The thermal and metallurgical state of steel strip during hot rolling: Part I. Characterization of heat transfer

The Thermal and Metallurgical State of Steel Strip during Hot Rolling: Part I. Characterization of Heat Transfer

C. DEVADAS, I.V. SAMARASEKERA, and E.B. HAWBOLT

A technique using intrinsic thermocouples was developed to monitor the thermal response of steel samples during hot rolling. A series of hot-rolling tests was conducted with the thermocouple- instrumented samples on CANMET's pilot mill to simulate individual stands of Stelco's Lake Erie Works hot-strip mill. A mathematical model of heat transfer in the roll bite has been employed to back calculate the roll/strip interface heat-transfer coefficients for lubricated and unlubricated conditions. The influence of reduction, rolling speed, and prerolling on roll-strip heat transfer has also been examined. For unlubricated rolling tests, the heat-transfer coefficient in the roll bite increased with time, reaching a steady-state value of 57 k W / m 2 ~ The corre- sponding number for the lubricated tests was 3 1 k W / m 2 ~ The observed variation in the interface heat-transfer coefficient with increasing strain and interface pressure points to a strong dependence on the real area of contact between the strip and rolls. Therefore, it appears that heat transfer between the two surfaces occurs primarily by conduction across asperity contacts. The high heat-transfer coefficients attained at the roll/strip interface promote chilling of the strip to a depth of approximately one-eighth of the thickness. To validate the overall heat- transfer model, predicted surface temperatures of the strip have been compared with interstand temperature measurements obtained on the industrial mill using pyrometers.

I. INTRODUCTION

IMPROVING the processing of steel sheet and strip is one major focus of the steel industry, owing to the in- creasingly stringent specifications being imposed by end users, such as automobile manufacturers, and also as a response to the increasing threat of loss of markets through substitution of other materials. New rolling practices are being developed to roll high-strength low-alloy steels, high-formability dual-phase steels, and very low-carbon interstitial-free and rephosphorized steels, while research continues on the development of newer grades with su- perior properties. These new rolling practices are largely being established empirically based on the operating practice applied to the traditional grades, such as the C-Mn steels. The development of fundamentally based process control models that can link operating variables in the mill to the microstructure and mechanical properties of the finished product is a very desirable research priority, because it provides the necessary technical framework for process control and optimization, eliminating the need for costly on-line experimentation. As newer steels are developed, these models will also serve as vehicles for the rapid transfer of laboratory-based knowledge to industrial operation, thus hastening commercial production.

The first step in the development of fundamentally based models for hot-strip rolling is the quantification of the thermal history and deformation rates as functions of mill parameters. It is also necessary to characterize the com- bined effects of structure-modifying processes, such as

C. DEVADAS, formerly Graduate Student, The Centre for Metallurgical Process Engineering, The University of British Columbia, is Research Engineer, Comalco Research Centre, Melbourne, Victoria 3074, Australia. I.V. SAMARASEKERA, Professor, The Centre for Metallurgical Process Engineering, and E.B. HAWBOLT, Professor, Department of Metals and Materials Engineering, are with The University of British Columbia, Vancouver, BC V6T 1W5 Canada.

Manuscript submitted September 5, 1989.

static and dynamic recrystallization, grain growth, phase transformations, and precipitation during processing, bearing in mind that these phenomena are strongly in- fluenced by composition, temperature, strain rate, strain, and stress.

Several investigators ~1-7] have attempted to model hot rolling as a means of predicting the microstructural evolution within a product during the forming process. Sellars tl] recognized the importance of temperature and an accurate knowledge of its distribution within the deformation zone for extrusion and rolling processes. He acknowledged the usefulness of computer models in providing a reliable way of determining the through-thickness temperature field and analyzing laboratory and in-plant measurements to define the roll/steel interface heat- transfer coefficients. Saito e t a l . t2j have modeled con- trolled rolling and cooling after hot rolling to obtain optimal mechanical properties of plain-carbon steels. They have employed Sellars 'tl] and Sellars and Whiteman's t3] restoration relationships and resorted to an extremely simple temperature model. Suehiro e t al. 141 and Yada [5] have also developed models for predicting the strength of hot-rolled low-carbon sheet steels. Their empirical models are based on dislocation density, a parameter very difficult to quantify and measure. Choquet e t al. [61 at Institut de Recherches de la Sidtrurgie Francaise, Saint Germain-en-Laye (IRSID), France have modeled both flow stress and microstructural evolution during the hot rolling of strip, while Anelli e t al. [71 have examined plate rolling. In most of the above models, [2'4-7j very little at- tention has been paid to accurately describing the surface and subsurface temperatures during rolling. Instead, an average through-thickness temperature in the deformation region has been employed in determining the structural changes. This approach ignores the chilling effect of the work roll, which results in a higher strength and a different structure at the surface and subsurface region and increased roll forces required for deformation.

METALLURGICAL TRANSACTIONS A VOLUME 22A, FEBRUARY 1991--307

Very few studies have been conducted to determine the heat-transfer coefficient between the strip and the work rolls during rolling, making accurate computation of the thermal field difficult. Sellars m has described experiments to determine the interface heat-transfer coefficient by instrumenting the centerline of a test sample with thermocouples and monitoring the response during an experimental rolling schedule. He has reported that although values tend to vary from slab to slab, due to the presence of oxide, a unique value for the heat-transfer coefficient can be obtained for a multipass schedule from measured temperatures. For a stainless steel, a heat- transfer coefficient of 200 k W / m 2 ~ has been reported by Sellars. m This value is considerably higher than the values of 37 k W / m 2 ~ and 18 k W / m 2 ~ reported by Stevens et al. ,t81 who instrumented the subsurface region of a work roll with thermocouples and determined the thermal response during rough rolling. Karagiozis and Lenard t91 have attempted to simulate hot-strip rolling on a laboratory mill with an instrumented slab 38 mm thick. The authors have not attempted to back calculate the magnitude of the heat-transfer coefficient variation with time from their data but have computed average values based on an energy balance. Fletcher et al., ~1~ on the other hand, have reported values as low as 2 k W / m 2 K, which is an order of magnitude lower than Stevens et al.t8J The application of these data to strip rolling is of some concern because of the extremely short contact times with the rolls (-~0.04 second). None of the investigators have discussed the problems associated with the thermocouple response time in their studies, and their experiments have, in general, been conducted for low-speed roiling. Murata et al. [lu and Semiatin et al. ~ have attempted to simulate the conditions that occur at the interface of the tool and workpiece during metal forming by conducting instrumented compression and ring upsetting tests, respectively. Depending on the prevailing surface conditions at the interface, a range of heat-transfer coefficients has been reported. However, the applicability of these data to hot rolling is questionable because of the absence of relative motion and the relatively long contact time in the experimental setup.

recovery, recrystallization, and grain growth, through established relationships and by conducting the necessary testing and validation simulation experiments; and (d) finally, to develop a model incorporating heat flow and structure-modifying phenomena to evaluate the influence of processing parameters on austenite grain size evolution.

