1. Introduction

2. IMS bearing dataset and signal analysis techniques

2.1. Description of IMS dataset 1

As already mentioned, the signals which will be analyzed come from an open access dataset released in 2014 by the NASA Center for Intelligent Maintenance Systems (IMS) [19]; the focus is on the results of the first of three run-to-failure experimental campaigns carried out at the University of Cincinnati, Ohio, USA, with support from Rexnord Corp., Milwaukee, Wisconsin.

The test rig included four rolling bearings installed on a common shaft, set in rotation at a constant speed of 2000 RPM by an AC motor coupled to the shaft via rub belts (Figure 1). The four double row bearings were of type Rexnord ZA-2115, force lubricated by a circulation system that regulated the flow and the temperature and charged with a 26690 N (6000 lbs) constant radial load applied by a spring mechanism. Eight PCB 353B33High Sensitivity Quartz ICP accelerometers were installed on the bearing housing (two sensors for each bearing, mounted orthogonally along the $x$ and $y$ axes), the sampling frequency was set to 20480 Hz. The dataset consists of individual files that are 1-second vibration signal snapshots recorded at specific intervals, every 5 (for the first 54 acquisitions) or 10 minutes, but sometimes subjected to a series of interruptions which makes the time history not continuous (Figure 2).

The experiment was stopped conventionally when the accumulation of debris on a magnetic plug exceeded a certain level, indicating the possibility of an impending failure. The resulting endurance duration was equal to 49 680 minutes (i.e. 34 days and 12 hours), exceeding bearing designed life time, which was more than 100 million revolutions.

The most relevant experimental set-up characteristics and findings of IMS dataset 1 are reported in Table 1. It should be stressed that this dataset is particularly valuable because the bearing degradation was left evolve naturally and was not artificially induced, as it may often happen to speed up the experimental test.

Vibrational data collection was conducted with the National Instruments LabVIEW program thanks to a NI DAQ Card-6062E data acquisition and the analysis that will be presented in this paper was developed with the software platform MATLAB 2021b by The MathWorks [20].

Table 2. Rolling bearing mechanical characteristics and working conditions (from [19]).

Table 2. Rolling bearing mechanical characteristics and working conditions (from [19]).

Model	Rexnord ZA-2115
Pitch diameter D	71.5 mm (2.815 inch)
Rolling element diameter d	8.4 mm (0.331 inch)
Number of rolling elements per row n	16
Load contact angle ϕ	15.17°
Static load Q	26690 N (6000 lbs.)
Shaft angular velocity ω	2000 rpm

Considering the rolling bearing mechanical characteristics and working conditions of Table 2, it is possible to compute the value of the characteristic frequencies of the faults they’re typically subjected to during their operating life, i.e., the fault signatures, by using the following formulas:

$$\mathrm{B}\mathrm{P}\mathrm{F}\mathrm{O}=\frac{n{f}_r}{2}\left(1-\frac{d}{D}\mathrm{c}\mathrm{o}\mathrm{s}\varphi \right)$$

(1)

$$\mathrm{B}\mathrm{P}\mathrm{F}\mathrm{I}=\frac{n{f}_r}{2}\left(1+\frac{d}{D}\mathrm{c}\mathrm{o}\mathrm{s}\varphi \right)$$

(2)

$$\mathrm{F}\mathrm{T}\mathrm{F}=\frac{f_r}{2}\left(1-\frac{d}{D}\mathrm{c}\mathrm{o}\mathrm{s}\varphi \right)$$

(3)

$$\mathrm{B}\mathrm{S}\mathrm{F}=\frac{f_{r}D}{2d}\left[1-{\left(\frac{d}{D}\mathrm{c}\mathrm{o}\mathrm{s}\varphi \right)}^2\right]$$

(4)

where:

• $\mathrm{B}\mathrm{P}\mathrm{F}\mathrm{O}\left(BallPassFrequency,OuterRace\right)$ is the frequency representing the fault signature on the outer race,
• $\mathrm{B}\mathrm{P}\mathrm{F}\mathrm{I}\left(BallPassFrequency,InnerRace\right)$ is the frequency representing the fault signature on the inner race,
• $\mathrm{F}\mathrm{T}\mathrm{F}\left(FundamentalTrainFrequency\right)$ is the frequency representing the fault signature on the bearing cage,
• $\mathrm{B}\mathrm{S}\mathrm{F}\left(BallSpinFrequency\right)$ is the frequency representing the fault signature on the rolling element,

see the rolling element bearing of Figure 3.

