Mill 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 reduction roll, a data processing device, a data processing program, a stress calculation system including the reduction roll and the data processing device, and a stress calculation method. [Background technology]

[0002] Non-Patent Document 1 teaches a method of measuring the strain inside a rolling roll and estimating the stress on the roll surface from the measured strain. To estimate the stress, 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 Summary of the Invention [Problem to be solved by the invention]

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

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

[0006] One aspect of the present invention provides a reduction roll including 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, it is possible to eliminate noise that may be contained in each measurement result. 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 radial positions and 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 radial positions and measure the strain of the roll body in two or more different directions.

[0009] According to the above configuration, the accuracy of stress estimation 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 include a core roll and a sleeve attached to the outer periphery of the core roll to form the surface of the roll body, and the strain gauge may be disposed on the sleeve.

[0011] According to the above-mentioned configuration, it is possible to easily create roll bodies having various roll materials and roll roughnesses. In order to obtain accurate stress on the roll surface, it is better to place the strain gauge as close to the surface as possible. This can be achieved by placing the strain gauge on the sleeve.

[0012] The sleeve may include a first sleeve and a second sleeve adjacent in the axial direction, the first sleeve having a rib protruding from the outer peripheral edge of the surface facing the second sleeve to form the surface of the roll body, and the strain gauge may be provided on the surface of the second sleeve facing the first sleeve and positioned radially toward the center of the rib.

[0013] According to the above configuration, the strain gauge can be placed in the gap surrounded 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 normal force acts on the strain gauge, improving the accuracy of strain measurement. Although the rib contributes to the formation of the gap, the rib is provided not on the second sleeve on which the strain gauge is installed, but on the first sleeve facing it. Because the second sleeve on which the strain gauge is installed has a uniform cylindrical shape, the accuracy of stress estimation improves.

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

[0015] Another aspect of the present invention provides a data processing program for causing a computer to execute the steps of determining a stress function based on strains measured by four or more strain measuring devices arranged inside a roll body of a rolling roll, and calculating the stress on the surface of the roll body from the coefficients of the stress function.

[0016] Another aspect 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 gauges that measure 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 gauges, and calculate the stress on the surface of the roll body from the coefficients of the stress function.

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

[0018] In these devices, programs, systems, and methods, four or more strain measurement results are also obtained. By determining the stress function using a large number of measurement results, it is possible to eliminate noise that may be included in each measurement result. Therefore, the estimation accuracy of the stress on the roll surface of the rolling roll is improved.

[0019] In the strain measuring step, strain in the same direction may be measured at four or more different radial positions, or strain in two or more different directions may be measured at two or more different radial positions.

[0020] According to the above configuration, the accuracy of stress estimation 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.

[0021] The data processing step may include subjecting the measured strains to a Fourier series expansion before determining the stress function.

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

[0023] The data processing step may use radial derivatives of the measured strain.

[0024] According to the above configuration, signal noise can be reduced.

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

[0026] According to the above configuration, high-order coefficients can be stably calculated regardless of noise, and the accuracy of stress estimation is improved. Effect of the Invention

[0027] According to the present invention, it is possible to improve the accuracy of estimating the stress on the roll surface of a reduction roll. [Brief description of the drawings]

[0028] [Figure 1] FIG. 1 is a front view of a rolling mill including a rolling roll according to an embodiment. [Diagram 2] FIG. 1 is a conceptual diagram showing a stress calculation system according to an embodiment. [Diagram 3] FIG. 2 is a cross-sectional view of the reduction roll taken along line III-III in FIG. [Figure 4] FIG. 2 is a cross-sectional view of the reduction roll taken along line IV-IV in FIG. [Diagram 5] Enlarged view of Figure 4. [Figure 6] 2 is a side view showing an assembly process of the roll shown in FIG. 1. [Figure 7] 4 is a flowchart showing a stress calculation method according to an embodiment (including a data processing program according to the embodiment). [Figure 8] Conceptual diagram showing the process of converting measured strain (time history) into rotation angle (spatial coordinates). [Figure 9] 4 is a graph showing an example of the measurement results of the strain of a roll body. [Figure 10] 13 is a graph showing the estimated results of stress on the roll surface. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0029] Hereinafter, an embodiment will be described with reference to the drawings. Note that the same or corresponding elements are designated by the same reference numerals throughout the drawings, and detailed description thereof will be omitted.

