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tsaregular

Regular signal of a time-synchronous averaged signal

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Syntax

Y = tsaregular(X,fs,rpm,orderList)
Y = tsaregular(X,t,rpm,orderList)
Y = tsaregular(XT,rpm,orderList)
[Y S] = tsaregular (___)
___= tsaregular(___,Name,Value)
tsaregular(___)

Description

example

Y= tsaregular(X,fs,rpm,orderList)computes the regular signalYof the time-synchronous averaged (TSA) signal vectorXusing sampling ratefs, the rotational speedrpm, and the orders to be retainedorderList.Yis computed by retaining the primary frequency, the components inorderList, and their respective harmonics fromX. You can useYto further extract condition indicators of rotating machinery for predictive maintenance. For example, extracting theFM0indicator fromYis useful in identifying major changes such as gear tooth breakage or heavy wear in a gear box.

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Y= tsaregular(X,t,rpm,orderList)computes the regular signalYof the TSA signal vectorXwith corresponding time values fromt.

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Y= tsaregular(XT,rpm,orderList)computes the regular signalYof the TSA signal stored in the timetableXT.XTmust contain a single numeric column variable.

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[Y,S) = tsaregular (___)returns the amplitude spectrumSof the regular signalY.Sis the amplitude spectrum computed using the normalized fast Fourier transform (FFT) ofY.

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___= tsaregular(___,Name,Value)allows you to specify additional parameters using one or more name-value pair arguments. You can use this syntax with any of the previous input and output arguments.

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tsaregular(___)with no output arguments plots the time-domain and frequency-domain plots of the raw and regular TSA signals.

Examples

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Open Live Script

Consider a drivetrain with six gears driven by a motor that is fitted with a vibration sensor, as depicted in the figure below. Gear 1 on the motor shaft meshes with gear 2 with a gear ratio of 17:1. The final gear ratio, that is, the ratio between gears 1 and 2 and gears 3 and 4, is 51:1. Gear 5, also on the motor shaft, meshes with gear 6 with a gear ratio of 10:1. The motor is spinning at 180 RPM, and the sampling rate of the vibration sensor is 50 KHz. To retain the signal containing the meshing components of the gears 1 and 2, gears 3 and 4 and, the shaft rotation, specify their gear ratios of 17 and 51 inorderList. The signal components corresponding to the shaft rotation (order = 1) is always implicitly included in the computation.

rpm = 180; fs = 50e3; t = (0:1/fs:(1/3)-1/fs)';% sample timesorderList = [17 51]; f = rpm/60*[1 orderList 10];

In practice, you would use measured data such as vibration signals obtained from an accelerometer. For this example, generate TSA signalX, which is the simulated data from the vibration sensor mounted on the motor.

X = sin(2*pi*f(1)*t) + sin(2*pi*2*f(1)*t) +...%电机轴旋转和谐波3*sin(2*pi*f(2)*t) + 3*sin(2*pi*2*f(2)*t) +...% gear mesh vibration and harmonic for gears 1 and 24*sin(2*pi*f(3)*t) + 4*sin(2*pi*2*f(3)*t) +...% gear mesh vibration and harmonic for gears 3 and 42*sin(2*pi*10*f(1)*t);% gear mesh vibration for gears 5 and 6

Compute the regular signal of the TSA signal using the sample time, rpm, and the mesh orders to be retained.

Y = tsaregular(X,t,rpm,orderList);

The outputYis a vector containing everything except the gear mesh signal and harmonics for gears 5 and 6.

Visualize the regular signal, the raw TSA signal, and their amplitude spectrum on a plot.

tsaregular(X,fs,rpm,orderList)

Figure contains 2 axes. Axes 1 with title Regular Signal contains 2 objects of type line. These objects represent Raw Signal, Regular Signal. Axes 2 with title Order Amplitude Spectrum contains 2 objects of type stem. These objects represent Raw Signal, Regular Signal.

From the amplitude spectrum plot, observe the following components:

  • The retained component at the 17th order and its harmonic at the 34th order

  • The second retained component at the 51st order and its harmonic at the 102nd order

  • The filtered mesh components for gears 5 and 6 at the 10th order

  • The retained shaft component at the 1st and 2nd orders

  • The amplitudes on the spectrum plot match the amplitudes of individual signals

Open Live Script

In this example,sineWavePhaseMod.matcontains the data of a phase modulated sine wave.XTis a timetable with the sine wave data andrpmused is 60 RPM. The sine wave has a frequency of 32 Hz and to recover the unmodulated sine wave, use 32 as theorderList.

