Electronic temperature control roll (ETCR) technology is a new roll profile control technology based on the principle of the semiconductor cooling and heating effect. The thermoelectric cooler (TEC) is the core component for controlling roll profiles in this technology. The TEC layout and the roll structure can affect the bulging ability of the roll, the bulging uniformity and the uniformity of the roll temperature field. To research the influence of the TEC layout and the roll structure on these factors, a circumferential finite element model of ETCR is established by the finite element software MSC.MARC, and is verified on the experimental platform of ETCR. After analysis, it was found that increasing the roll diameter or decreasing the diameter of the roll inner hole can increase the bulging ability of the roll, improve the bulging uniformity and weaken the temperature ratchet. Increasing the temperature of TEC or decreasing the single piece influence angle can increase the bulging ability of the roll and improve the temperature ratchet, while the effect of changing the single piece influence angle on the bulging uniformity is larger than that of the temperature of TEC. In view of the difficulty of circumferential uniform bulging when the single piece influence angle is large, a scheme of adding a metal layer of high thermal conductivity material in the roll inner hole is proposed. The results showed that the copper layer has little influence on the bulging ability of the roll and can reduce the circumferential bulging difference.
Research Article
Analysis of the circumferential bulging capacity and uniformity under different TEC layout and the roll structure in the ETCR
https://doi.org/10.21203/rs.3.rs-1537486/v1
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Electronic temperature control roll technology
thermoelectric cooler
TEC layout
roll structure
temperature ratchet
The roll profile is an active factor that changes the load-bearing roll gap shapes in the strip rolling process, which further controls the strip flatness. The roll profile control includes the design of the grinding roll profile and the dynamic control of the roll profile. The design of the grinding roll profile can achieve different control functions by designing a specific roll profile curve. Lu et al [1]. designed a third-order CVC roll profile to reduce the axial force of the working roll. Li et al [2]. proposed a design method of a fourth-order CVC roll profile to improve the ability of the mill to control the strip flatness. Cao et al [3]. proposed a varying contact-length backup roll (VCR) to extend the crown control domain of the roll gap shape and improve the lateral stiffness of the mill. Wang et al [4]. proposed an edge variable crown (EVC) roll to control the edge drop in the rolling process. However, the grinding roll profile curve has difficulty changing the roll profile without reprocessing. Furthermore, the design of the grinding roll profile is also a difficult point in the development of new curves. To solve these problems, dynamic control of the roll profile is proposed based on a force or heat source. Masui et al [5]. proposed a variable crown (VC) roll, which can improve the roll profile by adjusting the oil pressure in the hydraulic chamber of the roll. Zhang et al [6]. studied the shape control capability of a dynamic shape roll (DSR) based on hydraulic cylinder control. The results showed that the shape control range of DSR rolling mills was significantly improved compared with that of ordinary rolling mills. However, the hydraulic pressure bulging ability can be affected by the sealing performance of the hydraulic device, and it is difficult to apply it to heavy-duty conditions for a long time. Sumitomo Metal Industries proposed a thermally bulging roll based on electric-heating rods, which can control the roll profile by heating the roll inner wall [7]. It is still in the patent stage. Liu et al. proposed an electromagnetic control roll based on the principle of roll profile electromagnetic control technology [8]. The results showed that the bulging amount of the roll is approximately dozens of microns. However, the rolls lack the necessary cooling devices in the Sumitomo Metal Industries’ and Liu’s technologies. The axial temperature of the roll and the stability of the roll profile are not easy to control. Therefore, this paper proposes an electronic temperature control roll (ETCR) based on the principle of the semiconductor cooling and heating effect. A thermoelectric cooler (TEC) can achieve cooling at one end and heating at the other end after the TEC is powered on. Multigroup TEC forms are used on the roll inner wall to produce a multistage controllable electronic temperature control roll profile. Considering the time-domain characteristics of regulation, ETCR can be used to preset the roll profile and dynamically compensate for the worn roll profile.
