JP5121335B2 - Tension measuring device and tension measuring method - Google Patents

Description

  The present invention relates to a tension measuring device and a tension measuring method capable of grasping the tension state of a band by measuring the vibration of the band such as a copper plate.

In general, strips or windings of strips such as copper plates, aluminum plates, and steel plates are arranged with rolls on the front and back of the strip travel path, and are fed out while supporting the strips with these rolls, and with a predetermined tension. Is applied to the belt-like body. At this time, if a change in tension between rolls or a break in the tension balance in the width direction occurs, problems such as unstable running of the belt-like body and occurrence of winding deviation occur.
Moreover, in the production line of a rolling process, when the fluctuation | variation of a tension | tensile_strength and the collapse of the tension balance of the width direction arise at the entrance / exit of a rolling roll, the problem that the board | plate thickness of a strip | belt shaped body will arise will arise.

  Therefore, in the production line of strips, knowing the tension and the tension balance in the width direction has become extremely important for improving productivity and quality, and conventionally, the tension and tension balance of strips have been measured. Various methods have been implemented and proposed. As a conventional measuring method, there are a contact type in which a measuring member such as a sensor is brought into direct contact with a belt-like body, and a non-contact type in which no contact is made.

  As a method for measuring tension by a contact method, a method using a split roll method is generally employed. This is a method of measuring the internal stress of the band-shaped body by directly bringing the divided roll divided in the axial direction into contact with the band-shaped body.

  As a non-contact type measurement method, the displacement amount of a plurality of measurement points arranged in the width direction of the strip is measured by a non-contact displacement meter, and the tension of the strip or the band is measured based on the frequency characteristics of the displacement signal. There is a method for measuring the tension distribution.

  For example, the tension measuring device described in Patent Document 1 detects displacement amounts of three measurement points located at the left and right end portions and the center portion of the strip in the width direction with a non-contact displacement meter, and The primary natural frequency at each measurement point is obtained from the frequency characteristics, the tension at each measurement point is calculated based on the relationship between the tension of the strip and the primary natural frequency, and the tension is averaged. Calculate the total tension.

  Further, the tension measuring device described in Patent Document 2 determines the number of natural frequencies (number of vibration modes) to be extracted from the frequency characteristics based on the past average tension measurement data and the dimension data of the belt-like body. . And in order to calculate the tension | tensile_strength in a certain position of a strip | belt shaped object, a weighted average frequency is calculated based on the amplitude of the some vibration mode in the position. By substituting this weighted average frequency into the relational expression between the primary natural frequency and the tension, the tension at that position is calculated. In this way, the tension distribution of the band-shaped body is obtained by calculating the tension at a number of positions in the width direction of the band-shaped body.

JP 2000-39369 A JP 7-218358 A

  However, according to the above-described split roll method, there is a problem that when the tension is measured by pressing the split roll against the strip, the surface of the strip is damaged.

  Further, in the case of a belt-like body made of a material with low bending rigidity such as an aluminum thin plate, there are many natural frequencies corresponding to the tension, and the tension distribution in the width direction is complicated. In the method disclosed in Patent Document 1, the total tension is obtained by averaging the tensions at a plurality of measurement points of the strip, but since the tension distribution of the strip is not grasped in this method, the total of the strips is determined. The tension cannot be calculated accurately.

  Moreover, since the method disclosed in Patent Document 2 requires past average tension measurement data, it is difficult to put it to practical use immediately.

  Therefore, an object of the present invention is to provide a tension measuring device and a tension measuring method that can determine the tension state of the band with high accuracy without damaging the surface of the band.

Means for Solving the Problems and Effects of the Invention

The tension measuring apparatus according to claim 1 is a tension measuring apparatus that measures a tension state by measuring vibration of a band supported at two positions in the longitudinal direction, and is arranged in the width direction of the band. Based on the non-contact displacement amount detecting means for detecting the displacement amount in the out-of-plane direction of the strip at a plurality of measurement points, and the signals related to the displacement amounts detected at the plurality of measurement points, a frequency characteristic deriving means for deriving a frequency characteristic for each measurement point, on the basis of the frequency characteristic deriving means a plurality of frequency characteristics derived in the natural frequency extraction means for extracting a plurality of primary natural frequency, the Vibration mode deriving means for deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to a plurality of primary natural frequencies, and further normalizing amplitudes of the plurality of vibration mode shapes; Shake The width direction length of the section in which the amplitude is larger than the predetermined amplitude line common to all the vibration modes, extracted for each mode shape, and the value added for all the vibration modes is the sum of the band-like bodies. Based on the effective width setting means for setting the length in the width direction equal to the entire width as the effective width of the plurality of vibration modes, and the primary natural frequency of each vibration mode, the tension corresponding to the vibration mode A tension component calculating means for calculating a component, and adding the value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the total width of the strip for all vibration modes, And a total tension calculating means for determining the total tension of the body.

  A tension component calculated from the natural frequency of the vibration mode corresponding to the effective width mainly acts on the widthwise region of the band-shaped body in which the effective width is set. Therefore, according to the present invention, even when the tension distribution of the band-like body is complicated in the width direction, the tension distribution of the band-like body can be grasped. Further, the total tension of the band can be calculated with high accuracy by adding the value obtained by multiplying the tension component of each mode by the ratio of the effective width to the total width of the band for all modes. Further, the displacement amount of the strip for obtaining the tension is detected in a non-contact manner by the displacement amount detecting means. Thereby, the tension state such as the tension distribution in the width direction and the total tension of the strip can be measured without damaging the strip.

  According to a second aspect of the present invention, there is provided the tension measuring device according to the first aspect, wherein the displacement amount detecting means is disposed opposite to each other at the center in the longitudinal direction of the belt-like body.

  In the primary mode vibration of the belt-like body supported at two positions in the longitudinal direction, the belt vibrates with the center in the longitudinal direction of the belt-like body as an antinode. Therefore, in the frequency characteristic derived by the vibration mode deriving means, the peak value of the first-order mode amplitude is clearly larger than the peak value of the higher-order mode amplitude. Accordingly, when the natural frequency is extracted from the frequency characteristic, the primary natural frequency can be easily extracted without extracting the high-order natural frequency.

