Experimental Vibration Studies of Deep Groove Ball Bearings Having Damaged Surfaces

Abstract

Bearing plays vital role in dynamic characteristic of any rotating machine. Vibration study of rolling element bearings in the presence of either local defect or distributed defect have been carried out by many researchers. In the present study experimental vibration studies of bearing in the presence of local defect on one of the bearing race and waviness on another race have been carried out. Moreover, the effects of local defect width, waviness order, radial load, rotational speed, presence of lubricant on vibration amplitude in the presence of local defect and race waviness have also been analyzed. Frequency peaks at both characteristic defect frequencies, based on location and type of defect have been observed in the presence of combined defects. The local defect frequency amplitude of inner race/outer race is affected by presence of distributed defect on outer race/inner race and vice versa. However, the waviness frequency amplitude found dominant as compared to local defect frequency amplitude. This study will be helpful to practicing engineers in analyzing the complex vibrations generated by defective rolling elements bearings.

Introduction

Rolling element bearings are used extensively in rotating machinery to support the load and to reduce the friction. Defects found in bearing elements are mainly categorized as local defect and distributed defect. Defects like brinelling, pits, indentations and crack on bearing elements are considered as local defect of bearings while, off size rolling elements, waviness of balls and races, surface roughness, misalignment of races and eccentric races due to manufacturing errors are considered as distributed defect. Bearing defects can excite higher frequencies, which can be used as a basis for detecting incipient damage. Many of researchers have derived dynamic models to study vibration characteristics of defective bearings theoretically [1,2,3,4]. Authors of references [5,6,7,8,9,10,11,12,13] have identified bearing local defects through time domain analysis and frequency domain analysis of vibration data. Moreover, vibration responses of bearings with distributed defect have been analyzed by authors of references [14,15,16,17,18]. In recent paper, Shah and Patel [19] have studied effect of operating parameters like rotational speed, radial load, presence of lubricant and waviness order on vibrations generated by bearing with distributed defect.

Dolenc et al. [20] have shown experimentally that features extracted from vibrations in fault-free, localized and distributed fault conditions form clearly separable clusters, thus enabling diagnosis. The interaction of rolling element with waviness (distributed defect) on bearing race generates high contact stresses as compared to healthy bearing race. Due to these higher contact stresses, the local defects on one of the races with combination of distributed defect on another bearing race may also occur [20]. To study the vibration due to combined local defect on inner and outer races, Patel and Upadhyay [21] have derived 9 dof dynamic model of cylindrical roller bearing-rotor system.

Authors of this paper found that there is dearth of vibration studies for bearing having combined defects (local and distributed defects) on bearing races. Therefore, in the present paper vibrations generated by rolling element bearings in the presence of combined defect have been studied exhaustively. The waviness order of race waviness (present on either race) and width of local defect (present on another race) have been varied simultaneously to study the vibrations generated by deep groove ball bearing in the presence of combined defects. The effects of radial load, shaft rotational speed, local defect size, waviness order and EHD lubrication on vibration velocity amplitude have also been studied in detail. However, the effect of parameters like centrifugal force, gyroscopic couple generated at higher speed, friction, misalignment, radial clearance and unbalance have not been studied. Authors of paper believe that present experimental study will be helpful to the researchers and practicing engineers for condition monitoring of shaft-bearing system having complex bearing faults.

Experimentations

The photographic view of actual experimental setup is shown in Fig. 1a. As shown in Fig. 1a, the shaft was supported on rollers and received power from AC motor through belt and pulley mechanism. The shaft speed variations were controlled by means of variable frequency drive (VFD) of electric motor. The change of shaft speed was measured by digital tachometer. The schematic representation of shaft-bearing system under investigation is shown in Fig. 1b. A split-type housing permitted ease of assembles and disassembles of test bearings during experimentations. The enlarged view of test bearing along with its housing is shown in Fig. 1b. The static radial load was applied at the bottom of test bearing housing by means of attached hook and hanger arrangement. A permanent magnet-type piezoelectric accelerometer was mounted on top of test bearing housing to capture vibrations signals generated by test bearing. The stored time domain data in form of acceleration verses time were transferred to MATLAB^R16 [22] software for frequency analysis.

