TWI382171B - Method for analyzing vibrations of mechanism system by exponential decay frequencies - Google Patents

Method for analyzing vibrations of mechanism system by exponential decay frequencies Download PDF

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TWI382171B
TWI382171B TW97138299A TW97138299A TWI382171B TW I382171 B TWI382171 B TW I382171B TW 97138299 A TW97138299 A TW 97138299A TW 97138299 A TW97138299 A TW 97138299A TW I382171 B TWI382171 B TW I382171B
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vibration
signal
exponential decay
mechanical system
envelope signal
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TW201015056A (en
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Yuh Tay Sheen
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Univ Southern Taiwan Tech
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以指數衰減分析機械系統振動的方法Method for analyzing mechanical system vibration by exponential decay

本發明係有關於一種以指數衰減分析機械系統振動的方法，尤其是指一種運用包絡線訊號求得指數衰減常數，而顯示損壞軸承狀態，藉以該指數衰減之診斷分析方法而有效應用於機械損壞之診斷分析的發明應用者。The invention relates to a method for analyzing vibration of a mechanical system by exponential decay, in particular to an exponential decay constant obtained by using an envelope signal, and displaying a damaged bearing state, thereby effectively applying the mechanical damage to the diagnostic analysis method of the exponential decay. The inventor of the diagnostic analysis.

按，機械系統元件運作狀況之診斷分析過程，一般可分為資料擷取、訊號處理與頻譜圖等三階段。首先利用振動感測器(如位移計、速度規或加速規)將振動之物理量轉換為電壓形式，再經由放大器將電壓適度放大後，透過類比轉數位轉換介面將電壓輸入電腦中進行數位式訊號處理，最後取振動頻譜以呈現出振動訊號之頻率特性，並經由頻譜的頻率分布與模式(pattern)來判斷機械系統元件的損壞與否。According to the diagnostic analysis process of the mechanical system components, it can be divided into three stages: data acquisition, signal processing and spectrum analysis. First, the vibration sensor (such as a displacement meter, speed gauge or accelerometer) is used to convert the physical quantity of the vibration into a voltage form, and then the voltage is moderately amplified by the amplifier, and the voltage is input into the computer through the analog-to-digital conversion interface to perform digital signal. Processing, finally taking the vibration spectrum to present the frequency characteristics of the vibration signal, and determining the damage of the mechanical system components via the frequency distribution and pattern of the spectrum.

由於機械系統元件的損壞將造成系統運作產生敲擊振動，並由於機械系統中多數運動元件均屬於旋轉元件，若此類元件上發生損壞將會產生週期性敲擊，因此診斷機械元件之運作狀況則在於偵測此一週期性振動訊號的發生。但由於在機械系統振動訊號中滲有相當程度之雜訊，若元件損壞較輕微則其產生之振動訊號能量較小，因此將會被雜訊所掩蓋而難以察覺，只有到發生相當嚴重損壞時其產生之振動訊號能量才變大，並較明顯大於雜訊振動能量，但由於此時元件損壞已變嚴重，所以機械系統將隨時可能因而造成嚴重故障停止運轉。此種現象為一般頻譜分析儀在分析機械振動訊號時所面臨的困難，亦是在實際運 用時無法發揮損壞診斷預警效果之重大缺失。The damage of the mechanical system components will cause the system to operate with percussion vibration, and since most of the moving components in the mechanical system belong to the rotating components, if such components are damaged, periodic tapping will occur, thus diagnosing the operation of the mechanical components. It is to detect the occurrence of this periodic vibration signal. However, due to the considerable amount of noise in the mechanical system vibration signal, if the component damage is slight, the vibration signal energy generated is small, so it will be hidden by the noise and it is difficult to detect, only when serious damage occurs. The vibration signal energy generated by the vibration signal becomes larger and more obvious than the noise vibration energy, but since the component damage has become serious at this time, the mechanical system may cause serious failure to stop operation at any time. This phenomenon is the difficulty faced by the general spectrum analyzer in analyzing mechanical vibration signals. When using it, it is impossible to exert a major lack of damage diagnosis and warning effect.