The roll profile calculation of ETCR involves the calculation of the temperature field. Arif et al. analysed the influence law of an external input thermomechanical load on the loaded thermal roll profile for this kind of problem [9]. According to the external input heat during hot rolling, Zhang et al. proposed a two-dimensional axisymmetric difference model to analyse the transient temperature field of the working roll and solve the corresponding hot roll profile [10]. The model has been compared with the production line and has a good degree of agreement. Park et al. suggested that the factors of increasing the roll crown are heat flux, roll width, and rolling speed in the twin casting rolling process [11]. Benasciutti et al. proposed that periodic heat sources can cause rolls to produce uneven surface thermal distributions and further induce uneven thermal stresses [12]. Jiang et al. proposed a precision online model of a thermal crown, which can consider the influence of external periodic cooling and rolling heat input [13]. Chen et al. established a finite difference model that can be used to calculate the temperature field of rolls online and pointed out that the adjustment range of the thermal crown as a function of the working roll shifting is approximately ± 30 µm [14]. The above studies have carried out detailed studies on the influence of the temperature field on the hot roll profile, but the circumferential boundaries are simplified to axisymmetric conditions to facilitate the solution. Therefore, the studies mainly focused on the axial heat transfer characteristics, and there is little research on circumferential heat transfer. Regarding circumferential heat transfer, Yang et al. analysed the influence of the circumferential slot structure of the electromagnetic stick on the bulging ability and bulging uniformity of RPECT [15]. The results showed that increasing the slot number and size can reduce the bulging value. Hajmohammadi et al. analysed the heat exchange capacity of array fins in a circular channel [16]. The results showed that the heat exchange capacity of a nonuniform fin structure can be increased by 46% compared with that of a traditional channel. Ding et al. analysed the heat dissipation characteristics of vertically oriented three-dimensional (3-D) finned tubes, and the results showed that the Nusselt number of tubes with such fins was 207% higher than that of smooth tubes [17]. The above studies revolve around the circumferential heat transfer capacity of the cylinder, but the involved objects are different from the ETCR. Considering the technical characteristics of ETCR, TEC is distributed on the roll inner wall as the temperature control device, forms different temperature fields and then makes the roll bulge. Therefore, the circumferential temperature difference can also cause the bulging difference.
Given the crucial influence of the ETCR circumferential characteristics on the roll profile control ability, an electronic temperature control model in the circumferential direction of the roll is established and verified on the experimental platform. To analyse the difference in the circumferential regulation of the ETCR, this paper compares and analyses the different aspects of the ETCR: bulging ability, bulging difference, and temperature field distribution. In addition, the influence of roll structure parameters, TEC layout and TEC parameters on the electronic temperature control capability are also discussed, and the improvement methods are analysed.
In the prediction of the ETCR roll profile, the roll can be divided into multiple TEC adjustment sections in the axial direction, and every section needs to be given a thermal boundary of the axisymmetric prediction model. In fact, TEC is often prepared in the form of a sheet rather than a ring. Therefore, the circumferential bulging of a TEC adjustment section is often jointly controlled by a plurality of TECs. Considering that the thermal boundary is not uniform at this time, it is necessary to equivalently simplify this thermal boundary. TEC usually adopts a layout with equal angular intervals in the circumferential direction in a TEC adjustment section. According to this feature, the concepts of single piece influence angle Degs, direct influence angle αs and indirect influence angle βs can be proposed. A schematic diagram of the structure is shown in Fig. 1. The single-piece influence angle Degs is the circumferential angle that a TEC is responsible for when n TECs are installed circumferentially in the roll inner wall. The calculation Formula (1) is as follows,
$${Deg}_{s}=\frac{2\pi }{n}$$
1
The direct influence angle αs is the circumferential angle corresponding to the TEC application area in a Degs. The calculation Formula (2) is as follows:
$${\alpha }_{s}=\text{arcsin}\frac{L}{2R}$$
2
where R is the roll radius and DR is the roll diameter.
The indirect influence angle βs is the circumferential angle corresponding to the no-TEC application area in a Degs. The calculation Formula (3) is as follows.
$${\beta }_{s}=\frac{\pi }{n}-\text{arcsin}\frac{L}{2R}$$
3
Figure 1 Schematic diagram of TEC influence angle
If the TEC control temperature is Tc, the circumferential function of the heat source in the roll inner wall can be obtained according to the periodic distribution characteristics of the TEC layout, as shown in Formula (4).
$$f\left(\theta \right)=\left\{\begin{array}{c}{T}_{c} \frac{2\pi }{n}\left(i-1\right)-k\le \theta \le \frac{2\pi }{n}\left(i-1\right)+k\\ 0 \frac{2\pi }{n}\left(2i-3\right)\le \theta \le \frac{2\pi }{n}\left(i-1\right)-k \cup \frac{2\pi }{n}\left(i-1\right)+k\le \theta \le \frac{2\pi }{n}(2i-1)\end{array}\right.$$
4
Where, \(i=1, 2, 3, \dots , n.\),\(k=arcsin\frac{d}{2R}\), d is the length of the TEC.