Load the data and the required variables.

load('sineWavePhaseMod.mat','XT','rpm','orders') head(XT,4)
ans=4×1 timetableTime Data ______________ _______ 0 sec 0 0.00097656 sec 0.2011 0.0019531 sec 0.39399 0.0029297 sec 0.57078

Note that the time values inXTare strictly increasing, equidistant, and finite.

Compute the regular signal and its amplitude spectrum. Set the value of'Domain'to'frequency'since the orders are in Hz.

[Y S] = tsaregular (XT,rpm,orders,'Domain','frequency')
Y=1024×1 timetableTime Data ______________ __________ 0 sec -2.552e-15 0.00097656 sec 0.14928 0.0019531 sec 0.29283 0.0029297 sec 0.42512 0.0039062 sec 0.54108 0.0048828 sec 0.63624 0.0058594 sec 0.70695 0.0068359 sec 0.75049 0.0078125 sec 0.7652 0.0087891 sec 0.75049 0.0097656 sec 0.70695 0.010742 sec 0.63624 0.011719 sec 0.54108 0.012695 sec 0.42512 0.013672 sec 0.29283 0.014648 sec 0.14928 ⋮
S =1024×1 complex0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i ⋮

The outputYis a timetable that contains the regular signal, that is, the unmodulated sine wave, whileSis a vector that contains the amplitude spectrum of the regular signalY.

Open Live Script

In this example,sineWaveAmpMod.matcontains the data of an amplitude modulated sine wave.Xis a vector with the amplitude modulated sine wave data obtained at a shaft speed of 60 RPM. The unmodulated sine wave has a frequency of 32 Hz and amplitude of 1.0 units.

Load the data, and plot the regular signal of the amplitude modulated TSA signalX. To retain the unmodulated signal, specify the frequency of 32 Hz inorderList. Set the value of'Domain'to'frequency'.

load('sineWaveAmpMod.mat','X','t','rpm','orderList') tsaregular(X,t,rpm,orderList,'Domain','frequency');

Figure contains 2 axes. Axes 1 with title Regular Signal contains 2 objects of type line. These objects represent Raw Signal, Regular Signal. Axes 2 with title Amplitude Spectrum contains 2 objects of type stem. These objects represent Raw Signal, Regular Signal.

From the plot, observe the waveform and amplitude spectrum of the regular and raw signals, respectively. Observe that the regular signal contains the unmodulated sine wave with an amplitude of 1.0 units and frequency of 32 Hz.

Input Arguments

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Time-synchronous averaged (TSA) signal, specified as a vector. The time-synchronous averaged signal is computed from a long and relatively periodic raw signal through synchronization, resampling, and averaging. For more information on TSA signals, seetsa.

Time-synchronous平均是一种方便的方法of background noise reduction in a spectrum of complex signals. It is effective in concentrating useful information that can be extracted from a time-domain signal for predictive maintenance. The synchronization typically requires a tachometer pulse signal in addition to the raw sensor data. The TSA signal depicts measurements at equally spaced angular positions over a single revolution of a shaft of interest.

Time synchronous averaged (TSA) signal, specified as a timetable.XTmust contain a single numeric column variable corresponding to the TSA signal. Time values inXTmust be strictly increasing, equidistant, and finite.

Sampling frequency of the TSA signal in Hertz, specified as a positive scalar.

Sample times of the TSA signal, specified as a positive scalar or a vector of positive values.

Iftis:

  • A positive scalar, it contains the time interval or duration between samples. You must specifytas adurationvariable.

  • A vector of positive values, it contains sample times corresponding to elements inX. The time values must be strictly increasing, equidistant, and finite. You can specifytas adoubleordurationvariable.

Rotational speed of the shaft, specified as a positive scalar.tsaregularuses a bandwidth equal to the shaft speed and the value of 'NumSidebands' around the frequencies of interest to computeYfrom the TSA signal. Specifyrpmin revolutions per minute. The signal components corresponding to this frequency, that is,order = 1are always retained.