  A tension measuring device according to a third aspect is the tension measuring device according to the first or second aspect, wherein a plurality of the displacement amount detection means are provided, and the plurality of measurement points of the at least two displacement amount detection means are respectively in the longitudinal direction center. It is located symmetrically, and the natural frequency extracting means extracts a specific natural frequency based on the displacements detected at the two symmetrically located measurement points, respectively. When the displacement amounts of the two measurement points are opposite to each other, the natural frequency is not extracted as the primary natural frequency.

  In the first mode vibration of the belt-like body supported at the two points in the longitudinal direction, the displacement amount at the position symmetric with respect to the center in the hand direction of the belt-like body has the same phase. On the other hand, in the even-order vibration including the secondary mode, the amount of displacement at the position symmetric with respect to the center in the longitudinal direction of the belt-like body has an opposite phase. Therefore, when a natural frequency is extracted from the frequency characteristics of two measurement points that are symmetric with respect to the center in the longitudinal direction of the belt-like body, the natural frequency is obtained when the displacements at the natural frequency are opposite to each other. By not extracting the natural frequency in the extraction unit, the primary natural frequency can be easily extracted.

The tension measuring device according to claim 4 is a tension measuring device for measuring a tension state by measuring vibration of a belt supported at two positions in the longitudinal direction, and is arranged in the width direction of the belt. Non-contact type displacement amount detecting means for detecting the amount of displacement in the out-of-plane direction of the band at a plurality of measurement points, and out-of-plane deformation area determination for determining an area where the out-of-plane deformation of the band is generated means, said plurality of based on the detected signal relating to the displacement amount at the measurement point, and the frequency characteristic deriving means for deriving a frequency characteristic for each of the plurality of measuring points, a plurality of which are derived by said frequency characteristic deriving means Based on the frequency characteristics, natural frequency extraction means for extracting a plurality of primary natural frequencies, and vibration mode shapes of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies are derived. Multiple vibration modes The vibration mode deriving means for normalizing the amplitude of the vibration shape and the width of the section where the amplitude is larger than the predetermined amplitude line common to all the vibration modes, extracted for each of the normalized vibration mode shapes The direction length and the sum of all vibration modes is equal to the value obtained by subtracting the width of the out-of-plane deformation area determined by the out-of-plane deformation area determination means from the total width of the strip. Based on the effective width setting means for setting the width direction length as the effective width of the plurality of vibration modes and the primary natural frequency of each vibration mode, the tension component for calculating the tension component corresponding to the vibration mode A value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the value obtained by subtracting the width of the out-of-plane deformation region from the total width of the band-shaped body is calculated for all the vibration means. Summing the mode, characterized by having a a total tension calculating means for calculating a total tension of the strip.

  The out-of-plane deformation of the band-shaped body is that a force compressing in the longitudinal direction acts on a partial area in the width direction of the band-shaped body, and the area is deformed in the out-of-plane direction. At this time, the stress is not applied in the out-of-plane deformation region because the stress is released. By specifying the out-of-plane deformation region and obtaining the tension state for the region excluding the out-of-plane deformation region, the entire tension state of the belt-like body can be measured.

  A tension measuring device according to a fifth aspect includes the vibration measuring unit according to the fourth aspect, wherein the band-shaped body is vibrated, and the out-of-plane deformation region discriminating unit compares the frequency characteristics before and after the vibration, thereby It is characterized by determining the presence or absence of deformation.

  Out-of-plane deformation often occurs periodically in the longitudinal direction of the strip. When the strip is traveling at a constant speed, an amplitude peak occurs at a specific frequency due to the out-of-plane deformation in the frequency characteristics of the measurement point where the out-of-plane deformation occurs. Since no tension acts on the out-of-plane deformation region, the peak value of this amplitude does not change when the strip is vibrated by the vibrating means. On the other hand, in the region where there is no out-of-plane deformation, the vibration of the primary mode increases when the vibration is applied by the vibration means. Therefore, it is possible to determine the presence or absence of out-of-plane deformation by extracting a specific frequency having a peak amplitude value from the frequency characteristics at a certain measurement point and comparing the magnitude of the amplitude of the frequency characteristics before and after excitation. Can do.

The tension measuring method according to claim 6 is a tension measuring method for measuring a tension state by measuring vibration of a band supported at two positions in the longitudinal direction, and is arranged in the width direction of the band. Based on a displacement amount detection step of detecting the displacement amount in the out-of-plane direction of the strip in a plurality of measurement points in a non-contact manner, and the plurality of measurements based on signals related to the displacement amounts detected at the plurality of measurement points. A frequency characteristic deriving step for deriving a frequency characteristic for each point; a natural frequency extracting step for extracting a plurality of primary natural frequencies based on the plurality of frequency characteristics derived in the frequency characteristic deriving step; A vibration mode deriving step of deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to the first natural frequencies of the first vibration frequency, and normalizing amplitudes of the plurality of vibration mode shapes; and the plurality of normalized vibrations The length in the width direction of the section where the amplitude is larger than the predetermined amplitude line common to all the vibration modes extracted for each of the vibration modes, and the value added for all the vibration modes is the band-like body Corresponding to the vibration mode based on the effective width setting step of setting the length in the width direction so as to be equal to the full width of the plurality of vibration modes as the effective width of the plurality of vibration modes and the primary natural frequency of each vibration mode. A tension component calculation step for calculating a tension component, and a value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the total width of the belt-like body for all vibration modes, And a total tension calculating step for obtaining a total tension of the belt-like body.

  A tension component calculated from the natural frequency of the vibration mode corresponding to the effective width mainly acts on the widthwise region of the band-shaped body in which the effective width is set. Therefore, according to the present invention, even when the tension distribution of the band-like body is complicated in the width direction, the tension distribution of the band-like body can be grasped. Further, the total tension of the band can be calculated with high accuracy by adding the value obtained by multiplying the tension component of each mode by the ratio of the effective width to the total width of the band for all modes. Further, the displacement amount of the strip for obtaining the tension is detected in a non-contact manner by the displacement amount detecting means. Thereby, the tension state such as the tension distribution in the width direction and the total tension of the strip can be measured without damaging the strip.

