Issue
Metall. Res. Technol.
Volume 119, Number 1, 2022
Article Number 103
Number of page(s) 17
DOI https://doi.org/10.1051/metal/2021098
Published online 20 December 2021

© EDP Sciences, 2021

1 Introduction

The roll gap shape is the main control index of the strip rolling process and can be used to control strip thickness and flatness. Roll profile electromagnetic control technology (RPECT) is a new roll gap shape control technology with multistage roll profile regulation and flexible roll crown control. In RPECT, an electromagnetic stick (ES) installed in the roll’s inner hole is selected as the basic unit element and then induction heated in the regulation process. Through the thermal expansion of the ES and the internal constraint of the roll, the contact force between the ES and the roll can be generated. The contact force and the internal heat of the roll form the thermal force bulging of the electromagnetic control roll (ECR). Due to the thermal-force bulging characteristic, the electromagnetic control roll profile has certain temperature sensitivity, so it is suitable for cold rolling with weak heat exchange between strip and roll. Considering that the technology has flexible roll profile control ability, it can be loaded on the working roll of the cold rolling mill. Regarding RPECT, Liu et al. [1,2] established an electromagnetic-thermal-structure coupled model to analyse the problem of roll profile control in RPECT and proposed a roll profile test technology to conduct experimental research on RPECT. Feng et al. [3] analysed the ability of a large-size sleeved backup roll to control its roll profile. Yang et al. [4] studied the electromagnetic control characteristics of RPECT within the ES limit control range. The above research provides support for the development of RPECT, proving that RPECT has a certain roll profile control ability. However, the position of the ES in the roll cannot be changed during the RPECT process. When the flatness defect position is not entirely within the influence area of the electromagnetic control roll profile, changing the electromagnetic parameter values of different ES induction coils can change the position of the influence area, but the position adjustment ability is limited. Therefore, it is necessary to consider using external control methods to change the influence area of the electromagnetic control roll profile to address the problem of flatness defects.

According to Liu et al. [5], roll profiles can be changed by using roll surface cooling for ECRs. Therefore, the liquid cooling method can be considered an external method of adjusting the roll profile in RPECT. The liquid surface cooling method, which is based on convective heat transfer, has been widely studied and applied. Horský et al. [6] studied the effect of spray cooling intensity on the final material structure in the hot rolling process of long products. Wang et al. [7] developed a two-dimensional finite difference program based on an inverse heat conduction model that calculated the local surface convective heat transfer coefficients and analysed the effect of the cooling water jet flow rate on the surface temperature. Labergue et al. [8] investigated the cooling of hot surfaces in full cone sprays and compared the results with the cooling effects of liquid jets. Smakulski et al. [9] analysed the heat removal capabilities of direct cooling technology by using porous media, microchannel heat sinks and spray cooling. Saboonchi et al. [10] studied the effect of water spray geometric parameters on the working roll temperature. The above research focused on the heat transfer effect of overall cooling for different objects. However, there have been few studies on the impact of zoning and subsection cooling. In the field of RPECT, the effects of zoning and subsection cooling have not been studied.

To improve the flexibility of RPECT, this paper proposes using external segmented cooling to control the heat axial transfer in ECRs and the roll profile. Given the importance of the roll profile segmentation control strategy on the roll profile status, this paper compared and studied the bulging ability, crown control ability, ECR temperature field variation and adaptability of different ES structures, as well as discussed the advantages and disadvantages of different roll profile segmentation control strategies.

