JPH06249725A - Tension distribution measuring method - Google Patents
Tension distribution measuring methodInfo
- Publication number
- JPH06249725A JPH06249725A JP3705993A JP3705993A JPH06249725A JP H06249725 A JPH06249725 A JP H06249725A JP 3705993 A JP3705993 A JP 3705993A JP 3705993 A JP3705993 A JP 3705993A JP H06249725 A JPH06249725 A JP H06249725A
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- JP
- Japan
- Prior art keywords
- distribution
- tension
- vibration
- uniform
- strip
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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- Force Measurement Appropriate To Specific Purposes (AREA)
Abstract
Description
【０００１】[0001]
【産業上の利用分野】本発明は、鋼板等の帯状体に張力
を印加した時の、幅方向張力分布を測定する方法に関す
る。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of measuring a tension distribution in the width direction when a tension is applied to a strip such as a steel plate.
【０００２】[0002]
【従来の技術】鋼板等の帯状体に張力を印加した場合、
帯状体の形状（平坦度ともいう）の不良により幅方向の
張力分布は必ずしも均一にはならない。逆にこのことを
利用して、張力印加状態で潜在化した形状を張力分布と
して計測することが行われている。幅方向の張力分布を
計測する方法として、帯状体の機械振動を利用し、帯状
体の幅方向の振動分布を計測することによって張力分布
を求める方法が考案されている。例えば、特公昭４５−
２９４６９号公報には、帯状体の幅方向複数箇所で測っ
た振動の固有周波数の違いを用いて、張力分布を求める
方法が開示されている。また、特公昭５０−４００２２
号公報に開示されている方法では、振動の幅方向の振幅
分布を測ることによって、形状を求めている。2. Description of the Related Art When tension is applied to a strip such as a steel plate,
The tension distribution in the width direction is not always uniform due to a defective shape (also referred to as flatness) of the strip. On the contrary, utilizing this fact, the latent shape in the tension applied state is measured as the tension distribution. As a method of measuring the tension distribution in the width direction, a method has been devised in which mechanical vibration of the strip is used to measure the vibration distribution in the width direction of the strip to obtain the tension distribution. For example, Japanese Patent Publication No. 45-
Japanese Patent No. 29469 discloses a method of obtaining a tension distribution by using the difference in natural frequency of vibration measured at a plurality of positions in the width direction of the strip. In addition, Japanese Examined Japanese Patent Publication No.
In the method disclosed in the publication, the shape is obtained by measuring the amplitude distribution of vibration in the width direction.
【０００３】[0003]
【発明が解決しようとする課題】しかし、本発明者らが
振動と張力分布の関係を詳細に調べた結果、振動の固有
周波数や振幅の幅方向分布と、張力分布との関係はそれ
ほど単純ではなく、前に述べたような従来技術では必ず
しも正確な測定が出来ない場合があることが分かった。
例えば、図６に示したものは、中のびの鋼板を加振した
時の振動振幅を幅方向に３チャンネルで計測し、ＦＦＴ
アナライザーによりスペクトルを求めたもので、図６
（ｂ）は幅方向中央のチャンネルに，図６（ａ）及び図
６（ｃ）は幅方向両サイドのチャンネルに対応してい
る。これら３枚のスペクトルを比較した時、８，９，１
０，１１，１２，１３，のような大きなスペクトルピー
クはどのチャンネルでも同一周波数のところに現れてい
るため、幅方向の振動周波数分布から張力分布を求める
ことはできない。他にも小さなピークがいくつか存在す
るが、その周波数から張力分布を求めることも難しい。
また、この例で分かるように、最も周波数の低いスペク
トルピーク８の大きさは、幅方向中央のチャンネルのス
ペクトルピーク８ｂが最も大きく、この固有周波数を持
つ振動モードの幅方向振幅分布は幅方向の張力分布情報
あるいは形状情報を含んでいることを示唆している。し
かしながら、従来技術による方法では、特定の振動モー
ドだけでなくあらゆる振動モードを含んだ状態で振動振
幅を求めていたので、振動振幅分布から求めた張力分布
が必ずしも実際の張力分布に合わないという問題があっ
た。However, as a result of detailed investigations by the present inventors on the relationship between vibration and tension distribution, the relationship between the natural frequency and amplitude widthwise distribution of vibration and the tension distribution is not so simple. However, it was found that accurate measurement may not always be possible with the conventional techniques described above.
