JP5756211B2 - Total tension measuring device for strips - Google Patents

Description

  The present invention relates to a total tension measuring device for measuring the total tension of a strip.

  In a line that passes through strips such as metal plates, resin plates, paper, etc., and continuously performs various treatments such as rolling, heat treatment, surface treatment, printing, etc. In order to carry out the treatment satisfactorily, tension is often applied in the running direction of the strip. If the tension applied to the strip is too high, the strip may be broken, and if it is too low, meandering may occur or proper processing cannot be performed, so depending on the strength and cross-sectional dimensions of the strip. Thus, the total tension is set to a predetermined value.

  Conventionally, when measuring the total tension applied to the strip in this way for control or monitoring, the traveling strip is supported at two locations in the traveling direction by a roll or the like. Many contact-type total tension measuring devices that roll-contact a tension detection roll between support parts are used (for example, refer to Patent Documents 1 and 2). In the device described in Patent Document 1, the total tension is measured by detecting the pressing reaction force of the tension detecting roll pressed against the belt-like body with a load cell. In the technique described in Patent Document 2, the tension detection roll of the rotating looper is pressed against the belt-like body, the torque of the electric motor that rotates the looper is detected, and the total tension is measured. There is also a type in which a tension detection roll is pressed against a belt-like body with a constant force, and the displacement of the belt-like body at that time is detected to measure the total tension.

  The contact-type total tension measuring device described above may be wrinkled on the surface of the strip by the tension detection roll pressed against the traveling strip. In order to eliminate the difficulty of such a contact-type total tension measuring device, the non-contact measurement of the total frequency of the strip supported by two parts in the running direction is performed. A contact-type total tension measuring device has been proposed (see, for example, Non-Patent Document 1). The non-contact type total tension measuring device described in Non-Patent Document 1 naturally generates vibration in the belt-like body that travels between the two support parts. There is also an advantage that the device configuration can be simplified.

Note that the total tension T of the belt-like body that vibrates between the two support portions is expressed as follows: the density of the belt-like body is ρ; When the number and f _1, is calculated by the following equation.
T = 4ρAL ² f ₁ ² (1)
Here, ρAL is the mass of the belt-like body between the support parts. When a predetermined span L is set, the total tension T is calculated from the mass ρAL of the belt-like body and the natural frequency f ₁ .

JP-A-7-128164 JP-A-7-265930

Hiroki Ueda, Satoshi Sakatani, Munekazu Harada, Hideo Utsuno, “Noncontact Plate Tension Measurement Technology by Vibration Method”, R & D Kobe Steel Engineering Reports, Vol. 56, no. 1 (April 2006), p. 59-63

  The non-contact type total tension measuring device described in Non-Patent Document 1 can measure the total tension of the belt-shaped body with a simple configuration without wrinkling the belt-shaped body. When measuring the total tension of a strip such as a metal plate, resin plate, or paper, or a strip that is dense but thin, the vibrating strip is affected by the fluid such as air that is in contact with it. The above formula (1) for obtaining the total tension does not take into account the additional mass of the fluid, and therefore there is a problem that the total tension cannot be measured accurately.

  Accordingly, an object of the present invention is to provide a non-contact type total tension measuring device that can accurately measure the total tension with a simple configuration even if the band is a low density or a thin band. .

In order to solve the above-mentioned problems, the present invention is to measure the total tension of a belt-like body that is tensioned in the running direction between the support parts supported by two parts in the running direction. In the measuring apparatus, a means for measuring the vibration displacement of the belt-like body between the two support parts in a non-contact manner is provided, and the natural frequency of the belt-like body obtained from the measured vibration displacement is measured between the support parts. The total tension of the strip is calculated and measured from the mass of the strip and the additional mass of the fluid in contact with the strip between the support portions, and the surface of the strip between the support portions is minutely measured. Dividing into multiple elements of area, calculating the added mass of the fluid in each element from the sound pressure acting on each element by the vibration displacement , and integrating the added mass of the fluid in each element for all elements by doing, The added mass of the serial fluid, adopting the configuration of obtaining a concentrated mass which acts to concentrate at one point on the strip between the support portion.