2 Principle of the external adjustment method of RPECT roll profiles and model establishment

2.1 Principle of the external adjustment method of RPECT roll profiles

The RPECT roll profile can be used as a kind of displacement roll profile to participate in the roll gap shape control process. In the flatness control process, the roll profile of ECR can be changed to another roll profile according to the demand of the strip control. The RPECT roll profile consists of a force contribution roll profile and a thermal contribution roll profile. The thermal contribution roll profile exists because heat from the ES after electromagnetic induction heating can be transferred to the ECR, causing the ECR to thermally bulge. The force contribution roll profile is due to the contact area of the ES being heated, causing the ECR to bulge. In the general control, the rapid variation of the roll profile relies on the electromagnetic parameters and the control temperature of the ES, and the buling amount of 160 µm can be realized in 300 s. If the demands for the regulation time and the bulging amount increase, the magnetic parameter value and the ES control temperature value are often increased. However, the heat source is located in the induction heating zone of the ES, the response time of the force contribution roll profile is less than that of the thermal contribution roll profile in the control process. Therefore, on the basis of weakening the thermal contribution roll profile, the control mode based on force contribution roll profile is conducive to shorten the time to reach the target roll profile and improve the stability of the target roll profile. According to the results in the literature [5], the surface cooling strategy mainly affects the thermal contribution roll profile while having little effect on the force contribution roll profile. This paper proposes an external adjustment method for RPECT roll profiles, which can improve the flexibility of RPECT. In this control method, the temperature field of different ECR segments can be changed by adjusting the external cooling intensities of different segments and changing the thermal contribution roll profile. Figure 1 shows a diagrammatic sketch of the external adjustment method of the RPECT roll profile.

The segmented electromagnetic stick can be thought of as a basic component for adjusting the RPECT roll profile. The external cooling area of the segmented electromagnetic stick is divided into three areas: cooling area I, cooling area II and cooling area III. Cooling area I and cooling area III are symmetrical and equally spaced on both sides of cooling area II. According to different control strategies, changing the cooling intensities of different cooling areas can change the temperature field of the ECR to achieve the adjustment of the comprehensive roll profile.

thumbnail Fig. 1

Diagrammatic sketch of the division method of cooling areas of the surface of the ECR.

2.2 Model establishment

The RPECT process involves the simulation of the electromagnetic field, temperature field and stress field, which is an electromagnetic-thermal-structural coupling problem. Therefore, the electromagnetic-thermal-structure module of MARC software must be used to analyse this process. Due to the large simulation requirements of the three-dimensional multifield coupling model, the RPECT FE model needs to be simplified. The ECR, ES and induction coils are all revolving bodies with the same revolving axes, and the model can be simplified as an axisymmetric model to reduce the calculation time. In the process of roll cooling, the heat transferred to the rolls is decreased with time, and the distribution of circumferential cooling zone is periodic. Cerni et al. [11] converts convective cooling conditions along the circumference into a linear heat source. Troeder et al. [12] uses the same assumption to analyse the transient stress of hot rolled shell. Therefore, this FE model assumes that the external cooling is a linear heat source, and simplifies the model to an axisymmetric model, which is convenient for simulation. Based on the principles of the external adjustment method for the RPECT roll profile, variations in the ECR profile under different external adjustment methods can be simulated by changing the cooling intensity of the roll surface and the section lengths of the same cooling intensities. The configurations of the ES structure and cooling areas are the same as those in Figure 1. The induction zone temperature control mode is used as the control mode. In this mode, the temperature of the induction heating zone can be controlled by dynamically adjusting the induction current to ensure that the temperature of the induction zone is essentially stable at the target temperature. Table 1 shows the parameters of the FE model.

Based on the above parameters, the RPECT electromagnetic-thermal-structural axisymmetric model is established in Figure 2. To ensure the simulation accuracy of the electromagnetic field and temperature field, the model includes not only the ECR, ES and induction coil, but also air units. The outermost cells of the air units are set as potential zero and magnetic potential zero. Contact heat transfer occurs between the ECR and the ES. According to Yovanovich et al. [13], the contact heat transfer ability is related to the contact stress and contact face. Because hot charging is used to assemble the ECR and the ES, prestress exists in the contact area of RPECT. Therefore, the ECR and ES must be in good contact before regulation. According to the literature [5], the heat transfer coefficient is a constant with a value of 3 kW/(m2 · K). The heat transfer between the RPECT element and air is comprehensive heat transfer include convective heat transfer and radiative heat transfer, and the coefficient is 0.03 kW/(m2 · K) [14]. The initial temperature of the model is 30 °C.

Table 1

Parameters of the FE model.

thumbnail Fig. 2

RPECT electromagnetic-thermal-structural axisymmetric model with segmented cooling.

2.3 Model validation

To verify the accuracy of this model, the roll profile electromagnetic control experiment platform is used as shown in Figure 3a. The platform includes: a power supply, an ECR, a temperature detector, an acquisition system, acquisition channels and a test system. According to the data of the acquisition channels, the radial bulging of the roll can be calculated by Formula (1).(1) (2)where θ is the angle of a foil gauge, R is the original radius of the roll, l is the original length of a foil gauge, ԑc is the strain value of a strain gauge, Δθ is the angle variation after bulging, ΔR is the radius variation after bulging.

