JPS5862528A - Monitoring method for periodical motion body - Google Patents

Monitoring method for periodical motion body

Info

Publication number
JPS5862528A
JPS5862528A JP16129081A JP16129081A JPS5862528A JP S5862528 A JPS5862528 A JP S5862528A JP 16129081 A JP16129081 A JP 16129081A JP 16129081 A JP16129081 A JP 16129081A JP S5862528 A JPS5862528 A JP S5862528A
Authority
JP
Japan
Prior art keywords
periodic
frequency
motion body
series data
periodical motion
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.)
Granted
Application number
JP16129081A
Other languages
Japanese (ja)
Other versions
JPS6260011B2 (en
Inventor
Kazuhiro Takeyasu
数博 竹安
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
Sumitomo Metal Industries Ltd
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 Sumitomo Metal Industries Ltd filed Critical Sumitomo Metal Industries Ltd
Priority to JP16129081A priority Critical patent/JPS5862528A/en
Publication of JPS5862528A publication Critical patent/JPS5862528A/en
Publication of JPS6260011B2 publication Critical patent/JPS6260011B2/ja
Granted legal-status Critical Current

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01HMEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00Measuring characteristics of vibrations in solids by using direct conduction to the detector

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

PURPOSE:To reliably detect a trouble on a periodical motion body, by a method wherein the vibration of the periodical motion body is sampled at a given period, a bicoherence regarding a frequency arbitrarily selected is found, and it is compared with that which is obtained at a time when the motion body is normal. CONSTITUTION:A time series data is obtained by sampling a vibration of a periodical motion body at a given period, a bicoherence regarding a frequency arbitrarily selected from the data is found from said data, it is compared with a bicoherence regarding a frequency obtained at a time when the periodical motion body is normal, and this detects a trouble on the periodical motion body. In this case, even if a noise, which is difficult to discriminate, is included in the time series data, unlike the case where a trouble is detected using a power spectrum grapsed by a two-dimentional amount, the bicoherence is grasped by a three-dimensional amount, and as a result, this method is excellent in noise resistance.

Description

【発明の詳細な説明】 本発明はぺ了りンク、歯車等の如く周期運動ケ行う1ク
ノ体即ち周期運動体の監視方法に関し、更に??’述す
れば周期運動体を備えた機器の大小、周期運動体の回転
速度、負荷の大小等に影響さnず、しかも周期運動体の
振動から得らnた時系列データ中に弁別しにくい鍵音が
含まnる場合であっても周期運動体の異常を検知できる
方法を提案するものである0 従来ペアリング、歯車等の周期運動体及びこnを倫えた
機器において部品の傷、回転軸の偏心、潤滑の不良等の
異常が発生した場合には、とt′1を放置するとペアリ
ーング、歯車等の部品のみhらず、こnらを備えた機器
全体の故障、破壊1に惹起する0従ってこのような異常
を正確に検知することはベアリング、歯車等を有する機
器の保守管理上、惨めて重俊な課題である。
DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for monitoring a periodic moving body such as a link or a gear, and furthermore? ? In other words, it is not affected by the size of the equipment equipped with a periodic moving body, the rotational speed of the periodic moving body, the size of the load, etc., and is difficult to distinguish in time series data obtained from the vibration of the periodic moving body. This paper proposes a method that can detect abnormalities in periodic moving objects even when key sounds are included. If an abnormality such as shaft eccentricity or poor lubrication occurs, if t'1 is left unattended, it may cause failure or destruction of not only parts such as pairings and gears, but also the entire equipment equipped with these parts. Therefore, accurately detecting such an abnormality is a serious problem in terms of maintenance and management of equipment including bearings, gears, etc.