For example, in the one shown in FIG. 6, the vibration amplitude when a stretched steel plate is excited is measured in three channels in the width direction, and the FFT is performed.
Fig. 6 shows the spectrum obtained by an analyzer.
6B corresponds to the center channel in the width direction, and FIGS. 6A and 6C correspond to the channels on both sides in the width direction. When these three spectra are compared,
Since large spectral peaks such as 0, 11, 12, 13 appear at the same frequency in all channels, the tension distribution cannot be obtained from the vibration frequency distribution in the width direction. There are some other small peaks, but it is difficult to obtain the tension distribution from the frequency.
Further, as can be seen from this example, the size of the spectrum peak 8 having the lowest frequency is the largest in the spectrum peak 8b of the center channel in the width direction, and the amplitude distribution in the width direction of the vibration mode having this natural frequency is in the width direction. It suggests that it contains tension distribution information or shape information. However, in the method according to the conventional technique, since the vibration amplitude is obtained in a state including not only the specific vibration mode but also all the vibration modes, the tension distribution obtained from the vibration amplitude distribution does not always match the actual tension distribution. was there.
【０００４】特定の振動モードを抽出して、その振動情
報から張力分布を求める方法は非常に有力な方法であ
り、特願平０３−２７６７４３号に出願されている。し
かし、この方法でも、張力分布を近似的に求めることは
可能であるものの、分布を正確に求めることは困難とい
う問題があった。このことを以下に詳しく説明する。A method of extracting a specific vibration mode and obtaining a tension distribution from the vibration information is a very effective method, and is filed in Japanese Patent Application No. 03-276743. However, even with this method, although the tension distribution can be approximately calculated, there is a problem that it is difficult to accurately calculate the distribution. This will be described in detail below.
【０００５】図３は、幅方向の張力分布が均一な帯状体
が、長さ方向両端で単純支持され幅方向両端は自由であ
る場合の振動モードの例を描いたものである。図３
（ａ）は１−１次モードと呼ばれ、長さ方向には両端の
支持部を除いて節と呼ばれる部分が一個もなく、また幅
方向には全体が一様に同一振幅で動いている。図３
（ｂ）は１−２次モードとよばれるモードで、長さ方向
は１−１次モードと同じであるが、幅方向には両端が逆
位相になったいわゆるねじれの動きをする。図３（ｃ）
は１−３次のモードであり、長さ方向には前記２つのモ
ードと同一であるが、幅方向には２箇所に節を持つ動き
になっている。図４は、この３モードについて長さ方向
中央部における振幅の幅方向分布を描いたもので、図４
（ａ）が１−１次モード，図４（ｂ）が１ー２次モー
ド，図４（ｃ）が１−３次モードに対応している。ここ
で振幅が負になっている部分は、正の部分に対して逆位
相の動きをしていることを表す。実際の帯状体の振動で
は、長さ，幅両方向とも、より高次のモードが無限に存
在し、これらの多数のモードが混在して振動している。
均一な張力分布の場合は、振動の微分方程式を解析的に
解くことが可能であり、その結果は上記内容と一致す
る。また、計算機を用いて数値計算により求めることも
でき、同様な結果が得られる。FIG. 3 shows an example of a vibration mode in which a strip having a uniform tension distribution in the width direction is simply supported at both ends in the length direction and free at both ends in the width direction. Figure 3
(A) is called a 1-1-order mode, and there is no single part called a node in the length direction except the supporting parts at both ends, and the whole moves uniformly with the same amplitude in the width direction. . Figure 3
(B) is a mode called 1-2 order mode, which is the same as the 1-1 order mode in the length direction, but has a so-called twisting motion in which both ends have opposite phases in the width direction. Figure 3 (c)
Is a 1-3rd order mode, which is the same as the above two modes in the length direction, but has two joints in the width direction. FIG. 4 shows the widthwise distribution of the amplitude in the central portion in the lengthwise direction for these three modes.