In RPECT, the bulging of roll is circumferential uniform bulging. The Δθ is zero, ΔR is equal to ԑrR. ԑr is the radial strain value of the roll. Therefore, Formula (1) and (2) can be combined into Formula (3).(3)

To sum up, Formula (3) can be used to calculated the radial bulging. The experimental conditions were as follows: the structure parameters of ECR and ES are the same as Table 1, the initial temperature of the model is 17 °C, the heating model of ES is continue heating, and the cooling mode of roll surface is air cooling with the cooling intensity is 0.03 kW/(m2 · K). The control current frequency is 400 Hz, and the variation of the current is shown in Figure 3b.

Figure 4 is the temperature variation of ES induction area and the roll crown variation of ECR. The results show that the maximum temperature difference between experiments and simulations is less than 8.4 °C, and the roll crown difference is less than 2.2 µm. The experimental and simulation error of ES temperature is 5.33%, and the experimental and simulation error of roll crown is 6.36%. The experimental results and the simulation results show the FE model has a high accuracy, and can be used to analyse the control ability of RPECT.

thumbnail Fig. 3

Roll profile electromagnetic control experiment platform and the variation of the current. (a) roll profile electromagnetic control experiment platform and (b) the variation of the current.

thumbnail Fig. 4

Temperature variation of ES induction area and the roll crown variation of ECR with time. (a) temperature variation, and (b) roll crown variation.

3 Results and discussion

3.1 Analysis of the symmetrical segmented cooling strategy

To increase and decrease the roll profile control ability of RPECT, a symmetrical segmented cooling strategy is proposed. In this strategy, cooling areas I and III are considered the edge cooling areas, while cooling area II is considered the middle cooling area. The cooling intensity of the edge cooling area and middle cooling area can be adjusted to change the roll profile control ability of RPECT. The cooling intensities of cooling areas I and III are equal, with the heat transfer coefficient of HTC-E, while the heat transfer coefficient of the middle cooling area is HTC-M. The length of the cooling area is 100 mm, and the cooling intensity ranges from 0.03 kW/(m2 · K) to 3 kW/(m2 · K). Based on the parameter differences of the cooling areas, the symmetrical segmented cooling strategy can be divided into Strategy I, which keeps HTC-M constant while changing HTC-E, and Strategy II, which changes HTC-M while keeping HTC-E constant.

3.1.1 The bulging ability and the variation of the roll crown

To analyse the effects of the symmetrical segmented cooling characteristics, the bulging amount of the edge cooling area is defined as C1, the bulging amount in the middle cooling area is defined as C2, the bulging amount of the roll edge is defined as C3, and the roll crown is defined as C, as shown in Figure 1. The roll crown is the difference between C2 and C3.

Figure 5 shows the variations of C1, C2 and C for different HTC-M values when HTC-E is changed. When HTC-M is kept constant while HTC-E is increased, C1 and C2 gradually decrease while C gradually increases. The reason for this is that increasing HTC-E can improve heat exchange at the edge of the ECR and reduce bulging at the edge of the ECR. Due to the whole temperature field of the ECR, temperature variations at the edge of the ECR affect the temperature variations in the middle of the ECR. Therefore, changing HTC-E can affect the values of C1 and C2. As HTC-M is increased from 0.03 kW/(m2 · K) to 3 kW/(m2 · K), the variations of C1 with increasing HTC-E are 6.17 µm, 6.01 µm, 5.8 µm, 5.57 µm; the variations of C2 with increasing HTC-E are 3.02 µm, 2.25 µm, 1.69 µm, 1.43 µm; and the variations of C with increasing HTC-E are 0.06 µm, 1.22 µm, 1.74 µm, 1.99 µm. For different HTC-Ms, the effects of increasing HTC-E are the same for C1 and C2. When the cooling intensity of the middle cooling area is high, the effect of increasing HTC-E on C1 and C2 is weakened. The reason for this is that the ES is the thermal-force bulging driving device of RPECT, and its installation position is the same as that of the middle cooling area. When the cooling intensity of the middle cooling area is increased, the heat inside the ECR is reduced, and thus the effect of increasing HTC-E on the roll profile of RPECT is reduced. Therefore, strategy I can improve the roll crown of the ECR, but the variation in the ECR roll crown is small.