The tension measuring method according to claim 7 is a tension measuring method for measuring a tension state by measuring vibration of a band supported at two points in the longitudinal direction, and is arranged in the width direction of the band. A displacement amount detecting step for detecting the amount of displacement in the out-of-plane direction of the belt-like body in a non-contact manner at a plurality of measurement points, and an out-of-plane deformation region discriminating step for discriminating a region where the belt-like body is deformed out of plane. And a frequency characteristic deriving step for deriving a frequency characteristic for each of the plurality of measurement points based on a signal relating to the displacement detected at the plurality of measurement points, and a plurality of frequencies derived in the frequency characteristic deriving step. Based on the characteristics, a natural frequency extraction step of extracting a plurality of primary natural frequencies, and a vibration mode shape of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies are derived. Vibration mode The vibration mode derivation step for normalizing the amplitude of the shape, and the width direction of the section in which the amplitude is larger than a predetermined amplitude line common to all the vibration modes, extracted for each of the normalized vibration mode shapes A width that is a length and the sum of all vibration modes is equal to a value obtained by subtracting the width of the out-of-plane deformation area determined by the out-of-plane deformation area determination step from the total width of the band-shaped body. Based on the effective width setting step of setting the direction length as the effective width of the plurality of vibration modes and the primary natural frequency of each vibration mode, the tension component calculation for calculating the tension component corresponding to the vibration mode A value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the value obtained by subtracting the width of the out-of-plane deformation region from the total width of the strip. Summed for over de, characterized by having a a total tension calculation step of obtaining a total tension of the strip.

  Since the stress is released in the out-of-plane deformation region, no tension is applied. By specifying the out-of-plane deformation region and obtaining the tension state for the region excluding the out-of-plane deformation region, the entire tension state of the belt-like body can be measured.

[First embodiment]
Hereinafter, the first embodiment will be described. As shown in FIG. 1, the tension measuring device 4 of the present embodiment is applied to a production line for a strip 1 such as a copper plate, an aluminum plate, or a steel plate. In this production line, two rolls 2 and 3 are respectively arranged before and after (two points) in the traveling direction (longitudinal direction) of the strip 1. The two rolls 2 and 3 support the belt-like body 1 while applying a predetermined tension to the belt-like body 1 by controlling the rotation speed by a tension control device (not shown). It is designed to send out.

  The tension of the strip 1 is measured by the tension measuring device 4. The tension measuring device 4 includes a displacement amount measuring device 5 that detects the vibration of the strip 1 in a non-contact manner, a Fourier transform device 6, and a tension computing device 7. As shown in FIG. 1, the displacement measuring device 5 is connected to a tension computing device 7 via a Fourier transform device 6.

  As shown in FIG. 1, the displacement measuring device 5 is disposed so as to face the upper surface of the central portion in the longitudinal direction of the strip 1. Further, the displacement measuring device 5 includes five non-contact displacement meters 21 to 25 arranged in the width direction of the strip 1. The non-contact displacement meters 21 to 25 detect the displacement amounts of the five measurement points 31 to 35 of the band 1 facing each other. Examples of the non-contact displacement meters 21 to 25 include a light reflection type distance sensor. Further, the non-contact displacement meter 23 is positioned on the upper surface of the central portion in the width direction of the strip 1, and the non-contact displacement meters 21 and 25 are positioned on the upper surfaces of both ends in the width direction of the strip 1. The non-contact displacement meters 21 to 25 are arranged at equal intervals in the width direction of the strip 1.

  The non-contact displacement meters 21 to 25 are respectively connected to the Fourier transform device (frequency characteristic deriving means) 6 and output signals corresponding to the displacement amounts of the measurement points 31 to 35, respectively. The Fourier transform device 6 converts the displacement amount signal into a digital signal, and then performs a fast Fourier transform (FFT) to calculate the frequency characteristics of vibrations at the measurement points 31 to 35, respectively. Output.

  The tension calculating device 7 includes a natural frequency extracting unit (natural frequency extracting unit) 10, a vibration mode deriving unit (vibration mode deriving unit) 11, an effective width setting unit 12 (effective width setting unit), and a tension component calculation. A section 13 (tension distribution calculation means), a total tension calculation section 14 (total tension calculation means), and a storage section 15 are provided, which are composed of a CPU, a ROM, a RAM, and the like.

  The tension calculation device 7 can execute the tension calculation routine of FIG. Details of the tension calculation method by the tension calculation routine will be described later. The natural frequency extraction unit 10 extracts a plurality of primary natural frequencies from the frequency characteristics of the five measurement points 31 to 35 calculated by the Fourier transform apparatus 6. The vibration mode deriving unit 11 creates a vibration mode shape in the width direction of the strip 1 for each of the extracted primary natural frequencies, and normalizes the amplitude for each vibration mode. Then, the effective width setting unit 12 sets the effective width for each vibration mode based on these normalized vibration mode shapes. The tension component calculation unit 13 calculates tension components corresponding to a plurality of vibration modes. The total tension calculation unit 14 calculates the total tension of the strip 1 using the tension component calculated by the tension component calculation unit 13 and the effective width set by the effective width setting unit 12.

  Further, the tension calculation device 7 is connected to a display device (not shown) for displaying the calculated tension on a screen and a tension control device (not shown). This tension control device feedback controls the rotational speeds of the two rolls 2 and 3 so that the tension becomes a preset target tension.

Next, a tension measuring method using the tension measuring device 4 will be described.
A predetermined tension is applied to the traveling band 1 by rotating the two rolls 2 and 3 that support the front and rear of the band 1 in the traveling direction. Since the belt-like body 1 is in a state where both ends in the running direction are supported by the rolls 2 and 3, respectively, the belt-like body 1 mainly vibrates freely with the central portion in the longitudinal direction between the rolls 2 and 3 as a vibration antinode. And the tension | tensile_strength provided to the strip | belt shaped object 1 and a primary natural frequency have a relationship of (1) Formula. In general, higher-order mode natural vibrations are caused by first-order mode natural vibrations, and thus are not directly related to the tension applied to the belt-like body.

