JP3600445B2 - Roll profile measurement method - Google Patents

Description

【００１４】
第１変位検出器２ａ及び第２変位検出器２ｂによる形状測定演算（第１組）
【００１５】
▲１▼合成測定値ｙ２ａ２ｂ（ｘ_ｎ ） の算出
ｙ２ａ（ｘ_ｎ ） とｙ２ｂ（ｘ_ｎ ） との差分として定義される合成測定値ｙ２ａ２ｂ（ｘ_ｎ ） を（２） 式により求める。
【数２】

（２） 式からわかるように、合成測定値ｙ２ａ２ｂ（ｘ_ｎ ） からはｅ_ｚ （ｘ） に関する項が相殺されてなくなる。ｅ_ｚ （ｘ） が小さい時、（２） 式は（３） 式のように近似することができる。
【数３】

（３） 式からわかるように、合成測定値ｙ２ａ２ｂ（ｘ_ｎ ） は近似的に測定したい形状ｍ（ｘ_ｎ ） と間隔Ｌｂだけ位相のずれたｍ（ｘ_ｎ ＋Ｌｂ）とが重ね合わされたものとなっている。
【００１６】
▲２▼対象物形状ｍ（ｘ_ｎ ） の再生
合成測定値ｙ２ａ２ｂ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）から、フーリエ変換の手法を利用してｍ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）を再生することができる。
ここで、ｍ（ｘ_ｎ ） を（４） 式のようにフーリエ級数和の形で表して考える。
【数４】

ここで、Ｌは対象物形状測定長さ、Ｃ_ｋ はｍ（ｘ_ｎ ） のｋ次の形状成分の振幅、φ_ｋ はｋ次成分の位相ずれ量である。（４） 式を（３） 式に代入して整理することにより、（５） 式が得られる。
【数５】

Ｆ_ｋ ，Ｇ_ｋ を用いて対象物形状ｍ（ｘ_ｎ ） は（６） 式のように表される。
【数６】

【００１７】
即ち、合成測定値データ列ｙ２ａ２ｂ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）をフーリエ変換してｃｏｓｋ次成分、ｓｉｎｋ次成分の係数Ｆ_ｋ ，Ｇ_ｋ を求めれば、係数Ｆ_ｋ ，Ｇ_ｋ と、測定系によって定まる値δ_ｋ とを用いて対象物形状ｍ（ｘ_ｎ ） を（６） 式で求めることができる。
【００１８】
第１変位検出器２ａ及び第２変位検出器２ｂでの測定値を基に、ロールプロフィールｍ２ａ２ｂ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）を求める。ｍ２ａ２ｂ（ｘ_ｎ ） は（７） 式のように表すことができる。
【数７】

【００１９】
ここに、Ｅｒ２ａ２ｂ（ｘ_ｎ ） は（１） 式のピッチング運動誤差成分Ｌｂ・ｅ_ｐ （ｘ_ｎ ） に起因する誤差成分である。
合成測定値（＝ｍ（ｘ_ｎ ＋Ｌｂ） −ｍ（ｘ_ｎ ） ）からｍ（ｘ_ｎ ） を再生する方法であることから考えると、Ｅｒ２ａ２ｂ（ｘ_ｎ ） とｅ_ｐ （ｘ_ｎ ） との関係として、（８） 式が得られる。
【数８】

【００２０】
第１変位検出器２ａ及び第３変位検出器２ｃによる形状測定演算（第２組）
【００２１】
第１変位検出器２ａ及び第３変位検出器２ｃでの測定値を基に前述と同様にロールプロフィールｍ２ａ２ｃ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）を求める。ｍ２ａ２ｃ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）は（９） 式のように表すことができる。
【数９】

ここに、Ｅｒ２ａ２ｃ（ｘ_ｎ ） は（１） 式のピッチング運動誤差成分（Ｌｂ＋Ｌｃ）・ｅ_ｐ （ｘ_ｎ ） に起因する誤差成分である。
また、同様に、Ｅｒ２ａ２ｃ（ｘ_ｎ ） とｅ_ｐ （ｘ_ｎ ） との関係として（１０）式が得られる。
【数１０】

