Vibration analysis for Bearing outer race condition diagnostics

Vibration Analysis for Bearing Outer Race Condition Diagnostics

J. Shiroishi

Y. Li, S. Liang

S. Danyluk

T. Kurfess

The GWW School of Mechanical Engineering

Georgia Institute of Technology

Atlanta, GA 30332

[e-mail]

Abstract

This paper investigates defect detection methodologies for rolling element bearings through vibration analysis. Specifically, the utility of a new signal processing scheme combining the High Frequency Resonance Technique (HFRT) and Adaptive Line Enhancer (ALE) is investigated. The accelerometer is used to acquire data for this analysis, and experimental results have been obtained for outer race defects. Results show the potential effectiveness of the signal processing technique to determine both the severity and location of a defect.

The HFRT utilizes the fact that much of the energy resulting from a defect impact manifests itself in the higher resonant frequencies of a system. Demodulation of these frequency bands through use of the envelope technique is then employed to gain further insight into the nature of the defect while further increasing the signal to noise ratio. If periodic, the defect frequency is then present in the spectra of the enveloped signal.

The ALE is used to enhance the envelope spectrum by reducing the broadband noise. It provides an enhanced envelope spectrum with clear peaks at the harmonics of a characteristic defect frequency. It is implemented by using a delayed version of the signal and the signal itself to decorrelate the wideband noise. This noise is then rejected by the adaptive filter that is based upon the periodic information in the signal.

Results have been obtained for outer race defects. They show the effectiveness of the methodology to determine both the severity and location of a defect. In two instances, a linear relationship between signal characteristics and defect size is indicated.

Keywords:Bearing Vibration, Machine Diagnostics, Machine Monitoring, Signal Processing

Introduction

Bearings are of paramount importance to almost all forms of rotating machinery, and are among the most common of machine elements. As a consequence of their importance and widespread use, bearing failure is also one of the foremost causes of breakdown in rotating machinery. In fact, it is so important to machine maintenance and automation process that research on the cause and analysis of bearing failure has been actively conducted for four decades (Gustaffson and Tallian, 1962).

Ball and roller bearings have three components that typically experience damage. They are the rolling element, inner race, and outer race. The signature produced varies according to the damaged component and whether or not the impact location is in a loaded zone of the bearing. It has been shown that defect signatures are enhanced by the amount of loading in the area of impact (Monk, 1972). This makes the signature potentially harder to recognize. A defect present on a rotating component produces periodic pulses that depend on the load characteristic of the system, with the largest pulses originating in the peak of a loaded zone. A defect on a stationary race in a loaded zone is intuitively easiest to detect, with a pulse of constant frequency (assuming constant rotational velocity) and higher magnitude.

Most difficulties posed in bearing initial fault detection stem from the presence of a variety of noises and the wide spectrum of a bearing defect signal. Therefore, the success of bearing fault detection methods usually depends on increasing a bearing defect signal-to-noise ratio. Identification and quantification of key signal features dictating the condition of the element is then the main priority.

To date, most work only serves to identify the presence of a defect, or at best differentiate based on qualitative measures such as light, medium, or heavy damage without practical, quantitative grounds for fault identification (Alfredson and Mathew, 1985, Carney, Mann, and Gagliardi, 1994, Daadbin and Wong 1991, Kim, 1987, Li and Ma, 1992, Martin and Hornarvar, 1995, and Martin and Thorpe, 1992). There has been a deficiency in the development of a relationship between various detection methodologies and defect size. A defect becomes a failed bearing when an applicable definition of failure has been satisfied. For example, a defect that has reached a size of 0.0645 mm² (0.01 in.²) is commonly defined to be a failure by industry standards (Lawrentz, 1996). To date, the development of such a diagnostic capability that lends itself to possible prognostics has not been addressed.

The methodology presented here serves to address these issues. First, the signal-to-noise ratio is greatly increased through processing. This allows defects of smaller magnitude to be detected, well before failure occurs. Second, results indicate a direct relationship between signal features and defect size, yielding a diagnostic tool that can be used to effectively quantify the defect.

