Inhomogeneity of temperature distribution through ... - SAGE Journals

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Inhomogeneity of temperature distribution through thickness of the aluminium strip during hot rolling H R Rezaei Ashtiani1*, H Bisadi1, and M H Parsa2 1 Department of Solid Mechanics, School of Mechanical Engineering, Iran University Science and Technology (IUST), Tehran, Iran 2 School of Metallurgy and Materials Engineering, University College of Engineering, University of Tehran, Tehran, Iran The manuscript was received on 28 October 2010 and was accepted after revision for publication on 11 April 2011. DOI: 10.1177/0954406211408951

Abstract: Temperature distribution and inhomogeneity of its through thickness of the strip play an essential role in hot rolling processes, where both the strip and work-roll behaviour are affected strongly by these temperature fields and the microstructural and mechanical properties through thickness of hot rolled strip depend on this temperature inhomogeneity within the strip being deformed during hot rolling. In this investigation, a mathematical model was developed to predict the thermal history and inhomogeneity of temperature through thickness of an aluminium alloy strip undergoing single-stand hot plate rolling using the commercial finite element (FE) package, ABAQUS/Explicit in three dimensions. To estimate the reliability of the numerical analysis, the FE model was validated using experimental roll force and torque data and also temperature history at the centre-line of strip; good agreement was found between the two sets of predicated and experimental results. The effects of various process parameters, such as rolling speed, interface heat-transfer and friction coefficients between strip and work roll, initial thickness of the strip, and work-roll temperature and diameter on the temperature inhomogeneity, is considered. Keywords: hot rolling, heat transfer, inhomogeneity of temperature distribution, aluminium alloy, finite element method

1

INTRODUCTION

Strip rolling process is widely used for manufacturing semi-finished flat products. This process is usually carried out in hot working conditions to increase the workability of the metal being rolled and decrease the required deformation load and torque, therefore reducing the energy consumption [1]. It is, generally, confirmed that temperature is the most significant parameter for determining product properties, such as the microstructural and mechanical properties, in hot deformation processes. Temperature has also a *Corresponding author: School of Mechanical Engineering Department of Solid Mechanics, Iran University Science and Technology (IUST), Narmak, Tehran 16846-13114, Iran. email: [email protected] Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

dominating influence on the dimensional accuracy of the rolled strip. Besides temperature, parameters, such as amount of reduction, interface conditions, rolling speed, and inter-stand cooling rate, are the variables which influence the dimensional accuracy and microstructural and mechanical properties of the rolled strip. All of mentioned parameters can be evaluated using thermo-mechanical analysis which is an important aspect for controlling the properties, dimensional accuracy of the product, and energy consumption in hot rolling. For controlling hot rolling, it is critical to know the temperature distribution and its inhomogeneity within the strip, since temperature is the dominant parameter controlling the kinetics of microstructural trans-formations, specifically grain size and the flow stress of the rolled metal.

Inhomogeneity of temperature distribution through thickness of the aluminium strip during hot rolling

For evaluation of the above-mentioned parameters, numerous studies have been carried out. Hollander [2] developed a thermal model for flat rolling using the finite difference (FD) technique. After a few years, Harding [3] developed a more detailed analysis that forms the basis of the FD model of SLIMMER [4]. Serajzadeh et al. [5] showed that the microstructural changes, the mechanical properties as well as the final dimensions of the product and roll-force depend on inhomogeneity of the temperature distribution within the metal being rolled. The evolution of temperature distribution during hot rolling has been performed by various scholars and scientists, in recent years [6–8]. Figure 1 shows the general configuration of strip rolling and heat fluxes that was mostly used for analysis. The width of the plate or strip is much greater than its thickness. It is, therefore, justified to neglect heat conduction in the width direction [9]. Therefore, temperature inhomogeneity through thickness of the strip that is produced by different heat transfer and heat generation conditions, has a significant role on the inhomogeneity of microstructural and mechanical properties through thickness of the hot rolled strip, and this is investigated on the hot plate mill rolling of aluminium strips in this article. Three different approaches, the analytical, the finite-difference method (FDM) and the finiteelement method (FEM) are currently used to calculate the temperature variation through strip thickness in the roll gap. There are quite significant differences between these approaches in their consideration of heat generation and heat loss. The analytical approach only takes into account heat transfer between the strip and roll by conduction [10]. The computed temperature is only true under certain

