JP2015175628A - Stress distribution measurement instrument, strain distribution measurement instrument, and stress distribution measurement program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To allow accurate measurement of a fine distribution of non-uniform strain locally generated in a breadthwise direction of a band-like body.SOLUTION: Oscillatory displacement generated in a band-like body due to an oscillatory load applied to the band-like body 1 is measured by first displacement meters 8 respectively provided for a plurality of first measurement points 1b arrayed on the band-like body 1, at the corresponding first measurement points 1b. The oscillatory displacement generated in the band-like body due to the oscillatory load applied to the band-like body 1 is measured by second displacement meters 9 respectively provided for second measurement point groups 1d provided on the band-like body 1, at a plurality of second measurement points 1c in the corresponding second measurement points 1d. Intervals of the second measurement points 1c in each of the second measurement point groups 1d is shorter than the shortest interval out of intervals of the first measurement points 1b.

Description

  The present invention relates to a stress distribution measuring device and a stress distribution measuring program for measuring a stress distribution in the width direction of a strip, and a strain distribution measuring device for measuring a strain distribution in the width direction of the strip.

  For example, in a manufacturing process of a strip-like body such as a steel plate or an aluminum thin plate, a shape defect may occur such that the strip-like body distorts due to deformation of a roll during rolling or thermal deformation during heat treatment. This shape defect may be caused by the middle extension of the strip in the width direction, the otic waves distorted at both ends of the strip in the width direction, or the stretch of one side of the strip in the width direction, depending on the line operating conditions. , Occur in various patterns. In particular, since the ear waves cause a coating failure at both ends in the width direction of the belt-like body in the painting line in the lower process, detection of the ear waves is extremely important for quality assurance.

  Therefore, Patent Document 1 discloses a strip-shaped body shape measuring device that measures the shape of a strip-shaped body in order to detect an ear wave. In this shape measuring apparatus, the surface of the rolled material conveyed in the longitudinal direction is irradiated with slit light in the longitudinal direction from a light source, and the slit light is imaged with a two-dimensional camera, so that the shape of the belt-like body along the traveling track is obtained. Is measuring.

JP 2011-242298 A

  However, since the shape measuring apparatus of Patent Document 1 is configured to measure the shape of the belt-like body along the longitudinal direction, which is the conveying direction of the rolled material, the non-uniform strain distributed in the width direction of the rolled material is measured in detail. It is difficult to do. Further, in the case where tension is applied in the longitudinal direction of the belt-like body, since the strained shape is stretched in the longitudinal direction to be an apparently flat shape, Patent Document 1 that measures the shape of the belt-like body along the longitudinal direction. Measurement methods cannot be applied.

  An object of the present invention is to provide a stress distribution measuring device, a strain distribution measuring device, and a stress distribution measuring program capable of accurately measuring a detailed distribution of non-uniform strain locally generated in the width direction of a strip. It is to be.

  The present invention is a stress distribution measuring apparatus for measuring a stress distribution in a width direction of a belt-like body to which a tension is applied in a longitudinal direction between support parts supported by two parts in the longitudinal direction, Vibration load adding means for applying a vibration load to the band between the supporting portions of the location, and vibration displacement generated in the band by the vibration load applied to the band. Based on the vibration measurement means for measuring at a plurality of measurement points provided side by side in the width direction, and the natural frequency and vibration mode of the strip obtained from the vibration displacement measured at the plurality of measurement points, Stress distribution calculation means for calculating a stress distribution in the width direction of the belt-like body, and the plurality of measurement points are composed of a plurality of first measurement points and a plurality of second measurement points, and at least one of the above-mentioned measurement points A first measurement point and a plurality of the second measurement points Second measurement point groups consisting of measurement points are alternately arranged, and the interval between the second measurement points in the second measurement point group is narrower than the shortest interval among the intervals between the first measurement points. The vibration measurement means is provided for each of the first measurement points, and a plurality of first vibration measurement means for measuring vibration displacement generated in the belt-like body at the corresponding first measurement points, A second vibration measuring unit that is provided for each second measurement point group and measures vibration displacement generated in the belt-like body at each of the plurality of second measurement points in the corresponding second measurement point group; It is characterized by.

  According to the present invention, the first vibration measurement unit that measures the vibration displacement at the corresponding first measurement point, and the second vibration measurement that measures the vibration displacement at each of the plurality of second measurement points in the corresponding second measurement point group. Means. Since the interval between the second measurement points in the second measurement point group is narrower than the shortest interval among the intervals between the first measurement points, the vibration displacement at the location where the second measurement point group is provided is described in detail. It can be measured. As a result, it is possible to accurately measure non-uniform distortion at the location where the second measurement point group is provided. Therefore, the location where the second measurement point group is provided is set in the both ends in the width direction of the strip, the center in the width direction of the strip, and the region closer to the center by a quarter width from both ends in the width direction of the strip. By doing so, it is possible to accurately measure the ear waves, the medium elongation, and the quarter distortion. As a result, it is possible to accurately measure the detailed distribution of non-uniform distortion that occurs locally in the width direction of the belt-like body.

  In addition, if the number of measurement points is increased over the entire length of the strip in the width direction, the number of measurement data increases and the calculation time required to calculate the stress distribution becomes longer. It is not preferable. However, by providing the second measurement point group at the desired location in the width direction of the strip and increasing the number of measurement points only at this location, the increase in the number of measurement data can be suppressed, greatly increasing the calculation time. Can be shortened.

It is a figure which shows the structure of a distortion distribution measuring apparatus. It is a perspective view of a 2nd displacement meter. It is a perspective view of a 2nd displacement meter. It is a schematic diagram of an ear wave. It is a schematic diagram of quarter distortion. It is a schematic diagram of middle elongation. It is a figure which shows the hardware constitutions of an arithmetic unit. It is a figure which shows an example of a setting input screen. It is a figure which shows an example of a bar graph display screen. It is a figure which shows an example of a three-dimensional graph display screen. It is a figure which shows an example of a data sheet. It is a figure which shows the structure of a strain distribution measuring system. It is a figure which shows the function of a strain distribution measurement program. It is a figure which shows a two-dimensional non-uniformly spaced mass point system model. It is a flowchart which shows the procedure which measures strain distribution. It is a graph which shows the relationship between a board width direction position and stress distribution. It is a graph which shows the relationship between a board width direction position and stress distribution. It is a graph which shows the relationship between a board width direction position and strain distribution. It is a graph which shows the relationship between a board width direction position and stress distribution. It is a graph which shows the relationship between a board width direction position and stress distribution. It is a graph which shows the relationship between a board width direction position and strain distribution. It is a figure which shows the time-dependent change of strain distribution. It is a flowchart which shows the procedure which measures strain distribution. It is a conceptual diagram of the calculation model of additional mass. It is explanatory drawing explaining the method of calculating additional mass. It is a figure which shows the example of calculation of additional mass distribution. It is explanatory drawing explaining the method of reducing the mass in each node of the longitudinal direction of a strip | belt shaped object to the equivalent mass of one point. It is explanatory drawing explaining the method to reduce an additional mass distribution to the longitudinal direction of a strip | belt shaped object. It is explanatory drawing explaining the reduction method in the width direction of additional mass distribution. It is explanatory drawing explaining the reduction method in the width direction of additional mass distribution. It is a flowchart which shows the procedure which measures strain distribution. It is a figure which shows the structure of a distortion distribution measuring apparatus. It is a figure which shows the structure of a distortion distribution measuring apparatus.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

[First Embodiment]
(Configuration of strain distribution measuring device)
The strain distribution measuring apparatus 101 according to the first embodiment of the present invention includes all the configurations of the stress distribution measuring apparatus 100 according to the present embodiment. As shown in FIG. 1 which is a configuration diagram, the stress distribution measuring apparatus 100 is configured to support the stress distribution in the width direction of the belt-like body 1 applied with tension in the traveling longitudinal direction at two portions in the longitudinal direction. , 2b is measured between the support parts supported by 2b. The strain distribution measuring apparatus 101 calculates the strain distribution in the width direction of the strip 1 based on the calculated stress distribution.

  The strain distribution measuring apparatus 101 amplifies a load signal input to the vibration load applying apparatus 3 (vibration load adding means) 3 for applying a vibration load to the strip 1 between two support parts and the vibration load adding apparatus 3. And an amplifier 6.

  The vibration load applying device 3 applies a vibration load to the band 1 by intermittently injecting air toward the band 1. The vibration load applying device 3 includes a device that intermittently ejects liquid such as water and oil, and a device that applies a vibration load to the band 1 by magnetic force, electrostatic force, eddy current due to electromagnetic induction, sound waves, and the like. You can also Moreover, it can also be set as the apparatus which strikes one point of the strip | belt-shaped body 1, or the apparatus which vibrates either support roll 2a, 2b. The amplifier 6 amplifies a load signal described later.

  In addition, the strain distribution measuring apparatus 101 includes a plurality of measurement points 1a provided on the strip 1 in a line in the width direction of the strip 1 with vibration displacement generated in the strip 1 due to the vibration load applied to the strip 1. A plurality of non-contact displacement gauges (vibration measuring means) 4 for measuring in FIG.

  Here, the plurality of measurement points 1a includes a plurality of first measurement points 1b and a plurality of second measurement points 1c. On the strip 1, a plurality of first measurement points 1 b and a second measurement point group 1 d including a plurality of second measurement points 1 c are provided alternately.

  In the present embodiment, three first measurement points 1b are provided at equal intervals in the center of the strip 1 in the width direction. The interval between the first measurement points 1b is, for example, about 100 mm. In addition, the number of the 1st measurement points 1b and the space | interval of the 1st measurement points 1b are not limited to this. Further, the interval between the first measurement points 1b is not limited to an equal interval, and for example, the closer to the end in the width direction of the band 1, the closer to the center in the width direction of the band 1, and the closer to the center. , Unequal intervals may be used.