従来このような異常を検知する方法として周期運動体に
センサf:取り付け、その出力信号から得られる時系列
データより下記(1)式にて定義さnるR M B (
 Root Mean Square)l[ fとる方
法但し x(t、):時系列データ(t=1,2・・N
)IJ二データ数 X : x(t)の平均値 捷lこII ’?千列データx (t)より下記(2)
式にて得らnる2次相間関数(自己相関関数)R(τ)
を、フーリエ?4;・′117て下ン(3)式のように
表わされるパワースペクトルケチニックする7−r法、 Ji(rl=h:  r  X(tl−X  Ct−1
−7)  )   ・−−+21世し 、I・::平均
操作 x(t+τ) : x(tlが侍らj、た時点からτだ
けIl+r過した時点におけるデータ 、+ : r&数単位 ゛また]・記パワースペクトルケ下記(41式の如く粕
分しft (++’+’ (パワースペクトル積分値)
Sprとる方法世し Ifo、f、)  :第1ζ分区
間等が考えらnでいるが、RMS(1i’Qびパワース
ペクトル積分値sp#i、周期運動体を備えた機器のサ
イズ、周期運動体の回転速度、9荷の大小等によって区
々に異なり、普遍的な判断基準を設けることができず、
個々の正常時のデータを蓄積しておく必をがあるため、
一般VcViパワースペクトルをチェックする方法が多
用さnでいる0しかしコノ方法による場合も周期傅動体
の振動から得られる時系列データ中に弁別しにくい雑音
が含まれるときは周期運動体に異常が発生しているにも
拘らず、パワースペクトルにはそnが明瞭に現れず、周
期運動体の異常が検知できないことがままあるO本発明
は斯かる事情に鑑みてなされたものであり、周期運動体
を偏見た機器のサイズ、周期運動体の回転速度、負荷の
大小等に影響されず、しかも周期運動体の振動から得ら
れる時系列データ中に弁別しにくい雑音が含まれる場合
であっても周期運動体の異常を検知できる方法を提供す
ることj、’li 全目的とする。
Conventionally, as a method of detecting such an abnormality, a sensor f is attached to a periodic moving body, and from time series data obtained from its output signal, n R M B (
Root Mean Square)l[f Method of taking x(t,): Time series data (t=1,2...N
)IJ2 data number X: Average value of x(t)? From the 1,000-column data x (t), the following (2)
n quadratic correlation function (autocorrelation function) R(τ) obtained by the formula
, Fourier? 4;・'117The 7-r method that performs the power spectrum as shown in equation (3), Ji(rl=h: r X(tl-X Ct-1
−7) ) ・−−+21st generation, I・::Average operation x(t+τ) : x(data at the time when tl has passed by Il+r by τ from the time when tl was Samurai j), + : r & several units ゛also]・The power spectrum is as shown below (divided as shown in formula 41) ft (++'+' (power spectrum integral value)
Ifo, f, ): The first ζ-minute interval, etc. are considered in n, but RMS (1i'Q, power spectrum integral value sp#i, size of equipment with periodic motion body, periodic motion It differs depending on the rotation speed of the body, the size of the nine loads, etc., and it is not possible to establish a universal judgment standard.
Because it is necessary to accumulate individual normal data,
Generally, the method of checking the VcVi power spectrum is often used. However, even when using the Kono method, if noise that is difficult to distinguish is included in the time series data obtained from the vibration of a periodic body, an abnormality will occur in the periodic body. However, in spite of the fact that the periodic motion body is not clearly visible in the power spectrum, it is often impossible to detect abnormalities in the periodic motion body. It is not affected by the size of the equipment that biases the body, the rotational speed of the periodic moving body, the size of the load, etc., and even if the time series data obtained from the vibration of the periodic moving body contains noise that is difficult to distinguish. The overall purpose is to provide a method that can detect abnormalities in periodic moving bodies.

本発明に係る周期運動体の監視方法は、周期運動体の振
動を一定周期でサンプリングして時系列データを得、該
時系列データから、任意に選択した周波数に関するパイ
コヒーレンスを求め、仁れを前記周期運動体が正常であ
る場合の同周波数に関するパイコヒーレンスと比較する
ことにより前記周期運動体の異常を検知することを特徴
とする。
The monitoring method for a periodic moving body according to the present invention obtains time series data by sampling the vibrations of the periodic body at a constant period, and from the time series data, calculates the pi coherence regarding an arbitrarily selected frequency, and The method is characterized in that an abnormality in the periodic body is detected by comparing it with pi-coherence regarding the same frequency when the periodic body is normal.