【００２２】
ｍ２ａ２ｂ（ｘ_ｎ ） とｍ２ａ２ｃ（ｘ_ｎ ） からのｅ_ｐ （ｘ_ｎ ） の導出
【００２３】
（７） 式，（９）式で与えられるｍ２ａ２ｂ（ｘ_ｎ ） 、ｍ２ａ２ｃ（ｘ_ｎ ） からピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） を求める演算処理手順について説明する。
【００２４】
Ｅｒ２ａ２ｂ（ｘ_ｎ ） 、Ｅｒ２ａ２ｃ（ｘ_ｎ ） 、ｅ_ｐ （ｘ_ｎ ） を（１１）式のようにｍ次までのｃｏｓ，ｓｉｎ の級数和の形で表現して考える。
【数１１】

（１１）式を（８） 式に代入して整理することにより、その係数関係から（１２）式が得られる。
【数１２】

【００２５】
同様に、（１１）式を（１０）式に代入して整理することにより、その係数関係から（１３）式が得られる。
【数１３】

（１２）式及び（１３）式から（ａ^２ _ｋ −ａ^１ _ｋ ）は（１４）式のように表せる。
【数１４】

であり、測定系によって定まる値である。
【００２６】
（１４）式から、ｅ_ｐ （ｘ_ｎ ） を与える係数ｃ_ｋ ，ｄ_ｋ は（１５）式のように表せる。
【数１５】

一方、（７） 式及び（９） 式で与えられる形状ｍ２ａ２ｂ（ｘ_ｎ ） とｍ２ａ２ｃ（ｘ_ｎ ） との差分ｍｒ（ｘ_ｎ ） を求めると、（１１）式との関係からｍｒ（ｘ_ｎ ） は（１６）のように表せる。
【数１６】

