: A COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED ROLLING TORQUE
USING HOT ROLLING BLAND AND FORD’S THEORY BASED ON RMS MEAN ROLLING
TEMPERATURE.
SPEC
EXPT. ROLL'G
CALC.ROLL'G
NO
TORQUE
TORQUE
[Nm]
[Nm]
%ERROR
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
1.00
H20
4474.00
4498.58
-0.55
2.00
H25
3965.50
4632.13
-16.81
3.00
H22
3830.00
3964.33
-3.51
4.00
H23
3525.00
3761.39
-6.71
5.00
H24
3728.00
3797.88
-1.87
6.00
H31
4270.60
3752.74
12.13
7.00
H27
3965.60
3702.52
6.63
8.00
H28
3694.40
3359.26
9.07
9.00
H29
3287.70
3154.07
4.06
10.00
H30
3321.60
3186.61
4.06
11.00
H32
4067.20
3447.05
15.25
12.00
H33
3660.50
3243.89
11.38
13.00
H34
3186.00
3113.72
2.27
14.00
H35
2860.60
2781.55
2.76
15.00
H36
3219.90
3206.64
0.41
16.00
H37
2101.40
1862.24
11.38
17.00
H39
5761.90
6276.27
-8.93
18.00
H41
7693.90
8745.00
-13.66
19.00
H43
9829.20
11180.62
-13.75
20.00
H38
1965.80
1684.95
14.29
21.00
H40
4779.00
4899.38
-2.52
22.00
H42
6541.50
7172.93
-9.65
23.00
H44
8202.30
9124.43
-11.24
24.00
H50
3660.50
3417.21
6.65
25.00
H51
2281.00
2385.33
-4.57
26.00
H52
2914.90
2902.07
0.44
27.00
H53
1796.40
2087.22
-16.19
28.00
H54
3084.00
2948.46
4.39
29.00
H55
3186.00
3331.62
-4.57
30.00
H56
2745.40
2614.72
4.76
31.00
H57
2508.10
2546.28
-1.52
22
International Journal of Engineering Research in Africa Vol. 26
TABLE 4: A COMPARISON BASED ON THE RATIO OF EXPERIMENTAL TO CALCULATED ROLLING
LOAD BETWEEN REVERSE SANDWICH MODEL [SHOBOWALE], RSM - HRBF [ALAMU] AND HRBF
BASED ON RMS MEAN ROLLING TEMPERATURE.
SPEC.
LOG(10)Z
NO
RATIO OF
EXP/CAL.
LOAD
RATIO OF
EXP/CAL.
LOAD
RATIO OF
EXP/CAL.
LOAD
[SHOBOWALE]
[ALAMU]
HRBF
[BASED ON
RMS TEMP.]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
H20
20.66
1.20
1.03
1.02
H25
19.80
1.18
0.98
1.00
H22
19.97
1.16
0.99
0.98
H23
20.28
1.10
0.99
0.95
H24
19.36
1.08
0.92
0.92
H31
19.68
1.20
1.10
1.08
H27
18.82
1.15
1.03
1.04
H28
19.00
1.12
1.03
1.04
H29
19.24
1.10
0.95
0.99
H30
18.35
1.22
0.94
0.93
H32
18.80
1.16
1.10
1.05
H33
17.98
1.14
1.04
1.03
H34
18.09
1.04
0.94
0.90
H35
18.38
1.13
0.94
0.90
17.56
1.22
0.99
0.95
H36
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
P30
20.06
1.14
1.06
1.01
P32
20.57
1.12
1.05
1.10
P33
19.29
1.22
1.12
1.08
P34
19.45
1.27
1.05
1.10
P31
19.57
1.30
1.03
1.03
P35
19.24
1.10
0.95
0.95
P36
18.30
1.18
0.98
0.94
P37
18.40
1.14
1.02
0.98
P38
18.64
1.30
1.05
1.00
P40
18.66
1.43
1.02
0.98
P41
18.26
1.20
1.03
0.99
P42
18.56
1.25
1.05
1.02
P43
17.57
1.16
1.04
0.99
P44
17.61
1.38
1.07
1.02
P45
17.70
1.27
1.05
1.01
P55
19.31
1.35
1.16
1.11
P48
19.45
1.20
1.03
0.98
P50
19.38
1.10
0.98
0.94
P47
18.65
1.40
1.22
1.01
P49
18.82
1.15
0.96
1.21
P51
18.69
1.20
0.00
0.96
P53
18.55
1.10
1.00
0.96
International Journal of Engineering Research in Africa Vol. 26
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TABLE 5: A COMPARISON BASED ON THE RATIO OF EXPERIMENTAL TO CALCULATED ROLLING
TORQUE BETWEEN REVERSE SANDWICH MODEL [SHOBOWALE], RSM-HRBF [ALAMU] AND HRBF
BASED ON RMS MEAN ROLLING TEMPERATURE
SPEC.
LOG Z
RATIO OF
NO
EXP/CAL. TORQ.
RATIO OF
EXP/CAL.
TORQ.
RATIO OF
EXP/CAL.
TORQ.
[SHOBOWALE]
[ALAMU]
HRBF
[BASED ON
RMS TEMP.]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
H20
20.66
1.20
1.04
0.99
H25
19.80
1.10
1.01
0.86
H22
19.97
1.23
1.01
0.97
H23
20.28
1.15
0.98
0.94
H24
19.36
1.16
1.02
0.98
H31
19.68
1.30
1.19
1.14
H27
18.82
1.31
1.12
1.07
H28
19.00
1.34
1.15
1.10
H29
19.24
1.28
1.09
1.04
H30
18.35
1.30
1.09
1.04
H32
18.80
1.36
1.23
1.18
H33
17.98
1.30
1.18
1.13
H34
18.09
1.20
1.07
1.02
H35
18.38
1.20
1.07
1.03
H36
17.56
1.17
1.05
1.00
1
1
1.06
1
2
0.96
[Pexp/Pcal]
1.01
2
3
5
3
3
4
5
4
4
2
5
0.91
LOG
0.86
17.00
H32-H36, Tf=1200 C
17.50
18.00
(10)
Z
H31-H30, Tf=1125 C
18.50
19.00
ε1˂ε2˂ε3˂ε4˂ε5
H20-H24,Tf=1050 C
19.50
20.00
20.50
21.00
Fig.3.1: Dependence of Ratio of Experimental Load to Calculated Load on Zener-Hollomon Parameter for
HCSS316 Rolled on Mill A at r = 10%, Different Tf , Varying strain Rates (Based on RMS Mean Rolling
Temperature)
24
International Journal of Engineering Research in Africa Vol. 26
1.40
1.20
5
0.60
0.40
5
4
3
3
1
4
2
1
3
5
4
2
[Gexp/Gcal]
1.00
0.80
1
2
ε1˂ε2˂ε3˂ε4˂ε5
0.20
H32-H36, Tf=1200 C
0.00
17.00
17.50
H31-H30, Tf=1125 C
18.00
18.50
H20-H24, Tf=1050 C
LOG(10)19.00
Z
19.50
20.00
20.50
21.00
Fig.3.2: Dpendence of Ratio of Experimental Torque to Calculated Torque on Zener-Hollomon Parameter for
HCSS316 Rolled on Mill A at r=10%, Different Tf, Varying Strain Rates (Based on RMS Mean Rolling
Temperature)
1.20
1.00
3
4
5
1
2
2 4
3
5
2
4
3
5
1
1
0.60
0.40
[Pexp/Pcal]
0.80
ε1˂ε2˂ε3˂ε4˂ε5
0.20
P35-P40, TF = 11250C
P41-P45, TF = 12000C
0.00
17.00
P30-P31, TF= 10510 C
LOG(10)Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig.3.3: Dependence of Ratio of Experimental Load to Calculated loadon Zener-Hollomon Parameter for
HCSS316 Rolled on Mill B at r = 10%, Different Tf, Varying Strain Rates ( Based on RMS Mean Rolling
Temperature)
International Journal of Engineering Research in Africa Vol. 26
