JPH05264335A - Method and apparatus for analyzing rotational order ratio - Google Patents
Method and apparatus for analyzing rotational order ratioInfo
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- JPH05264335A JPH05264335A JP6321292A JP6321292A JPH05264335A JP H05264335 A JPH05264335 A JP H05264335A JP 6321292 A JP6321292 A JP 6321292A JP 6321292 A JP6321292 A JP 6321292A JP H05264335 A JPH05264335 A JP H05264335A
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Abstract
Description
【０００１】[0001]
【産業上の利用分野】本発明は回転機の回転に起因する
振動の分析方法及び装置に関わり、特に小型で高速の回
転機の回転次数比分析方法及び装置に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for analyzing vibration caused by rotation of a rotating machine, and more particularly to a method and apparatus for analyzing the rotation order ratio of a small-sized and high-speed rotating machine.
【０００２】[0002]
【従来の技術】回転機の振動，騒音の分析には回転周波
数を基準にした回転次数比分析方法が用いられている。
回転次数比分析は蒸気タービンブレードの振動解析，自
動車エンジンの振動解析等で有名であり、回転器の振動
解析には極めて有用な方法である。図３にアナログ方式
の従来の回転次数比分析の方法を示す。この方法では被
測定物１の回転の周波数を検出するための回転パルス発
生器２が必要で回転軸に継ぎ手３を設け、回転パルス発
生器２に接続して回転パルスを取り出すことになる。振
動は振動ピックアップ４，騒音の場合はマイクロホン５
で取り出し、トラッキングフィルター６に送られる。一
方、回転パルス発生器２からの回転パルスは周波数−電
圧変換器７により回転周波数に比例した直流電圧に変え
られ、トラッキングフィルター６の通過周波数を決定す
る。これにより、常に回転周波数の振動または騒音を取
り出すことが出来る。回転周波数の２倍，３倍などの周
波数についても周波数−電圧変換器７の出力電圧を２
倍，３倍にすることにより分析が行われる。分析した結
果はＸＹレコーダーに回転次数−振動または騒音特性，
キャンベル線図などの形で表示される。2. Description of the Related Art A rotational order ratio analysis method based on a rotational frequency is used to analyze vibration and noise of a rotating machine.
Rotational order ratio analysis is famous for steam turbine blade vibration analysis, automobile engine vibration analysis, etc., and is a very useful method for rotor vibration analysis. FIG. 3 shows a conventional method of analyzing the rotational order ratio using an analog method. In this method, the rotation pulse generator 2 for detecting the frequency of rotation of the DUT 1 is required, and the joint 3 is provided on the rotation shaft and connected to the rotation pulse generator 2 to extract the rotation pulse. Vibration is a vibration pickup 4, and in the case of noise, a microphone 5
And sent to the tracking filter 6. On the other hand, the rotation pulse from the rotation pulse generator 2 is converted into a DC voltage proportional to the rotation frequency by the frequency-voltage converter 7, and the pass frequency of the tracking filter 6 is determined. As a result, it is possible to take out vibration or noise of the rotation frequency at all times. The output voltage of the frequency-voltage converter 7 is set to 2 even for frequencies twice or three times the rotation frequency.
The analysis is performed by doubling and tripling. The analysis result shows that the XY recorder has rotational order-vibration or noise characteristics,
It is displayed in the form of a Campbell diagram.
