Rolling roll, data processing device, data processing program, stress calculation system, and stress calculation method

Abstract

To improve accuracy in estimating stress of a roll surface of a mill roll.SOLUTION: A stress calculation system 10 comprises a mill roll 11 and a data processing device 30. The mill roll 11 comprises a cylindrical roll body 12 and four or more distortion measuring instruments 20 that measure distortions of the roll body 12, inside the roll body 12. The data processing device 30 is configured to determine stress function on the basis of the distortions measured by the four or more distortion measuring instruments 20 to calculate stress of a roll surface 12a from a coefficient of the stress function.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a rolling roll, a data processing device, a data processing program, a stress calculation system comprising the rolling roll and the data processing device, and a stress calculation method. [Background technology]

[0002] Non-patent document 1 teaches a method for measuring the strain inside a rolling roll and estimating the stress on the roll surface from the measured strain. For stress estimation, the strain is expanded into a Fourier series. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Daniel Weisz-Patrault, et al., "Experimental evaluation of contact stress during cold rolling process with optical fiber Bragg gratings sensors measurements and fast inverse method", Journal of Materials Processing Technology 223: 105-123 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] The estimation results disclosed in Non-Patent Document 1 are represented by smooth curves. From this, it can be inferred that a higher-order Fourier series expansion has not been performed. There is room for improvement in the estimation accuracy of the stress on the roll surface.

[0005] The present invention aims to improve the accuracy of estimating the stress on the roll surface of a rolling roll. [Means for solving the problem]

[0006] One aspect of the present invention provides a rolling roll, comprising: a cylindrical roll body; and four or more strain gauges that measure strain of the roll body inside the roll body.

[0007] According to the above configuration, four or more strain measurement results can be obtained. By using a large number of measurement results, noise that may be included in each measurement result can be eliminated. Therefore, the estimation accuracy of the stress on the roll surface of the rolling roll is improved.

[0008] The four or more strain gauges may include four or more strain gauges arranged at different positions in the radial direction to measure the strain of the roll body in the same direction, or the four or more strain gauges may include two or more strain gauges arranged at different positions in the radial direction to measure the strain of the roll body in two or more different directions.

[0009] According to the above configuration, the stress estimation accuracy is improved by measuring strains at four or more different radial positions, or two or more types of strains at two or more different radial positions.

[0010] The roll body may comprise a core roll and a sleeve mounted on the outer peripheral side of the core roll to form the surface of the roll body, and the strain gauge may be arranged on the sleeve.

[0011] According to the above configuration, roll bodies having various roll materials and roll roughnesses can be easily produced. In order to obtain accurate stress on the roll surface, the strain gauge is preferably arranged as close to the surface as possible. This can be achieved by arranging the strain gauge on the sleeve.

[0012] The sleeve includes an axially adjacent first sleeve and a second sleeve, the first sleeve having ribs that protrude from the outer peripheral edge of the surface facing the second sleeve and form the surface of the roll body, and the strain measuring instrument may be provided on the surface of the second sleeve facing the first sleeve and positioned radially towards the center of the ribs.

[0013] According to the above configuration, a strain gauge can be placed in the gap enclosed by the rib, the surface of the first sleeve facing the second sleeve, and the surface of the second sleeve facing the first sleeve. No vertical force acts on the strain gauge, improving the accuracy of strain measurement. Although the rib contributes to the formation of the gap, it is located on the first sleeve facing the second sleeve where the strain gauge is installed, rather than on the second sleeve where the strain gauge is installed. Since the second sleeve where the strain gauge is installed has a uniform cylindrical shape, the accuracy of stress estimation is improved.

[0014] Another embodiment of the present invention provides a data processing device configured to determine a stress function based on strain measured by four or more strain measuring instruments placed inside the roll body of a rolling mill, and to calculate the stress on the surface of the roll body from the coefficients of the stress function.

[0015] Another embodiment of the present invention provides a data processing program for causing a computer to perform the steps of: determining a stress function based on strain measured by four or more strain measuring instruments placed inside the roll body of a rolling mill; and calculating the stress on the surface of the roll body from the coefficients of the stress function.

[0016] Another embodiment of the present invention provides a stress calculation system comprising a rolling roll and a data processing device, wherein the rolling roll comprises a cylindrical roll body and four or more strain measuring instruments for measuring the strain of the roll body inside the roll body, and the data processing device is configured to determine a stress function based on the strain measured by the four or more strain measuring instruments and to calculate the stress on the surface of the roll body from the coefficients of the stress function.