Fig. 1

a Photographic view of experimental setup. b Schematic representation of shaft-bearing system [19]

The artificial local defect having width (W) equal to 0.5 mm (represent small defect) and 1 mm (represents large defect) and depth of 0.1 mm on inner and outer raceway was created on bearing races using electric discharge machining (EDM). These artificial defects represent fatigue crack on bearing race. The waviness orders (N_w) 7, 8 and 20 on inner races and 8, 9 and 20 on outer races were generated artificially using manual lapping process. These waviness order has been selected based on number of balls (number of balls in bearing, N_b = 8), nearest integer (i) to number of balls (N_b ± i, i = 1) and waviness order (2 × N_b ± i) [14, 19, 25]. The images of inner race waviness and outer race local defect generated on test bearing are shown in Fig. 2a, b, respectively.

Fig. 2

Image of bearing defects a Inner race waviness b outer race local defect

Experimental Vibration Response due to Combined Defect on Bearing Races

In present study polymer cage test bearings (SKF BB1B 420206) have been used for easy assemble and disassemble for creation of artificial defects on bearing races. The vibration velocity spectra of defective test bearings having combined waviness and local defect on either of races in the presence of lubricant have been presented here. The test bearing specifications and other necessary data used during the present study are mentioned in Table 1.

Table 1 Bearing specifications

Vibration Response of Bearing Having Inner Race Waviness and Local Defect on Outer Race

It is necessary to mention here that expected/computed wave passage frequency for inner race, WPFI (bearing having waviness on its inner race, waviness order 8), is N_b × (f_s − f_c) = 122.72 Hz and ball pass outer race defect frequency, BPFO (bearing having defect on its outer race) at shaft rotational speed of 1500 rpm, is (N_b/2) × (N_s/60) × (1 − (d/D))) = 77.28 Hz.

The experimental vibration spectra for inner race waviness order 8 and outer race local defect width 0.5 mm are plotted in Fig. 3a, b, respectively. The frequency peaks at shaft rotational frequency f_s = 24.98 Hz, WPFI = 122.40 Hz along with its side bands at WPFI − f_s = 96.78 Hz, WPFI + f_s = 147.40 Hz and their harmonics are clearly visible in Fig. 3a. However, in case of outer race local defect, shaft rotational frequency f_s = 25 Hz, BPFO = 76.13 Hz and their harmonics are clearly visible in Fig. 3b. Moreover, the vibration spectrum for a bearing with inner race waviness of waviness order 8 and having local defect of 0.5 mm width on its outer race of width 0.5 mm is presented in Fig. 3c. The dominant vibration peaks at N_b × (f_s − f_c) = 119.90 Hz along with side bands N_b × (f_s − f_c) − f_s = 95.91 Hz and N_b × (f_s − f_c) + f_s = 146 Hz are clearly observed in Fig. 3c. The rise in amplitude of waviness defect frequency (as compared to Fig. 3a) in the presence of outer race defect can be noticed in Fig. 3c. Simultaneously, increment in frequency amplitude of outer race defect frequency BPFO = 78.47 Hz (as compared to Fig. 3b) in the presence of inner race waviness can also be observed in Fig. 3c.

