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# gearMeshFaultBands

Construct frequency bands around the characteristic fault frequencies of meshing gears for spectral feature extraction

## Description

example

FB = gearMeshFaultBands(FR,Ni,No) generates characteristic fault frequency bands FB of gear mesh using the rotational speed of the input gear FR and the number of teeth on the input Ni and output gear No respectively. The values in FB have the same implicit units as FR

example

FB = gearMeshFaultBands(___,Name,Value) allows you to specify additional parameters using one or more name-value pair arguments.

example

[FB,info] = gearMeshFaultBands(___) also returns the structure info containing information about the generated fault frequency bands FB.

example

gearMeshFaultBands(___) with no output arguments plots a bar chart of the generated fault frequency bands FB.

## Examples

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For this example, consider a simple gear set with an 8-toothed pinion on the input shaft meshing with a 42-toothed spur gear on the output shaft. Assume that the input shaft is spinning at 20 rpm. Construct the gear mesh frequency bands using the physical characteristics of the gear set.

Ni = 8;
No = 42;
FR = 20;
[FB,info] = gearMeshFaultBands(FR,Ni,No)
FB = 5×2

19.0000   21.0000
2.8095    4.8095
79.0000   81.0000
159.0000  161.0000
159.0000  161.0000

info = struct with fields:
Centers: [20 3.8095 80 160 160]
Labels: ["1Fi"    "1Fo"    "1Fa"    "1Fm"    "1Fm"]
FaultGroups: [1 2 3 4 5]

FB is a 5x2 array which includes the primary frequencies 1Fi, 1Fo, 1Fa and 1Fm respectively. The structure info contains the center frequencies and labels of each frequency range in FB.

For this example, consider a simple gear set with an 8-toothed pinion on the input shaft meshing with a 42-toothed spur gear on the output shaft. Assume that the input shaft is driven at 20 Hz. The dataset motorSignal.mat contains vibration data for the gear mesh sampled at 1500 Hz.

First, construct the gear mesh frequency bands using the physical characteristics of the gear set. Construct the frequency bands with the first 3 sidebands and specify the 'Domain' as 'order'.

Ni = 8;
No = 42;
FR = 20;
FB = gearMeshFaultBands(FR,Ni,No,'Sidebands',1:3,'Domain','order')
FB = 15×2

0.9500    1.0500
0.1405    0.2405
3.9500    4.0500
4.9500    5.0500
5.9500    6.0500
6.9500    7.0500
8.9500    9.0500
9.9500   10.0500
10.9500   11.0500
7.3786    7.4786
⋮

FB is a 15x2 array which includes the primary frequencies and their sidebands.

Load the vibration data and compute PSD and frequency grid using pspectrum. Use a frequency resolution of 0.5.

fs = 1500;
[psd,freqGrid] = pspectrum(C,fs,'FrequencyResolution',0.5);

Now, use the frequency bands and PSD data to compute the spectral metrics.

spectralMetrics = faultBandMetrics(psd,freqGrid,FB)
spectralMetrics=1×46 table
PeakAmplitude1    PeakFrequency1    BandPower1    PeakAmplitude2    PeakFrequency2    BandPower2    PeakAmplitude3    PeakFrequency3    BandPower3    PeakAmplitude4    PeakFrequency4    BandPower4    PeakAmplitude5    PeakFrequency5    BandPower5    PeakAmplitude6    PeakFrequency6    BandPower6    PeakAmplitude7    PeakFrequency7    BandPower7    PeakAmplitude8    PeakFrequency8    BandPower8    PeakAmplitude9    PeakFrequency9    BandPower9    PeakAmplitude10    PeakFrequency10    BandPower10    PeakAmplitude11    PeakFrequency11    BandPower11    PeakAmplitude12    PeakFrequency12    BandPower12    PeakAmplitude13    PeakFrequency13    BandPower13    PeakAmplitude14    PeakFrequency14    BandPower14    PeakAmplitude15    PeakFrequency15    BandPower15    TotalBandPower
______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    ______________    ______________    __________    _______________    _______________    ___________    _______________    _______________    ___________    _______________    _______________    ___________    _______________    _______________    ___________    _______________    _______________    ___________    _______________    _______________    ___________    ______________

0.82564              1             0.1542         0.057165           0.1875         0.011175        0.29169              4            0.055249        0.011486             5           0.0021583        0.070117             6            0.013877         1.0514              7            0.21675        0.0077621             9            0.001577        0.004752             10          0.0010282        0.012155             11          0.0025085         7.7318             7.4375           1.4057           4.2222              7.625           0.79678          0.92456            7.8125           0.1924          0.030489            8.1875          0.0060835        0.069138             8.375          0.012642         0.068649            8.5625          0.012578          2.8848

spectralMetrics is a 1x46 table with peak amplitude, peak frequency and band power calculated for each frequency range in FB. The last column in spectralMetrics is the total band power, computed across all 15 frequencies in FB.