Fig. 1

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conditions. The FDM gives a better prediction than the analytical approach by considering heat generation through the strip thickness and applying friction work to the surface elements, in addition to the conduction between roll and strip (Fig. 1) [9, 11]. Three-dimensional (3-D) FD models are noticeably difficult to manage because remeshing conveniences do not exist. The FEM is theoretically the best method because it considers all factors, such as variation of thermal properties or differing rates of internal heat generation with position and time and can easily contain remeshing [12]. It clears that inhomogeneities of temperature have significant effects on the inhomogeneity of microstructural and mechanical properties through thickness of the hot rolled strips. These are produced by different heat transfer and heat generation conditions. In the following sections, formulation used for the analysis of temperature distribution, boundary conditions, and results will be presented. 2 MATHAMATICAL MODELLING 2.1 Thermal equations Heat transfer plays an important role in hot rolling processes, where both the strip and work-roll behaviour are affected strongly by the temperature fields. In order to find the temperature distribution within the strip, the governing heat conduction equations for both the strip and the work rolls are solved iteratively. Because the thermo-physical attributes and the flow stress are assumed to be functions of temperature, in each iteration, it is required that the thermo-physical properties be updated. The governing equation for the steady-state conditions is assumed to be a convection/conduction equation. To simplify the

General configuration of strip rolling with heat fluxes Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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H R Rezaei Ashtiani, H Bisadi, and M H Parsa

equation of temperature distribution in the work roll, it is assumed that heat conduction in the work roll along the peripheral direction (i.e. co-ordinate) is negligible compared with the bulk heat flow, and that the thermal conduction at the top interface of the strip is identical to that at the bottom. The z coordinate axis runs along the length of the work roll [13]. Thus 1 @ @T @ @T @T kr r kr ð1Þ þ ¼ r cr r @r @r @z @z @t During the hot rolling process, the temperature distribution in the strip can be calculated using the governing partial differential equation (3-D) shown in equation (2) [14]. @ ks @T @ ks @T @ ks @T þ þ @x @x @y @y @z @z ð2Þ @T þ q_ ¼ s cs @t where x is the distance along the length of the strip, y the distance through the thickness, and z the distance 3 _ along the strip width and q(W/m ) is a heat generation term representing the heat released due to plastic work. Subscripts r and s are for roll and strip, respec_ is calculated using tively. The heat generation term q, equation (3). q_ ¼ "_

2.2 Thermal boundary conditions The accuracy of thermo-mechanical models of the hot rolling process depends on the proper description of the boundary conditions. The boundary conditions for the strip at the deformation zone can be expressed as follows. @T ¼ hc ðT Tr Þ qfric @n

ð4Þ

Also, for the work roll, equation (5) is governing. @T ¼ hc ðTs T Þ r¼R qfric ks @n

Temperature distibution condition: (a) 3-D model and (b) 2-D model

ð3Þ

where is the efficiency of conversion of deformation energy to heat; the latter is assumed to be 0.95 for aluminium alloys, which is considered reasonable. Since the heat lost from the strip is gained by the work roll in the roll gap, a simultaneous solution of the governing equations of both the strip and the work roll is required (Fig. 2). To do so, the heat transfer in the work roll can be written as equations (1) and (2).

kr

Fig. 2

ð5Þ

It should be noted that conduction heat transfer takes place between the work roll and strip, while Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

the interface heat-transfer coefficient controls the thermal continuity between these two media. Therefore, the boundary conditions can be defined as follows: 1. The symmetrical thermal boundary condition at the centre-line of the strip can be expressed as ks