【０００３】図４にディジタル方式の従来の回転次数比
分析方法を示す。この方法では被測定物１の回転の周波
数を検出するための回転パルス発生器２が必要で回転軸
に継ぎ手３を設け、回転パルス発生器２に接続して回転
パルスを取り出すことになる。振動は振動ピックアップ
４，騒音の場合はマイクロホン５で取り出し、２チャン
ネルのＡ／Ｄコンバーター９の片方のチャンネルに送ら
れる。一方、回転パルス発生器２からの回転パルスは周
波数−電圧変換器１０により回転周波数に比例した直流
電圧に変えられ、Ａ／Ｄコンバータ９のもう一つのチャ
ンネルに送られる。さらに１０では回転パルスから１回
転あたり２のｎ乗個のパルスを作り、Ａ／Ｄコンバータ
９のサンプリング周波数として用いる。Ａ／Ｄ変換され
た信号はフーリエ変換器１１に送られ、フーリエ変換さ
れ、周波数領域の信号となる。この信号がＸＹレコーダ
８に送られ、回転次数−振動または騒音特性，キャンベ
ル線図などの形で表示される。１回転あたり２のｎ乗個
のパルスが必要なのはフーリエ変換が２の整数乗のデー
タ数を必要とすること、および洩れ（leakage）を発生
させないためである。FIG. 4 shows a conventional digital rotation order ratio analysis method. In this method, the rotation pulse generator 2 for detecting the frequency of rotation of the DUT 1 is required, and the joint 3 is provided on the rotation shaft and connected to the rotation pulse generator 2 to extract the rotation pulse. The vibration is picked up by the vibration pickup 4 and the microphone 5 in case of noise, and sent to one channel of the 2-channel A / D converter 9. On the other hand, the rotation pulse from the rotation pulse generator 2 is converted into a DC voltage proportional to the rotation frequency by the frequency-voltage converter 10 and sent to another channel of the A / D converter 9. Further, at 10, 2 n power pulses are generated per rotation from the rotation pulse and used as the sampling frequency of the A / D converter 9. The A / D-converted signal is sent to the Fourier transformer 11 and Fourier-transformed into a frequency domain signal. This signal is sent to the XY recorder 8 and displayed in the form of rotational order-vibration or noise characteristics, Campbell diagram or the like. The 2n pulses per revolution are required because the Fourier transform requires a data number that is an integer power of 2 and does not cause leakage.
【０００４】[0004]
【発明が解決しようとする課題】これら従来の方法では
回転パルス発生器，回転継ぎ手が必要であるため、特に
小型の回転機に対しては適用しにくく、また継ぎ手を接
続することで振動系が変化したり、負荷が大きくなるな
どの問題があった。さらにディジタル方式の場合、回転
数の整数倍の周波数はサンプリングクロックと同期がと
れているが、整数倍でない周波数に対しては、フーリエ
変換特有の漏れ（leakage)が発生して周波数，振幅とも
正しい値が得られない問題がある。これを防止するた
め、各種の窓関数が用いられるが十分ではなかった。Since these conventional methods require a rotary pulse generator and a rotary joint, it is difficult to apply them especially to a small rotating machine. There were problems such as changes and increased load. Furthermore, in the case of the digital system, the frequency that is an integral multiple of the rotation speed is synchronized with the sampling clock, but for frequencies that are not an integral multiple, leaks peculiar to the Fourier transform occur and both frequency and amplitude are correct. There is a problem that the value cannot be obtained. To prevent this, various window functions have been used, but they have not been sufficient.
【０００５】さらに、上記の技術では、次の問題があっ
た。Further, the above technique has the following problems.
【０００６】１）測定のために回転パルスを検出する装
置を付加する必要があり、測定が大がかりになるため、
小型の回転機器の測定には不向きである。1) Since it is necessary to add a device for detecting a rotation pulse for measurement, the measurement becomes large,
It is not suitable for measuring small rotating equipment.
【０００７】２）ディジタル方式の場合には回転周波数
の整数倍でない周波数の分析に誤差が生じていた。2) In the case of the digital method, an error occurred in analysis of a frequency that was not an integral multiple of the rotation frequency.
【０００８】本発明の目的は上記の欠点を解消し、簡単
な方法で精度よく回転次数比分析を行なう方法及び装置
を提供することにある。SUMMARY OF THE INVENTION An object of the present invention is to solve the above drawbacks and to provide a method and apparatus for performing a rotation order ratio analysis with high accuracy by a simple method.
【０００９】[0009]
【課題を解決するための手段】本発明では、上記の目的
を達成するために、窓関数を用いないで行なうフーリエ
変換の結果から真の回転周波数、さらに回転周波数に比
例して変わる周波数とそれぞれの真の振幅を求めること
により、回転次数比分析を行なうのである。According to the present invention, in order to achieve the above-mentioned object, the true rotation frequency is determined from the result of the Fourier transform performed without using the window function, and the frequency changing in proportion to the rotation frequency. The rotation order ratio analysis is performed by obtaining the true amplitude of.
