International Journal of Scientific Engineering and Technology Volume No.3 Issue No.
2, pp : 186 192
(ISSN : 2277-1581) 1 Feb 2014
Condition Monitoring of Ball Bearings Using Statistical Analysis
Dhavalikar Mangesh N., Dr. S.B.Wadkar Department of Mechanical Engineering (Mechatronics), Sinhgad College of Engineering, University of Pune, Pune India E-mail : mangesh.dhavlikar@gmail.com, sbwadkar.scoe@sinhgad.edu
Abstract The study investigated the variation of statistical parameters of vibration signals acquired from Ball bearings with respect to speed using an experimental set up. Accelerometers mounted on the bearing housing and connected to Sound and Vibration Analyzer (SVAN) 954 were used to measure the radial accelerations from the bearing housing. The RMS value & kurtosis analysis validates that the ball bearing health can be fairly monitored using frequency domain Analysis. The method proves to be a simple, quick & cost effective method in the condition monitoring of ball bearings & is most suitable for random signals such as from bearings. Keywords SVAN 954, RMS Value, Kurtosis analysis, Ball bearing health, Random signals [ii] in 2002 did a preliminary vibration analysis of a rolling element passing over a single point defect on the outer ring of a ball bearing using FEA software ANSYS. Author extracted vibration signals for two different defect sizes and proposed an index for comparison of different defect sizes. Sadettin Orhan et al. [iii] in 2005 presented vibration monitoring and analysis case studies and examined those in machineries that were running in real operating conditions using spectral analysis. Robert B. Randall et al.[iv] in 2010 presented a tutorial to guide the reader in the diagnostic analysis of acceleration signals from rolling element bearings in the presence of strong masking signals from other machine components such as gears. M.S.Patil et al. [v] in 2010 presented an analytical model for predicting the effect of a localized defect on the ball bearing vibrations. Authors also investigated the effect of the defect size and its location on the ball bearing vibrations. Sylvester A. Aye [vi] in 2011 investigated on the sensitivity of using a contact and a non contact method in condition monitoring of taper roller bearings. II. Material and Methodology An experimental set up developed is as shown in Figure 2. A shaft is supported by 2 test bearings at its ends which is driven by a variable Speed DC motor. A V-belt drive connects motor to the system to achieve higher speeds of rotation. SVAN 954 Vibration Analyzer is used to pick up the acceleration signals. The signals for healthy & faulty bearings were obtained for various speeds with different unbalance mass on the shaft.
Introduction
Maintenance cost is one of the major operating costs in manufacturing companies. It involves spare parts cost, breakdown cost and manpower cost. Unexpected breakdowns, replacement and repair expenses from catastrophic failures indulge in loss of output due to machinery downtime. Adoption of predictive and preventive maintenance procedures significantly reduces these losses. This is essential in maintenance management to enhance the product quality. Predictive maintenance requires continuous measurement of machine operating parameters such as temperature, power consumption, vibration, noise, forces. A Condition Based Monitoring (CBM) program consists of three key steps as shown in Figure 1. A) Data acquisition (Information collecting): A data or signal relevant to system health is collected. B) Data processing (Information handling): A data or signal collected is analyzed for its better interpretation. C) Maintenance (Decision making): Here, efficient maintenance policies are recommended. Data acquisition Data processing Maintenance
Figure 1: Steps in CBM N. Tandon et al. [i] in 1997 proposed an analytical model for predicting the vibration frequencies of rolling bearings and the amplitudes of significant frequency components due to a localized defect on outer race or inner race or on one of the rolling elements under radial and axial loads. Arnaz S. Malhi Figure 2: Experimental Set Up The block diagram of instrumentation is as shown in Figure 3. It consists of an Acceleration Sensor, FFT Spectrum Analyzer, dimmerstat & a digital tachometer. Acceleration Sensor has a
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magnetic base for mounting on the bearing housing & the other end is connected to the FFT Spectrum Analyzer. FFT Spectrum Analyzer is used to record the corresponding vibration spectrum. Dimmerstat is used for varying the voltage supplied to DC motor to vary its speed. A digital tachometer is used to measure different shaft speeds.