This paper, which is the first in a series of three t14,15] on this research program, describes the technique developed for monitoring the temperature response of steel samples during rolling. The measured thermal response of the steel samples was employed in a previously developed mathematical model to back calculate the heat- transfer coefficients that were obtained at the strip/work roll interface. This information is utilized to predict the thermal field in the roll bite. The overall model has been validated by comparing model predictions with measurements of surface temperature on Stelco's Lake Erie Works hot-strip mill.

In the second [lal in this series of three papers, the thermal field in the roll bite serves as the basis for calculation of roll forces, while in the third paper, t~51 it is utilized in the prediction of microstructural evolution.

III. EXPERIMENTAL MEASUREMENT OF THE THERMAL RESPONSE OF

STEEL DURING HOT ROLLING

To determine the heat-transfer coefficient between the steel strip and work roll, the thermal response of either the steel strip or the work roll must be measured during rolling. This is not an easy task, since the total time of contact during a single pass in high-speed rolling is extremely short (of the order of 0.04 second) and the contact pressures are large. A number of preliminary trials were conducted at the University of British Columbia to arrive at a suitable test method. The technique developed was subsequently incorporated in a test program at the pilot rolling facility at CANMET to determine the thermal response during rolling under conditions similar to an industrial mill.

II. SCOPE AND OBJECTIVES

A research program directed at predicting the microstructural evolution during the hot rolling of steel was initiated at the Centre for Metallurgical Process Engineering at the University of British Columbia. The objectives of the overall program were

(a) to establish techniques to determine the roll/strip interface heat-transfer coefficient and to incorporate this information into the previously developed heat-transfer model II3J for a more accurate determination of the thermal field in the roll bite; (b) to develop techniques to compute the roll forces, based on the calculated thermal field, to carry out measurements to establish the flow stresses for the strain rates "employed in Stelco's Lake Erie Works hot-strip mill, and to develop appropriate constitutive equations for incor- poration into the heat-transfer model; (c) to quantify microstructural phenomena, such as

A. Laboratory Tests to Evaluate Thermocouple Design and Data Acquisition

The sensing device suitable for measuring the thermal response of the strip during rolling should be capable of withstanding heavy deformation and have a sufficiently fast response time. Thermocouples have a finite thermal mass and, hence, a finite response time. However, an intrinsic thermocouple has less thermal mass than a beaded thermocouple and is considered more attractive for this application. CHROMEL-ALUMEL* wires were spot-

*CHROMEL-ALUMEL is a trademark of Hoskins Manufacturing Company, Hamburg, MI.

welded to the surface of a sample to form an intrinsic thermocouple with junctions approximately 0.4 mm apart.

To arrive at an optimum wire diameter, INCONEL*

*INCONEL is a trademark of Inco Alloys International, Inc., Huntington, WV.

308--VOLUME 22A, FEBRUARY 1991 METALLURGICAL TRANSACTIONS A

sheathed CHROMEL-ALUMEL thermocouples of di- ameters 0.038, 0.25, and 0.81 mm were attached to individual samples for testing in the laboratory mill. Preliminary hot-rolling tests (900 ~ for 10 to 20 pct reduction) using the INCONEL sheathed thermocouples established that the 0.25-mm diameter gave a satisfac- tory thermal response consistent with the time of roll contact and remained intact during the rolling tests.

The thermal data were recorded on a data acquisition system, consisting of a portable microcomputer (COMPAQ*), a DT2805 data translation board, and a

*COMPAQ is a trademark of Compaq Computer Corp., Houston, TX.

DT707T external board. The data acquisition system was triggered manually, just prior to rolling, to include a short time delay before the samples entered the rolling mill. Data were acquired over a 3-second period at a total acquisition rate of 4500 Hz for the four channels com- prised of three thermocouples and one load cell measurement.

B. Instrumentation of Samples for Pilot Mill Tests

For the hot-strip mill simulation experiments, hot-rolling trials were conducted on CANMET's pilot-scale rolling mill. Since the objective of the exercise was to determine the heat-transfer coefficient at the roll/steel interface, it was considered important that the interface conditions in the test be similar to those which would be obtained in the first and subsequent stands of a hot-strip mill. Trans- fer bar entering the first stand of the finishing mill is essentially free from loose scale, since it is descaled by high-pressure hydraulic descale sprays just prior to entry. In the absence of a lubricant, the only medium on the surface of the rolls is cooling water, which is drawn into the roll bite. In view of this, it was considered that the test specimens should also be free of scale and the rolls water-cooled. The presence of small amounts of loose scale could considerably alter the interface heat-transfer coefficient. Thus, 316 austenite stainless steel was chosen as the test material, since the scale formation on plain- carbon transfer bar samples was sufficiently severe that thermocouples frequently detached with the loose scale upon heating and rolling. It is acknowledged that the thermal properties of stainless steel are considerably different for plain-carbon steel and will affect the measured thermal response; hence, to determine the heat-transfer coefficient from the measured thermal response, the properties of stainless steel have been employed in the model to back calculate the former. Whether the measured heat-transfer coefficient for stainless steel was valid for plain-carbon steels was unknown at the time of the study, since prior to this work, no fundamental studies had been conducted to elucidate the effect of variables, such as material properties, surface roughness, reduction, speed, and lubrication, on the interface heat-transfer coefficient. It will be shown later that the results of this study have provided, for the first time, basic knowledge which has delineated how future measurements should be made to fully replicate industrial rolling.

The 150 • 150 • 25 mm 3 test samples shown in

Figure 1 were employed for the pilot mill trials. The sample thickness is the same as that for transfer bar entering the fLrst stand of the industrial mill. Three grooves, 1.5 mm deep and 1.55 mm wide, were milled on the surface, as shown. Two of the grooves were placed on the right side, approximately 12.5 mm apart along the rolling direction. The third groove on the left had a step of 0.5 mm at the end, as shown. An INCONEL sheathed thermocouple was placed in each of the grooves. In the case of the right-hand grooves, the bare thermocouple wires were individually spot-welded on the surface of the plate adjacent to the edge of the grooves. The thermocouples in the two right-hand grooves were, thus, identical and their responses served as a check on the reproducibility of the measurement technique. On the left- hand groove, the individual wires were spot-welded on the surface of the step, 0.5 mm below the surrounding surface. The distance between the bare ends of each thermocouple was measured using a traveling micro- scope and found to range from 0.27 to 0.5 mm. A 10-mm rod, approximately 1.2 m long, was fitted into the tail end of the plate to enable ease of handling of the assem- bled unit. Electrical tests were conducted to check for electrical continuity, and the thermocouple calibration was checked at two reference temperatures (0 ~ and 100 ~ The voltage signal, compensated using an elec- tronic ice point, was transmitted to the data acquisition system using fiberglass-insulated CHROMEL-ALUMEL extension wires.