そして任意に選択する周波数は、周期運動体の振動に関
連づけて、例えば周期運動体から得られる固有周波数と
その高調波周波数を選択する。
As the arbitrarily selected frequency, for example, a natural frequency obtained from the periodic movement body and its harmonic frequency are selected in relation to the vibration of the periodic movement body.

以下本発明の原理について、歯車を診断する場合を例に
とって説明する。先ず検出される時系列データx(t)
Fi下記(5)式で表現されるものとすると、但し a
m:振幅 fz:基本周波数 φm 二位相 n(t):雑音 そのパワースペクトル5XX(fH−を下記(6)式の
ように、またパイスペクトルBxXx(fl、fz)は
下記(7)式のようになる。
The principle of the present invention will be explained below, taking the case of diagnosing a gear as an example. First, the detected time series data x(t)
Assuming that Fi is expressed by the following equation (5), provided that a
m: amplitude fz: fundamental frequency φm two-phase n(t): noise its power spectrum 5XX (fH- as shown in equation (6) below, and pi spectrum BxXx (fl, fz) as shown in equation (7) below become.

但し a:ディラックのデルタ関数 8nn(f) :雑音のパワースペクトルー−1,))
〕×δ(f、−Ifz)δ(fl−mfz) ・−・f
i+但し al 、 a1+。:振幅 ≠19φ1十m:位相 fl、f、:係り合いをみる2つの周波数ここで歯車に
異常が生じた場合、検出されるデータX (t) H下
記(8)式のようになる。
However, a: Dirac delta function 8nn(f): Noise power spectrum -1,))
]×δ(f, -Ifz)δ(fl-mfz) ・-・f
i+However, al, a1+. : Amplitude ≠ 19φ10m : Phase fl, f, : Two frequencies to check the engagement If an abnormality occurs in the gear here, the detected data X (t) H will be as shown in equation (8) below.

但し δm:不規則位相 そしてこのパイスペクトル吋’l”Y (fl、f 2
 )Id下記(9)式で表わすことができる0 −一1+m)) ) XB[exp(j (早1−δ□
+m))〕Xδ(f、−1f2)δ(f2−mf、) 
++・(91但し δ□、δ1+m:不規則位相 従って異常信号のパイスペクトルは正常時のそれに比し
て不規則付相分だけ、即ちE(exp(j(J、+δ。
However, δm: irregular phase and this pi spectrum 吾'l''Y (fl, f 2
) Id can be expressed by the following formula (9) 0 - - 1 + m)) )
+m))]Xδ(f,-1f2)δ(f2-mf,)
++・(91 However, δ□, δ1+m: Irregular phase Therefore, the pi spectrum of the abnormal signal is compared to the normal one by the amount of the irregular phase, that is, E(exp(j(J, +δ.

−δ□□、丹〕だけ振幅が減少することきなり、こnを
チェックすることにより歯車の異常が検知できる。一般
VCは各調和成分の位相とその振幅も変化するので下記
(10)式に示すパイコヒーレンスBIC1T”i””
’R”f+、fz八へち時系列データから得らnる3次
相関関数をフーリエ変換した値を任意に週休した周波数
におけるパワースペクトルにて除して正規化した値を用
いる〇 ・・・(]0) 但し BYT? (’s 、’t ) : x (t)
から得られる3次相関関数をフーリエ変換したパイスペ
クトル”rr(f) :周波数fにおけるパワースペク
トル このように本発明け、異常が発生すると原糸列信号の波
形が乱れ、ある特定周波数とその高調波周波数との間の
相関が低下することに着目し、2つの周波数f1.f、
の間の係り合いの指標として上記パイコヒーレンスを用
いて異常を検知する方法である。
-δ□□, Tan], and by checking this, an abnormality in the gear can be detected. In general VC, the phase and amplitude of each harmonic component also change, so the pi coherence BIC1T"i"" shown in the following equation (10)
'R'' f+, fz 8 Hehi Use the value obtained by Fourier transforming the cubic correlation function n obtained from the time series data and dividing it by the power spectrum at an arbitrary frequency of weekly holidays and normalizing it〇... (]0) However, BYT? ('s,'t): x (t)
The pi spectrum obtained by Fourier transform of the cubic correlation function obtained from ``rr(f): Power spectrum at frequency f In this way, in the present invention, when an abnormality occurs, the waveform of the yarn train signal is disturbed, and a certain frequency and its harmonics are distorted. Focusing on the fact that the correlation between the wave frequency and the wave frequency decreases, the two frequencies f1.f,
This is a method of detecting an abnormality using the pi-coherence described above as an index of the relationship between