[0017] Another embodiment of the present invention provides a stress calculation method comprising: a strain measurement step of measuring the strain of a rolling roll using four or more strain measuring instruments arranged inside the roll body of the rolling roll; and a data processing step of determining a stress function based on the measured strain and calculating the stress on the surface of the roll body from the coefficients of the determined stress function.

[0018] These devices, programs, systems, and methods also acquire four or more strain measurement results. By determining the stress function using multiple measurement results, it becomes possible to eliminate noise that may be present in each measurement result. Therefore, the accuracy of estimating the stress on the roll surface of the rolling roll is improved.

[0019] In the strain measurement step, strain in the same direction may be measured at four or more locations that are different in the radial direction, or strains in two or more different directions may be measured at two or more locations that are different in the radial direction.

[0020] According to the above configuration, the accuracy of stress estimation is improved by measuring strain at four or more different radial positions, or two or more types of strain at two or more different radial positions.

[0021] In the data processing step, the measured strain may be expanded into a Fourier series before determining the stress function.

[0022] According to the above configuration, it is possible to derive a relational expression for determining the coefficients of the stress function.

[0023] In the aforementioned data processing step, the radial derivative of the measured strain may be used.

[0024] The above configuration can reduce signal noise.

[0025] In the data processing step, the coefficients of the stress function may be calculated using the constraint coefficient and the least squares method.

[0026] With the above configuration, higher-order coefficients can be calculated stably regardless of noise, improving the accuracy of stress estimation. [Effects of the Invention]

[0027] According to the present invention, the accuracy of estimating the stress on the roll surface of a rolling roll can be improved. [Brief explanation of the drawing]

[0028] [Figure 1] A front view of a rolling mill equipped with rolling rolls according to an embodiment. [Figure 2] A conceptual diagram showing a stress calculation system according to an embodiment. [Figure 3] A cross-sectional view of the rolling mill roll, shown by cutting along the line III-III in Figure 1. [Figure 4] A cross-sectional view of the rolling mill roll, shown by cutting along the line IV-IV in Figure 1. [Figure 5] Enlarged view of Figure 4. [Figure 6] A side view showing the assembly process of the rolling mill rolls shown in Figure 1. [Figure 7] A flowchart illustrating the stress calculation method according to the embodiment (including the data processing program according to the embodiment). [Figure 8] A conceptual diagram illustrating the process of converting measured strain (time history) into rotation angle (spatial coordinates). [Figure 9] A graph showing an example of measurement results for the strain of a rolled body. [Figure 10] A graph showing the estimated stress on the roll surface. [Modes for carrying out the invention]

[0029] The embodiments will be described below with reference to the drawings. The same reference numerals are used throughout the drawings for identical or corresponding elements to avoid redundant detailed descriptions.

[0030] First, with reference to Figures 1 to 6, the configuration of the stress calculation system according to the embodiment, as well as the rolling rolls and data processing device provided therewith, will be described.

[0031] Referring to Figure 1, the rolling mill 1 is equipped with a plurality of rolling rolls 11. In the illustrated example, the rolling mill 1 is a two-high type and is equipped with a pair of work rolls 11a and 11b as an example of rolling rolls 11. The material to be rolled 2 passes between the rotating pair of work rolls 11a and 11b and is rolled. The rolling may be done hot or cold, and the lubrication state of the work rolls 11a and 11b is not particularly limited. The material to be rolled 2 is a metal such as steel or aluminum alloy.

[0032] Referring to Figure 2, the stress calculation system 10 according to this embodiment includes rolling rolls 11. In this embodiment, among the multiple rolling rolls 11 constituting the rolling mill 1, the upper work roll 11a is the target of stress estimation. However, the target of stress estimation may also be the lower work roll 11b (see Figure 1). The rolling mill 1 may be a 4-high type or a 6-high type, and the target of stress estimation may be a rolling roll other than the work rolls 11a and 11b. Hereinafter, the target of stress estimation among the multiple rolling rolls 11 constituting the rolling mill 1 may simply be referred to as "rolling roll 11".

[0033] The rolling roll 11 comprises a cylindrical roll body 12. The roll body 12 is rotationally driven around a central axis C by a rolling actuator 1a. The roll body 12 comprises a core roll 13 and a sleeve 14. The sleeve 14 is mounted on the outer circumference of the core roll 13 and forms the outer surface (roll surface 12a) of the roll body 12. The sleeve 14 includes axially adjacent first sleeve 15 and second sleeve 16.

[0034] The second sleeve 16 is positioned on one axial side (right side of the paper in Figure 2) relative to the first sleeve 15. The end face on one axial side of the first sleeve 15 is the first opposing surface 15a that faces the second sleeve 16 in the axial direction. The end face on the other axial side (left side of the paper in Figure 2) of the second sleeve 16 is the second opposing surface 16a that faces the first sleeve 15 in the axial direction.