@T ¼ 0 @ t 4 0, y ¼ 0 @y

ð6Þ

2. An adiabatic condition can be assumed at a 6 mm radial distance below the work roll surface. This condition has been represented by equation (7). To ensure the validity of this condition, the thickness of the work roll must be sufficient to avoid increases in temperature along the inner radius of the model. kr

@T ¼ 0 @ t 4 0, r ¼ r6mm @r

ð7Þ

3. The thermal boundary condition between the strip and the work roll is defined by equation (8). qstrip ¼ qroll ¼ hc ðTs Tr Þ @ t 4 0, y ¼

H ðt Þ or r ¼ R 2 ð8Þ


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where H(t) (in mm) is the total thickness of the strip in each time of t during hot rolling and q (W/m2) the heat flux. 2.3 Mechanical boundary conditions Contact boundary condition describing the mechanical interaction of the strip and the work roll was imposed along the strip/roll interface. Interfacial friction for the contact area is proportional to the normal pressure, as shown in equation (9). cr ¼ P

ð9Þ

where cr is the critical shear stress at which sliding starts (Pa), the coefficient of friction, and P the pressure (Pa). The coefficient of friction is extracted from tests. Therefore, the produced heat by the friction can be calculated by [14] qfric ¼ cr Ac jvr vs j

ð10Þ

where ðvr vs Þ is the relative speed of work roll and strip. For this study, static friction has been assumed without transition to or from dynamic friction conditions. Deformation symmetry in the strip is maintained through a zero displacement boundary condition in the through-thickness direction along the strip centre-line. This allows the reduction in geometric complexity and computational time. Therefore, the general FE model, Fig. 3(a), can be replaced by the quarter of FE model, Fig. 3(b), for simplicity and time providence. 2.4 Implementation of finite element modelling In this way, a 3-D rolling model has been constructed to simulate a single pass of the hot plate mill rolling process for aluminium alloys of AA1100 using the commercial FE software package, ABAQUSTM (Fig. 3(b)). Although a 2-D rolling model can decrease simulation time, investigations show that its accuracy is lower than a 3-D rolling model. As will be explained in Section 3.2 (Fig. 7), due to non-homogeneity of boundary condition at central and lateral regions of strip, inhomogeneity of temperature distribution through width of the strip can only be determined by a 3-D model. A 2-D model can often be utilized to solve the heat conduction equation in the work rolls under the plane strain rolling conditions. In order to implement the material behaviour in the model, tables of flow stress data at specified strain rates and temperatures were generated and inputted to ABAQUSTM. For every temperature and strain rate within the model, the flow stress at each integration

Fig. 3

Strip and work-roll in FE model (a) the general; and (b) the quarter of the models

point is calculated based on a linear interpolation between the tabular data points. For example, the flow stress data for strain rate of 0.1 s1 and different temperatures used in this FE model have been illustrated in Fig. 4. Also, the used values of the elastic constants for AA1100, as a function of temperature, are listed in Table 1 [15]. The thermo-physical properties for AA1100 are presented in Table 2 [16]. The density of the strip was assumed to be constant at 2710 kg/m3 [17]. The steel work roll was defined as an elastic material with a Young’s modulus of 200 GPa. The large difference in the elastic modulus between the work roll and the strip causes the work roll to behave as a virtually rigid material. The thermo-physical properties of the steel work roll are exhibited in Shahani et al. [18]. On the other hand, hot rolling is a thermomechanical process and therefore, elements of strip and work roll in this model have been selected as C3D8T with an eight-node thermally coupled brick, trilinear displacement, and proper temperature. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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Fig. 4

