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The quantification of the spall zone size remains the significant challenging area in health monitoring of rolling element bearings (REBs). Size estimation for the spall zone of a rolling element bearing (REB) is playing a crucial role in bearing performance degradation assessments, damage severity evaluation and remaining useful life prediction. The conventional algorithms of spall zone size estimation are focused on establishing a robust signal processing technique to measure the width of the spall zone based on the analysis of vibrations. In this paper, a new analytical model is proposed for size estimation of the spall zone located on the outer race of a REB. An investigation into the kinematic mechanism of the passing process of the rolling element over the spall zone is carried out, the excitation mechanism of the entry and exit responses excited by a spall located on the REB outer race is studied and the contact models of rolling element-spall interaction are presented in this paper. The dual-impulse time separation (DTS) is determined from the pre-whitened vibration signal. As a result, a spall zone size estimation model which is a function of the DTS and the relationship of rolling element-spall zone interaction is developed based on the Hertzian contact theory. Experiments for four sizes of seeded spall are carried out to validate the proposed model for quantitatively estimating the spall zone size. All of the results which are given by the proposed analytical model present a good agreement with the real size of the spall width of the REB. Comparison between the estimated values of spall zone size calculated from the proposed model and the actual spall zone sizes of the rolling element bearing shows that the proposed model of spall zone size estimation is effective in quantifying the size of the bearing spall.

The dual-impulse behavior, which is produced by the spall located on the surface of the bearing raceway, is closely related to the size of the spall zone. This allows to establish an accurate mechanism of quantitative fault diagnosis and spall size estimation. However, dynamic model of dual-impulse behavior, which couples the nonlinear excitation force and the impact force induced by the interaction between the rolling element and the spall zone, have not been proposed before, especially under the elastohydrodynamic lubrication (EHL) condition. To address this issue, the corresponding dual-impulse excitation mechanism is investigated and explained, and the force produced by the collision of the rolling element with the trailing edge of the spall zone is derived. A coupled nonlinear dynamic model of the rolling element bearing (REB) with a spall on the inner race is proposed in this paper, in which the displacement and excitation force originating from the passing process of the rolling element over the spall zone are modeled as a piecewise function. The transient collision force excited by the strike of the rolling element on the trailing edge of the spall area is introduced, and the contact between the rolling elements and both the bearing races under EHL condition is modeled. To validate the proposed model, the dual-impulse time spacing (DITS) is analysed, and the vibration responses and its corresponding envelope spectra under simulation and experimental conditions are studied theoretically and experimentally. The simulated results agree well with the experimental results.

The Einstein–Podolsky–Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of a local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of “quantum nonlocality,” which manifests itself in three types: quantum entanglement, quantum steering, and Bell’s nonlocality. Although Bell’s nonlocality is more often used to show “quantum nonlocality,” the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality, thus making it amenable to experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is friendlier for experimental implementation, i.e., one may measure the observables only in the x , y , or z axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.