【００１０】[0010]
【作用】すなわち、フーリエ変換によって得られた値は
位相情報を持つため、複素数になるのでこれの絶対値を
とることにより、振幅を求めることが出来る。ここで、
あらかじめ与えた周波数範囲の中で振幅が極大となる周
波数、振幅とその前後で次に振幅が大きくなる周波数と
振幅を求め、これらの値から計算により、真の周波数と
真の振幅を予測できる。In other words, since the value obtained by the Fourier transform has phase information, it becomes a complex number, and the amplitude can be obtained by taking the absolute value of this. here,
It is possible to predict the true frequency and the true amplitude by calculating the frequency at which the amplitude becomes maximum in the frequency range given in advance, the amplitude and the frequency and amplitude at which the amplitude increases next before and after the amplitude, and calculating from these values.
【００１１】[0011]
【実施例】本発明の実施例を図１に示す。FIG. 1 shows an embodiment of the present invention.
【００１２】図１は本発明の構成を示す図で、被測定物
１からの振動を振動ピックアップ４または騒音をマイク
ロホン５により検出して１チャンネルのＡ／Ｄコンバー
タ１２に送るのである。回転周波数とは独立の発振器１
３から供給されるクロック信号によりＡ／Ｄコンバータ
１２の中でサンプリングされ、ディジタル信号に変換さ
れる。その後、１チャンネルのフーリエ変換器１４によ
りフーリエ変換され、周波数領域の信号が得られる。こ
の信号から回転周波数を推定し、それをもとに回転周波
数に比例する周波数の成分の分析を行ない、回転次数比
と振幅の関係図，キャンベル線図などをＸＹレコーダ８
に表わすのである。このときの真の周波数，振幅の推定
は次のようにして求める。FIG. 1 is a diagram showing the configuration of the present invention, in which vibration from the DUT 1 is detected by a vibration pickup 4 or noise by a microphone 5 and sent to a 1-channel A / D converter 12. Oscillator 1 independent of rotation frequency
The signal is sampled in the A / D converter 12 by the clock signal supplied from the circuit 3 and converted into a digital signal. After that, Fourier transform is performed by the one-channel Fourier transformer 14, and a signal in the frequency domain is obtained. The rotation frequency is estimated from this signal, and the component of the frequency proportional to the rotation frequency is analyzed based on the estimated rotation frequency, and the relationship diagram between the rotation order ratio and the amplitude, the Campbell diagram, etc. are analyzed by the XY recorder 8.
Is represented in. The true frequency and amplitude at this time are estimated as follows.
【００１３】図２に真の振幅Ｖとフーリエ変換により得
られた極大となるｋ，ｋ＋１番目の絶対値Ｒk，ＲK+1と
真の周波数とｋ番目の周波数の差を（１／Ｔ）で割った
値αとの関係を示す。FIG. 2 shows the true amplitude V and the maximum k, k + 1th absolute values R k , R K + 1 obtained by Fourier transform and the difference between the true frequency and the kth frequency (1 / T ) Shows the relationship with the value α.
【００１４】真の周波数と振幅はサンプリング周波数と
回転周波数が同期している時（すなわち、サンプリング
周波数が１回転あたり２のｎ乗になっている）には振幅
が極大になる周波数と振幅に一致する。しかし、同期の
関係がくずれると漏れ（leakage)の効果により真の振幅
より小さくなるので、これを計算により補正するのであ
る。The true frequency and amplitude coincide with the frequency and amplitude where the amplitude becomes maximum when the sampling frequency and the rotation frequency are synchronized (that is, the sampling frequency is 2 to the n-th power per rotation). To do. However, when the synchronization relationship is broken, the amplitude becomes smaller than the true amplitude due to the effect of leakage, and this is corrected by calculation.
【００１５】すなわち、振動または騒音の信号Ｆ（ｔ）
を数１１のように与える。That is, the vibration or noise signal F (t)
Is given as in Equation 11.
【００１６】[0016]
【数１１】 [Equation 11]
【００１７】ここに ｋ：整数、α：０≦α≦１、Ｔ：サンプリング時間、
ｔ：時間、ａ：振幅 これに数１２のハニング窓関数Ｗ（ｔ）をかけてフーリ
エ変換すると数１３のＱ(ｋ)が得られる。Where k is an integer, α is 0 ≦ α ≦ 1, T is a sampling time,
t: Time, a: Amplitude When this is multiplied by the Hanning window function W (t) of Formula 12, the Fourier transform is performed, and Q (k) of Formula 13 is obtained.