本發明人根據上述之缺失，於先前已研發一種以系統共振模態取得包絡線訊號及其運用與運算式，且於 鈞局申請編列為第095137475號發明專利(申請中)，其主要係：一種以系統共振模態取得包絡線訊號，其係由機械系統振動訊號之振動頻譜決定共振模態數，並取得各共振模態之共振頻率，且以步階函數(stepwise function)來近似該振動訊號之包絡線訊號(envelope signal)，則振動訊號可映射於以共振頻率所建立之三角函數基底上，再以線性最小平方估測法(linear least squares estimation)求取其映射係數對，由所得係數對之平方和開根號可獲得機械振動訊號於各共振模態之包絡線訊號。Based on the above-mentioned shortcomings, the inventors have previously developed an envelope signal obtained by the system resonance mode, and its application and operation formula, and the application for the invention patent No. 095137475 (in the application) is mainly: An acquisition of an envelope signal by a system resonance mode, wherein a resonance mode number is determined by a vibration spectrum of a mechanical system vibration signal, and a resonance frequency of each resonance mode is obtained, and the vibration is approximated by a stepwise function. The envelope signal of the signal, the vibration signal can be mapped to the trigonometric function base established by the resonant frequency, and then the linear least squares estimation method is used to obtain the mapping coefficient pair. The square of the coefficient pair and the opening number can obtain the envelope signal of the mechanical vibration signal in each resonance mode.

而上述所獲得之結果為一種振動訊號的包絡線訊號，將該包絡線訊號除以在該敲擊週期之最大值即可得指數衰減函數，再將指數衰減函數取自然對數則可得一線性函數，由此線性函數之斜率可求出機械系統之指數衰減常數，進而將指數衰減常數除以其共振頻率可求出機械系統之阻尼參數，並將指數衰減常數除以其共振頻率則可得機械系統之阻尼參數。The result obtained above is an envelope signal of a vibration signal, and the envelope signal is divided by the maximum value of the tapping period to obtain an exponential decay function, and then the exponential decay function is taken as a natural logarithm to obtain a linearity. Function, the slope of the linear function can be used to find the exponential decay constant of the mechanical system, and then the exponential decay constant is divided by its resonant frequency to obtain the damping parameter of the mechanical system, and the exponential decay constant is divided by its resonant frequency. Damping parameters of the mechanical system.

而此包絡線訊號之取得為運用於機械系統之阻尼參數的運算，今本發明人隨科技發展之腳步，經研發製作及實驗之過程，特再提供一種以指數衰減分析機械系統振動的方法，以有效應用於機械損壞之診斷分析。The acquisition of the envelope signal is the operation of the damping parameter applied to the mechanical system. Now the inventor has developed a method of analyzing the vibration of the mechanical system by exponential decay with the development of technology and the process of research and development. For effective analysis of diagnostic analysis of mechanical damage.

本發明係有關於一種以指數衰減分析機械系統振動的方法，其係由機械系統振動訊號而取得各共振模態之包 絡線訊號，將包絡線訊號經取自然對數轉換後，以矩陣式表示而得一系列敲擊訊號之解析，再由線性最小平方法(linear least square analysis)求解則可得包絡線訊號之指數衰減常數，以上述方法應用於軸承損壞分析結果，可顯示在不同模態中其指數衰減常數隨模態數大幅增加，而且損壞軸承所求得之指數衰減常數均遠大於正常軸承之指數衰減常數；因此，以指數衰減之診斷分析方法確可有效應用於機械損壞之診斷分析者。The present invention relates to a method for analyzing vibration of a mechanical system by exponential decay, which is obtained by a vibration signal of a mechanical system to obtain a package of resonance modes. The signal of the envelope signal is obtained by natural logarithm transformation, and the series of tapping signals are represented by a matrix, and then the linear least square analysis is used to obtain the index of the envelope signal. The attenuation constant is applied to the bearing damage analysis result by the above method. It can be shown that the exponential decay constant increases greatly with the modal number in different modes, and the exponential decay constant obtained by the damaged bearing is much larger than the exponential decay constant of the normal bearing. Therefore, the diagnostic analysis method with exponential decay can be effectively applied to diagnostic analysts of mechanical damage.