(A) corresponds to the 1-1 order mode, FIG. 4 (b) corresponds to the 1-2 order mode, and FIG. 4 (c) corresponds to the 1-3 order mode. Here, the portion where the amplitude is negative represents that the movement is in the opposite phase with respect to the positive portion. In the actual vibration of the band-shaped body, there are an infinite number of higher-order modes in both the length and width directions, and a large number of these modes coexist.
In the case of uniform tension distribution, it is possible to analytically solve the differential equation of vibration, and the result agrees with the above contents. It can also be obtained by numerical calculation using a computer, and similar results can be obtained.
【０００６】不均一な張力分布が存在する場合、振動の
微分方程式を解析的に解くことはできず、計算機を用い
た数値計算あるいは実験に頼るしかない。数値計算結果
の例を図５に示す。図５（ａ）は幅方向張力分布であ
り、図５（ｂ），図５（ｃ），図５（ｄ）はそれぞれ１
−１次，１−２次，１−３次の振動モードについて、長
さ方向中央部の幅方向振幅分布を計算したものである。
図４と図５から分かるように、１−１次モードの振幅分
布は張力分布と定性的に一致する。しかしながら、張力
分布を定量的に精度良く求めるには振幅分布を張力分布
に変換する変換式が必要であるが、該変換式は解析的に
求めることは出来ない。あらゆる張力分布パターン，帯
状体の材質やサイズについて該変換式を正確に定めるに
は膨大な実験や数値計算が必要であり極めて困難であ
る。そのためある程度の近似的な張力分布推定で我慢せ
ざるを得なかった。When a non-uniform tension distribution is present, the differential equation of vibration cannot be solved analytically, and it is only possible to rely on numerical calculation or experiments using a computer. An example of the numerical calculation result is shown in FIG. FIG. 5 (a) shows the tension distribution in the width direction, and FIG. 5 (b), FIG. 5 (c) and FIG.
The amplitude distributions in the width direction at the central portion in the length direction are calculated for the −1st, 1-2nd and 1-3rd vibration modes.
As can be seen from FIGS. 4 and 5, the amplitude distribution of the 1-1 order mode qualitatively matches the tension distribution. However, in order to quantitatively and accurately obtain the tension distribution, a conversion formula for converting the amplitude distribution into the tension distribution is necessary, but the conversion formula cannot be analytically obtained. It is extremely difficult to accurately determine the conversion formula for any tension distribution pattern, material and size of the band, which requires enormous experiments and numerical calculations. Therefore, I had to put up with a certain degree of approximate tension distribution estimation.
【０００７】本発明はかかる問題点を解決するためにな
されたもので、帯状体の張力分布が複雑なパターンをし
ている場合でも、その分布を正確に測定可能であるよう
な、振動を用いた新しい計測方法を提供することを目的
とする。The present invention has been made in order to solve the above problems, and even if the tension distribution of the band-shaped body has a complicated pattern, the vibration can be accurately measured. The purpose is to provide a new measurement method.
【０００８】[0008]
【課題を解決するための手段】本発明の方法では、帯状
体の幅方向の温度分布を変え、熱による膨張または収縮
の違いにより本来存在していた張力分布をキャンセルさ
せ、結果として張力分布が均一になるようにし、張力分
布が均一であることを１−１次振動モードにより確認す
るようにし、そのときの１−１次モードの固有振動数か
ら均一張力の値を求めるようにしている。また、均一張
力になった時の帯状体の温度分布を計測しておき、張力
分布を求めようとする任意の温度分布との間の、熱膨張
または熱収縮の大きさの幅方向分布を求めるようにして
いる。このようにして求めた均一張力の値及び、熱によ
る膨張または収縮の大きさの分布から、所望の温度分布
の時の張力分布を計算するようにしている。In the method of the present invention, the temperature distribution in the width direction of the strip is changed to cancel the originally existing tension distribution due to the difference in expansion or contraction due to heat. It is made uniform, and it is confirmed by the 1-1-order vibration mode that the tension distribution is uniform, and the value of uniform tension is obtained from the natural frequency of the 1-1-order mode at that time. In addition, the temperature distribution of the strip when the tension becomes uniform is measured in advance, and the widthwise distribution of the magnitude of thermal expansion or contraction with the arbitrary temperature distribution for which the tension distribution is to be obtained is obtained. I am trying. The tension distribution at a desired temperature distribution is calculated from the value of the uniform tension thus obtained and the distribution of the magnitude of expansion or contraction due to heat.