T = 4L ² f ² δA (1)
Here, T is a tension value, L is a length between supports, f is a natural frequency, δ is a specific gravity of a strip, and A is a cross-sectional area of the strip.

<Displacement detection process>
Temporal changes in the displacement amounts of the measurement points 31 to 35 of the band 1 are respectively measured by the non-contact displacement meters 21 to 25, and signals corresponding to the displacement amounts of the measurement points 31 to 35 are respectively output to the Fourier transform device 6. Is done.

<Frequency characteristics deriving process>
The Fourier transform device 6 takes in the displacement amount signal, calculates the frequency characteristic of vibration for each of the measurement points 31 to 35, and outputs it to the tension calculation device 7.

  At this time, the tension calculation device 7 executes the tension calculation routine of FIG. 2, and the frequency characteristics for each of the measurement points 31 to 35 output to the tension calculation device 7 are stored in the storage unit 15 (S1).

<Natural frequency extraction process>
Next, the natural frequency extraction unit 10 extracts the maximum peak frequencies f1 to f5 having the maximum peak value of the amplitude one by one from the frequency characteristics of the measurement points 31 to 35 (S2).

  Here, the vibration in the primary mode of the belt-like body supported at two points in the longitudinal direction of the belt-like body has the center in the longitudinal direction of the belt-like body 1 as an antinode. Therefore, in the frequency wave number characteristic derived based on the displacement measured by the displacement measuring device 5 located in the longitudinal center of the strip 1, the amplitude of the first mode is clearly higher than the amplitude of the higher mode. growing. Accordingly, the primary natural frequency can be extracted by extracting the maximum peak frequency at which the amplitude becomes the maximum peak value. That is, by disposing the displacement amount measuring device 5 so as to face the center in the longitudinal direction of the strip 1, the primary natural frequency can be easily extracted from the frequency characteristics at the measurement points 31 to 35.

  The extracted primary natural frequencies f1 to f5 may partially overlap. If there is an overlap, the primary natural frequencies f1 to f5 are arranged, and a plurality of primary natural frequencies are extracted (S3). In the present embodiment, it is assumed that three primary natural frequencies f11 to f13 are extracted. The primary natural frequencies f11 to f13 are set in ascending order of frequency. The vibration mode numbers are set to mode 1, mode 2, and mode 3 for each primary natural frequency f11, f12, and f13.

<Vibration mode derivation process>
Next, the vibration mode deriving unit 11 derives three vibration mode shapes for each of the three primary natural frequencies f11 to f13 based on the frequency characteristics of the measurement points 31 to 35 (S4). The vibration mode shape indicates the amount of displacement (amplitude) of the band with respect to the position in the width direction of the band at a specific natural frequency. When deriving the vibration mode shape of mode 1, the displacement amount at the primary natural frequency f11 is extracted from the frequency characteristics of the five measurement points 31 to 35, respectively, and the horizontal axis indicates the width from the end in the width direction on the measurement point 31 side. After plotting 5 points by taking the distance in the width direction and the amount of displacement (amplitude) on the vertical axis, a curve approximation is performed by quadratic function interpolation, for example. Similarly, mode 2 and mode 3 vibration mode shapes are derived.

  The amplitude of the vibration mode shape is normalized for each of modes 1 to 3 (S5). Thereby, as shown in FIG. 3, the horizontal axis (x axis) is the distance in the width direction from the end in the width direction on the measurement point 31 side, and the vertical axis (y axis) is the normalized amplitude. A normalized vibration mode shape is obtained.

  Here, normalization is an operation of extracting the maximum amplitude of one vibration mode shape and dividing all the amplitudes of the vibration mode shape by this maximum amplitude. Therefore, the maximum value of the normalized amplitude of the normalized vibration mode shape is 1.

<Effective width setting process>
The effective width setting unit 12 (effective width setting means) sets a common effective width setting line R in modes 1 to 3 (S6). Then, D1 to D3 are obtained for each of the modes 1 to 3 based on the effective width setting line R and the normalized vibration mode shapes of the modes 1 to 3 (S7). Specifically, as shown in FIG. 3, in the normalized vibration mode shape of mode number i, the width direction length of a section where the normalized amplitude is larger than the effective width setting line R is Di. That is, when the normalized vibration mode shape is expressed as yi = gi (x), the range of x that satisfies | yi | ≧ R is defined as Di. Di may be divided into a plurality of D2a, D2b, and D2c as in D2 of mode 2 in FIG.

  Then, it is determined whether or not ΣDi = W is established (S8). That is, it is determined whether or not the value obtained by adding D1 to D3 is equal to the full width W of the band 1.

  If the sum of D1 to D3 is not equal to the full width W of the strip 1 (S8, NO), the effective width setting line R is adjusted (S9), and S7 is re-executed using this effective width setting line R. Is done.

  On the other hand, as shown in FIG. 4, when the sum total of D1 to D3 is equal to the full width W of the strip 1 (S8, YES), this D1 to D3 is determined as the effective width.

<Tension component calculation process>
Then, the tension component calculation unit 13 substitutes the primary natural frequencies f11 to f13 into the above-described equation (1), thereby calculating the tension components T1 to T3 of modes 1 to 3 (S10).

  The tension component T3 of the mode 3 acts on the region in the width direction of the strip 1 corresponding to the effective width D3 of the mode 3. In addition, there are cases where areas in the width direction partially overlap as in the effective width D1 and effective width D2 of mode 1 and mode 2. The tension acting on this overlapping region is affected by both mode 1 and mode 2. In this case, it is possible to determine which mode is strongly influenced by comparing the magnitudes of the normalized amplitudes of mode 1 and mode 2. In the overlapping region of the effective width D1 and the effective width D2b, the normalized amplitude in mode 1 is larger than the normalized amplitude in mode 2, so that it can be determined that the influence of the tension component T1 in mode 1 is large. Thus, the tension distribution in the width direction of the strip 1 can be grasped based on the calculated normalized mode shapes of the modes 1 to 3, the effective widths D1 to D3, and the tension components T1 to T3. .