  In the present embodiment, the second measurement point group 1 d is provided at both ends in the width direction of the strip 1. The intervals between the second measurement points 1c in the second measurement point group 1d are equal intervals, and are narrower than the intervals between the first measurement points 1b. Note that the interval between the second measurement points 1c is not limited to an equal interval. For example, the closer to the end in the width direction of the band 1, the closer the band 1 The unequal intervals may be used, such as closer to the center in the width direction of 1. The interval between the measurement points 1a is an unequal interval in which the interval between the first measurement points 1b and the interval between the second measurement points 1c are mixed.

  When the intervals between the first measurement points 1b are unequal, the interval between the second measurement points 1c in the second measurement point group 1d is shorter than the shortest interval among the intervals between the first measurement points 1b. Narrowed.

  The displacement meter 4 measures vibration displacement at each of a first displacement meter (first vibration measurement means) 8 that measures vibration displacement at the first measurement point 1b and a plurality of second measurement points 1c in the second measurement point group 1d. And a second displacement meter (second vibration measuring means) 9 for measuring.

  The first displacement meter 8 is provided for each of the plurality of first measurement points 1b, and measures the vibration displacement at the corresponding first measurement point 1b. In the present embodiment, three first displacement meters 8 are provided.

  In the present embodiment, the first displacement meter 8 is a light reflection type laser displacement meter. The first displacement meter 8 is arranged directly above the corresponding first measurement point 1b, and images the laser beam reflected and irradiated on the first measurement point 1b with a camera. Therefore, the three first displacement meters 8 are arranged at equal intervals in the width direction of the strip 1 above the strip 1. The interval between the first displacement meters 8 is the same as the interval between the first measurement points 1b.

  The first displacement meter 8 has a configuration in which an irradiation unit that irradiates the first measurement point 1b with a laser and an imaging unit that captures the laser light reflected at the first measurement point 1b with a camera are separated from each other. The laser may be irradiated obliquely with respect to the surface of the body 1. In this case, the first displacement meters 8 do not need to be arranged in the width direction of the strip 1 above the strip 1. When the strip 1 is conductive, the first displacement meter 8 can be an eddy current displacement meter that detects the magnitude of the eddy current generated in the strip 1 or the strip 1 and the sensor. It can also be a capacitance displacement meter or the like that detects the capacitance between the head and the head. Furthermore, some of the first displacement meters 8 may be movable in the width direction of the band 1.

  The second displacement meter 9 is provided for each second measurement point group 1d, and measures the vibration displacement at each of the plurality of second measurement points 1c in the corresponding second measurement point group 1d. In the present embodiment, two second displacement meters 9 are provided.

  In the present embodiment, the second displacement meter 9 is a light reflection type laser displacement meter. The second displacement meter 9 includes a second measurement provided directly above the second measurement point group 1 d provided at one end portion in the width direction of the strip 1 and at the other end portion in the width direction of the strip 1. Laser light that is arranged directly above the point group 1d and is irradiated and reflected on each of the plurality of second measurement points 1c in the second measurement point group 1d is imaged by a camera. Therefore, the two second displacement meters 9 are arranged in the width direction of the strip 1 together with the three first displacement meters 8 above the strip 1.

  In the present embodiment, the second displacement meter 9 irradiates the strip 1 with a sheet laser 9a having a two-dimensional spread as shown in FIG. 2A, which is a perspective view. The second displacement meter 9 can measure the vibration displacement in all the linear regions on the strip 1 irradiated with the sheet laser 9a. That is, the second measurement point 1c is provided in all the linear regions on the belt-like body 1 irradiated with the sheet laser 9a.

  The second displacement meter 9 has a configuration in which an irradiation unit that irradiates the second measurement point group 1d with the sheet laser 9a and an imaging unit that captures the sheet laser light reflected by the second measurement point group 1d with a camera are separated. In this case, the sheet laser 9a may be irradiated obliquely with respect to the surface of the band 1. In this case, the two second displacement meters 9 do not need to be arranged in the width direction of the strip 1 together with the three first displacement meters 8 above the strip 1. Furthermore, some of the second displacement meters 9 may be movable in the width direction.

  Further, as shown in FIG. 2B which is a perspective view, the second displacement meter 9 may irradiate the strip 1 with a plurality of spot-like lasers 9b. That is, the second displacement meter 9 includes a plurality of displacement meters (third vibration measuring means) similar to the first displacement meter 8. The number of the lasers 9b is about 10, and the interval between the lasers 9b is about 10 mm. That is, ten second measurement points 1c are arranged at intervals of about 10 mm at locations on the strip 1 irradiated with the laser 9b. The number of lasers 9b and the interval between the lasers 9b are not limited to this, and the interval may be set to 20 mm or 5 mm depending on the fineness of the strain distribution to be evaluated.

  Here, due to deformation of the roll at the time of rolling or thermal deformation at the time of heat treatment, there may be a shape defect in which the strip 1 is distorted so as to wave. This shape defect occurs in various patterns depending on the operating conditions of the line. 3A, which is a schematic diagram, has a shape defect in which both end portions in the width direction of the band 1 are distorted. The quarter distortion shown in FIG. 3B, which is a schematic diagram, is a defective shape in which a region closer to the center is distorted by about ¼ width from both ends in the width direction of the band 1. The middle elongation shown in FIG. 3C, which is a schematic diagram, is a defective shape in which the central portion in the width direction of the band 1 is distorted.

  Therefore, in this embodiment, as shown in FIG. 1, the second measurement point group 1d is provided at both ends in the width direction of the strip 1 to measure the vibration displacement at both ends of the strip 1 in detail. Yes. That is, the present embodiment is configured to measure the ear waves shown in FIG. 3A in detail.

  Further, as shown in FIG. 1, the strain distribution measuring apparatus 101 calculates the strain distribution in the width direction of the strip 1 based on the outputs of the first displacement meters 8 and the second displacement meters 9. have.

  The arithmetic unit 5 includes a modeling unit (modeling unit) 5a, a load signal output unit 5b, a vibration signal input unit 5c, a vibration characteristic calculation unit 5d, a spring constant calculation unit (spring constant calculation unit) 5e, Spring constant conversion unit (spring constant conversion unit) 5f, stress distribution calculation unit (stress distribution calculation unit) 5g, strain distribution calculation unit (strain distribution calculation unit) 5h, strain distribution graph display unit 5i, and data sheet creation Part 5j.

  The modeling unit 5a models the strip 1 into a two-dimensional unequal interval multi-mass point system model. The load signal output unit 5 b outputs a load signal toward the vibration load adding device 3. The vibration signal input unit 5c includes a vibration signal related to the vibration displacement of each first measurement point 1b measured by each first displacement meter 8 and each second measurement point 1c measured by each second displacement meter 9. A vibration signal related to the vibration displacement is input.

  The vibration characteristic calculation unit 5d calculates vibration characteristics such as a natural frequency and a vibration mode from the vibration signal input to the vibration signal input unit 5c. The spring constant calculation unit 5e calculates the spring constant of the two-dimensional unequal interval multi-mass point system model from the calculated natural frequency and vibration mode. The spring constant conversion unit 5f converts each spring constant of the calculated linear spring into a stress value at each measurement point 1a. The stress distribution calculation unit 5g calculates the stress distribution in the width direction of the strip 1 from the converted stress value at each measurement point 1a.

  The strain distribution calculation unit 5h calculates a strain distribution in the width direction of the strip 1 based on the calculated stress distribution. The strain distribution graph display unit 5i displays the calculated strain distribution as a strain distribution graph. The data sheet creation unit 5j outputs the calculated strain distribution as a data sheet.

  The arithmetic unit 5 includes, for example, a CPU (Central Processing Unit), a program executed by the CPU, a storage device that stores data used for these programs in a rewritable manner, and a program execution like a general personal computer Any device may be used as long as it includes a temporary storage device such as a RAM (Random Access Memory) that temporarily stores data. Each of the functional units 5a to 5j included in the arithmetic device 5 is constructed in cooperation with these hardware and software in the storage device. For example, the software includes a program for analyzing the natural frequency and the vibration mode from the measured vibration displacement. Note that the arithmetic device 5 is not limited to a single unit, and the functions of the functional units 5a to 5j are distributed to a plurality of devices each having the hardware and software in the storage device. It may be a thing.

  The stress distribution measuring apparatus 100 of the present embodiment includes a modeling unit 5a, a load signal output unit 5b, a vibration signal input unit 5c, and a vibration characteristic calculation unit 5d among the functional units 5a to 5j included in the arithmetic device 5. And a spring constant calculation unit 5e, a spring constant conversion unit 5f, and a stress distribution calculation unit 5g. In addition to the functional units 5a to 5g included in the stress distribution measuring device 100, the strain distribution measuring device 101 of the present embodiment includes a strain distribution calculating unit 5h, a strain distribution graph display unit 5i, a data sheet creating unit 5j, have.

(Hardware configuration of arithmetic unit)
Next, the hardware configuration of the arithmetic device 5 is shown in FIG. The arithmetic device 5 includes a CPU 11, a temporary storage device 12, a storage device 13, a signal input / output device 14, a setting input device 15, a display device 16, and a data sheet creation device 17. The CPU 11 is a circuit that executes a strain distribution measurement program, which will be described later, and performs general numerical calculations such as band-shaped body modeling calculation, additional mass modeling calculation (only in the second embodiment), vibration characteristic calculation, and strain distribution calculation.

  The temporary storage device 12 temporarily stores the program body when executing the strain distribution measurement program. In addition, the temporary storage device 12 determines the dimensions and physical properties of the strips necessary for various calculations performed by the CPU 11 and the interval information of the measurement points 1a (the interval between the first measurement points 1b and the interval between the second measurement points 2c. Related information), additional mass information (only in the second embodiment), model data after modeling of the band, vibration characteristic data, calculated spring constant, stress distribution, strain distribution data, and the like are temporarily stored. The temporary storage device 12 is configured by a device capable of transferring relatively small data such as a RAM at a high speed.