【００２７】
即ち、（１５）式中の値（ａ^２ _ｋ −ａ^１ _ｋ ）、（ｂ^２ _ｋ −ｂ^１ _ｋ ）はｍｒ（ｘ_ｎ ） をフーリエ変換した時のｃｏｓ，ｓｉｎ の係数として求めることができる。以上の手順から係数ｃ_ｋ ，ｄ_ｋ が求まり、これを（１１）式に代入することによりピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） が求まる。
【００２８】
ピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） の補正によるロールプロフィールの高精度測定
【００２９】
前述した手順で求めたピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） の値を、例えば（１） 式を用いてＬｂ・ｅ_ｐ （ｘ_ｎ ） の項を除去することが可能になり、第１変位検出器２ａ及び第２変位検出器２ｂによる測定を実施してピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） の影響を受けない高精度な測定が可能となる。
【００３０】
上述したロールプロフィール計測方法をまとめると、以下の▲１▼〜▲８▼のようになる。
【００３１】
▲１▼図１に示すように、取付台３上に第１変位検出器２ａ、第２変位検出器２ｂ及び第３変位検出器２ｃを間隔Ｌｂ，Ｌｃ で載置し、ワークロール１の軸線に沿ってその表面の凹凸量を同時に計測して（１） 式で与えられる測定データ列を得る。
▲２▼第１変位検出器２ａ及び第２変位検出器２ｂの組み合わせによる測定結果の演算を行い、（７） 式で与えられるｅ_ｐ （ｘ_ｎ ） の影響による誤差分を含んだ形状ｍ２ａ２ｂ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）を求める。
【００３２】
▲３▼同様に、第１変位検出器２ａ及び第３変位検出器２ｃの組み合わせによる測定結果の演算を行い、（８） 式で与えられる形状ｍ２ａ２ｃ（ｘ_ｎ ） （ｎ＝０，１，２・・・Ｎ−１）を求める。
▲４▼（１６）式で与えられる演算によって得られた形状ｍ２ａ２ｂ（ｘ_ｎ ） とｍ２ａ２ｃ（ｘ_ｎ ） との差分ｍｒ（ｘ_ｎ ） を求める。
【００３３】
▲５▼ｍｒ（ｘ_ｎ ） をフーリエ変換し、そのｃｏｓ，ｓｉｎ 成分の係数、即ち、（１６）式中の係数（ａ^２ _ｋ −ａ^１ _ｋ ）、（ｂ^２ _ｋ −ｂ^１ _ｋ ）（ｋ＝０，１，２・・・ｍ）を求める。
▲６▼▲５▼で求めた係数（ａ^２ _ｋ −ａ^１ _ｋ ）、（ｂ^２ _ｋ −ｂ^１ _ｋ ）と（１４）式中で示したＡ_ｋ ，Ｂ_ｋ とから（１５）式によりｅ_ｐ （ｘ_ｎ ） を与える係数ｃ_ｋ ，ｄ_ｋ を求める。
【００３４】
▲７▼係数ｃ_ｋ ，ｄ_ｋ から（１１）式によってｅ_ｐ （ｘ_ｎ ） を求め、例えば、（１） 式の測定データｙ２ｂ （ｘ_ｎ ） からＬｂ・ｅ_ｐ （ｘ_ｎ ） を除去する。
▲８▼ｅ_ｐ （ｘ_ｎ ） を除去した測定データ列ｙ２ｂ （ｘ_ｎ ） とｙ２ａ （ｘ_ｎ ） を用いて演算を行い、ｅ_ｐ （ｘ_ｎ ） の影響を受けない真のロールプロフィールｍ（ｘ_ｎ ） を求める。
【００３５】
尚、（１１）式によってｅ_ｐ （ｘ_ｎ ） を求め、（１） 式の測定データｙ２ｃ （ｘ_ｎ ） からＬｂ・ｅ_ｐ （ｘ_ｎ ） を除去し、除去した測定データ列ｙ２ｃ （ｘ_ｎ ） とｙ２ａ （ｘ_ｎ ） を用いてｅ_ｐ （ｘ_ｎ ） の影響を受けない真のロールプロフィールｍ（ｘ_ｎ ） を求めることも可能である。
【００３６】
上述したロールプロフィール測定方法は、演算により求めたｅ_ｐ （ｘ_ｎ ） の影響分を含んだ２組のロールプロフィールに基づいて測定時のｅ_ｐ （ｘ_ｎ ） の値を求め、これを実際の測定データから除去した後に、あらためて演算を行ってｅ_ｐ （ｘ_ｎ ） の影響分を含まないロールプロフィールを求めることができる。このため、測定時の取付台３のピッチング運動誤差成分ｅ_ｐ （ｘ_ｎ ） の大きい条件下でも、高精度なロールプロフィール測定が可能となる。
【００３７】
【発明の効果】
本発明のロールプロフィール計測方法は、ワークロールの軸線方向に移動自在に取付台を設け、取付台上に第１変位検出器及び第２変位検出器及び第３変位検出器をワークロールの軸線方向に所定の間隔で載置し、取付台をワークロールの軸線方向に移動させて取付台移動時の並進運動誤差とピッチング運動誤差の影響を含んだワークロールの軸線方向の凹凸量データを３個の変位検出器によってそれぞれ測定し、第１変位検出器と第２変位検出器との組み合わせを第１組とすると共に、第１変位検出器と第３変位検出器との組み合わせを第２組とし、第１組及び第２組の変位検出器に対応するワークロールの軸線方向の凹凸量データに基づいて取付台移動時のピッチング運動誤差の影響を含んだワークロールの軸線方向の凹凸量データを２組演算し、２組のワークロールの軸線方向の凹凸量データに基づく形状から取付台移動時のピッチング運動誤差を演算し、３個の変位検出器によってそれぞれ測定されたワークロールの軸線方向の凹凸量データをピッチング運動誤差を用いて補正してピッチング運動誤差の影響を除去したワークロールの軸線方向の凹凸量データ列を求め、このデータ列に基づいてワークロールの軸線方向の凹凸形状を演算するようにしたので、ピッチング運動誤差の成分の大きい条件下であっても高精度なロールプロフィール測定が可能となる。この結果、ロールプロフィールの計測を高精度に実施することが可能となる。
【図面の簡単な説明】
【図１】本発明の一実施形態例に係るロールプロフィール計測方法を実施するための計測装置の概略構成図。
【図２】図１中の要部を模式化した概念図。
【符号の説明】
１ ワークロール
２ａ 第１変位検出器
２ｂ 第２変位検出器
２ｃ 第３変位検出器
３ 取付台
４ ガイドレール
５ ねじ軸
６ モータ
７ ハウジング
８ 変位検出器支持筒[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a roll profile measuring method for measuring in-line a surface unevenness amount of a work roll, that is, a roll profile, in a plate rolling mill such as a hot rolling mill.
[0002]
[Prior art]
In a plate rolling mill such as a hot rolling mill, generally, only a portion of a work roll that comes into contact with a material to be rolled is locally worn. Therefore, in order to roll a sheet having a normal thickness distribution, it is necessary to shift the rolling order of the rolled material from a wide width to a narrow width. And a rolling sequence for shifting. However, such regulation of the rolling order based on the sheet width is a major factor that hinders improvement in productivity, and there is an increasing demand for eliminating this regulation.
[0003]
As a measure for eliminating the rolling order regulation, a so-called on-line roll grinding means for grinding a surface of a work roll into a desired shape in a state of being incorporated in a rolling mill stand has been proposed. The most important thing in performing online roll grinding is to always grasp the roll profile of the roll to be ground before, during or after roll grinding.
[0004]
[Problems to be solved by the invention]
Various methods have conventionally been considered for measuring the roll profile of the roll to be ground, such as evaluating the amount of displacement by moving a displacement detector in the axial direction of the roll to be ground. However, in the conventional method, an error in the roll radial direction or an error in pitching motion at the time of movement of the displacement detector occurs, and it cannot be said that the roll profile is always measured with high accuracy.
[0005]
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a roll profile measurement method capable of performing roll profile measurement with high accuracy.
[0006]
[Means for Solving the Problems]
