Invariant Correlation Analysis of the Vibration of Rolling Bearing with Defects on its Outer and Inner Races

• Published in: Materials science (New York, N.Y.) N.Y.), 2017-05, Vol.52 (6), p.866-874
• Main Authors: Mats’ko, І. I., Yavors’kyi, І. M., Yuzefovych, R. M., Shevchyk, V. B.
• Format: Article
• Language: English
• Subjects: Analysis; Bearing races; Bearings; Characterization and Evaluation of Materials; Chemistry and Materials Science; Computer simulation; Correlation analysis; Defects; Invariants; Materials Science; Nonlinear differential equations; Probability theory; Random processes; Randomness; Solid Mechanics; Stochastic processes; Structural Materials; Vibration analysis
• ISSN: 1068-820X; 1573-885X
• DOI: 10.1007/s11003-017-0033-7

By the methods of vector periodically correlated random processes, we analyze the vibration of a rolling bearing simulated by its stochastic dynamic model in the form of a system of second-order nonlinear differential equations with periodically varying coefficients. It is shown that the linear and quadratic invariants of the correlation tensor function for this class of random processes improve the efficiency of identification of the defects and enable one to split the defects on the inner and outer races, investigate their space properties, and determine their location. We also established the characteristic changes in the space-and-time structure of the invariants caused by the growth of defect.