Flow stress curves of AA1100 at 0.1 s1 and different temperatures

In order to estimate the reliability of this FE model, a comparison was made between the roll force and roll torque predicted by simulations and the experimental results data of the hot rolling of AA1100 obtained by Hum et al. [19]. It is clear from Fig. 5 that roll force and torque results of the experimental data and simulation have proper accordance by varying thickness reduction. Also, the assumed FE model is validated by comparing the predicted temperature variations and experimentally measured values at the centre-line of the strip. The predicated temperature history at the centre-line of strip for hot plate rolling of AA1100 has been compared to experimental data obtained by Chun and Lenard [20]. In the test, the strip was reduced to 35 per cent, using an initial temperature of 507.9 C. Figure 6 illustrates the temperature histories for the experimental data and simulation results (with

values of 20, 40, and 60 kW/m2 K). They show a proper accordance by varying the rolling time. Therefore, this FE modelling can be a proper selection for temperature simulation of this material during hot rolling. Knowledge of the heat-transfer coefficient at the hot strip and work-roll interface is required for acceptable simulation. As illustrated in Fig. 6, the investigations show that, for the worst case, the error between the predicted and measured temperature history at the centre of the hot rolled strip is lower than 1 per cent (0.99 per cent) for the heattransfer coefficient of 40 kW/m2 K, whereas the errors between the simulation and experimental results of the temperature history at the centre of the hot rolled strip are 2.9 per cent and 3.5 per cent for the heat-transfer coefficients of 60 and 20 kW/m2 K, respectively. Therefore, the value of 40 kW/m2 K gives a reasonable prediction for the temperature distribution of strip within the roll bites when the heat-transfer coefficient is changed from 20 to 60 kW/m2 K and this value is used in all future computations and in the following sections.

Table 1

Table 2

3

SIMULATION RESULTS AND DISCUSSIONS

3.1 Validation of simulation model

Elastic modulus and Poisson ratio for AA1100 [15]

Temperature 300 350 400 450 500 600

Elastic modulus (GPa) 59.4 57.3 55.1 52.9 50.7 46.4

Thermo-physical properties used for AA1100 [16]

Temperature

Thermal conductivity (W/m K)

Heat capacity (J/kg K)

41 280 306 410 505

170 190 195 200 205

900 960 980 1020 1130

Poisson ratio values 0.356 0.359 0.362 0.365 0.368 0.337

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3.2 Temperature distribution In the FE model, the work roll has been assumed to have a radius of 125 mm and a roll speed of 80 r/min. The initial temperature of the strip has also been selected as 500 C. The 6.3 mm strip thickness has been assumed to have a width of 50 mm and thickness reduction of 30 per cent. The temperature distribution of upper half of the strip during hot rolling is shown by Fig. 7. As it is clear, the temperature distribution in the various regions of the strip is not uniform and temperature variations of the surface region are more than of the central regions. In other words, temperature inhomogeneity is observed through thickness of the rolled strip. Also, as it expected, the maximum heat transfer occurs in the contact region between the strip and work roll that induces a reduction in the surface temperature. Figure 8 shows the temperature changes at different positions through thickness of the strip during hot rolling. It is obvious that surface area endures the maximum variations of temperature while temperature of the interior regions does not change significantly. As the surface temperature tolerates severe temperature variations ranging between 335 C and 500 C, in the subsurface layer with a depth of 0.788 mm, these variations are limited to 85 C. The centre-line temperature shows a peak during the rolling process due to the heat released as a

Fig. 6

Fig. 5

Reliability of the FE model in comparison with experimental results of roll: (a) force; and (b) torque

result of plastic deformation (equation (3)) and adiabatic heating effect in this region, while the temperature profile drops at the surface due to the interface heat-transfer condition between the roll and the strip.

