bearingFaultBands
Generate frequency bands around the characteristic fault frequencies of ball or roller bearings for spectral feature extraction
Syntax
Description
generates characteristic fault frequency bands FB
= bearingFaultBands(FR
,NB
,DB
,DP
,beta
)FB
of a roller or ball
bearing using its physical parameters. FR
is the rotational speed of
the shaft or inner race, NB
is the number of balls or rollers,
DB
is the ball or roller diameter, DP
is the
pitch diameter, and beta
is the contact angle in degrees. The values
in FB
have the same implicit units as FR
.
allows you to specify additional parameters using one or more name-value pair
arguments.FB
= bearingFaultBands(___,Name,Value)
Examples
Frequency Bands Using Bearing Specifications
For this example, consider a bearing with a pitch diameter of 12 cm with eight rolling elements. Each rolling element has a diameter of 2 cm. The outer race remains stationary as the inner race is driven at 25 Hz. The contact angle of the rolling element is 15 degrees.
With the above physical dimensions of the bearing, construct the frequency bands using bearingFaultBands
.
FR = 25; NB = 8; DB = 2; DP = 12; beta = 15; FB = bearingFaultBands(FR,NB,DB,DP,beta)
FB = 4×2
82.6512 85.1512
114.8488 117.3488
71.8062 74.3062
9.2377 11.7377
FB
is returned as a 4x2 array with default frequency band width of 10 percent of FR
which is 2.5 Hz. The first column in FB
contains the values of , while the second column contains all the values of for each characteristic defect frequency.
Frequency Bands for Roller Bearing
For this example, consider a micro roller bearing with 11 rollers where each roller is 7.5 mm. The pitch diameter is 34 mm and the contact angle is 0 degrees. Assuming a shaft speed of 1800 rpm, construct frequency bands for the roller bearing. Specify 'Domain
' as 'frequency
' to obtain the frequency bands FB
in the same units as FR
.
FR = 1800; NB = 11; DB = 7.5; DP = 34; beta = 0; [FB1,info1] = bearingFaultBands(FR,NB,DB,DP,beta,'Domain','frequency')
FB1 = 4×2
104 ×
0.7626 0.7806
1.1994 1.2174
0.3791 0.3971
0.0611 0.0791
info1 = struct with fields:
Centers: [7.7162e+03 1.2084e+04 3.8815e+03 701.4706]
FaultGroups: [1 2 3 4]
Labels: {'1Fo' '1Fi' '1Fb' '1Fc'}
Now, include the sidebands for the inner race and rolling element defect frequencies using the 'Sidebands
' name-value pair.
[FB2,info2] = bearingFaultBands(FR,NB,DB,DP,beta,'Domain','order','Sidebands',0:1)
FB2 = 8×2
4.2368 4.3368
5.6632 5.7632
6.6632 6.7632
7.6632 7.7632
1.7167 1.8167
2.1064 2.2064
2.4961 2.5961
0.3397 0.4397
info2 = struct with fields:
Centers: [4.2868 5.7132 6.7132 7.7132 1.7667 2.1564 2.5461 0.3897]
FaultGroups: [1 2 2 2 3 3 3 4]
Labels: {'1Fo' '1Fi-1Fr' '1Fi' '1Fi+1Fr' '1Fb-1Fc' '1Fb' '1Fb+1Fc' '1Fc'}
You can use the generated fault bands FB
to extract spectral metrics using the faultBandMetrics
command.
Visualize Frequency Bands Around Characteristic Bearing Frequencies
For this example, consider a damaged bearing with a pitch diameter of 12 cm with eight rolling elements. Each rolling element has a diameter of 2 cm. The outer race remains stationary as the inner race is driven at 25 Hz. The contact angle of the rolling element is 15 degrees.
With the above physical dimensions of the bearing, visualize the fault frequency bands using bearingFaultBands
.
FR = 25; NB = 8; DB = 2; DP = 12; beta = 15; bearingFaultBands(FR,NB,DB,DP,beta)
From the plot, observe the following bearing specific vibration frequencies:
Cage defect frequency,
Fc
at 10.5 Hz.Ball defect frequency,
Fb
at 73 Hz.Outer race defect frequency,
Fo
at 83.9 Hz.Inner race defect frequency,
Fi
at 116.1 Hz.
Frequency Bands and Spectral Metrics of Ball Bearing
For this example, consider a ball bearing with a pitch diameter of 12 cm with 10 rolling elements. Each rolling element has a diameter of 0.5 cm. The outer race remains stationary as the inner race is driven at 25 Hz. The contact angle of the ball is 0 degrees. The data set bearingData.mat
contains power spectral density (PSD) and its respective frequency data for the bearing vibration signal in a table.