[0035] Referring to Figures 2 to 4, the core roll 13 is shaft-shaped and constitutes the axial center of the roll body 12. The first sleeve 15 and the second sleeve 16 are cylindrical and fastened to the core roll 13 by countersunk keys 17. For fastening using countersunk keys 17, axially extending key grooves 13a, 15b, and 16b are provided on the outer circumferential surface of the core roll 13, the inner circumferential surface of the first sleeve 15, and the inner circumferential surface of the second sleeve 16, respectively. A tunnel 15c is further provided on the inner circumferential surface of the first sleeve 15. The tunnel 15c extends axially and opens at both end faces of the first sleeve 15. The key groove 15b and the tunnel 15c are spaced apart from each other in the circumferential direction.

[0036] The first sleeve 15 has a rib 15d that protrudes axially in one direction from the outer peripheral edge of the first opposing surface 15a. The rib 15d is cylindrical and extends around the entire circumference. The end edge of the rib 15d abuts against the second opposing surface 16a. The outer peripheral surfaces of the first sleeve 15 (including the outer peripheral surface of the rib 15d) and the outer peripheral surface of the second sleeve 16 are connected to each other axially and constitute the roll surface 12a. Inside the roll body 12, an annular gap 12b is defined by the first opposing surface 15a, the second opposing surface 16a, the outer peripheral surface of the core roll 13, and the inner peripheral surface of the rib 15d.

[0037] The rolling mill roll 11 is equipped with a strain measuring instrument 20 that measures the strain of the roll body 12 from within the roll body 12. Two cables 29 are connected to each strain measuring instrument 20.

[0038] The strain gauge 20 is positioned on the sleeve 14. The measured strain is used to estimate the stress on the roll surface 12a. Because the strain gauge 20 is positioned close to the roll surface 12a, the stress on the roll surface 12a can be accurately estimated based on the strain measurement results.

[0039] The strain gauge 20 is mounted on the second opposing surface 16a of the second sleeve 16. The strain gauge 20 is housed within the gap 12b and positioned radially towards the center of the rib 15d. The strain gauge 20 is not sandwiched between the first sleeve 15 and the second sleeve 16, and no vertical force (in this case, the axial force of the roll body 12) acts on the strain gauge 20. Therefore, the accuracy of strain measurement is improved.

[0040] The rib 15d contributes to the formation of the gap 12b and, consequently, to the avoidance of the action of the normal force. The rib 15d is provided not on the second sleeve 16 on which the strain gauge 20 is installed, but on the first sleeve 15 which is axially opposite to the second sleeve 16. Therefore, the second sleeve 16 is maintained in a uniform cylindrical shape while enabling the formation of the gap 12b. As described later, the stress function used to estimate the stress is defined in a cylindrical coordinate system. Therefore, the stress on the roll surface 12a can be accurately estimated based on the measurement results from the strain gauge 20 installed on the second sleeve 16, which has a uniform cylindrical shape.

[0041] Referring to Figures 4 and 5, it is preferable to have as many strain measuring devices 20 as possible, and at least four or more. Multiple strain measuring devices 20 include two or more strain measuring devices 21, 22 positioned at different locations in the radial direction, and these two or more strain measuring devices 21, 22 measure two or more types of strain from radial strain, circumferential strain, and shear strain. Radial strain, circumferential strain, and shear strain are strains in different directions from each other.

[0042] In this embodiment, a plurality of strain measuring instruments 20 include a circumferential strain measuring instrument 21 and a radial strain measuring instrument 22. The strain measuring instrument 20 can measure two types of strain: circumferential strain and radial strain. Metal strain gauges (strain gauges using isotropic conductors) are preferred examples of strain measuring instruments 20. The strain gauges may be linear or foil type. For example, the "FBYV-06-11-005LE" manufactured by Tokyo Sokki Kenkyusho can be used as the circumferential strain measuring instrument 21. The "FBXV-04-11-005LE" manufactured by Tokyo Sokki Kenkyusho can be used as the radial strain measuring instrument 22.

[0043] The circumferential strain measuring device 21 includes five strain gauges 21a, 21b, 21c, 21d, and 21e. Each strain gauge has a pair of terminals and a resistive element that extends in a zigzag pattern between the pair of terminals. The five strain gauges 21a, 21b, 21c, 21d, and 21e are mounted on an insulating film 21A and arranged in a direction perpendicular to the terminal-facing direction. The resistive element of each strain gauge extends in the gauge arrangement direction while meandering in the terminal-facing direction. The circumferential strain measuring device 21 is attached to the second opposing surface 16a such that the gauge arrangement direction is along the radial direction of the roll body 12 and the terminal-facing direction is along the circumferential direction of the roll body 12. The circumferential strain measuring device 21 measures the circumferential strain of the roll body 12 at five locations that are radially different from each other.