Reliability of the FE model with different values of heat-transfer coefficient in comparison with experimental results of the time–temperature history of the hot rolled aluminium at the centre-line of strip Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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Fig. 7

Mesh distortion and temperature distribution during hot rolling of AA1100 for a reduction of 30 per cent and initial temperature of the strip of 550 C

Fig. 8

Temperature changes at different points through thickness of strip with rolling time

For this sample, it should be noted that temperatures at different positions reach an equal amount due to thermal conductance in the thickness direction with the passage of rolling time. The temperature distribution and temperature gradient through thickness of the strip, during hot rolling process, depend on several parameters investigated in detail in the following sections and they are: rolling speed, interface heat-transfer coefficient, friction coefficient between strip and work roll, initial thickness of strip, and the work-roll temperature and diameter, respectively. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

3.3 Influence of rolling speed Roll speed is one of the most important parameters during hot rolling, since this factor directly controls the strain rate, flow stress, roll force, heat of deformation, and the interface heat transfer. Figure 9 shows the effects of this parameter on the temperature variation in the surface and the centre regions of the strip. It can be explained that more roll speed results in shorter contact time, which decreases the heat flow from the strip to the work roll. Whereas increasing of the roll speed, increases the roll force and the


Fig. 9

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Effect of roll speed on the temperature changes during rolling time for points at the centre and surface of the strip

Fig. 10

Inhomogeneity of temperature through thickness for different roll speeds

deformation of heat. Consequently, there is reduction in the cooling rate of the strip in the deformation zone. As the rolling speed increases, time of heat losses to the work roll decreases and thereby the surface temperature of the strip increases. Therefore, the higher the rolling speeds, the greater will be the surface temperature of the strip. Also, heat flux from centre to surface of the strip decreases (because of reduction in the temperature gradient between

the centre and the surface regions of the strip). Therefore, the temperature of the strip centre increases with increase in the rolling speed (Fig. 9). For the central point, increase in the rolling speed causes the temperature to reach 501 C at the beginning of deformation. It can be observed that decreasing the rolling speed extremely decreases the temperature gradient by raising the heat transfer at a very low rolling speed such as 40 r/min. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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Fig. 11

Effect of heat-transfer coefficient on the temperature history for two points at the centre and surface of strip

It is clear from the Fig. 10 that the amount of temperature inhomogeneity through thickness of rolled strip will be decreased by increasing the roll speed from 20 to 200 r/min, progressively, at a rolling time of 0.03 s. Also, the temperature increases with increasing the roll speed. It is hard to find a significant temperature inhomogeneity through thickness of the rolled strip with a rolling speed of less than 40 r/min. 3.4 Influence of heat-transfer coefficient Heat-transfer coefficient between strip and work roll is another important parameter affecting the temperature distribution and temperature inhomogeneity through thickness of the strip during hot rolling. It should also be noted that the interfacial heat-transfer

coefficient is a function of roll force, lubrication, and surface condition [5] and can vary across a range of values from 10 to 60 kW/m2 K [21]. The interface heattransfer coefficient can considerably change the temperature distribution and the depth of the thermally affected zone. Figure 11 shows the effect of interface heat-transfer coefficient on temperature at centre and surface of the strip. Also, roll exit plane (i.e. rolling finish point) has been mentioned as exit plane line in this figure. Heat-transfer coefficient is directly responsible for the magnitude of the heat flow from hot strip to the work rolls. The rate of heat flow is increased by increasing the heat-transfer coefficient [22]. Thus, as the heat-transfer coefficient is increased, the surface temperature of the strip is reduced. The amount of temperature inhomogeneity through thickness of the strip has been shown in Fig. 12 at a rolling time of 0.02 s. As it is clear from this figure, this temperature inhomogeneity has been decreased by decreasing heat conductivity between work roll and strip. Also, simulations results show that heat-transfer coefficient have a significant effect on the amount of temperature inhomogeneity through thickness of the hot rolled strip. 3.5 Influence of friction

Fig. 12

Inhomogeneity of temperature through thickness for different heat conductivities


Friction coefficient between strip and work roll also influences the state of temperature distribution within the strip during hot rolling. The interface


Fig. 13

Effect of friction coefficient on the temperature history for points at centre and surface of the strip

friction coefficient can change the temperature distribution and the depth of the thermally affected zone. Figure 13 shows the effect of friction coefficient on temperature at centre and surface of the strip. The simulations clarify that higher friction coefficient value between strip and work roll leads to a decrease in temperature drop within the strip being hot rolled and therefore, the temperature gradient between the central and the surface regions is reduced. This means, friction work can be converted to heat, thereby increasing strip temperature (equation (10)). Therefore, this occurrence postpones fall in the temperature of the rolled strip. The inhomogeneity of temperature distributions through thickness of the rolled strip resulting from different friction coefficients between strip and