[0030] First, the configurations of a stress calculation system according to the embodiment, and a reduction roll and a data processing device provided therein will be described with reference to Figs. 1 to 6.

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

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

[0033] The rolling roll 11 includes 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 includes a core roll 13 and a sleeve 14. The sleeve 14 is attached to the outer periphery of the core roll 13 and forms the outer surface (roll surface 12a) of the roll body 12. The sleeve 14 includes a first sleeve 15 and a second sleeve 16 adjacent to each other in the axial direction.

[0034] The second sleeve 16 is disposed on one axial side (the right side in FIG. 2 ) with respect to the first sleeve 15. An end face on one axial side of the first sleeve 15 is a first opposing surface 15a that faces the second sleeve 16 in the axial direction. An end face on the other axial side of the second sleeve 16 (the left side in FIG. 2 ) is a second opposing surface 16a that faces the first sleeve 15 in the axial direction.

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

[0036] The first sleeve 15 has a rib 15d that protrudes from the outer circumferential edge of the first opposing surface 15a to one side in the axial direction. The rib 15d is cylindrical and provided around the entire circumference. The edge of the rib 15d abuts against the second opposing surface 16a. The outer circumferential surface of the first sleeve 15 (including the outer circumferential surface of the rib 15d) and the outer circumferential surface of the second sleeve 16 are continuous with each other in the axial direction to form 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 circumferential surface of the core roll 13, and the inner circumferential surface of the rib 15d.

[0037] The rolling roll 11 is provided with a strain gauge 20 for measuring the strain of the roll body 12 inside the roll body 12. Two cables 29 are connected to each strain gauge 20.

[0038] The strain gauge 20 is disposed on the sleeve 14. The measured strain is used to estimate the stress on the roll surface 12a. Since the strain gauge 20 is disposed close to the roll surface 12a, the stress on the roll surface 12a can be estimated with high accuracy based on the strain measurement results.

[0039] The strain gauge 20 is provided on the second opposing surface 16a of the second sleeve 16. The strain gauge 20 is housed in the gap 12b and disposed closer to the center in the radial direction than the rib 15d. The strain gauge 20 is not sandwiched between the first sleeve 15 and the second sleeve 16, and a vertical force (in this case, a force in the axial direction of the roll body 12) does not act on the strain gauge 20. This improves the accuracy of strain measurement.

[0040] The rib 15d contributes to the formation of the gap 12b and thus to the prevention of the action of normal force. The rib 15d is provided not on the second sleeve 16 on which the strain gauge 20 is provided, but on the first sleeve 15 which faces the second sleeve 16 in the axial direction. Therefore, the second sleeve 16 is maintained in a uniform cylindrical shape while allowing the gap 12b to be formed. 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 by the strain gauge 20 provided on the second sleeve 16, which has a uniform cylindrical shape.

[0041] 4 and 5, the number of strain gauges 20 is preferably as large as possible, and is at least four or more. The multiple strain gauges 20 include two or more strain gauges 21, 22 arranged at different radial positions, and these two or more strain gauges 21, 22 measure two or more types of strain among radial strain, circumferential strain, and shear strain. The radial strain, circumferential strain, and shear strain are strains in different directions.