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Rolling element passage frequency of inner race (Defect frequency of inner race) ep = Hz (2)
Ball passage frequency (Ball Spin frequency) ip = Hz (3)
Theoretical calculation of the above listed frequencies at different Speeds (RPM) is shown in Table I. rp = Hz (4)
Table I : Theoretical Calculation of the Frequencies at Different Speeds Figure 3: Instrumentation Used The defect to the outer race of two test bearings was produced by Wire Cut EDM (Electro Discharge Machining). It consists of a through circular hole of 0.8 mm diameter to the outer race of a bearing as shown in Figure 4.
RPM Rotational frequency (Hz) i 2298 1054 1474 1000 1078 1724 38.3 17.5 24.5 16.6 17.9 28.7 e 0 0 0 0 0 0 c 14.7 6.75 9.44 6.4 6.9 11.0 ip 306.4 140.4 196.4 133.2 143.6 229.8 Defect frequency (Hz) ep 191.5 87.8 122.8 83.3 89.8 143.6 rp 78.5 36.0 50.3 34.1 36.8 58.9
III Results and Tables A. Procedure
1. Experimental readings were taken for different shaft Speeds and different unbalances on the shaft, for LHS (Left Hand Side) & RHS (Right Hand Side) bearings respectively. As the defect was introduced only in the LHS Bearing, we discuss the same further. An unbalance in the form of mass of bolt was added on the circular disc. The six cases considered for obtaining results were healthy bearing with no bolt, healthy bearing with one bolt, healthy bearing with two bolts, and defective bearing with no bolt, defective bearing with one bolt, and defective bearing with two bolts. 2. An Acceleration sensor with its magnetic probe was attached to test bearing housing. A FFT Spectrum Analyzer was powered by external DC Source & connected to the sensor. 3. A DC Motor was started. The shaft speed was measured using Digital Tachometer. At the known RPM of a shaft, the spectrum was recorded through FFT Spectrum Analyzer. 4. The Speed of motor was gradually increased using dimmerstat which was connected in series with motor. The corresponding spectra were recorded through FFT Spectrum Analyzer. 5. For introducing unbalance, a mass equal to mass of one bolt was added on the circular disc. The Steps 3 & 4 were now repeated.
Figure 4: A Defect Introduced When a rolling element cage rotates with a constant rotational frequency of c, a parametrically excited vibration signal is generated & transmitted through outer race. Defect in the outer race, inner race & rolling element generate vibrations at distinct frequencies. Assuming no slip & outer race to be stationary, the general form of bearing defect frequency equations are given below [v]. Rolling element passage frequency of outer race (Defect frequency of outer race) Cage frequency = c = Hz (1)
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6. For increasing unbalance, another bolt was added on the circumferential hole of a circular disc. The Steps 3 & 4 were repeated further. 7. The test bearing was then dismantled from the housing. A known defect was introduced in the same & further it was reassembled. 8. The steps 3,4,5,6 were repeated for the defective Bearing. Thus the six cases were experimentally tested.
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B. Observed Spectra
For each case, the spectrum was recorded for 10 different shaft Speeds. The observed acceleration spectra for each of the six cases are as shown in the following Figures. Case I: Healthy Bearing with No Bolt (Speed= 2298 rpm) Figure 7: Acceleration Spectrum for Case III at 1474 rpm and for Case IV at 1000 rpm Case V: Defective Bearing with One Bolt (Speed = 1078 rpm)
Figure 5: Acceleration Spectrum for Case I at 2298 rpm Case II: Healthy Bearing with One Bolt (Speed= 1054 rpm) Case VI: Defective Bearing with Two Bolts (Speed = 1724 rpm)
Figure 6: Acceleration Spectrum for Case II at 1054 rpm Case III: Healthy bearing with Two Bolts (Speed= 1474 rpm) Figure 8: Acceleration Spectrum for Case V at 1078 rpm and for Case VI at 1724 rpm
C. Inference from the Experimental Results
1. For healthy bearings, the peak amplitudes of acceleration (m/s2) were observed at whole & half multiples of natural frequency of cage rotation. (3.5 c, 7 c etc.) 2. For defective bearings, the peak amplitudes of acceleration (m/s2) were observed ata) Whole & half multiples of natural frequency of cage rotation.(13 c, 19.5 c etc.) Case IV: Defective bearing with No Bolt (Speed = 1000 rpm) b) Whole & half multiples of defect frequency of outer race (ep, 0.5 ep).