<Total tension calculation process>
Next, the total tension calculator 14 calculates the total tension Tt of the strip 1 (S11). Specifically, by adding the values obtained by multiplying the tension components T1 to T3 of modes 1 to 3 by the ratios of the effective widths D1 to D3 to the total width W of the band 1 for all modes, the total of the band 1 The tension Tt is calculated. That is, the total tension Tt is expressed by equation (2). In addition, as described above, the tension affected by the two modes is acting on the region where the effective width overlaps, but the overlapping region of the effective width is smaller than the entire width, so the total tension Can be ignored.

  Tt = Σ (Ti × Di / W) (2)

  When the total tension Tt of the strip 1 is obtained as described above, the total tension Tt is transmitted to a tension control device (not shown). The tension control device that has received the total tension Tt controls the belts 1 and 3 to apply a predetermined tension by controlling the rotational speeds of the rolls 2 and 3. Thereby, the strip | belt-shaped body 1 can be drive | worked adjusting total tension.

  Further, the tension components T1 to T3 of the strip 1 are displayed on the display device (not shown) as numerical values and figures together with the normalized vibration mode shape and the effective widths D1 to D3. An operator who visually observes the display device can grasp the tension distribution in the width direction of the belt-like body 1, and therefore can confirm whether or not the belt-like body 1 is stretched and distortion such as an ear wave is generated.

Next, simulation was performed on the belt-like body under the following conditions, and the tension applied to the belt-like body was compared with the total tension Tt obtained by applying the tension measuring device 4. The band-shaped body has a support length L of 1150 mm, an overall width W of 1130 mm, a density of 2.7 g / cm ³ , a tension of 5884 N, and distortion in the central portion in the width direction.

  As a result, three primary natural frequencies f11 (32.8 Hz), f12 (40.0 Hz), and f13 (42.2 Hz) were extracted from the frequency characteristics. By substituting these natural frequencies f11 to f13 and the conditions of the belt-like body into the above equation (1), the tension components T1 (4081.5N), T2 (6069.6N), T3 of each mode 1 to 3 (6755.5N) was calculated. Furthermore, the values D1 / W (0.22), D2 / W (0.45), and D3 / W (0.33) obtained by dividing the effective width of each mode by the total width of the band are substituted into the expression (2). A total tension Tt of 5858N was obtained. This value has an error of 0.5% with respect to the tension applied to the belt. Therefore, it was confirmed that the total tension applied to the belt can be known with high accuracy by the tension measuring device 4 of the present embodiment.

  In the natural frequency extracting unit 10, the number of primary natural frequencies extracted from the maximum peak frequencies f1 to f5 is not limited to three. When the tension distribution in the width direction of the strip 1 is complicated, the number of extracted primary natural frequencies increases.

  Further, the number of non-contact displacement meters (number of measurement points) is not limited to five. As a general distorted state of the band 1, a state in which distortion occurs in the central part in the width direction of the band 1 (so-called medium elongation), a state in which distortion occurs in the end in the width direction (so-called ear waves), an end in the width direction There is a state where distortion occurs at a position of 1/4 of the full width from the part (so-called quarter buckle) and the like, and there is a state where at least two of the above states are combined. Therefore, the number of measurement points needs to be at least 5 or more. In order to obtain the tension distribution and the total tension with high accuracy, it is desirable that the number of measurement points is large.

  Further, the position of the displacement measuring device 5 is not limited to the center in the longitudinal direction of the strip 1. Instead of arranging one at the center in the longitudinal direction, two displacement measuring devices 5 may be arranged at positions symmetrical with respect to the center in the longitudinal direction of the strip 1 as shown in FIG. Since the vibration in the primary mode vibrates with the center in the longitudinal direction of the strip 1 as an antinode, the displacement of the primary mode at the measurement point symmetric with respect to the center in the longitudinal direction of the strip 1 has the same phase. On the other hand, the displacement amount of the natural vibration of the even-order vibration mode including the secondary mode has an antiphase at a measurement point symmetrical with respect to the center in the longitudinal direction. When the natural frequency extraction unit 10 extracts a common maximum peak frequency from two frequency characteristics derived on the basis of the displacement amounts of two measurement points symmetrical with respect to the center in the longitudinal direction, two measurements at the frequency are performed. When the amount of displacement of the point is in antiphase, this frequency is not extracted as the primary natural frequency. In this way, since the natural frequency is extracted by excluding the even-order natural frequency including the secondary mode, the primary natural frequency can be easily extracted.

  Further, one displacement amount measuring device 5 may be disposed at the center in the longitudinal direction of the belt-shaped body 1, and further, two devices may be disposed at positions symmetrical with respect to the center in the longitudinal direction.

[Second Embodiment]
Next, the tension measuring device according to the second embodiment will be described. However, about the thing which has the structure similar to 1st embodiment, the same code | symbol is attached | subjected and the description is abbreviate | omitted suitably.

  In addition to the displacement measuring device 5, the Fourier transform device 6, the tension calculating device 7 and the like of the first embodiment, the tension measuring device 4 of this embodiment further adds a tension calculating device belt 1a. A vibration device 8 (vibration means) for vibrating is provided. In addition to the configuration of the first embodiment, the tension calculation device 7 further includes an out-of-plane deformation determination unit 16 (out-of-plane deformation area determination unit) that determines an area where out-of-plane deformation has occurred. I have.

  Here, the out-of-plane deformation means that the band-shaped body 1a is subjected to a compressive force in the longitudinal direction due to factors such as the material of the band-shaped body 1a, the type of process, the rotational speed of the roll, and is deformed by being pushed out of the plane. It points to that. Therefore, in this out-of-plane deformation region, the stress is released and no tension is applied. Further, as shown in FIG. 6, the out-of-plane deformation region does not change abruptly with respect to the longitudinal direction of the strip 1a, and the convex out-of-plane deformation portion is periodically generated with respect to the longitudinal direction of the strip 1a. ing.