【００１８】[0018]
【数１２】 [Equation 12]
【００１９】[0019]
【数１３】 [Equation 13]
【００２０】図２に示すように絶対値Ｒk，Ｒk+1が得ら
れた場合、ＲkとＲk+1とαの関係は数１４により表わさ
れる。When absolute values R k and R k + 1 are obtained as shown in FIG. 2, the relationship between R k , R k + 1 and α is expressed by equation (14).
【００２１】[0021]
【数１４】 [Equation 14]
【００２２】かくして真の周波数は(ｋ＋α)／Ｔにより
求めることができる。Thus, the true frequency can be obtained by (k + α) / T.
【００２３】真の振幅Ｖは数１５により求める。The true amplitude V is obtained by the equation 15.
【００２４】[0024]
【数１５】 [Equation 15]
【００２５】このように所定の周波数範囲の中で振幅が
極大となる周波数，振幅、その前後で次に振幅が大きい
周波数と振幅を用いることにより、真の周波数と振幅を
推定するのである。As described above, the true frequency and the amplitude are estimated by using the frequency and the amplitude having the maximum amplitude within the predetermined frequency range, and the frequency and the amplitude having the next largest amplitude before and after the frequency.
【００２６】次に数１１に数１６のハミング窓関数Ｗ
(ｔ)をかけてフーリエ変換すると数１７のＱ(ｋ)が得ら
れる。Next, the Hamming window function W of Eq.
By multiplying (t) and performing Fourier transform, Q (k) of the equation 17 is obtained.
【００２７】[0027]
【数１６】 [Equation 16]
【００２８】[0028]
【数１７】 [Equation 17]
【００２９】図２に示すように絶対値Ｒk，Ｒk+1が得ら
れた場合、ＲkとＲk+1とαの関係は数１８により表わさ
れる。When the absolute values R k and R k + 1 are obtained as shown in FIG. 2, the relationship between R k , R k + 1 and α is expressed by Equation 18.
【００３０】[0030]
【数１８】 [Equation 18]
【００３１】数１８はαの３次式なので解くことが出来
る。Equation 18 can be solved because it is a cubic expression of α.
【００３２】かくして真の周波数は（ｋ＋α）／Ｔによ
り求めることができる。Thus, the true frequency can be calculated by (k + α) / T.
【００３３】真の振幅Ｖは数１９により求められる。The true amplitude V is calculated by the equation (19).
【００３４】[0034]
【数１９】 [Formula 19]
【００３５】となる。[0035]
【００３６】数１２のハニング窓関数を用いた場合に
は、求められたＲk，ＲK+1を用いて数１４によりαを求
め、数１５に代入することにより、真の振幅Ｖが求めら
れる。真の周波数は数２０から求められる。When the Hanning window function of Equation 12 is used, α is obtained by Equation 14 using the obtained R k and R K + 1, and is substituted into Equation 15 to obtain the true amplitude V. Be done. The true frequency is obtained from equation (20).
【００３７】[0037]
【数２０】 [Equation 20]
【００３８】数１６のハミング窓関数を用いた場合に
は、求められたＲk，ＲK+1を用いて数１８をαについて
解くのである。解かれたαを数１９に代入することによ
り、真の振幅Ｖを数２１に代入することによって、真の
周波数が求められるものである。When the Hamming window function of Equation 16 is used, Equation 18 is solved for α by using the obtained R k and R K + 1 . By substituting the solved α into Eq. 19 and substituting the true amplitude V into Eq. 21, the true frequency is obtained.
【００３９】[0039]
【数２１】 [Equation 21]
【００４０】[0040]
【発明の効果】本発明によれば、回転パルス発振器，回
転継ぎ手を用いる必要がないため、小型の回転機器の振
動，騒音の回転次数比分析を簡単に、迅速に行うことが
出来るので、振動，騒音の対策も容易に出来、低振動，
低騒音の回転機器を得ることが出来る。According to the present invention, since it is not necessary to use a rotary pulse oscillator and a rotary joint, it is possible to easily and quickly analyze the rotation order ratio of vibration and noise of a small rotating machine. ， Measures against noise are easy and low vibration,
It is possible to obtain a low-noise rotating device.
【図１】本発明の実施例を示す構成図である。FIG. 1 is a configuration diagram showing an embodiment of the present invention.
【図２】本発明の実施例におけるハニング窓関数を使っ
た場合の計算手順を示す図である。FIG. 2 is a diagram showing a calculation procedure when a Hanning window function is used in the embodiment of the present invention.