Figure 6 shows the variations in C1, C2 and C for different HTC-E values while HTC-M is changed. When HTC-E is kept while HTC-M is increased, then C1, C2 and C decrease. The reason for this is that the installation position of the ES is the same as that of the middle cooling area, and thus increasing HTC-M can increase the radial heat transfer ability, decreasing the whole temperature of the ECR. This phenomenon leads to a decrease in the overall bulging amount of the ECR. As HTC-E are increased from 0.03 kW/(m2 · K) to 3 kW/(m2 · K), the variations of C1 with increasing HTC-M are 1.64 µm, 2.01 µm, 2.03 µm, 2.47 µm; the variations of C2 with increasing HTC-M are 13.07 µm, 11.87 µm, 11.69 µm, 11.48 µm; and the variations of C with increasing HTC-M are 13.59 µm, 12.48 µm, 11.96 µm, 11.66 µm. For different HTC-E, the effects of increasing HTC-M are the same for C1 and C2, and the trend can be described as follows: as HTC-E increases, the variation decreases. The impact on C1 is less than on C2. As a result of strategy II, the roll crown can be decreased with increasing HTC-M. The difference between the cases is that as HTC-M increases, the bulging amount of the ECR edge decreases, while the bulging amount of the ECR middle remains relatively constant. Because the variation of the bulging amount at the ECR edge is smaller than that in the ECR middle, the effects of roll crown weakening are nearly identical under different cases of strategy II. Therefore, strategy II has the effect of reducing the roll crown of the ECR. A comprehensive comparison of the results in Figure 5 and Figure 6 shows that the maximum effect of roll crown weakening can reach 13.59 µm, while the maximum effect of roll crown enhancement is 2 µm. The roll crown weakening ability is stronger than the roll crown enhancement under different cooling strategies.

thumbnail Fig. 5

Variations in C1, C2 and C under Strategy I. (a) C1, (b) C2 and (c) C.

thumbnail Fig. 6

Variations of C1, C2 and C under Strategy II. (a) C1, (b) C2 and (c) C.

3.1.2 The ECR temperature gradient

To further evaluate the state of the thermal contribution roll profile under Strategies I and II, P1, P2 and P3 are selected as marked points, as shown in Figure 7. P1 is the midpoint of the roll surface; P2 is the midpoint of the radial line in the middle of the ECR, 45 mm away from P1; and P3 is at the edge of the ES effect area, on the ring surface of the ECR with the same radius as P2. Based on the above points, radial and axial temperature gradients can be determined.

The radial temperature gradient is the temperature gradient from P2 to P1, denoted as GradTr. The axial temperature gradient is the temperature gradient from P2 to P3, denoted as GradTa. The calculation formulas are as follows:(4) (5)where TP1 is the temperature of P1, TP2 is the temperature of P2, TP3 is the temperature of P3, and lES is the length of the ES.

Figure 8 shows the variations in the radial and axial temperature gradients under Strategy I. In Figure 8, when HTC-M is increased from 0.03 kW/(m2 · K) to 3 kW/(m2 · K), the variations in GradTr with increasing HTC-E are −0.0032 °C/mm, 0.0132 °C/mm, −0.008 °C/mm, and −0.0095 °C/mm; and the variations in GradTa with increasing HTC-E are 0.0345 °C/mm, 0.0363 °C/mm, 0.0362 °C/mm, and 0.0359 °C/mm. Based on the contact relationship between the ES and the ECR, the inner section of the ECR can be divided in two sections: the roll section with the ES and the roll section without the ES. As HTC-E increases, the temperature of the roll section without the ES decreases. Marking point P3 is located at the intersection of the roll section with the ES and the roll section without the ES. Under Strategy I, the temperature of P3 can be decreased, leading to an increase in GradTa. Marking points P1 and P2 are located in the middle of the roll section with the ES. Although changing HTC-E can affect the temperature of this section, the effect is not obvious, and the temperature variations of P1 and P2 are small. Therefore, GradTr is essentially constant.

