Ultrasonic measurement of lubricating film thickness with oblique incident waves facing on tapered roller bearings

Tapered roller bearings serve as the core components of wind turbines. To improve their reliability, the in-situ measurement of lubricating film thicknesses, serving as the most direct indicator of lubrication failure, is necessary. Ultrasonic-based methods are suitable for this purpose due to its strong penetration. However, current methods rely on the principle of vertical reflection of ultrasound. For oblique incident waves, the reflection mechanism remains unclear. This paper focuses on the propagation of oblique incident ultrasound that enables a wide-range measurement of lubricating film thickness under oblique conditions. Firstly, the propagation model of oblique incident waves is established by investigating the properties of the oblique incidence. Next, the analytical formula of the reflection coefficient is deduced from the wave superposition principle. Based on this, the complex model and resonance model are constructed for oblique incidence, by which wide-range film thicknesses can be computed. Furthermore, a finite element simulation is carried out to validate the accuracy of the proposed two methods. For the complex model, compared with the classical vertical-incidence method, the results show a low error below 1% within 0°-50° incident angles whereas for the vertical-incidence method the errors increase positively with incident angles and reach 5% when the incident angle exceeds 15°. Moreover, for the proposed resonance model, the method maintains errors less than 2.5%. Finally, linearity calibration experiments are carried out and reveal that the resonance model represents a higher robustness to noise and the complex model exhibits a decreasing uncertainty with thinner films.