# gearMeshFaultBands

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

## Syntax

## Description

allows you to specify additional parameters using one or more name-value pair
arguments.`FB`

= gearMeshFaultBands(___,Name,Value)

## Examples

### Frequency Bands of Pinion and Gear Mesh

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`

.

### Frequency Bands and Spectral Metrics of Gear Train

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.

```
Ni = 8;
No = 42;
FR = 20;
FB = gearMeshFaultBands(FR,Ni,No,'Sidebands',1:3)
```

`FB = `*15×2*
19.0000 21.0000
2.8095 4.8095
79.0000 81.0000
99.0000 101.0000
119.0000 121.0000
139.0000 141.0000
179.0000 181.0000
199.0000 201.0000
219.0000 221.0000
147.5714 149.5714
⋮

`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.

load('motorSignal.mat','C'); 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
______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ ______________
0.0054125 19 0.0051216 0.55167 4.25 0.41848 0.0022699 81 0.0029792 0.0012756 99.438 0.0019134 0.0023457 119.25 0.0032812 0.0030216 139.75 0.0036398 0.0015424 180.06 0.0021249 0.0023163 200.81 0.0029269 0.013511 221 0.012079 0.0037697 148.06 0.003914 0.0020528 151.56 0.0025637 0.0021721 156.5 0.0022927 0.0020822 162.81 0.0015729 0.0015305 168.25 0.001575 0.0010234 170.44 0.0013135 0.46577

`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`

.

### Visualize Frequency Bands for Pinion and Gear Set

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 HzInput shaft defect frequency,

`1Fi`

at 1800 HzAssembly phase defect frequency,

`1Fa`

at 5400 HzGear mesh defect frequency,

`1Fm`

at 10800 Hz

## Input Arguments

`FR`

— Rotational speed of the input gear

positive scalar

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.

`Ni`

— Number of teeth on the input gear

positive integer

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

`No`

— Number of teeth on the output gear

positive integer

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

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

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

`Harmonics`

— Harmonics of the fundamental frequency to be included

`1`

(default) | vector of positive integers

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`

— Sidebands around the fundamental frequency and its harmonics to be included

`0`

(default) | vector of nonnegative integers

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`

— Width of the frequency bands centered at the nominal fault frequencies

`10`

percent of the fundamental frequency (default) | positive scalar

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.

`Domain`

— Units of the fault band frequencies

`'frequency'`

(default) | `'order'`

`Folding`

— Logical value specifying whether negative nominal fault frequencies have to be folded about the frequency origin

`false`

(default) | `true`

Logical value specifying whether negative nominal fault frequencies have to be folded about the frequency origin, specified as the comma-separated pair consisting of '`Folding`

' and either `true`

or `false`

. If you set '`Folding`

' to `true`

, then `faultBands`

folds the negative nominal fault frequencies about the frequency origin by taking their absolute values such that the folded fault bands always fall in the positive frequency intervals. The folded fault bands are computed as $$\left[\text{max}\left(0,\text{}\left|F\right|-\frac{W}{2}\right),\text{}\left|F\right|+\frac{W}{2}\right]$$, where `W`

is the '`Width`

' name-value pair and `F`

is one of the nominal fault frequencies.

## Output Arguments

`FB`

— Fault frequency bands

`Nx2`

array

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, $$\left[F-\frac{W}{2},\text{}F+\frac{W}{2}\right]$$, 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.

`info`

— Information about the fault frequency bands

structure

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.

## Version History

**Introduced in R2019b**

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