Experimental Validation and Numerical Simulation of Flexible and Micro-scale Roll Gap Control Technology

: To obtain a better ability of strip flatness control, this paper proposes a new flexible 13 and micro-scale roll gap control technology. According to the principle of roll profile electromagnetic 14 control technology (RPECT), a new electromagnetic control rolling mill with the function of roll 15 profile control and large diameter ratio rolling is designed and built. To analyze the flatness control 16 ability of this mill, a comprehensive finite element model (FEM) is established and verified, which 17 includes a FEM for predicting the electromagnetic control roll profile and a FEM of rolling process. 18 The simulation results show that the crown control ability of RPECT is stronger than the quadratic 19 crown control ability, and the effect of tension on the roll gap shape crown is small. The results in the 20 indentation experiment and the rolling experiment show that increasing the roll crown of 21 electromagnetic control roll can adjust the strip shape form edge wave to non-wave, and middle wave. The feasibility of using RPECT to adjust the roll gap shape has been verified, and the roll gap control 23 goal of uniform transverse size distribution can be achieved. μm. When the ECR roll crown is 40 μm, the strip has a good transverse thickness distribution. The results show that under this working condition, the roll crown obtained

with the VCR, and the results showed that the strip crown control range and the roll gap stiffness can 71 be increased when VCR was applied [14]. Wang   developed an integrated design of roll contours for EDW and matched VCR, which can be used to 76 solve strip edge drop and crown problem for accurate "dead flat" transverse thickness profile of 77 electrical steel sheet in 4-high tandem cold rolling mills [17]. In practical application, the above 78 technologies have achieved different control effects, and provided support for strip production. 79 with an arbor and a sleeve, which can control the strip profile by regulating the oil pressure [20].   The single-roll-driven asymmetric strip rolling mill can be divided into two asymmetrical roll 124 systems. The rolls of the upper system are common rolls, including two supporting rolls and one 125 working roll. The roll of the lower system is an ECR with a segmented electromagnetic stick, and can 126 be used to control the roll profile. The diameter ratio of the lower working roll to the upper working 127 roll is 3.375. Due to the large diameter ratio, the bending of the upper working roll is larger than that 128 of the lower working roll. If the ECR is not applied, the edge roll gap value is less than the middle 129 value, which leads to the instability of strip edge extension and the double edge wave problem.

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To solve these problems, the roll profile control function of ECR needs to be started, and the 131 control principles of electromagnetic control rolling mill are shown in Fig.1. The ECR roll crown can 132 be increased with controlling, and compensate for the deflection of the upper working roll to eliminate 133 the flatness problems. If the ECR roll crown is continuously controlled, the middle roll gap value can 134 be less than that on the edge, and the instability of the middle elongation of the strip and the middle 135 wave problem can be generated. Therefore, in the control process, the strip flatness can be controlled 136 from the double edge wave to the non-wave, and then to the middle wave, which indicates that the 137 mill has flatness control ability and can achieve the goal of flatness defect adjustment.   Therefore, the FE model needs to be simplified. In the traditional solving process of roll gap, the 147 roll gap is considered to be formed by the influence of the original roll profile, the roll deflection, 148 roll flattening, etc. Considering that the ECR roll profile is a steady-state roll profile curve in 149 RPECT, the ECR roll profile can be brought into the roll gap in the form of the origin roll profile.      Table. 2.

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To analyze the roll gap shape, the curve equation can be used to fit the roll gap. In this paper, 215 the roll gap shape is mainly described by quartic polynomial.
Where f(x) is the shape curve of loaded roll gap, x is the strip width normalized, a0, a2 and a4 are the  (a) Variation of the roll gap shape/μm Variation of the roll gap shape/μm X-axis/mm Variation of the roll gap shape/μm X-axis/mm According to formula (1) and formula (2), the quadratic crown and the quartic crown of different 243 working conditions in Fig. 8 can be calculated, as shown in Table 3. The results show that the rolling 244 force and the ECR roll crown can affect the roll gap shape, and the influence of the ECR roll crown 245 on the roll gap is more obvious. When the rolling force is constant and the ECR roll crown is increased, 246 the quadratic crown can be decreased, and the quartic crown can be increased. As increasing the ECR 247 roll crown, the variation of quadratic crown is relatively large, about 15 μm; the variation of quartic 248 crown is relatively small, about 1.5 μm. When the ECR roll crown is constant and the rolling force is 249 increased, the quadratic crown and the quartic crown of the roll gap are increased. Therefore, the 250 quadratic crown and the quartic crown can be adjusted by changing the ECR roll crown. Its control 251 ability of controlling the quadratic crown is stronger than that of the quartic crown. In addition, the 252 rolling force can also cause the variation of the quadratic crown and the quartic crown. But the 253 variation of the rolling force also changes the rolling condition, the control strategy of changing the 254 rolling force alonely cannot be used to control the strip flatness.  It is worth noting that the change of roll gap shape in Fig. 8 (c) is special. When the rolling 257 force is 20 t and the ECR roll crown is 0 μm, the roll gap shape curve has a bulging at the strip 258 center and a depression at 50 mm away from the strip center, as shown in Fig. 8 (c). Considering the 259 metal transverse flow, the lateral displacement of strip in Fig. 8 (c) is extracted, as shown in Fig. 9.