  That is, there is provided a means for measuring the vibration displacement of the belt-like body between the two support parts in a non-contact manner, the natural frequency of the belt-like body obtained from the measured vibration displacement, and the mass of the belt-like body between the support parts. By calculating and measuring the total tension of the strip from the additional mass of the fluid in contact with the strip between the support parts, even if it is a strip with a low density or a thin strip, Taking into account the additional mass of the surrounding fluid that affects it, the total tension can be measured accurately. In addition, this total tension measuring device for strips can be installed with a simple configuration simply by placing the natural frequency measuring means on the strip line, and the accuracy of the conventional total tension measuring device installed on the existing line It can be suitably used for verification and the like.

  The calculation of the total tension of the strip is simplified by calculating the total tension of the strip as a concentrated mass that acts on the strip between the support portions at one location. be able to.

  By providing means for measuring the vibration displacement of the belt-like body at an intermediate position between the two support parts, the vibration displacement of the belt-like body having the maximum amplitude at the intermediate position between the support parts can be measured with higher accuracy. can do.

  The strip total tension measuring device according to the present invention is provided with means for measuring the vibration displacement of the strip between two support parts, the natural frequency of the strip obtained from the measured vibration displacement, and the support Since the total tension of the strip was calculated from the mass of the strip between the parts and the additional mass of the fluid in contact with the band between the support parts, the density of the strips with low density Even in the case of a thin strip, the total tension can be accurately measured in consideration of the additional mass of the surrounding fluid that affects the vibration. In addition, this total tension measuring device for strips can be installed with a simple configuration simply by placing the natural frequency measuring means on the strip line, and the accuracy of the conventional total tension measuring device installed on the existing line It can be suitably used for verification and the like.

The block diagram which shows embodiment of the total tension measuring apparatus of a strip | belt-shaped body The flowchart which shows the procedure which measures total tension with the total tension measuring device of FIG. Conceptual diagram of additional mass calculation model using simplified calculation formula used in Reference Example Graph showing the total tension measurement result in the reference example compared with the FEM analysis result Graph showing the total tension measurement result in the reference example compared with the experimental result Conceptual diagram of a calculation model for additional mass by the distance / fluid force curve method used in the examples Explanatory drawing explaining the method of calculating additional mass with the calculation model of FIG. Example of calculation of additional mass distribution using the calculation model of FIG.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. As shown in FIG. 1, the total tension measuring device for the belt-like body is supported by the support rolls 2a and 2b at the two locations in the running direction for the total tension of the belt-like body 1 given tension in the running direction. The measurement is performed between the support parts. The displacement meter 3 that measures the vibration displacement of the strip 1 in a non-contact manner at an intermediate position between the support parts, and the total tension T of the strip 1 based on the output of the displacement gauge 3. And an arithmetic unit 4 that calculates

  The displacement meter 3 is a light reflection type laser displacement meter, but may be a non-contact type. When the strip 1 is conductive, an eddy current displacement meter that detects the magnitude of the eddy current generated in the strip 1 or the capacitance between the strip 1 and the sensor head is detected. A capacitance displacement meter or the like can also be used.

The arithmetic device 4 includes an additional mass modeling unit 4a that models an additional mass M _add of air as a fluid that is in contact with the strip 1 between support portions, and an additional mass calculation that calculates the modeled additional mass M _add. Part 4b, a vibration characteristic calculation part 4c for calculating the primary natural frequency f ₁ of the strip 1 from the output of the displacement meter 3, and the calculated natural frequency f ₁ and additional mass M _add The tension calculating unit 4d calculates the total tension T by the following equation from the span L between the supporting portions and the mass M of the belt-like member between the supporting portions determined by the span L.
T = 4L (M + M _add ) f ₁ ² (2)
The expression (2) is an expression representing the relationship between the total tension T and the natural frequency f ₁ when the additional mass M _{add of} air is a concentrated mass that acts in a concentrated manner on the band between the support parts at one location. It is. The mass M is represented by the following equation, where ρ is the density of the strip and A is the cross-sectional area.
M = ρAL (3)
Details of the additional mass modeling unit 4a and the additional mass calculating unit 4b will be described later.