25
1.2
1
1
1
0.8
0.4
4
3
2
3
2
3
3
4 2
1
4
[Pexp/Pcal]
0.6
2
1
1: r = 5%, 2: r = 15%, 3: r = 20%, 4: r = 25%
HIGH SRT.SPECIMEN H38-H44
0.2
LOW STR.SPECIMEN P55-P50
HIGH SRT.SPECIMEN P47-P53
0
18.20
18.40
18.60
18.80
LOG(10)Z
19.00
19.20
LOW STR. SPECIMEN H37-H43
19.40
19.60
19.80
Fig.3.4: Dependence of Ratio of Experimental Load to Calculated Load on Zenner-Hollomon Parameter for
0
Different Reductions, Hot Rolling on Mill A & B at Low & High Strain Rates, Tf = 1125 C (Based on RMS Mean
Rolling Temperature)
1.10
1
1
1.05
3
2
[Gexp/Gcal]
1.00
2
0.95
3
4
1:5% r,
4
2:15%r,
HIGH SRT.SPECIMEN H38-H34
0.90
18.2
3:20%r
4:25%r
LOW SRT.SPECIMEN H37-H43
LOG(10)Z
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
Fig.3.5: Dependence of Experimental Torque to Calculated Torque on Zener-Holllomon Parameter for Different
0
Reduction, Hot Rolling on Mill A and Mill B at Low & High Strain Rates, Tf = 1125 C ( Based on RMS Mean
Rolling Temperature)
26
International Journal of Engineering Research in Africa Vol. 26
1.2
3
1
2
1
4
4
2
3
0.4
[Pexp/Pcal]
0.8
0.6
1: W/H0 = 5.3
2: W/H0 = 6.3
HIGH SRT.SPECIMEN H54-H57
HIGH SRT.SPECIMEN P62-P65
0.2
0
18.40
3
2
1
18.60
18.80
1
4
4: W/H0 = 9.4
LOW SRT.SPECIMEN P58-P61
19.20
4
2
3: W/H0 = 7.5
19.00
3
LOG(10)Z
19.40
LOW SRT.SPECIMEN H50-H53
19.60
19.80
20.00
Fig. 3.6: Dependence of Ratio of Experimental Load to Calculated Load on Zener-Hollomon Parameter for
0
Rolling of Different Geometry (W/H0) at R = 10%, Tf = 1125 C at Fast Slow Strain Rates on Mill A & Mill B
(Based on RMS Mean Rolling Temperature)
1.20
1.10
1
3
1
[Gexp/Gcal]
0.70
2
2
0.90
0.80
3
4
1.00
4
1: W/H0 = 5.3
2:
W/H0 = 6.3
3: W/H0 = 7.5
4:
W/H0 = 9.4
0.60
0.50
0.40
18.2
HIGH SRT.SPECIMEN H54-H57
LOW SRT.SPECIMEN H50-H53
LOG(10) Z
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
Fig.3.7: Dependence of Ratio of Experimental Torque to Calculated Torque on Zener-Hollmon Parameter for
0
Different Geometry (W/H0) Hot Rolled on Milll A & Mill B at Low & High Strain Rates, Tf = 1125 C, r = 10%
(Based on RMS Mean Rolling Temperature)
International Journal of Engineering Research in Africa Vol. 26
27
1.40
1.20
2
2
2
5
5
5
1.00
3
3
3
4
4
0.60
0.40
2
2
2
1 5
4 5
3
2
3
5
4 5
5
3
2
1
1
1
4
4
4
3
H31-H30, TF = 1125 C
[SHOBOWALE]
H31-H30, TF=1125 C [ALAMU]
H32-H36, TF= 1200C [ALAMU]
17.9
H20-H24, TF = 1050 C [SHOBOWALE]
H31-H30, TF =1125 C
[HRBF]
H32-H36 TF = 1200C [HRBF]
0.00
17.4
4
4
1
1
1 2
ε1˂ε2˂ε3˂ε4˂ε5
H32-H36, TF =1200 C [SHOBOWALE]
0.20
3
3
5
[PEXPTL./PCALCTD.]
0.80
1
1
18.4
18.9
H20-H24, TF=1050 C [ALAMU]
LOG(10)Z
H20-H24,TF = 1050 C [HRBF]
19.4
19.9
20.4
Fig.3.8: A Comparison among RSM [SHOBOWALE], RSM- HRBF[ALAMU] & HRBF Theory (RMS Mean
Rolling Tp.) for Dependence of Ratio of Exptl. to Calctd. Load on Zener-Hollomon Parameter for HCSS316
Rolled on Mill A at R = 10%, diff.TF & Strain Rates.
1.60
1.40
1.20
1.00
0.80
[GEXPTL./GCALTD.]
2
5
5
5
2
2
3
3
3
5 4
5
5 4
4
H32- H36, TF =1200 0C [SHOBOWALE]
H32- H36, TF =1200 0C [ALAMU]
0.20
H32- H36, TF =1200 0C [HRBF]
0.00
17.00
1
4
4
4
5
5
5
1
1 2 3
2 3
2
3
1
1
4
4
1
4
ε1˂ε2˂ε3˂ε4˂ε5
0.60
0.40
1
2 3
1
1 3
2
2 3
H20 - H24, TF = 1050 0C [SHOBOWALE]
H31-H30, TF = 1125 C
[SHOBOWALE]
H31-H30, TF = 1125 C [ALAMU]
H20 - H24, TF = 1050 0C [ALAMU]
H20 - H24, TF = 1050 0C [HRBF]
H31-H30, TF = 1125 C [HRBF]
LOG(10) Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig.3.9: A Comparison among RSM [Shobowale], RSM-HRBF Theory [Alamu] & HRBF (based on RMS Mean
Rolling Temp.) for Dependenceof Ratio of Exptl. Torque to Calctd.Torque on Zener- Hollomon Parameter for
HCSS316 rolled on Mill A at R = 10%, diff. TF and Strain Rates
28
International Journal of Engineering Research in Africa Vol. 26
1.40
1.20
3
0.80
0.60
0.40
1
3 4
2
1
4
2 3
1 2 3 4
4 5
3
3 45
[PEXPTL./PCALCTD]
1.00
4 5
P41 - P45, TF = [ALAMU]
P35- P40, TF = 1125 C
[SHOBOWALE]
P35- P40 TF = 1125 C [ALAMU]
P35 - P40, TF = 1125 C [HRBF]
P41 - P45, TF = 1200 C [HRBF]
0.00
17.00
1
2
2
2
1
1
ε1˂ε2˂ε3˂ε4˂ε5
P41-P45, TF = 1200 C [SHOBOWALE]
0.20
23 4 5
23 4 5
2 3 4 5
5
1
5 1
1
5
P30 - P31, TF = 105 C [SHOBOWALE]
P30 - P31, TF = 1050 C [ALAMU]
P30 - P31, TF = 1050 C [HRBF]
LOG(10) Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig. 3.10: A Comparison among RSM [Shobowale], RSM-HRBF Theory[Alamu]& HRBF (based on RMS Mean
Rolling Temp.) for Dependence of Ratio of Exptl. Load to Calctd. Load on Zener- Hollomon Parameter for
HCSS316 rolled on Mill B at R = 10%, diff.TF and Strain Rates.
REFERENCES
[1]
AFONJA, A.A. and SANSOME, D.H. (1973), “A Theoretical Analysis of the Sandwich
Rolling Process” Int. J. Mech. Sci., Vol. 15, pp. 1 – 14
[2]
AIYEDUN, P.O. (1984), “A Study of Loads and Torques for Light Reduction in Hot Flat
Rolling at Low Strain Rates” Ph.D. Thesis, University of Sheffield.
[3]
AIYEDUN, P.O. (1986), “Hot Flat Rolling Simulation by Use of the Bland and Ford’s Cold
Rolling Theory for HCCSS316 at Low Reduction and Low Strain Rates”, Proc, Int. AMSE
Conf., Vol. 3, pp. 14 – 36.