Signal Processing Methodology

In this work, an adaptive line enhancer (ALE) is used to increase the detectability of a periodic defect signal. It enhances the spectrum of the envelope signal provided to it by the high frequency resonance technique (HFRT). Fig. 1 displays a block diagram of the signal flow for the overall processing scheme. The HFRT takes advantage of the large amplitudes of a defect signal in the range of a high frequency system resonance, and provides a demodulated signal with a high defect signal-to-noise ratio in the absence of low frequency mechanical noise. The ALE is expected to reduce wideband noise of the obtained demodulated signal and, therefore, enhance the envelope spectrum of the defect signal with clear peaks at the harmonics of the characteristic defect frequency.

High Frequency Resonance Technique

A bearing defect signal s(t) can be represented by bursts of exponentially decaying sinusoidal vibration at a system resonant frequency (Braun and Datner, 1979). The high frequency resonance technique (Mcfadden and Smith, 1984) is illustrated in Fig. 1 and Fig. 2 and involves 3 steps. First, bandpass a measured signal (Fig. 2 (a)) around a selected high frequency band with the center at a chosen resonant frequency of system, resulting in Fig. 2 (b). Second, demodulate the bandpassed signal with a non-linear rectifier, resulting in Fig. 2 (c). Third, use a low pass filter to cancel high frequency components and retain the low frequency information associated with bearing defects, resulting in Fig. 2 (d)

In order to cancel the high frequency components and retain the low frequency information associated with a bearing defect, s_d(t) is passed through a low pass filter. A pure bearing defect signal, s(t)has nonzero magnitude only at the harmonics of a characteristic defect frequency. Therefore, the spectrum of s_e(t) will have nonzero values only at the harmonics of the characteristic defect frequency that are less than the bandwidth of a used bandpass filter shown in Fig. 2(d). The nonzero values of an envelope spectrum at the harmonics of a particular characteristic defect frequency indicate the occurrence of a defect, and the location of the defect can be determined by its unique defect frequency.

Adaptive line enhancer

The envelope signal of a damaged bearing obtained by the above method is contaminated by broad band noise making it difficult to detect the early damage of the bearing. A real time envelope signal x(k) can be considered as the sum of narrow band signals S_e(k) spaced at the harmonics of a characteristic defect frequency but corrupted by broad band noise n(k).

x(k) = S_e(k) + n(k) (1)

The adaptive line enhancer (ALE) is used herein to separate the narrow band signals from the broad band noise. ALE was first introduced by Widrow (1975) and its performance studied by (Treichler, 1979). The delayed version of x(K) is used as the reference input of an adaptive filter. The output of the filter is then subtracted from the primary input signal x(k) to form an error sequence e(k). The error sequence is fed back to adjust the filter weights, shown in Fig. 1.

The delay of an input signal causes the decorrelation between the broad band noise components of reference input and primary input while the narrow band signal is still highly correlated. To minimize the error power of the filter, the adaptive filter compensates for the correlated signal so that it can be canceled at the summing junction. Since the filter can not compensate for the decorrelation of the broad band noise components, only the narrow band signal is output from the adaptive filter. In the frequency domain, the filter weights will tend to form a bandpass function about the center frequencies of the narrow band input components. Therefore, the broad band noise components of delayed input are rejected while the narrow band signal information is retained. Here a recursive least mean squares (LMS) algorithm is used for this adaptive filter because of its computational simplicity. The output of the filter is:

(2)

where W_k^T is the weight vector of the filter and input vector X_k is

(3)

Then the error is:

e(k) = x(k) - y(k) (4)

The mean square error (MSE) is the expected value of e(k). The LMS algorithm controls the weight vector of the filter so that the mean square error is minimized. The optimal weight vector W* that minimizes the MSE is

W* = R_-1P (5)

where the input signal autocorrelation vector P is

(6)

and the autocorrelation matrix R is:

(7)

(Widrow, 1975).