[0042] In this embodiment, the multiple strain gauges 20 include a circumferential strain gauge 21 and a radial strain gauge 22. The strain gauge 20 can measure two types of strain: circumferential strain and radial strain. A metal strain gauge (a strain gauge using an isotropic conductor) is a suitable example of the strain gauge 20. The strain gauge may be of either a linear type or a foil type. For example, the circumferential strain gauge 21 may be "FBYV-06-11-005LE" manufactured by Tokyo Measuring Instruments Laboratory. The radial strain gauge 22 may be "FBXV-04-11-005LE" manufactured by Tokyo Measuring Instruments Laboratory.

[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 resistor extending in a zigzag pattern between the pair of terminals. The five strain gauges 21a, 21b, 21c, 21d, and 21e are provided on an insulating film 21A and arranged in a direction perpendicular to the terminal facing direction. The resistors of each strain gauge extend 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 so 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 points that are different from each other in the radial direction.

[0044] The radial strain gauge 22 is disposed close to the circumferential strain gauge 21 in the circumferential direction of the roll body 12. The radial strain gauge 22 also includes five strain gauges 22a, 22b, 22c, 22d, and 22e arranged in a direction perpendicular to the terminal facing direction on the insulating film 22A. The resistors of each strain gauge extend 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 so 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 points that are different from each other in the radial direction.

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

[0046] 6, in assembling 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 taken 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] 2 and 6, next, while drawing out the cable 29, the second sleeve 16 is brought close to the first sleeve 15, the rib 15d is brought into contact with the second sleeve 16, and the strain gauge 20 is housed in the gap 12b. Furthermore, the cover 18a is fastened to the surface of the first sleeve 15 opposite the first opposing surface 15a, and the cover 18b is fastened to the surface of the second sleeve 16 opposite the second opposing surface 16a. In this way, the reduction roll 11 is completed.

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

[0049] With reference to FIG. 2, the stress calculation system 10 includes, in addition to the reduction roll 11, a data processing device 30, a communication device 41, a receiving device 42, a display device 43, and a rolling mill control device 44.

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

[0051] When strain occurs in the roll body 12, the signal values ​​of the strain gauges 21a to 21e, 22a to 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 obtains 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 central processing unit (CPU) or a micro processing unit (MPU) that cooperates with software to realize a predetermined function. The data processing device 30 may be configured with hardware circuits such as dedicated electronic circuits or reconfigurable electronic circuits designed to realize a predetermined function, or may be configured with various semiconductor integrated circuits. Examples of various semiconductor integrated circuits include a microcomputer, a digital signal processor (DSP), a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC), in addition to a CPU and an MPU. The data processing device 30 may include a storage device such as a random access memory (RAM) and a read only memory (ROM). Specifically, the data processing device 30 may be configured with, for example, an information processing device such as a desktop personal computer, a notebook computer, a workstation, or a tablet terminal, or a printed circuit board having an equivalent function.

[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 as a computer to execute a process of estimating the stress on the roll surface 12a.

[0054] The data processing program includes, in addition to the process of estimating the stress on the roll surface 12a, a process of displaying the estimated stress on the display device 43 and a process of outputting the estimation result to the rolling mill control device 44.

[0055] An operator can refer to the display on the display device 43 and 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 allows the amount of reduction, roll speed, rolling tension, etc. to be adjusted, optimizing the rolling process. Estimation results (feature values) transferred to the rolling mill control device 44 include the minimum value of the contact pressure and the distance from just below the roll when the contact pressure is at the minimum value (see FIG. 10).

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

[0058] 7, first, the measured strain (time history) is acquired (step S1). The strain measuring device 20 measures strain at a total of 10 locations. In this 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 this 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 this case, it becomes possible to measure strain approximately 3200 times per rotation of the roll and per measurement point. As described later, the data processing device 30 executes a high-order Fourier series expansion. To achieve this, it is considered that a sampling number of approximately 1000 times per rotation is necessary, and the above example satisfies this condition sufficiently.

[0060] Next, the data processing device 30 converts the information on the measured time history of the strain into information on 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 the strain (step S2). Fig. 8 conceptually illustrates this step S2. Fig. 8 illustrates the generation of information on 13 rotation angles θ from the time history of the strain, but in the above example, information on 3200 rotation angles θ is actually generated.