In order to achieve the above object, a roll profile measuring method according to the present invention provides a mounting base movably in an axial direction of a work roll, and a first displacement detector, a second displacement detector, and a third displacement detection on the mounting base. The work table is placed at a predetermined interval in the axial direction of the work roll, and the mounting table is moved in the axial direction of the work roll.The axial direction of the work roll includes the translational motion error and the pitching motion error when the mounting table moves. Are measured by three displacement detectors, respectively, and the combination of the first displacement detector and the second displacement detector is set as a first set, and the first displacement detector, the third displacement detector, The second set is a combination of the first and second sets of displacement detectors. Based on the data of the amount of unevenness in the axial direction of the work roll, the work roll includes axis Two sets of direction unevenness data were calculated, and pitching motion errors during movement of the mounting base were calculated from the shapes based on the axial direction unevenness data of the two sets of work rolls, and each was measured by three displacement detectors. The work roll axis unevenness amount data is corrected using the pitching motion error to remove the influence of the pitching movement error to obtain a work roll axial unevenness amount data sequence, and the work roll axis line is determined based on the data sequence. The method is characterized in that the uneven shape in the direction is calculated.
[0007]
BEST MODE FOR CARRYING OUT THE INVENTION
FIG. 1 is a schematic configuration of a measuring device for performing a roll profile measuring method according to an embodiment of the present invention, and FIG. 2 is a schematic diagram of a main part in FIG. 1 for explaining the roll profile measuring method. The concept is shown.
[0008]
In FIG. 1, 1 is a work roll to be measured, 2a is a first displacement detector, 2b is a second displacement detector, and 2c is a third displacement detector. Reference numeral 3 denotes a mount for the displacement detector. The mounting base 3 is slidably fitted on the guide rail 4 and reciprocates in the axial direction of the work roll 1 by driving the screw shaft 5 with the motor 6. The guide rail 4, the screw shaft 5, the motor 6 and the like are attached to a support beam (not shown), and the support beam and the work roll 1 are supported by a housing 7.
[0009]
In FIG. 1, reference numeral 8 denotes a displacement detector support cylinder, on which the first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c are mounted. It has a structure that can move forward and backward facing the roll 1. The first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c measure the unevenness of the surface of the work roll 1, so that the displacement detectors are arranged at intervals Lb, Lc with respect to the axial direction of the work roll 1. It is placed on the support tube 8. The first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c are projected toward the work roll 1 by a predetermined distance by the displacement detector support tube 8.
[0010]
Therefore, with the first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c protruding in the direction of the work roll 1 by the displacement detector support cylinder 8, the mounting table 3 is moved along the axis of the work roll 1. The first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c simultaneously measure the unevenness of the surface of the work roll 1 by moving the work roll 1 in the direction.
[0011]
Hereinafter, a roll profile measurement method using three first displacement detectors 2a, second displacement detectors 2b, and third displacement detectors 2c will be described with reference to FIG.
[0012]
In FIG. 2, x is a coordinate value based on the position of the first displacement detector 2a, m (x) is straight shape in the coordinate value x (roll profile error), e z _(x) is the coordinate value x the relative translational motion error between mount 3 and the work rolls 1, e p _(x) in indicates the relative pitching motion error component between mount 3 and the work roll 1 in the coordinate value x.
[0013]
The first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c at the moving position x _n (n = 0, 1, 2,. The measured values y2a ( _xn ), y2b ( _xn ), and y2c ( _xn ) of the first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c are expressed by Equation (1). .
(Equation 1)