【０００９】[0009]
【作用】前に述べたように、不均一な張力分布が存在す
る状態での振動情報から直接張力分布を正確に計算する
ことは困難であるが、本発明の方法のように均一張力で
あるか否かを振動情報により判定することは容易であ
る。即ち、均一張力の時には１−１次モードの振動振幅
が幅方向に一様になり、また逆に１−１次モードの振動
振幅が幅方向に一様な時は張力分布が均一になっている
ので、このことを利用して張力分布が均一になっている
ことを容易に精度良く確認することができる。As described above, it is difficult to accurately calculate the tension distribution directly from the vibration information in the presence of the non-uniform tension distribution, but it is the uniform tension as in the method of the present invention. It is easy to determine whether or not it is based on the vibration information. That is, when the uniform tension is applied, the vibration amplitude of the 1-1 order mode becomes uniform in the width direction, and conversely, when the vibration amplitude of the 1-1 order mode is uniform in the width direction, the tension distribution becomes uniform. Therefore, it is possible to easily and accurately confirm that the tension distribution is uniform by utilizing this fact.
【００１０】また、一般に各振動モードはそれぞれ固有
の振動周波数を持っているが、不均一張力の場合には振
動方程式が解析的に解けないため、各振動モードの固有
周波数と張力分布との関係は簡単ではない。しかし、均
一張力の場合には振動方程式を解析的に解くことがで
き、各振動モードの固有周波数は簡単な数式で表される
ため、１−１次振動モードの固有周波数から簡単に張力
が計算できる。In general, each vibration mode has its own vibration frequency. However, in the case of non-uniform tension, the vibration equation cannot be analytically solved, so the relationship between the natural frequency of each vibration mode and the tension distribution. Is not easy. However, in the case of uniform tension, the vibration equation can be solved analytically, and the natural frequency of each vibration mode is expressed by a simple mathematical formula. Therefore, the tension can be easily calculated from the natural frequency of the 1-1st order vibration mode. it can.
【００１１】さらに、本発明の方法では、均一張力にな
った時の帯状体の幅方向温度分布を測定するようにして
いるので、所望の温度分布との間の熱膨張または熱収縮
の大きさの幅方向分布を簡単に計算することができ、前
記均一張力値と該熱膨張・収縮分布とから、所望の温度
分布の時の張力分布を求めることができる。Further, according to the method of the present invention, since the temperature distribution in the width direction of the strip is measured when the tension is uniform, the magnitude of the thermal expansion or the thermal contraction with the desired temperature distribution is measured. The distribution in the width direction can be easily calculated, and the tension distribution at a desired temperature distribution can be obtained from the uniform tension value and the thermal expansion / contraction distribution.
【００１２】[0012]
【実施例】以下本発明を実施例により詳細に説明する。
図１は本発明の一実施例の装置構成を示す概略図であ
る。図において、帯状体１は長さ方向に張力を印加され
た状態でロール２ａ，２ｂにより支持されており、加振
器３により加振されその後自由振動をする。この自由振
動はロール２ａ，２ｂ間のほぼ中央位置に設置された変
位センサー４により計測され、その信号はＦＦＴアナラ
イザー５により周波数分析される。本実施例では変位セ
ンサー４は４ａから４ｅまで帯状体の幅方向に５チャン
ネル設置している。EXAMPLES The present invention will be described in detail below with reference to examples.
FIG. 1 is a schematic diagram showing a device configuration of an embodiment of the present invention. In the figure, the strip 1 is supported by rolls 2a and 2b in a state where tension is applied in the length direction, and is vibrated by a vibrator 3 and then freely vibrates. This free vibration is measured by a displacement sensor 4 installed at a substantially central position between the rolls 2a and 2b, and the signal thereof is subjected to frequency analysis by an FFT analyzer 5. In this embodiment, the displacement sensor 4 is provided with 5 channels from 4a to 4e in the width direction of the strip.