D. RMS Value
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For a dispersed data having N number of data points & X m as an arithmetic mean, a root mean square value is defined as square root of sum of squares of all deviation values divided by Number of samples, where Xi is ith data point. RMS
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(5)
E. Kurtosis For a dispersed data having N number of data points & Xm as arithmetic mean, a Kurtosis is a measure of peakedness of the probability distribution of a real valued random variable. Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. The kurtosis is calculated by following formula-
Figure 9: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case I The data points & variation of RMS & kurtosis values of Acceleration with Speed for the Case II are given in Table III & Figure 10 respectively. Case II: Healthy Bearing with One Bolt Table III : Data points for RMS & Kurtosis values of Acceleration with Speed
Speed (RPM) 500 765 900 1054 1222 1400 1550 1754 1988 2126 2314 RMS Value (m/s2) 0.0457 0.06237 0.07244 0.0881 0.104 0.125 0.147 0.169 0.199 0.201 0.206 Kurtosis 3.815 5.081 11.37 16.21 14.89 16.72 35.77 35.15 35.76 40.58 54.51
Kurtosis
(6)
Where Xi = ith Data Point, RMS = Root Mean Square Value
F. RMS Value & Kurtosis Analysis
The data points & variation of RMS and Kurtosis values of Acceleration with Speed for the Case I are given in Table II & Figure 9 respectively. Case I : Healthy Bearing with No Bolt Table II : Data points for RMS and Kurtosis values of Acceleration with Speed
Speed(RPM) 1136 1454 1692 1852 2118 2298 2440 2544 RMS Value (m/s2) 0.0944 0.128 0.173 0.19 0.211 0.223 0.239 0.285 Kurtosis 6.73 50.8 24.4 29.53 26.83 21.25 36.57 120.68
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Figure 10: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case II The data points & variation of RMS & Kurtosis values of Acceleration with Speed for the Case III are given in Table IV & Figure 11 respectively. Case III: Healthy Bearing with Two Bolts Table IV: Data points for RMS and Kurtosis values of Acceleration with Speed
Speed (RPM) 756 1040 1278 1474 1762 2154 2290 2340 2442 RMS (m/s2) 0.081 0.12 0.153 0.197 0.248 0.272 0.309 0.346 0.342 Kurtosis 152.9815 121.2058 18.06846 51.83483 29.45817 26.37381 119.7005 43.16412 43.16412 1000 1162 1318 1512 1638 1818 2300 2666 1.274 0.923 1.023 1.23 1.38 1.603 2.541 3.126
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40.115 10.639 58.395 125.78 9.7145 11.369 13.573 16.023
Figure 12: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case IV The data points & variation of RMS & kurtosis values of Acceleration with Speed for the Case V are given in Table VI & Figure 13 respectively. Figure 11: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case III The data points & variation of RMS & Kurtosis values of Acceleration with Speed for the Case IV are given in Table V & Figure 12 respectively. Case IV: Defective Bearing with No Bolt Table V: Data points for RMS & Kurtosis values of Acceleration with Speed
Speed (RPM) 595 885 RMS Value (m/s2) 0.479 0.75 Kurtosis 3.0133 16.288
Case V: Defective Bearing with One Bolt Table VI: Data points for RMS and Kurtosis values of Acceleration with Speed
Speed (RPM) 986 1078 1146 1252 1332 1428 1589 1804 2008 2630 RMS Value (m/s2) 0.676 0.804 0.804 0.767 0.881 1.000 1.303 1.718 2.042 2.398 Kurtosis 19.9489 59.1757 173.477 7.23465 20.8541 5.05221 60.2190 12.2214 27.5438 36.5781
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Figure 14: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case VI
G. Inference from RMS Value & Kurtosis Analysis
Table VIII shows the Slopes of RMS Value Vs Speed Best fit curve for the six cases considered. Table VIII: Slopes of RMS Value Vs Speed Best fit curve for the six cases
