Spectrum Estimation in Autocalibration of Ultrasonic Reflectometry Methods for Lubrication Film Thickness Measurements

Reliable and efficient mechatronic systems is the focus of a large number of engineers today. From this it follows that experimental techniques to study critical locations with respect to wear and energy dissipation, such as tribological contacts, are receiving much attention. A fundamental problem is that friction is not an intrinsic material property, but a system property, and this gap between real tribological systems and idealized laboratory test systems is a main research challenge in tribology today. An appealing approach to overcome this problem is the use of non-invasive experimental techniques. Ultrasound based techniques to study lubrication film thickness measurements is in this regard a tempting tool, however the calibration procedure for this technology can be challenging and the robustness of the calibration is limited in highly dynamic environments, such as fluid power pumping and motoring units. In this paper the fundamental linear regression of an autocalibration algorithm is presented, which generalize previous results, and show that the dot product of the incident and reflected wave spectrum vectors is proportional to the squared magnitude of the reflected wave spectrum. In consequence, the incident wave spectrum should in general be obtainable by use of linear adaptive filtering techniques.