  The storage device 13 is a device that stores data calculated by the CPU 11 and stores it as a database. The storage device 13 includes, for example, an HDD (Hard Disk Drive) that is a nonvolatile storage device, a flash memory, an optical disk, and the like. The storage device 13 stores model data after modeling of the belt-like body, vibration characteristic data, calculated spring constant, stress distribution, strain distribution data, and the like. For example, when the size of the strip changes, the strip model data or the like needs to be updated to a model calculated with a new size. However, when a strip having the same dimensions is passed, it is possible to omit the modeling calculation by reading again the value calculated and stored in the previous measurement.

  The signal input / output device 14 outputs a load signal toward the vibration load applying device 3 (see FIG. 1) and is sent from each first displacement meter 8 and each second displacement meter 9 (see FIG. 1). A device to which a vibration signal is input. The signal input / output device 14 includes, for example, a transmitter, a data logger, an AD / DA board, and the like.

  The setting input device 15 is a device for a user to make various inputs. The setting input device 15 includes, for example, a mouse, a keyboard, and a touch panel provided so as to be superimposed on the screen of the display device 16. The user starts, stops, and terminates the strain distribution measurement program via the setting input device 15, and measures the dimensions and physical properties of the strip, the interval information of the measurement points 1 a, and the physical properties of air for calculating additional mass (first 2 only). An example of the setting input screen is shown in FIG. Further, by operating the setting input device 15, for example, the strain distribution data is read from the storage device 13 storing the strain distribution data measured in the past and displayed on the display device 16 or a data sheet is created. can do.

  Returning to FIG. 4, the display device (display means) 16 is a device that displays the measured strain distribution data, stress distribution data, total tension data, and the like so that the user can confirm them. The display device 16 includes, for example, an LCD (Liquid Crystal Display) or a CRT (Cathode Ray Tube). A CPU (graphing means, display control means) 11 graphs strain distribution data and the like and causes the display device 16 to display the graph. An example of the bar graph display screen is shown in FIG. 6, and an example of the three-dimensional graph display screen is shown in FIG.

  Returning to FIG. 4, the data sheet creation device (data sheet creation means) 17 is a device for the user to output measured strain distribution data, stress distribution data, total tension data, and the like as a data sheet. The data sheet creation device 17 includes, for example, a printer that prints data on paper, software that converts the data into electronic data such as a PDF file, and the like. A CPU (sampling means, data sheet creation control means) 11 samples strain distribution data and causes the data sheet creation device 17 to create a data sheet based on the strain distribution data. An example of data sheet output is shown in FIG.

(Configuration of strain distribution measurement system)
Next, the configuration of the strain distribution measurement system is shown in FIG. The load signal output from the personal computer 21 is input to the electromagnetic valve drive circuit (amplifier) 23 via the AD / DA board 22 and amplified. For example, an impulse waveform or a frequency sweep waveform is used as the load signal. In particular, when a vibration load is applied in the frequency range where the natural frequency of the band-like body exists using the frequency sweep waveform, the natural vibration mode is excited and effective measurement is possible.

  The electromagnetic valve 24 is driven by the load signal amplified and output from the electromagnetic valve drive circuit 23. As a result, the air nozzle 26 connected to the factory air pipe 25 is opened, and air is jetted from the air nozzle 26 toward the band 27. The vibration of the excited band 27 is measured by a displacement meter 28 including a first displacement meter 8 and a second displacement meter 9 (see FIG. 1) installed in the width direction. The vibration signal output from the displacement meter 28 is input to the personal computer 21 via the AD / DA board 22. The personal computer 21 executes mode analysis using the measured vibration signal, calculates vibration characteristics such as the natural frequency and vibration mode of the band 27, and calculates the stress distribution from the natural frequency and vibration mode. Then, the personal computer 21 calculates a strain distribution from the calculated stress distribution and displays the calculation result on the screen. When the measurement is finished, the process is finished as it is, and when the measurement is not finished, the same operation is repeatedly executed from where the load signal is outputted.

(Function of strain distribution measurement program)
Next, FIG. 10 shows functions of a strain distribution measurement program executed by the personal computer 21 of FIG. 9, more specifically, the CPU 11 of FIG. This strain distribution measurement program includes all the configurations of the stress distribution measurement program of the present embodiment. The stress distribution measurement program measures the stress distribution in the width direction of the belt-like body 1 given tension in the running longitudinal direction between the support parts supported by the support rolls 2a and 2b at two parts in the longitudinal direction. To make the computer function. The strain distribution measurement program causes the computer to function to calculate the strain distribution in the width direction of the strip 1 based on the calculated stress distribution.

  The user inputs the dimensions and physical properties of the band 1 (hereinafter referred to as band information) and the interval information of the measurement points 1a to the band information input unit 31. The band information input by the user, the interval information of the measurement points 1a, and the like are displayed on the band information display unit 32. Therefore, the user can confirm the set value. In a second embodiment to be described later, the user inputs physical properties of air, pressure and temperature conditions (hereinafter referred to as additional mass information) to the additional mass information input unit 33. The additional mass information input by the user is displayed on the additional mass information display unit 34. Therefore, the user can confirm the set value.

  The strain distribution measurement program searches past model data stored in the storage unit 35 from the input band information (in the second embodiment, band information and additional mass information). If the same model is found, the model data is copied to the temporary storage unit 36. On the other hand, when the same model is not found, a two-dimensional model of the band is created by the band modeling unit 37 using the input band information. In the second embodiment, the additional mass modeling unit 38 creates an additional mass model using the input additional mass information. The strain distribution measurement program stores the created model data in the temporary storage unit 36 and stores a copy of the model data in the storage unit 35.

  Next, the strain distribution measurement program outputs a load signal from the load signal output unit 39 to the vibration load applying device 3 (see FIG. 1), and each first displacement meter 8 and each first input to the vibration signal input unit 40. The vibration signal from the two-displacement meter 9 (see FIG. 1) is stored in the temporary storage unit 36. Then, the vibration characteristic calculation unit 41 calculates vibration characteristics such as the natural frequency and vibration mode of the strip from the measured vibration signal, and stores the vibration characteristics in the temporary storage unit 36.

  Next, the strain distribution measurement program calculates the spring constant of the belt-shaped body model in the spring constant calculation unit 42 from the model data and vibration characteristic data stored in the temporary storage unit 36 and stores it in the storage unit 45. Further, the stress distribution calculation unit 43 calculates the stress distribution from the spring constant and stores it in the storage unit 45. Further, the strain distribution calculation unit 44 calculates the strain distribution from the stress distribution value and stores it in the storage unit 45.

  Next, the strain distribution measurement program graphs the stress distribution data and strain distribution data stored in the storage unit 45 and causes the display unit 46 to display the graph. Further, the data sheet creation unit 47 is made to create a data sheet in accordance with a user operation.

(2D non-uniformly spaced mass model)
Next, FIG. 11 shows a two-dimensional unequal interval multi-mass point system model in which the band 1 is modeled by the modeling unit 5a (see FIG. 1). This two-dimensional unequal-interval multi-mass point system model is obtained by adding each node 51 to a node 51 corresponding to each measurement point 1a (each first measurement point 1b and each second measurement point 1c) in the band 1 between the support parts. A straight spring 52 simulating the stress acting on the slab is connected and simplified to a two-dimensional model of the width direction of the strip 1 and the vibration direction of each measurement point 1a. Each node 51 is connected to a fixed surface 53 extending so as to coincide with the width direction of the belt-like body 1 by each linear spring 52 perpendicular thereto. Further, adjacent nodes 51 are connected by a connecting member 54 that is rotatable in a two-dimensional plane. Further, the adjacent connecting members 54 are connected by a rotation spring 55. The mass of each connecting member 54 is the mass of the strip 1 at the width direction portion. The spring constant of the rotary spring 55 is the bending rigidity of the strip 1 at each node 51.

Here, the order of the plurality of measurement points 1a is assumed to be first, second, third,..., I-th (i = 1 to n) from left to right in the width direction of the strip 1. n is a natural number. k _i is a spring constant simulating the stress at the i-th measurement point 1a. m _{i, i + 1} is the partial mass of the strip 1 between the i-th measurement point 1a and the (i + 1) -th measurement point 1a. J _{i, i + 1} is a partial moment of inertia of the strip 1 between the i-th measurement point 1a and the (i + 1) -th measurement point 1a. l _{i, i + 1} is the distance between the i-th measurement point 1a and the (i + 1) -th measurement point 1a. τ _i is the rotational spring constant of the strip 1 at the i-th measurement point 1a.

  In this way, the two-dimensional unequally spaced multi-mass point system model was vibrated by the vibration load adding device 3 while paying attention to the correlation between the magnitude of the tension of the strip 1 and the magnitude of the natural frequency. Assuming that the vibration displacement at each measurement point 1 a of the strip 1 is equal to the vibration displacement at each node 51 of each linear spring 52, the stress distribution in the width direction of the strip 1 is defined as a change in the spring constant of the linear spring 52. It is modeled to grasp.

(Strain distribution measurement method)
Next, FIG. 12 shows a procedure of a strain distribution measuring method in which the strain distribution measuring apparatus 101 according to the first embodiment calculates the strain distribution in the width direction of the strip 1. This strain distribution measuring method is executed by the strain distribution measuring program described above using the strain distribution measuring apparatus 101 described above. Hereinafter, a description will be given with reference to FIGS. 1 and 4.