  As shown in FIG. 6, the vibration device 8 is disposed at the lower part of the strip 1 a and vibrates the strip 1 a in the out-of-plane direction. As the vibration device 8, a non-contact type vibration device is used. Examples of the non-contact type vibration device include a vibration device using an induced electromotive force, an air vibration device, and a vibration device using an attractive force due to a magnetic force.

  The tension calculation device 7 includes an out-of-plane deformation determination unit 16. The out-of-plane deformation determination unit 16 determines the presence or absence of out-of-plane deformation for each of the measurement points 31 to 35 by comparing the frequency characteristics of the measurement points 31 to 35 before and after excitation. Thereby, the out-of-plane deformation region of the strip 1a is determined.

  Next, a tension measuring method using the tension measuring device 4 will be described.

<Displacement amount detection step and frequency characteristic derivation step>
First, before the vibrating body 8 vibrates the band 1 a, vibration due to the tension of the band 1 a is measured by the displacement measuring device 5, and a displacement signal is output to the Fourier transform device 6. The Fourier transform device 6 calculates frequency characteristics of the measurement points 31 to 35 and outputs them to the tension calculation device 7.

  At this time, the tension calculation device 7 executes the tension calculation routine of FIG. 7, and the frequency characteristics before the vibration of the measurement points 31 to 35 are stored in the storage unit 15 (S20).

  Next, the belt-like body 1 a is vibrated by the vibration device 8, and the temporal change in the displacement amount of the belt-like body 1 a is measured by the displacement amount measuring device 5. Then, the displacement amount signal is output to the Fourier transform device 6. The Fourier transform device 6 calculates frequency characteristics of the measurement points 31 to 35 and outputs them to the tension calculation device 7.

  And the frequency characteristic after the vibration of the measurement points 31-35 output to the tension calculating device 7 is memorize | stored in the memory | storage part 15 (S21).

<Natural frequency extraction process>
Next, the natural frequency extraction unit 10 extracts the maximum peak frequencies f21 to f25 from the frequency characteristics of the measurement points 31 to 35 before vibration (S22).

  Here, the frequency characteristic of a measurement point with out-of-plane deformation has a peak value of amplitude at a specific frequency. This frequency corresponds to the number of times that the convex portion of the out-of-plane deformation passes this measurement point in one second. That is, the maximum peak frequency extracted from the frequency characteristic of the measurement point with out-of-plane deformation is not due to the vibration of the strip 1a.

<Out-of-plane deformation area discrimination process>
Next, an out-of-plane deformation area determination process is performed by the out-of-plane deformation determination unit 16 (S23). That is, by executing the out-of-plane deformation area determination routine of FIG. 8, first, the frequency characteristics of the measurement point 31 before and after excitation are compared (S40), and the amplitude at the maximum peak frequency f21 is large before and after excitation. It is determined whether or not (S41).

  When the region having no out-of-plane deformation is vibrated, it vibrates with a larger amplitude than before the vibration. As shown in FIG. 6, no out-of-plane deformation occurs at the measurement point 31. The maximum peak frequency f21 extracted from the frequency characteristics of the measurement point 31 before excitation is the primary natural frequency of the strip 1a. Therefore, as shown in FIG. 9A, when comparing the frequency characteristics of the measurement point 31 before and after excitation, the amplitude at the maximum peak frequency f21 is greater after excitation than before excitation.

  Thus, when the amplitude at the maximum peak frequency is greater than or equal to a certain value before and after excitation at a certain measurement point (S41, YES), it is determined that there is no out-of-plane deformation (S44).

  On the other hand, since the tension is not applied to the out-of-plane deformation region, it hardly vibrates even immediately after being excited. As shown in FIG. 6, out-of-plane deformation occurs at the measurement point 35. As described above, the maximum peak frequency f25 extracted from the frequency characteristics of the measurement point 35 is not caused by the vibration of the strip 1a but is caused by out-of-plane deformation. Therefore, as shown in FIG. 9B, when the frequency characteristics of the measurement point 35 before and after excitation are compared, the amplitude at the maximum peak frequency f25 hardly changes before and after excitation.

  Thus, when the amplitude at the maximum peak frequency is not large before and after excitation at a certain measurement point (NO in S41), the amplitude at the maximum peak frequency and the amplitude at other frequencies in the frequency characteristics before excitation. Are compared. Then, it is determined whether or not there is an amplitude greater than 20% of the amplitude at the maximum peak frequency (S42).

  In the out-of-plane deformation region, no tension is applied, so the frequency characteristic has an amplitude peak value due to out-of-plane deformation, but there should be no amplitude peak value due to vibration. Therefore, the accuracy of discriminating the out-of-plane deformation region can be improved by comparing the amplitude of the maximum peak frequency with the amplitude of another frequency region.

  When an amplitude larger than 20% of the amplitude at the maximum peak frequency exists (S42, YES), it is determined that this measurement point has no out-of-plane deformation (S44).

  On the other hand, as shown in FIG. 8B, when there is no amplitude larger than 20% of the amplitude at the maximum peak frequency (S42, NO), it is determined that the measurement point has out-of-plane deformation (S43). Then, it is determined whether or not determination has been made for all measurement points (S45). If determination has not been made for all measurement points (S45, NO), S40 is re-executed for the remaining measurement points. On the other hand, if determination is made for all measurement points (S45, YES), the process proceeds to the next step.

  As described above, the presence / absence of out-of-plane deformation is determined for each measurement point, thereby discriminating a region having out-of-plane deformation and a region having no out-of-plane deformation. Then, a plurality of primary natural frequencies are extracted from the maximum peak frequency at the measurement point determined as having no out-of-plane deformation (S24). In the present embodiment, it is assumed that three natural frequencies f11, 12, and 13 are extracted.