[4]
AIYEDUN, P.O., SPARLING, L.G.M. and SELLARS, C. M., (1997), “Temperature Change
in Hot Flat Rolling of Steels at low Strain Rates and Low Reduction”. Pro. Instn. Mech.
Engrs. Vol. 211, Part B, pp.261-254.
[5]
AIYEDUN, P.O. (1999), “Yield Stress Variation across Thickness for Steel (HC SS316)
Specimen hot rolled at Low Reduction and Low Strain Rates”. NSE Technical Transactions,
Vol. 34, pp. 46 - 70
[6]
AIYEDUN, P.O. and ALIU, S. A (2009), “Rolling Temperature for Steel Hot Flat rolled at
Low Strain Rates”, Advanced Materials Research, Vol. 62-64, pp. 317-323.
[7]
ALAMU, O.J. (2001), “Integration of the Reverse Sandwich Model into the Hot Rolling
Bland and Ford’s Theory (HRBF) of Load and Torque Calculation”, MSc. Thesis, University
of Ibadan.
[8]
ALAMU, O.J. and AIYEDUN, P.O. (2003) “A Comparison of Temperature Gradient in Hot
Rolling at Low and High Strain Rates”. J. Sci. Engr. Tech., 10(1): 4644 – 4654.
[9]
FARAG, M.M. and SELLARS, C.M. (1998), “Hot Working and Forming Processes”. Proc.,
Metals Society Conference, Sheffield.
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[10] LENARD, J.G. (1980), “Roll Deformation in Cold Strip Rolling’’ Journal of Engineering
Materials and Technology”, ASME Vol. 102, pp. 382 – 383.
[11] SADIQ, T.O. (2012), “Calculated Rolling Load and Torque for Hot Flat Rolling of Hcss316
at Low Strain Rates based on Better Mean Rolling Temperature”. MSc. Thesis, University of
Ibadan.
[12] SELLARS, C.M. (1981), “Les Traitments Thermomecaniques”, 24eme Colloque de
Metallurgie, Institut National des Sciences et Technique Nucleaires, Sanclay, pp. 111 - 120.
[13] SHOBOWALE, B. (1998), “The Reverse Sandwich Effect in HC SS316 Hot Flat Rolled at
Low Strain Rates and Low Reductions”, M.Sc. Thesis, University of Ibadan.
ISSN: 1663-4144, Vol. 26, pp 11-29
doi:10.4028/www.scientific.net/JERA.26.11
© 2016 Trans Tech Publications, Switzerland
Submitted: 2016-04-05
Revised: 2016-07-04
Accepted: 2016-07-11
Online: 2016-10-07
Numerical Estimation of Rolling Load and Torque for Hot Flat Rolling of
Hcss316 at Low Strain Rates Based on Mean Temperature
1
1
Sadiq, T O, a Fadara T G, b Aiyedun, P. O and *Idris, J
Manufacturing Department, Engineering Materials Development Institute
KM4, Ondo Road, P.M.B 611, Akure, Ondo State, Nigeria
a
Department of Mechanical Engineering, College of Engineering
Federal Polytechnic, Ede, Osun State, Nigeria
b
Department of Mechanical Engineering, College of Engineering
Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
*
Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia, UTM, Skudai 81310, Johor Bahru, Malaysia
*
Corresponding Author: +6075534659
E-mail addresses: adisaolohunde@yahoo.com (T.O. Sadiq), Jamaliah@fkm.utm.my (J. Idris)
Keywords: Rolling Process, Numerical Estimation, Rolling Load, Torque, Strain Rates, Yield
Stress, Zener–Hollomon Parameter.
ABSTRACT. Numerical estimation of rolling load and torque often showed large discrepancies
when compared with experimental values. This was attributed to difficulty in estimating the mean
rolling temperature from the available data. This work is thus directed at obtaining a good estimate
for the mean rolling temperature which can effectively be used for load and torque estimates. Hot
flat rolling stimulation by use of the Bland and Ford’s cold rolling (HRBF) theory confirmed the
reverse sandwich effect in selected carbon steels at low strain rates. In this work, the effect of pass
reduction on rolling temperature distribution, yield stress and rolling load were studied for AISI
Type 316 stainless steel (HSCSS316). For this new simulation, at low and high strain rates, results
showed that the ratio of experimental to calculated rolling load and torque were higher at lower
reduction than at higher reduction. These results confirmed excess load and torque in the hot rolling
of HSCSS316 low reductions. The results obtained from Hot Rolling Bland and Ford’s Theory
based on Root Mean Square rolling temperature were in good agreement with values obtained using
Reverse Sandwich Model and the Reverse Sandwich- Hot Rolling Bland and Ford’s Program under
the same rolling conditions.
1.
INTRODUCTION
It was discovered that measured load and torque were excessive when compared with calculated
values using Simple Rolling Theories such as Sims, Bland and Ford, and a simple rolling
temperature based on the mean entry temperature into the roll gap [2], for hot flat rolling at low
strain rates and low reduction. These Theories all gave correct results for high strain rates range
regarded as normal rolling conditions.
The strength of a material is dependent on its microstructure and the condition during testing of
which temperature and strain rate are very important. The structure of the material is equally very
much dependent on temperature. For hot rolling at low strain rates, the contact times with the rolls
become increasingly large and the effect of this is manifested in pronounced temperature variations
as slab is being rolled. It can then be concluded that temperature effects are the most important
factors during hot rolling at low strain rates. From previously conducted investigations, the cause
was traced to the fact that hot rolling at low strain rates actually occur at a temperature much lower
than the mean entry temperature into the roll gap.
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12
International Journal of Engineering Research in Africa Vol. 26
These low mean rolling temperatures lead to higher stress in materials since the strength of the
material is dependent on temperature. Consequently, higher load and torque were experienced in
material since they are also dependent on the yield stresses. The key to unravelling the mystery is
then left to be found in the determination of the correct mean rolling temperature. In this work,
efforts are aimed at using a suitable method in summarising the set of temperatures encountered
during roll contact time into a single one. This single one is used to obtain the correct flow stress
and hence correct load and torque. In clearer language, the best average temperature is desired. This
will be done by considering various methods of obtaining averages and using each to ascertain the
mean rolling temperature which is most suitable for the computation of loads and torques.
1.2
OBJECTIVES
To estimate the Mean Rolling Temperatures using the different averaging methods and to use these
results obtained in estimating Yield Stresses which will be subsequently used in calculating the
Rolling Load and Torque. Also, to make comparison between the Rolling Load and Torque with
results obtained by other Researchers.
2.
METHODOLOGY
2.1
Hot Rolling Bland and Ford’s Theory
The Bland and Ford’s Theory (HRBF) is a cold rolling theory, where sliding takes place throughout
the arc of contact. It has however been found to be applicable to a hot rolling situation where sliding
exists throughout the roll gap. This is the situation for hot rolling of HCSS316 at 9000C – 12000C;
reductions of 0 -15%; strain rates of 0.07 -1.5 ; and geometrical factor of 4.0 – 20.00 as reported
in the literatures [2, 3, 4].
Rolling Load (P) and rolling torque (T) are respectively given by equation (1) and (2);
∅
=
+
1
∅
2
=
Where:
=
=
. .
. .
.
3
.
4
.
=
=
.
=
.
+
.
5
6
+
−
7
International Journal of Engineering Research in Africa Vol. 26
Where;
Α
K
θ
∅
R’
R0
S
h1,2
N
μ
13
Angle of entry i.e. maximum value of θ in radians
Instantaneous yield stress (N/m2)
Angle subtended by a point on roll surface w.r.t. line joining roll centres in radians.