[0044] The radial strain gauge 22 is positioned close to the circumferential strain gauge 21 and the roll body 12 in the circumferential direction. The radial strain gauge 22 also includes five strain gauges 22a, 22b, 22c, 22d, and 22e arranged on the insulating film 22A in a direction perpendicular to the terminal-facing direction. The resistive element of each strain gauge extends in the terminal-facing direction while meandering in the gauge arrangement direction. The radial strain gauge 22 is also attached to the second opposing surface 16a such that the gauge arrangement direction is along the radial direction of the roll body 12 and the terminal-facing direction is along the circumferential direction of the roll body 12. The radial strain gauge 22 measures the radial strain of the roll body 12 at five locations that are radially different from each other.

[0045] Thus, in this embodiment, the strain measuring device 20 is composed of 10 strain gauges. Note that the term "strain measuring device" in the phrase "four or more strain measuring devices" is intended to include individual strain gauges. Twenty cables 29 extend from each of the 20 terminals.

[0046] Referring to Figure 6, in the assembly of the rolling roll 11, the core roll 13 is inserted into the first sleeve 15. The strain gauge 20 is attached to the second sleeve 16. The cable 29 is inserted into the tunnel 15c of the first sleeve 15 from the opening on the first opposing surface 15a side, and the cable 29 is pulled out from the opening on the opposite side of the tunnel 15c. In this state, the second sleeve 16 is fitted onto the core roll 13.

[0047] As can be seen in Figures 2 and 6, the second sleeve 16 is then brought closer to the first sleeve 15 while the cable 29 is pulled out, the rib 15d is abutted against the second sleeve 16, and the strain measuring instrument 20 is placed in the gap 12b. Furthermore, the cover 18a is fastened to the side of the first sleeve 15 opposite to the first opposing surface 15a, and the cover 18b is fastened to the side of the second sleeve 16 opposite to the second opposing surface 16a. This completes the rolling roll 11.

[0048] Before the rolling roll 11 is installed in the rolling mill 1 (see Figure 1), the cable 29 is connected to a strain gauge amplifier. The strain gauge amplifier may be located outside the rolling mill 1 or at the end of the core roll 13. In this embodiment, as schematically shown in Figure 2, the strain gauge amplifier is located at the core roll 13, and therefore the cable 29 terminates at the rolling roll 11.

[0049] Referring to Figure 2, the stress calculation system 10 further comprises a data processing device 30, a communication device 41, a receiving device 42, a display device 43, and a rolling mill control device 44, in addition to the rolling rolls 11.

[0050] The communication device 41 is attached to the end of the core roll 13 together with the strain gauge amplifier. The receiving device 42 is configured to communicate wirelessly with the communication device 41. The data processing device 30 is configured to communicate with the receiving device 42, or has the receiving device 42 as part of it.

[0051] When strain occurs in the roll body 12, the signal values ​​of the strain gauges 21a~21e and 22a~22e change in accordance with the change in the electrical resistance of the resistor. The strain gauge amplifier amplifies the signal. The communication device 41 wirelessly outputs the amplified signal to the receiving device 42. The receiving device 42 receives the signal output from the communication device 41. The data processing device 30 acquires a signal indicating the strain measured by the strain measuring instrument 20 from or at the receiving device 42.

[0052] The data processing device 30 includes, for example, a CPU (Central Processing Unit) or MPU (Micro Processing Unit) that works in cooperation with software to realize predetermined functions. The data processing device 30 may consist of hardware circuits such as dedicated electronic circuits or reconfigurable electronic circuits designed to realize predetermined functions, or it may consist of various semiconductor integrated circuits. Examples of various semiconductor integrated circuits include, in addition to CPUs and MPUs, microcomputers, DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate Arrays), and ASICs (Application Specific Integrated Circuits). The data processing device 30 may also include storage devices such as RAM (Random Access Memory) and ROM (Read Only Memory). Specifically, the data processing device 30 may consist of, for example, an information processing device such as a desktop PC, a notebook PC, a workstation, or a tablet terminal, or a printed circuit board having equivalent functions.

[0053] The storage device stores a data processing program according to the embodiment, and information used in the program, for causing the data processing device 30, which acts as a computer, to perform a process to estimate the stress on the roll surface 12a.

[0054] The data processing program includes processes for estimating the stress on the roll surface 12a, as well as processes for displaying the estimated stress on the display device 43 and outputting the estimation results to the rolling mill control device 44.

