JPS5981508A - Measuring device for straightness of steel material strip between runs - Google Patents

Measuring device for straightness of steel material strip between runs

Info

Publication number
JPS5981508A
JPS5981508A JP19217082A JP19217082A JPS5981508A JP S5981508 A JPS5981508 A JP S5981508A JP 19217082 A JP19217082 A JP 19217082A JP 19217082 A JP19217082 A JP 19217082A JP S5981508 A JPS5981508 A JP S5981508A
Authority
JP
Japan
Prior art keywords
rail
straightness
long
distance
metal material
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.)
Pending
Application number
JP19217082A
Other languages
Japanese (ja)
Inventor
Yukio Nakamori
中森 幸雄
Kouji Babazono
馬場園 浩二
Shinichi Kamimura
真一 上村
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nippon Steel Corp
Original Assignee
Nippon Steel Corp
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Nippon Steel Corp filed Critical Nippon Steel Corp
Priority to JP19217082A priority Critical patent/JPS5981508A/en
Publication of JPS5981508A publication Critical patent/JPS5981508A/en
Pending legal-status Critical Current

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/30Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring roughness or irregularity of surfaces

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)

Abstract

PURPOSE:To measure the straightness of a steel material strip between runs in a short time with high precision by providing an arithmetic processor which inputs a signal from a detecting means for the movement speed of a long-sized metallic material and a distance detection signal for the distance to a side surface of the long-sized metallic material from a distance detecting means and calculates the curvature extent of the long-sized metallic material. CONSTITUTION:When a rail material runs on a conveyance table 10 from the right, the amounts of displacement detected by respective capacity type sensors 1-3 are amplified by amplifiers 4-6, which supply DC voltages proportional to the amounts of displacements to a signal processor 9. The signal processor 9 also inputs the movement speeds of the rail material detected by speed detectors 7 and 8 as line speeds. The signal process 9 reads the respective signals by an A/D converter to calculate the straightness to the overall length of the rail by a model. The result of the calculation is displayed and recorded on a display recorder 10. A checker decides on whether the rail material is within a permissible range or not by the result.

Description

【発明の詳細な説明】 本発明は、走間中における条鋼材の真直度測定装置に関
するものである。
DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an apparatus for measuring the straightness of a steel bar during running.

軌条、鋼矢板、H形鋼等は複雑な形状を有し、圧延工程
、冷却時に曲り、反シが長手方向に発生し、矯正作業を
行っている。しかしながら曲り、反シの状態によっては
、ユーザーの要求を満足する真直度が確保されるとは限
らない。
Rails, steel sheet piles, H-beams, etc. have complex shapes, and during the rolling process and cooling, bends and warps occur in the longitudinal direction, which requires straightening work. However, depending on the state of bending or unevenness, it is not always possible to ensure straightness that satisfies the user's requirements.

現在、条鋼材の真直度測定は、検定者2Å以上によって
、条鋼材に基準真直計(例えばストレッチ等)をあて、
条鋼材とのすき問責を測定して、単位m当シの曲り量を
算出して許容限度内か否かを判定している。従って次の
問題点がある。、(1)測定者によシ個々にバラツキが
生じる。
Currently, the straightness of long steel products is measured by an examiner of 2 Å or more, applying a standard straightness tester (for example, stretch) to the long steel material.
The clearance between the bar and the steel bar is measured, and the amount of bending in units of meters is calculated to determine whether or not it is within the allowable limit. Therefore, there are the following problems. (1) Individual variations occur depending on the measurer.

(2)測定時には条鋼等は停止しなければならない。(2) Bars, etc. must be stopped during measurement.

(3)測定に時間がかかる。(3) Measurement takes time.

とれらの問題点を解決すべく特開昭57−61907等
が提案されているが基本的な解決に至っていない。即ち
(1)の問題点は解決されているが、(2) 、 (3
)の問題点は未解決である。
In order to solve these problems, Japanese Patent Laid-Open No. 57-61907 and the like have been proposed, but no fundamental solution has been reached. In other words, although problem (1) has been resolved, (2) and (3
) issues remain unresolved.