[0014]
Shape measurement calculation by first displacement detector 2a and second displacement detector 2b (first set)
[0015]
▲ 1 ▼ determined by combining measurements y2a2b _(x n) calculated y2a _(x n) and y2b _(x n) defined as the difference between the the composite measurement Y2a2b a _(x n) ₍₂₎ expression.
(Equation 2)

(2) As can be seen from the equation, eliminating been canceled out section on _e z (x) from the composite measurement y2a2b _(x n). When _ez (x) is small, equation (2) can be approximated as equation (3).
(Equation 3)

As can be seen from the equation (3), the composite measured value y2a2b ( _xn ) is obtained by superimposing the shape m ( _xn ) to be measured approximately and the m ( _xn + Lb) shifted in phase by the interval Lb. Has become.
[0016]
{Circle around (2)} From the reconstructed and synthesized measured value y2a2b ( _xn ) (n = 0, 1, 2,..., N−1) of the object shape m ( _xn ), use the Fourier transform technique to obtain m ( _xn). (N = 0, 1, 2,..., N−1) can be reproduced.
Here, m (x _n ) is represented in the form of a Fourier series sum as in Equation (4).
(Equation 4)

Here, L is the measured length of the object shape, C _k is the amplitude of the k- _th shape component of m (x _n ), and φ _k is the phase shift amount of the k-th component. By substituting equation (4) into equation (3) and rearranging, equation (5) is obtained.
(Equation 5)

Using F _k and G _k , the object shape m (x _n ) is expressed as in equation (6).
(Equation 6)

[0017]
That is, if the combined measured value data sequence y2a2b ( _xn ) (n = 0, 1, 2,..., N-1) is Fourier-transformed to obtain the coefficients F _k and G _k of the cosk-order component and the sink-order component, Using the coefficients F _k and G _k and the value δ _k determined by the measurement system, the object shape m (x _n ) can be obtained by the equation (6).
[0018]
A roll profile m2a2b ( _xn ) (n = 0, 1, 2,..., N-1) is obtained based on the measured values of the first displacement detector 2a and the second displacement detector 2b. m2a2b ( _xn ) can be expressed as in equation (7).
(Equation 7)

[0019]
Here, Er2a2b _(x n) is an error component due to (1) of the pitching motion error component _{Lb · e p (x n)} .
Composite measurement Considering the fact from _{(= m (x n + Lb} ) -m (x n)) is a method of reproducing the m _(x n), the relationship between the Er2a2b _(x n) and _e p _(x n) Equation (8) is obtained.
(Equation 8)

[0020]
Shape measurement calculation by first displacement detector 2a and third displacement detector 2c (second set)
[0021]
The roll profile m2a2c ( _xn ) (n = 0, 1, 2,..., N-1) is obtained in the same manner as described above, based on the measured values of the first displacement detector 2a and the third displacement detector 2c. m2a2c ( _xn ) (n = 0, 1, 2,..., N-1) can be expressed as in equation (9).
(Equation 9)