According to Formula (4), the period of the periodic problem can be obtained \(T=\frac{2\pi }{n}\),\(a=\frac{j}{\pi }arcsin\frac{d}{2R}\). Ac, ording to the Fourier expansion (5), the Fourier expansion can be performed to obtain Formula (6).
$$f\left(\theta \right)=\left\{\begin{array}{c}1 \left|\theta \right|\le \frac{aT}{2}\\ 0 \left|\theta \right|>\frac{aT}{2}\end{array}\right.$$
5
Where, \({a}_{0}=\frac{2}{T}{\int }_{-\frac{aT}{2}}^{\frac{aT}{2}}f\left(\theta \right)d\theta =2a\), \({a}_{j}=\frac{2}{T}{\int }_{-\frac{aT}{2}}^{\frac{aT}{2}}f\left(\theta \right)\text{cos}\left(\frac{2\pi j\theta }{T}\right)d\theta =\frac{2}{j\pi }\text{s}\text{i}\text{n}\left(ja\pi \right)\).
Therefore, Formula (6) is further simplified, and Formula (7) is obtained.
Where, j = 1, 2, 3, ……
The above formulas have the ability to solve the equivalent heat source. The heat sources of the TEC are periodically fixed on the roll inner wall, so the equivalent process easily ignores the thermal ratchet effect caused by the TEC distribution. If the thermal ratchet is so severe that it produces a corresponding bulging ratchet, it can further affect the bulging effect of the ETCR. Therefore, it is necessary to analyse the influence of the ratchet of ETCR to determine the applicability of the equivalent relationship.
3.1 Circumferential FE model of ETCR establishment
To analyse the influence law of the ratchet of ETCR, a circumferential FE model of ETCR is established, as shown in Fig. 2. Considering that the axial layout of the TEC is usually close-packed, the ETCR model can be simplified to a plane strain model. The model includes a TEC heat source, silicone grease, electronic temperature control roll and air unit. According to the principle of ETCR, the temperature of the TEC control terminal Tc can be adjusted based on the stable temperature of the TEC reference terminal Tr, and the dynamic adjustment of Tc can be realized by adjusting the TEC control current. The stability time for Tc is generally within 60 s, which is far less than the control time of the ETCR. Therefore, it can be assumed that Tc can reach the preset temperature at the initial state in the FE model of the ETCR. Therefore, Tc is applied to one end of the silicone grease in the form of a thermal boundary. The other end of the silicone grease is bonded to the electronic temperature control roll, which can transfer the heat of the TEC control terminal to the electronic temperature control roll. The specific parameters of the FE model are shown in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Roll diameter | 140–420 mm | Hole diameter | 80–120 mm |
| TEC size | 40 mm × 40 mm | TEC thickness | 5 mm |
| TEC control current | 1–5 A | Silicone grease thickness | 2 mm |
| TEC amount | 3–5 | TEC control time | 1200 s |
| TEC control mode | Hot end control | Initial temperature | 23 ℃ |
In the process of solid contact heat transfer, the heat transfer capacity is related to factors such as the pressure between two objects, the microscopic unevenness degree of the contact surface, and the effective contact area. Considering that the TEC and the roll are bonded with silicone grease, silicone grease has a certain viscosity and can effectively fill the area between the TEC and the roll. Therefore, the roll and silicone grease can be considered an adhesive contact. The contact heat transfer coefficient, which is equal to the thermal conductivity of the thermally conductive silicone grease, is 2.4 W/(m2·K). The roll material is C45, the density is 7.85 g/cm3, and the thermal property parameters are shown in Fig. 3. The roll is cooled through air cooling, and its heat transfer coefficient is 5 W/(m2·K).