そこで本発明はこれらの問題点を基本的に解決し、走間
中に迅速に真直度を測定する装置を提案するものである
Therefore, the present invention basically solves these problems and proposes a device that quickly measures straightness during running.

条鋼材の非接触位置測定方式としてはレーザ利用による
レーザ方式、渦電流を利用した渦電流式ギヤツブ計等が
ある。これら二つの方式は次に述べる欠点がある。即ち
レーザ方式は、ある場所の小宴な面積(2咽ψ程度)の
位1σ測定であるから条鋼表面の凹凸や光面に附看した
物質の影響を受ける。渦電流式は、条鋼材の成分によっ
て決まる電気抵抗の影響を受ける。
Non-contact position measurement methods for steel bars include a laser method that uses a laser, an eddy current gear gauge that uses eddy current, and the like. These two methods have the following disadvantages. That is, since the laser method measures 1σ of a small area (approximately 2 ψ) in a certain place, it is affected by irregularities on the surface of the bar steel and substances attached to the light surface. The eddy current method is affected by the electrical resistance determined by the composition of the steel bar.

また、走間中の測定においては、第1図に示す如く条鋼
材(レール)20の上下振動(点線と矢印で示す゛)に
よシ測定位置がズレ、このズレによって消測上大きな誤
浬を生じる。なおこの図で21はレーザ式距離計、22
は渦屯流式ギャップ計を示す。本発明μこれらの欠点を
解決ナベ〈種々検討してなされたものである。以下に本
発明を図面VCよって詳細に説明する。
In addition, during measurement during running, the measurement position shifts due to the vertical vibration of the steel bar (rail) 20 (indicated by dotted lines and arrows) as shown in Fig. 1, and this shift causes large errors in measurement. occurs. In this figure, 21 is a laser distance meter, 22
indicates a vortex flow gap meter. The present invention has been developed after various studies to solve these drawbacks. The present invention will be explained in detail below with reference to drawing VC.

第2図に本発明の静電容量式センサの基本原理を示す。FIG. 2 shows the basic principle of the capacitive sensor of the present invention.

この測定原理は、特願昭56−66397で先に提案し
た。第2図に示す如く、一つの電極23に交流発信4a
25を接続し、もう一方の電極24に交流増巾器26を
接続している。この方式は、検出器27と被測定対象2
0との間隔tに比例する電極23.24間の静電容量C
xを測定する。
This measurement principle was previously proposed in Japanese Patent Application No. 56-66397. As shown in FIG. 2, an AC transmitter 4a is connected to one electrode 23.
25 is connected to the other electrode 24, and an AC amplifier 26 is connected to the other electrode 24. This method consists of a detector 27 and an object to be measured 2.
The capacitance C between the electrodes 23 and 24 is proportional to the distance t from 0
Measure x.

次に第3図に示す軌条材にて本発明を説明する。Next, the present invention will be explained using the rail material shown in FIG.

軌条材の真直度の測定は、通常、頭部20aを測定する
。20bは腹部である。第3図(、)に示す様に、頭部
20aの高さhに対して、静電容量式センサ(以下容量
式センサと云う)27の電極の高さHが2h程度であれ
ば、軌条20の上下振動に対して誤差は第4図に示す様
になる。即ち、±10町以内の振動の影響を全く受けな
い特性となる。
The straightness of the rail material is usually measured at the head 20a. 20b is the abdomen. As shown in FIG. 3(,), if the height H of the electrode of the capacitive sensor (hereinafter referred to as capacitive sensor) 27 is about 2 h with respect to the height h of the head 20a, the rail The error for the vertical vibration of 20 is as shown in FIG. In other words, the characteristic is that it is completely unaffected by vibrations within ±10 degrees.

また、第3図(b)に示す如く、腹部20b測定用容を
式七ンサにおいてもはソ同様の結果を得た(但し、h’
 220 tars +H’の条件である)。
Furthermore, as shown in Fig. 3(b), similar results were obtained when the abdominal 20b measurement volume was used with the formula 7 analyzer (however, h'
220 tars +H').

