Exact analytical solution to ultrasonic interfacial reflection enabling optimal oil film thickness measurement

Abstract

The ultrasonic reflection from a lubricated interface has been widely analyzed to measure fluid film thickness, with different algorithms being applied to overcome measurement accuracy and resolution issues. Existing algorithms use either the amplitude or the phase angle of the ultrasonic interfacial reflection. In this paper, a new algorithm (named the “exact model – complex”) that simultaneously utilizes both the amplitude and the phase of the complex ultrasonic reflection coefficient is proposed and mathematically derived. General procedures for theoretical analysis in terms of measurement accuracy and uncertainty are proposed and applied to the new algorithm, the beneficial features of which (as compared to other existing algorithms) can be summarized as: 1) a direct calculation, instead of an iterative approximation, 2) guaranteed maximum measurement accuracy, and 3) acceptable measurement uncertainty. None of the existing methods have showed this combination of benefits. Moreover, two groups of raw data from previous experimental studies are utilized to further validate the practical feasibility of the new algorithm. Overall, the proposed “exact model – complex” algorithm fully exploits the potential of ultrasonic reflection for oil film thickness measurement, with an accurate and a convenient calculation suited to practical implementation.