Fig. 14

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Inhomogeneity of temperature through thickness for different friction coefficient values

work roll in the exit plane (Fig. 13) is shown in Fig. 14. As illustrated in this figure, friction coefficient does not have a significant effect on the temperature inhomogeneity through thickness of strip; nonetheless, it can be claimed that temperature inhomogeneity through thickness of strip has been decreased by increasing the friction coefficient. As illustrated in equation (10), part of the heat that is generated by friction at the work roll/strip interface, increases surface temperature of strip and this phenomenon decreases temperature inhomogeneity through thickness. 3.6 Influence of the initial thickness of strip The effect of initial thickness of the strip on the temperature distribution of hot strip rolling is also investigated. Figure 15 shows the effects of initial thickness on the temperature variation at the centre and the surface regions of the strip. Initial thickness influences on the amount of mechanical work and the heat generated because of mechanical work. The heat flow through thickness of the strip is also affected by initial thickness of the strip. Thermal conductance between the centre and the surface of the strip is increased by increasing the initial thickness of the strip. This is obvious from Fig. 15 that increasing the initial thickness of strip causes more mechanical work and heat generation of mechanical work and therefore, lower temperature drop in the surface and centre of the strip. It is clear from the Fig. 16 that the amount of temperature inhomogeneity through thickness of rolled Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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Fig. 15

Effect of initial strip thickness on the temperature history for points at centre and surface of the strip

Fig. 16

Temperature inhomogeneity through thickness for different initial thicknesses

strip has been decreased by increasing the initial thickness from 6.6 to 15.6 mm, progressively, at a rolling time of 0.02 s. Also, the amount of temperature at the centre of the strip increases, with increasing the initial thickness value for a hot rolled strip. 3.7 Influence of work-roll temperature During hot plate mill rolling, the strip surface is chilled as it contacts the working rolls, whereas the Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

work rolls receive heat from the strip. The work rolls are also subject to surface cooling by water spray and air. Therefore, the work-roll temperatures can be controlled and regulated at a proper value by water spray. As it is clear from Fig. 17, initial temperature of work rolls significantly influences the temperature distribution and inhomogeneity of through thickness of the strip (Fig. 18) during hot rolling. Figure 17 shows the temperature history of centre and surface of strip during a hot plate rolling pass.


Fig. 17

Effect of initial temperature of work roll on the temperature history for points at centre and surface of the strip

Fig. 18

Temperature inhomogeneity through thickness for different initial temperatures of work roll

As the work-roll temperature increases, heat loss from strip to the work rolls decrease and thereby the surface temperature of the rolled strip is increased. Therefore, the higher the work-roll temperature, the greater will be the surface temperature of the strip. Also, heat flux from centre to surface of the strip decreases and the temperature at the centre of the strip also increases. Figure 18 shows the amount of temperature inhomogeneity through thickness of the rolled strip at a rolling time of 0.02 s; it is obvious that the amount of temperature inhomogeneity through thickness of the

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strip has been decreased by increasing the work-roll temperature as this temperature gradient through strip thickness can be obtained the least by increasing of the work-roll temperature to 360 C.