而為令本發明之技術手段能夠更完整且清楚的揭露，茲請一併參閱所附圖式及圖號，並詳細說明如下：首先，本發明一種以指數衰減分析機械系統振動的方法，其中：係由機械系統振動訊號之振動頻譜決定共振模態數，且分別設定共振頻率為其模態中之最高尖峰頻率，做為各共振模態之初始共振頻率，應用包絡線訊號分析法而獲得振動訊號於各共振模態之包絡線訊號(envelope signal)，將求得之包絡線訊號經取自然對數轉換後，以矩陣式表示而得一系列敲擊訊號之解析，再由線性最小平方法(linear least square analysis)求解則可得包絡線訊號之指數衰減常數，以上述方法應用於軸承損壞分析結果，可顯示在不同模態中其指數衰減常數隨模態數大幅增加，而且損壞軸承所求得之指數衰減常數均遠大於正常軸承之指數衰減常數；因此，以指數衰減之診斷分析方法確可有效應用於機械損壞之診斷分析者。In order to make the technical means of the present invention more complete and clear, please refer to the drawings and drawings, and explain in detail as follows: First, the present invention relates to a method for analyzing mechanical system vibration by exponential decay, wherein : The resonance mode number is determined by the vibration spectrum of the mechanical system vibration signal, and the resonance frequency is set as the highest peak frequency in the mode, respectively, as the initial resonance frequency of each resonance mode, and is obtained by applying the envelope signal analysis method. The envelope signal of the vibration signal in each resonance mode is converted into a natural logarithm by the obtained envelope signal, and then expressed in a matrix form, and a series of tapping signals are analyzed, and then the linear least square method is used. The linear least square analysis can obtain the exponential decay constant of the envelope signal. The above method can be applied to the bearing damage analysis result. It can show that the exponential decay constant increases greatly with the modal number in different modes, and the bearing is damaged. The exponential decay constants obtained are much larger than the exponential decay constants of normal bearings; therefore, the diagnostic analysis method of exponential decay Effectively applicable to mechanical damage by the diagnostic analysis.

根據上述的方式，於此係列舉一較佳的實施例作為說 明，且配合以數學模式表示；而包絡線訊號的取得係可採用各種可行的方式獲得，下列所表示之求得的包絡線訊號僅為其一之方式而以，其如下：在機械之振幅調變訊號可表示為 In accordance with the above-described manner, a preferred embodiment of the series is illustrated and illustrated in a mathematical mode; and the acquisition of the envelope signal can be obtained in various feasible ways, and the envelope signal obtained as follows is obtained. For the other way, it is as follows: the amplitude modulation signal in the machine can be expressed as

其中：L 則為系統振動模的數量；md 是表示損壞數量；d m (t )是表示損壞的脈衝；q m (t )是表示與敲擊相關的能量因素；a 1m (t )是表示振動傳遞路徑的函數；σ 1 是表示指數衰減常數；f l 是表示第1 模之共振頻率；此振動訊號v (t )之頻率特性將呈現以共振頻率為中心頻率所展開之頻帶。此一現象即為振幅調變。Where: L is the number of system vibration modes; md is the number of damages; d m ( t ) is the pulse indicating damage; q m ( t ) is the energy factor associated with the tap; a 1m ( t ) is the transfer function of the vibration path; [sigma] 1 is an exponential decay constant; f l is a resonance frequency of the first die; the vibration signal v (t) will exhibit a frequency characteristic of the resonant frequency as the center frequency of the band expand. This phenomenon is the amplitude modulation.

假如在連續兩敲擊間，振動訊號d m (t )將完全衰減，而且相較於系統共振頻率，其指數衰減頻率較小。因此，在第(1)式之積分項中，q m (t )與a m (t )可視為常數；故第(1)式又可表示為 且，t' ＝mod(t ,1/f dm )，f dm 為敲擊頻率。將第(2)式展開可改寫為 If between two consecutive taps, the vibration signal d m ( t ) will be completely attenuated, and its exponential decay frequency is smaller than the system resonance frequency. Therefore, in the integral term of the formula (1), q m ( t ) and a m ( t ) can be regarded as constants; therefore, the equation (1) can be expressed as And , t' = mod( t , 1 / f dm ), f dm is the tap frequency. Expanding the formula (2) can be rewritten as

此外，在一共振頻率週期中，u m (t )q m (t )a lm (t )可近似為一常數。因此，可將振動訊號以步階函數來近似表示為 Furthermore, in a resonant frequency period, u m ( t ) q m ( t ) a lm ( t ) can be approximated as a constant. Therefore, the vibration signal can be approximated as a step function as