Figure 3 Thermal property parameters of C45
3.2 FE model verification
An experimental ETCR platform is built and used to measure circumferential bulging in different cases, as shown in Fig. 4. The platform includes a DC power supply, detection channel, ETCR, strain gauge, test system, regulating current device and cooling water tank. In the platform, strain gauges are applied on the ETCR in the manner shown in Fig. 4(b), which can be used to measure the circumferential strain of the roll. Figure 4(c) shows the changes in the strain gauges before and after roll bulging. According to the geometric relationship, the geometric relationship before and after deformation is Formula (8) and Formula (9).
$$R\theta =L$$
8
$$\left(R+\varDelta R\right)\theta =L+\varDelta L$$
9
where R is the roll radius before bulging; ΔR is the radial bulging amount of the roll, and its value is equal to εrR; εr is the radial strain; L is the length of the strain gauge before bulging; ΔL is the stretching amount of the strain gauge, and its value is equal to εcL; εc is the radial strain; and θ is the central angle corresponding to the length of the strain gauge.
Formula (8) and Formula (9) are combined to obtain Formula (10).
$${\epsilon }_{r}={\epsilon }_{c}$$
10
Therefore, the radial bulging amount of the roll can be obtained from the actual measured value of the strain gauge. TECs are assembled on the electronic temperature control ring, as shown in Fig. 4(d), installed in the middle of the roll inner wall. The outer ring surface of the electronic temperature control ring can be equipped with multiple TECs along the circumferential direction, and the inner ring is a cooling water path through which cooling water can flow, as shown in Fig. 4(e). The silicone grease marked with bright colour in Fig. 4(e) is used for bonding between the TEC and the roll inner wall to ensure the heat transferability of the TEC to the roll.
Figure 4 Experimental platform of ETCR and detection principle
Based on the above experimental platform, the roll diameter is φ140 mm, the roll inner wall diameter is 100 mm, and the roll length is 300 mm. TEC adopts 5 pieces in the circumferential direction of the roll, which are spliced on the electronic temperature control ring and installed in the middle of the roll inner wall. The experimental conditions were as follows: the ambient temperature was 20°C, the cooling water temperature was 18°C, the TEC control current was 3 A, and the control time was 1200 s. Figure 5 is a comparison diagram of the experiment and simulation of the maximum radial bulge of the roll. The results show that the maximum bulging amount can increase rapidly in the early stage of regulation and gradually stabilize. In the first 15 minutes, the experimental result is slightly lower than the simulated result, and the difference between the two is within 1.3 µm. After the first 15 minutes, the difference between the experiment and the simulation was reduced to 0.5 µm. The reason for the difference is that the model considers that the TEC is completely attached to the roll inner wall, but in the experiment, there is a certain gap due to the paste, which causes the heat transfer effect of the experiment to be inferior to the simulation effect and causes the difference between the two. However, overall, the two trends are basically the same. The experimental results no longer increase before and after 20 minutes, which can be considered at steady-state conditions. More experiments have been carried out on the platform with similar results as shown in Fig. 4. Therefore, the FE model has a certain simulation accuracy and can be applied to ETCR research.
In addition, according to the results in Fig. 5, at 1200 s, the electronic temperature control roll enters a steady-state, while Tc has already entered a steady-state at this time. Therefore, the variation in Tc with the TEC control current when Tr is 18°C is shown in Fig. 6. The results show that the TEC control currents from 1 A to 5 A correspond to Tc values of 35 ℃, 50 ℃, 78 ℃, 116 ℃, and 152 ℃.
4.1 The diameter of the roll and the diameter of the roll inner hole
To analyse the influence of the TEC layout on the bulging uniformity, the maximum bulging difference is defined as the CED, which is the difference between the maximum and minimum bulging amounts in the radial direction of the roll, and the calculation formula is shown in Formula (11).
$${C}_{ED}={C}_{max}-{C}_{min}$$
11
where Cmax is the maximum bulging amount and Cmin is the minimum bulging amount.
Figure 7 shows the variation of Cmax and CED with DR under different Degs. The Tc is 50°C in these cases, and a uniform heat flow condition is established to provide a reference. In the uniform case, the element edges on the roll inner wall are set as the first thermal boundary with a value of 50 ℃. In Fig. 7 (a), Cmax can be increased with increasing DR and has similar change laws under different Degs. The law can be described as follows: with increasing DR, the increasing rates of Cmax gradually decrease. After the DR reaches 420 mm, Cmax begins to stabilize and no longer increases as the DR increases. Compared with the cases of different Degs, when Degs is decreased from 120° to 60°, Cmax can be gradually increased. Meanwhile, the influence value of DR on Cmax is 6.97 µm, 8.53 µm, 9.56 µm, and 10.3 µm, and the value is 10.88 µm in the uniform case. In Fig. 7 (b), CED can be gradually decreased as DR increases. When DR is large enough, CED is almost 0 µm. When the DR is small, the unevenness of roll bulging is more serious, and the larger the Degs is, the more obvious the bulging ratchet effect of ETCR. When Degs is reduced from 120° to 60°, the maximum CED values are 3.87 µm, 0.88 µm, 0.49 µm, and 0.09 µm, respectively. After Degs is reduced to 90°, the CED is less than 1 µm.
