# In-Process Quality Inspection of Rolling Element Bearings Based on the Measurement of Microelastic Deformation of Outer Ring

Authors: Kuosheng Jiang; Lianghe Li; Liubang Han; Shuai Gou
Journal: Shock and Vibration
 (2019)

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## Abstract

Quality inspection is the necessary procedure before bearings leaving manufacturing factories. A testing machine with low shaft speed and light radial load condition is generally used to test the dynamic quality of bearings, which avoids creating any potential damages to testing bearings. However, the signal of defective bearings is easily polluted by very weak noise using the traditional vibration-based measurement method due to the low shaft speed and light radial load condition specified for nondestructive inspection, which needs complicated and time-consuming calculation and is not suitable for online inspection. Thus, there are problems about special operating conditions and weak fault severity in quality inspection of bearings, which is quite different from the fault diagnosis of bearings. In this paper, a novel dynamic quality evaluation technique is proposed based on the measurement of Hertz deformations. The measurement system is mainly composed of an eddy current sensor, sensor fixture, and data acquisition platform with less transfer path than the vibration-based measurement system. The sensor fixture is optimized through numerical simulations to obtain signals with a high signal-to-noise ratio. Accurate evaluation of dynamic quality can be implemented reliably with simple signal processing. The proposed method can be used with a rotating speed of 100 rev/min and test load of 100 N, which is remarkably lower than the traditional quality inspection machineries with a rotating speed of around 1000 rev/min and the test load of 400 N. Both simulation and experiment studies have verified the proposed method.


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## Body

## 1. Introduction

Bearing is one of the most important components in machines. The main life cycle management of bearings undergoes the progress of the quality evaluation, the condition monitoring, and the fault diagnosis. Currently, researches of the condition monitoring and the fault diagnosis progress emerges endlessly, which regard that the main detection method is the vibration-based signal processing technique in association with various signal processing methods [1–8].These signal processing methods can be classified into steady work conditions [5], high loading with low-speed work conditions [9], high speed conditions [10], very low-speed conditions, [11] and nonstationary work conditions [12] by different work conditions. Although these methods are effective, they do not qualify for bearing quality inspection due to the low shaft speed and light radial load condition specified for nondestruction inspection. Some researches even use fault bearing samples made by the wire-electrode cutting process with big damage [13, 14].The accurate evaluation of dynamic quality of bearings is fairly important for machines, and it can effectively avoid serious mechanical failure. The advantage of bearing quality testing is that shaft speed and radial load can be set based on the stationary working condition which means the signal is a stationary signal. However, the dynamic quality evaluation test is demanded to be done under very low shaft speed and light radial load to avoid the introduction of any extra damages to bearings. This key industry requirement results in that the signal characteristic of defective bearings is too weak to be picked up by the conventional vibration-based approaches. Currently, there are few research methods for bearing dynamic quantity evaluation. The classification and selection standard of bearings is mainly based on energy indexes of vibration signals, and a series of bearing quality inspection instruments has been developed by many bearing manufacturers using energy indexes such as amplitude peak and root-mean-square (RMS) values of vibration signals. The RMS value is quite qualified to evaluate the energy average intensity of signals, while this index cannot reflect specific questions of the distribution location of bearing defects. There are some weak signal processing methods such as average time-domain synchronization technology [15], wavelet and wavelet entropy [16], chaotic oscillator [17], difference oscillator [18], the empirical mode decomposition [19], and stochastic resonance (SR) [12, 20]. However, these methods are mainly used in fault diagnosis of bearings. For example, SR is a nonlinear amplifier which will distort the output signal, and the complexity and low accuracy of amplitude inversion result in poor maneuverability. The acoustic emission [21] and ultrasonic testing technology [22] are also widely used in weak fault prognosis, while they all have the problem of high cost of equipment, high installation requirements, need a coupling agent, and so on.To overcome the above problem and meet the requirement of dynamic quality evaluation of bearings under low shaft speed and light radial load conditions, a new evaluation method based on the measurement of Hertz deformation of the outer ring using the eddy current displacement sensor is proposed in this paper. Both theoretical studies and implementation of the novel measurement system are carried out to obtain signals with higher signal-to-noise ratio compared with acceleration signals. Then, a newK indicator with a reliable peak matching signal processing method is developed for an accurate and reliable evaluation of bearing quality (K indicator is proposed based on the test and is explained in Section 3.3.3 in detail).


## 2. Microelastic Deformation-Based Bearing Inspection

There are three main characteristics of the quality inspection technology of rolling bearings.First, the advantage of bearing quality testing is that shaft speed and radial load can be set based on the stationary working condition which means the signal is a stationary signal.Second, the dynamic quality evaluation test is demanded to be done under low shaft speed and light radial load to avoid the introduction of any extra damages to bearings, which result in that the signal characteristic of defective bearings is quite weak for the conventional vibration-based approaches.Finally, the dynamic quality evaluation test is specially used in bearing factory inspection, and it allows researchers to drill on the bearing block to release the deformation of the outer ring, which will change the stiffness of bearing block and is forbidden in the real mechanical device.The deformation of the outer ring is named Hertz deformation [23, 24] which is produced by the periodic extrusion between the outer ring and balls on the load-local area of bearing. The deformation is extremely small and may be offset by the interference between the outer ring and bearing block as the pretightening force. In this section, the theory and the specific technical implementation of the Hertz deformation principle and the method of the signal acquisition are analyzed numerically.