【図３】アナログ方式による従来の回転次数比分析方法
を示す図である。FIG. 3 is a diagram showing a conventional rotation order ratio analysis method by an analog method.
【図４】ディジタル方式による従来の回転次数比分析の
方法を示す図である。FIG. 4 is a diagram showing a conventional method of rotational order ratio analysis by a digital method.
１…被測定物、２…回転パルス発生器、３…回転継ぎ
手、４…振動ピックアップ、５…マイクロホン、６…ト
ラッキングフィルタ、７…周波数−電圧変換器、８…Ｘ
Ｙレコーダ、９…２チャンネルのＡ／Ｄコンバータ、１
０…周波数−電圧変換器、１１…２チャンネルのフーリ
エ変換器、１２…１チャンネルのＡ／Ｄコンバータ、１
３…発信器、１４…１チャンネルのフーリエ変換器。1 ... Object to be measured, 2 ... Rotating pulse generator, 3 ... Rotating joint, 4 ... Vibration pickup, 5 ... Microphone, 6 ... Tracking filter, 7 ... Frequency-voltage converter, 8 ... X
Y recorder, 9 ... 2 channel A / D converter, 1
0 ... Frequency-voltage converter, 11 ... 2-channel Fourier transformer, 12 ... 1-channel A / D converter, 1
3 ... Oscillator, 14 ... 1-channel Fourier transformer.
Claims (17)
該回転体の回転周波数を推測し、該回転周波数に比例す
る周波数を持つ成分の分析を行なうことを特徴とする回
転次数比分析方法。1. A method for analyzing a rotational order ratio, which comprises estimating a rotational frequency of a rotating body from a vibration or noise signal of each part of the rotating body and analyzing a component having a frequency proportional to the rotating frequency. ..
騒音をディジタル信号に変換後、フーリエ変換した値の
絶対値が所定の周波数範囲の中で極大となる周波数，振
幅とその前後の周波数，振幅とから該回転周波数を求め
ることを特徴とする回転次数比分析方法。2. The frequency according to claim 1, wherein the vibration or noise of the rotating body is converted into a digital signal, and the absolute value of the Fourier-transformed value becomes maximum within a predetermined frequency range, and the frequencies before and after the amplitude. , A rotational order ratio analysis method, wherein the rotational frequency is obtained from the amplitude.
騒音をディジタル信号に変換後、フーリエ変換した値の
絶対値が所定の周波数範囲の中で極大となる周波数，振
幅とその前後の周波数の振幅とから、該回転周波数に比
例する周波数の振動または騒音の振幅を求めることを特
徴とする回転次数比分析方法。3. The frequency according to claim 2, wherein the vibration or noise of the rotating body is converted into a digital signal, and the frequency of the absolute value of the Fourier-transformed value becomes maximum in a predetermined frequency range, and the frequencies before and after the amplitude. The amplitude of vibration or noise having a frequency proportional to the rotation frequency is calculated from the amplitude of the rotation frequency.
いてフーリエ変換した値の絶対値が極大となる周波数及
びその前後で２番目に値が大きくなる周波数を下から順
にＦk，Ｆk+1、絶対値をそれぞれＲk，Ｒk+1、真の周波
数ｆを 【数１】 として求めることを特徴とする回転次数比分析方法。4. The frequency at which the absolute value of the value Fourier-transformed by using the Hanning window function is maximum and the frequency at which the value is second largest before and after the frequency are F k and F k in order from the bottom. +1 and absolute values are R k and R k + 1 , respectively, and the true frequency f is A method for analyzing a rotational order ratio, characterized by:
をサンプリング時間Ｔで割った値をαとしたとき、真の
周波数に対応するフーリエ変換の絶対値をＶ0 とすると 【数２】 で求めることを特徴とする回転次数比分析方法。5. When α is a value obtained by dividing the difference between the true frequency and F k by the sampling time T, the absolute value of the Fourier transform corresponding to the true frequency is V 0. 2] A method for analyzing the rotational order ratio, which is characterized by
いてフーリエ変換した値の絶対値が極大となる周波数及
びその前後で２番目に値が大きくなる周波数を下から順
にＦk，Ｆk+1、絶対値をそれぞれＲk，Ｒk+1、サンプリ
ング時間をＴとした時、真の周波数ｆを 【数３】 を解いて得られるαを用いて 【数４】 として求めることを特徴とする回転次数比分析方法。6. The frequency at which the absolute value of the value Fourier-transformed using the Hamming window function is maximum and the frequency at which the value is second largest before and after the frequency are F k and F k in order from the bottom. +1 and absolute values are R k and R k + 1 respectively, and the sampling time is T, the true frequency f is Using α obtained by solving A method for analyzing a rotational order ratio, characterized by:
