Журнал Российского общества по неразрушающему контролю и технической диагностике
The journal of the Russian society for non-destructive testing and technical diagnostic
 
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22 | 11 | 2024
2021, 12 December

DOI: 10.14489/td.2021.12.pp.046-062

Burda E. A., Zusman G. V., Kudryavtseva I. S., Naumenko A. P.
METHODS OF CONDITION MONITORING AND DIAGNOSTICS OF ROLLING BEARINGS OF CENTRIFUGAL MACHINES AND MECHANISMS
(pp. 46-62)

Abstract. The perfection of methods and means of non-destructive testing and technical diagnostics is determined by the level of development of science and modern industrial technologies. The desire to develop technologies determines the growing needs for monitoring the state of substances, materials, products, and now the control of the state of the natural environment is becoming more and more relevant. Methods and means of condition monitoring and diagnostics of rolling bearings have been developed and developed for more than 60 years. Despite certain successes, today there is no information about the veracity of ways to solve this problem. The paper provides a fairly brief overview of methods and methods for monitoring the condition and diagnosis of rolling bearings, and also describes one of the newest trends in this field – the analysis of the properties of the characteristic function of vibroacoustic signals in order to determine the condition of the objects of control and, in particular, rolling bearings. It is shown that the magnitude of the module and the area of the characteristic function of the vibroacoustic signal are very effective criteria for assessing the technical condition of a rolling bearing.

Keywords: rolling bearing, condition monitoring, condition criterion, diagnostics, characteristic function, vibroacoustic signal.

E. A. Burda (Federal State Educational Institution of Higher Education “Omsk State Technical University”, Omsk, Russiа)
G. V. Zusman (Closed Joint-Stock Company “Scientific Research Institute of Introscopy of MNPO “Spectr”, Moscow, Russia)
I. S. Kudryavtseva, A. P. Naumenko (Federal State Educational Institution of Higher Education “Omsk State Technical University”, Omsk, Russiа)

1. Abramova E. V. (2014). Thermal control in industrial safety expertise. Kontrol'. Diagnostika, (3), pp. 93 – 95. [in Russian language] DOI: 10.14489/td.2014.03.pp.093-095
2. Birger I. A. (2019). Technical diagnostics. 2nd ed. Moscow: URSS. [in Russian languahe] ISBN 978-5-9710-6012-3.
3. Burda E. A., Naumenko A. P., Odinets A. I. (2021). Entropy approach in the analysis of vibration signals and partial discharges. Problems of Mechanical Engineering: Proceedings of the V International Scientific and Technical Conference, pp. 308 - 315. Omsk: OmGTU. [in Russian language] DOI 10.25206/978-5-8149-3246-4-2021-308-315.
4. Kudryavtseva I. S., Naumenko A. P., Demin A. M., (2019). Odinets A.I. Probabilistic-statistical criterion for assessing the state by the parameters of a vibroacoustic signal. Dinamika sistem, mekhanizmov i mashin, Vol. 7, (2), pp. 113 – 122. [in Russian language]
5. Veshkurtsev Yu. M., Veshkurtsev N. D., Titov D. A. (2018). Instrumentation based on the characteristic function of random processes. Novosibirsk: Izdatel'stvo ANS «SibAK». [in Russian language] ISBN 978-5-4379-0592-0.
6. Veshkurtsev Yu. M. (2003). Applied analysis of the characteristic function of stochastic processes. Moscow: Radio i svyaz'. [in Russian language] ISBN 5-256-01705.
7. Veshkurtsev Yu. M. (2013). Efficiency of estimates of the characteristic function of random processes. Novosibirsk: Nauka. [in Russian language] ISBN 978-5-02-019111-2.
8. Genkin M. D., Sokolova A. G. (1987). Vibroacoustic diagnostics of machines and mechanisms. Moscow: Mashinostroenie. [in Russian language]
9. Gerike B. L., Abramov I. L., Gerike P. B. (2007). Vibration diagnostics of mining machines and equipment. Kemerovo: Izdatel'stvo KuzGTU. [in Russian language] ISBN 978-5-89070-581-5.
10. Gioev Z. G. (2008). Fundamentals of vibroacoustic diagnostics of electromechanical systems of locomotives. Moscow: Uchebno-metodicheskiy tsentr po obrazovaniyu na zheleznodorozhnom transporte. [in Russian language] ISBN 978-5-89035-522-5.