Figure 7 Variation in Cmax and CED with increasing DR under different Degs
In the ETCR, the reason for the roll profile variation is that the internal heat source changes the temperature field of the roll and further changes the thermal bulging effect. Therefore, the ratchet characteristic of the ETCR is related to the temperature field distribution. According to the result in Fig. 7, a severe bugling ratchet exists in the case with Degs = 120°. To select the evaluation criterion of the ratchet, the roll internal temperature fields with serious bulging ratchets are extracted, as shown in Fig. 8. Compared with the results in Fig. 8, the temperature range above 28°C can reflect the thermal ratchet of the ETCR. Considering that the corresponding cases in Fig. 8 are the worst cases of roll bulging uniformity, 28°C can be selected as the lowest temperature value of the thermal ratchet.
Figure 8 Roll internal temperature fields when Degs is 120°
Figure 9 shows the variation of the 28℃ temperature-affected zone inside the roll with DR under different Degs. The results show that with increasing Degs, the thermal ratchet is alleviated, which is consistent with the result in Fig. 7 (b). With a smaller DR, reducing Degs can alleviate the thermal ratchet problem caused by the TEC layout to a certain extent. When Degs is 60°, the thermal ratchet degree is lower, and uniform heat flow on the roll inner wall can be realized. With a larger roll diameter, except for the case where Degs is 120°, the ratcheting phenomenon of the temperature field in other cases can basically be eliminated.
Figure 9 Variation in the 28℃ temperature-affected zone under different DR
To further evaluate the thermal ratchet degree, the circumferential unit temperature rise control quantity is defined as ΔT. ΔT is the ratio of the temperature difference to Degs, and can be calculated by Formula (12).
$${\varDelta T}_{c}=\frac{{T}_{Deg-max}-{T}_{Deg-min}}{{Deg}_{s}}$$
12
where TDeg−max is the maximum temperature value within Degs, and TDeg−min is the minimum temperature value within Degs.
Figure 10 shows the change in ΔT of the inner wall and outer wall of the roll with changing DR under different Degs. In Fig. 10(a), ΔT can be decreased as DR increases, and the rate of decrease can be gradually decreased. Under the same DR, ΔT can be increased with increasing Degs. When Degs is changed from 60° to 120°, ΔT can be gradually increased with increasing DR, which indicates that increasing Degs can cause the ratchet phenomenon on the roll inner wall to become more serious. In Fig. 10 (b), the change in ΔT can be divided into two stages: the first stage is [140 mm, 220 mm], ΔT can be decreased rapidly with increasing DR, and the rate of decrease slowly declines. The second stage is [220 mm, 420 mm], the decrease rate declines further and finally stabilizes, and with the continuous increase in DR, ΔT finally approaches 0 ℃/°. Similarly, under the same DR, the increase in Degs can increase ΔT. When DR is 140 mm and Degs decreases from 120° to 60°, ΔT can decrease from 0.03 ℃/° to 0.01 ℃/°. The larger the Degs is, the larger the drop is. When Degs is 120°, the maximum drop is 0.03 ℃/°.
Figure 10 Variation in ΔT of the inner and outer walls of the roll with changing DR under different Degs
According to the above results, when Degs exceeds 90°, the ratio of β/α is too great, and the thermal ratchet phenomenon of the roll and the maximum difference value of roll bulging are both large, which is not suitable for ETCR. When Degs is less than 90°, the maximum difference value of roll bulging is small, and it can be further reduced by increasing DR, so it is suitable for ETCR.