第5図に本発明の軌条材のオンライン走間真直度計の計
測システムを示す。本システムは、頭部位置測定用容量
式センサl〜3と、増幅器4〜6と、軌条材移動速度検
出器7、信号処理器8、表示記録装置9から構成されて
いる。10は表示記録装置、11は搬送テーブル、11
aはその搬送ロールである。第5図(a)に示す様に容
量式センサを3ケ所に配置している。同図(、)に幾何
学的配置を示す。容量式センサ1,2と3との間隔Wは
、軌条の頭部の幅と容量式センサの測長によって決定さ
れている。容量式センサ1と2の間隔りは、真直度の許
容限界量によって決定している。また容量式センサl〜
3の立体的配置を同図(b)に示す。
FIG. 5 shows a measurement system for an online running straightness meter for rail materials according to the present invention. This system is comprised of capacitive sensors 1 to 3 for head position measurement, amplifiers 4 to 6, a rail material movement speed detector 7, a signal processor 8, and a display/recording device 9. 10 is a display/recording device; 11 is a transport table; 11
a is its transport roll. As shown in FIG. 5(a), capacitive sensors are arranged at three locations. The geometrical arrangement is shown in the figure (,). The distance W between the capacitive sensors 1, 2, and 3 is determined by the width of the head of the rail and the measured length of the capacitive sensors. The distance between the capacitive sensors 1 and 2 is determined by the permissible straightness limit. Also, capacitive sensor l~
The three-dimensional configuration of No. 3 is shown in the same figure (b).

容量式センナの配置を同一面側に2ケ所、対向面側に1
ケ所配置する。理由は、軌条材の搬送において、左右上
下に振動することは常であシ、上下の振動対策について
は前述した如くである。左右振動がある場合、同一面上
に複数個以上のセンサを配置してもその影響を防止でき
ない。そのために対向面に設けた。また本装置の場合、
同一面上の2ケ所の配置:で゛あるから、真直度の精度
向上対策として対向面積容量式センサ3も必要である。
Two capacitive sensors are placed on the same side and one on the opposite side.
Place it in several places. The reason is that when conveying rail materials, vibrations occur horizontally, vertically, and vertically, and countermeasures against vertical vibrations are as described above. If there is left-right vibration, the influence cannot be prevented even if a plurality of sensors are arranged on the same surface. For this purpose, it was placed on the opposite side. In addition, in the case of this device,
Since the two locations on the same surface are arranged, opposing areal capacitance type sensors 3 are also required as a measure to improve the accuracy of straightness.

軌条材の移動速度を2ケ所で検出している。一般に移り
の速度は、搬送テーブル10のロールの回転によって決
定されてン4る。実際は、スリップ等により移動速度が
変動するので、これを防止するために2ケ所の速度を測
定している。空間フィルター全利用した非接触速度計等
を利用する場合は、絶対速度の測定が可能である。
The moving speed of the rail material is detected at two locations. Generally, the speed of transfer is determined by the rotation of the rolls of the transport table 10. In reality, the moving speed fluctuates due to slips, etc., so to prevent this, the speed is measured at two locations. If you use a non-contact speedometer that makes full use of a spatial filter, it is possible to measure absolute speed.