### 2.1. Measurement Principle of the Hertz Deformation

The measurement principle of the Hertz deformation is shown in Figure1(a), an eddy current sensor is fixed on a sensor fixture, and it is used to measure the periodic extrusion deformation of the outer ring caused by the ball passed. The output signal of the eddy current sensor with good signal-to-noise ratio is shown in Figure 1(b). The signal has the same frequency as the roller element passes by one point on the outer ring. Bearings with good quality will generate a smooth periodic signal with almost no impacts or burrs, while signals of bearings with defects will be added with periodic fluctuations and impacts. Therefore, the dynamic quality evaluation can be done by detecting and identifying characteristics of the signal. However, the deformation of the outer ring is extremely small, with the amplitude about 1μm, as shown in Figures 1(b) and 1(c), and thus, it brings higher requirements for the sensor and the whole measurement system.Figure 1
Principle and detection technology of the Hertz deformation: (a) measurement principle of the Hertz deformation; (b) high-quality signal of the eddy current sensor for bearing; (c) signals for bearings with defects on elements.
(a)
(b)
(c)Suppose there is a spalling point on the outer raceway of rolling bearing in the loading zone, the pressure between the raceway and the passing roller will suddenly release when rollers pass by. The sudden release of pressure will cause the phenomenon of elastic recovery in the moment of deformation of the outer raceway and then a negative spike (relative peak) will appear on the curve of the time-domain waveform. The peak interval caused by the bruise of the outer raceway can be expressed as follows:(1)αOR=360°f0,where f0 is the passing frequency of rollers, as shown in Equation (1). The spalling point of the outer ring is not located in the installation position of the sensor probe, but within the supporting region of bearings. The instantaneous loss of load will lead to the load redistribution of other rollers, and there will be an instant mutation in the signal detected by the sensor probe when the roller passes through this spalling point. The passing period of the roller through the spalling point of the outer ring is the same as that of the outer ring deformation because the outer ring is fixed.The bruise will contact the rolling body with the frequency offi times per revolution of the axis with the fault occurring on the inner raceway of the rolling bearing. Therefore, the contact interval between two adjacent rollers and the bruise point can be expressed as follows:(2)αIR=360°fi,where fi is the passing frequency of the inner raceway. When the moving bruise point is in the effective area near the probe, the eddy current displacement sensor probe will detect the negative peak value due to the load, and pressure was lost in an instant with the contact between the roller under load and the inner ring bruise point.If there is a rolling roller with bruise, it will come into contact with the inner and outer raceways at the frequency of 2fr (rotation frequency of rollers). A negative spike is detected in the time-domain waveform when the roller is defective and in contact with the inner raceway or outer raceway in the effective area near the probe, while the roll body is rotated by the retainer at a fixed frequency of fc.


### 2.2. Fixture of the Measurement Sensor

As discussed in Section2.1, the signal of Hertz deformation is very small. To use this signal for quality assessment, the measurement system must be developed with high accuracy. The mechanical structure, named as the probe unit, is shown in Figure 2(a) and photo of the real product is presented in Figure 2(b). The unit allows a testing bearing to be loaded and unloaded conveniently, which is important for in-process evaluation of dynamic quality of bearings. Especially, the width of Dc is critical in producing the Hertz deformation.Figure 2
Measurement method: (a) probe unit schematic; (b) inspection setup.
(a)
(b)Vibration-based measurement method is widely used to pick up bearing signals, and the basic path of signal transmission is the bearing inner ring, rolling element, outer ring, bearing seat (shell), and acceleration sensor, as shown in Figure3. The vibration signals picked up by the acceleration sensor on the bearing seat are not sensitive to the early minor damages of the inner ring and the rolling body elements of the rolling bearing due to the multiple transfer paths and large energy loss of the signals.Figure 3
Transfer path of the pickup vibration signal by the acceleration sensor.Acceleration vibration signal includes vibration caused by the bearing structure and assembly error, vibration caused by rolling bearing fault, vibration of bearing seat (shell), inherent vibration of the inner ring, rolling body, and outer ring caused by fault impact, resonance of the sensor, and so on. Therefore, the vibration of system consisted of bearing and housing is complex, which makes the vibration signal component of picking very complex, the noise interference is large, and the signal-to-noise ratio is low. The characteristic signal of bearing (characteristic frequency of fault), especially the weak signal, is often submerged and difficult to extract. It is difficult to diagnose bearing failure by common analysis methods such as the resonance demodulation, and multiwavelet-based methods are mature technology to obtain the fault characteristic of the bearing.As discussed above, the vibration-acceleration signal of rolling bearing with quality problems (not fault diagnosis of bearings) has the disadvantages of complex vibration, large noise interference, low signal-to-noise ratio, and insensitivity to the signal low frequency band.Therefore, a new detection method based on the reasons above is adopted in this paper. It directly detects outer ring deformation of the bearing by inserting a high-precision displacement sensor into the bearing seat and obtains the vibration displacement signal. As shown in Figure4, this method has the characteristics of low noise interference and high signal-to-noise ratio due to the fact that the sensor directly opposite to the bearing outer ring reduces the energy loss of the signal transfer path and other interference from vibration sources. Furthermore, the vibration displacement signal is sensitive to low frequency and can provide good analytical and diagnostic ability. On this basis, this paper focuses on the analysis and research of the characteristics of the time domain and frequency domain in the vibration displacement signals caused by the deformation in the outer ring of the fault of each component of the rolling bearing and has a corresponding in-depth research and discussion on the analysis and processing methods of the displacement signals.Figure 4
Transfer path of the pickup signal by the high-precision displacement sensor.Moreover, as shown in Figure4, the proposed detection method has less transfer path than the vibration-acceleration-based method. Thus, it can eliminate the interferences caused by the vibration of the test bench and other sources such as the driving motor.