In addition to the roll diameter, the diameter of the roll inner wall DIH is also a parameter that can affect the effectiveness of the ETCR. In Fig. 7, the cases where DR is 260 mm have good bulging ability and small CED and can be selected as the basic condition. To analyse the influence of DIH on ETCR, DIH and Degs are changed to analyse the bulging ability. Figure 11 shows the variation of Cmax and CED with DIH under different Degs. The results in Fig. 11 (a) show that with the increase of DIH, Cmax can be decreased, and the decrease rate of Cmax is the same under different Degs. Under the same DIH, the increase in Degs can reduce Cmax. When Degs is increased from 72° to 120°, the change in Cmax with increasing DIH is -1.13 µm, -1.37 µm, and − 1.4 µm. On the whole, under the same Tc, changing DIH has a small influence on Cmax, and the influence value is less than 2 µm. The results in Fig. 11 (b) show that CED gradually increases with increasing DIH. When Degs is 120°, the increased value of CED is the largest, and the value is 1.48 µm. When the Degs are 90° and 72°, the change values of CED are 0.29 µm and 0.11 µm, respectively.
Figure 11 Variation in Cmax and CED with increasing DIH under different Degs
In addition, the results in Fig. 11 (a) also show that the change trend of Cmax in the uniform case is different from those in other cases. Cmax can be gradually increased with increasing DIH in the uniform case, while Cmax can be decreased with increasing DIH in the other cases. The case with Degs of 120° is the most serious. To analyse the reason, the node temperature, which is located in the radial path from the roll inner wall to the maximum bulging point of the roll surface, is extracted when Degs is 120°, as shown in Fig. 12. The results show that the larger the DIH is, the lower the point temperature at the same distance from the roll inner wall, so the corresponding thermal bulge is lower at the same position. The reason is that under a constant roll diameter, the expansion of DIH is equivalent to reducing the roll wall thickness. The area close to the roll surface can obtain a higher temperature and form a larger thermal bulge. However, this law exists when there is no difference or a small difference in the roll circumferential temperature. When the heat source is uniformly distributed in the circumferential direction, the bulging ability can be improved by decreasing the roll wall thickness. In addition to the uniform case, the heat source is nonuniform in the circumferential direction, so increasing DIH reduces the roll wall thickness and increases the distances among TECs. For two adjacent TECs, the symmetry plane between two TECs is also the symmetry plane of the heat transfer influence zone. With increasing DIH, the circumferential heat transfer between the adjacent TEC is also more obvious, which leads to a decrease in Cmax.
Figure 13 shows the internal temperature fields of the roll with changing DIH. The results show that in Fig. 13(a), (d), and (g), when Degs is 120°, regardless of the DIH value, there is a severe thermal ratchet problem in the internal temperature field of the roll. When Degs is reduced to 100°, the temperature ratchet is relieved, but when DIH is larger, such as Fig. 13 (h), there is still a severe thermal ratchet. If Degs is further reduced, the thermal ratchet in the case in which the DIH is 120 mm can also be relieved. The above changes are because the reduction in Degs can increase the total direct influence angle, so the input heat flow distribution on the roll inner wall is more uniform. In addition, it is not easy to produce thermal ratchet. When DIH is increased, the total direct influence angle can be decreased and the indirect influence angle can be increased, so the uniformity of the input heat flow can be decreased on the roll inner wall, and the thermal ratchet effect is aggravated.
Figure 13 Variation of the roll temperature field under different DIH and Degs
Figure 14 shows the change in ΔT of the inner and outer walls with DIH under different Degs. In Fig. 14 (a), the ΔT of the inner wall of the roll can be increased with increasing DIH, but the growth rate gradually decreases. Under the same DIH, the larger the Degs, the larger the ΔT, and the worse the uniformity of the heat flow in the roll inner wall. In Fig. 14 (b), the ΔT of the roll outer wall can also be increased with increasing DIH, but the growth rate gradually increases. The difference in the growth rate of ΔT between Fig. 14 (a) and (b) is that increasing DIH can reduce the distance between the heat source and the roll surface, and the thermal ratchet caused by different Degs is more likely to appear on the outer wall of the roll.
Figure 14 Variation in ΔT of the inner and outer walls of the roll with changing DIH under different Degs
In summary, increasing DR can increase Cmax and decrease CED, while increasing DIH can decrease Cmax and increase CED. Changing Degs can affect the effects of DR and DIH. Comparing the results of Fig. 7(b) and Fig. 11(b), the cases in which Degs is less than 90° have a relatively small maximum difference value of roll bulging, so these cases are more suitable for ETCR than the cases in which Degs is more than 90°. Because Degs is the parameter of TEC, it is necessary to further analyse the influence of TEC parameters on the effect of ETCR.
