EXPERIMENTAL APPLICATIONS ON THE INFLUENCE OF INTERNAL OPERATION CLEARANCE OF THE FAULTY ROLLING BEARINGS UPON THEIR REMAINING LIFETIME

In the calculation of the rolling bearings lifetime are taking in to consideration the distribution of the work load on each rolling elements, obliquity, internal operation clearance and pre-stressing. In the case of a rolling bearing with a defect, the internal operation clearance have an influence upon the evolution of its deterioration and remaining lifetime by: internal manufacturing clearance; the expansion of the inner ring when the rolling bearing is mounted on a adapter sleeve; the contraction of the outer ring when the rolling bearing is mounted in the housing; and the temperature difference between rolling bearing rings during operation. This paper presents an experimental study regarding to the influence of the internal operation clearance of the ZKL 1205K rolling bearing upon the remaining lifetime in same operating conditions.


Aspects regarding to the ZKL 1205K bearing characteristics
From all bearings types the most utilized are the radial ball bearings and radial roller bearings.This aspect it was tacked in to consideration when was chosen in the experimental application to use the self-aligning ball bearing with tapered bore (1:12), type ZKL 1205K (Figure 1).The geometrical characteristics of this rolling bearing are present in Figure 2 and values specific for the principal characteristics are present in the Table 1 [1].The self-aligning ball bearing with tapered bore, type ZKL 1205K is manufacturing in accordance with the tolerance ABEC 1 or P0.These tolerances classes are specified in ISO 199 and ISO 492.The outer dimensions for mounting the rolling bearing are in accordance with ISO 15 [1].where: C2, CN, C3, C4 and C5 represent the radial clearance classes.

Calculation of ZKL 1205K rolling bearing lifetime
The calculation of a rolling bearing lifetime can be expressed by [2][3][4]: where: C is the basic load specified in the catalog; P represent the effective load or equivalent dynamic load (force applied on the rolling bearing); r -a constant which depend by the rolling bearing geometry and material (r = 3, in the case of ball bearings; r is 4/3, for the other type of rolling bearings).
At a constant rotation speed (n) the nominal lifetime (in hours) can be calculated by relation [2,3]: This equations has been accepted by ISO but was complemented by introducing correction factors resulting the notion of corrected nominal lifetime.Thus the equation is [2][3][4][5]: where: a 1 is reliability factor; a 2 -factor which depend by material; a 3 -operating conditions factor which depend by lubrication conditions.
The interdependence of these last correction factors lead to their cumulating into a single factor, a 23 .Thus the equation ( 3) becomes [2,3,5]: where: a 23 is factor which depend by material, lubrication, production technology and operating conditions.
In the recent researches for the a 1 , a 2 , a 3 and a 23 coefficients are presented different values in which the equation is completed with new coefficients, with some particularizations for different execution and operation conditions for the rolling bearings [2,3,5,6].

The influence of internal operational clearance upon the remaining lifetime of the faulty rolling bearing
The term "internal clearance" means the distance between the rolling elements and rings (raceways), which permit a relative displacement (radial and axial) of the rolling bearing rings [6][7][8].
Radial clearance of the rolling bearing unassembled represents the distance (clearance) between the raceways and rolling elements measured in normal plane on the rolling bearing axis.The axial clearances represent the total displacement of a rolling bearing ring from an extreme position to the other extreme position relative to the other ring which is fixed in the axial direction (the rings are co-axial) [6-9].
To ensure a good operating condition for a rolling bearing is necessary to take in to consideration the internal operating clearances, which differ from the internal manufacturing clearance [1,8].This internal operating clearances j f can be express by [6, 8, 9]: f r m T def j jjjj (5) where: j r is internal manufacturing clearance; j m -clearance reduction due to fit between bearing components and ad joint parts (adapter sleeves, shaft and housing); j T -clearance reduction due to temperature difference between inner and outer rings; j def -clearance reduction due to deformations of bearing components under operation load which produces a relative radial movement of the rings and an increase in radial clearance.
By analyzing this equation, in the case of ZKL 1205K rolling bearing, can be specified that the internal operation clearance influence the deterioration stage when on the one of components occurs an defect by the next aspects: internal manufacturing clearance j r presented by the producer with j rmin = 15 µm and j rmax = 28 µm, which determine high energies of the shock pulses, when the clearance is minimal, and low energies of the shock pulses, when the clearance is maximal for a faulty rolling bearing; by expansion of the inner ring when the rolling bearing is mounted on a adapter sleeve and contraction of the outer ring when the rolling bearing is mounted in the housing, the internal operation clearance is modified with j m ; by temperature difference between the rolling bearing rings during operation the internal operation clearance is modified with j T ; by deformations of the rolling bearing elements due to work load the internal operation clearance is modified with j def [6,9].