其中，i 和j 分別為步階數和取樣點，而 則為步階函數，q m (i )與a m (i )分別為q m (t )與a m (t )在第i 步階中之近似常數值；。為估測α l (i )與β l (i )，在第i 步階中之取樣點數設為N 且N 2L ，並以矩陣式表示，則如下式 若簡化上式之表示式，則可表示為 以線性最小平方估測法(linear least squares estimation)求取上式的係數，則可得 因此，對應第(1)式之第1 模之包絡線訊號可得 Where i and j are the number of steps and sampling points, respectively Then is the step function, q m ( i ) and a m ( i ) are the approximate constant values of q m ( t ) and a m ( t ) in the i-th step, respectively; To estimate α l ( i ) and β l ( i ), the number of sampling points in the i-th step is set to N and N. 2 L , and expressed in a matrix, the following formula If the expression of the above formula is simplified, it can be expressed as Calculate the coefficient of the above formula by linear least squares estimation Accordingly, a first envelope signal corresponding to a first mode of (1) can be obtained of the formula

對應此一包絡線訊號與傳統解調分析法具有分析運算簡易之優點，而此包絡線訊號僅為其一之方式而以。請參閱第一圖所示為顯示機械系統之敲擊，經上述振動模態分析後，在不同模態之振動頻譜。而將(7)式之解代入(6)式，則可還原振動訊號 Corresponding to this envelope signal and the traditional demodulation analysis method has the advantage of simple analysis and calculation, and the envelope signal is only one of the ways. Please refer to the first figure for the vibration spectrum of different mechanical modes after the mechanical vibration of the mechanical system. And if the solution of (7) is substituted into (6), the vibration signal can be restored.

將第(9)式之還原訊號相較於(6)式之振動訊號具有雜訊去除能力，請再參閱第二圖所示，在最左側為低頻雜訊，比較(a)與(b)可發現還原訊號振動頻譜之低頻雜訊明 顯減少，可獲得印證。而第三圖(a)為原始振動訊號，(b)~(e)則分別為第1~4模態之包絡線訊號，可明顯呈現對(a)之包絡線分析結果，(f)則是將(b)~(e)4個模態合成後還原之振動訊號，亦明顯呈現與(a)原始振動之高度相似。此外，所得之包絡線頻譜具較佳敲擊特徵頻率之凸顯能力，比較第四圖與第五圖可獲得印證。The reduction signal of the equation (9) has the noise removal capability compared to the vibration signal of the equation (6). Please refer to the second figure, the low frequency noise on the far left, compare (a) and (b) Low frequency noise can be found in the vibration spectrum of the restored signal Significantly reduced, can be confirmed. The third figure (a) is the original vibration signal, and (b)~(e) are the envelope signals of the first to fourth modes, respectively, which can clearly show the envelope analysis result of (a), and (f) It is a vibration signal that is reduced after the four modes of (b)~(e) are synthesized, and is also apparently similar to the height of (a) the original vibration. In addition, the resulting envelope spectrum has a better ability to highlight the characteristic frequency, and the fourth and fifth figures can be verified.

在系統振動信號的頻譜中，其振動信號利用缺乏低頻率機械噪聲，以敲擊變化在包絡線訊號上為損壞軸承會是瑕疵衝擊和一個高指數衰減的頻率，相反，包絡線訊號的指數阻止的頻率為正常軸承會是降低，相對應地，根據包絡線訊號的指數衰減能診斷分析軸承損壞。一項研究以指數衰減分析機械系統振動的方法是如下：假設在連續兩敲擊間，在方程式(1)之振動訊號將完全衰減，而且q m (t )a lm (t )的頻率遠低於u m (t )的頻率，則在任一敲擊週期中q m (t )a lm (t )之大小值可近似為常數，因此由方程式(8)所求得其敲擊期間△t 之第1 模態包絡訊號可表示為 In the spectrum of the system vibration signal, the vibration signal utilizes the lack of low-frequency mechanical noise, and the impact of the change on the envelope signal is a shocking frequency and a high-exponential attenuation frequency. On the contrary, the index of the envelope signal is blocked. The frequency of the normal bearing will be reduced, and correspondingly, the bearing damage can be diagnosed and analyzed according to the exponential decay of the envelope signal. A study to analyze the vibration of a mechanical system by exponential decay is as follows: Assume that between two consecutive taps, the vibration signal in equation (1) will be completely attenuated, and the frequency of q m ( t ) a lm ( t ) is much lower. At the frequency of u m ( t ), the magnitude of q m ( t ) a lm ( t ) can be approximated as constant in any tapping cycle, so the tapping period Δ t is obtained by equation (8). The first mode the envelope signal can be expressed as

若任一敲擊期間上式之包絡訊號共有k取樣點，則上式取自然對數轉換後可寫成矩陣式 其簡化式可表示為 對此一系列敲擊訊號之解析，由線性最小平方法(linear least square analysis)求解，則可得 If the envelope signal of the above formula has a k-sampling point during any tapping period, the above formula can be written in a matrix after natural logarithmic transformation. Its simplified form can be expressed as The analysis of a series of tapping signals is solved by linear least square analysis.