Fig. 3

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aNⁱⁿ_w = 8 bW_out = 0.5 mm cNⁱⁿ_w = 8 and W_out = 0.5 mm

To study the effect of outer race local defect on amplitude of inner race waviness defect frequency and the effect of inner race waviness on amplitude of outer race local defect frequency, more experiments have been conducted. Figure 4 shows the vibration spectra of bearing with inner race waviness of order 8 (Fig. 4a), outer race local defect of width 1 mm (Fig. 4b) and combination of both defects (Fig. 4c). The dominant vibration peaks at WPFI along with its side bands WPFI ± f_s can be observed in Fig. 4a, c. The frequency peak at BPFO has suppressed in the presence of waviness on inner race. However, the amplitude of defect frequencies, WPFI and BPFO, has increased in the presence of both defects.

Fig. 4

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aNⁱⁿ_w = 8 bW_out = 1 mm cNⁱⁿ_w = 8 and W_out = 1 mm

In another experiment inner race waviness order was changed to 7. Vibration spectra of bearing having (a) inner race waviness order of 7, (b) outer race local defect of width 1 mm and (c) inner race waviness order of 7 in combination of outer race local defect 1 mm are presented in Fig. 5. It is necessary to mention here that frequency peaks at side bands of wave passage frequency = N_b × (f_s − f_c) ± f_s for waviness order 7 are observed in Fig. 5a, while frequency peaks at BPFO can be observed in Fig. 5b. Moreover, the amplitudes of side band frequencies and BPFO have increased in the presence of combined defects in Fig. 5c.

Fig. 5

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aNⁱⁿ_w = 7 bW_out = 1 mm cNⁱⁿ_w = 7 and W_out = 1 mm

Figure 6a shows the vibration spectrum of bearing having inner race waviness of order 20. Dominant frequency peaks at N_b × (f_s − f_c) + f_s = 146 Hz and fifth harmonic of WPFI = 614.7 Hz are visible. A dominant frequency peak at fifth harmonic of WPFI = 614.7 Hz is clearly visible, but the frequency peak of outer race defect is submerged in side bands of WPFI (Fig. 6c) in the presence of both defects.

Fig. 6

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aNⁱⁿ_w = 20 bW_out = 1 mm cNⁱⁿ_w = 20 and W_out = 1 mm

Effect of Inner Race Waviness on BPFO Amplitude

More experiments have been conducted to study effect of presence of inner race waviness on amplitude of outer race local defect frequency. The amplitude of ball pass frequency of outer race (outer race defect width 0.5 mm and 1 mm) under different radial loads in the presence and absence of inner race waviness of order 8 is presented in Fig. 7. The amplitude of outer race defect frequency, BPFO, has increased in the presence of waviness on inner race as compared to the absence of inner race waviness under all loading conditions. The increment in BPFO amplitude with increase in outer race defect size in the absence of inner race waviness can also be noticed from Fig. 7a–c. However, the amplitude of BPFO has reduced with increase in defect width in the presence of inner race waviness under radial load of 22 kg and unloading condition.

Fig. 7

Vibration amplitude at BPFO for W_out = 0.5 mm and W_out = 1 mm in the presence of inner race waviness (Nⁱⁿ_w = 8) at N_s = 1500 rpm under radial load of aP = 22 kg bP = 32 kg cP = 0 kg

Effect of EHD Lubrication

The frequency amplitude at BPFO obtained through experimentations carried out in the presence and absence of lubricant is compared in Fig. 8. In these experiments, bearings having outer race defect of 1 mm width and different inner race waviness order were used under different radial loads. It is necessary to mention here that SKF make lithium-based grease (NLGI-3) was applied for bearing lubrication. Reduction in frequency amplitude at BPFO can be observed in the presence of lubricant as compared to dry contact bearings in all loading conditions and inner race waviness order. The frequency amplitude has decreased due to damping provided by lubricant.