第5図(、)に示す如く、右側よシ軌条材が搬送テーブ
ル10上を走行すれば、まず速度検出器7゜8にて軌条
材速度を検知する。次に容量式センサ2が軌条の到着を
検出する。更に容量式センサ3゜1が検知する。容量式
センサ1が軌条の到着を検知すると、信号処理器9は真
直度算出の演算を始める。各容量式センサ1,2.3で
検出された変位量(容量式センサーと軌条間の距離)は
、増幅器4,5.6で増幅される。増幅器4,5.6は
交流発振器とAC増幅器、フィルター、およびAC/D
C変換器を内蔵している。増幅器4.5.6は変位量に
比例した直流(DC)電圧を信号処理器9に与えている
。信号処理器9には、軌条材の移動速度が速度検出器7
,8にて検出され、ライン速度として入力されている。
As shown in FIG. 5(,), when the right side rail material runs on the conveying table 10, the speed of the rail material is first detected by the speed detector 7.8. Capacitive sensor 2 then detects the arrival of the rail. In addition, a capacitive sensor 3°1 detects. When the capacitive sensor 1 detects the arrival of the rail, the signal processor 9 starts calculating the straightness. The displacement amount (distance between the capacitive sensor and the rail) detected by each capacitive sensor 1, 2.3 is amplified by an amplifier 4, 5.6. Amplifiers 4, 5.6 are AC oscillators, AC amplifiers, filters, and AC/D
Built-in C converter. The amplifier 4.5.6 provides the signal processor 9 with a direct current (DC) voltage proportional to the amount of displacement. The signal processor 9 includes a speed detector 7 that detects the moving speed of the rail material.
, 8 and input as the line speed.

ライン速度は最大lrQ/seeであシ、両方の速度検
出器7.8の出力によシ平均速度を求めている。なおこ
れらはいづれか一方でもよい。
The line speed is at maximum lrQ/see, and the average speed is determined from the outputs of both speed detectors 7.8. Note that either one of these may be used.

信号処理器9はA/D変換器にて、各信号を読取ってい
る。読取周期は、ライン速度Vcに比例させている。今
、速度検出器7,8でのライン速度をvc、読取周期を
Δtとすれば、第6図に示すようにΔを時間での軌条の
移動量ΔtはΔL = Vc・Δt−Vc(tz  t
+)、(但し、tz = t、十Δt、t3=t2+Δ
t)となる。従ってΔを時間毎のサンプリング状態は、
第6図(a)に示す様になる。
The signal processor 9 reads each signal using an A/D converter. The reading cycle is made proportional to the line speed Vc. Now, if the line speed of the speed detectors 7 and 8 is vc, and the reading period is Δt, then as shown in FIG. t
+), (however, tz = t, 10Δt, t3=t2+Δ
t). Therefore, the sampling state of Δ for each time is
The result is as shown in FIG. 6(a).

容量式センサ1,2の一軌条材からの変位量tは1、 
、12.センサ間隔はLであるから勾配が求まる。
The displacement t of the capacitive sensors 1 and 2 from the single rail material is 1,
, 12. Since the sensor interval is L, the gradient can be found.

谷11式センサ3の変位量はtz、L/2のd点の位置
はd = W −(A3+W’ )  但しW′は軌条
頭部の幅である。従って、第6図(b)の状態が連続的
に求めることができる。
The displacement amount of the valley type 11 sensor 3 is tz, and the position of point d at L/2 is d = W - (A3 + W') where W' is the width of the rail head. Therefore, the state shown in FIG. 6(b) can be continuously obtained.

信号処理器9ではモデルによシ軌条全長にわたって真直
度を算出している。算出された結果は、表示記録装置1
0によって表示され、記録されている。検定者はこの結
果にて、許容限界内か否かの判定をしている。信号処理
器9の出力信号をプロセス耐算磯等に入力すれは、自動
判定が可能である。
The signal processor 9 calculates the straightness over the entire length of the rail based on the model. The calculated results are displayed on the display/recording device 1.
0 is displayed and recorded. The examiner uses the results to determine whether or not the results are within the allowable limits. It is possible to automatically determine whether the output signal of the signal processor 9 is input to a process load-bearing block or the like.

軌条が搬送され、容量式センサ2の位置を通過した瞬時
に容量式センサ2の変位量が最大となる。
The moment the rail is transported and passes the position of the capacitive sensor 2, the amount of displacement of the capacitive sensor 2 becomes maximum.

従って増巾器5の出力電圧も最大とな9、信号処理器9
は、軌条の通過を検知し、モデル演算を停止し、次の軌
条の到着の待状態となる。
Therefore, the output voltage of the amplifier 5 is also maximum 9, and the signal processor 9
detects the passing of a rail, stops model calculation, and enters a waiting state for the arrival of the next rail.