Figure 9 shows the variations in the radial and axial temperature gradients under Strategy II. The results show that with increasing HTC-M, GradTr increases and GradTa decreases. In Figure 9, when HTC-E is increased from 0.03 kW/(m2 · K) to 3 kW/(m2 · K), the variations in GradTr with increasing HTC-M are 0.2410 °C/mm, 0.2272 °C/mm, 0.2219 °C/mm, and 0.2183 °C/mm; and the variations in GradTa with increasing HTC-M are −0.0478 °C/mm, −0.0478 °C/mm, −0.0474 °C/mm, and −0.0469 °C/mm. Therefore, when HTC-E is different, the difference in GradTa is small, and changing HTC-M can affect the temperature of the roll section with the ES, increasing the temperature difference between P1 and P2. The reason for this is that the temperature increase in the roll section without the ES is due to heat transfer from the roll section with the ES, and the cooling effect of the middle cooling area can affect the temperature distribution in the roll section without the ES.

The above results show that in the symmetrical segmented cooling strategy, changing the cooling intensity of different cooling areas symmetrically can enhance or weaken the ECR roll crown. The reason for the crown variation is that the use of symmetrical segmented cooling can change the heat contribution roll profile, which leads to directional changes in the comprehensive roll profile.

thumbnail Fig. 7

Schematic diagram of the temperature gradient marking points.

thumbnail Fig. 8

Variations of the radial and axial temperature gradients under Strategy I. (a) GradTr and (b) GradTa.

thumbnail Fig. 9

Variations of the radial and axial temperature gradients under Strategy II. (a) GradTr and (b) GradTa.

3.2 Analysis of symmetrical segmented cooling characteristics with variable coefficients

To analyse the effect of the cooling area length, this section analyses the roll profile control ability under different cooling area length ratios. A component cooling ratio coefficient that can quantify the configuration of symmetrical segmented cooling is proposed. The coefficient is defined as the ratio of the length of cooling area II to the length of the ES; the formula is shown in Formula (6).(6)where η is the component cooling ratio coefficient, lCII is the length of cooling area II, and lES is the length of the ES.

The basic length of the ES is 150 mm, and the basic cooling intensity is 0.03 kW/(m2 · K). The cooling intensity ranges from 0.03 kW/(m2 · K) to 3 kW/(m2 · K).

3.2.1 The bulging ability and the variation of roll crown

Figure 10 shows the variations in C1, C2 and C under Strategy I for different η. When comparing the results to those in Figure 5, changing η does not affect the variation trend of C1 and C2, but it can affect the variation of C. With increasing η, the variations of C1 are −8.27 µm, −6.01 µm, and −5.28 µm; the variations of C2 are −7.39 µm, −3.02 µm, and −1.21 µm; and the variations of C are −4.14 µm, 0.06 µm, and 2.34 µm. When η is increased, the effect of increasing HTC-E on the control ability of C1 and C2 is weakened. The difference in the weakening effect is that the effect on C1 is weakened as a whole, whereas the effect on C2 is decreased slowly when the cooling intensity is 0.03 kW/(m2 · K). Due to the difference between C1 and C2, C can be changed from a decreasing trend to an increasing trend with increasing HTC-E. The reason for this is that when the value of η is small, the edge cooling areas have a greater effect on the temperature field in the middle of the ECR and can increase the variations of C2, resulting in the transformation from crown enhancement to crown weakening. When the value of η is large, the temperature field in the middle of the ECR is less likely to be affected by the edge cooling areas. With increasing η, the variation in the C2 value decreases, and the value of C1 decreases, thus ensuring that the crown is enhanced. Therefore, when configuring the symmetrical segmented cooling strategy in RPECT for crown enhancement, it is necessary to take into account the length distribution of the cooling areas. If η is too small, it is difficult to achieve the effect of roll crown enhancement, but it is easy to produce the effect of crown weakening.

Figure 11 shows the variations of C1, C2 and C under Strategy II for different η. When the value of η is changed, the variation trends of C1, C2 and C are the same as those in Figure 6. Increasing η decreases the control ability of C1 while increasing the effects of changing HTC-M on C2 and C. Therefore, increasing η can increase the crown weakening ability.

thumbnail Fig. 10

Variations in the values of C1, C2 and C under Strategy I for different η. (a) C1, (b) C2, and (c) C.

thumbnail Fig. 11

Variations in the values of C1, C2 and C under Strategy II for different η. (a) C1, (b) C2, and (c) C.