Fig. 8

Vibration amplitude at BPFO in the presence and absence of lubricant for Nⁱⁿ_w = 7, Nⁱⁿ_w = 8, Nⁱⁿ_w = 20 and W_out = 1 mm at N_s = 1500 rpm aP = 22 kg bP = 32 kg cP = 0 kg

Effect of Outer Race Local Defect on Amplitude of Inner Race Waviness Defect Frequency

The effect of the presence of outer race local defect on amplitude of inner race wave passage frequency and its sideband has been studied for inner race waviness order 7, 8 and 20 under radial loads of 12 kg, 22 kg, 32 kg and 0 kg (no-load condition). The experiments were performed in the presence and absence of 1-mm outer race local defect at shaft rotational speed of 900 rpm, 1200 rpm and 1500 rpm. The comparison of distributed defect frequency under various loads at different shaft speeds is presented in Figs. 9, 10 and 11.

Fig. 9

Inner race waviness defect frequency amplitude for Nⁱⁿ_W = 7, 8 and 20 at N_s = 900 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

Fig. 10

Inner race waviness defect frequency amplitude for Nⁱⁿ_W = 7, 8 and 20 at N_s = 1200 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

Fig. 11

Inner race waviness defect frequency amplitude for Nⁱⁿ_W = 7, 8 and 20 at N_s = 1500 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

It is necessary to mention here that dominant frequency peaks are observed at frequency = N_b × (f_s − f_c) − f_s = 95.91 Hz in the presence of waviness order of 7 and at frequency = N_b × (f_s − f_c) = 119.9 Hz in the presence of waviness order of 8 and 20. Increase in waviness frequency amplitudes in the presence of outer race local defect as compared to frequency amplitude in the absence of outer race defect can be observed from all graphs presented in Figs. 9, 10 and 11 under all radial load and speed combinations. The excitation forces increase in the presence of local defects, as a result of that vibration amplitude at waviness defect frequency has increased in the presence of outer race local defect. Based on experiments and above presented graphs other important observations have also been made in subsequent sections to study effect of radial load, waviness order and rotational speed.

Effect of Radial Load

Figure 12 shows the comparison of inner race waviness defect frequency amplitude in the presence of 1 mm width outer race local defect under different loading condition and waviness order. A specific relationship between radial load and inner race waviness defect frequency amplitude has not been observed. This variation of vibration amplitude has occurred due to variation of contact forces, because of rotation of inner race waviness at shaft rotational speed. The deformation magnitude varies at ball and defect contact, deformation increases when contact occurs in loaded region and while it decreases during unloaded region contact [6, 7, 14, 19, 23, 24].

Fig. 12

Inner race waviness defect frequency amplitude under different radial load at N_s = 1500 rpm in the presence of 1 mm outer race local defect

Effect of Inner Race Waviness Order

The vibration amplitudes at first harmonic of inner race waviness frequency (N_b × (f_s − f_c)) = 119.9 Hz in the presence of 1 mm outer race local defect are plotted in Fig. 13. Maximum amplitude of defect frequency has been found for waviness order 8. This increase in amplitude occurs due to increase in excitation forces at waviness order equal to number of balls under all radial loads. This observation is in line with theoretical and experimental results presented by authors of references [14, 19, 25].

Fig. 13

Inner race wave pass frequency amplitude for different waviness order at shaft speed 1500 rpm in the presence of 1 mm outer race local defect

Effect of Shaft Rotational Speed

The increase in vibration amplitude at inner race defect frequency with increase in speed can be noticed in Fig. 14. This has occurred due to increase in excitation force amplitude at higher speed. However, the defect frequency value also changes with speed. The increment in vibration amplitude with increase in speed has also been observed by authors of references [6, 8, 19] during their theoretical and experimental study.