[0061] Referring to Fig. 9, when the rolling roll 11 is rotated continuously for multiple revolutions and the spatial distribution of strain is measured, it can be seen that the spatial distribution of strain varies according to the rotation angle θ, and that this variation is repeated in a period of 2π (corresponding to one revolution of the rolling roll 11). Fig. 9 shows an overlap of multiple measurement results obtained each time the rolling roll 11 makes one revolution. In step S2, the measurement results of 10 strain gauges during at least one revolution of the rolling roll 11 are obtained by linking them to the rotation angle θ. As described above, approximately 3200 measurement results of each strain gauge are obtained during one revolution of the rolling roll 11.

[0062] Next, the relationship between the coefficients of the n-th order Fourier series expansion of the strain and the coefficients of the stress function X is obtained as matrix coefficients (step S3).

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

[0064]

number

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

[0066]

number

[0067] Unknown variables and each stress component (radial stress σ r , circumferential stress σ θ , and shear stress τ rθ ) and the relationship between stress and strain based on elastic theory, each strain component (radial strain ε r , circumferential strain ε θ , and shear strain γ rθ ) can be expressed as the radial strain ε r is expressed by the following equation (3).

[0068]

number

[0069] On the other hand, the spatial distribution of the strain measured by each strain gauge obtained in step S2 is expressed by the following equation (4) by expanding it into a Fourier series.

[0070]

number

[0071] From equations (3) and (4), the following relational expressions (5) and (6) are obtained.

[0072]

number

[0073] In other words, from the strain measurement results, K n 1 (ε r :r) and K n 2 (ε r :r) are determined, and the unknown is A n ~H n There are eight unknowns A n ~H nTo obtain the strain, it is necessary to identify four types of strain measured independently of each other. Equations (5) and (6) depend on the measured strain direction and measurement position (radial position). Therefore, the four types of strain are strains measured at four different radial positions, or two types of strains measured at two different radial points with different strain directions (two points x two directions = four types).

[0074] In this embodiment, five circumferential strains and five radial strains are measured. There are multiple combinations of four types of strains selected from these total of 10 so as to satisfy the above condition.

[0075] The measurement results of the strain gauge 20 always contain measurement errors. Therefore, for each selected combination, the unknown A n ~H n The calculation results are different.

[0076] As can be seen from equation (2), the stress function X includes terms of n or -n powers. Therefore, when the Fourier order n becomes large, the numerical value of the term becomes very small or large, and the accuracy of stress estimation decreases. In some cases, even if the Fourier order n is not so large, the unknown A n ~H n And the unknown coefficient a n ~h n If the error in is large (unknown coefficient a n ~h n If the deviation to the larger value of is large, the n-th or -n-th 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 the measurement results containing noise, without including the results of higher-order calculations, and the accuracy of the stress estimation will be further reduced.

[0077] Therefore, in order to determine the unknowns using as much information as possible, the least squares method is adopted. To achieve this, the evaluation functions are defined as shown in the following equations (7) and (8).

[0078]

number

[0079] Radial strain ε r If you want to use something other than the Fourier series expansion of θ , and the radial derivative of strain ∂ε r / ∂r,∂ε θr Taking into account / ∂r, the more generalized evaluation functions are defined as the following equations (9) and (10). θ The radial differential value ∂ε is calculated from the measurement results of the strain gauge 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 By taking these factors into consideration, it is possible to remove synchronous electrical noise contained in the distortion signal.

[0080]

number

[0081] The unknown A that minimizes such an evaluation function n ~H n Then, we can find the unknown A in the higher order terms as small as possible. n ~H n In order to constrain the unknowns A as shown in the following equations (11) and (12), n ~H n The quadratic sum of is considered as a correction term.