  First, it is determined whether or not the model data of the strip 1 having the same dimensions as the strip 1 to be measured (see FIG. 1) is stored in the storage device 13 (see FIG. 4) of the arithmetic unit 5 (step S1). Hereinafter, this is simply referred to as S1, and so on. When it is determined that the same type of model data is not stored in the storage device 13 (S1: NO), the band information input from the setting input device 15 (see FIG. 4) by the user (such as the dimensions of the band 1) Based on the physical properties and the like and the interval information of the measurement points 1a (see FIG. 1), the modeling unit 5a (see FIG. 1) models the strip 1 into a two-dimensional unequal interval multi-mass point system model (S5). . Then, the model data is stored in the storage device 13 (S7). On the other hand, when it is determined that the same type of model data is stored in the storage device 13 (S1: YES), the same type of model data is read from the storage device 13 (S8).

  Hereinafter, a description will be given with reference to FIG. After S7 or S8, a load signal is output from the load signal output unit 5b toward the vibration load applying device 3 so that a load is applied to the strip 1 by the vibration load adding device 3 (S11). Then, the vibration displacement of the strip 1 is measured by each first displacement meter 8 and each second displacement meter 9 (S12). The vibration signal related to the measured vibration displacement is input to the vibration signal input unit 5c. The vibration characteristic calculation unit 5d calculates vibration characteristics such as the natural frequency and vibration mode of the modeled strip 1 (S13). The spring constant of the strip 1 is calculated by the spring constant calculator 5e (S14). The spring constant conversion unit 5f converts the spring constant into a stress value, and the stress distribution calculation unit 5g calculates the stress distribution in the width direction of the strip 1 from the stress value (S15).

  Then, based on the calculated stress distribution, the strain distribution calculation unit 5h calculates the strain distribution of the strip 1 (S16). The strain distribution graph display unit 5i displays the calculated strain distribution on the display device 16 (see FIG. 4) as a strain distribution graph (S17). Thereafter, it is determined whether or not to end the measurement (S18). When the measurement is continued (S18, NO), the process returns to step S11 and the measurement is repeated. On the other hand, when the measurement is finished (S18, YES), the data sheet creation unit 5j causes the data sheet creation device 17 (see FIG. 4) to create a data sheet based on the calculated strain distribution (S19). After creating the data sheet, the flow ends.

(Measurement method of stress distribution)
Next, a method for measuring the stress distribution of the strip 1 using the strain distribution measuring apparatus 101 described above will be specifically described with reference to FIGS.

The equation of motion of the two-dimensional unequally spaced multi-mass point system model is that the mass matrix of the strip 1 is M, the displacement vector of each node 51 is x, the acceleration vector is α, and the tension stiffness matrix corresponding to the spring constant of each linear spring 52 Is represented by Equation (1), where K _{T is} a bending stiffness matrix corresponding to the spring constant of the rotary spring 55, and Kτ.
Mα + (K _T + Kτ) x = 0 (1)

Here, the mass matrix M of the strip 1 is a known matrix calculated from the dimensions and physical properties of the strip 1 and is represented by Expression (2).

Eigenvalue analysis is performed using equation (3) so that the eigenvalue λ and eigenvector φ satisfying M ⁻¹ (K _T + Kτ) φ = λφ are calculated from the equation of motion of equation (1).
(Φ ^T MΦ) ⁻¹ Φ ^T (K _T + Kτ) Φ = Λ (3)
Here, Λ is a diagonal matrix having eigenvalues as diagonal elements, and Φ is an orthogonal matrix having eigenvectors as column vectors.

The eigenvalue Λ and the eigenvector Φ calculated by the eigenvalue analysis are expressed by equations (4), (5), and (6), respectively.
Φ = [φ ₁ φ ₂ ... φ _n ] (5)
φ _i = {φ _i1 φ _i2 ... φ _in } (6)

In the vibration characteristic calculation unit 5d, the natural frequency ω (angular frequency) and the vibration mode vector v are determined based on the vibration displacement measured at each measurement point 1a (each first measurement point 1b and each second measurement point 1c). Calculated. The i-th order natural frequency ω _i and the vibration mode vector v _i are expressed by equations (7) and (8).
ω _i = {ω _i1 ω _i2 ... ω _in } ^T (7)
v _i = {v _i1 v _i2 ... v _in } ^T (8)
Here, n is the number of measurement points 1a.

The tension stiffness matrix K _T corresponding to the spring constant of the linear spring 52 included in the function of the eigenvalue Λ and the eigenvector Φ calculated by Expression (3) is an unknown. The bending stiffness matrix Kτ for bending the belt-like body 1 in the width direction is a known number determined by the cross-sectional second moment with respect to the bending. The bending stiffness matrix Kτ is expressed by Expression (9) using the spring constant τ _j (j = 1 to n−2) of the rotary spring 55.

Therefore, in the spring constant calculation unit 5e, the eigenvalue Λ and the eigenvector Φ shown in the equations (3) and (4), (5), and (6) are calculated in the vibration characteristic calculation unit 5d, respectively. A tension stiffness matrix K _T that matches the natural frequency ω _i and the vibration mode vector v _i shown in (7) and (8) is determined using the evaluation function J shown in Expression (10).
Here, the integration number m is the mode order of vibration. Specifically, to calculate the evaluation function J and the initial values to the tension stiffness matrix K _T. Then, the value of the tension stiffness matrix K _T when the change amount of the evaluation function J in the repetitive calculation in which the value of the tension stiffness matrix K _T is changed little by little is the spring constant k _j (j = 1 to n). And j is a node number.

This evaluation function J squares the difference between each component of the eigenvector φ _i and the vibration mode vector v _i and the value obtained by dividing the square difference between the eigenvalue λ _i and the natural frequency ω _{i by} the square of the natural frequency ω _i. It is to be summed up. Since the spring constant k _j takes a physically positive value, each straight line is obtained by the steepest descent method, the quasi-Newton method, or the like so that the evaluation function J is minimized with the constraint that k _j > 0. The spring constant k _{j of the} spring 52 is determined.

The stress distribution calculation unit 5g calculates the stress distribution based on the fact that the stress T _{j at} the measurement point j of the strip 1 is expressed by the equation (11).
T _j = 4LM _j f _j ² (11)
Here, M _j is the mass of an element at the measurement point j, and is expressed by the equation (12), where ρ is the density of the strip 1 and A _j is the partial cross-sectional area of the element at the measurement point j.
M _j = ρA _j L (12)
L is the span between the support portions of the strip 1 and f _j is the natural frequency of the one-degree-of-freedom vibration system when the spring constant of the element of the partial cross-sectional area A _j is k _j . The subscript j means a numerical value at the measurement point j.

In general, the natural frequency of a one-degree-of-freedom vibration system without damping is expressed by Expression (13).
Here, m ′ is the mass of the one-degree-of-freedom vibration system, and k ′ is the spring constant.

Therefore, as to match the natural frequency of the natural frequency f _j is represented by a spring constant k _j of the linear spring 52, f _j is expressed by Equation (14).
Here, M _eqj is the equivalent mass of the strip 1 at the measurement point j at the mode order i, and is expressed by the equation (15).
M _eqj = M _modal / v _ij ² (15)
Here, M _modal is the mode mass of the strip 1 and is calculated from [Φ] ^T [M] [Φ]. Further, v _ij is a component of the i-th vibration mode vector measured at the measurement point j.

Therefore, the stress distribution T _j of the band-like body 1 at each measurement point j, using the mass M _j of the band-like body 1 shown in formula (12) can be calculated from equation (16).
T _j = (k _j LM _j ) / (π ² M _eqj ) (16)

(Measurement method of strain distribution)
Next, a method for calculating the strain distribution based on the stress distribution will be described.

  First, as shown in FIG. 13A showing the relationship between the position in the plate width direction and the stress distribution, a straight line passing through any two nodes among the nine nodes arranged in the plate width direction is drawn. In FIG. 13A, three straight lines 61, 62, 63 are shown. This is performed for all combinations of nine nodes, and the slope and intercept of each straight line are calculated. Here, when there are n nodes, a straight line is drawn for each of n × (n−1) / 2 combinations, and the respective slopes and intercepts are calculated.

  As shown in FIG. 13A, when the stress value has a downwardly convex distribution, the number of nodes at which the stress value is equal to or greater than the value of the straight line is counted for each straight line, and the stress value is equal to or greater than the value of the straight line. A straight line having two nodes is selected. For example, the number of nodes where the stress value is equal to or greater than the value of the straight line is 9 for the straight line 61 and 8 for the straight line 62. As shown in FIG. 13B showing the relationship between the position in the plate width direction and the stress distribution, when the stress value has a downward convex distribution, the straight line to be selected is a straight line 64 passing through the two nodes at both ends. Become. By subtracting the stress distribution from the straight line 64, a stress distribution component corresponding to the strain distribution of the belt-like body, which is the difference between the straight line and the stress distribution, is obtained. In FIG. 13B, this stress distribution component is indicated by hatching. Then, by dividing the stress distribution component by the Young's modulus of the belt-like body, the strain distribution is calculated as shown in FIG. 13C showing the relationship between the plate width direction position and the strain distribution.

  On the other hand, as shown in FIG. 14A showing the relationship between the position in the plate width direction and the stress distribution, when the stress value has a convex distribution upward, if a straight line passing through any two nodes is drawn, There are a plurality of straight lines having two nodes whose value is equal to or greater than the value of the straight line. For example, each of the straight lines 65, 66, and 67 shown in FIG. 14A has two nodes where the stress value is equal to or greater than the value of the straight line. Therefore, when the stress value has an upwardly convex distribution, the stress distribution component that is the difference from the stress distribution for each of the straight lines having two nodes where the stress value is equal to or greater than the straight line value. Ask for. Then, a straight line having the smallest vector size of the stress distribution component is selected. In the case shown in FIG. 14A, a stress distribution component is obtained for each of a plurality of straight lines including straight lines 65, 66, and 67, the magnitudes of the stress distribution component vectors are compared, and the magnitude of the stress distribution component vector is the smallest. A certain straight line 66 is selected. Next, as shown in FIG. 14B, which shows the relationship between the position in the plate width direction and the stress distribution, the stress distribution is subtracted from the selected straight line 66, and the difference between the straight line and the stress distribution corresponds to the strain distribution of the belt-like body. The stress distribution component to be obtained is obtained. In FIG. 14B, this stress distribution component is indicated by hatching. Then, by dividing the stress distribution component by the Young's modulus of the strip, the strain distribution is calculated as shown in FIG. 14C showing the relationship between the position in the plate width direction and the strain distribution.