### 2.3. Optimization of the Probe Unit

#### 2.3.1. Simulation of the Fixture

In this section, a simulation model of the fixture is built using finite element analysis. Parameters of the test bearing are shown as Figure5 and Table 1. Sliding friction of bearings is not taken into account as the speed is very low.Figure 5
Picture of the bearing structure and variables explanation.Table 1
Parameters of the test bearing.
Parameters
Size
Inner diameter of bearing
d
=
120
mm
Outside diameter of bearing
D
=
215
mm
Width of bearing
B
=
40
mm
Roller diameter
d
w
=
26
mm
Roller nominal length
L
w
=
28
mm
Number of rollers
Z
=
17
Central circle diameter of the roller group
D
P
=
169.5
mm
Diameter of the outer ring raceway
D
e
=
195.5
mm
Diameter of the inner ring raceway
D
e
=
143.5
mmIn Figure6, the inner ring and rolling elements are hidden for the brevity of observation. The outer ring deformation reaches its maximum value of about 5.84μm when the rolling element passes through the sensor. In detail, Figures 6(b)∼6(h) show the gradual increase process of the outer ring deformation from the entrance of the sensor measurement range up to the vertical position of the sensor, showing a clear gradual increase of the deformation. Obviously, there will be a gradual decrease process when the element is rolling away from the sensor.Figure 6
Simulation of the probe unit and bearing.


#### 2.3.2. Ascertain the Size ofDc

In this paper, the fixture is specially designed for the dynamic quality evaluation of bearings under low shaft speed and light radial load condition. The size ofDc as shown in Figure 2 influences the value of deformations and is optimized using finite element analysis. The size of Dc should be between the diameter of the sensor and the roller. A series of values Dc=8mm, Dc=16mm, and Dc=25mm are chosen, and corresponding largest deformations are 3.05,4.25to5.85μm, as shown in Figure 7. The greater the outer deformation signal, the easier it is to obtained by the sensor. Therefore, Dc=25mm is finally chosen in the current system.Figure 7
Ascertain the size ofDc.
(a)
(b)
(c)


### 2.4. Calibration of the Linear Range of the Eddy Current Displacement Sensor

The eddy current displacement sensor is a nondestructive testing sensor. In this paper, a high precision of JX–3b-type vibration calibration table is adopted to calibrate the eddy current displacement sensor to ensure the linear range and high-precision measuring Hertz deformation. The precision of the sensor is0.1μm. The calibration system is shown in Figure 8. On the calibration test rig, the distance between the sensor and the measuring plane was set to 0 mm, 0.1 mm, …, and 10 mm using the micrometer, and the output voltage of the sensor was measured by the Tektronix Oscilloscope. Then, the coefficient of the sensor can be calculated using the distance values divided by voltage values.Figure 8
The calibration system for the eddy current displacement sensor.
(a)
(b)The calibration result is shown in Figure9. The results indicated that the distance between the probe of the eddy current displacement sensor and outer ring of bearings should be adjusted and fixed about for 14V in the initial measurement. After the calibration, the coefficient of the using sensor is 40mm/V.Figure 9
Coefficient of the using sensor.


## 2.1. Measurement Principle of the Hertz Deformation

The measurement principle of the Hertz deformation is shown in Figure1(a), an eddy current sensor is fixed on a sensor fixture, and it is used to measure the periodic extrusion deformation of the outer ring caused by the ball passed. The output signal of the eddy current sensor with good signal-to-noise ratio is shown in Figure 1(b). The signal has the same frequency as the roller element passes by one point on the outer ring. Bearings with good quality will generate a smooth periodic signal with almost no impacts or burrs, while signals of bearings with defects will be added with periodic fluctuations and impacts. Therefore, the dynamic quality evaluation can be done by detecting and identifying characteristics of the signal. However, the deformation of the outer ring is extremely small, with the amplitude about 1μm, as shown in Figures 1(b) and 1(c), and thus, it brings higher requirements for the sensor and the whole measurement system.Figure 1
Principle and detection technology of the Hertz deformation: (a) measurement principle of the Hertz deformation; (b) high-quality signal of the eddy current sensor for bearing; (c) signals for bearings with defects on elements.
(a)
(b)
(c)Suppose there is a spalling point on the outer raceway of rolling bearing in the loading zone, the pressure between the raceway and the passing roller will suddenly release when rollers pass by. The sudden release of pressure will cause the phenomenon of elastic recovery in the moment of deformation of the outer raceway and then a negative spike (relative peak) will appear on the curve of the time-domain waveform. The peak interval caused by the bruise of the outer raceway can be expressed as follows:(1)αOR=360°f0,where f0 is the passing frequency of rollers, as shown in Equation (1). The spalling point of the outer ring is not located in the installation position of the sensor probe, but within the supporting region of bearings. The instantaneous loss of load will lead to the load redistribution of other rollers, and there will be an instant mutation in the signal detected by the sensor probe when the roller passes through this spalling point. The passing period of the roller through the spalling point of the outer ring is the same as that of the outer ring deformation because the outer ring is fixed.The bruise will contact the rolling body with the frequency offi times per revolution of the axis with the fault occurring on the inner raceway of the rolling bearing. Therefore, the contact interval between two adjacent rollers and the bruise point can be expressed as follows:(2)αIR=360°fi,where fi is the passing frequency of the inner raceway. When the moving bruise point is in the effective area near the probe, the eddy current displacement sensor probe will detect the negative peak value due to the load, and pressure was lost in an instant with the contact between the roller under load and the inner ring bruise point.If there is a rolling roller with bruise, it will come into contact with the inner and outer raceways at the frequency of 2fr (rotation frequency of rollers). A negative spike is detected in the time-domain waveform when the roller is defective and in contact with the inner raceway or outer raceway in the effective area near the probe, while the roll body is rotated by the retainer at a fixed frequency of fc.