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Due to the symmetry of the model, the direction from the center to the edge of the strip is selected 261 as the positive direction of the metal transverse flow.

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When the roll gap is in good condition, the metal transverse flow usually shows monotonic 263 increase or monotonic decrease. However, the results in Fig. 9 show that the negative direction range  Lateral displacement/mm X-axis/mm Fig. 10. Variation of lateral displacement when the ECR roll crown is different and the rolling force is 20 t 289 Therefore, RPECT can effectively control the roll gap shape by changing the ECR roll crown. 290 When the roll gap size isn't uniform due to excessive rolling force, the metal transverse flow state 291 can be changed by adjusting the ECR roll profile. conditions. The distribution trend of the roll gap shape in Fig. 11 is similar to that in Fig. 8. When the 298 tension is constant, the variation of roll gap shape can be increased with increasing ECR roll crown.

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When the roll crown is constant, the variation of roll gap shape is also improved with increasing 300 tension value. However, the influence of the tension is weaker than that of the ECR roll crown. Variation of the roll gap shape/μm X-axis/mm Variation of the roll gap shape/μm X-axis/mm Variation of the roll gap shape/μm X-axis/mm Fig. 11. Variation of the roll gap shape under different tension conditions. (a) Tension is 10 MPa, (b) Tension is 20 304

MPa, and (c) Tension is 30 MPa 305
According to formula (1) and formula (2), the quadratic crown and quartic crown of roll gap 306 shape are calculated, as shown in Table 4 Under different tension conditions, the change of ECR roll crown can affect the roll gap crown.

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When the tension is constant, the quadratic crown can be decreased and the quartic crown can be

Experimental equipment and scheme 321
The indentation experiment is carried out on the electromagnetic control rolling mill. The roll 322 arrangement and logical relationship are shown in Fig. 12. The lower working roll is an ECR, and ES 323 is located in the ECR inner hole. The parameters of the electromagnetic control rolling mill are the 324 same as those of the above models. Before experiment, ES needs to be heated and be used to obtain 325 the target ECR roll profile. After the target roll profile is formed, the strip is fed into the roll gap and 326 the rolling force is adjusted. When the strip is rolled for a short distance, the rolling is stopped and the roll is lifted to complete the indentation test.

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The thickness distribution of strip under the same rolling force should be the same, but the results 340 in Fig. 13 show that there are some differences in the thickness distribution obtained at different times.

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The main reason is as follows: in the experiment, a group of indentation experiments need to be 342 pressed once, and the rolling force of every experiment fluctuates to a certain extent. Therefore, the 343 error caused by the rolling force can affect the thickness variation of strip. Although there are some 344 differences in the thickness distribution each time, the thickness distribution trend is similar.  roll crown is 30 μm, the middle of strip appears the phenomenon of thickness reduction, and the 359 strip crown is -3 μm. When the ECR roll crown is 40 μm, the strip crown is -9 μm. As the ECR roll 360 crown increases from 0 μm to 40 μm, the strip crown gradually decreases from 4 μm to -9 μm. 361 Fig.14 shows that when the ECR roll crown is 20 μm and the rolling force is 10 t, the thickness 362 distribution of the roll gap shape is uniform. This case has a good control effect of the roll gap.

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Therefore, if a good thickness distribution needs to be obtained in the large rolling force, the roll 364 crown of the lower working roll needs to be further increased.    roll diameter is 120 mm and the tension is 35 MPa. Under such conditions, the roll diameter is more 433 than 80 mm, and the roll deflection is less than that in Fig. 18. Therefore, the ECR roll crown is added 434 20 μm in addition. When the ECR roll crown is 0 μm, obvious edge waves appear on the strip edge.  Fig. 19 (d) is more obvious than that in Fig.18 (c). The reason is that the stiffness of the upper 448 working roll can be increased with increasing roll diameter, and the size of the middle roll gap regulated by RPECT is smaller than that in Fig. 18 (c), which leads to more obvious middle wave.  This technology can be used to adjust the roll gap shape and control the strip flatness by using ECR.

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(2) By changing the ECR roll crown, the control ability of quadratic crown and quartic crown 462 of roll gap can be enhanced. The control ability increment of quadratic crown is greater 463 than that of quartic crown.

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(3) In the indentation experiment, the roll profile obtained by intermittent regulation is stable, 465 and the corresponding roll gap is also stable. The ECR roll crown can compensate for the 466 roll deflection, and adjust the roll gap shape. With increasing regulation amount, ECR can 467 adjust the strip with edge wave defects to the strip without defects, and then adjust it to the 468 strip with middle wave defects.

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(4) In the strip rolling experiment, the problem of edge wave can be solved through RPECT,470 and the strip with good shape can be obtained. When the ECR roll crown is further 471 increased, RPECT can adjust the edge wave to the middle wave, which fully proves that RPECT equipped on this platform has considerable control ability for thin strip rolling.