3.8 Influence of work-roll diameter Finally, influences of the work-roll diameter on the temperature distribution and temperature inhomogeneity through thickness during hot strip rolling are investigated using various simulations. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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Fig. 19

Effect of work-roll diameter on the temperature history for points at centre and surface of the strip

Fig. 20

Temperature inhomogeneity through thickness for different of work-roll diameters

As it is clear from the Fig. 19, work-roll diameter does not have a significant influence on the temperature distribution and inhomogeneity through thickness of the strip (Fig. 20) during hot rolling. Figure 19 demonstrates the temperature history of centre and surface of strip during a hot plate rolling pass. As the work-roll diameters increase, the surface temperature of the hot rolled strip is increased. Also, heat flux from centre to surface of the strip decreases and the temperature at the centre of the strip increases. The inhomogeneity of temperature distributions through thickness of the rolled strip resulting of the Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

different work-roll diameters is shown in Fig. 20 at a rolling time of 0.035 s. As the friction coefficient, workroll diameter does not have a significant effect on the temperature inhomogeneity through thickness of strip; nonetheless, it can be claimed that temperature inhomogeneity through thickness of strip has been decreased by increasing the work-roll diameter. 4 CONCLUSION With regard to importance of inhomogeneity of temperature distribution on microstructural and


mechanical properties of hot rolled strip, controlling temperature distribution and inhomogeneity through thickness of the strip has been investigated in this study. Special attention was paid to prediction of the temperature distribution through the thickness of the hot rolled strip. In this study, a mathematical model based on the FE analysis is proposed to predict temperature distributions during hot strip rolling operations. The model is able to consider the effects of rolling parameters such as rolling speed, heat transfer and friction coefficients, initial thickness of strip, and initial temperature of work roll. At first, comparisons between the FEM simulation results and the experimental data show the validity of the FEM model. Results of these simulations show that temperature distribution is not homogeneous in the rolled strip and so the surface region of the strip endures more temperature variations during deformation as compared to the centre of the strip. Investigations show that temperature inhomogeneity through the strip thickness has been decreased by increasing the amount of roll speed. The value of heat-transfer coefficient between strip and work roll is the most important parameter affecting the temperature distribution and inhomogeneity through thickness during hot strip rolling; as, if the heattransfer coefficient between strip and work roll is increased, temperature of the surface and centre of the strip will decrease and inhomogeneity of temperature through the strip thickness will increase. Frictional work between strip and work roll is converted to heat in the strip, similar to plastic work, and it increases the surface temperature of the strip. Simulation results show that higher friction coefficient value leads to a reduction in temperature drop within the strip being rolled and also the temperature gradient between the centre and the surface of the strip reduces. Also, simulation results show that mechanical work and deformational heat increase at the central regions of the hot rolled strip, and therefore, inhomogeneity of temperature through the strip thickness decreases, with increase in the initial thickness of the strip. The influence of work-roll temperature on temperature distribution showed that the amount of temperature inhomogeneity through thickness of the rolled strip has been decreased by increasing the work-roll temperature. In the end, investigations show that temperature inhomogeneity through the strip thickness has been slowly decreased by increasing of the work-roll diameter. Finally, simulation results show that the most important parameters on inhomogeneity of temperature distribution through thickness of the hot rolled