## 2.2. Fixture of the Measurement Sensor

As discussed in Section2.1, the signal of Hertz deformation is very small. To use this signal for quality assessment, the measurement system must be developed with high accuracy. The mechanical structure, named as the probe unit, is shown in Figure 2(a) and photo of the real product is presented in Figure 2(b). The unit allows a testing bearing to be loaded and unloaded conveniently, which is important for in-process evaluation of dynamic quality of bearings. Especially, the width of Dc is critical in producing the Hertz deformation.Figure 2
Measurement method: (a) probe unit schematic; (b) inspection setup.
(a)
(b)Vibration-based measurement method is widely used to pick up bearing signals, and the basic path of signal transmission is the bearing inner ring, rolling element, outer ring, bearing seat (shell), and acceleration sensor, as shown in Figure3. The vibration signals picked up by the acceleration sensor on the bearing seat are not sensitive to the early minor damages of the inner ring and the rolling body elements of the rolling bearing due to the multiple transfer paths and large energy loss of the signals.Figure 3
Transfer path of the pickup vibration signal by the acceleration sensor.Acceleration vibration signal includes vibration caused by the bearing structure and assembly error, vibration caused by rolling bearing fault, vibration of bearing seat (shell), inherent vibration of the inner ring, rolling body, and outer ring caused by fault impact, resonance of the sensor, and so on. Therefore, the vibration of system consisted of bearing and housing is complex, which makes the vibration signal component of picking very complex, the noise interference is large, and the signal-to-noise ratio is low. The characteristic signal of bearing (characteristic frequency of fault), especially the weak signal, is often submerged and difficult to extract. It is difficult to diagnose bearing failure by common analysis methods such as the resonance demodulation, and multiwavelet-based methods are mature technology to obtain the fault characteristic of the bearing.As discussed above, the vibration-acceleration signal of rolling bearing with quality problems (not fault diagnosis of bearings) has the disadvantages of complex vibration, large noise interference, low signal-to-noise ratio, and insensitivity to the signal low frequency band.Therefore, a new detection method based on the reasons above is adopted in this paper. It directly detects outer ring deformation of the bearing by inserting a high-precision displacement sensor into the bearing seat and obtains the vibration displacement signal. As shown in Figure4, this method has the characteristics of low noise interference and high signal-to-noise ratio due to the fact that the sensor directly opposite to the bearing outer ring reduces the energy loss of the signal transfer path and other interference from vibration sources. Furthermore, the vibration displacement signal is sensitive to low frequency and can provide good analytical and diagnostic ability. On this basis, this paper focuses on the analysis and research of the characteristics of the time domain and frequency domain in the vibration displacement signals caused by the deformation in the outer ring of the fault of each component of the rolling bearing and has a corresponding in-depth research and discussion on the analysis and processing methods of the displacement signals.Figure 4
Transfer path of the pickup signal by the high-precision displacement sensor.Moreover, as shown in Figure4, the proposed detection method has less transfer path than the vibration-acceleration-based method. Thus, it can eliminate the interferences caused by the vibration of the test bench and other sources such as the driving motor.


## 2.3. Optimization of the Probe Unit

### 2.3.1. Simulation of the Fixture

In this section, a simulation model of the fixture is built using finite element analysis. Parameters of the test bearing are shown as Figure5 and Table 1. Sliding friction of bearings is not taken into account as the speed is very low.Figure 5
Picture of the bearing structure and variables explanation.Table 1
Parameters of the test bearing.
Parameters
Size
Inner diameter of bearing
d
=
120
mm
Outside diameter of bearing
D
=
215
mm
Width of bearing
B
=
40
mm
Roller diameter
d
w
=
26
mm
Roller nominal length
L
w
=
28
mm
Number of rollers
Z
=
17
Central circle diameter of the roller group
D
P
=
169.5
mm
Diameter of the outer ring raceway
D
e
=
195.5
mm
Diameter of the inner ring raceway
D
e
=
143.5
mmIn Figure6, the inner ring and rolling elements are hidden for the brevity of observation. The outer ring deformation reaches its maximum value of about 5.84μm when the rolling element passes through the sensor. In detail, Figures 6(b)∼6(h) show the gradual increase process of the outer ring deformation from the entrance of the sensor measurement range up to the vertical position of the sensor, showing a clear gradual increase of the deformation. Obviously, there will be a gradual decrease process when the element is rolling away from the sensor.Figure 6
Simulation of the probe unit and bearing.


### 2.3.2. Ascertain the Size ofDc

In this paper, the fixture is specially designed for the dynamic quality evaluation of bearings under low shaft speed and light radial load condition. The size ofDc as shown in Figure 2 influences the value of deformations and is optimized using finite element analysis. The size of Dc should be between the diameter of the sensor and the roller. A series of values Dc=8mm, Dc=16mm, and Dc=25mm are chosen, and corresponding largest deformations are 3.05,4.25to5.85μm, as shown in Figure 7. The greater the outer deformation signal, the easier it is to obtained by the sensor. Therefore, Dc=25mm is finally chosen in the current system.Figure 7
Ascertain the size ofDc.
(a)
(b)
(c)


## 2.3.1. Simulation of the Fixture

In this section, a simulation model of the fixture is built using finite element analysis. Parameters of the test bearing are shown as Figure5 and Table 1. Sliding friction of bearings is not taken into account as the speed is very low.Figure 5
Picture of the bearing structure and variables explanation.Table 1
Parameters of the test bearing.
Parameters
Size
Inner diameter of bearing
d
=
120
mm
Outside diameter of bearing
D
=
215
mm
Width of bearing
B
=
40
mm
Roller diameter
d
w
=
26
mm
Roller nominal length
L
w
=
28
mm
Number of rollers
Z
=
17
Central circle diameter of the roller group
D
P
=
169.5
mm
Diameter of the outer ring raceway
D
e
=
195.5
mm
Diameter of the inner ring raceway
D
e
=
143.5
mmIn Figure6, the inner ring and rolling elements are hidden for the brevity of observation. The outer ring deformation reaches its maximum value of about 5.84μm when the rolling element passes through the sensor. In detail, Figures 6(b)∼6(h) show the gradual increase process of the outer ring deformation from the entrance of the sensor measurement range up to the vertical position of the sensor, showing a clear gradual increase of the deformation. Obviously, there will be a gradual decrease process when the element is rolling away from the sensor.Figure 6
Simulation of the probe unit and bearing.


