Geometrical optimization of an ultrasonic tactile plate

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Abstract

The Tactile plate consists of piezoceramics glued on a copper-beryllium resonator. Its purpose is to create programmable tactile sensations, which give the illusion of finely textured surfaces. The illusion originates from the variable friction between a finger and the vibrating resonator, caused by the squeeze film effect. In order to obtain a maximal deflection of the plate for a minimal supply voltage, an optimization is carried out of the length, thickness, and width of both the resonator and the ceramics. Constraints are realistic geometrical dimensions, a resonance frequency of at least 25 kHz, and a low supply voltage. The plate is modelled by both an analytical and a numerical model. The maximal dynamical deflection per volt was achieved with thin piezoceramics (0.5 mm) at the minimal frequency of 25 kHz. A high deflection can be obtained in a wide range of the resonator length. With increasing length, the optimal resonator thickness increases too. The plate width seems to have little influence. Experiments are carried out on two plates with different geometry.

Introduction

A tactile stimulator provides information to a user through the sense of touch. It can be used as a texture or shape simulator into an immersive virtual environment, or as an input–output tactile pad as those found on any new electronic hand-held device.

The stimulator described in this article is named “the tactile plate” as it uses a vibrating plate to produce tactile stimuli.The working principle of the tactile plate is based on the squeeze film effect: if the thin layer of air between the plate and the finger is compressed an expanded very rapidly by the vibration, then an overpressure is generated that tries to lift the finger. The squeeze film effect reduces the friction between the plate and the finger during the vibration of the plate. Several experimental studies have shown that it is possible to create tactile feedback with this operating principle. For example [1] modifies roughness perception of samples of sand papers, while [2] has shown that it is possible to give the illusion of touching finely textured surfaces with a programmable spatial period.

There exist several designs which produce tactile feedback based on friction reduction: [1] uses two langevin transducers to make a thin iron plate vibrate; [3] uses a disc shape ring resonator to reduce the size of the device. In [2], a rectangular copper plate with thin piezoelectric elements bonded on it was designed. This solution uses a standing wave with multiple wavelength propagating on top of the device. This design allows a large exploration area, with a small thickness and thus results in size reduction. However, in each case, squeeze film effect is effectual if the vibration amplitude is in the order of several micrometers at 25 kHz or above [4].

Optimization of the tactile plate is required in order to obtain a large vibration amplitude for a low supply voltage, without violating the several constraints. These constraints are (1) realistic dimensions of the plate; (2) resonance frequency above 25 kHz to have the squeeze film effect; (3) low supply voltage for safety reasons and for low power consumption to avoid heating of the plate. The optimization uses a 3D numerical model in combination with an analytical model to accelerate the computation.

After explaining these models in Section 2, we analyze the influence of several geometrical parameters in Section 3 in order to find some general design rules, similar to [5], [6], [7]. Next to geometrical parameters, also the issue of damping is discussed. Experiments are carried out for two geometries (Section 4). Finally, the conclusion summarizes which parameters are important to develop an efficient tactile plate.

Section snippets

Analytical model

The first model is an analytical model based on the one in [4]. It is recalled in the following paragraphs. Firstly, the static deflection is studied on a simply-supported beam (see Fig. 1) whose length is half of the wavelength λ. Secondly, the dynamic deflection is calculated. Thirdly, the resonance frequency is determined, and finally, the cost calculation is explained.

Resonator thickness and length of the piezoceramics

For all simulations and experiments, the resonator is made from a copper-beryllium alloy, and the ceramics are lead titanate zirconate ceramics type PI-91, manufactured by Saint-Gobain Quartz. The characteristics of the materials are given in Table 1. Additional properties of the ceramics can be found in [4]. As already mentioned, the voltage supply of the piezoceramics is set to 15 V in order to avoid dangerous voltages. For this section, the quality factor Q is chosen constant and equal to

Experiments

Two tactile plates were manufactured according to optimization’s results (Fig. 15). However, we could not be supplied with hi=0.673 mm, we have chosen hi=0.75 mm instead. We name these two plates P1 and P2, and they have the following characteristics respectively:

  • P1: hp=1.0 mm, hi=0.75 mm and λ=20.56 mm,

  • P2: hp=0.5 mm, hi=0.5 mm and λ=15.66 mm.

Dynamical deflection, resonance frequency , and the voltage necessary to reach 1.15μ m were measured. Results are presented in the following paragraphs.

Conclusion

This paper presents the optimization process of a tactile plate. Optimized plates require higher deflection for the same voltage level and a resonance frequency higher than 25 kHz to allow squeeze film effect. We obtained two optimized plates which were manufactured and characterized. The new designs present more transverse mode than on the original plate configuration, and a resonance frequency slightly lower than the optimization condition. However, more deflexion at lower voltage level is

Acknowledgment

This work was carried out within the framework of the INRIA Alcove project and is supported by the IRCICA (Institut de Recherche sur les Composants logiciels et matériels pour l’ Information et la Communication Avancée) and The European Commission (FEDER). Furthermore, this work was supported by the FWO project G.0082.06, by the GOA project BOF 07/GOA/006 and by the Interuniversity Attraction Poles (IAP) project P6/21. The first author is a postdoctoral researcher of the FWO.

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