Experimental technique
To determine the influence of internal operation clearance on the remaining lifetime of a faulty rolling bearing was used two self-aligning ball bearing with tapered bore (1:12), type ZKL 1205K.These two rolling bearings were tested in the same operation conditions respectively: 1000 rpm, constant load of 42 N and grease lubrication.For this two rolling bearings it was implemented a defect so that to obtain, in a short time, an accelerate degradation but also to obtain the advanced deterioration stages used in the determination of their remaining lifetime (the breakdown of the rolling bearings respectively the passing from the 3rd to 4th deterioration stage).
For the experimental testing's it was implemented an artificial defect on the outer raceway so that the defect length to be perpendicular on this (Figure 3a).The sizes of the artificial defect are present in the Figure 3b.In order to establish the deterioration stages of the faulty rolling bearing and to determine their remaining lifetime in this research were acquired the vibration and health state signals in the frequency domain through which it were analyzed the trends of overall vibration velocity and of BCU overall health state as well as FFT and BCS spectra.
It was realized two experiments (noted E1 and E2) where for each experiment the rolling bearing worked for 16 hours.Measurements of vibration and of health state were made as follows: the first measurement was acquired at the beginning of the experiment then another 8 measurements at intervals of two hours.

Experimental installation
In this research was performed an experimental test rig consisting of a base on which the electric motor-gearboxcoupling-shaft assembly was mounted, as it present in Figure 4.The rotation speed of the shaft was 1000 rpm with the utilization of the ZKL 1205K rolling bearings.The measurements were carried out on the housing of the rolling bearing in the left part of experimental test rig in the horizontal, vertical and axial axes.For loading the rolling bearings were used three steel disks with 1.4 kg mass mounted on the shaft and for lubrication was used the Liten LT-43 grease.For this operation condition of the ZKL 1205K rolling bearing, where the radial equivalent dynamic load is much lower than the base load, the internal operation clearance doesn't change by deformations of the rolling bearing elements due to work load ( j def ) because they values are negligible.So the internal operation clearance will depend on: the internal manufacturing clearance (j r ); the expansion of the inner ring when the rolling bearing is mounted on a adapter sleeve and the contraction of the outer ring when the rolling bearing is mounted in the housing ( j m ); the temperature difference between the rolling bearing rings during operation ( j T ).
The acquisition of the vibration and health state measurements was performed by using a piezoelectric accelerometer (Figure 5a) connected to the VIBROTEST 60 device (Figure 5b) from Bruel & Kjaer Vibro.Measurements were recorded in the PC-card of VIBROTEST 60 device (Figure 5c), then transferred for their analysis in the XMS software (extended monitoring software).

RESULTS AND DISCUSSION
As was present at the point 2, it was realized two experiments (noted E1 and E2) where for each experiment the rolling bearing worked for 16 hours.For each experiment was established a measurement at the start of experiment and other eight at an interval of two hours.