因此，第1 模態包絡訊號之指數衰減常數σ l 即可求得，實際應用則以求取20次之平均值來表示系統之指數衰減常數。以上述方法應用於軸承損壞分析結果如表1與表2所示： Thus, the first mode of the signal envelope exponential decay constant σ l can be obtained, followed by the practical applications is the average value of 20 is obtained to represent the exponential decay constant of the system. The results of applying the above method to bearing damage analysis are shown in Tables 1 and 2:

表1為轉速800 rpm時之分析結果，顯示分別在不同模態中其指數衰減常數隨模態數大幅增加，而且損壞軸承所求得之指數衰減常數均遠大於正常軸承之指數衰減常數。Table 1 shows the analysis results at 800 rpm. It shows that the exponential decay constant increases greatly with the modal number in different modes, and the exponential decay constant obtained by the damaged bearing is much larger than the exponential decay constant of the normal bearing.

表2為轉速1600 rpm時之分析結果，亦呈現與表1相同之結果；因此，本發明之診斷分析方法確可有效應用於機械損壞之診 斷分析。Table 2 shows the analysis results at 1600 rpm, and also shows the same results as Table 1. Therefore, the diagnostic analysis method of the present invention can be effectively applied to the diagnosis of mechanical damage. Break analysis.

前述之實施例或圖示並非限定本發明之結構樣態或尺寸，任何所屬技術領域中具有通常知識者之適當變化或修飾，皆應視為不脫離本發明之專利範疇。The above-mentioned embodiments or the illustrations are not intended to limit the structure or the dimensions of the present invention, and any suitable variations or modifications of the present invention will be apparent to those skilled in the art.

綜上所述，本發明實施例確能達到所預期之使用功效，又其所揭露之具體構造，不僅未曾見諸於同類產品中，亦未曾公開於申請前，誠已完全符合專利法之規定與要求，爰依法提出發明專利之申請，懇請惠予審查，並賜准專利，則實感德便。In summary, the embodiments of the present invention can achieve the expected use efficiency, and the specific structure disclosed therein has not been seen in similar products, nor has it been disclosed before the application, and has completely complied with the provisions of the Patent Law. And the request, the application for the invention of a patent in accordance with the law, please forgive the review, and grant the patent, it is really sensible.

第一圖(a)：為分解振動訊號第1模之振動頻譜第一圖(b)：為分解振動訊號第2模之振動頻譜第一圖(c)：為分解振動訊號第3模之振動頻譜第一圖(d)：為分解振動訊號第4模之振動頻譜第二圖(a)：為原始振動訊號頻譜第二圖(b)：為以第一圖(a)~(d)之4個模合成的振動訊號頻譜第三圖(a)：為原始振動訊號第三圖(b)：第1模之包絡線振動訊號第三圖(c)：第2模之包絡線振動訊號第三圖(d)：第3模之包絡線振動訊號第三圖(e)：第4模之包絡線振動訊號第三圖(f)：為以第一圖(a)~(d)之4個模合成之還原振動訊號第四圖(a)：分解振動訊號第1模之解調頻譜第四圖(b)：分解振動訊號第2模之解調頻譜第四圖(c)：分解振動訊號第3模之解調頻譜第四圖(d)：分解振動訊號第4模之解調頻譜第五圖(a)：高頻解調分析法在帶通1kHz~3kHz之解調頻譜第五圖(b)：高頻解調分析法在帶通3kHz~5kHz之解調頻譜第五圖(c)：高頻解調分析法在帶通6kHz~8kHz之解調頻譜 第五圖(d)：高頻解調分析法在帶通8.5kHz~10.5kHz之解調頻譜The first figure (a): the vibration spectrum of the first mode for decomposing the vibration signal, the first figure (b): the vibration spectrum of the second mode for decomposing the vibration signal, the first picture (c): the vibration of the third mode for decomposing the vibration signal The first spectrum (d) of the spectrum is the vibration spectrum of the fourth mode of the vibration signal. The second picture (a): the spectrum of the original vibration signal (Fig. 2): the first picture (a) to (d) The third model of the vibration signal spectrum of the four modes (a): the original vibration signal, the third picture (b): the first mode of the envelope vibration signal, the third picture (c): the second mode of the envelope vibration signal Figure 3 (d): Envelope vibration signal of the third mode (Fig. 3): Envelope vibration signal of the fourth mode (Fig. 3): 4 (a) to (d) The fourth figure of the reduced vibration signal of the modular synthesis (a): the demodulation spectrum of the first mode of the decomposition vibration signal, the fourth picture (b): the demodulation spectrum of the second mode of the decomposition vibration signal, the fourth picture (c): the decomposition vibration The fourth spectrum of the demodulation spectrum of the third mode of the signal (d): the demodulation spectrum of the fourth mode of the decomposed vibration signal. (fi) (a): the demodulation spectrum of the bandpass 1 kHz to 3 kHz. Figure (b): High-frequency demodulation analysis method for band-passing 3 kHz to 5 kHz demodulation spectrum Figure 5 (c): High-frequency demodulation analysis method for band-passing 6 kHz to 8 kHz demodulation spectrum Figure 5 (d): High-frequency demodulation analysis method for demodulation spectrum of bandpass 8.5kHz~10.5kHz