以上本発明の走間中における軌条材のオンライン真直度
測定方式について説明した。本発明は更に次の特徴があ
る。
The online straightness measurement method of a rail material during running according to the present invention has been described above. The present invention further has the following features.

(1)軌条以外の条鋼(鋼矢板、型鋼等)材、鋼管等に
も適用可能である。
(1) It can also be applied to materials other than rails, such as steel bars (sheet piles, shaped steel, etc.), steel pipes, etc.

(2)センサの設置は同一面上に少なくとも2ケ所以上
、対向面に1ケ所以上必要である。これにより被測定材
料の振動の影響をほとんど受けず真直度を高精度で測定
出来る。
(2) Sensors must be installed in at least two locations on the same surface and at least one location on the opposing surface. As a result, straightness can be measured with high accuracy, almost unaffected by vibrations of the material to be measured.

(3)非接触測定であるから、装置が簡易となり、メン
テナンス性が非常によい。
(3) Since it is a non-contact measurement, the device is simple and maintainability is very good.

(4)容量式センサによる測定例を示したが、材量の上
下振動の誤差が小さければ、特にこだわるものではない
(4) Although an example of measurement using a capacitive sensor has been shown, there is no particular concern as long as the error in vertical vibration of the material amount is small.

(5)冷間材、熱間材とはず測定できる。(5) Can measure cold and hot materials.

次に実施例を挙げる。第7図(a) 、 (b)にスト
レッチによる測定値と、オンライン走間中の測定値を示
す。ライン速度は0.5m/see、対象は軌条材、セ
ンサは容量式センナで測長10〜80mrn、3台であ
る。高精度で測定していることがわかる。
Next, examples will be given. Figures 7(a) and 7(b) show the measured values during stretching and the measured values during online running. The line speed is 0.5 m/see, the target is rail material, and the sensors are capacitive sensors measuring lengths of 10 to 80 mrn, and there are 3 units. It can be seen that the measurements are made with high precision.

【図面の簡単な説明】[Brief explanation of drawings]

第1図は従来方式の測定原理を示す説明図であり、第2
図は本発明に使用した静電容量式センサの基本原理を示
す説明図であシ、第3図は本発明におけるセンサの被測
定材に対する設置位置とセンサの構造を示す説明図であ
り、第4図は被l1lll定材の上下振動による測定誤
差を示すグラフであり、第5図は本発明の真直度計測シ
ステムを示すプロ)り図であり、第6図はサンプリング
の状況を示す説明図であシ、そして第7図はストレッチ
実測値の比較を余すグラフである。 図面で、11は搬送路、20はi尺金属材料、7.8は
速度検出器、1〜3は距離検出手段、9は演算処理装置
である。 昭和58年2月 7日 特許庁長官 若 杉 和 夫 殿 1、事件の表示 昭和57年特許願第192170号 2、発明の名称 走間中における条鋼材の真直度測定装置3、補正をする
者 事件との関係   特許出願人 住所 東京都千代田区大手町二丁目6番3号名称 (6
65,)新日本製鐵株式会社代表者  武 1)  豊 4、代 理 人  〒101 6、補正により増加する発明の数    な し7、補
正の対象 明細書の発明の詳細な説明の欄および 図面 (1)明細書第4頁12行のrh’220■+H/Jを
r h’> 20期+H’Jに補正する。 (2)同第4頁16行〜18行の「検出器7〜表示記録
装置、」を「検出器7,8、信号処理器9、表示記録装
置10から構成されている。Jに補正する。 (3)同第5頁16行の「搬送テーブル10」を「搬送
テーブル11」に補正する。 (4)図面第5図(a)を別紙のとおり補正する。
Figure 1 is an explanatory diagram showing the measurement principle of the conventional method.
The figure is an explanatory diagram showing the basic principle of the capacitive sensor used in the present invention, and Fig. 3 is an explanatory diagram showing the installation position of the sensor with respect to the material to be measured and the structure of the sensor in the present invention. Figure 4 is a graph showing the measurement error due to vertical vibration of the fixed material to be measured, Figure 5 is a professional diagram showing the straightness measurement system of the present invention, and Figure 6 is an explanatory diagram showing the sampling situation. Figure 7 is a graph showing a comparison of actual stretch measurements. In the drawings, 11 is a conveyance path, 20 is an i-scale metal material, 7.8 is a speed detector, 1 to 3 are distance detection means, and 9 is an arithmetic processing unit. February 7, 1980 Kazuo Wakasugi, Commissioner of the Japan Patent Office1, Indication of the case, Patent Application No. 192170 of 19872, Title of the invention Device for measuring the straightness of a bar during running 3, Person making the correction Relationship to the case Patent applicant address 2-6-3 Otemachi, Chiyoda-ku, Tokyo Name (6
65,) Nippon Steel Corporation Representative Takeshi 1) Yutaka 4, Agent 〒101 6. Number of inventions increased by amendment None 7. Column for detailed description of the invention and drawings in the specification subject to amendment (1) Correct rh'220■+H/J on page 4, line 12 of the specification to rh'>20+H'J. (2) On page 4, lines 16 to 18, "detector 7 - display/recording device," is corrected to "composed of detectors 7, 8, signal processor 9, and display/recording device 10." (3) Correct "transport table 10" on page 5, line 16 to "transport table 11". (4) Amend Figure 5(a) of the drawing as shown in the attached sheet.