FIG. 2 shows a procedure for measuring the total tension T using the total tension measuring apparatus described above. First, the additional mass modeling unit 4a models the additional mass M _add of air (step 1), and the modeled additional mass M _add is calculated by the additional mass calculating unit 4b (step 2). After that, along with the travel of the strip 1, the displacement displacement of the strip 1 is measured by the displacement meter 3 (step 3), and the natural frequency of the strip 1 is measured by the vibration characteristic calculator 4 c from the measured vibration displacement. f ₁ is calculated (step 4), and the tension calculator 4d calculates the total tension T using the equation (2) (step 5), and performs one tension measurement. After that, if necessary, the procedure from step 3 to step 5 is repeated, and a plurality of tension measurements are continuously performed. After a desired number of tension measurements, the measurement is terminated.

  In the embodiment described above, the vibration displacement of the free vibration that naturally occurs as the belt 1 travels is measured by the displacement meter 3, but vibration applying means for forcibly vibrating the belt 1 is provided to You may make it measure the vibration displacement of a vibration. In this case, the vibration displacement can be measured even in a state where the travel of the belt 1 is stopped.

Reference example

In the reference example, the total tension T of the belt-like body 1 was measured using the additional mass modeling unit 4a using the additional mass calculation model based on a simple calculation formula. FIG. 3 shows a calculation model of the additional mass by a simple calculation formula. In this calculation model, an additional mass M _{add of} air in contact with the strip 1 between the support portions is equal to the plate width W of the strip 1 and the length of the cylindrical portion 5 is equal to the span L between the support portions. The additional mass M _add calculated by the additional mass calculator 4b is expressed by the following equation.
M _add = ρ _air L (W / 2) ² π (4)
Here, ρ _air is the density of _{air and} is expressed by the following equation using the _air temperature T _air (° C.).
ρ _air = 1.293 × 273.2 / (273.2 + T _air ) (5)
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.

The graphs of FIGS. 4A and 4B show the measurement results of the examples in which the total tension T was measured using the additional mass calculation model based on the above-described simple calculation formula, and the total tension T was obtained by FEM analysis in consideration of the additional mass of air. This is shown in comparison with the analysis results obtained and the experimental results of measuring the total tension T with a strain gauge attached to the strip 1. Each graph also shows a measurement result of a comparative example in which the total tension T is measured using the equation (1) that does not consider the additional mass M _{add of} air.

The analysis conditions and the experimental conditions were that the strip 1 was an aluminum plate (ρ = 2699 kg / m ³ ) having a plate width W of 1 m and a plate thickness of 0.5 mm (cross-sectional area A = 5 × 10 ⁻⁴ m ² ). The span L between the support parts was 2 m, and the air temperature T _air was 20 ° C. (ρ _air = 1.205). In both the reference example and the comparative example, in the case of comparison with the analysis result shown in FIG. 4A, the natural frequency obtained by the eigenvalue analysis is input, and in the case of comparison with the experimental result shown in FIG. 4B. The natural frequency actually measured by the displacement meter 3 was input.

As can be seen from the comparison with these analysis results and experimental results, the measurement results of the comparative example that does not consider the added mass M _add are significantly different from the analysis results and experimental results, whereas the measurement result of the reference example is In contrast to the experimental results, although there are some deviations due to variations in the experiments, etc., the results agree well with the analytical results and the experimental results. From these measurement results, it was confirmed that in the total tension measurement of a belt-like body having a low density such as an aluminum plate, the measurement accuracy can be greatly improved by considering the additional mass M _{add of} air as in the present invention. It was.

In the example, the total tension T was measured in the additional mass modeling unit 4a by using an additional mass calculation model by the distance / fluid force curve method. FIG. 5 shows a calculation model of the added mass by the distance / fluid force curve method. In this calculation model, the surface of the band 1 between the support parts is divided into elements 6 having a small area, and as described below, the additional mass M _{add of} air is calculated from the sound pressure acting on each element 6 by vibration displacement. It is to calculate. The element 6 may be divided as long as the area of each element 6 is sufficiently small compared to the surface area of the strip 1, and may be, for example, a section of about 10 × 10 in length and width.