C. Pilot Mill Tests

The rolling facility at CANMET's Metals Technology Laboratories consists of a single two-high reversible hot- rolling stand. The feeding of the workpiece into the mill is done manually for the initial pass and all subsequent reversing passes, and all mill data are acquired by a mill computer.

The test sample was heated in a 0 . 2 5 - m m 3 GLOBAR*

*GLOBAR is a trademark of Standard Oil Engineered Materials Co., Niagara Falls, NY.

element furnace with digital programmable control, per- mitting control of the desired reheat temperature to within

5O/ 1 5 0 / - ~ ~ 5 0

Rolling / .~ / / Direction / .q~'/ IorEI 2

/ ~- /

I.Ll_l ~

//Steel Rod U IOX120 Dimensions in

millimeters

Fig. 1--Schematic diagram of the 316 stainless steel sample employed in the pilot mill heat-transfer experiments.


---5 ~ An ingot was placed at the center of the hearth, and the test samples were placed against the ingot to en- sure that the same average temperature was attained.

At the end of the reheating and soaking period, the thermocouple-instrumented test sample was transported to the rolling mill and a midthickness thermocouple was introduced into a small hole drilled at the midthickness plane. Just before entry into the roll gap, the data acquisition was switched on. Thermocouples 1 and 2 (TC1 and TC2) measured the surface temperature of the sample in the roll gap, while thermocouple 3 (TC3) measured the temperature at a depth of approximately 0.5 mm. In addition, by comparing the data from TC1 and TC2, the reproducibility of the surface temperature response was checked. After each test, the thermocouples were tested for mechanical and electrical sta- bility. I f the thermocouples were still functional, these specimens were reused to examine the effect of gage and rerolling.

A series of tests was conducted to determine the effect of reduction, lubrication, roiling speed, entry temperature, and transfer bar gage on the thermal response of the material during rolling, as shown in Table I. For each test, the rolling variables (speed and reduction) were chosen to simulate the industrial rolling schedules typical of Stelco's Lake Erie Works hot-strip mill given in Table II. The center temperature at entry to each stand has been calculated with the aid of the mathematical model. [131 Roll speeds of 45 and 60 rpm were utilized in the tests. To simulate the hot-strip roiling mill, the work rolls were sprayed with water (via a squirt bottle) on the exit end, producing a thin layer of water in the roll gap.

The effect of lubrication was examined by initially coating the top and bottom rolls with a thick layer of lubricant (HM 20, supplied by Stelco) and, subsequently, wiping the roll surfaces to leave a thin coating of the lubricant on the work rolls. The experiments were arranged so that all of the tests without lubrication were scheduled first.

Table I I . A Typical Rolling Schedule at Stelco's Lake Erie Works Hot-Strip Mill

Strain Center Stand Reduction Rate Temperature Iuterstand

Number (Pct) (s -1) at Entry (~ Time (s)

1 43 17.58 1077 3.04 2 41 38.03 1060 1.8 3 25 49.99 1020 1.24 4 17 57.1 970 - -

D. Thermal Response of Instrumented Samples

The typical temperature-time response for a test is shown in Figure 2. Thermocouples 1 and 2 show a well- defined reproducible cooling curve associated with roll contact followed by reheating after loss of contact. Thermocouple 3, which was placed on an exposed step 0.5 mm below the surface of the sample, was forged up during rolling, causing its position to change and making it very susceptible to breakage. For this reason, the temperature response of TC3 was not used for calculation purposes. From the load cell signal, the distance of the thermocouples from the ends of the plate, and the velocity of the rolls, it was possible to accurately establish the total real time of deformation. This time compared favorably (within 5 pct) with the time associated with temperature decay for the thermocouples, providing validation of the test procedure.

The effects of reduction, lubrication, roiling speed, and prerolling on the temperature response of the surface thermocouples were monitored as outlined in the test conditions listed in Table I. The effect of the percent reduction on the response of TC 1 is shown in Figure 3. Decreasing the amount of deformation reduces both the time spent in the roll gap and the magnitude of the decrease in surface temperature associated with roll contact. Lubrication was also found to have a significant effect, as is evident from Figure 4. The presence of lu- bricating oil appears to reduce roll chilling in the roll

Table I. Details of Tests Conducted on CANMET's Pilot Mill for Thermal Response Measurements

Test Number

Centerline Strip Reduction Gage Rolling Temperature (~ Lubrication

(Pct) (cm) Speed (rpm) Furnace Rolling Condition

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 Tl l T12 T13 T14 T15 T16

50 2.554 45 1100 1012 water 50 2.560 45 1120 1045 water 35 2.570 45 1020 1070 water 50 2.554 60 1120 1075 water 35 2.554 60 1100 1012 water 50 2.553 45 1120 1070 oil (thin) 35 2.550 45 1120 1070 oil (thin) 50 2.542 60 1120 1060 oil (thin) 50 2.620 45 1100 1025 oil (thin) 25 2.567 60 1100 1030 oil (thin) 35 1.270 60 1100 980 water 35 1.270 60 1100 1010 oil (thin) 30 1.270 60 1100 1015 oil (thin) 30 1.651 60 1100 1030 oil (thin) 30 1.651 45 1100 1030 oil (thick) 25 1.270 45 1100 1030 oil (thick)


I 0 0 0 �9 | i i i i , i , ! ! ) i , ! !

/ 1-TC2 t~ E rr 6 0 0 20 v D

, o o , o

r I-- 2 0 0 6 0 (3

O O

0 80 J 0"71 0"73 0"75 0"77 079 0"81 0"83 0{35 0.87 0"89

TIME (s)

Fig. 2 - - T h e response of TC1 and TC2 and the load indicator for test T10.

bite by approximately 50 ~ Figure 5 shows the effect of rolling speed on surface temperature, from which it is evident that the sample rolled at a higher speed shows a marginally faster rate of decrease of surface temperature. Figure 6 presents the effect of prerolling on roll chilling by comparing tests T5 and T11. The rate of temperature decrease in T11 was appreciably higher than that in T5, indicating better contact and faster thermal response in the prerolled case (T11). A more detailed dis- cussion of the effect of rolling parameters on roll-gap heat transfer is presented later, following calculation of the heat-transfer coefficient.