11. Vibration. Terms and Definitions. (1980). Ru Standard No. GOST 24346–80. Moscow: Izdatel'stvo standartov. [in Russian language]
12. Condition monitoring and diagnostics of machines. Monitoring the condition of equipment in hazardous industries. Vibration of centrifugal pump and compressor units. (2014). Ru Standard No. GOST 32106–2013. Moscow: Standartinform. [in Russian language]
13. Condition monitoring and diagnostics of machines. Monitoring the condition of equipment in hazardous industries. Vibration of stationary reciprocating compressors. (2015). Ru Standard No. GOST R 56233–2014. Moscow: Standartinform. [in Russian language]
14. Non-destructive testing. Classification of types and methods. (2016). Ru Standard No. GOST R 56542–2015. Moscow: Standartinform. [in Russian language]
15. Condition monitoring and diagnostics of machines. General guide. (2016). Ru Standard No. GOST R 17359–2015. Moscow: Standartinform. [in Russian language]
16. Stationary steam turbine units. Vibration standards for shafting supports and general requirements for measurements. (1998). Ru Standard No. GOST 25364–97. Moscow: Izdatel'stvo standartov. [in Russian language]
17. Gas turbine engines for civil aviation. Vibration levels and general requirements for vibration control. (1985). Ru Standard No. GOST 26382–84. Moscow: Izdatel'stvo standartov. [in Russian language]
18. Technological equipment for pulp and paper production. Vibration standards. (1985). Technical requirements No. GOST 26493–85. Moscow: Izdatel'stvo standartov. [in Russian language]
19. Vibration. Centrifugal feed pumps for thermal power plants. Vibration standards and general measurement requirements. (2000). Ru Standard No. GOST 30576–98. Moscow: Izdatel'stvo standartov. [in Russian language]
20. Generating sets of alternating current driven by an internal combustion engine. Vibration measurement and vibration assessment. (2008). Ru Standard No. GOST 31249–2007 (ISO 8528-9:1995). Moscow: Standartinform. [in Russian language]
21. Vibration. Industrial fans. Vibration measurements. (2008). Ru Standard No. GOST 31351–2007 (ISO 14695:2003). Moscow: Standartinform. [in Russian language]
22. Rotating electrical machines. Part 14. Mechanical vibration of some types of machines with a rotation axis height of 56 mm or more. Measurement, Evaluation and Vibration Limits. (2015). International Standard No. GOST IEC 60034-14–2014 (IEC 60034-14:2007). Moscow: Standartinform. [in Russian language]
23. Vibration. Monitoring the condition of machines based on the results of vibration measurements on non-rotating parts. Part 1. General requirements. (2009). State All-Union Standard No. GOST ISO 10816-1–97. Moscow: Standartinform. [in Russian language]
24. Vibration. Monitoring the condition of machines based on the results of vibration measurements on non-rotating parts. Part 3. Industrial machines with a rated power of more than 15 kW and a rated speed of 120 to 15000 min–1. (2007). State All-Union Standard No. GOST ISO 10816-3–2002. Moscow: Standartinform. [in Russian language]
25. Vibration. Monitoring the condition of machines based on the results of vibration measurements on rotating shafts. Industrial machine complexes. (2007). State All-Union Standard No. GOST ISO 7919-3–2002. Moscow: Standartinform. [in Russian language]
26. Vibration. Monitoring the condition of machines based on the results of vibration measurements on non-rotating parts. Part 8. Piston compressor units. (2016). State All-Union Standard No. GOST R ISO 10816-8–2016. Moscow: Standartinform. [in Russian language]
27. Sokolova A. G., Balitskiy F. Ya., Markov V. V. et al. (2016). Using full spectra and other two-dimensional vibration characteristics in diagnostics of compressor equipment. Kontrol'. Diagnostika, (8), pp. 4 – 14. [in Russian language] DOI: 10.14489/td.2016.08.pp.004-014
28. Kostyukov V. N., Boychenko S. N., Naumenko A. P., Tarasov E. V. (2008). Comprehensive monitoring of technological objects of hazardous industries. Kontrol'. Diagnostika, (12), pp. 8 – 19. [in Russian language]
29. Kostyukov V. N., Naumenko A. P., Kudryavtseva I. S. (2014). Diagnostics of rolling bearings by the parameters of the characteristic function. Dinamika sistem, mekhanizmov i mashin, (4), pp. 142 – 145. [in Russian language]
30. Kostyukov A. V., Shchelkanov A. V., Burda E. A. (2017). Comprehensive automated diagnostics of dynamic equipment. Technique and technology of petrochemical and oil and gas production: materials of the 7th international scientific and technical conference, pp. 181 – 182. Omsk: OmGTU. [in Russian language]
31. Kostyukov V. N., Naumenko A. P., Sidorenko I. S. (2009). Using the characteristic function to diagnose piston machines. Dinamika sistem, mekhanizmov i mashin, (2), pp. 32 – 35. [in Russian language]
32. Kostyukov V. N. (2002). Production safety monitoring. Moscow: Mashinostroenie. [in Russian language] ISBN 5-217-03151-4.
