Simple Diagnosis Methods for Rolling Bearings
Methods for fault diagnosis by vibration signal analysis of rolling bearings can be divided into simple diagnosis methods and precise diagnosis methods.
The purpose of simple diagnosis is to preliminarily judge whether faults occur on rolling bearings under inspection; precise diagnosis aims to identify the fault type and root cause of bearings suspected to be faulty via simple diagnosis. Five common simple diagnosis methods are introduced as follows:1. Amplitude Diagnosis MethodThe amplitude values mentioned herein include peak value \(X_P\), mean value \(\bar{X}\) (the average value within half a cycle for simple harmonic vibration; the average value after absolute value processing for bearing impact vibration), and root mean square value (effective value) \(X_{\text{rms}}\). This is the simplest and most commonly used diagnosis method. Diagnosis is realized by comparing measured amplitude values with the specified values in judgment criteria.The peak value reflects the maximum amplitude at a certain moment, so it is suitable for diagnosing faults with transient impacts such as surface pitting corrosion. In addition, peak value diagnosis is frequently adopted under low rotating speed conditions (below 300 r/min).The diagnostic effect of the mean value is basically the same as that of the peak value. Its advantage lies in more stable detection readings, but it is generally applied under high rotating speed conditions (above 300 r/min).The root mean square value is averaged over time, so it is applicable to faults such as wear, where the amplitude changes slowly with time.2. Form Factor Diagnosis MethodThe form factor is defined as the ratio of peak value to mean value (\(X_P/\bar{X}\)). It is also one of the effective indicators for simple diagnosis of rolling bearings.
An excessively high \(X_P/\bar{X}\) indicates possible pitting corrosion on rolling bearings; a low \(X_P/\bar{X}\) value may suggest wear.3. Crest Factor Diagnosis MethodThe crest factor is defined as the ratio of peak value to root mean square value (\(X_P/X_{\text{rms}}\)).
The advantage of this indicator for simple diagnosis of rolling bearings is that it is not affected by bearing size, rotating speed, load, or sensitivity variation of primary and secondary instruments such as sensors and amplifiers. It is suitable for diagnosing pitting-type faults. By monitoring the variation trend of \(X_P/X_{\text{rms}}\) over time, early warning of rolling bearing faults can be effectively realized, and the development trend of faults can be reflected.When the rolling bearing is fault-free, \(X_P/X_{\text{rms}}\) maintains a small stable value. Once the bearing suffers damage, impact signals are generated and the vibration peak rises obviously, while the root mean square value does not increase significantly at this stage, resulting in an increased crest factor. As the fault expands continuously, after the peak value gradually reaches the limit, the root mean square value begins to rise, and \(X_P/X_{\text{rms}}\) decreases gradually until it returns to the magnitude under fault-free conditions.4. Probability Density Diagnosis MethodThe probability density curve of vibration amplitude for a fault-free rolling bearing is a typical normal distribution curve. Once a fault occurs, the probability density curve may exhibit skewness or dispersion.5. Kurtosis Coefficient Diagnosis MethodKurtosis (\(\beta\)) is defined as the normalized fourth-order central moment.For fault-free bearings whose amplitude complies with the normal distribution, the kurtosis value is approximately 3. As faults emerge and develop, the kurtosis value presents a variation trend similar to that of the crest factor. The advantage of this method is independence from bearing rotating speed, size and load, and it is mainly used for diagnosing pitting-type faults.In the test, fatigue failure occurred on the bearing at the 74th hour, and the kurtosis coefficient rose from 3 to 6 [Figure (a)], while the peak value [Figure (b)] and RMS value had no obvious increase at this time. The peak value and RMS value responded only after the fault deteriorated further.Tests were carried out under different rotating speeds (800 ~ 2700 r/min) and different loads (0 ~ 11 kN) to obtain the variation range of the above parameters. Obviously, the kurtosis coefficient has the smallest variation range, approximately ±8%. Operating conditions impose the least impact on it, which means higher reliability and consistency.Statistical data show that joint monitoring of rolling bearing vibration conditions using both kurtosis coefficient and RMS value can achieve a fault diagnosis success rate of over 96%.
