Study of Rayleigh waves interaction with a spherical ball in contact with a plane surface for the development of new NDT method for ball bearings

The monitoring of the integrity of the spherical balls inside a ball bearing can be challenging, as it needs to be disassembled in order to access every element of the structure. In this paper, an ultrasonic method is used to directly interrogate the spherical solids. The interaction wave-solid lets us extract material related information. The complex geometry of the ball bearing is simplified to a repetitive assembly of an elementary unit of a solid sphere setting on a plane surface. Understanding of the interaction between the ultrasonic wave and this elementary block is the key to a more general comprehension of the interaction with the complete ball bearing. To achieve this, the interaction between a Rayleigh Surface Acoustic Waves (SAWs) propagating on a plane and a spherical solid ball setting on that plane is studied, numerically and experimentally. In the experimental configuration, a steel ball is fixed to an aluminum block. Shear wave contact transducers are used to generate SAWs, while a laser vibrometer is employed to precisely measure the ensuing displacements. Subsequently, the collected time series data is carefully visualized and analyzed to discern distinct waves, such as the Rayleigh wave on the block, SAW on the sphere, and the waves generated by the sphere. To complement these experimental findings, a numerical model is created using finite element analysis, faithfully reproducing the experimental conditions. This approach facilitates a comprehensive examination of the displacement field, both on the surface of the sphere and the aluminum block. The extraction of the material related information of the spherical ball is based on the estimation of the resonance frequency of each vibrational mode of the solid sphere. Furthermore, 3D Gabor and dispersion curves from the spatio-temporal signals are used to estimate and analyze these frequencies and to compare the different waves involved in the interaction: the direct Rayleigh waves, the back-generated waves and the waves propagating on the surface of the sphere. The findings demonstrate that the transmitted waves toward the block (back-generated wave) preserve the waveform of the SAW propagating on the sphere, enabling the deduction of the dispersive behavior and extraction of material properties, such as the Rayleigh wave group velocity. The implications of this study are particularly relevant for non-destructive testing and evaluation (NDTE) of ball bearings, as the research provides insights into characterizing their integrity without disassembling them. The ability to extract material information from signals measured at the outer ring of ball bearings holds promise for practical applications in assessing their condition.