Experimental results obtained after E1 experiment
In the analysis of overall vibration velocity, as shown in Figure 6 was observed that values haven't exceeded the alarm and danger limits during the experiment in all measuring directions.Also, during the experiment in all measuring directions from this figure was observed an increase in values of overall vibration velocity.In the trend analysis of BCU overall health state as shown in Figure 7 was observed that in the horizontal and vertical directions, the BCU value increased significantly in the measurement 5 th (8 hours of operation), remained at a high level until the 7 th measurement (12 hours of operation) and then decreased up to the end of the experiment (16 hours of operation).In the axial direction it was observed that the values of BCU overall health state increased from the 1 st to the 7 th measurement (12 hours of operation) and then decreased until the end of the experiment (16 hours of operation).It is important to note that the values of BCU overall health state decreased from the 8th and 9th measurement although the rolling bearing was in an advanced deterioration stage.In FFT spectra analysis of the rolling bearing with this artificial defect on the outer raceway (Figure 8) for all measuring directions was observed the occurrence of the harmonics' amplitudes of F BPO frequency (outerraceway ball-pass frequency).In horizontal direction from 1st measurement (Figure 8) to 5th measurement (Figure 10) (8 hours of operation), were identified the fairly high amplitudes of the 1×Fc and 1×Fs sidebands around the 5×F BPO ÷ 7×F BPO harmonics.Also, the same observations were made by FFT spectra analysis in the vertical and axial directions from 1st measurement (Figure 8) to 5 th measurement (Figure 10) (8 hours of operation), except that were identified the high amplitudes of the 1×Fc and 1×Fs sidebands around the 6×F BPO ÷ 9×F BPO harmonics.Also, in FFT spectra analysis in horizontal direction from 6th measurement (Figure 12, 10 hours of operation) to 9th measurement (Figure 14, 16 hours of operation), were identified the fairly high amplitudes of the 1×Fc, 2×Fc, 1×Fs and 2×Fs sidebands around the 5×F BPO ÷ 7×F BPO harmonics, forming socalled "haystack".The same observations were made by FFT spectra analysis in the vertical and axial directions from 6st measurement (Figure 12) to 9th measurement (Figure 14), except that the "haystack" was formed around the 6×F BPO ÷ 9×F BPO harmonics.In BCS spectra analysis of the rolling bearing with this artificial defect on the outer raceway for all measuring directions were observed occurrence the amplitudes of F BPO frequency and its harmonics (Figure 9).In all measuring directions were observed that the amplitudes of F BPO frequency and its harmonics increased up to 8 hours of operation of rolling bearing (5 th measurement, Figure 11), and then decreased up to 16 hours of operation of rolling bearing (9 th measurement, Figures 13 and 15).Also, in BCS spectra analysis were identified the amplitudes of the 1×F c , 1×F s and 2×F s sidebands for all measuring directions.These observations were confirmed at the dismounting of the rolling bearing by the advanced deterioration stage of the rolling bearing.Thus, it was observed: a groove about 29 mm along the outer raceway (Figure 16 a); the balls from the row that passed over the artificial defect had a thermal wear (Figure 16 c); in addition to the thermal wear of the inner raceway there was also the small dimples (small removal of material, Figure 16 b).
As a result of these analyzes the remaining lifetime of the faulty rolling bearing from this experiment is L 10rh = 8 hours from 1 st to 5 th measurement when the rolling bearing was only in the 3 rd degradation stage.