Here, Er2a2c _(x n) is an error component due to (1) pitching motion error component _{(Lb + Lc) · e p} (x n).
Similarly, as the relationship between the Er2a2c _(x n) and _e p _(x n) is (10) is obtained.
(Equation 10)

[0022]
m2a2b _(x n) and m2a2c derivation of _e p _(x n) from _(x n) [0023]
(7) will be described ₍₉₎ m2a2b (x n) given by formula, the calculation procedure for obtaining the m2a2c _(x n) from pitching motion error component _e p _(x n).
[0024]
_{Er2a2b (x n), Er2a2c (} x n), cos of m th order as e p a _(x n) ₍₁₁₎ formula, considered to represent a form of a power series sum of sin.
(Equation 11)

By substituting equation (11) into equation (8) and rearranging, equation (12) is obtained from the coefficient relationship.
(Equation 12)

[0025]
Similarly, by substituting equation (11) into equation (10) and rearranging, equation (13) is obtained from the coefficient relationship.
(Equation 13)

From equations (12) and (13), (a ² _k −a ¹ _k ) can be expressed as equation (14).
[Equation 14]

Is a value determined by the measurement system.
[0026]
From _(14), the coefficient _c k, _{d k} which gives e p _(x n) can be expressed as (15).
[Equation 15]

On the other hand, (7) and (9) calculating a difference mr _(x n) and given shape m2a2b _(x n) m2a2c and _(x n) by the formula, (11) mr from the relationship between the expression _{(x n} ) Can be expressed as (16).
(Equation 16)

