Mathematical modelling analysis of deep groove ball bearing with misalignment

Deep groove ball bearing is prone to misalignment due to installation and long-term use, which requires research on the frequency characteristics and evolution mechanism excited by misalignment. This article first outlines a mathematical model of a rotor supported at both ends, which is used to describe the multi-body vibration mechanism of bearing-rotor system. The previous investigation on the misalignment dynamics of rolling bearings mainly focuses on the frequency harmonic characteristics of displacement signals. This article explores the acceleration frequency characteristics of misalignment bearings, involving their low-frequency and high-frequency vibrations, and explains the formation mechanism from the perspective of the balls passing through the stiffness change region. This modelling method can clearly describe the periodic impact and frequency modulation characteristics excited by misalignment, with characteristic frequencies including cage frequency [Formula: see text] and its harmonics, inner race relative to cage frequency [Formula: see text] and its harmonics and fault frequency [Formula: see text] and its sideband, thus providing more reasonable reference for design and diagnosis. Furthermore, a mean geometry indicator is developed from square envelope domain to evaluate the vibration frequency characteristics. With the advantages of mean geometry in characterizing nonlinear systems, the stability reliability is investigated to reveal the vibration mechanism and dynamic evolution law of the misalignment. Numerical calculations and experiments have shown that the multi-body vibration model and misalignment mathematical expression proposed in this article can illustrate the multi-frequency characteristics excited by misalignment, and the stability reliability can objectively describe the evolution mechanism of such dynamic system.