Experimental results obtained after E2 experiment
In the trend analysis of overall vibration velocity as shown in Figure 17 was observed that values increased but haven't exceeded the alarm and danger limits during the experiment in all measuring directions.In the trend analysis of BCU overall health state as shown in Figure 18 was observed that in all measuring directions, the BCU value decreased significantly in the measurement 6th (10 hours of operation) and then increased from the 7th measurement (12 hours of operation) to the end of the experiment (16 hours of operation).
In FFT spectra analysis of the rolling bearing with this artificial defect on the outer raceway (Figure 19) for all measuring directions was observed the occurrence of the harmonics' amplitudes of F BPO frequency.In horizontal direction from 1 st measurement (Figure 19) to 7 th measurement (Figure 21, 12 hours of operation), were identified the fairly high amplitudes of the 1×F c and 1×F s sidebands around the 5×F BPO ÷ 7×F BPO harmonics.Also, the same observations were made by FFT spectra analysis in the vertical and axial directions from 1 st measurement (Figure 19) to 7 th measurement (Figure 21), except that were identified the high amplitudes of the 1×F c and 1×F s sidebands around the 6×F BPO ÷ 9×F BPO harmonics.Also, in FFT spectra analysis in horizontal direction from 8 th measurement (Figure 23, 14 hours of operation) to 9 th measurement (Figure 25, 16 hours of operation), were identified the high amplitudes of the 1×F c , 2×F c ,1×F s and 2×F s sidebands around the 5×F BPO ÷ 7×F BPO harmonics, forming so-called "haystack".The same observations were made by FFT spectra analysis in the vertical and axial directions from 8 st measurement (Figure 23) to 9 th measurement (Figure 25), except that the "haystack" was formed around the 6×F BPO ÷ 9×F BPO harmonics.In BCS spectra analysis of the rolling bearing with this artificial defect on the outer raceway for all measuring directions were observed occurrence the amplitudes of F BPO frequency and its harmonics (Figure 20).In all measuring directions were observed from the 7 th measurement (Figure 22, 12 hours of operation) to the 9 th measurement (Figure 26, 16 hours of operation) that the amplitudes of F BPO frequency decreased and its harmonics decreased both numerically and also in amplitude.Also, in BCS spectra analysis were identified the amplitudes of the 1×F c , 1×F s and 2×F s sidebands for all measuring directions.
By FFT and BSC spectra analysis as well as by trends analysis of overall vibration velocity and of BCU overall health state has been observed that the rolling bearing was from the 1 st to the 7 th measurement (12 hours of operation) in the   As a result of these analyzes the remaining lifetime of the faulty rolling bearing from this experiment is L 10rh = 12 hours from 1 st to 7 th measurement when the rolling bearing was only in the 3 rd degradation stage.

CONCLUSIONS
In this paper, by these two experiments with the same defect size of the rolling bearings implemented on the outer raceway, which operated under identical conditions (same rotation speed, work load and lubrication) was observed the different evolution of deterioration for these two rolling bearings.
The different evolution of deterioration for these two rolling bearings has led to a different remaining lifetime of them.Thus for the faulty rolling bearing used in the first experiment the remaining lifetime was L10rh = 8 hours, and for the faulty rolling bearing used in the second experiment, remaining lifetime was L10rh = 12 hours.
The remaining lifetime of the rolling gearings was determined by using the trend analysis of overall vibration velocity and of BCU overall health state and by using the FFT and BCS spectra analysis.
If the trend of overall vibration velocity can be influenced by the faulty rolling bearing and other causes, the trend of BCU overall health state gives clear information only for the health state of the rolling bearing.Thus the values of BCU overall health state of these two rolling bearings during operation depend on their different internal operation clearance.When the internal operation clearance of the faulty rolling bearing is small will be generated the high energies of the pulse shock, and when the clearance is large will be generated the lower energies of the pulse shock.
By analyzing the FFT spectra, the degree deterioration of the rolling bearings is given by the occurrence of the harmonics' number of the characteristic defect frequencies and of so-called "haystack" for the advanced deterioration of the rolling bearings.However, the FFT spectra analysis doesn't provide information regarding the influence of the internal operation clearance upon the remaining lifetime of the faulty rolling bearing.Only by analyzing the trends of BCU overall health state and the BCS spectra, which provide information about the energies of the pulse shock resulting from the contacts between components of the faulty rolling bearing, was determined the influence of the internal operation clearance upon the remaining lifetime of the faulty rolling bearing.

Fig. 2 .
Fig. 2. Geometrical characteristics of the self-aligning ball bearing with tapered bore, type ZKL 1205K [1]: De is the outer diameter; d -internal diameter; Dbball diameter; B -width of the rolling bearing.