The purpose of simple diagnosis is to preliminarily judge whether faults occur on rolling bearings under inspection; precise diagnosis aims to identify the fault type and root cause of bearings suspected to be faulty via simple diagnosis. Five common simple diagnosis methods are introduced as follows:1. Amplitude Diagnosis MethodThe amplitude values mentioned herein include peak value \(X_P\), mean value \(\bar{X}\) (the average value within half a cycle for simple harmonic vibration; the average value after absolute value processing for bearing impact vibration), and root mean square value (effective value) \(X_{\text{rms}}\). This is the simplest and most commonly used diagnosis method. Diagnosis is realized by comparing measured amplitude values with the specified values in judgment criteria.The peak value reflects the maximum amplitude at a certain moment, so it is suitable for diagnosing faults with transient impacts such as surface pitting corrosion. In addition, peak value diagnosis is frequently adopted under low rotating speed conditions (below 300 r/min).The diagnostic effect of the mean value is basically the same as that of the peak value. Its advantage lies in more stable detection readings, but it is generally applied under high rotating speed conditions (above 300 r/min).The root mean square value is averaged over time, so it is applicable to faults such as wear, where the amplitude changes slowly with time.2. Form Factor Diagnosis MethodThe form factor is defined as the ratio of peak value to mean value (\(X_P/\bar{X}\)). It is also one of the effective indicators for simple diagnosis of rolling bearings.
An excessively high \(X_P/\bar{X}\) indicates possible pitting corrosion on rolling bearings; a low \(X_P/\bar{X}\) value may suggest wear.3. Crest Factor Diagnosis MethodThe crest factor is defined as the ratio of peak value to root mean square value (\(X_P/X_{\text{rms}}\)).
The advantage of this indicator for simple diagnosis of rolling bearings is that it is not affected by bearing size, rotating speed, load, or sensitivity variation of primary and secondary instruments such as sensors and amplifiers. It is suitable for diagnosing pitting-type faults. By monitoring the variation trend of \(X_P/X_{\text{rms}}\) over time, early warning of rolling bearing faults can be effectively realized, and the development trend of faults can be reflected.When the rolling bearing is fault-free, \(X_P/X_{\text{rms}}\) maintains a small stable value. Once the bearing suffers damage, impact signals are generated and the vibration peak rises obviously, while the root mean square value does not increase significantly at this stage, resulting in an increased crest factor. As the fault expands continuously, after the peak value gradually reaches the limit, the root mean square value begins to rise, and \(X_P/X_{\text{rms}}\) decreases gradually until it returns to the magnitude under fault-free conditions.4. Probability Density Diagnosis MethodThe probability density curve of vibration amplitude for a fault-free rolling bearing is a typical normal distribution curve. Once a fault occurs, the probability density curve may exhibit skewness or dispersion.5. Kurtosis Coefficient Diagnosis MethodKurtosis (\(\beta\)) is defined as the normalized fourth-order central moment.For fault-free bearings whose amplitude complies with the normal distribution, the kurtosis value is approximately 3. As faults emerge and develop, the kurtosis value presents a variation trend similar to that of the crest factor. The advantage of this method is independence from bearing rotating speed, size and load, and it is mainly used for diagnosing pitting-type faults.In the test, fatigue failure occurred on the bearing at the 74th hour, and the kurtosis coefficient rose from 3 to 6 [Figure (a)], while the peak value [Figure (b)] and RMS value had no obvious increase at this time. The peak value and RMS value responded only after the fault deteriorated further.Tests were carried out under different rotating speeds (800 ~ 2700 r/min) and different loads (0 ~ 11 kN) to obtain the variation range of the above parameters. Obviously, the kurtosis coefficient has the smallest variation range, approximately ±8%. Operating conditions impose the least impact on it, which means higher reliability and consistency.Statistical data show that joint monitoring of rolling bearing vibration conditions using both kurtosis coefficient and RMS value can achieve a fault diagnosis success rate of over 96%.