Orders to be retained from the TSA signal, specified as a vector of positive integers. Select the orders and harmonics to be retained from the TSA signal by observing them on the amplitude spectrum plot. For instance, specifyorderListas the known mesh orders in a gear train to retain the desired components and their harmonics. For more information, seeFind and Visualize the Regular Signal of a Compound TSA Signal. Specify the units oforderListby selecting the appropriate value for 'Domain'.

Name-Value Pair Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

Example:...,'NumSidebands',2

Number of shaft and gear meshing frequency harmonics to be filtered, specified as the comma-separated pair consisting of 'NumHarmonics' and a positive integer. Modify 'NumHarmonics' if your TSA signal contains more than two known harmonics of components to be filtered.

Number of sidebands to be retained from theorderListfrequencies and their harmonics, specified as the comma-separated pair consisting of 'NumSidebands”和nonnegative integer. The width of sidebands is determined using2*(rpm/60)*(NumSidebands+0.5). Modify 'NumSidebands' based on the number of sidebands to be retained fromXas observed in the amplitude spectrum plot.

Number of shaft rotations in the TSA signal, specified as the comma-separated pair consisting of 'NumRotations' and a positive integer. Modify 'NumRotations' if your inputXorXTcontains data for more than one rotation of the driver gear shaft. The function uses 'NumRotations' to determine the number of rotations to be shown on the x-axis of the plot. The filtering results inYare not affected by this value.

Units of theorderList值,指定为the comma-separated pair consisting of 'Domain' and one of the following:

  • 'frequency', if the orders inorderListare specified as frequencies in units of Hertz.

  • 'order', if the orders inorderListare specified as number of rotations relative to the value ofrpm. For example, if the rotational speed of the driven gear is defined as a factor of the driver gear rpm, specify 'Domain' as'order'. Also, choose'order'if you are comparing data obtained from machines operating at different speeds.

Output Arguments

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Regular signal of the TSA signal, returned as:

  • A vector, when the TSA signal is specified as a vectorX.

  • A timetable, when the TSA signal is specified as a timetableXT.

Yis computed by retaining the primary frequency, the components inorderList, the first-order sidebands in 'NumSidebands', and their respective harmonics fromX. You can useYto further extract condition indicators of rotating machinery for predictive maintenance. For example, extracting the FM0 indicator fromYis useful in identifying major changes such as gear tooth breakage or heavy wear in a gear box. For more information on howYis computed, seeAlgorithms.

Amplitude spectrum of the regular signal, returned as a vector.Sis the normalized fast Fourier transform of the signalY.Sis the same length as the input TSA signalX. For more information on howSis computed, seeAlgorithms.

Algorithms

Regular Signal

The regular signal is computed from the TSA signal by retaining the following from the signal spectrum:

  • Shaft frequency and its harmonics

  • Gear meshing frequencies and their harmonics

  • Optionally, the sidebands specified in 'NumSidebands' at the gear meshing frequencies and their harmonics

tsaregularuses a bandwidth equal to the shaft speed times the value of 'NumSidebands', around the frequencies of interest, to computeYfrom the TSA signal. The regular signal is related to the residual signal through the equation Y r e g u l a r = X − Y r e s i d u a l . If the first-order sidebands are retained in the regular signal, then, Y r e g u l a r = X − Y d i f f e r e n c e .

Amplitude Spectrum

The amplitude spectrum of the regular signal is computed as follows,

S = fft ( Y ) length ( Y ) * 2

Here,Yis the regular signal.

References

[1] McFadden, P.D. "Examination of a Technique for the Early Detection of Failure in Gears by Signal Processing of the Time Domain Average of the Meshing Vibration."Aero Propulsion Technical Memorandum 434. Melbourne, Australia: Aeronautical Research Laboratories, Apr. 1986.

[2] Večeř,P, Marcel Kreidl, and R. Šmíd. "Condition Indicators for Gearbox Monitoring Systems."Acta Polytechnica45.6 (2005), pages 35-43.

[3] Zakrajsek, J. J., Townsend, D. P., and Decker, H. J. "An Analysis of Gear Fault Detection Methods as Applied to Pitting Fatigue Failure Data."Technical Memorandum 105950. NASA, Apr. 1993.

[4] Zakrajsek, James J. "An investigation of gear mesh failure prediction techniques." National Aeronautics and Space Administration Cleveland OH Lewis Research Center, 1989. No. NASA-E-5049.

See Also

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