【００１３】帯状体の幅方向中央部に節を持つ１−２次
振動モードは、張力分布が均一に近い場合は１−１次振
動モードと周波数による分離がしにくいことがあるの
で、本実施例では加振器３を帯状体１の幅方向中央部に
取り付け、均一張力時における１−２次振動モードの発
生を防ぎ、最も周波数の低いスペクトルピークが１−１
次振動モードに対応するようにしている。Since the 1-2nd order vibration mode having a node at the widthwise center of the band-shaped body may be difficult to separate from the 1-1st order vibration mode by frequency when the tension distribution is almost uniform, this embodiment is performed. In the example, the vibration exciter 3 is attached to the central portion in the width direction of the strip 1 to prevent the occurrence of the 1-2nd order vibration mode during uniform tension, and the spectrum peak with the lowest frequency is 1-1.
It corresponds to the next vibration mode.
【００１４】図１の装置構成において、帯状体１の下部
には近接して加熱体６が多数並べられている。加熱体６
の長さは十分長くし、帯状体１をロール２ａ，２ｂ間の
ほぼ全長にわたって長さ方向に同一の温度に加熱できる
ようにしてあり、また幅方向にはそれぞれが独立に加熱
能力を変えることができるようになっている。加熱体６
の一つ一つとしては、例えばニクロム線のように流す電
流の強さにより加熱温度を変えられるものを採用するこ
とができる。帯状体の幅方向（ｘ方向）温度分布は、温
度分布測定装置７によって計測されるようになってい
る。In the structure of the apparatus shown in FIG. 1, a large number of heating elements 6 are arranged adjacent to the lower part of the strip 1. Heating body 6
Has a sufficiently long length so that the strip 1 can be heated to the same temperature in the length direction over substantially the entire length between the rolls 2a and 2b, and the heating ability can be changed independently in the width direction. You can do it. Heating body 6
As each one of them, for example, a nichrome wire that can change the heating temperature depending on the strength of the electric current can be used. The temperature distribution measuring device 7 measures the temperature distribution in the width direction (x direction) of the strip.
【００１５】加熱体６による加熱を行わない時に、ＦＦ
Ｔアナライザー５によって得られる各チャンネルのスペ
クトルから、最も周波数の低いスペクトルピークを抽出
し、その大きさを幅方向にプロットすると例えば中のび
の場合には図２（ａ）のように幅方向中央部に山を持つ
分布が得られる。この分布の形から中のびであることが
分かり、均一な張力分布にするには加熱体６のうち両サ
イドに近いものを加熱する必要があることが容易に分か
る。このように、最も周波数の低いスペクトルピークの
大きさは、張力の小さい部分で大きくなるので、どの部
分を強く加熱すべきか、あるいはどの部分の加熱を弱め
るべきかの判断は容易であり、簡単に均一張力の状態を
作り出すことができる。このようにして、均一張力状態
にした時は、最も周波数の低いスペクトルピークはどの
チャンネルも同一の大きさになり、幅方向に振幅分布を
描くと図２（ｂ）のようになる。When the heating by the heating element 6 is not performed, FF
When the spectrum peak of the lowest frequency is extracted from the spectrum of each channel obtained by the T-analyzer 5 and its size is plotted in the width direction, for example, in the case of the middle spread, as shown in FIG. A distribution with a mountain at is obtained. From the shape of this distribution, it can be seen that the shape is medium and that it is necessary to heat the heating elements 6 close to both sides in order to obtain a uniform tension distribution. In this way, the magnitude of the spectrum peak with the lowest frequency becomes larger in the part with low tension, so it is easy to determine which part should be heated strongly or which part should be weakened, and it is easy to A state of uniform tension can be created. In this way, when the uniform tension state is set, the spectrum peak with the lowest frequency has the same magnitude in all channels, and the amplitude distribution in the width direction is as shown in FIG. 2 (b).