大となる周波数Ｆk との差をサンプリング時間Ｔで割っ
た値をα，絶対値をＲk としたとき、真の周波数に対応
するフーリエ変換の絶対値をＶ0 とすると 【数５】 で求めることを特徴とする回転次数比分析方法。7. When the difference between the true frequency and the frequency F k at which the absolute value has a maximum is divided by the sampling time T is α and the absolute value is R k , the true frequency corresponds to the true frequency. Let V 0 be the absolute value of the Fourier transform that A method for analyzing the rotational order ratio, which is characterized by
該回転体の回転周波数を推測し、該回転周波数に比例す
る周波数を持つ成分の分析を行なうことを特徴とする回
転次数比分析装置。8. A rotation order ratio analyzing apparatus, which estimates a rotation frequency of the rotating body from a signal of vibration or noise of each part of the rotating body and analyzes a component having a frequency proportional to the rotating frequency. ..
体の各部の振動または騒音をディジタル信号に変換後、
ハニング窓関数を用いてフーリエ変換した値の絶対値が
所定の周波数範囲の中で極大となる周波数，振幅とその
前後の周波数の振幅とから求めることを特徴とする回転
次数比分析装置。9. The rotating frequency according to claim 8, wherein after the vibration or noise of each part of the rotating body is converted into a digital signal,
A rotation order ratio analysis device, characterized in that the absolute value of a value Fourier-transformed using a Hanning window function is obtained from the frequency and amplitude at which the absolute value becomes maximum in a predetermined frequency range and the amplitudes of frequencies around it.
る周波数及び振幅について所定の周波数範囲のなかで極
大となる周波数と振幅とすぐ上の周波数，振幅またはす
ぐ下の周波数，振幅とから求めることを特徴とする回転
次数比分析装置。10. The method according to claim 9, wherein the frequency and amplitude proportional to the rotation frequency are obtained from the maximum frequency and the amplitude immediately above or below the frequency or amplitude immediately below the predetermined frequency range. A rotational order ratio analyzer characterized by:
た値の絶対値が極大となる周波数及びそのすぐ上下で次
に値が大きくなる周波数を下から順にＦk，Ｆk+1、絶対
値をそれぞれＲk，Ｒk+1、サンプリング時間をＴとした
時、真の周波数ｆを 【数６】 として求めることを特徴とする回転次数比分析装置。11. The frequency at which the absolute value of the Fourier-transformed value has a maximum and the frequency at which the value increases immediately above and below it are F k , F k + 1 , and the absolute value in order from the bottom. Let R k and R k + 1 be T, and the sampling time be T, and let the true frequency f be An order-of-rotational-ratio analysis device characterized by:
が極大となる周波数Ｆk との差をサンプリング時間Ｔで
割った値をα，絶対値をＲk としたとき、真の周波数に
対応するフーリエ変換の絶対値をＶ0 とすると 【数７】 で求めることを特徴とする回転次数比分析装置。12. When the difference between the true frequency and the frequency F k at which the absolute value is maximum is divided by the sampling time T is α, and the absolute value is R k , the true frequency is obtained. Let V 0 be the absolute value of the Fourier transform that A rotational order ratio analyzer characterized in that
転体の各部の振動または騒音をディジタル信号に変換
後、ハミング窓関数を用いてフーリエ変換した値の絶対
値が所定の周波数範囲の中で極大となる周波数，振幅と
その前後の周波数の振幅とから求めることを特徴とする
回転次数比分析装置。13. The rotation frequency according to claim 8, wherein an absolute value of a value obtained by performing Fourier transform using a Hamming window function after converting vibration or noise of each part of the rotating body into a digital signal is within a predetermined frequency range. A rotational order ratio analyzer characterized in that it is obtained from the frequency and amplitude that have the maximum at, and the amplitudes of the frequencies before and after.