## 2.3.2. Ascertain the Size ofDc

In this paper, the fixture is specially designed for the dynamic quality evaluation of bearings under low shaft speed and light radial load condition. The size ofDc as shown in Figure 2 influences the value of deformations and is optimized using finite element analysis. The size of Dc should be between the diameter of the sensor and the roller. A series of values Dc=8mm, Dc=16mm, and Dc=25mm are chosen, and corresponding largest deformations are 3.05,4.25to5.85μm, as shown in Figure 7. The greater the outer deformation signal, the easier it is to obtained by the sensor. Therefore, Dc=25mm is finally chosen in the current system.Figure 7
Ascertain the size ofDc.
(a)
(b)
(c)


## 2.4. Calibration of the Linear Range of the Eddy Current Displacement Sensor

The eddy current displacement sensor is a nondestructive testing sensor. In this paper, a high precision of JX–3b-type vibration calibration table is adopted to calibrate the eddy current displacement sensor to ensure the linear range and high-precision measuring Hertz deformation. The precision of the sensor is0.1μm. The calibration system is shown in Figure 8. On the calibration test rig, the distance between the sensor and the measuring plane was set to 0 mm, 0.1 mm, …, and 10 mm using the micrometer, and the output voltage of the sensor was measured by the Tektronix Oscilloscope. Then, the coefficient of the sensor can be calculated using the distance values divided by voltage values.Figure 8
The calibration system for the eddy current displacement sensor.
(a)
(b)The calibration result is shown in Figure9. The results indicated that the distance between the probe of the eddy current displacement sensor and outer ring of bearings should be adjusted and fixed about for 14V in the initial measurement. After the calibration, the coefficient of the using sensor is 40mm/V.Figure 9
Coefficient of the using sensor.


## 3. Test Rig and Data Collection System

### 3.1. Experimental Rig for the Measurement of Hertz Deformation

An experimental setup for bearing quality inspection is specially designed in this paper using the measurement of Hertz deformation. Including the fixture proposed in Figure2, the experimental rig is also composed of a servo motor, a supporting bearing, a loading bearing, load device, hydraulic jack, and the weighting sensor, as shown in Figure 10. An OR35 series vibration signal analyzer (sample equipment based on LabVIEW software and PCI extensions for instrumentation as shown in the bottom left corner of Figure 10) is used to acquire and analyze signals. The rotating speed of the main shaft is 100 rev/min, and test load is 100 N. The sampling frequency is 512 Hz. Parameters of test bearings are shown in Table 1.Figure 10
The test rig for bearing dynamic quality inspection.


### 3.2. Verification Test

Parameters of the test bearing are shown as Table1. The pass frequency of rollers which is equal to the frequency of outer race defect fo can be calculated as follows:(3)fo=Zfs21−dwDpcosα,(4)fo=1721−26169.5×fs≈7.196fs≈12Hz,where fs is the rotation frequency of the spindle. In this test, fs=100/60≈1.67Hz. The frequency of bearing retainer defect fc can be calculated as follows:(5)fc=fs21−dwDpcosα,fc=fs21−26169.5≈0.423fs≈0.7Hz.The frequency of inner race defectfi can be calculated as follows:(6)fi=zfs21+dwDpcosα,fi=1721+26169.5×fs≈9.804fs≈16.4Hz.In this paper, a special case of a bearing lack of one roller element is used to verify the validity of the method. The time-domain diagram and the spectrum diagram are shown in Figure11. The lack-roller passed period is quite clear in the time-domain diagram. The roller passed frequency, the rotation frequency of spindle, and its harmonic frequencies are also clearly seen in the spectrum diagram.Figure 11
The time-domain diagram and the spectrum diagram of the bearing lack of one roller element.It can be seen from Figure11 that there is less noise in the time-domain signal, which means high signal-to-noise ratio. The location phase information of the lack-roller element can also be clearly seen. A comparing test is shown in Figure 12.Figure 12
The time-frequency diagram of acceleration for the roller bearing lack of one roller.


### 3.3. Results of the Actual Test

#### 3.3.1. Signals of Quality Qualification Bearings

Figure13 is the time-domain diagram and the spectrum diagram of the quality qualification bearing. The roller element passed frequency is quite clear in the time-domain diagram with high signal-to-noise ratio. The passed frequency of the roller element, the rotation frequency of spindle, and its harmonic frequencies are clearly seen in Figure 13. The triple harmonic frequency of spindle is quite high, which is the main cause by the angle eccentric of the shaft. The high signal-to-noise ratio is obvious, shown as in Figure 13.Figure 13
The time-domain diagram and the spectrum diagram of the quality qualification bearing.


#### 3.3.2. Signals of the Roller Bearing with Bruise on Inner Raceway

Figure14 is the time-domain diagram and the spectrum diagram of for the cylindrical roller bearing with bruise on the inner raceway. The time-domain diagram is quite different from the signals of the quality qualification bearing, as shown in Figure 11. The rotation frequency of the spindle and its harmonic frequencies is quite higher than the passed frequency of the roller element in the frequency-domain spectrum. A comparing test is shown in Figure 15.Figure 14
The time-domain diagram and the spectrum diagram of the cylindrical roller bearing with bruise on the inner raceway.Figure 15
The time-frequency diagram of acceleration for the roller bearing with bruise on the inner raceway.