Neutral angles in radians
Deformed roll radius (mm)
Undeformed roll radius in mm
Normal roll pressure (N/mm2)
Entry and exit height (mm)
Number of measured values
Fractional coefficient
In rolling processes generally, it is vital to know the temperature distribution within the slab. The
literatures of previous researchers showed that temperature is the dominant parameter controlling
the kinetics of metallurgical transformations and the flow stress of the rolled metal. The mean
temperature used by Aiyedun (1984) in Hot Rolling Bland and Ford’s Theory is given in the
equation 8
=
+
Where: T1 and T2 are entry and exit temperatures.
8
The true yield stresses for load and torque calculation are respectively given as equations (9) and
(10);
=
9
=
Where:
=
10
=
r = reduction
The percentage rolling reduction is given as:
2.2
=
×
%
11
The Reverse Sandwich Model (RSM)
The reverse sandwich model predicts the rolling reduction, rolling temperatures and temperature
distribution along the through thickness of HCSS316. Detailed theoretical analyses of the model
have been reported [7, 8, 13].
With the specimen partitioned into 17 zones (n = 1 – 17), the model’s prediction of rolling
temperature follows equation (12) to (15).
The temperature at the specimen’s core is given as:
=
+
12)
14
International Journal of Engineering Research in Africa Vol. 26
Where:
TF
TM
TS
Furnace temperature,
The mean rolling temperature
Exist or entry temperature
=
13
+
=
K Reverse Sandwich Model constant, values of which are functions of the rolling speed.
1≤
≤4
8<
< 9,
5≤
15 ≥
≤7
≥ 12,
=
11 ≥
=
+
.
.
=
9,
≤
Where:
V
=
≤
≤
≤
≤
≤
,
≤ 10,
+
.
=
=
,
=
,
15
15
The rolling speed is related to the reverse sandwich model constant as follow:
9 ≤
14
1.59
.
.
=
15
16
16
16
.
16
Peripheral velocity of rolls (mm-1)
The approximate empirical equation of Farag and Sellars [9] was used in the model for
determination of mean strain rate thus:
δ
=
=
.
.
[
reduction (mm)
]
.
17
The Zener-Hollomon parameter was determined for each of the seventeen (17) zones along
thickness (Z1 – Z17) using the proposition of Zener and Hollomon equation [2, 3] written as;
=
Where:
R
T
Z
Q
=
=
=
=
=
Universal constant (8.314Jkg-1/ K)
Absolute temperature (0C)
Zener-Hollomon parameter
Thermal energy
18
International Journal of Engineering Research in Africa Vol. 26
15
The Z-values are uniquely related to the stress, and, hence the deformation of the material. For
HCSS316 specimen under the prevailing rolling condition, Q = 460 KJ/mol. [2, 3, 4]
2.3
Choice of Averaging Method for obtaining Mean Rolling Temperature.
Based on comparison of the results obtained with experimental values for the four averaging
methods of harmonic mean method, geometric mean method, arithmetic mean method and root
mean square method, the root square method gave the lowest error percentage. Hence was used in
Bland and Ford’s Theory to estimate the yield stresses for load and torque and hence rolling load
and torque for the various specimens.
2.4
Simulation of the Model
Simulation of the model was carried out using FORTRAN 77. The required input data are rolling
speed, roll radius, furnace temperature, initial and final height of the specimen, and specimen width.
From the output of the program, the temperature distribution, yield stress validation, rolling load
and torque distribution across the thickness of the rolled specimen at different pass reduction are
evident.
2.5
Experimental
Data used in validating the new hot rolling simulation was obtained through preliminary
metallographic, hot torsion tests, and hot rolling experiments performed on the as-received wrought
AISI316 with inclusions of Nb, V and Ti in the temperature range (600 – 1200) 0C and strain rate
range of 3.6 X 10-3s-1 to 1.4s-1. The wrought material was High Carbon Stainless Steel; ASME SA240 from Heat 38256-2C, product of G.O. Carlson Inc., P.A., and U.S.A. The material was cut into
slabs of small sizes and hot rolled. The hot rolling experiments were performed on two laboratory
mills; a 1000KN, 2-high, single stand, reversible mill with rolls of 254.0mm diameter by 266.0mm
barrel length and 50T (498KN) capacity, 2-high reversible, Hille 50T rolling mill with rolls of
diameter 139,7mm.
3.0
DISCUSSION OF RESULTS
The analyses presented above were used to write a Computer program which gave hot rolling load
and torque to a reasonable accuracy. The program made use of experimental and theoretical data
from a study of loads and torques for light reduction in hot flat rolling at strain rates carried out by
[2] and the results from the reverse sandwich effects in HCSS316 hot flat rolled at low strain rates
and low reductions investigated by [13] as input data.
In estimating the correct mean rolling temperature, four averaging methods of harmonic means,
geometric mean, arithmetic mean and root mean square were used to calculate mean rolling
temperature from the measured temperatures of various specimens of steels during roll contact. Due
to the least error involved when compared with experimental values, the root square method was
used in Bland and Ford’s Theory to calculate yield stresses and hence rolling loads and torques for
the various specimens.
The results presented in Table1 will be discussed under the following headings:
•
Rolling Load Estimation
•
Rolling Torque estimation
•
Results for different Rolling Conditions
•
Results of Comparison of the results obtained with other Researchers.
16
International Journal of Engineering Research in Africa Vol. 26
3.1
Rolling Load Estimation
With reference toTable2, the results obtained for rolling load at different hot rolling conditions
using the Hot Rolling Bland and Ford’s Theory (based on RMS mean rolling temperature) are in
very good agreement with experimental values obtained for the same rolling condition [2]. The
results gave a maximum and minimum error of 20.19% and .42% respectively.
3.2
Rolling Torque Estimation
The results obtained for rolling torque estimation at different hot rolling condition using the Hot
Rolling Bland and Ford’s Theory (based on RMS mean rolling temperature) are in good agreement
with the experimental results obtained [2] under the same rolling condition. The results gave a
minimum error of 0.41% and a maximum error of 22.54% (see Table 3).
3.3
Results for Different Rolling Conditions
The results for hot flat rolling of HCSS316 (with Nb, V and Ti inclusions) at low strain rates (0.08 –
1.5) s-1 and low reductions (r ≈10%) on Mills A and B for varying parameters (Appendix A) are
sub-divided into the following headings:
• Effect of Variation of Reduction at Low and High Strain Rates
•
Effect of Variation of Strain Rates and Furnace Temperature
•
Effect of Varying Geometry (W1/h1) at Low and High Strain Rates.
•
Effect of Shot Blasted and Smooth Specimen Rolling on Mills A and B at Varying Strain
Rates.
3.3.1
Effect of Variation of Strain Rates and Furnace Temperature
For varying strain rates and furnace temperature (TF) values, specimen H20 – H24, H30-H31 and
H32 – H36 in that order, the Table 4&5 plotted as Figs. 3.1 to 3.3, show that as the strain rates
increases, the ratio of experimental to calculated load decreases on Mill A.
The output also shows that as the furnace temperature increased from 10500C at lowest strain rates
i.e. specimen H20 to approximately 12000C (SpecimenH32), the ratio of experimental to calculated
to load and torque increased from 1.02 to 1.05 and 0.99 t0 1.18 respectively. (See Tables 4&5).
However, the results from rolling on Mill B show no significant variation of the ratio of
experimental to calculated load at highest and lowest strain rates (See Table 4).
3.3.2
Effect of Variation of Reduction at Low and High Strain Rates
With reference to Table4 and the plot of Fig. 3.4, the ratio of experimental to calculated load
decreases from 1.03 to 0.93 with increase in rolling reduction (specimen H37 – H43) (6.29% –
23.27%) for rolling on Mill A at low strain rates.
Also, at high strain rates, the ratio of experimental load to calculated load decreases from 0.92 to
0.76 as rolling reduction increases (Specimen H38 – H44).
From Table5 plotted as Fig. 3.5 shows that the ratio of experimental torque to calculated torque
decreases from 1.17 to 0.90 with increase in rolling reduction (6.87 %– 24.53%) for rolling at low
strain rates (Specimen H38 – H44) on Mill A.