In practice, R and P are generally unavailable because they require an expectation operation (E). The following recursive LMS algorithm is a practical method to find a approximate solution of equation . The weights of the filter are updated by:

(8)

where m is adaptive step size. The simulation results show that m needs to satisfy the following condition for asymptotic stability of adaptation: (Clarkson, 1993)

(9)

Therefore, given the input sequence x(k) and initial value of the weight vector, the values of filter output y(k), the error e(k) and the weight vector vv_k can be computed for all time by equations , and .

Without the requirement of a priori information, the ALE’s self-tuning capability allows it to find weak narrow band signals in wide band noise. Therefore, it has the potential to detect the line spectrum of a defect bearing HFRT signal in a noisy environment.

Defect Determination

Given that defect location and the shaft speed together with bearing geometry dictate the frequency of impact generation, it is a simple matter to calculate these frequencies. The Timken LM501310 cup and LM501349 cone were chosen for all testing. This is a tapered roller bearing with a bore diameter of 41.275 mm (1.625 in.) and an outer diameter of 73.4314 mm (2.8910 in.). At 1200 RPM this yields a defect frequency of 164.64 Hz for a cup defect. These frequencies are often the focus of frequency domain analysis techniques, and are also critical to the combination of the HFRT and ALE presented in this work.

A peak ratio (P.R., equation ) is defined as the sum of the peak values of the defect frequency, and harmonics, over the average value of the spectrum.

(10)

The peak ratio is a dimensionless ratio determined for damaged and undamaged bearings, and is only used to indicate the presence of a defect. The peak value of the first harmonic after HFRT is used to determine the magnitude of the defect. Therefore, once the peak ratio verifies that a defect is present, the peak value is used to estimate the size of the defect. In this study, the effectiveness of the peak ratio as a defect indicator is compared to that of other standard detection methods of kurtosis, RMS, and crest factor.

Test system

A schematic of the test system can be seen in Fig. 3. A four bearing system is contained within a test housing. A Wilcoxan 736T high frequency accelerometer is used to acquire vibration signals. A Krohn-Hite #3384 programmable filter is used to prevent aliasing, and low pass filters the accelerometer data at 10 kHz (half the sampling frequency).

Since the premise of the HFRT technique is based upon proper selection of a resonant frequency band, the resonances of the bearing test system had to be determined. Several distinct bands were located through hammer impact testing, and experimentation revealed that the band between 7.5 and 9.2 kHz is more readily excited by defect impacts.

Experimental results and discussion

In the testing, all physical damage takes the form of scratches made to the center of the outer raceway with a diamond scribe. All the scratches are approximately 2.54 mm (0.1 in.) in length. The width of the damage created is controlled by the number of passes that a scribe makes over the raceway. The defect widths examined range from 15.40 m m to 408.48 m m. It is useful to note that all of these defect sizes are well below industry standards for the definition of a failure.

Seven bearings of damage levels ranging from 0.00 mm to 34.93 mm in width were used to conduct the testing. The most significant result obtained from outer race damage experiments is the determination of a relationship between peak value and defect width for accelerometer data. These results were obtained under 1200 RPM and 1104 lb./bearing loading conditions. At least four data sets for each condition were taken and averaged to obtain each data point. The tabulated results of these experiments are found in Table 1. Fig. 4 shows the relationship between peak value and defect width. The method was able to determine the presence of defects in all six cases. This can be seen from the table where the peak ratios for defective bearings are substantially higher than that of the good bearing. The vertical variation for a given defect size represents a margin for error in measurements. Moreover, the y-intercept represents the noise level of the system. This directly affects the system sensitivity which lies between a defect of width 0.00 m m and 15.40 m m.

Unlike the peak value, the traditional signal features of RMS, kurtosis, and crest factor values do not follow a consistent trend. While the RMS and kurtosis values follow a generally increasing pattern, neither follow a continuously increasing pattern. The crest factor appears to be completely uncorrelated, randomly increasing and decreasing. It is possible that the resolution of these methods is insufficient to detect such small changes in defect size.