Fig. 14

Inner race waviness defect frequency amplitude under different load and speed in the presence of inner race waviness order 8 and 1 mm outer race local defect

Experimental Vibration Response of Bearing Having Outer Race Waviness and Local Defect on Inner Race

The same methodology has been adopted for experimentation and analysis of bearing having outer race waviness and inner race local defect. It is worth to mention here that the expected wave passage frequency of outer race waviness, WPFO = N_b × f_c = 77.28 Hz and ball pass frequency of inner race defect, BPFI = (N_b/2) × (N_s/60) × (1 + (d/D))) = 124.30 Hz for shaft rotational speed of 1500 rpm. The experimental vibration spectra for bearings having outer race waviness of order 8 and inner race local defect of width 0.5 mm under radial load of 22 kg and shaft rotational speed of 1500 rpm are plotted in Fig. 15a, b, respectively. The dominant frequency peaks at f_s = 24.98 Hz and WPFO = 78.05 Hz and its third harmonics = 226.70 Hz are clearly visible in Fig. 15a, while frequency peaks at f_s = 24.90 Hz, BPFI = 124.98 Hz, BPFI + f_s = 149.90 Hz and BPFI − f_s = 99.90 Hz are visible in Fig. 15b. The vibration spectra for bearing having both defects, i.e., waviness on outer race and local defect on its inner race, are shown in Fig. 15c. In addition to characteristic defect frequencies, second harmonics of WPFO (2 × WPFO = 152.6 Hz) and side band frequencies of BPFI (BPFI − f_s = 97.72 Hz and BPFI + f_s = 147.72 Hz) can be also observed in spectra of combined defect. The characteristics defect frequencies amplitude has also increased as compare to Fig. 15a, b in the presence of both defects on races.

Fig. 15

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aN^out_w = 8 bW_in = 0.5 mm cN^out_w = 8 and W_in = 0.5 mm

To study the effect of local defect width on vibration amplitude of waviness defect frequency, the inner race defect width has been increased to 1 mm. The frequency amplitude at BPFI has increased with increase in defect width (Fig. 16). The dominant vibration peaks at WPFO can be observed in Fig. 16c in the presence of both defects. The frequency peak at BPFI + f_s has merged with second harmonics of WPFO in the presence of both defects.

Fig. 16

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aN^out_w = 8 bW_in = 1 mm cN^out_w = 8 and W_in = 1 mm

In another experiment outer race waviness order was changed to 9. Vibration spectra of bearing having (a) outer race waviness order of 9, (b) inner race local defect of width 1 mm and (c) outer race waviness order of 9 in combination with inner race local defect of 1 mm are presented in Fig. 17. The dominant frequency peaks at shaft rotational frequency, f_s = 25 Hz, and second harmonics of wave passage frequency 2 × N_b × f_c= 152.6 Hz can be observed in Fig. 17a. However, a frequency peak at WPFO = N_b × f_c = 77.28 Hz has become visible in the presence of inner race defect. Also, the amplitudes of WPFO and BPFI have increased in case of combined defects (Fig. 17c).

Fig. 17

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aN^out_w = 9 bW_in = 1 mm cN^out_w = 9 and W_in = 1 mm

Figure 18a shows the vibration spectrum of bearing having outer race waviness order 20. Dominant frequency peaks at 2 × N_b × f_c = 152.6 Hz and fifth harmonic of WPFO = 5 × N_b × f_c = 383.6 Hz are visible clearly. Frequency peaks at BPFI are visible in vibration spectrum of Fig. 18b for this bearing with inner race local defect. The complex vibration spectrum observed for bearing having both outer race waviness of order 20 and inner race local defect of 1 mm is shown in Fig. 18c. A dominant frequency peak at fifth harmonic of WPFO = 383.6 Hz is clearly visible, but other frequency peaks are merged.

Fig. 18

Vibration response of defective bearing at N_s = 1500 rpm, P = 22 kg aN^out_w = 20 bW_in = 1 mm cN^out_w = 20 and W_in = 1 mm

Effect of Outer Race Waviness on BPFI Amplitude

Experiments have also been conducted to study effect of outer race waviness on amplitude of inner race local defect frequency. The amplitude of ball pass frequency of inner race (inner race defect width 0.5 mm and 1 mm) under different radial loads in the presence and absence of outer race waviness (of order 8) is presented in Fig. 19. The amplitude of BPFI has increased in the presence of outer race waviness under all loading conditions. This increment in BPFI amplitude with increase in inner race defect size in the absence of outer race waviness can be noticed from Fig. 19a–d). However, the amplitude of BPFI has been reduced with increase in defect width in the presence of outer race waviness under radial load of 12 kg and 22 kg.