IV. MATHEMATICAL MODEL OF HEAT FLOW IN THE ROLL BITE

A. The Roll-Gap Heat-Transfer Model

The heat-transfer model employed in this study to t~ack calculate heat-transfer coefficients is a submodel of the overall model developed to predict heat transfer in the strip during finish rolling. Since the overall model has been extensively described in an earlier publication, [13]

I 0 0 0 0

I.iJ

~ 8 0 0 F--

W

~ 60O F--

TI -,-4" (No Lubrication)

Lubrication)

4 0 0 , i , , i , I I I I i I

0.54 0.58 0.62 0.66 0.7 0.74 0.78 T I M E (s)

Fig. 4 - - Effect of lubrication on the temperature response of the stir- face thermocouple in tests TI (no lubrication) and T6 (with lubrication).

only the pertinent equations will be presented here. In the roll bite, under steady-state conditions neglecting heat flow in the width direction, the governing equation for heat conduction in the strip is

o x \ vo, ill

Employing the transformation

y = vt [2]

the equation becomes

--~X ] Jr- C1 = ps C p, ~ [31 \

where t is the time it takes for an elemental volume to travel a distance y in the roll bite. Assuming symmetrical cooling at the centerline for t > 0, x = 0

OT -k,-- = 0 [4 ]

a x

1050 , , ,

9 5 0 o

Lt.l n- 8 5 0 I -

Ix: tu 7 5 0 Q.

t.t.l

6 5 0

T 5

T4 ( 5 0 % Reduct ion:

o I i I i I I I I I

55 i'~6 I :.3 1':34 1'38 1"42 1'46

T I M E ( s )

Fig. 3--Effect of reduction on the temperature response of the surface thermocouple (TC1) in tests T4 (50 pct reduction) and T5 (35 pct reduction).

1050

9 5 0 o

la.i n- 8 5 0 I -

n,- tu 7 5 0 (2.

I.d

) - 6 5 0

I I ! ! I I i

45 rpm) T 4

(Speed 60 rpm)

55(3 ' ' ' ' ' ' ' 1"18 1-22 1"26 1"3 1'34 I"58 1"42 1'46 1'5

T IME (s )

Fig. 5 - - E f f e c t of rolling speed on the surface temperature in tests T2 (45 rpm) and T4 (60 rpm).

METALLURGICAL TRANSACTIONS A VOLUME 22A, FEBRUARY 1 9 9 1 - 311

1 0 5 0 | 1 I I I ! !

t_) 0 v

" ' 8 5 0 r r

t--

n,- uJ t3_

6 5 0 LIJ

TII (Gage

12.Tmm

T 5 (Goge 25 .4mm) /

\

4 5 0 , , I , m , , 12 1"24 1"28 1"32 1"36

TIME (s)

Fig. 6 - - E f f e c t of prerolling on the surface temperature response in tests T5 (25.4-mm gage) and T l l (prerolled from 25.4-mm to 12.7-ram gage).

At the surface for t > 0, x = d(t)/2

0T - k ~ - - = h(t) ( T - T') [5]

Ox

where h(t) is the local heat-transfer coefficient at the roll/ strip interface and T ' is the roll temperature. Similarly, for the work rolls, neglecting axial conduction, the governing equation is

1 0 ( r k r O T ' ] = wprcmOT' r Or Or / O0 [6]

With the transformation

0 = wt* [7]

the equation becomes

1 0 rkr = p ~ C p , - - [81 r Or Or / Ot*

where t* is the time it takes for an elemental volume of the rolls to rotate through an angle 0 measured from a reference point. The boundary conditions in the roll bite are

r = R 0 , t > 0

OT' - k r - - = h(t*) (T ' - T) [9]

Or

where h(t*) is the roll/strip interface heat-transfer coefficient. The cyclic temperature variation that occurs during each revolution of the roll is confined to a surface boundary layer, 6. For t > 0, R = R*, and 6 = R0 - R*

OT' - k ~ - - = 0 [101

Or

7R0 6 - [111

Pe is the Peclet number. Equations [3] and [81 are cou-

pied through the boundary condition given in Eqs. [5] and [9] and have to be solved simultaneously, com- mencing with an initial condition in the strip and roll prior to entry into the roll bite. An implicit finite-difference method, the details of which are described in an earlier publication, t~3J was employed to solve the equations.

B. Heat Generation in the Roll Bite

Heat is generated in the roll bite due to the work associated with the plastic deformation of the strip and to frictional work at the roll/strip interface. Pavlov's equation t16]

ATe~f - In [12] psCp,

has been employed to calculate the bulk temperature rise of the material due to plastic deformation. The frictional heat generation is given by

dll = Vrl~p [131

where p is the pressure in the arc of contact; an average value may be calculated from a knowledge of the roll- separating force. The relative velocity between the strip and work roll has been calculated in a manner similar to that of Seredynski. t~71 The frictional heat is considered to be generated along the roll/strip interface.

C. Heat-Transfer Coefficient at Roll~Strip Interface

The mathematical model described earlier has been employed to back calculate the heat-transfer coefficient from the thermal response measured in the pilot mill experiments. The properties of 316L stainless steel were employed together with the appropriate properties of the roll material. In performing the analysis, it was found that use of a constant heat-transfer coefficient in the model did not yield a thermal response that matched the measurements and, hence, a variable heat-transfer coefficient was employed. The back-calculated heat-transfer coefficient for a test involving 50 pct reduction and no lubrication (test T4, Table I) is shown in Figure 7. The heat transfer is seen to vary from 17 to 57 k W / m 2 K during the first 0.015 second in the roll gap and then to remain constant thereafter. The progressive increase in the heat-transfer coefficient in the first 0.015 second is thought to be due to the decrease in contact resistance with the increase in specific rolling pressure, which reaches a maximum at the neutral point. The veracity of this hypothesis will be confirmed later. Even though the roll pressure decreases beyond this point, it appears that the contact resistance remains unchanged. The model has been employed in the subsequent section to evaluate the influence of variables on this important boundary condition.