[0082]

number

[0083] After step S3, the constraint coefficient λ is set (step S4). In view of the objective of the evaluation function (finding the minimum value), the constraint coefficient λ is a positive value. Then, from equations (11) and (12), the coefficient of the stress function X is determined according to the evaluation function taking into account the constraint coefficient λ (step S5). Next, using the coefficient of the stress function X, the Fourier expansion coefficient of the stress on the roll surface 12a is derived (step S6). Next, from the Fourier expansion coefficient of the stress on the roll surface 12a, the stress is derived as a function of the rotation angle θ 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 an example in FIG. 10, according to this embodiment, since the noise contained in the coefficients of the stress function X is suppressed, even higher order terms do not diverge when the Fourier series expansion is performed. For example, the 100th order term does not diverge and can be included in the stress estimation result. Therefore, a complex waveform estimation result can be obtained, and high estimation accuracy can be achieved.

[0086] Although the embodiment of the present invention has been described above, the above configuration can be appropriately added to, modified, or deleted within the scope of the present invention.

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

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

[0089] The direction of strain measured by the strain gauge 20 is not limited to circumferential strain, radial strain, and shear strain, and strain in a direction tilted at any angle from the radial direction may be measured. In this case, the circumferential strain, radial strain, and shear strain are obtained from the measured values ​​of strain obtained by measuring in a plurality of directions, and the coefficients of the stress function can be determined based on them. In addition, if the stress function is modified according to the direction of the strain to be measured, the coefficients of the stress function can be determined from the measured values ​​without converting them into circumferential strain, radial strain, and shear strain.

[0090] In the above-described embodiment, the strain measuring device 20 is configured with ten strain gauges, but the present invention is not limited to this, and it is sufficient that at least four strain measuring devices (strain gauges) are included.

[0091] Here, it is preferable that each of the four strain measuring instruments has at least one of its radial position (radial position) and the direction of the strain to be measured (strain measurement direction) different from that of the other three measuring instruments, except for the case where the four strain measuring instruments are at the same radial position but have different strain measurement directions.

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

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

[0094] The present disclosure may include the following aspects. (Aspect 1) A cylindrical roll body; four or more strain gauges for measuring strain of the roll body inside the roll body; A rolling roll comprising: (Aspect 2) The four or more strain gauges include four or more strain gauges arranged at different radial positions and measure the strain of the roll body in the same direction; or The four or more strain gauges include two or more strain gauges arranged at different positions in the radial direction, and measure the strain of the roll body in two or more different directions. 2. The rolling roll according to claim 1. (Aspect 3) The roll body includes a core roll and a sleeve attached to the outer circumferential side of the core roll to form a surface of the roll body, The strain gauge is disposed in the sleeve. The rolling roll according to aspect 1 or 2. (Aspect 4) the sleeve includes a first sleeve and a second sleeve adjacent in an axial direction, the first sleeve has a rib protruding from an outer circumferential edge of a surface facing the second sleeve and forming the surface of the roll body, The strain gauge is provided on a surface of the second sleeve facing the first sleeve and is disposed radially toward the center side of the rib. 4. The rolling roll according to claim 3. (Aspect 5) determining a stress function based on strains measured by four or more strain gauges disposed inside a roll body of the rolling roll; Calculating the stress on the surface of the roll body from the coefficients of the stress function. The data processing device is configured as follows. (Aspect 6) determining a stress function based on strains measured by four or more strain gauges disposed inside a roll body of the rolling roll; calculating a stress on the surface of the roll body from the coefficients of the stress function; A data processing program for causing a computer to execute the above. (Aspect 7) A rolling roll and a data processing device are provided. The rolling roll is A cylindrical roll body; and four or more strain gauges for measuring strain of the roll body inside the roll body, The data processing device, determining a stress function based on the strains measured by the four or more strain gauges; Calculating the stress on the surface of the roll body from the coefficients of the stress function. It is configured as follows: Stress calculation system. (Aspect 8) a strain measuring step of measuring strain of the roll body by four or more strain gauges arranged inside the roll body of the rolling roll; 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 coefficients of the determined stress function; A stress calculation method comprising: (Aspect 9) In the strain measuring step, strain in the same direction is measured at four or more different radial positions, or strain in two or more different directions is measured at two or more different radial positions. 9. The stress calculation method according to claim 8. (Aspect 10) In the data processing step, the measured strain is expanded into a Fourier series before determining the stress function. The stress calculation method according to aspect 8 or 9. (Aspect 11) In the data processing step, a radial derivative of the measured strain is used. The stress calculation method according to any one of aspects 8 to 10. (Aspect 12) In the data processing step, the coefficients of the stress function are calculated using constraint coefficients and a least squares method. 12. The stress calculation method according to any one of aspects 8 to 11. [Explanation of symbols]