  Note that the entire belt-like body 1a may vibrate in the out-of-plane direction due to equipment vibrations such as vibrations when the roll rotates. In this case, amplitude peaks appear at the same frequency in the frequency characteristics of all measurement points. The amplitude of this frequency does not increase before and after excitation. However, in the case of out-of-plane deformation, an amplitude peak appears only in the frequency characteristics of some measurement points. Therefore, it is possible to distinguish between vibration of the equipment and out-of-plane deformation. Then, when extracting the maximum peak frequency from the frequency characteristics, the frequency resulting from the vibration of the equipment is not extracted.

<Vibration mode derivation process>
Next, the vibration mode deriving unit 11 derives the vibration mode shape for each of the primary natural frequencies f11 to f13 based on the frequency characteristics of the measurement points 31 to 33 other than the out-of-plane deformation region (S25). When the width direction region of the strip-shaped body 1a having the out-of-plane deformation is denoted by δ, the vibration mode shape is derived for the region excluding the range of the out-of-plane deformation region δ from the full width W of the strip-shaped body 1.

  The amplitude of the vibration mode shape is normalized for each mode (S26), and a normalized vibration mode shape is obtained.

<Effective width setting process>
The effective width setting unit 12 (effective width setting means) sets a common effective width setting line R in modes 1 to 3 (S27). Then, D1 to D3 are obtained for each of the modes 1 to 3 based on the effective width setting line R and the normalized vibration mode shapes of the modes 1 to 3 (S28).

  Then, it is determined whether or not ΣDi = W−δ is satisfied (S29). That is, it is determined whether or not the value obtained by adding D1 to D3 is the same as the value obtained by subtracting the out-of-plane deformation region δ from the full width W of the strip 1a. A value obtained by subtracting the out-of-plane deformation region δ from the entire width W of the strip 1a is defined as a vibration width d of the strip 1a.

  When the sum total of D1 to D3 is not the same as the vibration width d (S29, NO), the effective width setting line R is adjusted (S30), and S30 is re-executed using the effective width setting line R.

  On the other hand, when the sum total of D1 to D3 is the same as the vibration width d (S29, YES), these D1 to D3 are determined to be effective widths, and the process proceeds to the next step.

<Tension component calculation process>
The tension component calculation unit 13 substitutes the primary natural frequencies f11 to f13 into the above-described equation (1) to calculate the tension components T1 to T3 of modes 1 to 3 (S31). Based on the tension components T1 to T3, the normalized vibration mode shapes of modes 1 to 3, and the effective widths D1 to D3, the tension distribution in the region without the out-of-plane deformation of the strip 1a can be grasped. On the other hand, it has already been understood that no tension acts on the out-of-plane deformation region. Therefore, the tension in the width direction of the strip 1a is determined based on the normalized vibration mode shapes of the modes 1 to 3 derived by excluding the out-of-plane deformation region, the effective widths D1 to D3, and the tension components T1 to T3. The distribution can be grasped.

<Total tension calculation process>
Next, the total tension calculator 14 calculates the total tension Tt of the strip 1a (S32). Since no tension is applied to the out-of-plane deformation region, the total tension Tt applied to the strip 1a is equal to the total tension of the region without the out-of-plane deformation of the strip 1a. A specific calculation method first multiplies the tension components T1 to T3 of modes 1 to 3 by the ratio of the effective widths D1 to D3 to the vibration width d, respectively. And the total tension | tensile_strength of the strip | belt shaped object 1a is calculated by adding this value calculated for every mode 1-3 about all the modes. That is, the total tension Tt of the belt-like body 1a is expressed by equation (3).

Tt = Σ (Ti × Di / d)
= Σ {Ti × Di / (W−δ)} (3)

  The out-of-plane deformation determination unit 16 determines whether or not there is an amplitude larger than 20% of the amplitude at the maximum peak frequency, but the ratio of the amplitude serving as a determination criterion is limited to 20%. It is not a thing.

  Further, the out-of-plane deformation determination means is not limited to the above-described configuration. For example, the band 1a is irradiated with light, and a shadow generated on the surface of the band 1a is photographed with a camera. Then, the out-of-plane deformation region may be determined by performing image processing on the acquired image data.

It is explanatory drawing which shows the arrangement | positioning state of the tension measuring apparatus by 1st embodiment of this invention. It is a flowchart of a tension calculation routine. It is a graph which shows the normalized vibration mode shape of each vibration mode. It is explanatory drawing which shows the relationship between an effective width and the full width of a strip | belt shaped object. It is a top view which shows the example of a change of 1st embodiment. It is explanatory drawing which shows the arrangement | positioning state of the tension measuring apparatus by 2nd embodiment of this invention. It is a flowchart of a tension calculation routine. It is a flowchart of an out-of-plane deformation area discrimination routine. (A) is a graph which shows the frequency characteristic of the measurement point without an out-of-plane deformation, (b) is a graph which shows the frequency characteristic of the measurement point with an out-of-plane deformation.

Explanation of symbols

1, 1a Band 2, 3 Roll 4 Tension measuring device 5 Displacement measuring device (displacement detecting means)
6 Fourier transform device (frequency characteristic deriving unit)
7 Tension calculator 8 Exciter 10 Natural frequency extraction unit (natural frequency extraction means)
11 Vibration mode deriving section (vibration mode deriving means)
12 Effective width setting section (effective width setting means)
13 Tension component calculation unit (tension distribution calculation means)
14 Total tension calculator (total tension calculator)
16 Out-of-plane deformation discriminating section (out-of-plane deformation area discriminating means)
31, 32, 33, 34, 35 Measuring points

Claims (7)