[0027]
That is, the values (a ² _k −a ¹ _k ) and (b ² _k −b ¹ _k ) in the equation (15) can be obtained as the coefficients of cos and sin when the Fourier transform is performed on mr (x _n ). . The coefficients c _k and d _k are obtained from the above procedure, and the pitching motion error component e _p (x _n ) is obtained by substituting the coefficients into the equation (11).
[0028]
High-precision measurement of roll profile by correcting pitching motion error component e _p (x _n )
The value of the above-described procedure determined pitching motion error component _e p _(x n), it is possible to remove the section _Lb · e p _(x n) using, for example, (1), first displacement it is possible to detectors 2a and accurate measurement is not affected by the second displacement detector 2b pitching motion error component by performing measurements by e _{p (x n).}
[0030]
The roll profile measurement method described above is summarized as the following (1) to (8).
[0031]
(1) As shown in FIG. 1, the first displacement detector 2a, the second displacement detector 2b, and the third displacement detector 2c are placed on the mounting table 3 at intervals Lb and Lc, and the axis of the work roll 1 is set. Is simultaneously measured along the line to obtain a measurement data sequence given by the equation (1).
▲ 2 ▼ first performs a displacement detector 2a and the measurement results computation by the combination of the second displacement detector 2b, (7) shape including an error caused by the influence of _e p _(x n) given by equation M2a2b ( x _n ) (n = 0, 1, 2,..., N−1).
[0032]
{Circle around (3)} Similarly, the measurement result by the combination of the first displacement detector 2a and the third displacement detector 2c is calculated, and the shape m2a2c ( _xn ) (n = 0, 1, 2) given by the equation (8) is calculated. .. N-1).
▲ 4 ▼ (16) obtains a difference mr _(x n) of a shape obtained by calculation given m2a2b _(x n) and the formula m2a2c and _(x n).
[0033]
{Circle around (5)} Fourier transform is performed on mr (x _n ), and the coefficients of its cos and sin components, that is, the coefficients (a ² _k −a ¹ _k ) and (b ² _k −b ¹ _k ) in equation (16) k = 0, 1, 2,... m).
From the coefficients (a ² _k −a ¹ _k ) and (b ² _k −b ¹ _k ) obtained in (6) and (5) and A _k and B _k shown in the equation (14), the equation (15) is used. factor gives e _p a _(x n) _c k, obtains the _{d k.}
[0034]
▲ 7 ▼ coefficients _c k, determine the _e p _(x n) by the _{d k} (11) equation, for example, to remove the (1) Measurement data Y2b _(x n) from _Lb · e p _(x n) of the formula .
_{▲ 8 ▼ e p (x n} ) the measured data string y2b removal of a _(x n) performs a calculation using the _{y2a (x n), e p} (x n) true roll profile m which is not affected by ( _xn ).
[0035]
Note that (11) obtains the _e p _(x n) by the equation (1) of the measurement data Y2C _(x n) the _Lb · e p _(x n) is removed from the removed measurement data string Y2C _{(x n} ) and it is also possible to determine the _e p _(x n) true roll profile m which is not affected by _(x n) using y2a a _(x n).
[0036]
In the above-described roll profile measurement method, the value of e _p (x _n ) at the time of measurement is obtained based on two sets of roll profiles including the influence of e _p (x _n ) obtained by calculation, and this is used as the actual value. after removal from the measurement data can be obtained roll profile without the influence component of e _{p (x n)} by performing again operational. Therefore, even a large conditions pitching motion error component e _p of mount 3 at the time of measurement _{(x n),} thereby enabling highly accurate roll profile measurement.
[0037]
【The invention's effect】
According to the roll profile measuring method of the present invention, a mounting base is provided so as to be movable in the axial direction of a work roll, and a first displacement detector, a second displacement detector, and a third displacement detector are mounted on the mounting base in the axial direction of the work roll. At predetermined intervals, the mounting table is moved in the axial direction of the work roll, and three pieces of data on the amount of unevenness in the axial direction of the work roll including the effects of translational error and pitching motion error when the mounting table is moved. And the combination of the first displacement detector and the second displacement detector is referred to as a first set, and the combination of the first displacement detector and the third displacement detector is referred to as a second set. Based on the data of the amount of unevenness in the axial direction of the work roll corresponding to the first set and the second set of displacement detectors, the data of the amount of unevenness in the axial direction of the work roll including the effect of the pitching motion error when the mounting table is moved. 2 Calculate the pitching motion error when moving the mounting base from the shape based on the data of the amount of unevenness in the axial direction of the two work rolls, and calculate the amount of unevenness in the axial direction of the work roll measured by the three displacement detectors. The data is corrected using the pitching motion error to obtain a work roll axial unevenness data sequence from which the influence of the pitching motion error has been removed, and the work roll axial unevenness shape is calculated based on this data sequence. Therefore, a highly accurate roll profile measurement can be performed even under a condition where the component of the pitching motion error is large. As a result, the roll profile can be measured with high accuracy.
[Brief description of the drawings]
FIG. 1 is a schematic configuration diagram of a measuring device for performing a roll profile measuring method according to an embodiment of the present invention.
FIG. 2 is a conceptual diagram schematically illustrating a main part in FIG. 1;
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Work roll 2a 1st displacement detector 2b 2nd displacement detector 2c 3rd displacement detector 3 Mounting stand 4 Guide rail 5 Screw shaft 6 Motor 7 Housing 8 Displacement detector support cylinder

Claims (1)

A mounting base is provided movably in the axial direction of the work roll, and the first displacement detector, the second displacement detector, and the third displacement detector are mounted on the mounting base at predetermined intervals in the axial direction of the work roll, The mounting table is moved in the axial direction of the work roll, and the unevenness data in the axial direction of the work roll including the effects of the translational motion error and the pitching motion error when the mounting table is moved are measured by the three displacement detectors. The combination of the first displacement detector and the second displacement detector is a first set, the combination of the first displacement detector and the third displacement detector is a second set, and the first set and the second set are combined. Two sets of work roll axial unevenness data including the effect of pitching motion error when moving the mounting base are calculated based on work roll axial unevenness data corresponding to the displacement detector. Roll axis direction Pitching motion error when moving the mounting base is calculated from the shape based on the unevenness data, and pitch data by correcting the unevenness data in the axial direction of the work roll measured by the three displacement detectors using the pitching motion error. A roll profile measurement method comprising: obtaining a data row of unevenness in the axial direction of a work roll from which the influence of a motion error has been removed; and calculating an uneven shape in the axial direction of the work roll based on the data stream.

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