[0055] The worker can refer to the display on the display device 43 to check the stress estimated by the data processing device 30 in real time while the rolling mill 1 is in operation.

[0056] The rolling mill control device 44 controls the rolling actuator 1a based on the stress distribution estimated by the data processing device 30. This adjusts the reduction amount, roll speed, and rolling tension, optimizing the rolling process. The estimated results (features) transmitted to the rolling mill control device 44 include the minimum surface pressure and the distance from directly below the roll when the surface pressure is at its minimum (see Figure 10).

[0057] Next, with reference to Figures 7 to 10, the stress calculation method used in the stress calculation system 10 and the data processing program executed by the data processing device 30 of the stress calculation system 10 will be described.

[0058] As shown in Figure 7, first, the measured strain (time history) is acquired (step S1). The strain measuring instrument 20 measures strain at a total of 10 locations. In step S1, the measurement results of the strain at the 10 locations are acquired sequentially by the data processing device 30 at a predetermined sampling period, in synchronization with each other.

[0059] For example, the rolling speed of the rolling mill 1 may be 1 mpm (meters per minute), the diameter of the roll surface 12a may be 85 mm, and the circumference of the roll surface 12a may be 267 mm. In that case, the time required for one rotation of the rolling roll 11 is 16.02 seconds. The sampling period may be 5 ms (milliseconds). In that case, it becomes possible to measure strain approximately 3200 times per roll rotation and per measurement point. As described later, the data processing device 30 performs a higher-order Fourier series expansion. For this purpose, it is thought that a sampling rate of about 1000 times per rotation is necessary, and the above example fully satisfies this condition.

[0060] Next, the data processing device 30 converts the time history information of the measured strain into information of the rotation angle θ of the strain (circumferential position around the central axis C) based on the rotation speed of the rolling roll 11, and obtains the spatial distribution of strain (step S2). Figure 8 conceptually illustrates this step S2. Figure 8 schematically shows that 13 rotation angle θ pieces of information are generated from the time history of the strain, but in the above example, 3200 rotation angle θ pieces of information are actually generated.

[0061] Referring to Figure 9, when the rolling mill roll 11 is rotated continuously for multiple rotations and the spatial distribution of strain is measured, it can be seen that the spatial distribution of strain fluctuates according to the rotation angle θ, and that this fluctuation repeats with a period of 2π (corresponding to one rotation of the rolling mill roll 11). Figure 9 shows the superposition of multiple measurement results obtained each time the rolling mill roll 11 rotates. In step S2, the measurement results of 10 strain gauges are acquired and linked to the rotation angle θ during at least one rotation of the rolling mill roll 11. As described above, approximately 3200 measurement results for each strain gauge are acquired during one rotation of the rolling mill roll 11.

[0062] Next, we determine the relationship between the coefficients of the nth-order Fourier series expansion of the strain and the coefficients of the stress function X as matrix coefficients (Step S3).

[0063] Since the rolling roll 11 is an elastic body, the elastic stress-strain relationship holds. Also, from the force equilibrium equation, in the elastic roll, the Airy stress function X can be defined as shown in the following equation (1).

[0064] [Mathematical formula]

[0065] The rolling roll 11 is a cylindrical body. The general solution of the stress function X in cylindrical coordinates is known as the Michell solution, as shown in the following equation (2). Once the stress function is known, the stress inside the rolling roll 11 (which naturally includes the roll surface 12a) can be calculated.

[0066] [Mathematical formula] Here, a0 to h n are unknown coefficients for each order.

[0067] Based on the relational expressions (details are omitted here) between the unknown variables and each stress component (radial stress σ r , circumferential stress σ θ , and shear stress τ rθ ), and the stress-strain relationship based on elasticity theory, each strain component (radial strain ε r , circumferential strain ε θ , and shear strain γ rθ ) can be expressed using the unknown variables. The radial strain ε r is expressed by the following equation (3).

[0068] [Mathematical formula] Here, μ n εr→An (r) to μ n εr→An (r) are constants determined by the Fourier order n and r (the strain measurement position, the radial position of the strain gauge). A n to H n are the unknown coefficient an ~h n Each of these is obtained by multiplying it by a quadratic expression of Fourier degree n (for example, A n =-n(n+1)a n ). A n ~H n This is used for a simplified notation of the expression, A n ~H n Once the value is determined, the unknown coefficient a is calculated according to its Fourier order n. n ~h n This can be determined.

[0069] On the other hand, the spatial distribution of strain measured by each strain gauge, obtained in step S2, can be expressed by the following equation (4) by Fourier series expansion.

[0070]

number

[0071] From equations (3) and (4), we obtain the following relationships expressed by equations (5) and (6).

