tsaresidual

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 obtain the signal containing just the meshing components for gears 5 and 6, filter out the signal components due to the gears 1 and 2 and, 3 and 4 by specifying their gear ratios of 17 and 51 in orderList. 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 times
orderList = [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 signal X, 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) + ...     % motor shaft rotation and harmonic
    3*sin(2*pi*f(2)*t) + 3*sin(2*pi*2*f(2)*t) + ... % gear mesh vibration and harmonic for gears 1 and 2
    4*sin(2*pi*f(3)*t) + 4*sin(2*pi*2*f(3)*t) + ... % gear mesh vibration and harmonic for gears 3 and 4
    2*sin(2*pi*10*f(1)*t);                          % gear mesh vibration for gears 5 and 6

Compute the residual of the TSA signal using the sample time, rpm, and the mesh orders to be filtered out.

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

The output Y is a vector containing the gear mesh signal and harmonics for gears 5 and 6.

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

tsaresidual(X,fs,rpm,orderList)

From the amplitude spectrum plot, observe the following components:

In this example, sineWavePhaseMod.mat contains the data of a phase modulated sine wave. XT is a timetable with the sine wave data and rpm used is 60 RPM. The sine wave has a frequency of 32 Hz, and to filter out the unmodulated sine wave, use 32 as the orderList.

Load the data and the required variables.

load('sineWavePhaseMod.mat','XT','rpm','orders')
head(XT,4)

         Time          Data  
    ______________    _______

    0 sec                   0
    0.00097656 sec     0.2011
    0.0019531 sec     0.39399
    0.0029297 sec     0.57078

Note that the time values in XT are strictly increasing, equidistant, and finite.

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

[Y,S] = tsaresidual(XT,rpm,orders,'Domain','frequency')

Y=1024×1 timetable
         Time           Data   
    ______________    _________

    0 sec             2.552e-15
    0.00097656 sec     0.051822
    0.0019531 sec       0.10116
    0.0029297 sec       0.14566
    0.0039062 sec       0.18317
    0.0048828 sec       0.21188
    0.0058594 sec       0.23039
    0.0068359 sec       0.23776
    0.0078125 sec        0.2336
    0.0087891 sec       0.21803
    0.0097656 sec       0.19174
    0.010742 sec         0.1559
    0.011719 sec        0.11215
    0.012695 sec       0.062503
    0.013672 sec      0.0092782
    0.014648 sec      -0.045032
      ⋮

S = 1024×1 complex

  -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
   0.0000 + 0.0000i
      ⋮

The output Y is a timetable that contains the residual signal, that is, the phase modulation signal, while S is a vector that contains the amplitude spectrum of the residual signal Y.

In this example, sineWaveAmpMod.mat contains the data of an amplitude modulated sine wave. X is 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 residual signal of the amplitude modulated TSA signal X. To obtain the residual signal, filter out the unmodulated sine wave by specifying the frequency of 32 Hz in orderList. Set the value of 'Domain' to 'frequency'.

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

From the plot, observe the waveform and amplitude spectrum of the residual and raw signals, respectively.