D. Thermal Field in the Strip during Rolling

Characterization of the heat-transfer coefficient at the roll/strip interface permits quantification of the thermal field in the strip during rolling. Test T4 in Table I closely simulates the conditions for stand I at Stelco's Lake Erie Works hot-strip mill. Hence, the heat-transfer coefficient data in Figure 7 were employed to calculate the


60

50

z ~ 4 0

W =E w I0 o

0 0

I I I I I

I I l I I I I

0.01 0.02 0"03 0.04 TIME (s)

Fig. 7 - -Mode l -gene ra t ed variation of the heat-transfer coefficient in the roll gap for test T4 (50 pct reduction, no lubrication).

thermal field in the roll bite for the rolling of a 0.34 pct carbon steel on stand I of the industrial mill; the results are shown in Figure 8. The entry temperature distribution is clearly nonuniform due to the effects of the descale and backwash sprays and was computed with the overall heat-transfer model; [13] these results will be presented in Section VI. Within the roll bite, it is clear that owing to the high heat-transfer coefficient between the rolls and strip and the low temperature of the roils relative to the strip, the strip surface temperature is dras- tically reduced (as measured) and steep temperature gradients are set up. Roll chilling is seen to mask the effect of the heat generated due to deformation in the surface region, and a steep temperature gradient persists to a depth of approximately one-eighth of the final thickness. Furthermore, the temperature drop along the surface over the arc of contact is approximately 350 ~ It is also evident that in the central region of the strip, there is a significant increase in temperature due to mechanical working.

V. ROLL-GAP HEAT T R A N S F E R

To examine the influence of variables on the roll-gap heat-transfer coefficient, the mathematical model has been

-g E

_z _J

z w o 6

0

c.) z 2 I- r

]•010•' ' ' ROLL

800 9 5 0 6 0 0

1030

S T R I P

1 1050

I I I I0 20 30 40 50 DISTANCE INTO ROLL GAP (ram)

1 Fig. 8 - - Temperature distribution in the strip in the roll gap of stand I for a 0.34 pct carbon steel.

employed to back calculate the roll-gap heat-transfer coefficient for the different rolling conditions. A closer examination of the literature on boundary friction and contact between surfaces has yielded significant divi- dends with respect to understanding the observed influ- ences, and this work is referred to here. [18]

A. Effect of Lubrication

The effect of lubrication on the roll-gap heat-transfer coefficient determined from the measurements with the aid of the model is shown in Figure 9. It is evident that the maximum heat-transfer coefficient for tests T6 and T9, in which lubrication was employed, was approximately 31 k W /m 2 ~ as compared with 57 k W / m 2 ~ for test T4, in which only water was present on the rolls.

B. Effect of Rolling Speed

The effect of roiling speed on the roll-gap heat-transfer coefficient is shown in Figure 10. With a higher speed, the heat-transfer coefficient increases more rapidly but reaches the same maximum value as that reached with a lower speed rolling for the same reduction. This could be attributed to the higher rate of deformation with the higher speeds, resulting in a faster increase in specific pressure.

C. Effect of Reduction

Increasing the percent reduction from 35 to 50 increases the steady-state value of the heat-transfer coefficient from 50 k W / m 2 ~ to 57 k W /m 2 ~ as shown in Figure 11. The two curves were virtually parallel over the first 0.015 second because the rolling speed for both tests was 45 rpm. The difference in the steady-state values may be related to the difference in pressures, which would be lower for the smaller reduction.

D. Effect of Prerolling

Samples that had been rolled once and had retained operational thermocouples were rerolled. Figure 12 compares the heat-transfer coefficient calculated from the

6 0 I i ! !

. . . . i r cN

z

W I I I - o z0 / L 5OYo Re, u , oo t W E / i ~ Test T4 No Lubrication I " r ~ I0-/ J---Tes, T6 With Lubrica,ionJ

( 0

0 0 ' , , , 0.01 0.02 0.03 0.04 TIME (s)

Fig. 9 - - T h e influence of lubrication on the roll-gap heat-transfer coefficient, back calculated from measured temperatures for tests T4 and T6,


55

c n ~ ~ 3 5

~_ ~25 , , , , -2

" m5 o

50 0.04

I i , i ! I ,

I llll/g//i ~-- " % "% /_

/ / / ---~'0 L--~rication / / Test Speed (rpm)

/ _T s_ 60

I | I I I I I

0"01 0"02 0"03 TIME (s)

Fig. 1 0 - - T h e inf luence of ro l l ing speed on the ro l l -gap heat- t ransfer coeff ic ient , back ca lcu la ted f rom measured tempera tures for tests T3 and T5.

measured thermal response for samples of gage 12.7 and 25.5 mm. It is evident that for the prerolled sample, gage 12.7 mm, the heat-transfer coefficient does not reach a steady state but increases with time in the roll bite, reaching a maximum value of - 2 9 0 k W / m 2 ~

E. Basic Aspects of Roll-Steel Contact

To understand the fundamentals of heat transfer between the strip and rolls, a closer examination of the literature on boundary friction and contact between surfaces was recently conducted with significant divi- dends. [18] Pioneering work in this field was conducted by Bowden and Tabor, [19] who developed the adhesion theory of friction based on the concept that metal surfaces loaded against each other make contact only at the tips of asperities, as shown in Figure 13. Based on this concept, Samarasekera [~8] has proposed that the primary mode of heat transfer between the strip and rolls is by conduction across the contacting asperities, which offer

60

4O Z

I-- tD ~tE20

z~ lOy I

i I _ 1

/ / No Lubrication / / Test (%)Reduction r "1"4 50

/

/ T5 35 ! . . . . .

i i O0 0'01 0'02 0"63 0'04

TIME (s) Fig. l 1 - - T h e inf luence of reduct ion on the ro l l -gap heat- t ransfer coeff ic ient , back ca lcula ted f rom measured tempera tures for tests T4 and T5.

0 o

~E v

bJ

G ,r_

Z

I- l-- ILl "r

300

200

I00

I

/ /

/ /

/ I

/ I I

I /

/ !

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

d I I

0-10

TIME IN

I I I

Initial Reduction Thickness (%)

(ram) 25.5 50 12.7 35

0 I I [ 0 0 . 2 0 0 3 0

ROLL GAP (s)

Fig. 1 2 I T h e inf luence of prero l l ing on the ro l l -gap heat- t ransfer coeff ic ient , back ca lcu la ted f rom measu red tempera tures for tests T5 and T l l .

a markedly lower resistance to heat f low in comparison to noncontact zones where heat transfer must occur by conduction through air gaps. If this hypothesis is correct, then the roll-gap heat-transfer coefficient should show a strong dependency on the real contact area between two surfaces.

Links between the real contact area and interfacial pressure were first established by Wanheim and Bay. 12'1 They proposed that as the pressure increases, particularly when the workpiece is plastically deformed, the asperities become heavily worked and the real contact area increases. Although a linear relationship has been shown to exist between the real contact area and pressure, the former does not increase indefinitely with pressure and a limit is reached. Wanheim and Bay [2u have shown, using slip line field theory, that the real contact area only approaches the apparent contact area and complete contact never occurs. Wilson and co-workers also made important contributions to boundary lubrication through several studies [22.23] which demonstrated the influence of bulk strain and relative velocity between contacting surfaces on the fractional area of contact. By conducting an

Fig. 1 3 - - C o n t a c t be tween reM surfaces.