【００１６】次に、具体的な張力分布計算の方法につい
て説明する。いま帯状体の温度分布がＴ（ｘ）である時
の張力分布を求めるものとし、加熱して均一張力になっ
た時の温度分布がＴ0 （ｘ）であったとすれば、温度差
の幅方向分布ΔＴ（ｘ）はNext, a specific method of calculating the tension distribution will be described. Now, assume that the tension distribution when the temperature distribution of the strip is T (x) is obtained, and if the temperature distribution when heating to uniform tension is T 0 (x), the width of the temperature difference is The direction distribution ΔT (x) is
【数１】 である。温度差分布ΔＴ（ｘ）による長さ変化の分布Δ
Ｌ（ｘ）は、[Equation 1] Is. Distribution of length change Δ due to temperature difference distribution ΔT (x)
L (x) is
【数２】 で与えられる。ここでβは帯状体の線膨張係数で、Ｌは
ロール２ａ，２ｂ間の距離であり両ロールにより支持さ
れた帯状体の長さでもある。[Equation 2] Given in. Here, β is the coefficient of linear expansion of the strip, L is the distance between the rolls 2a and 2b, and is also the length of the strip supported by both rolls.
【００１７】一方、均一張力の場合には１−１次モード
の振動周波数ｆ0 と単位断面積当たりの張力δ0 との間
には次式On the other hand, in the case of uniform tension, between the vibration frequency f 0 of the 1-1st mode and the tension δ 0 per unit cross-sectional area,
【数３】 の関係がある。ここでρは帯状体の密度，Ｅは帯状体の
ヤング率，νは帯状体のポアソン比，ｈは帯状体の厚み
である。[Equation 3] Have a relationship. Here, ρ is the density of the strip, E is the Young's modulus of the strip, ν is the Poisson's ratio of the strip, and h is the thickness of the strip.
【００１８】ここで、ロール２ａ，２ｂにはさまれた長
さＬの帯状体が、温度分布Ｔ（ｘ）の時に張力の無い状
態では幅方向に長さ分布ＬT （ｘ）をもっているものと
すれば、張力を印加した時の単位断面積当たりの張力分
布δ（ｘ）は、ＬT （ｘ）がＬにほぼ等しいことを考慮
すれば、フックの法則により次式Here, a strip having a length L sandwiched between the rolls 2a and 2b has a length distribution L T (x) in the width direction when there is no tension when the temperature distribution is T (x). Then, considering that T T (x) is almost equal to L, the tension distribution δ (x) per unit cross-sectional area when a tension is applied is calculated by the following equation according to Hooke's law.
【数４】 で与えられる。加熱により均一張力分布が実現されてい
る時は、熱による長さ変化分布ΔＬ（ｘ）を考慮してフ
ックの法則を用いると次式[Equation 4] Given in. When uniform tension distribution is realized by heating, using Hooke's law in consideration of the length change distribution ΔL (x) due to heat, the following equation is obtained.
【数５】 が得られる。[Equation 5] Is obtained.
【００１９】［数１］〜［数５］から温度分布がＴ
（ｘ）である時の時の張力分布δ（ｘ）を求める式はFrom [Equation 1] to [Equation 5], the temperature distribution is T
The formula for obtaining the tension distribution δ (x) when (x) is
【数６】 となり、帯状体の線膨張係数β，ヤング率Ｅ，ポアソン
比ν，密度ρ，厚みｈ，ロール間距離Ｌ，が既知であれ
ば、加熱した後の帯状体温度分布Ｔ0 （ｘ）及び、１−
１次振動モードの振動周波数ｆ0 を計測することによ
り、温度分布がＴ（ｘ）である時の張力分布δ（ｘ）を
求めることができる。[Equation 6] If the linear expansion coefficient β, the Young's modulus E, the Poisson's ratio ν, the density ρ, the thickness h, and the distance L between the rolls of the strip are known, the temperature distribution T 0 (x) of the strip after heating and 1-
By measuring the vibration frequency f 0 of the primary vibration mode, the tension distribution δ (x) when the temperature distribution is T (x) can be obtained.