For rolling on mill B, the results in Table4 and Fig. 3.4 reveal that the ratio of experimental to
calculated load increases with rolling reduction at low strain rates (Specimen P55 – P50) and high
strain rates (Specimen P47- P53).
International Journal of Engineering Research in Africa Vol. 26
17
3.3.3. Effect of Varying Geometry (W/H0) at Low and High Strain Rates
At a reduction of about 10%, furnace temperature Tf = 11250C at low and high strain rates, the
following results were obtained:
From Table4 plotted as Fig.3.6 for specimens H50 - H53, H54 - H57 on Mill A as well as P58 –
P61, P62 – P65 on mill B, the average of the ratio of experimental to calculated rolling load is about
1.0 for hot rolling on both Mills at low and high strain rates with geometry (W/H0) varied between
5.0 and 10.00; an indication that there is no systematic effect of geometry variation on the ratio of
experimental to calculated load obtained using the Hot Rolling Bland and Ford’s approach.
3.3.4 Effect of Shot-blasted and Smooth Specimen Rolling on Mills A and B at Varying
Strain Rates, r ≈ 10%, Tf ≈ 10500C
Results showing the effect of rolling rough and smooth specimen on both Mills at varying strain
rates, reduction of about 10% and furnace temperature 10500C are reflected in Table 4 &Table 5.
For smooth specimen on mill A (Specimen H01H – H06H), the ratio of experimental to calculated
load and torque are higher (average of 1.138 and 1.208 respectively) than the values obtained for
rough specimen (Specimen H20 – H24) on the same mill (average of 0.974 and 0.948)
respectively).
However, on mill B, Table 4 shows that rough specimens (P30 – P31) have higher experimental to
calculated load ratio (average of 1.064) than smooth specimens (P21 – P19) with average value of
0.964.
3.4
COMPARISON OF THE RESULTS BASED ON THE RATIO OF EXPERIMENTAL
TO CALCULATED ROLLING LOAD AND TORQUE [HRBF] WITH RESULTS OF
REVERSE SANDWICH MODEL [SHOBOWALE] AND RSM-HRBF [ALAMU]
The accuracy or applicability of the Hot Rolling Bland and Ford’s Theory (based on RMS mean
rolling temperature) used in this work was investigated through comparison with results obtained
from the Reverse Sandwich Model [13] and RSM-HRBF Theory [7]. The comparison showed that
the results obtained were in good agreement.
3.4.1
Ratio of Experimental to Calculated Rolling Load and Torque
The following observations were made from the results presented in Table 7 and 8 plotted as Figs.
3.8, 3.9 and 3.10:
• The ratio of experimental load to calculated load (Pexp/Pcal) values obtained from HRBF
Theory (based on RMS mean rolling temperature) was lower than results obtained using
RSM-HRBF Theory [7] and Reverse Sandwich Model [13] for all rolling conditions
investigated on Mill A and Mill B, see Figs. 3.8 and 3.10. The results obtained from HRBF
Theory (based on RMS mean rolling temperature) usually fall below similar lines for the
RMS-HRBF Theory [7] and Reverse Sandwich Model [13].
• Also, the ratio of experimental to calculated torque (Gexp/Gcal) values was generally lower
using HRBF Theory (based on RMS mean rolling temperature) compared to ratio of
experimental to calculated torque (Gexp/Gcal) values using RMS-HRBF Theory [7] and
Reverse Sandwich Model [13] for all rolling conditions investigated on mill A, see Figs.3.9.
• Figures 3.8 and 3.10 revealed that the values of load obtained using HRBF Theory (based on
RMS mean rolling temperature) compared to RMS-HRBF Theory [7] and Reverse
Sandwich Model [13] values are closer to experimental values.
The points listed above show that the results obtained using HRBF Theory (based on RMS mean
rolling temperature) were in good agreement on both mills. This confirmed the applicability of the
HRBF Theory for estimating the Load and Torque in hot flat rolling of the HCSS316 based on
RSM Mean Rolling Temperature.
18
International Journal of Engineering Research in Africa Vol. 26
4.0
CONCLUSION
From the results obtained from the Hot Rolling Bland and Ford’s Theory based on RMS mean
rolling temperature, it can be concluded that:
• The mean rolling temperatures obtained were in very good agreement with experimental
values with a mean error of 3.60%.
•
The mean yield stress (for both Load and Torque calculations) obtained from the Hot
Rolling Bland and Ford’s Theory based on RMS mean rolling temperature was in very
good agreement with experimental values with a mean error of 10.14% and 7.13% for Load
and Torque calculations, respectively.
•
For varying reductions at low and high strain rates, furnace temperature of 11250C. The
following conclusions can be drawn.
(a) The ratio of experimental to calculated Load and Torque based on RMS mean rolling
temperature was higher at lower reduction of 5% than at higher reductions of 25% on
both mills.
(b) For 5% reduction on mill B, the ratio of experimental to calculated Load based on RMS
mean rolling temperature was about 1.03 at low strain rates and 0.93 at high strain rate.
(c) The ratio of experimental to calculated Torque based on RMS mean rolling temperature
on mill A was high about 1.17 at low reductions (5%) and low about 0.91 at higher
reduction.
•
For a furnace temperature of 11250C, 10% reductions at low and high strain rates for
varying geometry (W/H1), this conclusion can be drawn.
(a) The geometry (W/H1) varied between 5.0 and 10.0 has no systematic effect on the ratio
of experimental to calculated Load
(b) based on RMS mean rolling temperature on both mills but has a marked effect on the
ratio of experimental to calculated Torque based on RMS mean rolling temperature. It
increased from 0.99 to 1.05 on mill A.
•
Comparing smooth and rough specimens at a reduction of ̴ 10%, Tf ̴ 1050 0C and varying
strain rates, it can be concluded that:
(a) The ratio of experimental to calculated Load and Torque based on RMS mean rolling
temperature was both higher for smooth specimens than for rough specimens on mill A.
(b) The ratio of experimental to calculated Load based on RMS mean rolling temperature
was higher for rough specimens than for smooth specimens on mill B.
•
For varying furnace temperature (Tf) and varying strain rates at low reductions on mill A
and B, it can be concluded that:
(a) As the strain rate increases, the ratio of experimental to calculated Load and Torque
based on RMS mean rolling temperature decreases for a particular furnace temperature.
This confirms the presence of excess Load at low strain rate when greater chilling leads to
higher values of Z.
•
The
calculated
{(EXPT/CALC)LOAD}RMS
&
{(EXPT/CALC)TORQUE}RMS,
{(EXPT/CALC)LOAD}SHOBOWALE
&
{(EXPT/CALC)TORQUE}SHOBOWALE
and
{(EXPT/CALC)LOAD}ALAMU & {(EXPT/CALC)TORQUE}ALAMU were all in agreement,
indicating the applicability of the Hot Rolling Bland and Ford’s Theory based on RMS
mean rolling temperature for calculating Rolling Load and Torque at Low Strain Rates.