Case I Description Healthy Bearing With No Bolt Healthy Bearing With One Bolt Healthy Bearing With Two Bolts Defective Bearing With No Bolt Defective Bearing With One Bolt Defective Bearing With Two Bolts Slope of the RMS Value Vs Speed Best fit curve 0.0001 0.0001 0.0002 0.0012 0.0012 0.001
Figure 13: Variation of RMS and Kurtosis values with Speed & their Best Fit for Case V The data points & variation of RMS & Kurtosis values of Acceleration with Speed for the Case VI are given in Table VII & Figure 14 respectively. Case VI: Defective Bearing with Two Bolts Table VII: Data points for RMS and Kurtosis values of Acceleration with Speed
Speed (RPM) 750 920 1074 1204 1356 1492 1724 1950 2140 2342 2624 RMS Value (m/s2) 0.017 0.881 0.759 0.841 1.072 1.245 1.622 1.496 1.758 2.213 2.138 Kurtosis 8.00 173.05 10.10 4.11 10.57 20.71 55.11 43.34 23.09 17.06 20.01
II III IV V VI
1. For healthy bearings, slope of the RMS Value Vs Speed best fit curve gradually increases as unbalance increases. 2. As the defect is introduced in the bearing, the corresponding slope values shoot approximately to 10 times of their values for healthy bearings subjected to same unbalance . Table IX shows the Slopes of Kurtosis Vs Speed Best fit curve for the six cases considered. Table IX: Slopes of Kurtosis Vs Speed Best fit curve for the six cases
Case I II III IV V VI Description Healthy Bearing With No Bolt Healthy Bearing With One Bolt Healthy Bearing With Two Bolts Defective Bearing With No Bolt Defective Bearing With One Bolt Defective Bearing With Two Bolts Slope of the Kurtosis Vs Speed Best fit curve 0.017 0.0269 0.0129 0.0079
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1. For healthy bearings, slope of the Kurtosis Vs Speed best fit curve decreases with unbalance. The trend is reverse of the trend of RMS Values with speed. This can be validated by the Equation (6).
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References i. N. Tandon and A. Choudhury, A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings, Tribology International, Vol.32.(1999), 12th October 1999, Pp.469480.
ii. Arnaz S. Malhi, Finite element modelling of vibrations caused by a defect in the outer ring of a ball bearing, Proceedings of ASME on Finite Element Method and Applications, Vol.605. Amherst, Elab, Spring 2002, Pp.1-6. iii. Sadettin Orhan, Nizami Akturk, Veli Celik, Vibration monitoring for defect diagnosis of rolling element bearings as a predictive maintenance tool: Comprehensive case studies, NDT&E International, Vol.39.(2006), 29th August 2005, Pp.293298. iv. Robert B. Randall and Jerome Antoni, Rolling element bearing diagnostics -A Tutorial, Mechanical Systems and Signal Processing, Vol. 25.(2011), 29th July 2010, Pp. 485520. v. M.S. Patil, Jose Mathew, P.K. Rajendrakumar and Sandeep Desai, A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing, International Journal of Mechanical Sciences, Vol.52.(2010), 17th May 2010, Pp.11931201. vi. Sylvester A. Aye, Statistical Approach for Tapered Bearing Fault Detection using Different Methods, Proceedings of the World Congress on Engineering, Vol. III (2011), London, U.K., July 6-8, 2011.
Kurtosis
(6)
2. For defective bearings, slope of the Kurtosis Vs Speed best fit curve decreases with unbalance. 3. Bearing signals are not periodic but stochastic (or random) having indeterminacy. This allows them to be separated from deterministic signals such as from gears [v]. Thus, the kurtosis curves reflect an uncertainty in their trend.
IV. Conclusions
The development of bearing condition monitoring test rig was successfully carried out which can be used to determine the health of a bearing used in the rotating machinery. The RMS value analysis validates that the ball bearing health can be fairly monitored using frequency domain analysis. The Proposed Statistical analysis proves to be a simple, quick & cost effective method in the condition monitoring of ball bearings. The method proves to be most suitable for random signals such as from bearings.
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