The nominal rotation frequency of the transmission shaft $f_r$ can be directly obtained from the working conditions:

$$f_r=\frac{\omega }{2\pi }=\frac{2000\mathrm{r}\mathrm{p}\mathrm{m}}{2\pi ·60\mathrm{s}/\mathrm{m}\mathrm{i}\mathrm{n}}=33.3\mathrm{H}\mathrm{z}$$

(5)

where the corresponding characteristic frequencies of the faults are reported in Table 3.

3. Results

3.1. Fault detection

The computation of statistical parameters is of paramount importance to reveal the presence of an incoming fault, accomplishing the first phase of condition monitoring.

If parameter trend is examined along the time duration of the whole registration (made continuous with the exclusion of the interruptions of acquisition occurred in real time), it can be observed that Mean, Variance and Standard Deviation of bearings 1 and 2 (Figure 4(a) and Figure 5(a)) remain almost constant, with a slight increase just at the very end of the experiment, probably due to the propagation of vibrations produced by other damaged bearings and detected by sensors 1 and 3 because of the physical continuity of the testing, in which all the components are installed on a single shaft.

RMS value, Skewness and Kurtosis (Figure 4(b-d) and Figure 5(b-d)), albeit oscillating, don’t exhibit a global monotonicity too, except for in the last measurements for the reason just mentioned.

On the contrary, the presence of faults on the bearings 3 and 4 can be clearly deduced from the RMS value (Figure 6(b) and Figure 7(b)) and even more from the Kurtosis (Figure 6(d) and Figure 7(d)), which starting from a value around 3 typical of a Gaussian distribution, raises over 70 from the 1831^st second (31^st day of test) for the third bearing and from the 1486^th second (28^th day of test) for the fourth one. Consistent information is provided by other parameters such as Clearance Factor (Figure 10(a) and Figure 11(a)) and Impulse Factor (Figure 10(b) and Figure 11(b)), while Mean, Variance and Standard Deviation (Figure 6(a) and Figure 7(a)) remain mostly stable and Skewness (Figure 6(c) and Figure 7(c)) doesn’t show a clear reduction, as expected in case of fault.

Figure 6. First group of statistical parameters applied to the signal from sensor 5 on bearing 3: (a) Mean (red), Variance (green), Standard Deviation (blue); (b) RMS value; (c) Skewness; (d) Kurtosis.

Figure 6. First group of statistical parameters applied to the signal from sensor 5 on bearing 3: (a) Mean (red), Variance (green), Standard Deviation (blue); (b) RMS value; (c) Skewness; (d) Kurtosis.

Figure 7. First group of statistical parameters applied to the signal from sensor 7 on bearing 4: (a) Mean (red), Variance (green), Standard Deviation (blue); (b) RMS value; (c) Skewness; (d) Kurtosis.

Figure 7. First group of statistical parameters applied to the signal from sensor 7 on bearing 4: (a) Mean (red), Variance (green), Standard Deviation (blue); (b) RMS value; (c) Skewness; (d) Kurtosis.

Figure 8. Second group of statistical parameters applied to the signal from sensor 1 on bearing 1: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 8. Second group of statistical parameters applied to the signal from sensor 1 on bearing 1: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 9. Second group of statistical parameters applied to the signal from sensor 3 on bearing 2: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 9. Second group of statistical parameters applied to the signal from sensor 3 on bearing 2: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 10. Second group of statistical parameters applied to the signal from sensor 5 on bearing 3: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 10. Second group of statistical parameters applied to the signal from sensor 5 on bearing 3: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 11. Second group of statistical parameters applied to the signal from sensor 7 on bearing 4: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 11. Second group of statistical parameters applied to the signal from sensor 7 on bearing 4: (a) Peak (red), Crest Factor (blue), Clearance Factor (green); (b) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).

Figure 12, Figure 13, Figure 14 and Figure 15 display the trend of Hjorth’s parameters (omitting Activity, which is equivalent to Variance) and Detectivity; the latter has been computed using the first 5 days files (first 51 seconds of acquisition) to obtain the reference values involved in its formulation (11).

Their behaviour agrees with that of the previous parameters: Mobility (Figure 12(a) and Figure 13(a)) and Complexity (Figure 12(b) and Figure 13(b)) of the bearings 1 and 2 have opposite trends than those which would be associated to a fault, while for bearings 3 and 4 Mobility slightly decreases (Figure 14(a) and Figure 15(a)) and Complexity increases (Figure 14(b) and Figure 15(b)).

However, Detectivity is the parameter that offers the clearest signature of fault with a significant increase of its value (Figure 14(c) and Figure 15(c)), proving its efficacy in the field of predictive maintenance as a combination (and an informative summa) of Hjorth’s parameters. The same temporal occurrence of faults previously deduced via statistical parameters is also observed considering Detectivity, with a quite late fault on bearing 3 and an earlier one on bearing 4.

4. Discussion

5. Conclusions

References

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