[0072]

number

[0073] In other words, from the strain measurement results, K n 1 (ε r :r) and K n 2 (ε r The two values ​​of r) are determined, and the unknown is A. n ~H n There are 8 of them. 8 unknowns A n ~H nTo determine this, we need to identify four types of strain measured individually. Equations (5) and (6) depend on the measured strain direction and the measurement location (radial position). Therefore, the four types of strain are either strains measured at four points with different radial positions, or two types of strains measured at two radially different points with different strain directions (four types in 2 points x 2 directions).

[0074] In this embodiment, circumferential strain at 5 points and radial strain at 5 points are measured. From these 10 points, there are multiple combinations of selecting 4 types of strain to satisfy the above conditions.

[0075] The measurement results from the strain gauge 20 always include measurement error. Therefore, for each selected combination, unknown A n ~H n The calculation results differ.

[0076] As can be seen from equation (2), the stress function X contains terms of the power of n or the power of -n. Therefore, as the Fourier order n increases, the value of these terms becomes either very small or very large, reducing the accuracy of stress estimation. In some cases, even if the Fourier order n is not very large, the unknown A n ~H n And thus the unknown coefficient a n ~h n If the error is large (unknown coefficient a n ~h n If the deviation towards the larger side of the value is significant, the nth or -nth power terms may diverge, making it difficult or impossible to solve the stress function X. In this case, the stress function X must be determined based on noisy measurement results, without including higher-order calculation results, further reducing the accuracy of stress estimation.

[0077] Therefore, in order to determine the unknown using as much information as possible, we adopt the least squares method. To that end, we define the evaluation function as shown in equations (7) and (8) below.

[0078]

number

[0079] Radial strain ε r If you want to use methods other than the Fourier series expansion, circumferential strain ε θ , and the radial derivative of strain ∂ε r / ∂r,∂ε θr Considering / ∂r, a more generalized evaluation function is defined as shown in equations (9) and (10). Note that circumferential strain ε θ The radial derivative ∂ε is obtained from the measurement results of the strain measuring instrument 20, in the same manner as the radial strain εr. r / ∂r,∂ε θr / ∂r is the measured radial strain ε r and circumferential strain ε θ These are calculated from the given values. By taking these into consideration, synchronized electrical noise contained in the distorted signal can be removed.

[0080]

number

[0081] The unknown A that minimizes this evaluation function. n ~H n We just need to find that. Then, we need to find the smallest possible unknown A in the higher-order terms. n ~H n In order to constrain it, the unknown A is given by equations (11) and (12) below. n ~H n The sum of quadratic terms is considered as a correction term.

[0082]

number

[0083] After step S3, the constraint coefficient λ is set (step S4). In light of the purpose of the evaluation function (finding the minimum value), the constraint coefficient λ is a positive value. Then, from equations (11) and (12), the coefficients of the stress function X are determined according to the evaluation function that takes the constraint coefficient λ into account (step S5). Next, the Fourier expansion coefficients of the stress on the roll surface 12a are derived using the coefficients of the stress function X (step S6). Next, the stress is derived as a function of the rotation angle θ from the Fourier expansion coefficients of the stress on the roll surface 12a by inverse Fourier expansion (step S7). Each stress component is expressed by the following equations (13) to (15) using the stress function X.

[0084]

number

[0085] Next, the derived stress on the roll surface 12a is displayed on the display device 43 (step S8). As shown in Figure 10 as an example, according to this embodiment, since the noise included in the coefficients of the stress function X is suppressed, the Fourier series expansion does not diverge even in higher-order terms. For example, the 100th-order term does not diverge and can be included in the stress estimation result. Therefore, estimation results of complex waveforms can be obtained, and high estimation accuracy can be obtained.

[0086] Embodiments of the present invention have been described so far, but the above configurations can be added, modified, or deleted as appropriate within the scope of the spirit of the present invention.

[0087] In the embodiment described above, the strain measuring device 20 includes a circumferential strain measuring device 21 and a radial strain measuring device 22, measuring strain in two different directions. Alternatively, the strain measuring device 20 may include only one of the circumferential strain measuring device 21 or the radial strain measuring device 22, and measure strain in the same direction at four or more different locations in the radial direction.

[0088] The strain measuring instrument 20 may include a shear strain measuring instrument in place of, or in addition to, one or both of the circumferential strain measuring instrument 21 and the radial strain measuring instrument 22. That is, multiple strain measuring instruments 20 may measure strain in one, two, or three directions selected from circumferential strain, radial strain, and shear strain.