3.2.2 The ECR temperature gradient

Figure 12 shows the variations in GradTr and GradTa under Strategy I for different η. The results show that for different η, the trends of GradTr and GradTa with increasing HTC-E do not change. With increasing η, the variations in GradTr are 0.0484 °C/mm, 0.0132 °C/mm, and 0.0037 °C/mm, and the variations in GradTa are 0.0069 °C/mm, 0.0207 °C/mm, and 0.0187 °C/mm. The increase in η decreases the effect of HTC-E on GradTr, and its effect on GradTa can be described as follows: the effect on GradTa is first increased to a certain value and then decreased. In Figure 12b, the effects of the cases when η=0.67 are larger than those of other cases. In comparison to Figure 12a and Figure 12b, the effect on GradTr is stronger than on GradTa.

Figure 13 shows the variations in GradTr and GradTa under Strategy II for different η. The results show that under different η, the trends of GradTr and GradTa with increasing HTC-M do not change. Changing η has little effect on GradTr and GradTa.

thumbnail Fig. 12

Variations in the radial and axial temperature gradients under Strategy I for different η. (a) GradTr and (b) GradTa.

thumbnail Fig. 13

Variations in the radial and axial temperature gradients under Strategy II for different η. (a) GradTr and (b) GradTa.

3.3 Analysis of the asymmetrical segmented cooling characteristics

RPECT not only realizes the predefined roll profile but also switches among several roll profile states. This behaviour requires the ECR to be able to control the crown size and position. The symmetrical segmented cooling strategy can control crown size but cannot change the position of the maximum bulging point. Therefore, an asymmetric segmented cooling strategy is proposed. In this strategy, cooling areas I, II and III use different cooling intensities to adjust the maximum bulging amount. Table 2 shows examples of asymmetric segmented cooling strategies that are proposed to analyse the control ability. Cases A1∼A5 use a cooling strategy that changes the cooling intensity of one side cooling area. Cases A6∼A10 use a cooling strategy that changes the cooling intensities of one side cooling area as well as the middle cooling area.

Table 2

Cooling intensity configuration scheme of the asymmetric segmented cooling strategy.

3.3.1 The effects of single side cooling and edge and middle cooling

Figure 14 shows the roll profile at 300 s under Cases A1∼A10. Changing HTC-I can change the roll profile of the ECR and decrease the radial bulging of the corresponding area. For the transverse distribution of the bulging amount, the bulging amount of the ECR can be decreased with increasing HTC-I, and the maximum bulging position gradually moves away from the centre of the ECR. When the cooling intensity is increased from 0.03 kW/(m2 · K) to 3 kW/(m2 · K), the maximum bulging value decreases by 1.7 µm, and the maximum bulging position shifts by 5 mm. The case where HTC-I is 3 kW/(m2 · K) has the most noticeable effect on crown movement. In Cases A6∼A10, the effect of the segmented cooling strategy is mainly to reduce the ECR bulging amount. Although it can cause asymmetric bulging on both sides of the ECR, directional movement of the maximum bulging amount is difficult to achieve. Therefore, to asymmetrically control the roll profile, changing the transverse position of the maximum bulging point necessitates the use of cooling strategies in Cases A1∼A5.

thumbnail Fig. 14

The roll profile at 300 s under Cases A1∼A10. (a) Cases A1∼A5, and (b) Cases A6∼A10.

3.3.2 The effect of single side cooling under different η

To analyse the effect of η on the asymmetric segmented cooling strategy, different values for η and different cooling parameters are introduced into the FE model, and the results are shown in Figure 15. The basic cooling intensity is 0.03 kW/(m2 · K), and HTC-I ranges from 0.03 kW/(m2 · K) to 3 kW/(m2 · K). The result shows that increasing HTC-I causes the maximum bulging point to move away from the centre of the ECR and decreases the maximum bulging value.

Furthermore, increasing η can reduce the crown movement ability and the maximum bulging ability in the asymmetric segmented cooling strategy. When η is increased from 0.5 to 1, the maximum amount that the maximum bulging point shifts is 9.04 mm, 6.83 mm, and 3.98 mm, and the maximum bulging value decreases by 4.10 µm, 2.07 µm, and 0.55 µm. Therefore, in the asymmetric segmented cooling strategy, the maximum bulging point moves and maximum bulging value decreases simultaneously. By adjusting the value of η, the relationship between the maximum bulging position movement and the maximum bulging value can be coordinated.