33. Kostyukov V. N., Naumenko A. P., Kudryavtseva I. S. (2017). Estimation of the modulus of the characteristic function of a vibroacoustic signal for a given parameter for the limiting states of the diagnostic object. Dinamika sistem, mekhanizmov i mashin, Vol. 5, (4), pp. 239 – 244. [in Russian language]
34. Kostyukov V. N., Boychenko S. N., Tarasov E. V. (1994). Centrifugal electric driven pumping and compressor units equipped with computer monitoring systems to prevent accidents and control the technical condition of COMPACS. Vibration Performance Standards: Guidance Document. Moscow. [in Russian language]
35. Kramer G. (1975). Mathematical Methods of Statistics. Moscow: Mir. [in Russian language]
36. Kudryavtseva I. S., Naumenko A. P., Demin A. M. (2019). Criteria for assessing the vibration state of objects by the parameters of the characteristic function of the signal. Omskiy nauchniy vestnik, 166(4), pp. 97 – 104. [in Russian language]
37. Kudryavtseva I. S. (2016). Methodology for assessing the statistical properties of characteristic functions. Omskiy nauchniy vestnik. Seriya: Pribory, mashiny i tekhnologii, 149(5), pp. 121 – 124. [in Russian language]
38. Kumenko A. I., Timin A. V., Kuz'minyh N. Yu. (2016). Development of criteria for vibration reliability of turbine unit rotors. Dinamika sistem, mekhanizmov i mashin, Vol. 1, (1), pp. 58 – 63. [in Russian language]
39. Kumenko A. I., Kuz'minyh N. Yu. (2016). Development of reliability criteria and assessment of the technical condition of rotors in bearings on plain bearings under operating conditions. Vestnik Bryanskogo gosudarstvennogo tekhnicheskogo universiteta, 51(3), pp. 6 – 16. [in Russian language]
40. Levin B. R. (1989). Theoretical foundations of statistical radio engineering. 3rd ed. Moscow: Radio i svyaz'. [in Russian language] ISBN 5-256-00264-3.
41. Luk'yanov A. V. (1999). Classifier of vibrodiagnostic signs of defects in rotary machines: a handbook. Irkutsk: Izdatel'stvo Irkutskogo gosudarstvennogo tekhnicheskogo universiteta. [in Russian language] ISBN 5-8038-0088-0.
42. Basakin V. V., Kudryavtseva I. S., Teterin A. O., Zaytsev A. V. (2014). Method of experimental research of vibration of bearings. Dinamika sistem, mekhanizmov i mashin, (4), pp. 112 – 115. [in Russian language]
43. Naumenko A. P., Kostyukov V. N. (2013). Regulatory and methodological support for diagnostics and monitoring of reciprocating compressors. Bezopasnost' truda v promyshlennosti, (5), pp. 66 – 70. [in Russian language]
44. Naumenko A. P., Kostyukov V. N. (2014). Assessment of the risk of choosing the standard values of diagnostic signs. Dinamika sistem, mekhanizmov i mashin, (4), pp. 150 – 154. [in Russian language]
45. Klyuev V. V. (Ed.), Sosnin F. R. (2006). Non-destructive testing: handbook: in 8 volumes. Vol. 1: in 2 books. Book 1. Visual and measuring control. Book 2. Radiation monitoring. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
46. Klyuev V. V. (Ed.), Evlampiev A. I., Popov E. D., Sazhin S. G., Fedosenko Yu. K., Gerasimov V. G., Pokrovskiy A. D., Ostanin Yu. Ya. et al. (2006). Non-destructive testing: handbook: in 8 volumes. Vol. 2: in 2 books. Book 1. Leakage control. Book 2. Eddy current testing. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
47. Klyuev V. V. (Ed.), Ermolov I. N., Lange Yu. V. (2008). Non-destructive testing: handbook: in 8 volumes. Vol. 3. Ultrasonic testing. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
48. Klyuev V. V. (Ed.), Anisimov V. A., Katorgin B. I., Kutsenko A. N., Shelihov G. S., Filinov M. V. et al. (2006). Non-destructive testing: handbook: in 8 volumes. Vol. 4: in 3 books. Book 1. Acoustic tensometry. Book 2. Magnetic particle control method. Book. 3. Capillary control. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
49. Klyuev V. V. (Ed.), Vavilov V. P., Podmaster'ev K. V., Sosnin F. R., Korndorf S. F. et al. (2006). Non-destructive testing: handbook: in 8 volumes. Vol. 5: in 2 books. Book 1. Thermal control. Book 2. Electrical control. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
