Abstract
Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.
Highlights
Ball bearings are one of the main components in mechanical systems dealing with transferring the rotational movement and carrying loads, simultaneously assuring high reliability of the structure [1,2]
Rotating rolling element bearing generates vibrations related to the parametrical excitation called varying compliance (VC) [8] and characteristic frequencies referring to the specific bearing element [9]
In most of the papers related to the mathematical modeling of ball bearings, analyses of response frequencies or statistics-based approaches were proposed to identify faults, while the optimal working conditions and factors inducing vibrations are crucial for future design developments
Summary
Ball bearings are one of the main components in mechanical systems dealing with transferring the rotational movement and carrying loads, simultaneously assuring high reliability of the structure [1,2]. In most of the papers related to the mathematical modeling of ball bearings, analyses of response frequencies or statistics-based approaches were proposed to identify faults, while the optimal working conditions and factors inducing vibrations are crucial for future design developments. The shape errors in form of roundness or waviness of the rolling surface can be observed in form of numerous and small amplitude frequency peaks This effect is only measurable during the ball bearing’s assembly process or its disassembly. Ball bearings and other rotational systems generate rapidly changing vibrations in time and minor quantitative or qualitative changes in the dynamical response can be studied in short-time intervals. In this paper, it is used for the analysis of ball bearing’s nonlinear dynamics.
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