#### 3.3.3.K Indicator to Evaluate the Dynamic Quality of Bearings

As analyzed before, the displacement signal of the quality qualification bearing is a smooth cosine-like curve, and the passed frequency of rollers is the main component of signal. Due to lack of one roller, the energy moves to the passed frequency of rollers more. When defects appear on the outer raceway, inner raceway, or on the roller, there will be some fluctuations appearing on the curve and lower frequency harmonics. The energy will move to the rotation frequency of the spindle part as its low frequency characteristic. The amplitude of the rotation frequency of spindle changes less with the defect, while both of the amplitude of the passed frequency of rollers and the amplitude of the rotation frequency of spindle will change with a different assembly technique. Thus, a new indicator namedK is proposed in this paper:(7)K=Af0Afs,where Af0 is the amplitude of the passed frequency of rollers and Afs is the amplitude of the rotation frequency of spindle. A peak finding and measurement method [25] is used to find Af0 and Afs accuracy while avoid the effect of low frequency harmonics and noise.


#### 3.3.4. Comparison Test

To contrast and demonstrate the effectiveness of the proposed method, a vibration-acceleration sensor was installed on the fixture, as shown in Figure2(b). The adaptive multiwavelet ascension signal processing method [26–28], which is the state of the art, was used to extract effective feature of weak signals, which can indicate early fault signal effectively.The time-frequency signal analysis of the roller bearing lack of one roller is shown in Figure14. The singular characteristic of the fault characteristic period can be seen obviously in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition.The time-frequency signal analysis of the roller bearing with bruise on the inner raceway under low-speed and low-load operations is shown in Figure15. By contrast, there is no significant periodic component in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition in Figure 15.The comparison test shows that the traditional vibration-acceleration-based method can be well used in the fault diagnoses of significant failure of bearings, while being powerless for small defects detection under low-speed and low-load operations.


#### 3.3.5. Batch Test

To further verify the reliability of the proposed measurement and bearing quality evaluation method, five kinds of bearings with different quality problems are well designed as test samples. All of those experimental samples come from the manufacturing factory, and components of bearings with different quality problems are well chosen in the whole process of bearings before assembling. The roughness of the test bearings is tested before assembling, as shown in Table2. Bruise test bearings are specially selected before assembly. The bruise point is small, as shown in Figure 16.Table 2
Roughness of test bearings.
Quality problems
Roughness
Quality qualified bearings
0.08–0.12
Bearings with abnormal roughness on the outer raceway
0.64–0.71
Bearings with abnormal roughness on the inner raceway
0.56–0.61
Bruise on the outer raceway
Normal
Bruise on the inner raceway
NormalFigure 16
Pictures of bruise test bearings: (a) bruise on the outer raceway; (b) bruise on the inner raceway (Figure 6 in [24]).
(a)
(b)The calculation results ofK indicator of six kinds bearing are shown in Table 3, and the actual diagnose chart is shown in Figure 17, which indicates that the K indicator can distinguish different bearing qualities effectively. It is found that it is difficult to inspect defective distribution away from the test area of sensor in the outer ring, and the problem can be overcome by increasing the probe at multiple angles. The contrast test is also done using the vibration-acceleration sensor, and there is almost no signal output because of the low shaft speed and light radial load condition.Table 3
Dynamic evaluation of test bearings.
Types of bearings
Value ofK
Quality qualified bearings
5.05–5.92
Bruise on the inner raceway
1.20–1.75
Bruise on the outer raceway
2.74–3.69
Abnormal roughness on the inner raceway
3.32–3.55
Abnormal roughness on the outer raceway
4.12–4.46
Lack of one roller
19.5Figure 17
Chart of the actual diagnose.In addition, the proposed inspect method can also replace the speed sensor. It can produce 17 pulses for a spindle revolution which produces high precision in speed calculation than the normal photoelectric tachometer which can give only one pulse per revolution.


## 3.1. Experimental Rig for the Measurement of Hertz Deformation

An experimental setup for bearing quality inspection is specially designed in this paper using the measurement of Hertz deformation. Including the fixture proposed in Figure2, the experimental rig is also composed of a servo motor, a supporting bearing, a loading bearing, load device, hydraulic jack, and the weighting sensor, as shown in Figure 10. An OR35 series vibration signal analyzer (sample equipment based on LabVIEW software and PCI extensions for instrumentation as shown in the bottom left corner of Figure 10) is used to acquire and analyze signals. The rotating speed of the main shaft is 100 rev/min, and test load is 100 N. The sampling frequency is 512 Hz. Parameters of test bearings are shown in Table 1.Figure 10
The test rig for bearing dynamic quality inspection.


## 3.2. Verification Test

Parameters of the test bearing are shown as Table1. The pass frequency of rollers which is equal to the frequency of outer race defect fo can be calculated as follows:(3)fo=Zfs21−dwDpcosα,(4)fo=1721−26169.5×fs≈7.196fs≈12Hz,where fs is the rotation frequency of the spindle. In this test, fs=100/60≈1.67Hz. The frequency of bearing retainer defect fc can be calculated as follows:(5)fc=fs21−dwDpcosα,fc=fs21−26169.5≈0.423fs≈0.7Hz.The frequency of inner race defectfi can be calculated as follows:(6)fi=zfs21+dwDpcosα,fi=1721+26169.5×fs≈9.804fs≈16.4Hz.In this paper, a special case of a bearing lack of one roller element is used to verify the validity of the method. The time-domain diagram and the spectrum diagram are shown in Figure11. The lack-roller passed period is quite clear in the time-domain diagram. The roller passed frequency, the rotation frequency of spindle, and its harmonic frequencies are also clearly seen in the spectrum diagram.Figure 11
The time-domain diagram and the spectrum diagram of the bearing lack of one roller element.It can be seen from Figure11 that there is less noise in the time-domain signal, which means high signal-to-noise ratio. The location phase information of the lack-roller element can also be clearly seen. A comparing test is shown in Figure 12.Figure 12
The time-frequency diagram of acceleration for the roller bearing lack of one roller.