314- -VOLUME 22A, FEBRUARY 1991 METALLURGICAL TRANSACTIONS A

4 0 upper bound analysis on an indentation problem, 1221 they obtained a relationship between the fractional area of contact and workpiece strain. Measurements of changes in fractional contact area during a rolling experiment agreed with model predictions, as can be seen from Figure 14 [221 which shows that the fractional area of contact increases with increasing strain but eventually reaches an equilibrium value that remains invariant with increasing strain. In a subsequent paper, [23J with the aid of a friction model, Wilson has shown that at high relative velocities between the contacting surfaces, there is a decrease in the tendency for the two surfaces to conform and the equilibrium value of fractional contact area decreases with increasing relative velocities.

The relationship between the fractional or real contact area and the interface pressure, bulk strain, and relative velocity established by research on boundary friction has permitted a semiquantitative interpretation of the observed influence of variables on the roll-gap heat-transfer coefficient. [~s] First of all, the variation in the heat-transfer coefficient as a function of time along the arc of contact for the first-pass rolling tests shown in Figures 7, 10, and 11 resembles the variation in fractional contact area with the increase in bulk strain predicted by Wilson and Sheu [22] during rolling (Figure 14). Furthermore, the influence of the percent reduction on the heat-transfer coefficient shown in Figure 11 suggests an effect of pressure which has been shown to influence the fractional contact area. I2~ To explore this further and also to explain the dramatic differences in the heat-transfer coefficient between the first and second passes shown in Figure 12, the pressure distribution along the arc of contact for each of the two cases in Figure 12 has been computed t~81 and the results are shown in Figure 15. Despite

I ' O I I r

< / b.! r r < 0 . 8 l ~ - - "

I-- / 0 /

~ 0 . 6 ~ t 0 / r

z O . 4 l 0 Experiment It single pass

1 o multiple pass < rrLL 0 ' 2 ! Theory

curren! model - - - previous model

I I I 0 0.1 0.2 0.3

BULK STRAIN E

J f

0.4

Fig. 1 4 - - C o m p a r i s o n of the var ia t ions in the measured and fract ional contact areas dur ing rol l ing, tnl

~E / In i t ia l R e d u c t i o n / 36 / ~ Thickness

I ( m m ) ( % ) / ..e

I v 32 / - - 255 50 / w j 12.7 35 n- /

2 8 ( / ) /

!,1.1 / rr 24 ' ~ ~ a . / /

<{ 20 /

16

12 I , , 0 0"010 0"020 0"030

TIME IN ROLL BITE (s) Fig. 1 5 - - C o m p u t e d m e a n pressure dis t r ibut ion a long the arc of contact for two success ive passes on the pi lot mil l . o8]

the lower reduction associated with the second pass, the friction hill is steeper and the magnitude of the local pressure is higher, because the incoming material is only half as thick as that for the first pass. Combining Figures 12 and 15 yields Figure 16, from which a clearer picture of the relationship between the roll-strip heat- transfer coefficient and pressure is seen. For the first pass,

200

160 U o

E

120 I - t h i l U I,I. LL h i

o 80 0

fl:: h i I.I. (D Z

~: 40 I-"

I--

h i "1"

l I I I I/ I i

I I

I I

I I

I I

I I

I I

I

/ r /

/ !

/ /

I I

I I

I I

I I

I I

I I

i I

I I

/ Initial Reduction Thickness

(rnm) (%) 25'5 50 12'7 35

OI 0 I , , J , , 20 3 0 40 MEAN PRESSURE (kg/mm z)

Fig. 1 6 - - T h e re la t ionship be tween the rol l -gap heat- t ransfer coeffi- c ient and mean pressure a long the arc of contact for two success ive passes on the pi lot mil l .

METALLURGICAL TRANSACTIONS A VOLUME 22A, FEBRUARY 1991 - - 315

the heat-transfer coefficient increases linearly with increasing pressure up to 15 kg /mm 2 but deviates thereafter and approaches an equilibrium value due to the reason mentioned earlier. For the second pass, there is again a definite linear relationship between the interfacial heat-transfer coefficient and pressure, and the slope of the line is remarkably similar to the linear portion of the first curve. Because the maximum pressure occurs closer to the exit for the second pass, the heat-transfer coefficient does not reach an equilibrium value but increases linearly with pressure. The linear relationship between the interfacial heat-transfer coefficient and pressure shown in Figure 16 is indirect, but the compelling evidence that the interracial heat-transfer coefficient is strongly dependent on the real area of contact, and con- sequently, the primary mode of heat transfer must be the conduction across the contacting asperities.

It has been suggested that lubrication during hot rolling occurs by a mixed film mode, where the strip and rolls are separated by hydrodynamic pockets of lubricant without complete elimination of metal to metal contact at asperities.t2~ It is known that the effective coefficient of friction is reduced from 0.3 to - 0 . 4 to 0.2 to - 0 . 2 5 by the use of a lubricant during hot rolling, and it is logical to expect that the fractional contact area is reduced in the presence of a lubricant. These concepts are useful in rationalizing the influence of a lubricant on the interface heat-transfer coefficient shown in Figure 9. It is evident that in the presence of a lubricant, the maximum value of the heat-a'ansfer coefficient is lower, which could be attributed to the reduction in real contact area due to the lubricant. Since the resistance to heat flow across the liquid films is greater than that of the area in direct contact, conductive heat transfer via the liquid films does not appear to compensate for the loss of asperity contact area.

Thus, the fundamental mode of heat transfer between the strip and rolls appears to be conduction across asperity contacts. Although our knowledge is far from complete, the links established through this work provide know-how for the design of pilot mill experiments for the determination of heat-transfer coefficients applicable to industrial rolling. Clearly, roll finish is important, and the need to attain a pressure distribution and relative velocity similar to those in each stand of the industrial mill will dictate the material properties, gage, speeds, and reductions required for the simulations.

VI. INDUSTRIAL VALIDATION

A. Industrial Measurement

To aid in the validation of both the heat-transfer and roll-force models, which will be described in a subsequent paper, t~4] personnel from Stelco Research and Development (now Stelco Technical Services) with input from the University of British Columbia organized mill trials at Stelco's Lake Erie Works hot-strip mill. In addition to the mill pyrometers located at the exit from the coil box and on entry to and exit from the finishing mill, four single-color pyrometers were installed to measure the strip surface temperature at key locations. The first was located 1.5 m ahead of stand I and the other was

between three successive stands. Temperature data from all of the pyrometers were logged onto the mill computer, together with loads, currents, speeds, gages, reductions, flow rates, and the number of laminar cooling headers employed for final cooling.