ここで係り合いをみる2つの周波数f1.f、としては
、(1)基本周波数で2と2f2 (11)歯車噛み合一い周波数f。と2f。
Here we will look at the relationship between the two frequencies f1. f is (1) 2 and 2f2 at the fundamental frequency (11) Gear mesh frequency f. and 2f.

(Ill)固有振動のうちの最大周波数fKと2fK(
iV)パワースペクトルの最大値fMと2fM等を選ぶ
のが好ましく、最も好ましいものは監視対象に応じて集
積データに基いて選べ・絆よい。例えば小型軸受試験機
を用いた実験のi合、固有振動のうちの最大周波数fK
と2fKとを選ぶとよい結果が得られた。
(Ill) The maximum frequency fK and 2fK (
iV) It is preferable to select the maximum values fM, 2fM, etc. of the power spectrum, and the most preferable one can be selected based on the accumulated data depending on the monitoring target. For example, in an experiment using a small bearing testing machine, the maximum frequency fK of the natural vibrations
Good results were obtained by selecting and 2fK.

この周波数・は振動解析したところ、歯車の捩り尚有振
動数であった。
When this frequency was analyzed by vibration, it was found to be the frequency that still exists when the gear is torsion.

Wi カルパイコヒーレンスを用いて周期運動体の異常
を検知する場合は時系列データ中に弁別しにくい雑音が
含inでいても、2次元量で把握しているパワースペク
トルを用いて異常を検出する場□ 合と異なり、パイコヒーレンスは3次元量で把握してい
るために耐雑音性が優れており、異常を検知できる感度
が優n、ている0またパイコヒーレンスに0から1の間
で評価するために初期状況を知る必男°があるものの、
準絶対的な評価が可能であり、周期運動体を備えた機器
のサイズ、周期運動体の回転速度、狛荷の大小等に応じ
た(&〜1々のデータケ蓄積しておく必要がない0 次(τ本発明方法會その実施例を示す図面に基いて簡明
する。第1図は本発明方法の実施状態を示す模式図であ
って、減速機1には所定のギヤ比を持った歯車1a、l
bが内蔵さnており、その歯沖1aの中心孔に嵌通され
た軸1g1−を減速機1のハウジングに対設さn、たペ
アリンクlc、ldKよって支承さnlまた歯車1bの
中心孔に嵌通された軸1hは減速機1のハウジングに対
設さtl、喪ペアリ。ング1θ、’lfKよって支承さ
れている0軸1gはモータ2の出力軸に連動連結されて
おり、その回転は歯車1a、lbにより減速されて軸1
hに伝わり、更にプーリー、ベルトを介して9荷ポンプ
3に伝わるようになっている。ベアリングlc。
Wi When detecting anomalies in a periodic body using Kalpi coherence, even if the time series data contains noise that is difficult to distinguish, the anomaly is detected using the power spectrum, which is understood as a two-dimensional quantity. Unlike the case, pi-coherence has excellent noise resistance because it is understood as a three-dimensional quantity, and the sensitivity for detecting abnormalities is excellent. Although it is necessary to know the initial situation in order to
Quasi-absolute evaluation is possible, and it is possible to perform a The method of the present invention will be briefly explained based on the drawings showing an embodiment of the method of the present invention. FIG. 1a,l
The shaft 1g1-, which is fitted into the center hole of the gear 1a, is installed opposite to the housing of the reducer 1, and is supported by the paired links lc, ldK, and the center of the gear 1b. The shaft 1h fitted into the hole is installed opposite to the housing of the reducer 1. The 0 shaft 1g supported by the rings 1θ and 'lfK is interlocked and connected to the output shaft of the motor 2, and its rotation is decelerated by the gears 1a and lb.
h, and is further transmitted to the nine-load pump 3 via a pulley and belt. bearing lc.