First, construct the bearing frequency bands including the first 3 sidebands using the physical characteristics of the ball bearing.
FR = 25;
NB = 10;
DB = 0.5;
DP = 12;
beta = 0;
FB = bearingFaultBands(FR,NB,DB,DP,beta,'Sidebands',1:3)
FB = 14×2
118.5417 121.0417
53.9583 56.4583
78.9583 81.4583
103.9583 106.4583
153.9583 156.4583
178.9583 181.4583
203.9583 206.4583
262.2917 264.7917
274.2708 276.7708
286.2500 288.7500
⋮
FB
is a 14x2 array which includes the primary frequencies and their sidebands.
Load the PSD data. bearingData.mat
contains a table X
where PSD is contained in the first column and the frequency grid is in the second column, as cell arrays respectively.
load('bearingData.mat','X') X
X=1×2 table
Var1 Var2
________________ ________________
{12001x1 double} {12001x1 double}
Compute the spectral metrics using the PSD data in table X
and the frequency bands in FB
.
spectralMetrics = faultBandMetrics(X,FB)
spectralMetrics=1×43 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 TotalBandPower
______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ ______________ ______________ __________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ _______________ _______________ ___________ ______________
121 121 314.43 56.438 56.438 144.95 81.438 81.438 210.57 106.44 106.44 276.2 156.44 156.44 407.45 181.44 181.44 473.07 206.44 206.44 538.7 264.75 264.75 691.77 276.75 276.75 723.27 288.69 288.69 754.61 312.69 312.69 817.61 324.62 324.62 848.94 336.62 336.62 880.44 13.188 13.188 31.418 7113.4
spectralMetrics
is a 1x43 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 14 frequencies in FB
.
Input Arguments
FR
— Rotational speed of the shaft or inner race
positive scalar
Rotational speed of the shaft or inner race, specified as a positive scalar.
FR
is the fundamental frequency around which
bearingFaultBands
generates the fault frequency bands. Specify
FR
either in Hertz or revolutions per minute.
NB
— Number of balls or rollers
positive integer
Number of balls or rollers in the bearing, specified as a positive integer.
DB
— Diameter of the ball or roller
positive scalar
Diameter of the ball or roller, specified as a positive integer.
DP
— Pitch diameter
positive scalar
Pitch diameter of the bearing, specified as a positive scalar.
DP
is the diameter of the circle that the center of the ball or
roller travels during the bearing rotation.
beta
— Contact angle
non-negative scalar
Contact angle in degrees between a plane perpendicular to the ball or roller axis and the line joining the two raceways, specified as a positive scalar.
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'
Units of the fault band frequencies, specified as the comma-separated pair
consisting of 'Domain
' and either 'frequency'
or
'order'
. Select:
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 , where W
is the 'Width
' name-value pair and F
is one of the nominal fault frequencies.
Output Arguments
FB
— Fault frequency bands
array
Fault frequency bands, returned as an N-by-2 array, where
N is the number of fault frequencies. FB
is
returned in the same units as FR
, in either hertz or orders
depending on the value of 'Domain
'. Use the generated fault frequency
bands to extract spectral metrics using faultBandMetrics
. The generated fault bands, , are centered at:
Outer race defect frequency,
Fo
and its harmonicsInner race defect frequency,
Fi
, its harmonics and sidebands atFR
Rolling element (ball) defect frequency,
Fb
its harmonics and sidebands atFc
Cage (train) defect frequency,
Fc
and its harmonics
The value W
is the width of the frequency bands, which you can
specify using the 'Width
' name-value pair. For more information on
bearing frequencies, see Algorithms.
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 frequenciesLabels
— Labels describing each frequencyFaultGroups
— Fault group numbers identifying related fault frequencies
Algorithms
bearingFaultBands
computes the different characteristic bearing
frequencies as follows:
Outer race defect frequency,
Inner race defect frequency,
Rolling element (ball) defect frequency,
Cage (train) defect frequency,
References
[1] Chandravanshi, M & Poddar, Surojit. "Ball Bearing Fault Detection Using Vibration Parameters." International Journal of Engineering Research & Technology. 2. 2013.
[2] Singh, Sukhjeet & Kumar, Amit & Kumar, Navin. "Motor Current Signature Analysis for Bearing Fault Detection in Mechanical Systems." Procedia Materials Science. 6. 171–177. 10.1016/j.mspro.2014.07.021. 2014.
[3] Roque, Antonio & Silva, Tiago & Calado, João & Dias, J. "An approach to fault diagnosis of rolling bearings." WSEAS Transactions on Systems and Control. 4. 2009.
Version History
Introduced in R2019b
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