Figure 17 shows a sample of the temperature data from all of the pyrometers. It is evident that the head-to-tail end surface temperature variations in the strip are small, owing to the presence of the coil box. The other local fluctuations in temperature can be attributed to skid marks and scale formation. For the purposes of model validation, time averages and standard deviations of temperature were computed from the measurements for a variety of conditions.

B. Predictions of the Strip Thermal Model

The overall heat-transfer model of the mill, described in an earlier publication, t~31 has been employed with the heat-transfer coefficients determined in this study to predict strip temperature distribution in the finishing mill at Stelco's Lake Erie Works operation. Figure 18 compares model predictions with measured temperatures for a 0.34 pct carbon steel rolled to a finished gage of 3.56 mm. The agreement between measured and predicted interstand temperatures is seen to be good.

It is clear that the surface temperature of the strip ex- periences large variations as it passes through the mill. The descale sprays set up large thermal gradients through the thickness. The small spike in surface temperature that occurs after the two initial larger spikes related to descale sprays is due to a set of backwash sprays present before entry to the finishing mill. The next four spikes represent the four finishing stands. Although the chilling effect of the work rolls is dramatic, it is limited to a narrow zone near the surface of the strip and the surface temperature rebounds rapidly in the interstand regions. Figures 19 and 20 show the temperature distribution in the roll bite i n the second stand and in the interstand

1200

0

900 I , I

I- < 600 n- UJ

~- 3 0 0

! I ! I I !

~ ~ - _ - - . - -

".,! . . . . . . . .

= - ~ . . . . . __~ -=_ - - - -

I I I

Pyrometer Measurement F M Entry

........... P y r o I

. . . . . . . P y r o 2

. . . . . P y r o 3 - - - - - F M Exit . . . . Down Coi le r

m

0 40 80 120 TIME (s)

Fig. 17 - -S t r i p surface temperature measurement at several locations in the finishing mill.


t200

I100 (D o

- - I000 bJ re

~- 900 re LU a. 800 bJ I--

700

600

~-C." \_ ___"

{

c } n

5 0 0 0 I ' I 5 I0 15

, I , i i

Temperature Distance From (~ Surface (ram)

Surface Predicted ----- 0,45 0-89

. . . . . Centerline �9 Measured ~ Surface

I i I I

20 25 30 35 40 TIME (s)

Fig. 1 8 - - C o m p a r i s o n of measured surface temperatures with model predictions of the 3.56 nun , 0.34 pct carbon steel strip.

between stands II and III, respectively, for a 0.34 pct carbon steel strip. The chilling effect of the work roils is seen in Figure 19, and the surface temperature re- bounding due to conduction from the interior followed by cooling due to radiation is seen in Figure 20. It is important to note that due to the rapid rebound in surface temperature upon exit from a stand, interstand temperature measurements cannot effectively detect the extent of roll chilling or assess the accuracy of the roll-gap heat- transfer coefficient. This observation emphasizes the importance of conducting separate measurements to characterize the roll-bite heat-transfer coefficient, as was done in this study.

In the later stands of a finishing train, owing to the short contact times in the roll bite, the roll chilling effects are reduced and the temperature distribution through the thickness is more uniform. This is evident in Figure 21, which shows the temperature distribution in the roll bite in stand IV. The fourth stand was the last stand in the

l.,iJ z_ .J 8~ w l- z w o

0 tw h w z

a I I I

I 2 3 4 5 INTERSTAND DISTANCE (rn}

Fig. 20 - - Ternperature contours in the 0.34 pet carbon steel strip between stands II and llI.

mill when the trials were conducted. Stelco's Lake Erie Works mill is now a five-stand operation.

VII. S U M M A R Y

This paper describes the experimental work and mathematical modeling that were undertaken to characterize the thermal field in the roll bite of steel strip during hot rolling.

A technique has been developed to monitor the thermal response of steel samples during contact with the rolls. It consists of spot welding CHROMEL-ALUMEL wires to the surface of a sample to form an intrinsic cou- ple and feeding the millivolt response to a high-speed data acquisition system. A total of 16 tests was conducted on CANMET's pilot mill, in which the effects of rolling speed, reduction, lubrication, and rerolling on the thermal response of instrumented stainless steel samples have been monitored.

The heat-transfer coefficient at the roll/strip interface has been back calculated from measurements of the thermal response of samples during rolling in CANMET's pilot mill with the aid of a heat-transfer model of the roll bite. The interface heat-transfer coefficient increases with

"E6 i I i I I t I i

.EEBj ~ ROLL

w 4 I..- z

~ 9 0

b_ W z o STRIP /

I I I I I I I I I I

r~ 0 5 I0 1,5 20 25 30 :35 40 DISTANCE INTO ROLL GAP (ram)

Fig. 19- -Tempera tu re contours in the roll bite of the second stand for a 0.34 pet carbon steel strip.

2 z w

0 n- la- W Z

U3 Q

8oo

I 0 2

STRIP 9 6 0 _ . _ I - ~ ' ~ -

I I I I I I I I I

4 6 8 t0 12 14 16 18 DISTANCE INTO ROLL GAP (ram)

Fig. 21 - - C o n t o u r map of the temperature distribution within the roll gap in stand IV for a 0.34 pct carbon steel strip.


time in the roll bite and reaches a steady-state value during the first pass. However, in subsequent passes, the heat-transfer coefficient increases with time in the roll bite and does not reach a plateau. In the case of first- pass rolling, the maximum values of the heat-transfer coefficient were found to be 50kW/m2~ and 57 kW/m 2 ~ for reductions of 35 and 50 pct, respectively, in the absence of a lubricant and 31 kW/m ~ ~ for a 50 pct reduction in the presence of a lubricant.

Drawing upon knowledge of boundary friction, it has been postulated that because real surfaces make contact only at asperities, the primary mode of heat transfer between the strip and rolls is conduction across the asperity contacts. It has been shown that the variation in the interface heat-transfer coefficient with pressure and strain is analogous to the influence of these variables on the fractional area of contact between the two surfaces reported in boundary friction literature. These links support the postulated mechanism for heat transfer between the strip and rolls and provide know-how for the design of pilot mill experiments for the determination of heat- transfer coefficients applicable to industrial rolling.