【００２０】本実施例で、加熱する前の帯状体の温度分
布を温度分布測定装置７により測定しておき、その温度
分布をＴ（ｘ）として使用した場合は、実際にその時に
印加されていた張力分布を求めることができる。また、
Ｔ（ｘ）を定数とすれば、均一な温度分布にした時の張
力分布を求めることができる。In this embodiment, when the temperature distribution of the strip before heating is measured by the temperature distribution measuring device 7 and the temperature distribution is used as T (x), it is actually applied at that time. It is possible to obtain the tension distribution. Also,
If T (x) is a constant, the tension distribution when the temperature distribution is uniform can be obtained.
【００２１】なお、本実施例では温度分布を変えるのに
加熱したが、冷却しても良いし、又加熱と冷却を併用し
てももちろん良い。また、形状を求めたい場合には、張
力分布の絶対値は必要なく、幅方向の相対的な関係が分
かれば十分であるが、そのような用途にも勿論適用する
ことが可能である。In this embodiment, heating is performed to change the temperature distribution, but cooling may be performed, or heating and cooling may be used in combination. Further, when it is desired to obtain the shape, the absolute value of the tension distribution is not required, and it is sufficient if the relative relationship in the width direction is known, but it is of course applicable to such an application.
【００２２】[0022]
【発明の効果】以上の説明で明らかなように、本発明の
方法によれば振動の挙動が単純で数学的にもはっきり解
ける均一張力分布になるようにしてその時の均一張力の
値を求め、その均一張力を基準にして温度による膨張，
収縮の影響を計算により補正するようにしているので、
従来技術による方法よりはるかに精度良く張力分布を求
めることができるだけでなく、任意の温度分布に於ける
張力分布を計算することができ、張力や形状の管理精度
を大幅に向上させることができる。As is apparent from the above description, according to the method of the present invention, the value of the uniform tension at that time is determined by making the behavior of vibration into a uniform tension distribution which is simple and mathematically clear. Expansion due to temperature based on the uniform tension,
Since the effect of contraction is corrected by calculation,
Not only can the tension distribution be obtained with much higher accuracy than the method according to the related art, but also the tension distribution in an arbitrary temperature distribution can be calculated, and the control accuracy of tension and shape can be greatly improved.
【図１】本発明の一実施例の装置構成を示す概略図であ
る。FIG. 1 is a schematic diagram showing a device configuration of an embodiment of the present invention.
【図２】張力分布が不均一な場合と均一な場合の、最も
周波数の低いスペクトルピークの幅方向振幅分布の例を
示す説明図である。FIG. 2 is an explanatory diagram showing an example of an amplitude distribution in the width direction of a spectrum peak having the lowest frequency when the tension distribution is non-uniform and when the tension distribution is uniform.
【図３】張力分布が均一な場合の帯状体の振動モードの
例を示す斜視図である。FIG. 3 is a perspective view showing an example of a vibration mode of the strip in the case where the tension distribution is uniform.
【図４】図３に示した振動モードの幅方向振幅分布を示
す図である。FIG. 4 is a diagram showing a width-direction amplitude distribution of the vibration mode shown in FIG.
【図５】張力分布が不均一な場合の張力分布と、基本的
な振動モードの幅方向振幅分布の計算例を示す図であ
る。FIG. 5 is a diagram showing an example of calculation of a tension distribution when the tension distribution is non-uniform and a widthwise amplitude distribution of basic vibration modes.
【図６】帯状体の振動スペクトルの一例を示す図であ
る。FIG. 6 is a diagram showing an example of a vibration spectrum of a strip.
