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To detect some types of mechanical failures, vibration monitoring is used, using vibration sensors, which are mounted in certain places of interest of the machines.

The signal from a vibration sensor, in this case an accelerometer, is the sum of a series of simple sinusoids of different frequencies, amplitudes and phases, which, applying the Fast Fourier Transform, gives us information about the frequencies locations and their intensity.

Therefore, FFT allows data captured in the time domain to be displayed in the frequency domain.

The phase difference between two signals is measured in angular units. It only works if two signals are compared at the same time. To do this, it is necessary to mount another sensor, usually called a keyphasor, at a detectable radial point on a rotating axis. This serves as a reference to the zero point of the phase. Keyphasor is a trademark of Bently Nevada, but it has become a popularly used term.

To diagnose some types of faults using the information obtained from the FFT algorithm, rules are established to suggest a particular type of fault, such as imbalance, alignment, oil swirl, loose parts, etc., establishing location patterns and amplitude of fault frequencies. , along with their respective phase difference, although the latter is not taken into account in this example.

The Fourier transform will work very well when the frequency spectrum is stationary, in cases where the vibration signals vary in spectrum with time, that is, they are not stationary or dynamic, it may be useful to calculate more than one spectrum at the same time. time. Useful but not a replacement.

To do this, a joint synchronization technique called Gabor-Wigner-Wavelet can be used, and this is the focus of this research.

The Wavelet Transform provides information on what frequencies and signal amplitudes are present, just like FFT, but also indicates when these frequencies have occurred. It uses a series of functions called wavelets, each with a different scale. The word wavelet means small wave, and this is exactly what a wavelet is.

There are two types of Wavelet transform called continuous and discrete.

The output of a continuous wave transform results in a scalogram, this is a graphical representation in the plane. On the y-axis the frequency, on the x-axis represents the elapsed time of the signal measurement and the color gives us information about its amplitude.

The output of a discrete wavelet transform results in a matrix of with the different frequency coefficients, which can be represented graphically as shown below.

Next we will carry out an application example with a vibration signal whose fundamental frequency or operating speed varies with time during the sampling of vibration sensor, we will analyze how this variation affects the FFT algorithm and how in these cases the discrete wavelet transform can help.

To do this, we will use measured values from the publication “Bearing Vibration Data Collected Under Time Variable Rotational Speed Conditions” (Huang and Baddour, 2018)

We provide a short extract from of the experimental setup used in the referenced publication (Huang and Baddour, 2018); for more information, see the bibliography cited below.

Experimental set-up.

“Experiments are performed on a SpectraQuest machinery fault simulator (MFS-PK5M). The experimental set-up is shown in Fig. 1. The shaft is driven by a motor and the rotational speed is controlled by an AC drive. Two ER16K ball bearings are installed to support the shaft, the left one is a healthy bearing and the right one is the experimental bearing, which is replaced by bearings of different health conditions. An accelerometer (ICP accelerometer, Model 623C01) is placed on the housing of the experimental bearing to collect the vibration data. In addition, an incremental encoder (EPC model 775) is installed to measure the shaft rotational speed.” (Huang and Baddour, 2018)

(Huang and Baddour, 2018)

Dataset

We will compare signals of a healthy bearing and a inner fault bearing.

The following files were downloaded from the https://data.mendeley.com/datasets/v43hmbwxpm/1 site:

“Dataset H-A-1: the vibration data are collected from a healthy bearing and the operating rotational speed is increasing from 14.1 Hz to 23.8 Hz.” (Huang and Baddour, 2018)

“Dataset I-A-1: the vibration data are collected from a faulty bearing with an inner race defect and the operating rotational speed is increasing from 12.5 Hz to 27.8 Hz.” (Huang and Baddour, 2018)

“‘Channel_1’ is vibration data measured by the accelerometer and ‘Channel_2’ is the rotational speed data measured by the encoder.” (Huang and Baddour, 2018)

The files in the dataset are in mathlab file format (.mat), so we use the following chunk of code within Python from Scipy.io library to read the file in dictionary form and retrieve the signal values within the ‘Channel_1’ key:

import scipy.io as sio

file = sio.loadmat(‘pah to .mat file’)

data = test[‘Channel_1’]

Parameters of bearings

Parameter of bearing
(Huang and Baddour, 2018)

Speed increase from 14 to 27 Hz approximately.