Fig. 3 .
Fig. 3. Rolling bearings used in the experimental testing: a. the position of the artificial defect in the rolling bearing; b. defect dimensions: L -length, l -width and h -depth.

Fig. 6 .
Fig. 6.Trend of overall vibration velocity for all measuring directions at the E1 experiment.

Fig. 7 .
Fig. 7. Trend of BCU overall health state for all measuring directions at the E1 experiment.

Fig. 8 .
Fig. 8. FFT spectra (horizontal, vertical and axial directions) of the rolling bearing during E1 experiment for the 1st measurement (Photo diagram).

Fig. 9 .
Fig. 9. BCS spectra (horizontal, vertical and axial directions) of the rolling bearing during E1 experiment for the 1st measurement (Photo diagram).

Fig. 10 .
Fig. 10.FFT spectra of the rolling bearing during E1 experiment for the 5th measurement (Photo diagram).

Fig. 11 .
Fig. 11.BCS spectra of the rolling bearing during E1 experiment for the 5th measurement (Photo diagram).

Fig. 12 .
Fig. 12. FFT spectra of the rolling bearing during E1 experiment for the 6th measurement (Photo diagram).

Fig. 13 .
Fig. 13.BCS spectra of the rolling bearing during E1 experiment for the 6th measurement (Photo diagram).

Fig. 14 .
Fig. 14.FFT spectra of the rolling bearing during E1 experiment for the 9th measurement (Photo diagram).

Fig. 15 .
Fig. 15.BCS spectra of the rolling bearing during E1 experiment for the 9th measurement (Photo diagram).
) and from this measurement step to the end of experiment the rolling bearing was in the 4th deterioration stage (6 hours of operation) (Figures12 ÷ 15).

Fig. 16 .
Fig. 16.Deterioration of rolling bearing used in the E1 experiment: a) on outer raceway; b) on inner raceway; c) on balls.

Fig. 17 .
Fig. 17.Trend of overall vibration velocity for all measuring directions at the E2 experiment.

Fig. 18 .
Fig. 18.Trend of BCU overall health state for all measuring directions at the E2 experiment.

Fig. 19 .
Fig. 19.FFT spectra of the rolling bearing during E2 experiment for the 1st measurement (Photo diagram).

Fig. 20 .
Fig. 20.BCS spectra of the rolling bearing during E2 experiment for the 1st measurement (Photo diagram).

Fig. 21 .
Fig. 21.FFT spectra of the rolling bearing during E2 experiment for the 7th measurement (Photo diagram).

Fig. 22 .
Fig. 22. BCS spectra of the rolling bearing during E2 experiment for the 7th measurement (Photo diagram).

Fig. 23 .
Fig. 23.FFT spectra of the rolling bearing during E2 experiment for the 8th measurement (Photo diagram).

Fig. 24 .
Fig. 24.BCS spectra of the rolling bearing during E2 experiment for the 8th measurement (Photo diagram).
3 rd degradation stage (Figures 19 ÷ 22), from the 7 th to the 8 th measurement in the transition period (2 hours of operation) between the 3 rd degradation stage and 4 th deterioration stage (Figures 21 ÷ 24) and from this measurement step to the end of experiment the rolling bearing was in the 4th deterioration stage (2 hours of operation) (Figures 23 ÷ 26).

Fig. 25 .
Fig. 25.FFT spectra of the rolling bearing during E2 experiment for the 9th measurement (Photo diagram).

Table 1 .
Geometrical characteristics of the self-aligning ball bearing with tapered bore, type ZKL 1205K [1].Analyzing the symbols of this rolling bearing, 1205K, can be specified that the radial manufacturing clearance class is N c (normal class for normal clearances) or C o .Radial manufacturing clearance values are in accordance with ISO 5753 (values presented in Table2).Also, in the ZKL Company catalogs are presented the calculation of the nominal lifetime (L10) for this rolling bearing [1].

Table 2 .
Radial manufacturing clearance values for the self-aligning ball bearing with tapered bore [1].Radial