する周波数及び振幅について所定の周波数範囲のなかで
極大となる周波数と振幅とすぐ上の周波数，振幅または
すぐ下の周波数，振幅とから求めることを特徴とする回
転次数比分析装置。14. The method according to claim 13, wherein the frequency and amplitude proportional to the rotation frequency are obtained from the maximum frequency and the amplitude in the predetermined frequency range and the frequency immediately above or below the amplitude. A rotational order ratio analyzer characterized by:
した値の絶対値が極大となる周波数及びそのすぐ上下で
次に値が大きくなる周波数を下から順にＦk，Ｆk+1、絶
対値をそれぞれＲk，Ｒk+1、サンプリング時間をＴとし
た時、真の周波数ｆを 【数８】 を解いて得られるαを用いて 【数９】 として求めることを特徴とする回転次数比分析装置。15. The frequency at which the absolute value of the Fourier-transformed value has a maximum value and the frequency at which the value becomes the next largest value immediately above and below are F k , F k + 1 , and the absolute value in order from the bottom. Let R k and R k + 1 be the sampling time and T be the true frequency f. Using α obtained by solving An order-of-rotational-ratio analysis device characterized by:
が極大となる周波数Ｆk との差をサンプリング時間Ｔで
割った値をα，絶対値をＲk としたとき、真の周波数に
対応するフーリエ変換の絶対値をＶ0 とすると 【数１０】 で求めることを特徴とする回転次数比分析装置。16. When the difference between the true frequency and the frequency F k at which the absolute value is maximum is divided by the sampling time T is α, and the absolute value is R k , the true frequency corresponds to the true frequency. Let V 0 be the absolute value of the Fourier transform that A rotational order ratio analyzer characterized in that
周波数でサンプリングを行なうアナログ、ディジタル変
換器と該変換器のディジタル信号をフーリエ変換するフ
ーリエ変換器を各一組備えたことを特徴とする回転次数
比分析装置。17. An analog / digital converter for sampling at a frequency not in synchronization with the rotational frequency of the object to be measured, and a Fourier transformer for Fourier-transforming a digital signal of the converter. Rotational order ratio analyzer.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP6321292A JPH05264335A (en) | 1992-03-19 | 1992-03-19 | Method and apparatus for analyzing rotational order ratio |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP6321292A JPH05264335A (en) | 1992-03-19 | 1992-03-19 | Method and apparatus for analyzing rotational order ratio |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH05264335A true JPH05264335A (en) | 1993-10-12 |
Family
ID=13222668
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP6321292A Pending JPH05264335A (en) | 1992-03-19 | 1992-03-19 | Method and apparatus for analyzing rotational order ratio |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH05264335A (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH11271021A (en) * | 1998-03-20 | 1999-10-05 | Acute Kk | Waveform analyzer and displacement measuring apparatus using the analyzer |
| US20140013847A1 (en) * | 2012-07-13 | 2014-01-16 | Sicpa Holding Sa | Method and system for authenticating a timepiece |
| US9465367B2 (en) | 2012-07-13 | 2016-10-11 | Sicpa Holding Sa | Method and system for authenticating using external excitation |
| US9772607B2 (en) | 2013-08-23 | 2017-09-26 | Sicpa Holding Sa | Method and system for authenticating a device |
| US10331086B2 (en) | 2012-07-13 | 2019-06-25 | Sicpa Holding Sa | Method and system for authenticating a timepiece |
-
1992
- 1992-03-19 JP JP6321292A patent/JPH05264335A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH11271021A (en) * | 1998-03-20 | 1999-10-05 | Acute Kk | Waveform analyzer and displacement measuring apparatus using the analyzer |
| US20140013847A1 (en) * | 2012-07-13 | 2014-01-16 | Sicpa Holding Sa | Method and system for authenticating a timepiece |
| US9285777B2 (en) * | 2012-07-13 | 2016-03-15 | Sicpa Holding Sa | Method and system for authenticating a timepiece |
| US9465367B2 (en) | 2012-07-13 | 2016-10-11 | Sicpa Holding Sa | Method and system for authenticating using external excitation |
| US10331086B2 (en) | 2012-07-13 | 2019-06-25 | Sicpa Holding Sa | Method and system for authenticating a timepiece |
| US9772607B2 (en) | 2013-08-23 | 2017-09-26 | Sicpa Holding Sa | Method and system for authenticating a device |
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