Claims (4)

一種以指數衰減分析機械系統振動的方法，其中：係由機械系統振動訊號而取得各共振模態之包絡線訊號(envelope signal)，將求得之包絡線訊號經取自然對數轉換後，以矩陣式表示而得一系列敲擊訊號之解析，再由線性最小平方法(linear least square analysis)求解則可得包絡線訊號之指數衰減常數者。A method for analyzing mechanical system vibration by exponential decay, wherein: an envelope signal of each resonant mode is obtained by a mechanical system vibration signal, and the obtained envelope signal is converted by natural logarithm transformation to a matrix The expression represents a series of tapping signals, and then the linear least square analysis solves the exponential decay constant of the envelope signal. 如申請專利範圍第1項所述以指數衰減分析機械系統振動的方法，其中係可由機械系統振動訊號之振動頻譜決定共振模態數，且分別設定共振頻率為其模態中之最高尖峰頻率，做為各共振模態之初始共振頻率，應用包絡線訊號分析法而獲得振動訊號於各共振模態之包絡線訊號者。The method for analyzing the vibration of a mechanical system by exponential decay as described in the first claim of the patent scope, wherein the resonance mode number can be determined by the vibration spectrum of the mechanical system vibration signal, and the resonance frequency is respectively set as the highest peak frequency in the mode, As the initial resonance frequency of each resonance mode, the envelope signal signal is used to obtain the envelope signal of the vibration signal in each resonance mode. 如申請專利範圍第2項所述以指數衰減分析機械系統振動的方法，其中該包絡線訊號分析法為運用步階函數(stepwise function)來近似該振動訊號之包絡線訊號(envelope signal)，則振動訊號可映射於以共振頻率所建立之三角函數基底上，再以線性最小平方估測法(linear least squares estimation)求取其映射係數係數對，由所得係數對之平方和開根號可獲得振動訊號於各共振模態之包絡線訊號(envelope signal)。A method for analyzing mechanical system vibration by exponential decay as described in claim 2, wherein the envelope signal analysis method uses a stepwise function to approximate an envelope signal of the vibration signal. The vibration signal can be mapped to the trigonometric function base established by the resonance frequency, and then the linear least squares estimation method can be used to obtain the mapping coefficient coefficient pair, and the squared sum of the obtained coefficient pairs can be obtained. The vibration signal is an envelope signal of each resonant mode. 如申請專利範圍第1項所述以指數衰減分析機械系統振動的方法，其中上述之一種以指數衰減分析機械系統振動的方法係運用於機械損壞之診斷分析者。A method for analyzing mechanical system vibration by exponential decay as described in claim 1 of the patent application, wherein one of the above methods for analyzing mechanical system vibration by exponential decay is applied to a diagnostic analyzer for mechanical damage.
TW97138299A 2008-10-03 2008-10-03 Method for analyzing vibrations of mechanism system by exponential decay frequencies TWI382171B (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7317994B2 (en) * 2005-08-10 2008-01-08 General Electric Company Method and apparatus for signal signature analysis for event detection in rotating machinery
US20080234983A1 (en) * 2007-03-22 2008-09-25 Commtest Instruments Limited Method and system for vibration signal processing

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7317994B2 (en) * 2005-08-10 2008-01-08 General Electric Company Method and apparatus for signal signature analysis for event detection in rotating machinery
US20080234983A1 (en) * 2007-03-22 2008-09-25 Commtest Instruments Limited Method and system for vibration signal processing

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