4.2 The TEC control temperature
According to previous research results, the bulging control effect of the roll is more obvious and CED is small when DR is 260 mm and DIH is 100 mm. Therefore, these parameters are selected to analyse the influence of Tc on the thermal ratchet effect. Figure 15 shows the variation of Cmax and CED with Tc under different Degs. The results show that both Cmax and CED can increase linearly with increasing Tc. In Fig. 15(a), when Degs is reduced from 120° to 60°, the growth rate of Cmax is 0.25 µm/℃, 0.32 µm/℃, 0.38 µm/℃, and 0.43 µm/℃. Compared with the uniform case of 0.48 µm/℃, the smaller the value of Degs is, the closer the bulging effect of the roll is to the uniform case. In Fig. 15(b), in addition to the case in which Degs is 120°, other cases have lower CED. When Degs is decreased from 90° to 60°, the variation rate of CED is 0.005 µm/℃, 0.001 µm/℃, and 0.0001 µm/℃. The results indicate that cases in which Degs are 90°, 72°, and 60° can meet the requirements of uniform circumferential bulging.
Figure 15 Variation in Cmax and CED with increasing Tc under different Degs
Figure 16 shows the changes in the 28℃ temperature-affected zone with Tc under different Degs. The results show that when Degs is 120°, only the case with a larger Tc has a relatively small circumferential difference in the temperature field. In comparison, a case with a lower Tc has a more severe thermal ratchet phenomenon. Compared to the results in Fig. 15(b), even if Tc is increased, the cases with Degs of 120° are still not suitable as an optional form of TEC layout. When Degs is 90°, 72°, and 60°, the thermal ratchet phenomenon occurs only when the TEC control temperature is small, and the thermal ratchet phenomenon is eliminated after slightly increasing Tc.
Figure 16 Variation of the 28℃ temperature-affected zone with Tc under different Degs
Figure 17 shows the change in ΔT of the inner and outer walls of the roll with Tc under different Degs. The results show that the ΔT of the outer wall and inner wall also increases linearly with increasing Tc. In Fig. 17 (a), the growth rate of ΔT increases with increasing Degs, but the difference is not large. In the cases, the growth curves of Degs 90° and 120° almost coincide in value and trend, indicating that the heat flow uniformities of the roll inner wall under the two cases are approximately the same. On the other hand, under the same Tc, ΔT can be increased with increasing Degs, and the heat flow uniformity of the roll inner wall is worse. In Fig. 17 (b), the change value of ΔT in the roll outer wall with changing Tc is much smaller than that of the roll inner wall. The change rule of ΔT with Tc and Degs is the same as in Fig. 17(a). Therefore, in the cases of different Tc, the temperature uniformity of the roll inner wall is greatly affected by Tc, while the influence on the roll outer wall is very small. For the roll inner wall temperature, the increase in Tc and Degs can lead to an increase in the circumferential unevenness of the roll inner wall temperature.
Figure 17 Variation in ΔT of the inner and outer walls of the roll with changing Tc under different Degs
4.3 The single piece influence angle
In addition to Tc, the TEC amount is also an important parameter of TEC. The electronic temperature-controlled roll's circumferential sheet-carrying capacity is related to the diameter of the inner hole of the roll. Therefore, the parameters of the FE model are as follows: DR is selected as 260 mm, DIH is 80 mm, 100 mm, and 120 mm, and Tc is selected as 50°C. Figure 18 shows the variation in Cmax and CED with Degs under different DIH. The results showed that under different DIH, Cmax can be decreased and CED can be increased with increasing Degs. The change in CED is divided into two stages: when Degs is [40°, 90°], the difference in CED under different DIH is small. It can be considered that changing DIH cannot affect the effect of Degs on the radial bulging unevenness. When Degs exceeds 90°, the greater the DIH is, the more serious the radial bulging unevenness of the roll.
Figure 18 Variation of Cmax and CED with Degs under different DIH
Figure 19 shows the variation in the roll internal temperature field under different DIH and Degs. The results show that, regardless of DIH, with the increase in Degs, the thermal ratchet phenomenon can become increasingly obvious. Especially when Degs is 120°, the thermal ratchet phenomenon is so obvious that it affects the roll bulging ability and the circumferential uniformity of the roll bulging. Meanwhile, this effect can further increase as DIH increases. It can be seen from the temperature field distribution that the smaller the DIH is, the greater the Degs demand value that can ensure uniform bulging is. For example, for a case in which DR is 80 mm, the Degs demand value is 90°; for a case in which DR is 100 mm, the Degs demand value is 72°; and for a case in which DR is 120 mm, the Degs demand value is 60°.