  The change with time of the strain distribution is shown in FIG. The vertical axis is the time axis, and the horizontal axis is the position in the plate width direction. In the flow shown in FIG. 12, by repeating S11 to S18, new strain distributions are sequentially displayed on the old strain distribution along the time axis. Thereby, it can be grasped | ascertained how the strip | belt-shaped body is distorted in the width direction.

(effect)
As described above, according to the stress distribution measuring apparatus 100 and the stress distribution measuring program according to the present embodiment, as shown in FIG. 1, the first displacement meter 8 that measures the vibration displacement at the corresponding first measurement point 1b. And a second displacement meter 9 that measures vibration displacement at each of the plurality of second measurement points 1c in the corresponding second measurement point group 1d. Since the interval between the second measurement points 1c in the second measurement point group 1d is narrower than the shortest interval among the intervals between the first measurement points 1b, the vibration at the location where the second measurement point group 1d is provided. Displacement can be measured in detail. As a result, it is possible to accurately measure non-uniform distortion at a location where the second measurement point group 1d is provided. Therefore, by setting the locations where the second measurement point group 1d is provided at both ends in the width direction of the strip 1, it is possible to accurately measure the ear waves. Thereby, the detailed distribution of the nonuniform distortion which arises locally in the width direction of the strip 1 can be accurately measured.

  In addition, if the number of measurement points 1a is increased over the entire length in the width direction of the band 1, the number of measurement data increases, the calculation time required to calculate the stress distribution becomes longer, and the stress distribution is continuously measured. This is not preferable. However, an increase in the number of measurement data can be suppressed by providing the second measurement point group 1d at a desired location in the width direction of the strip 1 and increasing the number of measurement points 1a only at this location. Time can be significantly reduced.

  Further, as shown in FIG. 2A, the laser beam is irradiated linearly onto the band 1 from the second displacement meter 9, and thus the band 1 is generated in all of the linear regions irradiated with the laser beam. Vibration displacement can be measured. That is, since the second measurement point 1c is provided in all of the linear regions, the location where the second measurement point group 1d is provided can be measured in sufficient detail.

  As shown in FIG. 2B, the vibration displacement at each of the plurality of second measurement points 1c in the second measurement point group 1d is measured by a plurality of displacement meters provided on the second displacement meter 9. Also by this, the detailed measurement of the location where the 2nd measurement point group 1d was provided can be performed suitably.

  Further, by calculating the stress distribution of the band 1 by a two-dimensional unequal interval multi-mass point system model that physically approximates the band 1, even if the stress distribution has a complicated stress distribution in the width direction, Each of the stresses distributed at the measurement point 1a can be calculated with high accuracy using a simple physical model.

  Further, in the method of indirectly detecting the strain distribution state of the belt-like body 1 by the stress distribution, depending on the inclination due to the installation error of the support rolls 2a and 2b for passing plates and the inclination due to the installation error of the take-up reel (not shown). When a partial tension that increases the tension on one side in the width direction of the band 1 occurs, the non-uniform strain of the band 1 cannot be evaluated appropriately. According to the strain distribution measuring apparatus 101 according to the present embodiment, by calculating the strain distribution in the width direction of the band 1 based on the stress distribution in the width direction of the band 1, how the band 1 is in the width direction. You can see if it is distorted. Thereby, the shape of the strip | belt-shaped body 1 during driving | running | working can be grasped | ascertained directly.

  Further, by displaying the strain distribution in a graph and displaying it on the display device 16, it is possible to visually grasp the shape of the belt-like body 1 during traveling.

  Further, by sampling the strain distribution and creating a data sheet, it is possible to visually grasp the shape of the strip 1 during traveling.

[Second Embodiment]
(2D non-uniformly spaced mass model)
Next, a strain distribution measuring apparatus 201 according to the second embodiment of the present invention will be described. As shown in FIG. 1, the strain distribution measuring apparatus 201 of the present embodiment is configured to include all the configurations of the stress distribution measuring apparatus 200 of the present embodiment. The strain distribution measuring apparatus 201 of the present embodiment is different from the strain distribution measuring apparatus 101 of the first embodiment in that the mass of each connecting member 54 in the two-dimensional unequal interval multi-mass point system model shown in FIG. This is a point that is modeled as the mass of the strip 1 in the width direction portion plus the additional mass of air (fluid). That is, in the first embodiment, the effect of the vibrating strip 1 from the fluid such as air in contact with it is not considered, whereas in the present embodiment, the vibrating strip 1 is It takes into account the effects of fluids such as air coming into contact with it. Therefore, the mass of each connecting member 54 is obtained by adding the additional mass of air, which will be described later, to the mass of the band 1 in the width direction portion.

(Strain distribution measurement method)
FIG. 16 shows a procedure of a strain distribution measuring method in which the strain distribution measuring apparatus 201 of the present embodiment calculates the strain distribution in the width direction of the strip 1. This strain distribution measuring method is executed by the strain distribution measuring program of the present embodiment using the strain distribution measuring apparatus 201 described above. This strain distribution measurement program includes all the configurations of the stress distribution measurement program of the present embodiment. Hereinafter, a description will be given with reference to FIGS. 1 and 4.

  First, it is determined whether or not the model data of the strip 1 having the same dimensions as the strip 1 to be measured is stored in the storage device 13 of the arithmetic unit 5 (S1). If it is determined that the same type of model data is not stored in the storage device 13 (S1: NO), additional mass information (such as air physical properties, pressure and temperature conditions) input from the setting input device 15 by the user is used. Based on this, the modeling unit 5a models the additional mass of air as a fluid in contact with the strip 1 between the support portions (S2). Then, the modeled additional mass is calculated (S3), and the degree of freedom of the calculated additional mass is reduced as described later (S4). As is clear from FIG. 12, S2 to S4 are not executed in the first embodiment.

  After that, as in the first embodiment, the modeling unit 5a models the strip 1 into a two-dimensional unequal interval multi-mass system model (S5). Then, the model data is stored in the storage device 13 (S7). On the other hand, when it is determined that the same type of model data is stored in the storage device 13 (S1: YES), the same type of model data is read from the storage device 13 (S8).

  Since S7 or S8 is the same as in the first embodiment, the description thereof is omitted.

(Measurement method of stress distribution)
Next, a method for measuring the stress distribution of the strip 1 using the strain distribution measuring apparatus 201 described above will be specifically described with reference to FIGS. 1 and 11.

The equation of motion of the two-dimensional unequally spaced multi-mass system model is as follows: M for the mass matrix of the strip 1, m _add for the air additional mass matrix described later, x for the displacement vector of each node 51, α for the acceleration vector, and each straight line If the tension stiffness matrix corresponding to the spring constant of the spring 52 is K _T , and the bending stiffness matrix corresponding to the spring constant of the rotary spring 55 is Kτ, then it is expressed by Expression (17). Note that the mass matrix M of the strip 1 is represented by the formula (2) described above in the first embodiment.
(M + m _add ) α + (K _T + Kτ) x = 0 (17)

Eigenvalue analysis is performed using equation (18) so that the eigenvalue λ and eigenvector φ satisfying (M + m _add ) ⁻¹ (K _T + Kτ) φ = λφ are calculated from the equation of motion of equation (17).
{Φ ^T (M + m _add ) Φ} ⁻¹ Φ ^T (K _T + Kτ) Φ = Λ (18)
Here, Λ is a diagonal matrix having eigenvalues as diagonal elements, and Φ is an orthogonal matrix having eigenvectors as column vectors.

FIG. 17 shows a calculation model of the additional mass by the distance / fluid force curve method used in the modeling unit 5a. In this calculation model, the surface of the band 1 between the support parts is divided into elements 7 having a small area, and the additional mass m _{add of} air is calculated from the sound pressure acting on each element 7 by vibration displacement as described below. It is to calculate. The element 7 may be divided as long as the area of each element 7 is sufficiently smaller than the surface area of the strip 1, and may be, for example, a vertical and horizontal 10 × 10 division.

As shown in FIG. 18, which is an explanatory diagram for explaining a method of calculating the additional mass, assuming a semi-infinite plane, s is an oscillating element, i is an element on which sound pressure acts, and s is between element s and element i. Let r _is the distance. Further, the area of each element i, s is A _i , A _s , the speed of element s is v _s , the acceleration is α _s , and the sound pressure acting on element i is p _i . Force P _i by the sound pressure acting on the element i in the acoustic radiation due to the vibration of the strip 1 has the formula (19), represented by (20).
If i ≠ s,
If i = s,
Here, ρ _air is the density of air, ω is the angular frequency of vibration, c is the speed of sound in the air, and k is the wavelength constant (= ω / c). ρ _air is expressed by equation (21) using the _air temperature T _air (° C.).
ρ _air = 1.293 × 273.2 / (273.2 + T _air ) (21)
If the air temperature T _air does not change so much, for example, it is close to 0 ° C., ρ _air = 1.293 may be set.

On the other hand, the force P _i acting on the element i due to the generation of the sound pressure accompanying the vibration of the element s becomes a complex vector. The real part can be expressed by the coefficient c _air of the vibration speed v _s , and the imaginary part can be expressed by the coefficient m _air of the acceleration α _s that is 90 ° out of phase with the vibration speed as shown in Expression (22)
P _i = c _air v _s + m _air α _s (22)
Here, the real part is an additional attenuation term, the imaginary part is an additional mass term, and the coefficient m _{air of the} imaginary part can be regarded as the additional mass of air.