A tension measuring device that measures a tension state by measuring vibrations of a band supported at two positions in the longitudinal direction,
Non-contact displacement amount detecting means for detecting the displacement amount in the out-of-plane direction of the strip at a plurality of measurement points arranged in the width direction of the strip,
Frequency characteristic deriving means for deriving a frequency characteristic for each of the plurality of measurement points based on a signal relating to the displacement detected at the plurality of measurement points;
Natural frequency extracting means for extracting a plurality of primary natural frequencies based on the plurality of frequency characteristics derived by the frequency characteristic deriving means ;
Vibration mode derivation means for deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies, and further normalizing amplitudes of the plurality of vibration mode shapes;
The length in the width direction of the section where the amplitude is larger than the predetermined amplitude line common to all vibration modes, extracted for each of the normalized vibration mode shapes, and added for all vibration modes. Effective width setting means for setting the width direction length such that the value becomes equal to the full width of the strip, as the effective width of the plurality of vibration modes,
A tension component calculating means for calculating a tension component corresponding to the vibration mode based on the primary natural frequency of each vibration mode;
Total tension calculation means for adding the value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the total width of the strip for all the vibration modes to obtain the total tension of the strip When,
A tension measuring device comprising:   2. The tension measuring device according to claim 1, wherein the displacement amount detecting means is disposed to face the center in the longitudinal direction of the belt-like body. A plurality of the displacement amount detection means are provided, and the plurality of measurement points of at least two displacement amount detection means are respectively positioned symmetrically with respect to the longitudinal center.
When the natural frequency extraction means extracts a specific natural frequency based on the displacement amounts detected at the two measurement points located symmetrically, the displacement of the two measurement points at the natural frequency is extracted. 3. The tension measuring device according to claim 1, wherein the natural frequency is not extracted as the primary natural frequency when the quantities are in opposite phases to each other. A tension measuring device that measures a tension state by measuring vibrations of a band supported at two positions in the longitudinal direction,
Non-contact displacement amount detecting means for detecting the displacement amount in the out-of-plane direction of the strip at a plurality of measurement points arranged in the width direction of the strip,
An out-of-plane deformation area discriminating means for discriminating an area where out-of-plane deformation of the belt-like body occurs;
Frequency characteristic deriving means for deriving a frequency characteristic for each of the plurality of measurement points based on a signal relating to the displacement detected at the plurality of measurement points;
Natural frequency extracting means for extracting a plurality of primary natural frequencies based on the plurality of frequency characteristics derived by the frequency characteristic deriving means ;
Vibration mode derivation means for deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies, and further normalizing amplitudes of the plurality of vibration mode shapes;
The length in the width direction of the section where the amplitude is larger than the predetermined amplitude line common to all vibration modes, extracted for each of the normalized vibration mode shapes, and added for all vibration modes. The effective width of the plurality of vibration modes is set so that the width direction length is equal to a value obtained by subtracting the width of the out-of-plane deformation area determined by the out-of-plane deformation area determination means from the total width of the belt-like body. Effective width setting means to set,
A tension component calculating means for calculating a tension component corresponding to the vibration mode based on the primary natural frequency of each vibration mode;
A value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the value obtained by subtracting the width of the out-of-plane deformation region from the entire width of the band-like body is added for all vibration modes. A total tension calculating means for obtaining a total tension of the strip,
A tension measuring device comprising: A vibration means for vibrating the belt-like body;
5. The tension measuring apparatus according to claim 4, wherein the out-of-plane deformation area discriminating unit discriminates the presence or absence of out-of-plane deformation by comparing frequency characteristics before and after excitation. A tension measurement method for measuring a tension state by measuring the vibration of a band supported at two longitudinal positions,
At a plurality of measurement points arranged in the width direction of the belt-like body, a displacement amount detecting step for detecting the displacement amount in the out-of-plane direction of the belt-like body without contact;
A frequency characteristic deriving step of deriving a frequency characteristic for each of the plurality of measurement points based on a signal relating to the displacement detected at the plurality of measurement points;
A natural frequency extracting step of extracting a plurality of primary natural frequencies based on the plurality of frequency characteristics derived in the frequency characteristic deriving step ;
Deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies, and further, a vibration mode deriving step of normalizing amplitudes of the plurality of vibration mode shapes;
The length in the width direction of the section where the amplitude is larger than the predetermined amplitude line common to all vibration modes, extracted for each of the normalized vibration mode shapes, and added for all vibration modes. The effective width setting step of setting the width direction length such that the value becomes equal to the entire width of the strip, and the effective width of the plurality of vibration modes,
A tension component calculation step for calculating a tension component corresponding to the vibration mode based on the primary natural frequency of each vibration mode;
A total tension calculation step of adding the value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the total width of the band for all the vibration modes to obtain the total tension of the band When,
A method for measuring tension, comprising: A tension measurement method for measuring a tension state by measuring the vibration of a band supported at two longitudinal positions,
At a plurality of measurement points arranged in the width direction of the belt-like body, a displacement amount detecting step for detecting the displacement amount in the out-of-plane direction of the belt-like body without contact;
An out-of-plane deformation area determining step of determining an area where out-of-plane deformation of the belt-like body occurs;
A frequency characteristic deriving step of deriving a frequency characteristic for each of the plurality of measurement points based on a signal relating to the displacement detected at the plurality of measurement points;
A natural frequency extracting step of extracting a plurality of primary natural frequencies based on the plurality of frequency characteristics derived in the frequency characteristic deriving step ;
Deriving vibration mode shapes of a plurality of vibration modes respectively corresponding to the plurality of primary natural frequencies, and further, a vibration mode deriving step of normalizing amplitudes of the plurality of vibration mode shapes;
The length in the width direction of the section where the amplitude is larger than the predetermined amplitude line common to all vibration modes, extracted for each of the normalized vibration mode shapes, and added for all vibration modes. The effective width of the plurality of vibration modes is set so that the width direction length is equal to a value obtained by subtracting the width of the out-of-plane deformation region determined by the out-of-plane deformation region determination step from the total width of the strip. Effective width setting process to be set, and
A tension component calculation step for calculating a tension component corresponding to the vibration mode based on the primary natural frequency of each vibration mode;
A value obtained by multiplying the tension component of each vibration mode by the ratio of the effective width of each vibration mode to the value obtained by subtracting the width of the out-of-plane deformation region from the entire width of the band-like body is added for all vibration modes. A total tension calculating step for determining the total tension of the strip,
A method for measuring tension, comprising:

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