ld、Xs、if’′の外輪にはその振動を検出して電
気信号に変換する振動検出装置JIt4が増り付けられ
ており、該振動検出装置4の出力はサンプリング回路5
へ入力され、ここで一定周期毎にサンプリングされてア
ナログデータからデジタルデータに変換さnl、記憶装
置6へ順次ストアされてい〈0記憶装置6ヘストアされ
たディジタルデータは計算装置7へ入力され、(101
式に基いてパイコヒーレンスユ3□。、rTγ(ft*
fg)が各検出部毎に求められるようになっている。
A vibration detection device JIt4 is added to the outer ring of ld,
The digital data stored in the storage device 6 is input to the calculation device 7, where it is sampled at regular intervals, converted from analog data to digital data, and sequentially stored in the storage device 6. 101
Pi coherence Yu3□ based on the formula. , rTγ(ft*
fg) is determined for each detection unit.

斯かる装置を用いて正常な状態、無給油状態(ケース1
)、減速機の歯車に小さな傷を付した状態(ケース2)
、少し大きな傷を付した状態(ケース3)及び大きな傷
を付した状態(ケース4)についてパイコヒーレンスB
ib、γγ7(ft、fg) k求メて比較した結果を
示すグラフ(本発明方法)が第2図である0ここで保り
合いをみる2つの周波1父として目固有振動のうちの最
大の周波数fK(3480H2)とその2次高調波周波
数2fK(6960H2)とを選んだ。
Using such a device, normal conditions and non-lubricated conditions (Case 1)
), with small scratches on the reducer gear (Case 2)
, Pi coherence B for the state with a slightly large scratch (Case 3) and the state with a large scratch (Case 4)
ib, γγ7 (ft, fg) The graph (method of the present invention) showing the results of calculating and comparing k is shown in Figure 2. The frequency fK (3480H2) and its second harmonic frequency 2fK (6960H2) were selected.

なお第3図は、同条件にて得らn、た時系列データより
T(MSS値上って比較し九結果を示すグラフ(従来法
の一例である。図に示す如く本発明方法による場合に、
従来から用いらnているR’M S飴とよくit応がと
れており、史に異常の札1「をみる場合に1dRN4s
値より明瞭に差がでることも分かった0そしてこの差は
雑音が多く含まnるほど顕著にな氏以上詳述した如く本
発明による場合は、同期運動体の振動から得られる時系
列データに基いて3次相関関数を計算し、その値をフー
リエ変換した飴を、任意に選択した周波数におけるI(
ワースベクトルにて除して正規化したイーち]くイbヒ
ーレンスによって周期運動体の異常を検知する八で、周
期運動体を備えた機器のサイズ、周期運動体の回転速度
、負荷の大小鳩に左右されない周期運動体の監視方法が
可能となり、更に前記時系列データ中に弁別しにくい雑
音が含・まれる場合でも周期運動体の異常を検知でき、
本発明は回転体の異常検知技術等の向上に多大の貢献を
なすものであるへ
FIG. 3 is a graph showing the results of comparing the T(MSS) values from the time series data obtained under the same conditions (this is an example of the conventional method. As shown in the figure, when using the method of the present invention, To,
It corresponds well with the conventionally used R'M S candy, and when looking at the abnormal tag 1 in history, it is 1dRN4s.
It was also found that there is a clear difference between the values 0 and 0, and this difference becomes more pronounced the more noise is included. A cubic correlation function is calculated based on the value, and the value is Fourier-transformed to obtain the candy I(
Normalized by dividing by the worth vector] Detecting abnormalities in periodic moving bodies by heherence The size of equipment equipped with periodic moving bodies, rotational speed of periodic moving bodies, load size, etc. It is possible to monitor periodic bodies that are not affected by
The present invention will make a significant contribution to the improvement of abnormality detection technology for rotating bodies.

