faultBands

For this example, generate frequency bands for analyzing the signal components around the first 5 harmonics of the mains supply frequency.

With the fundamental frequency of 60 Hz, the frequency of the alternating current in the mains power supply, use faultBands to generate the first 5 harmonics of the mains supply.

F0 = 60;
N0 = 1:5;
FB = faultBands(F0,N0)

FB = 5×2

   58.5000   61.5000
  118.5000  121.5000
  178.5000  181.5000
  238.5000  241.5000
  298.5000  301.5000

FB is returned as a 5x2 array with default frequency band width of 5% of F0 which is 3 Hz. The first column in FB contains the values of $$F-\frac{W}{2}$$, while the second column contains all the values of $$F+\frac{W}{2}$$ for each harmonic.

For this example, consider an induction motor with broken rotor bars. Under normal operation with load, the rotor speed always lags the speed of the magnetic field allowing the rotor bars to cut magnetic lines of force and produce useful torque. This difference is called slip. Considering a slip value of 0.03 in the system with broken rotors, construct frequency bands for sideband components around the fundamental frequency of 60 Hz.

F0 = 60;
N0 = 1:2;
slip = 0.03;
F1 = 2*slip*F0;
N1 = 1:3;
[FB,info] = faultBands(F0,N0,F1,N1)

FB = 12×2

   47.7000   50.7000
   51.3000   54.3000
   54.9000   57.9000
   62.1000   65.1000
   65.7000   68.7000
   69.3000   72.3000
  107.7000  110.7000
  111.3000  114.3000
  114.9000  117.9000
  122.1000  125.1000
  125.7000  128.7000
  129.3000  132.3000
      ⋮

info = struct with fields:
           Centers: [49.2000 52.8000 56.4000 63.6000 67.2000 70.8000 109.2000 112.8000 116.4000 123.6000 127.2000 130.8000]
    HarmonicGroups: [1 1 1 1 1 1 2 2 2 2 2 2]
            Labels: {'1F0-3F1'  '1F0-2F1'  '1F0-1F1'  '1F0+1F1'  '1F0+2F1'  '1F0+3F1'  '2F0-3F1'  '2F0-2F1'  '2F0-1F1'  '2F0+1F1'  '2F0+2F1'  '2F0+3F1'}

Construct frequency bands for analyzing the signal components around the first three harmonics of the electrical mains supply frequency.

With the fundamental frequency of 60 Hz, the alternating current in the mains power supply, use faultBands to visualize the first 3 harmonics of the mains supply.

F0 = 60;
N0 = 1:3;
faultBands(F0,N0)

From the plot, observe the following:

To better capture the expected variations of the actual system signals around the nominal fault frequencies, set the widths of each band to 10 Hz.

faultBands(F0,N0,'Width',10)

For this example, consider an induction motor with static and dynamic rotor eccentricities. Construct and visualize the frequency bands for the 4 sideband components of an induction motor with 4 pole pairs around the fundamental frequency due to the rotor eccentricities.

F0 = 60;
N0 = 1;
slip = 0.029;
polePairs = 4;
F1 = 2*F0*(1-slip)/polePairs

F1 = 
29.1300

N1 = 0:4;
faultBands(F0,N0,F1,N1)

Warning: Truncated or removed negative fault frequency bands.

To avoid truncating negative fault frequency bands, set 'Folding' to true to fold them onto the positive frequency axis.

faultBands(F0,N0,F1,N1,'Folding',true)

Observe that the sideband frequencies 1F0-3F1 and 1F0-4F1 are now visible on the positive axis.