50. Klyuev V. V. (Ed.), Muzhitskiy V. F., Gorkunov E. S., Shcherbinin V. E., Filinov V. N., Ketkovich A. A., Filinov M. V., Matveev V. I. (2006). Non-destructive testing: handbook: in 8 volumes. Vol. 6: in 3 books. Book 1. Magnetic control methods. Book 2. Optical control. Book 3. Radio wave control. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
51. Klyuev V. V. (Ed.), Ivanov V. I., Vlasov I. E., Balitskiy F. Ya., Barkov A. V., Barkova N. A. et al. (2008). Non-destructive testing: handbook: in 8 volumes. Vol. 7: in 2 books. Book 1. Method of acoustic emission. Book 2. Vibration diagnostics. 2nd ed. Moscow: Mashinostroenie. [in Russian language]
52. Klyuev V. V. (Ed.), Ketkovich A. A., Krapivin V. F., Kovalev A. V. et al. (2005). Non-destructive testing: handbook: in 8 volumes. Vol. 8: in 2 books. Book 1. Environmental diagnostics. Book 2. Antiterrorist and forensic diagnostics. Moscow: Mashinostroenie. [in Russian language]
53. Pavlov A. N., Filatova A. E., Hramov A. E. (2011). Timefrequency analysis of non-stationary processes: concepts of wavelets and empirical modes. Izvestiya vysshih uchebnyh zavedeniy. Prikladnaya nelineynaya dinamika, Vol. 19, (2), pp. 141 – 157. [in Russian language]
54. Pavlov B. V. (1966). Cybernetic methods of technical analysis. Moscow: Mashinostroenie. [in Russian language]
55. Pavlov B. V. (1971). Acoustic diagnostics of mechanisms. Moscow: Mashinostroenie. [in Russian language]
56. Kostyukov V. N., Naumenko A. P., Boychenko S. N., Kudryavtseva I. S. Method of vibration diagnostics of mechanisms by characteristic vibration function. Ru Patent No. 2514119. Russian Federation. [in Russian language]
57. Kostyukov V. N., Naumenko A. P., Boychenko S. N., Kudryavtseva I. S. Method of vibration diagnostics of mechanisms by characteristic vibration function. Ru Patent No. 2517772. Russian Federation. [in Russian language]
58. Kostyukov V. N., Tarasov E. V., Kostyukov Al. V., Boychenko S. N. Method for diagnosing damage to machine parts. Ru Patent No. 2540195. Russian Federation. [in Russian language]
59. Kostyukov V. N., Tarasov E. V., Kostyukov Al. V., Boychenko S. N. Method for diagnosing damage to machine parts. Ru Patent No. 2606164. Russian Federation. [in Russian language]
60. Shkatov P. N., Elisov A. A. Method for measuring crack depth by electropotential method. Ru Patent No. 2527311. Russian Federation. [in Russian language]
61. Firsov A. V., Posadov V. V., Posadov V. V. A method for diagnosing vibrations of a turbomachine impeller. Ru Patent No. 2511773. Russian Federation. [in Russian language]
62. Sokolova A. G., Balitskiy F. Ya. (2018). Vibration diagnostics of sliding bearings according to the analysis of characteristics of two-dimensional distribution laws. Machines, technologies and materials for modern mechanical engineering. Izhevsk: Izhevskiy institut komp'yuternyh issledovaniy. [in Russian language]
63. Stepanova L. N., Bekher S. A., Tenitilov E. S. (2010). Method for determining the coordinates of defects during acoustic emission testing of free bearing rings. Kontrol'. Diagnostika, (4), pp. 61 – 65. [in Russian languae]
64. Kostyukov V. N., Naumenko A. P., Kostyukov A. V., Boychenko S. N. (2012). Standards in the field of monitoring the technical condition of equipment in hazardous industries. Bezopasnost' truda v promyshlennosti, (7), pp. 30 – 36. [in Russian language]
65. Kostyukov V. N., Naumenko A. P., Boychenko S. N., Kudryavtseva I. S. (2016). Formation of the vector of diagnostic signs based on the characteristic function of the vibroacoustic signal. Kontrol'. Diagnostika, (8), pp. 22 – 29. [in Russian language]
66. Antoni J. (2006). The Spectral Kurtosis: a Useful Tool for Characterising Non-Stationary Signals. Mechanical Systems and Signal Processing, Vol. 20, (2), pp. 282 – 307.