The temperature distribution within the strip during deformation in each stand of an industrial hot-strip mill has been computed with the aid of a mathematical heat- transfer model. The high heat-transfer coefficients obtained at the roll/strip interface promote roll chilling to a depth of approximately one-eighth of the thickness from the surface. Although the surface temperature at exit from the roll bite is depressed up to 350 ~ relative to the entry temperature, it rapidly rebounds in the interstand region due to conduction from the interior.

To validate the heat-transfer model, predictions of surface temperature in the interstand regions and at exit from the fourth stand have been compared with pyrometer measurements. Although the agreement between model predictions and measurements is good, it is important to note that due to the rapid rebound in surface temperature upon exit from a given stand, interstand temperature measurements cannot effectively detect the extent of roll chilling or assess the accuracy of the roll-gap heat-transfer coefficient. This finding underscores the importance of conducting separate measurements to characterize the roll- bite heat-transfer coefficient. These data are required to characterize the thermal field in the roll bite for the prediction of roll forces and microstructural evolution during rolling, which are the subjects of the second and third papers in this series, t14'lSJ

NOMENCLATURE

dl

d2

d h

kr

specific heat of strip, kJ/kg ~

specific heat of rolls, kJ/kg ~

thickness of transfer bar on entry to roll bite, m thickness of transfer bar on exit from roll bite, m instantaneous height of strip in roll bite, m instantaneous heat-transfer coefficient, kW/m 2 ~ thermal conductivity of strip, kW/m ~ thermal conductivity of rolls, kW/m ~

4 q: r

Ro t t* V Vr

w

X

Y

6 /x

P~ P~ o"

heat generation, kW frictional heat generated, kW radius, m roll radius, m time, s time for roll rotation, s velocity of strip, m/s relative velocity between the strip and rolls, m/s rotational speed of roll, rad/s strip through-thickness coordinate, m distance along direction of movement of strip, m depth of zone undergoing thermal cycling, m coefficient of friction density of rolls, kg/m 3 density of strip, kg/m 3 flow stress, MPa

10.

11.

12.

13.

14.

15.

ACKNOWLEDGMENTS

The authors are indebted to Stelco Technical Services, particularly to Mr. H. Averink and Mr. K.R. Barnes for their assistance in organizing plant trials. The efforts of Dr. G.E. Rudd/e in conducting pilot mill trials are greatly appreciated. The financial support of the Natural Sciences and Engineering Research Council of Canada and the University of British Columbia is gratefully acknowledged.

REFERENCES

1. C.M. Sellars: Mater. Sci. Technol., 1985, vol. 1, pp. 325-32. 2. Y. Saito, M. Saeki, M. Nishida, Y. Ito, T. Tanaka, and

S. Taldzawa: Proc. Int. Conf. on Steel Rolling, Iron Steel Inst. Jpn., Tokyo, 1980, pp. 1309-20.

3. C.M. Sellars and J.A. Whiteman: Met. Sci., 1979, Mar.-Apr. , pp. 187-94.

4. M. Suehiro, K. Sato, Y. Tsukana, H. Yada, T. senuma, and Y. Matsumura: Trans. Iron Steel Inst. Jpn., 1987, vol. 27, pp. 439-45.

5. H. Yada: Proc. Int. Syrup. of Accelerated Cooling of Rolled Steel, The Met. Soc. CIMM, Winnipeg, M_B, Canada, 1987, pp, 105-20.

6. P. Choquet, A. LeBon, and Ch. Perdrix: Proc. 7th Int. Conf. on the Strength of Metals and Alloys, H.J. McQueen, J.P. Bailon, J.I. Dickson, J.J. Jones, and M.G. Akben, eds., Montreal, 1985, Pergamon Press, New York, NY, pp. 1025-30.

7. E. Anelli, M. Ghersi, A. Mascanzoni, M. Paolicchi, A. Aprile, A. DeVito, and F. DeMitri: Proc. 7th Int. Conf. on the Strength of Metals and Alloys, H.J. McQueen, J.P. Bailon, J.I. Dickson, J.J. Jones, and M.G. Akben, eds., Montreal, 1985, Pergamon Press, New York, NY, pp. 1031-36.

8. P.G. Stevens, K.P. Ivens, and P. Harper: JISI, 1971, pp. 1-11. 9. A.N. Karagiozis and J.G. Lenard: The Science and Technology

of Flat Rolling, 4th Int. Steel Rolling Conf., Deauville, France, June 1-3, 1987, IRSID, Saint Germain-en-Laye, France, pp. B.3-B.7. A.J. Fletcher, A.G. Gibson, and J.A. Gonzales: Met. Technol., 1984, pp. 156-66. K. Murata, H. Morise, M. Mitsutsuka, H. Haito, T. Kumatsu, and S. Shida: Trans. Iron Steel Inst. Jpn., 1984, vol. 24 (9), p. B309. S.L. Semiatin, E.W. Collings, V.E. Wood, and T. Altan: J. Eng. Ind., 1987, vol. 109, pp. 49-57. C. Devadas and I.V. Samarasekera: lronmaking and Steelmaking, 1986, vol. 13 (6), pp. 311-21. C. Devadas, D. Baragar, G. Ruddle, I.V. Samarasekera, and E.B. Hawbolt: Metall. Trans. A, 1991, vol. 22A, pp. 321-33, C. Devadas, I.V. Samarasekera, and E.B. Hawbolt: Metall. Trans. A, 1991, vol. 22A, pp. 335-49.


16. W. Roberts: in Deformation Processing and Structures, G. Klaus, ed., ASM, Metals Park, OH, 1984, pp. 109-84.

17. K. Seredynski: J. Iron Steel Inst., 1973, vol. 211, pp. 197-203. 18. I.V. Samarasekera: Proc. Int. Syrup. on the Mathematical

Modelling of the Hot Rolling of Steel, 29th Annual Conf. of Metallurgists, CIMM, Hamilton, ON, Canada, Aug. 27-29, 1990, Pergamon Press, New York, NY, 1990, pp. 145-67.

19. F.P. Bowden and D. Tabor: The Friction and Lubrication of Solids, Clarendon Press, Oxford, 1950, Pt. I and 1964, Pt. II.

20. J.A. Schey: Tribology in Metal Working, ASM, Metals Park, OH, 1983, pp. 30-35.

21. T. Wanheim and N. Bay: Annals of CIRP, 1976, vol. 27 (1), pp. 189-93.

22. W.R.D. Wilson and S. Sheu: Int. J. Mech. Sci., 1988, vol. 30 (7), pp. 475-90.

23. W.R.D. Wilson: Friction Models for Metal Forming in the Boundary Lubrication Regime, ASME Winter Annual Meeting, Chicago, IL, Dec. 1988.


Documents

The thermal and metallurgical state of steel strip during hot rolling: Part I. Characterization of heat transfer