International Journal of Engineering Research in Africa Vol. 26
19
Acknowledgments
The Staff Members in the Department of Materials, Manufacturing and Industrial Engineering,
Faculty of Mechanical Engineering and ISI, Universiti Teknologi Malaysia are sincerely
appreciated for their financial and technical support during and after this work. This work was
partially supported by the Ministry of Higher Education of Malaysia (MOHE), Research
Management Centre, Universiti Teknologi Malaysia, through GUP no: 4F577
TABLE 1: VALUES OF YIELD STRESSES, LOADS AND TORQUE OBTANED USING HRBFAND MEAN
TEMPERATURE BY ROOT MEAN SQUARE METHOD
S/N
SP. NO
TM(0C)
LOG(10) Z
KP(N/mm2)
Kg(N/mm2)
P(KN)
G(Nm)
1
2
3
4
5
6
7
8
H20
H25
H22
H23
H24
H31
H27
H28
852.32
894.22
894.22
889.14
971.51
902.76
952.65
952.65
20.66
19.80
19.97
20.28
19.36
19.68
18.82
19.00
212.80
178.65
184.22
193.83
159.77
178.42
145.68
151.29
248.10
206.90
213.64
225.35
183.00
207.09
167.01
173.72
302.25
289.68
265.24
250.97
273.97
261.75
261.38
230.52
4498.58
4632.13
3964.33
3761.39
3797.88
3752.74
3702.52
3359.26
9
10
11
12
H29
H30
H32
H33
951.79
1040.91
954.92
1007.69
19.24
18.35
18.80
17.98
157.69
125.84
149.75
118.35
182.49
141.72
173.32
134.79
190.51
143.86
238.81
140.41
3154.07
3186.61
3447.05
3243.89
13
14
H34
H35
1007.69
1007.69
18.09
18.38
122.65
129.10
140.25
148.25
205.10
185.65
3113.72
2781.55
15
16
H36
H37
1099.48
904.11
17.56
19.73
97.71
173.47
109.99
205.36
188.64
167.25
3206.64
1862.24
17
18
19
H39
H41
H43
901.16
905.17
902.76
19.74
19.71
19.78
162.49
147.42
139.28
198.09
187.79
183.78
375.99
443.78
589.87
6276.27
8745.00
12180.62
20
21
22
23
24
25
H38
H40
H42
H44
H50
H51
1040.91
1045.53
1045.53
1045.53
898.75
904.12
18.32
18.33
18.35
18.31
19.78
19.72
135.95
115.52
108.57
103.42
185.16
183.73
144.57
137.36
135.60
134.44
213.51
211.60
151.03
285.33
366.98
433.27
260.26
251.09
1684.95
4899.38
7172.93
9124.43
3417.21
2385.33
26
27
28
29
30
31
H52
H53
H54
H55
H56
H57
898.03
900.35
1038.13
1039.06
1040.91
1041.83
19.89
19.97
18.43
18.47
18.51
18.58
155.97
156.27
128.81
128.81
133.58
129.73
183.92
197.83
144.82
146.33
149.20
149.46
266.60
233.92
221.08
218.90
201.34
236.80
2902.07
2087.22
2948.46
3331.62
2614.72
2546.28
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
32
P30
892.53
20.06
208.33
230.69
158.17
-
33
P32
888.29
20.57
199.20
233.03
179.67
-
34
P33
965.67
19.29
151.05
177.03
167.69
-
35
P34
967.81
19.45
161.35
186.13
178.04
-
36
P31
971.51
19.57
172.47
195.09
167.63
-
37
P35
944.18
19.24
157.10
182.31
171.63
-
38
P36
1023.23
18.30
123.74
140.04
159.24
-
39
40
41
42
43
44
45
P37
P38
P40
P41
P42
P43
P44
1025.97
1021.40
1034.43
1007.68
1012.77
1084.44
1093.64
18.40
18.64
18.66
18.26
18.56
17.57
17.61
127.32
134.38
140.87
125.04
134.73
100.56
103.81
144.12
153.67
156.36
143.73
155.36
111.60
113.98
153.63
168.56
150.03
135.10
123.33
122.27
122.27
-
20
International Journal of Engineering Research in Africa Vol. 26
TABLE 2: A COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED ROLLING LOAD USING
HOT ROLLING BLAND AND FORD’S THEORY BASED ON RMS MEAN ROLLING TEMPERATURE.
SPEC.
EXPERIMENTAL
CALCULATED
PERCENTAGE
NO
ROLLING LOAD
ROLLING LOAD
ERROR (%)
[KN]
[KN]
AIYEDUN]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
1
H20
300.60
302.25
-0.55
2
H25
271.48
289.68
-6.70
3
H22
251.18
265.24
-5.60
4
5
H23
H24
237.24
241.03
250.97
259.38
-5.79
-7.61
6
H31
257.34
261.75
-1.71
7
H27
232.46
261.38
-12.44
8
H28
227.09
230.52
-1.51
9
H29
197.98
190.51
3.78
10
H30
199.69
143.86
12.22
11
H32
251.18
238.81
4.93
12
H33
215.65
208.55
3.29
13
H34
185.22
205.10
-10.73
14
H35
167.48
185.65
-10.85
15
H36
178.84
188.64
-5.48
16
H37
159.94
167.25
-4.57
17
H39
345.18
375.99
-8.93
18
H41
455.54
443.78
2.58
19
H43
549.43
589.87
-7.36
20
H38
138.28
151.03
-9.22
21
H40
261.33
285.33
-9.18
22
H42
329.00
366.98
-11.54
23
H44
329.49
433.27
-10.09
24
H50
263.90
260.26
1.38
25
H51
225.90
251.09
-11.15
26
H52
265.19
266.60
-0.53
27
H53
208.00
233.92
-12.46
28
H54
202.96
221.08
-8.93
29
H55
209.33
218.90
-4.57
30
H56
215.65
201.34
6.64
31
H57
230.99
236.80
-2.52
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
32
P30
160.34
158.17
1.35
33
P32
180.43
179.67
0.42
34
P33
188.56
167.69
11.07
35
P34
187.03
178.04
4.81
36
P31
173.36
167.63
3.30
37
P35
157.13
171.63
-9.23
38
P36
149.03
159.24
-6.85
39
P37
149.86
153.63
-2.52
40
P38
169.59
168.56
0.61
41
P40
146.34
150.03
-2.52
International Journal of Engineering Research in Africa Vol. 26
21
42
P41
133.08
135.10
-1.52
43
P42
125.84
123.33
1.99
44
P43
121.61
122.27
-0.55
45
P44
128.61
122.27
4.93
46
P45
135.26
134.49
0.57
TABLE 3: A COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED ROLLING TORQUE
USING HOT ROLLING BLAND AND FORD’S THEORY BASED ON RMS MEAN ROLLING
TEMPERATURE.
SPEC
EXPT. ROLL'G
CALC.ROLL'G
NO
TORQUE
TORQUE
[Nm]
[Nm]
%ERROR
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
1.00
H20
4474.00
4498.58
-0.55
2.00
H25
3965.50
4632.13
-16.81
3.00
H22
3830.00
3964.33
-3.51
4.00
H23
3525.00
3761.39
-6.71
5.00
H24
3728.00
3797.88
-1.87
6.00
H31
4270.60
3752.74
12.13
7.00
H27
3965.60
3702.52
6.63
8.00
H28
3694.40
3359.26
9.07
9.00
H29
3287.70
3154.07
4.06
10.00
H30
3321.60
3186.61
4.06
11.00
H32
4067.20
3447.05
15.25
12.00
H33
3660.50
3243.89
11.38
13.00
H34
3186.00
3113.72
2.27
14.00
H35
2860.60
2781.55
2.76
15.00
H36
3219.90
3206.64
0.41
16.00
H37
2101.40
1862.24
11.38
17.00
H39
5761.90
6276.27
-8.93
18.00
H41
7693.90
8745.00
-13.66
19.00
H43
9829.20
11180.62
-13.75
20.00
H38
1965.80
1684.95
14.29
21.00
H40
4779.00
4899.38
-2.52
22.00
H42
6541.50
7172.93
-9.65
23.00
H44
8202.30
9124.43
-11.24
24.00
H50
3660.50
3417.21
6.65
25.00
H51
2281.00
2385.33
-4.57
26.00
H52
2914.90
2902.07
0.44
27.00
H53
1796.40
2087.22
-16.19
28.00
H54
3084.00
2948.46
4.39
29.00
H55
3186.00
3331.62
-4.57
30.00
H56
2745.40
2614.72
4.76
31.00
H57
2508.10
2546.28
-1.52
22
International Journal of Engineering Research in Africa Vol. 26
TABLE 4: A COMPARISON BASED ON THE RATIO OF EXPERIMENTAL TO CALCULATED ROLLING
LOAD BETWEEN REVERSE SANDWICH MODEL [SHOBOWALE], RSM - HRBF [ALAMU] AND HRBF
BASED ON RMS MEAN ROLLING TEMPERATURE.