Fast Fourier Transform (FFT)

For both signals (healthy and inner race failure), FFT algorithms were applied, using Python library: “numpy.fft”, as it looks quite noisy, making it difficult to interpret. Despite this, for each of the cases, information is provided on the theoretical location of the fault frequencies, with the extreme values of speed variation.

Healthy bearing

Measured Fast Fourier Transform for healthy bearing

Theoretical FFT for healthy bearing

Frequencies references:

  • X1: 14 and 27 Hz (first harmonic, fundamental, rotation speed)
  • X2: 28 and 54 Hz (second harmonic)
  • X3: 42 and 81 Hz (third harmonic) The relationship between the peaks of the fundamental frequency and the harmonic peaks is up to imbalance and looseness in the configuration, probably under tolerance.

Inner race fault bearing

Measured Fast Fourier Transform for inner race fault bearing

Theoretical FFT for inner race fault bearing

Frequencies references:

  • X1: 14 and 27 Hz (first harmonic, fundamental, rotation speed)

  • X2: 28 and 54 Hz (second harmonic)

  • X3: 42 and 81 Hz (third harmonic) The relationship between the peaks of the fundamental frequency and the harmonic peaks is up to imbalance and looseness in the configuration, probably under tolerance.

  • First harmonic BFPI = 76 and 146 Hz

  • 62 and 119 Hz Left band side of BFPI: difference frequency (76-14 and 146-27 Hz) between BPFI and motor speed.

  • 90 and 173 Hz Right band side of BFPI: difference frequency (76 + 14 and 146+27 Hz) between BPFI and motor speed.

  • Second harmonic BFPI second harmonic= 152 and 292 Hz

  • 138 and 265 Hz Left band side of BFPI: difference frequency (2x62*14 and 2x146-27 Hz) between second harmonic of BPFI and motor speed.

  • 166 and 319 Hz Right band side of BFPI: difference frequency (2x62+14 and 2x146-27 Hz Hz) between second harmonic of BPFI and motor speed.

Enveloping

It is a very useful technique, which consists of obtaining the envelope of the peaks of the impact signal. As shown below, for the case of the inner race failure, the peaks vary in a sinusoidal pattern, compatible with this type of failure. They were made using the Numpy Python library.

Discrete Wavelet Transform

The signal is broken down into different levels, each level has a high and low pass filter. The output of the high pass filter is the input of the filter of the next level, the output of the low pass filter becomes the coefficients of the current level.

Source of image : Wikipedia

Source of image : Wikipedia

A discrete wavelet transform algorithm was performed using Python’s pywt.wavedec library, the wavelet type ‘rbi 6.8’ and the calculated level was 16.

Below is a plot with the results of the coefficients:

Coefficients cD2 to cD10 shows how the amplitude of the frequencies varies with respect to time.

The coefficients cD2 to cD7 mark a clear difference between a healthy bearing and a bearing with an inner race fault.

Conclusions:

It is possible to apply a wavelet transform algorithm for the vibration signals, which can help to interpret some kind of fault. It can also facilitate the application of some machine learning algorithm to classify the type of failure, such as SVM or some kind of neural network. However, it should be considered that the identification of patterns, the resolution of scales and the acceptance criteria depend on the history, that is, on the initial analysis of the signals and their evolution over time.

Acknowledgements

We thank to Natalie Baddour and Huan Huang for the work carried out in their research and for making the data obtained available. To Mendeley Data for hosting information.

Bibliography:

Huan Huang , Natalie Baddour (2018). Bearing vibration data collected under time-varying rotational speed conditions,Data in Brief,Volume 21,2018,Pages 1745-1749,ISSN 2352-3409,https://doi.org/10.1016/j.dib.2018.11.019. (http://www.sciencedirect.com/science/article/pii/S2352340918314124) Abstract: Vibration signal analysis is an important means for bearing fault detection/diagnosis and bearings often operate under time-varying rotational speed conditions. This data article contains vibration datasets collected from bearings with different health conditions under different time-varying speed conditions. The health conditions of the bearing include healthy, faulty with an inner race defect, and faulty with an outer race defect. The operating rotational speed conditions for the dataset include increasing speed, decreasing speed, increasing then decreasing speed, and decreasing then increasing speed. Mendeley Data, http://dx.doi.org/10.17632/v43hmbwxpm.1.

Huang, Huan; Baddour, Natalie (2018), “Bearing Vibration Data under Time-varying Rotational Speed Conditions”, Mendeley Data, V1, doi: 10.17632/v43hmbwxpm.1