Fig. 19

Vibration amplitude at BPFI for W_in = 0.5 mm and W_in = 1 mm in the presence of outer race waviness (N^out_w = 8) at N_s = 1500 rpm under radial load of aP = 12 kg bP = 22 kg cP = 32 kg dP = 0 kg

Effect of EHD Lubrication

The frequency amplitude at BPFI obtained through experimental vibration analysis of bearing having 1 mm inner race defect in the presence and absence of lubricant is compared in Fig. 20a–d. During these experiments bearings with different outer waviness order are used to capture vibration signals. Reduction in frequency amplitude at BPFI can be observed in the presence of lubricant as compared to dry contact bearings in all loading conditions and outer race waviness order. This reduction in frequency amplitude occurs due to the presence of damping at lubricated contact.

Fig. 20

Vibration amplitude at BPFI in the presence and absence of lubricant for N^out_w = 8, N^out_w = 9, N^out_w = 20 and W_in = 1 mm at N_s = 1500 rpm aP = 12 kg bP = 22 kg cP = 32 kg dP = 0 kg

Effect of Inner Race Local Defect on Amplitude of Outer Race Waviness Defect Frequency

The effect of presence of inner race local defect on amplitude of outer race wave passage frequency has been studied for outer race waviness order 8, 9 and 20 under radial loads of 12 kg, 22 kg, 32 kg and 0 kg. The experiments have been performed in for bearings with 1 mm inner race local defect or no defect on inner race, at shaft rotational speed of 900 rpm, 1200 rpm and 1500 rpm in the presence of lubrication. The comparisons of waviness defect frequency amplitude under various load and different shaft speeds are presented in Figs. 21, 22 and 23.

Fig. 21

Outer race waviness defect frequency amplitude for N^out_W = 8, 9 and 20 at N_s = 900 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

Fig. 22

Outer race waviness defect frequency amplitude for N^out_W = 8, 9 and 20 at N_s = 1200 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

Fig. 23

Outer race waviness defect frequency amplitude for N^out_W = 8, 9 and 20 at N_s = 1500 rpm under radial load of a 12 kg b 22 kg c 32 kg d 0 kg

It is necessary to mention here that dominant frequency peaks were observed at N_b × f_c = 76.29 Hz in the presence of outer race waviness order of 8, 9 and 20. Increase in these frequency amplitudes in the presence of inner race local defect can be observed from all graphs presented in Figs. 21, 22 and 23 under all radial load and speed combinations.

Effect of Radial Load

Figure 24 shows the comparison of outer race waviness defect frequency amplitude in the presence of 1 mm inner race defect under different loading condition and waviness order. Reduction in wave passage frequency amplitude with increase in radial load can be observed for all waviness order. The reduction in vibration amplitude has occurred due to decrease in internal radial clearance between ball-raceway contacts with increase in radial load. It has also happened due to reduction of lubricant film thickness to support more load which enhanced lubricant film stiffness and damping along with nonlinear contact stiffness [19, 26, 27].

Fig. 24

Outer race waviness defect frequency amplitude under different radial load at N_s = 1500 rpm in the presence of 1 mm inner race local defect

Effect of Outer Race Waviness Order

To study the effect of outer race waviness on vibration amplitude, experiments have been conducted for bearings having waviness of different order on its outer race and 1 mm local defect on its inner race. The vibration amplitudes at first harmonic of outer race waviness frequency N_b × f_c = 76.29 Hz have been compared in Fig. 25. Maximum amplitude of defect frequency has been found for waviness order 8 (equal to number of balls) under all radial loads due to increase in excitation forces. Severities of vibration at waviness order equal to number of balls have also been observed by authors of references [14, 17,18,19] in the absence of local defect.