67. Antoni J., Randall R. B. (2006). The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines. Mechanical Systems and Signal Processing, Vol. 20, (2), pp. 308 – 331.
68. Aslamov Y., Davydov I., Zolotarev A., Aslamov A. (2018). Sparse Wavelet Decomposition of Signals for Solving Vibration Diagnostics Problems. 15th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies: Proceedings, pp. 1726 – 1736. New-York: Curran Associates, Inc.
69. Barszcz T., JabŁoński A. (2011). A Novel Method for the Optimal Band Selection for Vibration Signal Demodulation and Comparison with the Kurtogram. Mechanical Systems and Signal Processing, Vol. 25, (1), pp. 431 – 451.
70. Butler D. E. (1973). The shock-pulse method for the detection of damaged rolling bearings. Non-Destructive Testing, Vol. 6, (2), pp. 92 – 95.
71. Dybała J., Zimroz R. (2014). Rolling Bearing Diagnosing Method Based on Empirical Mode Decomposition of Machine Vibration signal. Applied Acoustics, Vol. 77, pp. 195 – 203.
72. Dyer D., Stewart R. M. (1978). Detection of Rolling Element Bearing Damage by Statistical Vibration Analysis. Journal of Mechanical Design, Vol. 100, (2), pp. 229 – 235.
73. Endo H., Randall R. B. (2007). Application of a Minimum Entropy Deconvolution Filter to Enhance Autoregressive Model Based Gear Tooth Fault Detection Technique. Mechanical Systems and Signal Processing, Vol. 21, (2), pp. 906 – 919.
74. Estupiñan E., Saavedra P. (2002). Diagnostic Techniques for the Vibration Analysis of Bearings. Vibrations Laboratory-Mechanical Engineering Department, Vol. 85, (1), pp. 1 – 9.
75. Goyal D., Pabla B. S. (2016). The Vibration Monitoring Methods and Signal Processing Techniques for Structural Health Monitoring: A Review. Archives of Computational Methods in Engineering, Vol. 23, (4), pp. 585 – 594.
76. Huang N. E., Wu Z. (2008). A Review on Hilbert-Huang Transform: Method and its Applications to Geophysical Studies. Reviews of Geophysics, Vol. 46, (2). Available at: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/ 2007RG000228 (Accessed: 21.03.2021). DOI 10.1029/2007RG000228
77. Robinson J. C., Berry J. E. (2001). Description of Peakvue and Illustration of its Wide Array of Applications in Fault Detection and Problem Severity Assessment. Emerson Process Management Reliability Conference. Available at: https://kupdf.net/download/peakvue-training_5b0b4311e2b6f 5924d5d5414_pdf (Accessed: 21.03.2021).
78. Jiang G. J., Knight J. L. (2002). Estimation of Continuous-Time Processes Via the Empirical Characteristic Function. Journal of Business & Economic Statistics, Vol. 20, (2), pp. 198 – 212.
79. Klausen A., Robbersmyr K. G., Karimi H. R. (2017). Autonomous Bearing Fault Diagnosis Method based on Envelope Spectrum. IFAC-PapersOnLine, Vol. 50, (1), pp. 13378 – 13383.
80. Kostyukov V. N., Naumenko A. P. (2015). Standardization in the Sphere of Vibrodiagnostic Monitoring of Piston Compressors. Procedia Engineering, Vol. 113, pp. 370 – 380. Available at: https://doi.org/10.1016/ j.proeng.2015.07.290 (Accessed: 21.03.2021).
81. Kudryavtseva I. S., Naumenko A. P., Odinets A. I., Demin A. M. (2019). Probabilistic and Statistical Criterions for Assessing the Condition by Vibroacoustic Signal Parameters. Dynamics of Systems, Mechanisms and Machines (Dynamics 2019). Omsk: Omsk State Technical University. Available at: https://ieeexplore.ieee.org/document/8944684 (Accessed: 21.03.2021).