SPEC.
LOG(10)Z
NO
RATIO OF
EXP/CAL.
LOAD
RATIO OF
EXP/CAL.
LOAD
RATIO OF
EXP/CAL.
LOAD
[SHOBOWALE]
[ALAMU]
HRBF
[BASED ON
RMS TEMP.]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
H20
20.66
1.20
1.03
1.02
H25
19.80
1.18
0.98
1.00
H22
19.97
1.16
0.99
0.98
H23
20.28
1.10
0.99
0.95
H24
19.36
1.08
0.92
0.92
H31
19.68
1.20
1.10
1.08
H27
18.82
1.15
1.03
1.04
H28
19.00
1.12
1.03
1.04
H29
19.24
1.10
0.95
0.99
H30
18.35
1.22
0.94
0.93
H32
18.80
1.16
1.10
1.05
H33
17.98
1.14
1.04
1.03
H34
18.09
1.04
0.94
0.90
H35
18.38
1.13
0.94
0.90
17.56
1.22
0.99
0.95
H36
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL B
P30
20.06
1.14
1.06
1.01
P32
20.57
1.12
1.05
1.10
P33
19.29
1.22
1.12
1.08
P34
19.45
1.27
1.05
1.10
P31
19.57
1.30
1.03
1.03
P35
19.24
1.10
0.95
0.95
P36
18.30
1.18
0.98
0.94
P37
18.40
1.14
1.02
0.98
P38
18.64
1.30
1.05
1.00
P40
18.66
1.43
1.02
0.98
P41
18.26
1.20
1.03
0.99
P42
18.56
1.25
1.05
1.02
P43
17.57
1.16
1.04
0.99
P44
17.61
1.38
1.07
1.02
P45
17.70
1.27
1.05
1.01
P55
19.31
1.35
1.16
1.11
P48
19.45
1.20
1.03
0.98
P50
19.38
1.10
0.98
0.94
P47
18.65
1.40
1.22
1.01
P49
18.82
1.15
0.96
1.21
P51
18.69
1.20
0.00
0.96
P53
18.55
1.10
1.00
0.96
International Journal of Engineering Research in Africa Vol. 26
23
TABLE 5: A COMPARISON BASED ON THE RATIO OF EXPERIMENTAL TO CALCULATED ROLLING
TORQUE BETWEEN REVERSE SANDWICH MODEL [SHOBOWALE], RSM-HRBF [ALAMU] AND HRBF
BASED ON RMS MEAN ROLLING TEMPERATURE
SPEC.
LOG Z
RATIO OF
NO
EXP/CAL. TORQ.
RATIO OF
EXP/CAL.
TORQ.
RATIO OF
EXP/CAL.
TORQ.
[SHOBOWALE]
[ALAMU]
HRBF
[BASED ON
RMS TEMP.]
MATERIAL: HCSS316 (SHOTBLASTED) ROLLED ON MILL A
H20
20.66
1.20
1.04
0.99
H25
19.80
1.10
1.01
0.86
H22
19.97
1.23
1.01
0.97
H23
20.28
1.15
0.98
0.94
H24
19.36
1.16
1.02
0.98
H31
19.68
1.30
1.19
1.14
H27
18.82
1.31
1.12
1.07
H28
19.00
1.34
1.15
1.10
H29
19.24
1.28
1.09
1.04
H30
18.35
1.30
1.09
1.04
H32
18.80
1.36
1.23
1.18
H33
17.98
1.30
1.18
1.13
H34
18.09
1.20
1.07
1.02
H35
18.38
1.20
1.07
1.03
H36
17.56
1.17
1.05
1.00
1
1
1.06
1
2
0.96
[Pexp/Pcal]
1.01
2
3
5
3
3
4
5
4
4
2
5
0.91
LOG
0.86
17.00
H32-H36, Tf=1200 C
17.50
18.00
(10)
Z
H31-H30, Tf=1125 C
18.50
19.00
ε1˂ε2˂ε3˂ε4˂ε5
H20-H24,Tf=1050 C
19.50
20.00
20.50
21.00
Fig.3.1: Dependence of Ratio of Experimental Load to Calculated Load on Zener-Hollomon Parameter for
HCSS316 Rolled on Mill A at r = 10%, Different Tf , Varying strain Rates (Based on RMS Mean Rolling
Temperature)
24
International Journal of Engineering Research in Africa Vol. 26
1.40
1.20
5
0.60
0.40
5
4
3
3
1
4
2
1
3
5
4
2
[Gexp/Gcal]
1.00
0.80
1
2
ε1˂ε2˂ε3˂ε4˂ε5
0.20
H32-H36, Tf=1200 C
0.00
17.00
17.50
H31-H30, Tf=1125 C
18.00
18.50
H20-H24, Tf=1050 C
LOG(10)19.00
Z
19.50
20.00
20.50
21.00
Fig.3.2: Dpendence of Ratio of Experimental Torque to Calculated Torque on Zener-Hollomon Parameter for
HCSS316 Rolled on Mill A at r=10%, Different Tf, Varying Strain Rates (Based on RMS Mean Rolling
Temperature)
1.20
1.00
3
4
5
1
2
2 4
3
5
2
4
3
5
1
1
0.60
0.40
[Pexp/Pcal]
0.80
ε1˂ε2˂ε3˂ε4˂ε5
0.20
P35-P40, TF = 11250C
P41-P45, TF = 12000C
0.00
17.00
P30-P31, TF= 10510 C
LOG(10)Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig.3.3: Dependence of Ratio of Experimental Load to Calculated loadon Zener-Hollomon Parameter for
HCSS316 Rolled on Mill B at r = 10%, Different Tf, Varying Strain Rates ( Based on RMS Mean Rolling
Temperature)
International Journal of Engineering Research in Africa Vol. 26
25
1.2
1
1
1
0.8
0.4
4
3
2
3
2
3
3
4 2
1
4
[Pexp/Pcal]
0.6
2
1
1: r = 5%, 2: r = 15%, 3: r = 20%, 4: r = 25%
HIGH SRT.SPECIMEN H38-H44
0.2
LOW STR.SPECIMEN P55-P50
HIGH SRT.SPECIMEN P47-P53
0
18.20
18.40
18.60
18.80
LOG(10)Z
19.00
19.20
LOW STR. SPECIMEN H37-H43
19.40
19.60
19.80
Fig.3.4: Dependence of Ratio of Experimental Load to Calculated Load on Zenner-Hollomon Parameter for
0
Different Reductions, Hot Rolling on Mill A & B at Low & High Strain Rates, Tf = 1125 C (Based on RMS Mean
Rolling Temperature)
1.10
1
1
1.05
3
2
[Gexp/Gcal]
1.00
2
0.95
3
4
1:5% r,
4
2:15%r,
HIGH SRT.SPECIMEN H38-H34
0.90
18.2
3:20%r
4:25%r
LOW SRT.SPECIMEN H37-H43
LOG(10)Z
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
Fig.3.5: Dependence of Experimental Torque to Calculated Torque on Zener-Holllomon Parameter for Different
0
Reduction, Hot Rolling on Mill A and Mill B at Low & High Strain Rates, Tf = 1125 C ( Based on RMS Mean
Rolling Temperature)
26
International Journal of Engineering Research in Africa Vol. 26
1.2
3
1
2
1
4
4
2
3
0.4
[Pexp/Pcal]
0.8
0.6
1: W/H0 = 5.3
2: W/H0 = 6.3
HIGH SRT.SPECIMEN H54-H57
HIGH SRT.SPECIMEN P62-P65
0.2
0
18.40
3
2
1
18.60
18.80
1
4
4: W/H0 = 9.4
LOW SRT.SPECIMEN P58-P61
19.20
4
2
3: W/H0 = 7.5
19.00
3
LOG(10)Z
19.40
LOW SRT.SPECIMEN H50-H53
19.60
19.80
20.00
Fig. 3.6: Dependence of Ratio of Experimental Load to Calculated Load on Zener-Hollomon Parameter for
0
Rolling of Different Geometry (W/H0) at R = 10%, Tf = 1125 C at Fast Slow Strain Rates on Mill A & Mill B
(Based on RMS Mean Rolling Temperature)
1.20
1.10
1
3
1
[Gexp/Gcal]
0.70
2
2
0.90
0.80
3
4
1.00
4
1: W/H0 = 5.3
2:
W/H0 = 6.3
3: W/H0 = 7.5
4:
W/H0 = 9.4
0.60
0.50
0.40
18.2
HIGH SRT.SPECIMEN H54-H57
LOW SRT.SPECIMEN H50-H53
LOG(10) Z
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
Fig.3.7: Dependence of Ratio of Experimental Torque to Calculated Torque on Zener-Hollmon Parameter for
0
Different Geometry (W/H0) Hot Rolled on Milll A & Mill B at Low & High Strain Rates, Tf = 1125 C, r = 10%
(Based on RMS Mean Rolling Temperature)
International Journal of Engineering Research in Africa Vol. 26
27
1.40
1.20
2
2
2
5
5
5
1.00
3
3
3
4
4
0.60
0.40
2
2
2
1 5
4 5
3
2
3
5
4 5
5
3
2
1
1
1
4
4
4
3
H31-H30, TF = 1125 C
[SHOBOWALE]
H31-H30, TF=1125 C [ALAMU]
H32-H36, TF= 1200C [ALAMU]
17.9
H20-H24, TF = 1050 C [SHOBOWALE]
H31-H30, TF =1125 C
[HRBF]
H32-H36 TF = 1200C [HRBF]
0.00
17.4
4
4
1
1
1 2
ε1˂ε2˂ε3˂ε4˂ε5
H32-H36, TF =1200 C [SHOBOWALE]
0.20
3
3
5
[PEXPTL./PCALCTD.]