Figure 19 Variation of the roll temperature field under different DIH and Degs
Figure 20 shows the change in ΔT of the inner and outer walls of the roll with changing Degs under different DIH. In Fig. 20(a), the changing trend of ΔT can be described as "increasing first and then becoming stable." The smaller the DIH is, the smaller the ΔT on the inner wall of the roll, and the better the uniformity of the inner wall heat flow. In Fig. 20 (b), ΔT increases with Degs, but its value is much smaller than that in Fig. 20(a); that is, the ΔT in the roll outer wall is smaller, and the temperature distribution is more uniform.
Figure 20 Variation in ΔT of the inner and outer walls of the roll with changing Degs under different DIHs
4.4 The copper layer
The above research shows that due to the influence of the bulging ratchet and the thermal ratchet, the case in which Degs is 120° cannot be suitable for ETCR. The main reason is the uneven temperature distribution of the circumferential direction. To improve this problem, a metal layer with high thermal conductivity can be arranged on the inner hole of the roll so that the heat source provided by TEC is uniform on the inner hole of the roll. In this paper, the beryllium copper layer is used as the metal layer of the roll inner hole, the thermal conductivity is 198 W/(m·K), and the value range of the layer thickness HCu is 0 mm to 12 mm. Figure 21 shows the variation in Cmax and CED with Tc under different HCu values. The results show that the increase in the beryllium copper layer has almost no effect on Cmax, but it can change the circumferential difference of the roll bulging. In Fig. 21, the application of the beryllium copper layer can effectively reduce the CED to 2 µm. If HCu is further increased, CED can be reduced by a small margin.
Figure 21 Variation in Cmax and CED with increasing Tc under different HCu
Figure 22 shows the change in ΔT of the inner and outer walls of the roll with changing Tc under different HCu values. In Fig. 22 (a), ΔT can be decreased with increasing HCu, indicating that the thermal ratchets near the roll inner wall have been well improved. In Fig. 22 (b), the influence of HCu on ΔT is the same as that in Fig. 22 (a), but the variation magnitude of ΔT is much smaller than that in Fig. 22(a). On the whole, by adding a thermally conductive metal layer to the roll inner wall, the thermal ratchet can be improved, thereby reducing CED and improving the availability of the ETCR.
Figure 22 Variation in ΔT of the inner and outer walls of the roll with changing Tc under different HCu
In this paper, for the circumferential bulging capacity and uniformity, the maximum bulging amount, the maximum bulging difference and the roll temperature field are analysed, and the effects of different parameters are discussed. The conclusions obtained are as follows:
(1) For the structure parameters of the roll, the increases of the roll diameter and the decrease of the diameter of the roll inner hole can increase the maximum bulging amount, decrease the maximum bulging difference. Meanwhile, the variation of the diameters can change the roll temperature field to decrease the difference of the circumferential temperature. Therefore, the roll diameter and the diameter of the roll inner hole need to be matched reasonably to give full play to the ability of ETCR.
(2) For the TEC layout, the increase of the TEC control temperature and the decrease of the single piece influence angle can increase the maximum bulging amount and improve the temperature ratchet. The effect of changing the single piece influence angle on the bulging uniformity is larger than that of the temperature of TEC. When the single piece influence angle is too large, the temperature ratchet is more serious and cannot even be used for the roll profile control of ETCR.
(3) To solve the problem that the case with a large single piece influence angle can not be used, adding an inner hole layer of a high thermal conductivity material is proposed to be used for improving the temperature ratchet in this paper. Through simulation analysis, the copper layer has little influence on the bulging ability of the roll and can reduce the circumferential bulging difference.
Funding
This work was supported by the Natural Science Foundation of China in Hebei Province (Grant No. E2021203129) for the support to this research.
Declaration of Interest Statement
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.
Author contributions
The analysis of bulging ability, temperature field were done by Tingsong Yang and Zhiqiang Xu; FE model establishment and FE model Validation were carried out by Tingsong Yang and Haonan Zhou; Experimental platform was built by Yang Hai with the support of Zhiqiang Xu and Fengshan Du; Tingsong Yang revised the paper. All authors have read and agreed to the published.
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