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strip are: the heat-transfer coefficient between strip and work roll, work-roll temperature, the initial thickness of the strip, roll speed, friction coefficient between strip and work roll, and work-roll diameter, respectively. ß Authors 2011 REFERENCES 1 Dieter, G. E. Mechanical metallurgy, 1987 (McGrawHill, New York). 2 Hollander, F. Mathematical models in metallurgical process development. Proceeding of the conference on Royal Garden Hotel, London, 12–13 February 1969, pp. 46–79 (Iron and Steel Institute, London). 3 Harding, R. A. Temperature and structure changes during hot rolling, PhD Thesis, University of Sheffield, UK, 1976. 4 Beynon, J. H. and Sellars, C. M. Modelling microstructure and its effects during multipass hot rolling. ISIJ Int, 1992, 32, 359–367. 5 Serajzadeh, S., Karimi, Taheri, A., and Mucciardi, F. Prediction of temperature distribution in the hot rolling of slabs. Modell. Simul. Mater. Sci. Eng, 2002, 10, 185–203. 6 Karagiozis, A. N. and Lenard, J. G. Temperature distribution in a slab during hot rolling. Trans. J. Eng. Mater. Tech, 1988, 110, 17–21. 7 Sheppard, T. and Wright, D. S. Structural and temperature variations during rolling of aluminium slabs. Metals Technol, 1981, 8, 46–57. 8 Pal, S. K. and Linkens, D. A. Temperature distribution in steel during hot rolling: pseudo-bond graph view. Simul. Modell. Pract. Theory, 2002, 10, 69–85. 9 Laasroui, A. and Jonas, J. J. Prediction of the temperature distribution, flow stress and microstructure during multipass hot rolling of steel plate and strip. ISIJ Int, 1991, 31, 95–l05. 10 Bradley, B. F., Cockett, W. A., and Peel, D. A. Transient temperature behaviour of aluminium during rolling and extrusion. In: Proceedings of the conference on Mathematical models in metallurgical process development, (ISI Publication 123), 1970, pp. 79–90 (Iron and Steel Institute, London). 11 Hand, R. J. Temperature changes during hot plane strain compression testing. Mater. Sci. Technol, 2000, 16, 442–450. 12 Galantucci, L. M. and Tricarico, L. Thermomechanical simulation of a rolling process with an FEM approach. J. Mater. Process. Technol, 1999, 92–93, 494–501. 13 Serajzadeh, S., Taheri, A. K., and Mucciardi, F. Unsteady state work-roll temperature distribution during continuous hot slab rolling. Int. J. Mech. Sci, 2002, 44, 2447–2462. 14 Wang, X. Q. and Yang, A. H. Calculation of thermal stress affecting strip flatness change during run-out table cooling in hot steel strip rolling. J. Mater. Process. Technol, 2008, 207, 130–146. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science

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15 Brown, S. B., Kim, K. H., and Anand, L. An internal variable constitutive model for hot rolling of metals. Int. J. Plast, 1989, 5, 95–130.. 16 RICE, J. R. Continuum mechanics and thermodynamics of plasticity in relation to micro scale deformation mechanisms. In In Constitutive Equations in Plasticity (Ed. A. S. Argon), 1975, pp. 23–77 (MIT Press, Cambridge). 17 W. H. Cubberly), Properties and selection: nonferrous alloys and pure metals. 2, Ninth edition, 1979, p. 777(American Society for Metals, Metals Park, Ohio). 18 Shahani, S., Setayeshi, A. R., Nodamaie, S., Asadi, S. A., and Rezaie, M. A. Prediction of influence parameters on the hot rolling process using finite element method and neural network. J. Mater. Process. Technol, 209, 2009, pp. 1920–1935. 19 Hum, B., Colquhoun, H. W., and Lenard, J. G. Measurements of friction during hot rolling of aluminum strips. J. Mater. Process. Technol, 1996, 60, 331–338. 20 Chun, M. S. and Lenard, J. G. Hot rolling of an aluminum alloy using oil/water emulsions. J. Mater. Process. Technol, 1997, 72, 283–292. 21 Lenard, J. G., Pietrzyk, M., and Cser, L. Mathematical and physical simulation of the properties of hot rolled products, 1999 (Elsevier, Amsterdam). 22 Devadas, C. and Samarasekara, I. V. Heat transfer during hot rolling of steel strip. Ironmaking Steelmaking, 1986, 13, 311–321.


APPENDIX NOTATION Ac cs cr hc ks kr qfric R T Tr Ts vr vs cr "_ r s

contact area between roll and strip (m2) specific heat of strip (J/kg/ C) specific heat of work roll (J/kg/ C) heat-transfer coefficient of the interface between the strip and the work roll (W/m2 K) thermal conductivity of strip (W/m/ C) thermal conductivity of work roll (W/m/ C) heat generation resulting from friction roll radius (m) temperature ( C or K) work-roll surface temperature ( C or K) strip surface temperature ( C or K) work roll speed (m/s) strip speed (m/s) coefficient of friction between strip and work roll critical shear stress (MPa) effective strain rate (s1) efficiency of conversion of deformation energy to heat effective flow stress (MPa) work-roll density ((kg/m3) strip density (kg/m3)