ｉ＝ｓの場合は、

ここに、ρ_airは空気の密度、ωは振動の角周波数、ｃは空気中の音速、ｋは波長常数（＝ω／ｃ）であり、ρ_airは、実施例１と同様に、（５）式から算出するか、または定数とすることができる。 As shown in FIG. 6, assuming a semi-infinite plane, s is an oscillating element, i is an element on which sound pressure acts, and ris _is a distance between the element s and the element i. If the area is A _i , A _s , the velocity of the element s is v _s , the acceleration is α _s , and the sound pressure acting on the element i is p _i , the sound pressure acting on the element i by acoustic radiation due to the vibration of the band 1 The force P _i is expressed by the following equation.
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, k is the wavelength constant (= ω / c), and ρ _air is (5 ) Or can be a constant.

図７は、（９）式で計算した付加質量ｍ_addの分布の計算例を示す。 On the other hand, the force P _i acting on element i in generation of the sound pressure caused by the vibration of the element s becomes a complex vector, the real part by a factor c _air vibration velocity v _s, the vibration velocity and the 90 ° phase the imaginary part The coefficient m _air of the shifted acceleration α _s can be expressed as the following equation.
P _i = c _air v _s + m _air α _s (8)
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. Accordingly, m _air obtained from the equations (6), (7) and (8) is integrated with respect to the vibrations of all elements s having the number n of elements, and doubled as the front and back surfaces of the band 1. Thus, the additional mass m _add of the element i can be calculated by the following equation.

FIG. 7 shows a calculation example of the distribution of the additional mass m _add calculated by the equation (9).

したがって、（１０）式で求めた付加質量Ｍ_addを（２）式に代入することにより、帯状体１の総張力Ｔを測定することができる。図示は省略するが、実施例で測定した総張力Ｔの測定結果も、図４Ａ、図４Ｂに示した参考例のものと同様に、解析結果および実験結果とよく一致することが確認された。 By integrating the air additional mass m _add of each element i calculated by the equation (9) for all the elements, the additional mass M _add as the concentrated mass can be obtained by the following equation.

Therefore, the total tension T of the strip 1 can be measured by substituting the additional mass M _add obtained by the equation (10) into the equation (2). Although illustration is omitted, it was confirmed that the measurement result of the total tension T measured in the example also agrees well with the analysis result and the experimental result, similarly to the reference example shown in FIGS. 4A and 4B.

  In the reference example and the example described above, the simple calculation formula and the distance / fluid force curve method are adopted for the calculation model of the added mass, but the boundary element method can be adopted instead.

  Further, in the reference examples and examples described above, the strip-shaped body to be measured is an aluminum plate, but the total tension measuring device for the strip-shaped body according to the present invention is a metal plate, a resin plate, paper, or the like having a low density. It is also suitable for measuring the total tension of a band-shaped body, or a strip-shaped body such as a metal foil or resin film having a very thin plate thickness.

DESCRIPTION OF SYMBOLS 1 Band 2a, 2b Support roll 3 Displacement meter 4 Arithmetic device 4a Additional mass modeling part 4b Additional mass calculation part 4c Vibration characteristic calculation part 4d Tension calculation part 5 Cylindrical part 6 Element

Claims (2)

In the total tension measuring device for a belt-like body that measures the total tension of the belt-like body given tension in the running direction between the support parts supported at two parts in the running direction, A means for measuring the vibration displacement of the belt-like body in a non-contact manner is provided, and the natural frequency of the belt-like body obtained from the measured vibration displacement, the mass of the belt-like body between the support parts, and between the support parts While calculating and measuring the total tension of the band from the additional mass of the fluid in contact with the band,
Dividing the surface of the strip between the support parts into a plurality of elements having a small area, and calculating an additional mass of the fluid in each element from the sound pressure acting on each element by the vibration displacement ;
The additional mass of the fluid in each element is integrated for all the elements, so that the additional mass of the fluid is obtained as a concentrated mass that acts on the band between the support portions in one place. A device for measuring the total tension of a belt-like body. The total tension measuring apparatus of the belt-shaped member according to claim 1, characterized in that the means for measuring the vibration displacement of the strip, is provided in an intermediate position between the supporting portion of the two places.

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