[0095] 1. Rolling mill 1a Rolling actuator 2. Rolled materials 10 Stress calculation system 11 Rolling mill 11a, 11b Work roll 12 Roll body 12a Roll surface 12b Gap 13 core roll 13a Key groove 14 Sleeve 15 First Sleeve 15a 1st facing surface 15b Key groove 15c Tunnel 15d Rib 16 Second Sleeve 16a Second facing surface 16b Key groove 17 Sunken Key 18a,18b Cover 20 Strain Measuring Instrument 21 Circumferential strain gauge 21A Insulating Film 21a, 21b, 21c, 21d, 21e Strain gauge 22 Radial strain gauge 22A Insulating Film 22a, 22b, 22c, 22d, 22e Strain gauges 29 Cable 30 Data processing device 41 Communication equipment 42 Receiving device 43 Display device 44 Rolling Mill Control Device

Claims

1. A cylindrical roll body; four or more strain gauges for measuring strain of the roll body inside the roll body; A rolling roll comprising:

2. The four or more strain gauges include four or more strain gauges arranged at different radial positions and measure the strain of the roll body in the same direction; or The four or more strain gauges include two or more strain gauges arranged at different positions in the radial direction, and measure the strain of the roll body in two or more different directions. The rolling roll according to claim 1 .

3. The roll body includes a core roll and a sleeve attached to the outer circumferential side of the core roll to form a surface of the roll body, The strain gauge is disposed in the sleeve. The rolling roll according to claim 1 or 2.

4. the sleeve includes a first sleeve and a second sleeve adjacent in an axial direction; the first sleeve has a rib protruding from an outer circumferential edge of a surface facing the second sleeve and forming the surface of the roll body, the strain gauge is provided on a surface of the second sleeve facing the first sleeve and is disposed radially toward the center side of the rib; The rolling roll according to claim 3.

5. determining a stress function based on strains measured by four or more strain gauges disposed inside a roll body of the rolling roll; Calculating the stress on the surface of the roll body from the coefficients of the stress function. The data processing device is configured as follows.

6. determining a stress function based on strains measured by four or more strain gauges disposed inside the roll body of the rolling roll; calculating a stress on the surface of the roll body from the coefficients of the stress function; A data processing program for causing a computer to execute the above.

7. A rolling roll and a data processing device are provided. The rolling roll is A cylindrical roll body; and four or more strain gauges for measuring strain of the roll body inside the roll body, The data processing device, determining a stress function based on the strains measured by the four or more strain gauges; Calculating the stress on the surface of the roll body from the coefficients of the stress function. It is configured as follows: Stress calculation system.

8. a strain measuring step of measuring strain of the roll body by four or more strain gauges arranged inside the roll body of the rolling roll; 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 coefficients of the determined stress function; A stress calculation method comprising:

9. In the strain measuring step, strain in the same direction is measured at four or more different radial positions, or strain in two or more different directions is measured at two or more different radial positions. The stress calculation method according to claim 8.

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

11. In the data processing step, a radial derivative of the measured strain is used. The stress calculation method according to claim 8.

12. In the data processing step, the coefficients of the stress function are calculated using constraint coefficients and a least squares method. The stress calculation method according to any one of claims 8 to 11.

Images