Fig. 5, 6 and 7 show results of analysis for three damage levels. These plots depict raw data, raw spectrum, HFRT spectrum, and HFRT with ALE spectrum. The defect frequencies and related harmonics are quite clear at 164 Hz and higher. It is clear from the plots that the defect frequency becomes more prominent as damage increases, even to the point that it is visible in the raw time signal. The advantage of the ALE routine is clearly seen in the weakest signal (Fig. 5), where the defect peaks become quite prominent after noise cancellation.

In addition to the relationship at 1200 RPM, several data sets were also taken at speeds ranging from 600 RPM to 2000 RPM to investigate the effect of RPM on system noise and dynamics. Analysis reveals that a distinction can be made between good, light, medium, and heavily damaged bearings as long as the peak ratio identifies the presence of the defect. Table 2 shows analysis at 2000 RPM, where the peak ratio, RMS, and kurtosis identify the heavily damaged bearing. Crest factor does not indicate damage even at the most severe damage level.

Particularly noticeable at higher speeds, the sensitivity decreases as the shaft speed deviates from 1200 RPM. This is expected as increasing speed is related to increasing energy in the system, and increasing noise. The defect signal is obscured under these increasing noise levels. Sensitivity here is defined as the smallest tested defect that a particular method can identify.

Conclusions

The ability of both the sensor and signal processing methods to detect and diagnose outer race defects has been demonstrated. The peak ratio is the most reliable indicator of localized defect presence out of the methods tested. It enjoys greater or equal success in every level of damage. Kurtosis and RMS are a close second in their reliability. Crest factor is quite insensitive, being the most unreliable method tested.

The HFRT utilizes the fact that much of the energy contained in a defect signal manifests itself in the higher resonant frequencies of a system. Demodulation through use of the envelope technique is employed to gain further insight into the nature of the defect while increasing the signal-to-noise ratio. A periodic defect signature is present in the spectra of the resulting signal. The ALE is then used to enhance the envelope spectrum by reducing broadband noise. It provides an enhanced envelope spectrum with clear peaks at the harmonics of the characteristic defect frequency. It is implemented by using a delayed version of the signal and the signal itself to decorrelate the wideband noise. The noise is then rejected by the ALE.

The peak ratio is used to determine the presence of a defect, while the peak value is used as a metric to evaluate its severity. After establishing baseline information, the peak ratio of a flawed bearing is compared to that of a good bearing to determine defect presence. After defect detection by the peak ratio, the peak value demonstrates a correlation to defect size.

To date, prior work does not provide a clear quantitative relationship between signal characteristics and defect size. Most previous work focuses on the identification of the defect presence with possible size differentiation based on qualitative categories such as light, medium, and heavy. This work provides a linear relationship between peak value and defect width at 1200 RPM has been outlined for outer race defects, with an R² correlation value of 0.9815. However, results from this study show that increasing RPM tends to decrease sensitivity to defects.

Acknowledgements

This work was funded by the Office of Naval Research under research grant number N00014-95-10539, entitled "Integrated Diagnostics." The Timken Company and The Torrington Company have provided valuable support as well. Any opinions, findings, and conclusions or recommendations are those of the author and do not necessarily reflect the views of the Office of Naval Research, The Timken Company, or The Torrington Company.

Nomenclature

A_i = Fourier coefficient

e(k) = Error sequence

f_d = Characteristic defect frequency

f_r = Defect frequency for roller defect

n(k) = Broadband noise signal

m = Number of harmonics in the spectrum = 600/f_d

N = Number of points

P = Autocorrelation vector

P_h = Amplitude value of the defect frequency harmonic h

R = Autocorrelation matrix

s(t) = Simulated defect impact signal

s_b(t) = Band pass of s(t)

s_d(t) = Non-linear rectified s(t)

s_e(t) = Enveloped s(t)

W_k^T= Weight vector of adaptive filter

x(t) = Signal

X_k = Filter input vector

y(k) = Filter output

m = Adaptive step size

Presented at DINAME 97 - 7th International Conference on Dynamic Problems in Mechanics, 3 - 7 March 1997, Angra dos Reis, RJ, Brazil. Technical Editor: Agenor de Toledo Fleury.

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Publication Dates

• Publication in this collection
  20 Nov 2002
• Date of issue
  Sept 1999