## 3.3. Results of the Actual Test

### 3.3.1. Signals of Quality Qualification Bearings

Figure13 is the time-domain diagram and the spectrum diagram of the quality qualification bearing. The roller element passed frequency is quite clear in the time-domain diagram with high signal-to-noise ratio. The passed frequency of the roller element, the rotation frequency of spindle, and its harmonic frequencies are clearly seen in Figure 13. The triple harmonic frequency of spindle is quite high, which is the main cause by the angle eccentric of the shaft. The high signal-to-noise ratio is obvious, shown as in Figure 13.Figure 13
The time-domain diagram and the spectrum diagram of the quality qualification bearing.


### 3.3.2. Signals of the Roller Bearing with Bruise on Inner Raceway

Figure14 is the time-domain diagram and the spectrum diagram of for the cylindrical roller bearing with bruise on the inner raceway. The time-domain diagram is quite different from the signals of the quality qualification bearing, as shown in Figure 11. The rotation frequency of the spindle and its harmonic frequencies is quite higher than the passed frequency of the roller element in the frequency-domain spectrum. A comparing test is shown in Figure 15.Figure 14
The time-domain diagram and the spectrum diagram of the cylindrical roller bearing with bruise on the inner raceway.Figure 15
The time-frequency diagram of acceleration for the roller bearing with bruise on the inner raceway.


### 3.3.3.K Indicator to Evaluate the Dynamic Quality of Bearings

As analyzed before, the displacement signal of the quality qualification bearing is a smooth cosine-like curve, and the passed frequency of rollers is the main component of signal. Due to lack of one roller, the energy moves to the passed frequency of rollers more. When defects appear on the outer raceway, inner raceway, or on the roller, there will be some fluctuations appearing on the curve and lower frequency harmonics. The energy will move to the rotation frequency of the spindle part as its low frequency characteristic. The amplitude of the rotation frequency of spindle changes less with the defect, while both of the amplitude of the passed frequency of rollers and the amplitude of the rotation frequency of spindle will change with a different assembly technique. Thus, a new indicator namedK is proposed in this paper:(7)K=Af0Afs,where Af0 is the amplitude of the passed frequency of rollers and Afs is the amplitude of the rotation frequency of spindle. A peak finding and measurement method [25] is used to find Af0 and Afs accuracy while avoid the effect of low frequency harmonics and noise.


### 3.3.4. Comparison Test

To contrast and demonstrate the effectiveness of the proposed method, a vibration-acceleration sensor was installed on the fixture, as shown in Figure2(b). The adaptive multiwavelet ascension signal processing method [26–28], which is the state of the art, was used to extract effective feature of weak signals, which can indicate early fault signal effectively.The time-frequency signal analysis of the roller bearing lack of one roller is shown in Figure14. The singular characteristic of the fault characteristic period can be seen obviously in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition.The time-frequency signal analysis of the roller bearing with bruise on the inner raceway under low-speed and low-load operations is shown in Figure15. By contrast, there is no significant periodic component in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition in Figure 15.The comparison test shows that the traditional vibration-acceleration-based method can be well used in the fault diagnoses of significant failure of bearings, while being powerless for small defects detection under low-speed and low-load operations.


### 3.3.5. Batch Test

To further verify the reliability of the proposed measurement and bearing quality evaluation method, five kinds of bearings with different quality problems are well designed as test samples. All of those experimental samples come from the manufacturing factory, and components of bearings with different quality problems are well chosen in the whole process of bearings before assembling. The roughness of the test bearings is tested before assembling, as shown in Table2. Bruise test bearings are specially selected before assembly. The bruise point is small, as shown in Figure 16.Table 2
Roughness of test bearings.
Quality problems
Roughness
Quality qualified bearings
0.08–0.12
Bearings with abnormal roughness on the outer raceway
0.64–0.71
Bearings with abnormal roughness on the inner raceway
0.56–0.61
Bruise on the outer raceway
Normal
Bruise on the inner raceway
NormalFigure 16
Pictures of bruise test bearings: (a) bruise on the outer raceway; (b) bruise on the inner raceway (Figure 6 in [24]).
(a)
(b)The calculation results ofK indicator of six kinds bearing are shown in Table 3, and the actual diagnose chart is shown in Figure 17, which indicates that the K indicator can distinguish different bearing qualities effectively. It is found that it is difficult to inspect defective distribution away from the test area of sensor in the outer ring, and the problem can be overcome by increasing the probe at multiple angles. The contrast test is also done using the vibration-acceleration sensor, and there is almost no signal output because of the low shaft speed and light radial load condition.Table 3
Dynamic evaluation of test bearings.
Types of bearings
Value ofK
Quality qualified bearings
5.05–5.92
Bruise on the inner raceway
1.20–1.75
Bruise on the outer raceway
2.74–3.69
Abnormal roughness on the inner raceway
3.32–3.55
Abnormal roughness on the outer raceway
4.12–4.46
Lack of one roller
19.5Figure 17
Chart of the actual diagnose.In addition, the proposed inspect method can also replace the speed sensor. It can produce 17 pulses for a spindle revolution which produces high precision in speed calculation than the normal photoelectric tachometer which can give only one pulse per revolution.