Claims (1)

【特許請求の範囲】[Claims] 搬送路上を移動している長尺金属材料の曲シを測定する
装置であって、前記長尺金属材料の移動速度を検出する
手段と、少なくとも3箇の、それぞれ長尺金属材料測面
1での距離を非接触で測定する距離検出手段を、長尺金
属材料長手方向に沿ってその両側に配設するとともに、
前記長尺金属材料移動速度検出手段からの信号と、距離
検出手段から長尺金属材料l111面までの距離検出信
号を入力され、長尺金属材料の曲υ蛍を演算々出する演
算処理装置とよりなる走間中における条鋼材の真直度測
定装置。
An apparatus for measuring the curvature of a long metal material moving on a conveyance path, the device comprising: means for detecting the moving speed of the long metal material; and at least three measuring surfaces 1 for each of the long metal materials. Distance detecting means for non-contactly measuring the distance of the long metal material are disposed on both sides along the longitudinal direction of the long metal material,
an arithmetic processing device which receives a signal from the elongated metal material movement speed detection means and a distance detection signal from the distance detection means to the elongated metal material 111 surface, and calculates the curve of the elongated metal material; Straightness measurement device for long steel products during running.
JP19217082A 1982-11-01 1982-11-01 Measuring device for straightness of steel material strip between runs Pending JPS5981508A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP19217082A JPS5981508A (en) 1982-11-01 1982-11-01 Measuring device for straightness of steel material strip between runs

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP19217082A JPS5981508A (en) 1982-11-01 1982-11-01 Measuring device for straightness of steel material strip between runs

Publications (1)

Publication Number Publication Date
JPS5981508A true JPS5981508A (en) 1984-05-11

Family

ID=16286844

Family Applications (1)

Application Number Title Priority Date Filing Date
JP19217082A Pending JPS5981508A (en) 1982-11-01 1982-11-01 Measuring device for straightness of steel material strip between runs

Country Status (1)

Country Link
JP (1) JPS5981508A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2013136064A (en) * 2011-12-28 2013-07-11 Jfe Steel Corp Method for measuring misalignment of pass line on piercer delivery side and bending of bar
CN104907359A (en) * 2015-06-26 2015-09-16 天津商业大学 Adjustable straightness detection tool for long-rod workpiece

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2013136064A (en) * 2011-12-28 2013-07-11 Jfe Steel Corp Method for measuring misalignment of pass line on piercer delivery side and bending of bar
CN104907359A (en) * 2015-06-26 2015-09-16 天津商业大学 Adjustable straightness detection tool for long-rod workpiece

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