[0089] The strain measuring instrument 20 is not limited to measuring circumferential strain, radial strain, and shear strain; it may also measure strain in any direction at an arbitrary angle from the radial direction. In this case, circumferential strain, radial strain, and shear strain can be determined from the measured strain values ​​obtained by measuring in multiple directions, and the coefficients of the stress function can be determined based on these values. Furthermore, by modifying the stress function according to the direction of the strain being measured, the coefficients of the stress function can be determined from the measured values ​​without converting them to circumferential strain, radial strain, and shear strain.

[0090] In the embodiment described above, the strain measuring device 20 is composed of 10 strain gauges, but the present invention is not limited thereto, and only needs to include at least 4 strain measuring devices (strain gauges).

[0091] Here, it is preferable that each of the four strain gauges differs from the other three in at least one of its radial position (radial position) and the direction of the strain it measures (strain measurement direction). However, this excludes the case where the radial positions of the four strain gauges are the same but the strain measurement directions are different from each other.

[0092] More specifically, it is preferable to include four strain measuring instruments configured as in any of the following (a) to (d). (a) The radial positions of all four strain gauges are different from each other. (b) Three of the four strain gauges are located at different radial positions from each other, and the remaining gauge is located at the same radial position as one of the other three, but its strain measurement direction is different from that of the other gauges. (c) Two of the four strain gauges are in the first position in the radial direction, the remaining two gauges are in a second position different from the first position in the radial direction, and the strain measurement directions of the two gauges that are in the same radial position are different from each other. (d) Three of the four strain gauges are located at the same radial position but measure strain in different directions, and the radial position of the remaining gauge is different from the other three.

[0093] Furthermore, "the same or different radial positions" means that the distances from the central axis of the cylindrical roll are equal or different. Therefore, any two locations that are equal in distance from the central axis of the roll are treated as having the same radial position, even if their circumferential positions are different.

[0094] This disclosure may include the following aspects: (Aspect 1) A cylindrical roll body, Four or more strain measuring instruments for measuring the strain of the roll body inside the roll body, A rolling roll equipped with a rolling mill. (Aspect 2) The four or more strain measuring devices include four or more strain measuring devices arranged at different positions in the radial direction, and measure the strain of the roll body in the same direction, or The four or more strain measuring devices include two or more strain measuring devices arranged at different positions in the radial direction, and measure the strain of the roll body in two or more different directions. A rolling roll according to Embodiment 1. (Aspect 3) The roll body comprises a core roll and a sleeve attached to the outer circumference of the core roll to form the surface of the roll body. The strain measuring device is positioned in the sleeve. A rolling roll according to embodiment 1 or 2. (Aspect 4) The sleeve includes an axially adjacent first sleeve and a second sleeve, The first sleeve has ribs that protrude from the outer peripheral edge of the surface facing the second sleeve and form the surface of the roll body, The strain measuring device is provided on the surface of the second sleeve facing the first sleeve and is positioned radially towards the center of the rib. A rolling roll according to embodiment 3. (Appendix 5) The stress function is determined based on the strain measured by four or more strain gauges placed inside the roll body of the rolling mill. The surface stress of the roll body is calculated from the coefficients of the stress function. A data processing device configured in such a way. (Aspect 6) A process of determining the stress function based on the strain measured by four or more strain measuring instruments placed inside the roll body of the rolling mill roll, A step of calculating the surface stress of the roll body from the coefficient of the stress function, A data processing program that causes a computer to execute a command. (Aspect 7) Equipped with rolling rolls and a data processing device, The rolling rolls A cylindrical roll body, The system comprises four or more strain measuring instruments for measuring the strain of the roll body inside the roll body, The data processing device, The stress function is determined based on the strain measured by the four or more strain measuring instruments mentioned above. The surface stress of the roll body is calculated from the coefficients of the stress function. It is structured in such a way. Stress calculation system. (Pattern 8) A strain measurement step in which the strain of the rolling roll is measured using four or more strain measuring instruments placed inside the roll body of the rolling mill roll, A data processing step which involves determining a stress function based on the measured strain and calculating the surface stress of the roll body from the coefficients of the determined stress function, A stress calculation method comprising the following features. (Aspect 9) In the strain measurement step, either measure strain in the same direction at four or more locations at different radial positions, or measure strain in two or more different directions at two or more locations at different radial positions. The stress calculation method described in Embodiment 8. (Aspect 10) In the aforementioned data processing step, before determining the stress function, the measured strain is expanded into a Fourier series. The stress calculation method described in aspects 8 and 9. (Aspect 11) In the aforementioned data processing step, the radial derivative of the measured strain is used. A stress calculation method according to any one of embodiments 8 to 10. (Aspect 12) In the data processing step, the coefficient of the stress function is calculated using the constraint coefficient and the least squares method. A stress calculation method according to any one of embodiments 8 to 11. [Explanation of Symbols]