82. Lei Y., Jing L., Zhengjia H., Ming J. Z. (2013). A Review on Empirical Mode Decomposition in Fault Diagnosis of Rotating Machinery. Mechanical Systems and Signal Processing, Vol. 35, (1 – 2), pp. 108 – 126. Available at: https://www.sciencedirect.com/science/article/pii/S0888327012003731?via%3Dihub-! (Accessed: 21.03.2021).
83. McFadden P. D., Smith J. D. (1984). Vibration Monitoring of Rolling Element Bearings by the High-Frequency Resonance Technique a Review. Tribology international, Vol. 17, (1), pp. 3 – 10.
84. Mori K., Kasashima N., Ueno Y. (1996). Prediction of Spalling on a Ball Bearing by Applying the Discrete Wavelet Transform to Vibration SIGNALS. Wear, Vol. 195, (1 – 2), pp. 162 – 168.
85. Prabhakar S., Mohanty A. R., Sekhar A. S. (2002). Application of Discrete Wavelet Transform for Detection of Ball Bearing Race Faults. Tribology International, Vol. 35, (12), pp. 793 – 800.
86. Randall R. B. (2011). Vibration-based Condition Monitoring: Industrial, Automotive and Aerospace Applications. West Sussex: Wiley.
87. Randall R. B., Antoni J. (2011). Rolling Element Bearing Diagnostics – A tutorial. Mechanical Systems and Signal Processing, Vol. 25, (2), pp. 485 – 520.
88. Robinson J. C., Vanvoorhis В., Miller W. (1999). Machine Fault Detection Using Vibration Signal Peak Detector. Patent No. 5895857. United States.
89. Sawalhi N., Randall R. B. (2005). Spectral Kurtosis Enhancement Using Autoregressive Models. ACAM Conference. Melbourne.
90. Sawalhi N., Randall R. B. (2005). Spectral Kurtosis Optimization for Rolling Element Bearings. International Symposium on Signal Processing and Its Applications (ISSPA), pp. 839 – 842. Sydney. DOI 10.1109/IS SPA.2005.1581069
91. Singleton K. J. (2001). Estimation of Affine Asset Pricing Models Using the Empirical Characteristic Function. Journal of Econometrics, Vol. 102, (1), pp. 111 – 141.
92. Tandon N., Choudhury A. (1999). A Review of Vibration and Acoustic Measurement Methods for the Detection of Defects in Rolling Element Bearings. Tribology international, Vol. 32, (8), pp. 469 – 480.
93. Robinson J. C., Vanvoorhis В., Miller W. (1999). Machine Fault Detection Using Vibration Signal Peak Detector. Patent No. 5895857. United States. Available at: https://patents.google.com/patent/US5895857A/en?oq=Patent+no.+5%2c895%2c857+US+ (Accessed: 09.04.2021)
94. Weichbrodt B., Smith К. А. (1999). Signature Analysis–nonintrusive Techniques for Incipient Failure Identification. Intrusive Techniques for Incipient Failure Identification – Application to Bearings and Gears', Proceedings of 5th Space Simulating Conference, National Bureau of Standards. Gaithersburg.
95. Xu M. (1999). Spike Energy™ Measurement and Case Histories. ENTEK IRD International Corporation Technical Report. Available at: http://domino.automation.rockwell.com/applications/gs/region/EntekWebST.nsf/files/Xu99.pdf/$file/Xu99.рdf (Accessed: 21.03.2021)
96. Yu J. (2004). Empirical Characteristic Function Estimation and its Applications. Econometric reviews, Vol. 23, (2), pp. 93 – 123.
97. Zusman G. (2016). Universal Single Sensor for Machinery Condition Monitoring: Vibration, Bearing Health and Temperature. 19th World Conference on Non-Destructive Testing (WCNDT 2016), Issue - 2016-07 – Articles. Munich. Available at: https://www.ndt.net/search/ docs.php3?id=19301 (Accessed: 2021.10.21)
98. Zusman G. V. (2014). Vibration Sensing Technique for Monitoring Condition of Ball/Rolling Bearings and Gearboxes. 11th European Conference on Non-Destructive Testing (ECNDT 2014), Issue - 2014-12 – Articles. Prague. Available at: https://www.ndt.net/search/ docs.php3?id=16501 (Accessed: 2021.10.21)

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