0.80
1
1
18.4
18.9
H20-H24, TF=1050 C [ALAMU]
LOG(10)Z
H20-H24,TF = 1050 C [HRBF]
19.4
19.9
20.4
Fig.3.8: A Comparison among RSM [SHOBOWALE], RSM- HRBF[ALAMU] & HRBF Theory (RMS Mean
Rolling Tp.) for Dependence of Ratio of Exptl. to Calctd. Load on Zener-Hollomon Parameter for HCSS316
Rolled on Mill A at R = 10%, diff.TF & Strain Rates.
1.60
1.40
1.20
1.00
0.80
[GEXPTL./GCALTD.]
2
5
5
5
2
2
3
3
3
5 4
5
5 4
4
H32- H36, TF =1200 0C [SHOBOWALE]
H32- H36, TF =1200 0C [ALAMU]
0.20
H32- H36, TF =1200 0C [HRBF]
0.00
17.00
1
4
4
4
5
5
5
1
1 2 3
2 3
2
3
1
1
4
4
1
4
ε1˂ε2˂ε3˂ε4˂ε5
0.60
0.40
1
2 3
1
1 3
2
2 3
H20 - H24, TF = 1050 0C [SHOBOWALE]
H31-H30, TF = 1125 C
[SHOBOWALE]
H31-H30, TF = 1125 C [ALAMU]
H20 - H24, TF = 1050 0C [ALAMU]
H20 - H24, TF = 1050 0C [HRBF]
H31-H30, TF = 1125 C [HRBF]
LOG(10) Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig.3.9: A Comparison among RSM [Shobowale], RSM-HRBF Theory [Alamu] & HRBF (based on RMS Mean
Rolling Temp.) for Dependenceof Ratio of Exptl. Torque to Calctd.Torque on Zener- Hollomon Parameter for
HCSS316 rolled on Mill A at R = 10%, diff. TF and Strain Rates
28
International Journal of Engineering Research in Africa Vol. 26
1.40
1.20
3
0.80
0.60
0.40
1
3 4
2
1
4
2 3
1 2 3 4
4 5
3
3 45
[PEXPTL./PCALCTD]
1.00
4 5
P41 - P45, TF = [ALAMU]
P35- P40, TF = 1125 C
[SHOBOWALE]
P35- P40 TF = 1125 C [ALAMU]
P35 - P40, TF = 1125 C [HRBF]
P41 - P45, TF = 1200 C [HRBF]
0.00
17.00
1
2
2
2
1
1
ε1˂ε2˂ε3˂ε4˂ε5
P41-P45, TF = 1200 C [SHOBOWALE]
0.20
23 4 5
23 4 5
2 3 4 5
5
1
5 1
1
5
P30 - P31, TF = 105 C [SHOBOWALE]
P30 - P31, TF = 1050 C [ALAMU]
P30 - P31, TF = 1050 C [HRBF]
LOG(10) Z
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
Fig. 3.10: A Comparison among RSM [Shobowale], RSM-HRBF Theory[Alamu]& HRBF (based on RMS Mean
Rolling Temp.) for Dependence of Ratio of Exptl. Load to Calctd. Load on Zener- Hollomon Parameter for
HCSS316 rolled on Mill B at R = 10%, diff.TF and Strain Rates.
REFERENCES
[1]
AFONJA, A.A. and SANSOME, D.H. (1973), “A Theoretical Analysis of the Sandwich
Rolling Process” Int. J. Mech. Sci., Vol. 15, pp. 1 – 14
[2]
AIYEDUN, P.O. (1984), “A Study of Loads and Torques for Light Reduction in Hot Flat
Rolling at Low Strain Rates” Ph.D. Thesis, University of Sheffield.
[3]
AIYEDUN, P.O. (1986), “Hot Flat Rolling Simulation by Use of the Bland and Ford’s Cold
Rolling Theory for HCCSS316 at Low Reduction and Low Strain Rates”, Proc, Int. AMSE
Conf., Vol. 3, pp. 14 – 36.
[4]
AIYEDUN, P.O., SPARLING, L.G.M. and SELLARS, C. M., (1997), “Temperature Change
in Hot Flat Rolling of Steels at low Strain Rates and Low Reduction”. Pro. Instn. Mech.
Engrs. Vol. 211, Part B, pp.261-254.
[5]
AIYEDUN, P.O. (1999), “Yield Stress Variation across Thickness for Steel (HC SS316)
Specimen hot rolled at Low Reduction and Low Strain Rates”. NSE Technical Transactions,
Vol. 34, pp. 46 - 70
[6]
AIYEDUN, P.O. and ALIU, S. A (2009), “Rolling Temperature for Steel Hot Flat rolled at
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[7]
ALAMU, O.J. (2001), “Integration of the Reverse Sandwich Model into the Hot Rolling
Bland and Ford’s Theory (HRBF) of Load and Torque Calculation”, MSc. Thesis, University
of Ibadan.
[8]
ALAMU, O.J. and AIYEDUN, P.O. (2003) “A Comparison of Temperature Gradient in Hot
Rolling at Low and High Strain Rates”. J. Sci. Engr. Tech., 10(1): 4644 – 4654.
[9]
FARAG, M.M. and SELLARS, C.M. (1998), “Hot Working and Forming Processes”. Proc.,
Metals Society Conference, Sheffield.
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[10] LENARD, J.G. (1980), “Roll Deformation in Cold Strip Rolling’’ Journal of Engineering
Materials and Technology”, ASME Vol. 102, pp. 382 – 383.
[11] SADIQ, T.O. (2012), “Calculated Rolling Load and Torque for Hot Flat Rolling of Hcss316
at Low Strain Rates based on Better Mean Rolling Temperature”. MSc. Thesis, University of
Ibadan.
[12] SELLARS, C.M. (1981), “Les Traitments Thermomecaniques”, 24eme Colloque de
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[13] SHOBOWALE, B. (1998), “The Reverse Sandwich Effect in HC SS316 Hot Flat Rolled at
Low Strain Rates and Low Reductions”, M.Sc. Thesis, University of Ibadan.