The m _air for each element obtained from the equations (19), (20) and (22) is converted into a nodal degree of freedom using the shape function N as shown in the equation (23). Double for both front and back sides. Thereby, the additional mass distribution M _add acting on the strip 1 can be calculated.

FIG. 19 shows a calculation example of the additional mass distribution M _add calculated by the equation (23). In this calculation example, in order to make the distribution state easy to see, the distribution of only the diagonal term of the additional mass matrix of each element is displayed.

Next, a method for reducing the additional mass distribution M _add calculated by the equation (23) in the longitudinal direction of the strip 1 in accordance with the degree of freedom of the two-dimensional unequal interval multi-mass system model will be described. As shown in FIG. 20, which is an explanatory diagram of the reduction method, an equivalent model is considered in which the mass m at each point in the longitudinal direction of the strip 1 of the non-uniformly spaced mass model is reduced to one equivalent mass _meq . Assuming that the mass matrix of each mass m is M and the vibration mode is φ, Equation (24) is obtained by assuming that the kinetic energy of both models is equal.
Here, X is the vibration displacement, and ω is the angular frequency of the vibration. If the vibration mode is normalized to X = 1, the equivalent mass m _eq can be obtained by equation (25).
m _eq = φ ^T Mφ (25)

Expression (25) is applied to the additional mass matrix M _add to reduce it to an equivalent mass matrix m _add added to one place in the longitudinal direction of the strip 1 as shown in FIG. . When the number of nodes in the longitudinal direction of the band 1 is 1 and the number of nodes in the width direction is n, the additional mass matrix M _add and the equivalent mass matrix m _add are submatrices M _ij (i, j = 1 to n), respectively. It is expressed by equations (26) and (27).
here,
φ = {sinθ ₁ sinθ ₂ ... sinθ _m } ^T (28)
θ _i = (i−1) π / (m−1) (i = 1 to m) (29)
The diagonal term m _ii (i = 1 to n) of the equivalent mass matrix m _add in Expression (27) means a distributed mass for each minute area on the surface of the belt-like body. Further, the off-diagonal term m _ij (i ≠ j) means a coupled mass between two different minute areas that are affected by a pressure distribution generated by vibration.

From equation (27), the reduced transformation matrix Φ and the equivalent mass matrix m _add are calculated by equations (30) and (31), respectively.
m _add = Φ ^T M _add Φ (31)
Therefore, the eigenvalue Λ and the eigenvector Φ are calculated by substituting the equivalent mass matrix m _add calculated by the equation (31) into the equation (18). The calculated eigenvalue Λ and eigenvector Φ are expressed by equations (32), (33), and (34), respectively.
Φ = [φ ₁ φ ₂ ... Φ _n ] (33)
φ _i = {φ _i1 φ _i2 ... φ _in } (34)

When the additional mass matrix M _add is reduced in the width direction, as shown in FIGS. 22A and 22B which are explanatory diagrams of the reduction method, the mass m distributed at each node in the width direction is divided and adjacent to each other. A simple reduction method that distributes to nodes can be adopted. That is, when the number of nodes is an odd number, the reduction conversion matrix Φ _1/2 is expressed by Equation (35), and when the number of nodes is an even number, the reduction conversion matrix Φ _1/2 is expressed by Equation (36).
Thereby, the equivalent mass matrix m _add can be calculated by the equation (37).
m _add = Φ _1/2 ^T M _add Φ _1/2 (37)

In the vibration characteristic calculation unit 5d, the natural frequency ω (angular frequency) and the vibration mode vector v are determined based on the vibration displacement measured at each measurement point 1a (each first measurement point 1b and each second measurement point 1c). Calculated. The i-th order natural frequency ω _i and the vibration mode vector v _i are expressed by equations (38) and (39).
ω _i = {ω _i1 ω _i2 ... ω _in } ^T (38)
v _i = {v _i1 v _i2 ... v _in } ^T (39)
Here, n is the number of measurement points 1a.

The tension stiffness matrix K _T corresponding to the spring constant of the linear spring 52 included in the function of the eigenvalue Λ and the eigenvector Φ calculated by Expression (18) is an unknown. The bending stiffness matrix Kτ for bending the belt-like body 1 in the width direction is a known number determined by the cross-sectional second moment with respect to the bending. The bending stiffness matrix Kτ is expressed by the equation (9) described above in the first embodiment.

Therefore, in the spring constant calculation unit 5e, the eigenvalues Λ and eigenvectors Φ shown in the equations (18) and (32), (33), and (34) are calculated in the vibration characteristic calculation unit 5d, respectively. A tension stiffness matrix K _T that matches the natural frequency ω _i and the vibration mode vector v _i shown in (38) and (39) is determined using the evaluation function J shown in equation (40).
Here, the integration number m is the mode order of vibration. Specifically, to calculate the evaluation function J and the initial values to the tension stiffness matrix K _T. Then, the value of the tension stiffness matrix K _T when the change amount of the evaluation function J in the repetitive calculation in which the value of the tension stiffness matrix K _T is changed little by little is the spring constant k _j (j = 1 to n). And j is a node number.

This evaluation function J squares the difference between each component of the eigenvector φ _i and the vibration mode vector v _i and the value obtained by dividing the square difference between the eigenvalue λ _i and the natural frequency ω _{i by} the square of the natural frequency ω _i. It is to be summed up. Since the spring constant k _j takes a physically positive value, a linear spring is obtained by the steepest descent method, the quasi-Newton method, or the like so that the evaluation function J is minimized with k _j > 0 as a constraint. The spring constant k _{j of} 52a to 52e is determined.

The stress distribution calculation unit 5g calculates the stress distribution based on the fact that the stress T _{j at} the measurement point j of the strip 1 is expressed by Expression (41).
T _j = 4LM _j f _j ² (41)
Here, M _j is the mass of an element at the measurement point j, and is expressed by the equation (42), where ρ is the density of the strip 1 and A _j is the partial cross-sectional area of the element at the measurement point j.
M _j = ρA _j L (42)
L is the span between the support portions of the strip 1 and f _j is the natural frequency of the one-degree-of-freedom vibration system when the spring constant of the element of the partial cross-sectional area A _j is k _j . The subscript j means a numerical value at the measurement point j.

In general, the natural frequency of a one-degree-of-freedom vibration system without damping is expressed by Expression (43).
Here, m ′ is the mass of the one-degree-of-freedom vibration system, and k ′ is the spring constant.

Therefore, as to match the natural frequency of the natural frequency f _j is represented by a spring constant k _j of the linear spring 52, f _j is expressed by Equation (44).
Here, M _eqj is the equivalent mass of the strip 1 at the measurement point j at the mode order i, and is expressed by the equation (45).
M _eqj = M _modal / v _ij ² (45)
Here, M _modal is the mode mass of the strip 1 and is calculated from [Φ] ^T [M] [Φ]. Further, v _ij is a component of the i-th vibration mode vector measured at the measurement point j.

Therefore, the stress distribution T _j of the band-like body 1 at each measurement point j, using the mass M _j of the band-like body 1 shown in formula (42) can be calculated from equation (46).
T _j = (k _j LM _j ) / (π ² M _eqj ) (46)

  Since other configurations are the same as those of the first embodiment, description thereof is omitted.

(effect)
As described above, according to the stress distribution measuring apparatus 200 and the stress distribution measurement program according to the present embodiment, even if the belt-like body 1 has a low density or has a thin plate thickness, the surroundings that affect the vibration are affected. The stress distribution can be accurately measured in consideration of the additional mass of the fluid.

[Third Embodiment]

(2D non-uniformly spaced mass model)
Next, a strain distribution measuring apparatus 301 according to the third embodiment of the present invention will be described. As shown in FIG. 1, the strain distribution measuring apparatus 301 of the present embodiment is configured to include all the configurations of the stress distribution measuring apparatus 300 of the present embodiment. The strain distribution measuring apparatus 301 of the present embodiment is different from the strain distribution measuring apparatus 101 of the first embodiment in that the bending in the width direction at each measurement point 1a in the two-dimensional unequal interval multi-mass point system model shown in FIG. The rigidity is modeled so as to be grasped as a change in the spring constant of the rotary spring 55 at each node 51. That is, in the first embodiment and the second embodiment, the spring constant of the rotary spring 55 that simulates the bending rigidity in the width direction is known, whereas in this embodiment, the spring constant of the rotary spring 55 is It is an unknown number.

(Strain distribution measurement method)
A strain distribution measuring method in which the strain distribution measuring apparatus 301 of the present embodiment calculates the strain distribution in the width direction of the band 1 is shown in FIG. This strain distribution measuring method is executed by the strain distribution measuring program of the present embodiment using the strain distribution measuring apparatus 301 described above. This strain distribution measurement program includes all the configurations of the stress distribution measurement program of the present embodiment. Hereinafter, a description will be given with reference to FIGS. 1 and 4.

  First, it is determined whether or not model data of a strip having the same dimensions as the strip 1 to be measured is stored in the storage device 13 of the arithmetic unit 5 (S1). When it is determined that the same type of model data is not stored in the storage device 13 (S1: NO), the strip information (such as the dimensions and physical properties of the strip) input from the setting input device 15 by the user and the measurement points Based on the interval information 1a and the like, the modeling unit 5a models the strip 1 into a two-dimensional unequal interval multi-mass point system model (S6). This modeling is different from step S5 in FIGS. 12 and 16 in that the bending stiffness in the width direction at each measurement point 1a is grasped as a change in the spring constant of the rotary spring 55 at each node 51. ing. Then, the model data is stored in the storage device 13 (S7). On the other hand, when it is determined that the same type of model data is stored in the storage device 13 (S1: YES), the same type of model data is read from the storage device 13 (S8).

  Since S7 or S8 is the same as that in the first embodiment, the description thereof is omitted.