## 3.3.1. Signals of Quality Qualification Bearings

Figure13 is the time-domain diagram and the spectrum diagram of the quality qualification bearing. The roller element passed frequency is quite clear in the time-domain diagram with high signal-to-noise ratio. The passed frequency of the roller element, the rotation frequency of spindle, and its harmonic frequencies are clearly seen in Figure 13. The triple harmonic frequency of spindle is quite high, which is the main cause by the angle eccentric of the shaft. The high signal-to-noise ratio is obvious, shown as in Figure 13.Figure 13
The time-domain diagram and the spectrum diagram of the quality qualification bearing.


## 3.3.2. Signals of the Roller Bearing with Bruise on Inner Raceway

Figure14 is the time-domain diagram and the spectrum diagram of for the cylindrical roller bearing with bruise on the inner raceway. The time-domain diagram is quite different from the signals of the quality qualification bearing, as shown in Figure 11. The rotation frequency of the spindle and its harmonic frequencies is quite higher than the passed frequency of the roller element in the frequency-domain spectrum. A comparing test is shown in Figure 15.Figure 14
The time-domain diagram and the spectrum diagram of the cylindrical roller bearing with bruise on the inner raceway.Figure 15
The time-frequency diagram of acceleration for the roller bearing with bruise on the inner raceway.


## 3.3.3.K Indicator to Evaluate the Dynamic Quality of Bearings

As analyzed before, the displacement signal of the quality qualification bearing is a smooth cosine-like curve, and the passed frequency of rollers is the main component of signal. Due to lack of one roller, the energy moves to the passed frequency of rollers more. When defects appear on the outer raceway, inner raceway, or on the roller, there will be some fluctuations appearing on the curve and lower frequency harmonics. The energy will move to the rotation frequency of the spindle part as its low frequency characteristic. The amplitude of the rotation frequency of spindle changes less with the defect, while both of the amplitude of the passed frequency of rollers and the amplitude of the rotation frequency of spindle will change with a different assembly technique. Thus, a new indicator namedK is proposed in this paper:(7)K=Af0Afs,where Af0 is the amplitude of the passed frequency of rollers and Afs is the amplitude of the rotation frequency of spindle. A peak finding and measurement method [25] is used to find Af0 and Afs accuracy while avoid the effect of low frequency harmonics and noise.


## 3.3.4. Comparison Test

To contrast and demonstrate the effectiveness of the proposed method, a vibration-acceleration sensor was installed on the fixture, as shown in Figure2(b). The adaptive multiwavelet ascension signal processing method [26–28], which is the state of the art, was used to extract effective feature of weak signals, which can indicate early fault signal effectively.The time-frequency signal analysis of the roller bearing lack of one roller is shown in Figure14. The singular characteristic of the fault characteristic period can be seen obviously in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition.The time-frequency signal analysis of the roller bearing with bruise on the inner raceway under low-speed and low-load operations is shown in Figure15. By contrast, there is no significant periodic component in the coloration mode of wavelet multiresolution and the time-domain signal after the decomposition in Figure 15.The comparison test shows that the traditional vibration-acceleration-based method can be well used in the fault diagnoses of significant failure of bearings, while being powerless for small defects detection under low-speed and low-load operations.


## 3.3.5. Batch Test

To further verify the reliability of the proposed measurement and bearing quality evaluation method, five kinds of bearings with different quality problems are well designed as test samples. All of those experimental samples come from the manufacturing factory, and components of bearings with different quality problems are well chosen in the whole process of bearings before assembling. The roughness of the test bearings is tested before assembling, as shown in Table2. Bruise test bearings are specially selected before assembly. The bruise point is small, as shown in Figure 16.Table 2
Roughness of test bearings.
Quality problems
Roughness
Quality qualified bearings
0.08–0.12
Bearings with abnormal roughness on the outer raceway
0.64–0.71
Bearings with abnormal roughness on the inner raceway
0.56–0.61
Bruise on the outer raceway
Normal
Bruise on the inner raceway
NormalFigure 16
Pictures of bruise test bearings: (a) bruise on the outer raceway; (b) bruise on the inner raceway (Figure 6 in [24]).
(a)
(b)The calculation results ofK indicator of six kinds bearing are shown in Table 3, and the actual diagnose chart is shown in Figure 17, which indicates that the K indicator can distinguish different bearing qualities effectively. It is found that it is difficult to inspect defective distribution away from the test area of sensor in the outer ring, and the problem can be overcome by increasing the probe at multiple angles. The contrast test is also done using the vibration-acceleration sensor, and there is almost no signal output because of the low shaft speed and light radial load condition.Table 3
Dynamic evaluation of test bearings.
Types of bearings
Value ofK
Quality qualified bearings
5.05–5.92
Bruise on the inner raceway
1.20–1.75
Bruise on the outer raceway
2.74–3.69
Abnormal roughness on the inner raceway
3.32–3.55
Abnormal roughness on the outer raceway
4.12–4.46
Lack of one roller
19.5Figure 17
Chart of the actual diagnose.In addition, the proposed inspect method can also replace the speed sensor. It can produce 17 pulses for a spindle revolution which produces high precision in speed calculation than the normal photoelectric tachometer which can give only one pulse per revolution.


## 4. Conclusions

A method of dynamic quality evaluation of bearings under low shaft speed and light radial load condition using eddy current signals, and associated measure method is proposed in this paper. The inspection technology and measurement principle of Hertz deformation is specially descripted, and the simulation has proved the effectiveness of the fixture of bearings. The proposed method can be used with the rotating speed of 100 rev/min and test load of 100 N, which is remarkably lower than the traditional quality inspection machineries with the rotating speed of around 1000 rev/min and test load of 400 N. The Hertz deformation can clearly reflect the healthy condition of each components of the bearing. And theK indicator can differentiate different quality bearings while avoiding bringing damage to bearings. The next step will be to study how to design and make the fixture easy to be applied in the automatic production line.



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*Source: 5656143-2019-05-07.xml*