１ 帯状体 ２，２ａ，２ｂ 支持ロール ３ 加振器 ４，４ａ，４ｂ，４ｃ，４ｄ，４ｅ 変位センサー ５ ＦＦＴアナライザー ６ 加熱体 ７ 温度分布測定装置 ８，８ａ，８ｂ，８ｃ 最も周波数の低い振動スペク
トルピーク ９，９ａ，９ｂ，９ｃ 振動スペクトルピーク １０，１０ａ，１０ｂ，１０ｃ 振動スペクトルピー
ク １１，１１ａ，１１ｂ，１１ｃ 振動スペクトルピー
ク １２，１２ａ，１２ｂ，１２ｃ 振動スペクトルピー
ク １３，１３ａ，１３ｂ，１３ｃ 振動スペクトルピー
ク1 band 2, 2a, 2b support roll 3 vibrator 4,4a, 4b, 4c, 4d, 4e displacement sensor 5 FFT analyzer 6 heating element 7 temperature distribution measuring device 8, 8a, 8b, 8c vibration with the lowest frequency Spectrum peak 9,9a, 9b, 9c vibration spectrum peak 10,10a, 10b, 10c vibration spectrum peak 11,11a, 11b, 11c vibration spectrum peak 12,12a, 12b, 12c vibration spectrum peak 13,13a, 13b, 13c vibration Spectral peak
Claims (1)
−１次振動モードの振幅分布が帯状体の幅方向に一様と
なるように帯状体の幅方向温度分布を変え、その時の温
度分布及び１−１次振動モードの振動周波数から、任意
の温度分布の時の帯状体の張力分布を求めることを特徴
とする帯状体の張力分布測定方法。1. A strip-shaped body 1 to which tension is applied in the longitudinal direction.
The temperature distribution in the width direction of the strip is changed so that the amplitude distribution of the −1st-order vibration mode becomes uniform in the width direction of the strip, and the temperature distribution at that time and the vibration frequency of the 1-1st vibration mode are used to determine an arbitrary temperature A method for measuring the tension distribution of a strip, which comprises obtaining the tension distribution of the strip at the time of distribution.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP3705993A JPH06249725A (en) | 1993-02-25 | 1993-02-25 | Tension distribution measuring method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP3705993A JPH06249725A (en) | 1993-02-25 | 1993-02-25 | Tension distribution measuring method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH06249725A true JPH06249725A (en) | 1994-09-09 |
Family
ID=12486997
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP3705993A Withdrawn JPH06249725A (en) | 1993-02-25 | 1993-02-25 | Tension distribution measuring method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH06249725A (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0775890A1 (en) | 1995-11-27 | 1997-05-28 | Kawasaki Steel Corporation | Strip shape detecting apparatus |
| JP2010091370A (en) * | 2008-10-07 | 2010-04-22 | Kobe Steel Ltd | Noncontact vibration applying apparatus of band, tension measurement apparatus using same, and tension measurement method |
| JP2013015366A (en) * | 2011-07-01 | 2013-01-24 | Kobe Steel Ltd | Total tension measuring apparatus for band-shaped body |
| JP2013024717A (en) * | 2011-07-21 | 2013-02-04 | Kobe Steel Ltd | Tension distribution measuring apparatus of belt-like body |
| WO2013179666A1 (en) * | 2012-06-01 | 2013-12-05 | バンドー化学株式会社 | Method for measuring stable-state tension of transmission belt |
-
1993
- 1993-02-25 JP JP3705993A patent/JPH06249725A/en not_active Withdrawn
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0775890A1 (en) | 1995-11-27 | 1997-05-28 | Kawasaki Steel Corporation | Strip shape detecting apparatus |
| JP2010091370A (en) * | 2008-10-07 | 2010-04-22 | Kobe Steel Ltd | Noncontact vibration applying apparatus of band, tension measurement apparatus using same, and tension measurement method |
| JP2013015366A (en) * | 2011-07-01 | 2013-01-24 | Kobe Steel Ltd | Total tension measuring apparatus for band-shaped body |
| JP2013024717A (en) * | 2011-07-21 | 2013-02-04 | Kobe Steel Ltd | Tension distribution measuring apparatus of belt-like body |
| WO2013179666A1 (en) * | 2012-06-01 | 2013-12-05 | バンドー化学株式会社 | Method for measuring stable-state tension of transmission belt |
| JP5400991B1 (en) * | 2012-06-01 | 2014-01-29 | バンドー化学株式会社 | Method for measuring the tension of a transmission belt when stable |
| KR101425388B1 (en) * | 2012-06-01 | 2014-08-01 | 반도 카가쿠 가부시키가이샤 | Method for measuring stable-state tension of transmission belt |
| US9052248B2 (en) | 2012-06-01 | 2015-06-09 | Bando Chemical Industries, Ltd. | Method for measuring stable-state tension of power transmission belt |
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