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

第1図は本発明方法の実施状態を示す模式図、第2図は
本発明方法により得られたデータを示すグラフ、第3図
は従来法により得られたデータを示すグラフである。 1−・・減速機 1a 、 l b ・・・歯車 1c
、ld、is。 1f・・・ベアリング 2・・・モータ 3・・・ボン
14・・・振動検出装置 特 許 出 願 人   住友金輌工業株式会社代理人
 弁理士  河 野 分 夫 、′、 手続補正書(自発) 昭和51i7iEIIO月19F−1 特許庁長官殿 /、 事件の表示 昭和56年特許願第161290号 2 発明の名称 周期運動体の監視方法 3 補正をする者 事件との関係   特許出願人 グ、  代  理  人 明細書の1発明の詳細な説明」の梱 Z、 補正の内容 (1)明細書の第8頁の2行目と3行目との聞に「即も 」 を挿入する。 (2)  11細書の第8頁の4行目と5行目との闇に
「R1」ち T:データ収得期間 X(f):原系列データX (f)のツーり置換*:共
役板素数             」全挿入する。
FIG. 1 is a schematic diagram showing the implementation state of the method of the present invention, FIG. 2 is a graph showing data obtained by the method of the present invention, and FIG. 3 is a graph showing data obtained by the conventional method. 1-...Reducer 1a, lb...Gear 1c
,ld,is. 1f...Bearing 2...Motor 3...Bon 14...Vibration detection device patent Applicant Sumitomo Metal Industries Co., Ltd. Agent Patent attorney Buno Kawano, ', Procedural amendment (voluntary) 1972 EIIO Monthly 19F-1 Mr. Commissioner of the Japan Patent Office / Indication of the case 1982 Patent Application No. 161290 2 Title of the invention Method for monitoring periodic moving bodies 3 Relationship with the case by the person making the amendment Patent applicant Gu, Agent Packing Z of 1. Detailed Description of the Invention in the Specification, Contents of the Amendment (1) ``Somomo'' is inserted between the 2nd and 3rd lines on page 8 of the specification. (2) “R1” in the darkness between the 4th and 5th lines on page 8 of the 11 specification T: Data acquisition period X (f): Original series data Insert all prime numbers.

Claims (1)

【特許請求の範囲】 ユ0周期aI動体の振′勤を一定周期でサンプリングし
て時系列データを得、該時系列データから、任意に選択
した周波数に関するパイコヒーレンスを求め、こnを前
記周期運動体が正常である場合の同周波数に関するパイ
コヒーレンスと比較することによ#1’ AtT k周
期運動体の異常ケ何知することを45徴とする周期運動
体の監視方法。 2、前記周波数は周期運動体の艙−動に関連づけて選択
される特許請求の範囲第1項%rJ軟の周期運動体の監
視方法。 3、前記周波数に周期運動体から得らnる固有同波数と
その冒調波周波数で売る特許請求の範囲第2項記畝の周
期連動体の監視方法0
[Claims] Time-series data is obtained by sampling the vibration of a moving object with period aI at a constant period, and from the time-series data, the pi coherence with respect to an arbitrarily selected frequency is calculated, and this #1'AtTk A method for monitoring a periodic body using 45 symptoms to identify abnormalities in a periodic body by comparing it with pi-coherence for the same frequency when the body is normal. 2. A method for monitoring a periodic moving body according to claim 1, wherein the frequency is selected in relation to the crawling motion of the periodic moving body. 3. A method for monitoring a periodic interlocking body of ridges as set forth in claim 2, which sells at the n characteristic same wave number obtained from the periodic moving body and its harmonic frequency at the frequency.
JP16129081A 1981-10-09 1981-10-09 Monitoring method for periodical motion body Granted JPS5862528A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP16129081A JPS5862528A (en) 1981-10-09 1981-10-09 Monitoring method for periodical motion body

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP16129081A JPS5862528A (en) 1981-10-09 1981-10-09 Monitoring method for periodical motion body

Publications (2)

Publication Number Publication Date
JPS5862528A true JPS5862528A (en) 1983-04-14
JPS6260011B2 JPS6260011B2 (en) 1987-12-14

Family

ID=15732291

Family Applications (1)

Application Number Title Priority Date Filing Date
JP16129081A Granted JPS5862528A (en) 1981-10-09 1981-10-09 Monitoring method for periodical motion body

Country Status (1)

Country Link
JP (1) JPS5862528A (en)

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