For this example, consider a simple pinion and gear set with an input shaft speed of 1800 rpm. Considering that the pinion on the input shaft has 6 teeth and the gear on the output shaft has 8 teeth, visualize the frequency bands for the gear mesh.

FR = 1800;
Ni = 6;
No = 8;
gearMeshFaultBands(FR,Ni,No)

From the plot, observe the following:

• Output shaft defect frequency, 1Fo at 1350 Hz

• Input shaft defect frequency, 1Fi at 1800 Hz

• Assembly phase defect frequency, 1Fa at 5400 Hz

• Gear mesh defect frequency, 1Fm at 10800 Hz

## Input Arguments

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Rotational speed of the input gear, specified as a positive scalar. FR is the fundamental frequency around which gearMeshFaultBands generates the fault frequency bands. Specify FR either in Hertz or revolutions per minute.

Number of teeth on the input gear, specified as a positive integer.

Number of teeth on the output gear, specified as a positive integer.

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: ...,'Harmonics',[1,3,5]

Harmonics of the fundamental frequency to be included, specified as the comma-separated pair consisting of 'Harmonics' and a vector of positive integers. The default value is 1. Specify 'Harmonics' when you want to construct the frequency bands with more harmonics of the fundamental frequency.

Sidebands around the fundamental frequency and its harmonics to be included, specified as the comma-separated pair consisting of 'Sidebands' and a vector of nonnegative integers. The default value is 0. Specify 'Sidebands' when you want to construct the frequency bands with sidebands around the fundamental frequency and its harmonics.

Width of the frequency bands centered at the nominal fault frequencies, specified as the comma-separated pair consisting of 'Width' and a positive scalar. The default value is 10 percent of the fundamental frequency. Avoid specifying 'Width' with a large value so that the fault bands do not overlap.

Units of the fault band frequencies, specified as the comma-separated pair consisting of 'Domain' and either 'frequency' or 'order'. Select:

• 'frequency' if you want FB to be returned in the same units as FR.

• 'order' if you want FB to be returned as number of rotations relative to FR.

## Output Arguments

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Fault frequency bands, returned as an Nx2 array, where N is the number of fault frequencies. FB is returned in the same units as FR, in either Hertz or orders. Use the generated fault frequency bands to extract spectral metrics using faultBandMetrics. The generated fault bands, , are centered at the characteristic defect frequencies and their harmonics and sidebands for:

• Input shaft defect frequency, Fi

• Output shaft defect frequency, Fo

• Gear mesh defect frequency, Fm

• Assembly phase pass defect frequency, Fa

When you specify the sidebands, gearMeshFaultBands computes the sidebands with respect to the input and output shaft defect frequencies:

• Fault frequency bands for input gear defects with its harmonics and the first sideband at Fi

• Fault frequency bands for output gear defects with its harmonics and the first sideband at Fo

gearMeshFaultBands truncates negative fault frequency bands automatically and generates a warning message.

The value W is the width of the frequency bands, which you can specify using the 'Width' name-value pair.

Information about the fault frequency bands in FB, returned as a structure with the following fields:

• Centers — Center fault frequencies

• Labels — Labels describing each frequency

• FaultGroups — Fault group numbers equal to the number of frequencies

## Algorithms

gearMeshFaultBands computes the different characteristic fault frequencies as follows:

• Input shaft defect frequency, ${F}_{i}=FR$

• Output shaft defect frequency, ${F}_{o}=\frac{Ni}{No}FR$

• Gear mesh defect frequency, ${F}_{m}=NiFR=No{F}_{o}$

• Assembly phase pass defect frequency,${F}_{a}=\frac{{F}_{m}}{\text{gcd}\left(Ni,No\right)}$

## References

[1] Lang, George Fox. “S&V geometry 101.” Sound and Vibration 33 (1999): 16-26.