(Measurement method of stress distribution)
Next, a method for measuring the stress distribution of the strip 1 using the strain distribution measuring apparatus 301 described above will be specifically described with reference to FIGS. 1 and 11.

The equation of motion of the two-dimensional unequally spaced multi-mass point system model is that the mass matrix of the strip 1 is M, the displacement vector of each node 51 is x, the acceleration vector is α, and the tension stiffness matrix corresponding to the spring constant of each linear spring 52 And K _T , and a bending stiffness matrix corresponding to the spring constant of the rotary spring 55 as Kτ, this is expressed by Expression (47). Note that the mass matrix M of the strip 1 is represented by the formula (2) described above in the first embodiment.
Mα + (K _T + Kτ) x = 0 (47)

The mass m and the moment of inertia J included in each element of the mass matrix M are calculated from the equivalent mass and the equivalent stiffness when the longitudinal vibration mode is approximated by a sine wave and reduced. The distance between the support rolls 2a and 2b is L, the thickness of the strip 1 is t, the density is ρ, and the length of the connecting member 54 is l. The equivalent mass m at the center between the support rolls 2a and 2b can be obtained by the equation (48) when the longitudinal vibration mode is the primary.
m = ρtlL / 2 (48)
In addition, the moment of inertia J is obtained by the equation (49) from the equivalent mass m obtained by the equation (48).
J = m (t ² + l ² ) / 12 (49)

The tension stiffness matrix _KT and the bending stiffness matrix Kτ are unknown matrices. The tension stiffness matrix K _T is expressed by the equation (50) using the spring constant k _j (j = 1 to n) of the linear spring 52. The bending stiffness matrix Kτ is expressed by the equation (9) described above in the first embodiment.

A conversion formula to the cross-sectional secondary moment I _j when the spring constant τ _i corresponding to the bending stiffness in the width direction included in each element of the bending stiffness matrix Kτ is calculated is expressed by Formula (51).
I _j = τ _j 1 / E (51)

Eigenvalue analysis is performed using equation (52) so that the eigenvalue λ and the eigenvector φ satisfying M ⁻¹ (K _T + Kτ) φ = λφ are calculated from the equation of motion of equation (47).
(Φ ^T MΦ) ⁻¹ Φ ^T (K _T + Kτ) Φ = Λ (52)
Here, Λ is a diagonal matrix having eigenvalues as diagonal elements, and Φ is an orthogonal matrix having eigenvectors as column vectors.

The eigenvalue Λ and the eigenvector Φ calculated by the eigenvalue analysis are expressed by equations (53), (54), and (55), respectively.
Φ = [φ ₁ φ ₂ ... φ _n ] (54)
φ _i = {φ _i1 φ _i2 ... φ _in } (55)

In the vibration characteristic calculation unit 5d, the natural frequency ω (angular frequency) and the vibration mode vector v are calculated based on the vibration displacement measured at each measurement point 1a. The i-th natural frequency ω _i and the vibration mode vector v _i are expressed by equations (56) and (57).
ω _i = {ω _i1 ω _i2 ... ω _in } ^T (56)
v _i = {v _i1 v _i2 ... v _in } ^T (57)
Here, n is the number of measurement points 1a.

The tension stiffness matrix K _T corresponding to the spring constant of the linear spring 52 included in the function of the eigenvalue Λ and the eigenvector Φ calculated by the equation (52) is an unknown. Further, the bending stiffness matrix Kτ that bends the belt-like body 1 in the width direction is an unknown number determined by the cross-sectional second moment with respect to the bending. Therefore, in the spring constant calculation unit 5e, the eigenvalue Λ and the eigenvector Φ shown in the equations (52), (54), and (55) are calculated in the vibration characteristic calculation unit 5d, respectively, A tension stiffness matrix K _T that matches the natural frequency ω _i and the vibration mode vector v _i shown in (56) and (57) is determined using the evaluation function J shown in equation (58).
Here, the integration number m is the mode order of vibration. Specifically, the evaluation function J is calculated by setting initial values in the tension stiffness matrix _KT and the bending stiffness matrix Kτ. Then, the value of the tension stiffness matrix K _T when the amount of change in the evaluation function J in the repeated calculation in which the values of the tension stiffness matrix K _T and the bending stiffness matrix Kτ are changed little by little is the spring constant k _j (j = 1 to n). Further, the value of the bending stiffness matrix Kτ when the change amount of the evaluation function J is minimized is set to a spring constant τ _j (j = 1 to n−2). j is a node number.

This evaluation function J squares the difference between each component of the eigenvector φ _i and the vibration mode vector v _i and the value obtained by dividing the square difference between the eigenvalue λ _i and the natural frequency ω _{i by} the square of the natural frequency ω _i. It is to be summed up. Since the spring constant k _j and the spring constant τ _j are physically positive values, the steepest descent is performed so that the evaluation function J is minimized with the constraint that k _j > 0 and τ _j > 0. The spring constant k _j of each linear spring 52 and the spring constant τ _j of the rotary spring 55 are determined by the method, the quasi-Newton method, or the like.

The stress distribution calculation unit 5g calculates the stress distribution based on the fact that the stress T _{j at} the measurement point j of the strip 1 is expressed by the equation (59).
T _j = 4LM _j f _j ² (59)
Here, M _j is the mass of the element having the measurement point j, and is expressed by the equation (60), where ρ is the density of the strip 1 and A _j is the partial cross-sectional area of the element at the measurement point j.
M _j = ρA _j L (60)
L is the span between the support portions of the strip 1 and f _j is the natural frequency of the one-degree-of-freedom vibration system when the spring constant of the element of the partial cross-sectional area A _j is k _j . The subscript j means a numerical value at the measurement point j.

In general, the natural frequency of a one-degree-of-freedom vibration system without damping is expressed by Expression (61).
Here, m ′ is the mass of the one-degree-of-freedom vibration system, and k ′ is the spring constant.

Therefore, as to match the natural frequency of the natural frequency f _j is represented by a spring constant k _j of the linear spring 52, f _j is expressed by Equation (62).
Here, M _eqj is the equivalent mass of the strip 1 at the measurement point j at the mode order i, and is expressed by the equation (63).
M _eqj = M _modal / v _ij ² (63)
Here, M _modal is the mode mass of the strip 1 and is calculated from [Φ] ^T [M] [Φ]. Further, v _ij is a component of the i-th vibration mode vector measured at the measurement point j.

Therefore, the stress distribution T _j of the band-like body 1 at each measurement point j, using the mass M _j of the band-like body 1 shown in formula (60) can be calculated from equation (64).
T _j = (k _j LM _j ) / (π ² M _eqj ) (64)

Further, the calculated spring constant τ _j of the rotary spring 55 is converted into the cross-sectional secondary moment I _j by the equation (51), and the bending stiffness distribution in the width direction is calculated.

  Since other configurations are the same as those of the first embodiment, description thereof is omitted.

(effect)
As described above, according to the stress distribution measuring apparatus 300 and the stress distribution measuring program according to the present embodiment, even if the belt-like body 1 whose bending rigidity in the width direction changes due to the partial manifestation of non-uniform strain, Distribution can be accurately measured.

[Fourth Embodiment]
(Configuration of strain distribution measuring device)
Next, a strain distribution measuring apparatus 401 according to the fourth embodiment of the present invention will be described. As shown in FIG. 24, which is a configuration diagram, the strain distribution measuring apparatus 401 of the present embodiment is configured to include all the configurations of the stress distribution measuring apparatus 400 of the present embodiment. The strain distribution measuring apparatus 401 of this embodiment is different from the strain distribution measuring apparatus 101 of the first embodiment in that the second measurement point group 1d is from both ends in the width direction of the strip 1 as shown in FIG. The point is that the quarter of the width of the band 1 is provided in a region closer to the center. That is, in the first to third embodiments, the earwaves shown in FIG. 3A are measured in detail, whereas in this embodiment, the quarter distortion shown in FIG. 3B is measured in detail. It is the composition to do.

  In the present embodiment, three first measurement points 1b are provided at equal intervals at both ends and the center in the width direction of the strip 1. Therefore, three first displacement meters 8 are provided above the strip 1 and are arranged at equal intervals in the width direction of the strip 1.

  Further, in the present embodiment, the second measurement point group 1 d is ¼ of the width of the band 1 from both ends in the width direction of the band 1 on the side of the first measurement point 1 b in the width direction of the band 1. It is provided in the area closer to the center. Therefore, two second displacement meters 9 are provided above the strip 1 and are arranged in the width direction of the strip 1 together with the three first displacement meters 8.

  In the present embodiment, the stress distribution is calculated from the stress at each measurement point 1a using the same stress distribution measurement method as in the first embodiment. However, the stress distribution measurement method is not limited to this, and the stress distribution may be calculated using the stress distribution measurement method described in the second embodiment or the third embodiment.

(effect)
As described above, according to the stress distribution measuring apparatus 400 and the stress distribution measuring program according to the present embodiment, as shown in FIG. The quarter distortion can be measured with high accuracy by setting it to an area closer to the center by about 1/4 width from both ends. Thereby, the detailed distribution of the nonuniform distortion which arises locally in the width direction of the strip 1 can be accurately measured.

[Fifth Embodiment]
(Configuration of strain distribution measuring device)
Next, a strain distribution measuring apparatus 501 according to the fifth embodiment of the present invention will be described. As shown in FIG. 25 which is a configuration diagram, the strain distribution measuring apparatus 501 of the present embodiment is configured to include all the configurations of the stress distribution measuring apparatus 500 of the present embodiment. The strain distribution measuring device 501 of the present embodiment is different from the strain distribution measuring device 101 of the first embodiment in that the second measurement point group 1d is a central portion in the width direction of the strip 1 as shown in FIG. It is a point provided in. That is, in the first embodiment, the configuration is a configuration that measures the ear waves shown in FIG. 3A in detail, whereas in this embodiment, the configuration is a configuration that measures the medium elongation shown in FIG. 3C in detail. Yes.