[0095] 1. Rolling mill 1a Rolling Actuator 2 Rolled material 10. Stress Calculation System 11 Rolling Rolls 11a, 11b Work Roll 12 rolls 12a Roll surface 12b Gap 13 Core Roll 13a Keyway 14 sleeves 15 First Sleeve 15a 1st facing surface 15b Keyway 15c Tunnel 15d rib 16. Second sleeve 16a Second facing surface 16b Keyway 17. Sink Key 18a, 18b Cover 20. Strain Gauge 21. Circumferential strain measuring instrument 21A insulating film 21a, 21b, 21c, 21d, 21e Strain gauges 22 Radial strain measuring instrument 22A insulating film 22a, 22b, 22c, 22d, 22e strain gauges 29 Cables 30 Data Processing Devices 41 Communication equipment 42 Receiving device 43 Display device 44 Rolling mill control device

Claims

1. A cylindrical roll body, Four or more strain measuring instruments for measuring the strain of the roll body inside the roll body, Equipped with, The four or more strain measuring instruments described above, It includes four or more strain measuring instruments positioned at four different radial locations to measure the strain of the roll body in the same direction, or The system includes four or more strain measuring instruments, each positioned at two or more different locations in the radial direction, for measuring the strain of the roll body in two or more different directions at each location. Rolling mill rolls.

2. The roll body comprises a core roll and a sleeve attached to the outer circumference of the core roll to form the surface of the roll body. The strain measuring device is positioned in the sleeve. The rolling roll according to claim 1.

3. The sleeve includes an axially adjacent first sleeve and a second sleeve, The first sleeve has ribs that protrude from the outer peripheral edge of the surface facing the second sleeve and form the surface of the roll body, The strain measuring device is provided on the surface of the second sleeve facing the first sleeve, and is positioned radially towards the center of the rib. The rolling roll according to claim 2.

4. The stress function is determined based on the strain measured by four or more strain gauges placed inside the roll body of the rolling mill. The surface stress of the roll body is calculated from the coefficients of the stress function. A data processing device configured as follows: The measured strain is, The strain is measured by four or more strain measuring instruments positioned at four different radial positions, and is the strain of the roll body in the same direction, or The strain of the roll body in two or more different directions at each of two different positions is measured by four or more strain measuring instruments, each of which is two or more instruments are arranged at two or more different positions in the radial direction. Data processing device.

5. A process of determining the stress function based on the strain measured by four or more strain measuring instruments placed inside the roll body of the rolling mill roll, A step of calculating the surface stress of the roll body from the coefficient of the stress function, A data processing program for causing a computer to execute, The measured strain is, The strain is measured by four or more strain measuring instruments positioned at four different radial positions, and is the strain of the roll body in the same direction, or The strain of the roll body in two or more different directions at each of two different positions is measured by four or more strain measuring instruments, each of which is two or more instruments are arranged at two or more different positions in the radial direction. Data processing program.

6. Equipped with rolling rolls and a data processing device, The rolling rolls A cylindrical roll body, The system comprises four or more strain measuring instruments for measuring the strain of the roll body inside the roll body, The four or more strain measuring instruments described above, It includes four or more strain measuring instruments positioned at four different radial locations to measure the strain of the roll body in the same direction, or It includes four or more strain measuring instruments, two or more of which are arranged at each of two different radial positions, and which measure the strain of the roll body in two or more different directions at each position. The data processing device, The stress function is determined based on the strain measured by the four or more strain measuring instruments. The surface stress of the roll body is calculated from the coefficients of the stress function. It is structured in such a way. Stress calculation system.

7. A strain measurement step in which the strain of the rolling roll is measured using four or more strain measuring instruments placed inside the roll body of the rolling mill roll, A data processing step which involves determining a stress function based on the strain measured in the strain measurement step, and calculating the surface stress of the roll body from the coefficients of the stress function, A stress calculation method comprising, In the strain measurement process, The strain of the roll body in the same direction is measured by four or more strain measuring instruments positioned at four different radial locations, or, The strain of the roll body in two or more different directions at each of two different positions is measured by four or more strain measuring instruments, each of which is arranged at two or more different positions in the radial direction. Stress calculation method.

8. In the aforementioned data processing step, before determining the stress function, the measured strain is expanded into a Fourier series. The stress calculation method according to claim 7.

9. In the aforementioned data processing step, the radial derivative of the measured strain is used. The stress calculation method according to claim 7.

10. In the data processing step, the coefficient of the stress function is calculated using the constraint coefficient and the least squares method. A method for calculating stress according to any one of claims 7 to 9.

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