In the present work, a method for the analysis of short time intervals in ball bearings is proposed. We study the effect of the internal clearance on the dynamics of ball bearings using recurrence plots and the recurrence quantification approach. In the proposed method, we focused on the analysis of dynamic states generated from the 2-DOF mathematical model, to which a function changing the damping coefficient in the clearance domain was added. Chosen recurrence methods showed the specific dynamic responses by different values of the radial clearance. The effect of self-consistency concerning the damping effect and vibration development is confirmed. The proposed method can be useful for the prediction of variable radial clearance in time by analysis of the acceleration response of ball bearing during its operation.
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.
This paper focuses on the influence of radial internal clearance on the dynamics of a rolling-element bearing. In the beginning, the 2—Degree of Freedom (DOF) model was studied, in which the clearance was treated as a bifurcation parameter. The derived nonlinear mathematical model is based on Hertzian contact theory and takes into consideration shape errors of rolling surfaces and eccentricity reflecting real operating conditions. The analysis showed characteristic dynamical behavior by specific clearance range, which reflects others in a low or high amplitude and can refer to the optimal clearance. The experimental validation was conducted with the use of a double row self-aligning ball bearing (SABB) NTN 2309SK in which the acceleration response was measured by various rotational velocities. The time series obtained from the mathematical model and the experiment were analyzed with the recurrence quantification analysis.
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