To further analyse the roll profile control ability under different values for η and different basic cooling intensities, the maximum bulging point movement and the maximum bulging value are extracted, as shown in Figures 16 and 17. The results in Figure 16 show that by increasing the basic cooling intensity HTC-B, the shifting amount of the maximum bulging point can be changed from positive to negative. When η is increased, the movement control range of the maximum bulging point can be reduced.

The results in Figure 17 show that increasing HTC-I reduces the maximum bulging value of the ECR. Increasing the basic cooling intensity can also reduce the maximum bulging value. However, in Figure 17c , when η exceeds a certain value, the effects of HTC-I on the maximum bulging value can be ignored.

thumbnail Fig. 15

Variations in the maximum bulging amount and the position of the maximum bulging point with increasing HTC-I. (a) The maximum shift of the maximum bulging point and (b) The maximum bulging amount.

thumbnail Fig. 16

The shifting amount of the maximum bulging point with increasing HTC-I under different HTC-B. (a) η = 0.5, (b) η = 0.67, and (c) η = 1.

thumbnail Fig. 17

The maximum bulging amount t with increasing HTC-I under different HTC-B. (a) η = 0.5, (b) η = 0.67, and (c) η = 1.

3.4 Analysis of the sectional cooling adaptability of different ES structures

To further explore the roll profile control characteristics of different ES structures, three structure types and a 1000 mm long ECR are selected to analyse the structural adaptability of the segmented cooling strategies. The diameter of the ES is 100 mm, the length of the induction heating zone is 25 mm, the length of the middle contact zone is 50 mm, and the length of the edge contact zone is 25 mm. The ES structures are shown in Figure 18. Because the ECR roll length is much longer than the length of the ES, the end of the ECR exceeds the influence area of a single ES; thus, the bulging amount at the end of the roll is small, and the roll crown at this time can be considered the maximum bulging amount at the centre of the ECR. HTC-B is set to 0.03 kW/(m2 · K), and the variable cooling intensities are 0.03 kW/(m2 · K), 1 kW/(m2 · K) and 3 kW/(m2 · K).

Figure 19 shows the variations in C2, GradTr and GradTa when HTC-M is equal to HTC-B and HTC-E changes. Figure 19a shows that the ES structure has little influence on C2 as the cooling intensity changes, but it can change the overall bulging value. The maximum bulging value decreases as the length of the ES decreases. When structure I is used, C2 can be reduced, but the reduction is small. Figure 19b and c shows that structure II and structure III have no effect on the variation laws of GradTr and GradTa, but the longer the length of the ES, the larger the temperature gradient. When structure I is used, increasing HTC-E leads to a significant increase in GradTr, which also corresponds to a decrease in C2. Comprehensive analysis of the results reveals a considerable difference between the change law of structure I and that of structures II and III. The reason for this is that structure I has a shorter length than structures II and III, and the internal temperature field of the ECR is greatly affected by the edge cooling areas. When HTC-E is increased, the middle area of the ECR in structure I can also be affected, resulting in a decline in the roll profile control ability.

Figure 20 shows the variations in C2, GradTr and GradTa when HTC-E is equal to HTC-B and HTC-M changes. The results show that structural changes in the ES have little effect on C2, GradTr and GradTa. When the length of the ES increases, the control values of the parameters decrease, but they all follow the same variation law.

thumbnail Fig. 18

Schematic diagrams of the ES structures.

thumbnail Fig. 19

Variations in the ECR status under Strategy I. (a) C2, (b) GradTr, and (c) GradTa.

thumbnail Fig. 20

Variations in the ECR status under Strategy II. (a) C2, (b) GradTr, and (c) GradTa.

4 Conclusion

  • Symmetrically changing the cooling intensities of different cooling areas can adjust the roll profile of the ECR. The segmented cooling strategy that changes the cooling intensities of cooling areas I and III can increase the roll crown of the ECR. The segmented cooling strategy that changes the cooling intensity of cooling area II can decrease the roll crown of the ECR. The crown enhancement ability is weaker than the convexity weakening ability.

