Abstract—Previously proposed models of the ultrasonic lubrication of a finger mediated by flat surfaces are not consistent with the experimental results for vibrational amplitudes greater than a few microns. This paper presents experimental data acquired through a dedicated tribometer and proposes an experimental model of ultrasonic lubrication at high vibrational amplitudes. I. INTRODUCTION The last few years have seen the emergence of ubiquitous mobile devices and tactile interfaces. The abundance of these novel interfaces raised the interest in touch based human- machine interactions and the lack of natural touch feedback. The problem was partly responsible for the slow adoption of the technology among consumers. Currently, multiple solutions are being explored to deliver improved haptic feedback on existing mobile platforms such as smartphones or tablets; one such feedback technology, vibrotactile stimulation, is already incorporated on most platforms but provides only a general vibration sensation to the hand and finger of users [1]. To improve upon this, tactile based solutions have been proposed in recent years such as electrovibration [2] and Ultrasonic Lubrication (UL) [3] [4]. The physics underlying electrovibration is well understood [5], but it is not the case for UL mediated by a flat surface. It has been proposed that this technology is able to reduce the perceived coefficient of friction of the user by creating a thin film of air between the finger and plate. The first attempts of modeling haptic UL were made by Watanabe and Fukui in a paper describing the potential usefulness of friction reduction for haptic rendering [6]. The proposed model, which was derived from the Reynolds equations, is based on the squeeze film effect and is thought to be the main contributor to the reduction of friction between a finger and a flat surface. Since the finger parameters (such as rigidity, roughness and humidity) can be extremely variable between subjects, it is difficult to estimate the actual area of contact between the fingerprint and the surface. This makes any calculation of the squeeze force subject to many simplifications. Moreover, an * This work was funded by the European Union under the FP7 programs FP7-PEOPLE-317100 PROTOTOUCH. T. Sednaoui and C. Chappaz are with L2EP-IRCICA and STMicroelectronics, Crolles F38920, France (e-mail: thomas.sednaoui@st.com, cedrick.chappaz@st.com). E. Vezzoli and B. Lemaire-Semail are with L2EP-IRCICA Laboratory, University of Lille 1, Lille, France, 59650 (phone: +33 362531632; e-mail: eric.vezzoli@ed.univ-lille1.fr, betty.semail@polytech-lille.fr). B. Dzidek and M. Adams are with school of chemical engineering, University of Birmingham, Edgbasto, B152TT, United Kingdom (e-mail: b.m.dzidek@bham.ac.uk, m.j.adams@bham.ac.uk). exhaustive measurement of finger UL has not been conducted in order to validate the proposed model across a range of users and usage parameters. The current paper demonstrates that the measured friction reduction between a finger pad and a flat surface subjected to ultrasonic vibration does not behave as predicted by the squeeze film effect only. Specifically, the friction reduction phenomenon approaches a lower limit with increasing amplitude of vibration, which is not predicted by the squeeze film model. Moreover, the lower limit corresponds to a coefficient of friction that is too large for persistent acoustic levitation. An experimental model from the measurements is proposed in order to simplify the design of future tactile stimulators. II. SQUEEZE FILM MODEL This section describes succinctly the analytic model of acoustic levitation usually applied to haptic feedback through the squeeze film effect. As previously theorized in [6] and [7], the vibration of a surface under a finger pad of a user generates an ultra-thin film of air (air gap) in the contact region. Figure 1 shows a simplified geometry of the film of air. The film is subject to compression and rarefaction at high frequencies corresponding to the relative displacement of the surfaces. Figure 1: Approximation of the finger pad ridges. The ridges of the finger pad are approximated by a cosine function and are considered to be rigid, or at least extremely stiff, at these frequencies. With ℎ  being the amplitude of vibration and ℎ ௥ the surface roughness, the thickness of the film can then be expressed by: ℎሺݐ,ݔሻ =ℎ ௥ +ℎ  [ͳ + cosሺݐሻ] + ℎ ௘ [ͳ + cos ( ߨʹ  ݔ)] ( 1 ) where the pulsation of the vibrating plate is given by . The relationship between the thickness, h , of the air-gap and the pressure, p, can be described by the Reynolds equations [16]: Experimental Evaluation of Friction Reduction in Ultrasonic Devices Thomas Sednaoui, Eric Vezzoli, Brigida Dzidek, Betty Lemaire-Semail, Member, IEEE, Cedrick Chappaz, and Michael Adams