  In the present embodiment, two first measurement points 1 b are provided at equal intervals at both ends in the width direction of the band 1. Therefore, four first displacement meters 8 are provided above the strip 1, and the four first displacement meters 8 are arranged in the width direction of the strip 1.

  In the present embodiment, the second measurement point group 1 d is provided at the center of the strip 1 in the width direction on the side of the first measurement point 1 b in the width direction of the strip 1. Therefore, one second displacement meter 9 is provided above the strip 1, and is aligned with the four first displacement meters 8 in the width direction of the strip 1.

  In the present embodiment, the stress distribution is calculated from the stress at each measurement point 1a using the same stress distribution measurement method as in the first embodiment. However, the stress distribution measurement method is not limited to this, and the stress distribution may be calculated using the stress distribution measurement method described in the second embodiment or the third embodiment.

(effect)
As described above, according to the stress distribution measuring apparatus 500 and the stress distribution measuring program according to the present embodiment, the location where the second measurement point group 1d is provided in the width direction of the strip 1 as shown in FIG. By setting the central portion, the medium elongation can be measured with high accuracy. Thereby, the detailed distribution of the nonuniform distortion which arises locally in the width direction of the strip 1 can be accurately measured.

(Modification of this embodiment)
The embodiment of the present invention has been described above, but only specific examples are illustrated, and the present invention is not particularly limited, and the specific configuration and the like can be appropriately changed in design. Further, the actions and effects described in the embodiments of the invention only list the most preferable actions and effects resulting from the present invention, and the actions and effects according to the present invention are described in the embodiments of the present invention. It is not limited to what was done.

DESCRIPTION OF SYMBOLS 1 Band-shaped body 1a Measurement point 1b 1st measurement point 1c 2nd measurement point 1d 2nd measurement point group 2a, 2b Support roll 3 Vibration load addition apparatus (vibration load addition means)
4 Displacement meter (vibration measuring means)
5 Arithmetic unit 5a Modeling unit (modeling means)
5b Load signal output section 5c Vibration signal input section 5d Vibration characteristic calculation section 5e Spring constant calculation section (spring constant calculation means)
5f Spring constant conversion part (spring constant conversion means)
5g Stress distribution calculation part (stress distribution calculation means)
5h Strain distribution calculation unit (strain distribution calculation means)
5i Strain distribution graph display unit 5j Data sheet creation unit 6 Amplifier 7 Element 8 First displacement meter (first vibration measuring means)
9 Second displacement meter (second vibration measuring means)
9a Sheet laser 9b Laser 11 CPU
12 Temporary Storage Device 13 Storage Device 14 Signal Input / Output Device 15 Setting Input Device 16 Display Device (Display Means)
17 Data sheet creation device (data sheet creation means)
DESCRIPTION OF SYMBOLS 21 Personal computer 22 AD / DA board 23 Electromagnetic valve drive circuit 24 Electromagnetic valve 25 Factory air piping 26 Air nozzle 27 Band 28 Displacement meter 31 Band information input part 32 Band information display part 33 Additional mass information input part 34 Additional mass Information display section 35 Storage section 36 Temporary storage section 37 Band body modeling section 38 Additional mass modeling section 39 Load signal output section 40 Vibration signal input section 41 Vibration characteristic calculation section 42 Spring constant calculation section 43 Stress distribution calculation section 44 Strain distribution Calculation unit 45 Storage unit 46 Display unit 47 Data sheet creation unit 51 Node 52 Linear spring 53 Fixed surface 54 Connecting member 55 Rotary spring 100, 200, 300, 400, 500 Stress distribution measuring device 101, 201, 301, 401, 501 Strain Distribution measuring device

Claims (10)

A stress distribution measuring device for measuring a stress distribution in a width direction of a belt-like body to which a tension is applied in a longitudinal direction between support parts supported by two parts in the longitudinal direction,
Vibration load adding means for applying a vibration load to the belt-like body between the two support parts;
Vibration measuring means for measuring vibration displacement generated in the band by the vibration load added to the band at a plurality of measurement points provided side by side in the width direction of the band on the band;
Stress distribution calculating means for calculating a stress distribution in the width direction of the strip based on the natural frequency and vibration mode of the strip obtained from the vibration displacement measured at the plurality of measurement points;
Have
The plurality of measurement points includes a plurality of first measurement points and a plurality of second measurement points,
At least one first measurement point and a second measurement point group composed of a plurality of the second measurement points are alternately arranged,
The interval between the second measurement points in the second measurement point group is narrower than the shortest interval among the intervals between the first measurement points,
The vibration measuring means is
A plurality of first vibration measuring means provided for each of the first measurement points, each of which measures vibration displacement generated in the belt-like body at the corresponding first measurement point;
A second vibration measuring means that is provided for each of the second measurement point groups, and that measures vibration displacement generated in the belt-like body at each of the plurality of second measurement points in the corresponding second measurement point group;
A stress distribution measuring apparatus comprising:   The second vibration measuring means irradiates laser light linearly on the band-like body, thereby causing vibration displacement generated in the band-like body at each of the plurality of second measurement points in the second measurement point group. The stress distribution measuring device according to claim 1, wherein the stress distribution measuring device is measured.   The second vibration measuring means is provided for each of the plurality of second measurement points in the second measurement point group, and measures a plurality of second vibration points generated at the band-like body at the corresponding second measurement points. The stress distribution measuring apparatus according to claim 1, further comprising three vibration measuring means. Modeling means for modeling the belt-like body into a two-dimensional unequally spaced multi-mass point system model including a linear spring that simulates a stress acting on each node corresponding to each measurement point;
The natural frequency and vibration mode at each node obtained from the eigenvalue analysis of the unequal-interval multi-mass point system model match the natural frequency and vibration mode obtained from the vibration displacement measured at each measurement point. Spring constant calculating means for calculating each spring constant of the linear spring;
Spring constant conversion means for converting each spring constant of the calculated linear spring into a stress value at each measurement point;
Further comprising
4. The stress distribution measurement according to claim 1, wherein the stress distribution calculation unit obtains a stress distribution in a width direction of the strip from the converted stress value at each measurement point. 5. apparatus. A two-dimensional non-uniformly-spaced mass point including the additional mass of the fluid in contact with the belt between the support portions and the linear spring that simulates the stress acting on each node corresponding to each measurement point. Modeling means for modeling into a system model;
The natural frequency and vibration mode at each node obtained from the eigenvalue analysis of the unequal-interval multi-mass point system model match the natural frequency and vibration mode obtained from the vibration displacement measured at each measurement point. Spring constant calculating means for calculating each spring constant of the linear spring;
Spring constant conversion means for converting each spring constant of the calculated linear spring into a stress value at each measurement point;
Further comprising
4. The stress distribution measurement according to claim 1, wherein the stress distribution calculation unit obtains a stress distribution in a width direction of the strip from the converted stress value at each measurement point. 5. apparatus. A two-dimensional non-uniformly spaced mass point including a linear spring that simulates the stress acting on each node corresponding to each measurement point and a rotary spring that simulates the bending rigidity in the width direction at each node. Modeling means for modeling into a system model;
The natural frequency and vibration mode at each node obtained from the eigenvalue analysis of the unequal-interval multi-mass point system model match the natural frequency and vibration mode obtained from the vibration displacement measured at each measurement point. Spring constant calculating means for calculating each spring constant of the linear spring and the rotary spring;
Spring constant conversion means for converting the calculated spring constants of the linear spring and the rotary spring into stress values and bending rigidity values at the respective measurement points;
Further comprising
4. The stress distribution measurement according to claim 1, wherein the stress distribution calculation unit obtains a stress distribution in a width direction of the strip from the converted stress value at each measurement point. 5. apparatus. The stress distribution measuring device according to any one of claims 1 to 6,
A strain distribution calculating means for calculating a strain distribution in the width direction of the strip based on the calculated stress distribution;
A strain distribution measuring apparatus comprising: Graphing means for graphing the strain distribution;
Display means capable of displaying a graph;
Display control means for displaying the graphed strain distribution on the display means;
The strain distribution measuring apparatus according to claim 7, further comprising: Sampling means for sampling the strain distribution;
A data sheet creation means capable of creating a data sheet;
Data sheet creation control means for causing the data sheet creation means to create a data sheet based on the sampled strain distribution;
The strain distribution measuring device according to claim 7, further comprising: A stress distribution measurement program for causing a computer to function to measure a stress distribution in a width direction of a belt-like body to which a tension is applied in a longitudinal direction between support parts supported by two parts in the longitudinal direction,
Vibration load adding means for applying a vibration load to the belt-like body between the two support parts;
Vibration measuring means for measuring vibration displacement generated in the band by the vibration load added to the band at a plurality of measurement points provided side by side in the width direction of the band on the band;
Based on the natural frequency and vibration mode of the band-shaped body, which are obtained from the vibration displacement measured at the plurality of measurement points including the plurality of first measurement points and the plurality of second measurement points, the width of the band-shaped body While making the computer function as a stress distribution calculation means for calculating the stress distribution in the direction,
The plurality of measurement points are composed of a plurality of first measurement points and a plurality of second measurement points,
Alternately arranging at least one first measurement point and a second measurement point group including a plurality of the second measurement points;
The interval between the second measurement points in the second measurement point group is made narrower than the shortest interval among the intervals between the first measurement points,
The vibration measuring means;
A plurality of first vibration measuring means provided for each of the first measurement points, each of which measures vibration displacement generated in the belt-like body at the corresponding first measurement point;
The computer functions as a second vibration measuring unit that is provided for each of the second measurement point groups and measures the vibration displacement generated in the belt-like body at each of the plurality of second measurement points in the corresponding second measurement point group. A stress distribution measurement program characterized by