  • Asymmetrically changing the cooling intensities of different cooling areas can shift the position of the maximum bulging point. Two movement strategies are proposed in this paper. The movement strategy with a single cooling area has a greater impact than that of the movement strategy with the edge and middle cooling areas and can be used for roll crown shifting.

  • The component cooling ratio coefficient is proposed as an index to evaluate the segmented cooling strategy. Improving the coefficient impacts the different segmented cooling strategies, which needs to be considered during the segmented cooling process.

  • Segmented regulation characteristics exist in different multistage ES structures. Only when the length of the ES is small does the control law reverse, and the effect of this variation is relatively small.

Credit author statement

Tingsong Yang: Conceptualization, Methodology, Writing- Reviewing and Editing. Yingwei Wang: Model analysis, Writing. Haijun Wang: Experiment, Methodology. Yang Hai: Experiment. Fengshan Du: Funding acquisition.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No. U1560206) and National Natural Science Foundation of China (Grant No. 51374184).

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Cite this article as: Tingsong Yang, Yingwei Wang, Haijun Wang, Yang Hai, Fengshan Du, Research on an external adjustment method for RPECT roll profiles based on the segmented cooling principle, Metall. Res. Technol. 119, 103 (2022)

All Tables

Table 1

Parameters of the FE model.

Table 2

Cooling intensity configuration scheme of the asymmetric segmented cooling strategy.

All Figures

thumbnail Fig. 1

Diagrammatic sketch of the division method of cooling areas of the surface of the ECR.

In the text
thumbnail Fig. 2

RPECT electromagnetic-thermal-structural axisymmetric model with segmented cooling.

In the text
thumbnail Fig. 3

Roll profile electromagnetic control experiment platform and the variation of the current. (a) roll profile electromagnetic control experiment platform and (b) the variation of the current.

In the text
thumbnail Fig. 4

Temperature variation of ES induction area and the roll crown variation of ECR with time. (a) temperature variation, and (b) roll crown variation.

In the text
thumbnail Fig. 5

Variations in C1, C2 and C under Strategy I. (a) C1, (b) C2 and (c) C.

In the text
thumbnail Fig. 6

Variations of C1, C2 and C under Strategy II. (a) C1, (b) C2 and (c) C.

In the text
thumbnail Fig. 7

Schematic diagram of the temperature gradient marking points.

In the text
thumbnail Fig. 8

Variations of the radial and axial temperature gradients under Strategy I. (a) GradTr and (b) GradTa.

In the text
thumbnail Fig. 9

Variations of the radial and axial temperature gradients under Strategy II. (a) GradTr and (b) GradTa.

In the text
thumbnail Fig. 10

Variations in the values of C1, C2 and C under Strategy I for different η. (a) C1, (b) C2, and (c) C.

In the text
thumbnail Fig. 11

Variations in the values of C1, C2 and C under Strategy II for different η. (a) C1, (b) C2, and (c) C.

In the text
thumbnail Fig. 12

Variations in the radial and axial temperature gradients under Strategy I for different η. (a) GradTr and (b) GradTa.

In the text
thumbnail Fig. 13

Variations in the radial and axial temperature gradients under Strategy II for different η. (a) GradTr and (b) GradTa.

In the text
thumbnail Fig. 14

The roll profile at 300 s under Cases A1∼A10. (a) Cases A1∼A5, and (b) Cases A6∼A10.

In the text
thumbnail Fig. 15

Variations in the maximum bulging amount and the position of the maximum bulging point with increasing HTC-I. (a) The maximum shift of the maximum bulging point and (b) The maximum bulging amount.

In the text
thumbnail Fig. 16

The shifting amount of the maximum bulging point with increasing HTC-I under different HTC-B. (a) η = 0.5, (b) η = 0.67, and (c) η = 1.

In the text
thumbnail Fig. 17

The maximum bulging amount t with increasing HTC-I under different HTC-B. (a) η = 0.5, (b) η = 0.67, and (c) η = 1.

In the text
thumbnail Fig. 18

Schematic diagrams of the ES structures.

In the text
thumbnail Fig. 19

Variations in the ECR status under Strategy I. (a) C2, (b) GradTr, and (c) GradTa.

In the text
thumbnail Fig. 20

Variations in the ECR status under Strategy II. (a) C2, (b) GradTr, and (c) GradTa.

In the text

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