Fig. 25

Outer race wave pass frequency amplitude for different waviness order at shaft speed 1500 rpm in the presence of 1 mm inner race local defect

Effect of Shaft Rotational Speed

The increase in vibration amplitude at outer race defect frequency with increase in speed can be noticed in Fig. 26. This is result of enhancement of contact forces and deflection between outer race and rolling elements occurred at higher speed. However, the defect frequency value also changes with speed. Increment in vibration amplitude with increase in rotational speed has also been observed by authors of references [19, 28] during theoretical and experimental vibration study.

Fig. 26

Outer race waviness defect frequency amplitude under different load and speed in the presence of outer race waviness order 8 and 1 mm inner race local defect

It is worth to mention here that the vibration amplitudes are also affected by higher speed, the presence of friction, unbalancing, misalignment and bearing radial clearance. These parameters have not been studied thoroughly in present paper.

Conclusions

Following observations have been made from experimental vibrations studies carried out in the presence of local and distributed bearing defects

• Frequency peaks at both characteristic defect frequencies (local and waviness) have been observed in the presence of combined defects. However, the defect frequency depends on location (outer race or inner race) and type of defect (local defect or race waviness).

• The amplitude of characteristic defect frequency increased in the presence of combined defects.

• The reduction in frequency amplitude at defect frequencies has been observed in the presence of lubricants.

• The amplitudes of wave passage frequency are found more as compared to amplitudes of local defect frequency.

• The maximum vibration amplitude at wave passage frequency (WPF) noticed in case of inner race waviness with combination of outer race local defect as compared to outer race waviness in combination of inner race local defect.

• It is difficult to identify the local defect on one of the bearing races in the presence of waviness on another race.

Appendix

The following general guidelines will be helpful to the practicing engineers for vibration analysis of defective bearing in the absence of misalignment and unbalanced shaft-bearing system:

• Frequency peaks only at shaft rotational frequency (f_s) and cage frequency with their harmonics can be observed in spectra of healthy (defect free) bearings.

• In addition to shaft rotation frequency, peaks at ball pass frequency of outer race (BPFO) and its harmonics can also be observed for bearings having defects on its outer race.

• The frequency peaks at ball pass frequency of inner race (BPFI) can be noticed for bearings having defects on its inner race. Moreover, the sidebands at shaft rotational frequency can also be observed due to rotation of inner race defect.

• The vibration amplitudes enhance in the presence of outer race local defect as compared to same size inner race local defect.

• The vibration amplitude at bearing characteristics defect frequency increases with increase in local defect width on either of races in the presence or absence of lubricant.

• In case of distributed defects, the dominant frequency peaks are governed by waviness order and waviness location.

• The waviness peak amplitude at wave passage frequency (WPF) = N_b × (f_s − f_c) can be observed for waviness order (N_w) = q × N_b, while the side band frequencies at N_b × (f_s − f_c) ± f_s have been noticed for waviness order of N_w = q × N_b ± 1.

• More complicated vibration patterns can be found for higher waviness order.

• In case of outer race waviness peak amplitude at ball pass frequency N_b × f_c and its harmonics can be observed irrespective of waviness order.

• Severe vibration amplitudes at wave passage frequency can be noticed for inner race waviness order equal to number of balls.

• The amplitude of characteristic local defect frequency (either BPFO or BPFI) increases in the presence of waviness on alternative/another race.

• The dominant peak at waviness defect frequency can be observed even in the presence of local defect and distributed defect on bearing races.

• Amplitude of characteristic distributed defect (wave passage frequency and side bands) increases in the presence of local defect on alternative/another race.

In general, bearing defect frequency amplitudes are also affected by magnitude of radial load, shaft rotational speed, location and size of defect, waviness order and presence of lubricant.