384 G. Chevallier et al. Friction Interfaces F a c d b F F F p Fig. 41.1 Different kinds of benchmark. (a) Beam element screwed together with a single bolt. (b) Beam elements screwed together over the length. (c) New testing device proposed by Peyret et al. [5] and [6]. (d) Lap joint loaded with pure shear forces 41.2 Measurement Principle As it was said in the introduction, the testing device is a constituted with two beam assembled with bolts. In order to measure the contact-stress field over the interface, one of the parts is made with a piezoceramic PIC 255 provided by PI Piezoceramics. The other one is made of steel, see Fig. 41.2. 41.2.1 Geometry and physics The manufacturers of piezos are able to provide thin patches. Here, the width of our patches is equal to 2 mm. Moreover for thin structure, the whole structure has to be thin in order to study low frequency vibrations. Both parts are linked with three bolted joints to obtain a quite homogeneous contact stress field. The width of the sheet of steel is equal to 0.5 mm in order to be as conformable as possible. All the dimensions are summarized on Fig. 41.3. To simulate the behavior of the sensor, we used finite element computations. Firstly, the patches is simulated alone with a pressure applied on the contact area, see Fig. 41.3 right. The S33 stress are plotted on Fig. 41.4, the associated voltage is plotted on the left. However, it is not possible to obtain a stress field as detailed as the one of Fig. 41.3 because of the presence of an electrode on the surface of the patch. This electrode constrains the voltage to be homogeneous on all the surface, see Fig. 41.5. The electrode acts as a filter which averages the electrical potentials on the surface. Nevertheless, it is possible to have a good representation of the stress field by making an electrode shaping on the surface. For this, we cut the electrode area in smaller areas on which the electric potential is uniform, see Fig. 41.5 right. 41.2.2 Static Measurement The measurement of static deformations using piezoceramics is an engineering challenge. A piezo electric strain gauge is generating an electric charge proportional to the strain. This charge will dissipate in a relatively short period of time due to the electric resistance of the data acquisition electronic devices.Smart Material has developped an electronic device: the store & hold technique which transfers the generated charge to a high-end, leakage free capacitor, while the charge proportional voltage across the capacitance can be measured with a special designed high impedance operational amplifier. This guarantees constant output signals over up to 3 min without any significant drift (Figs. 41.6 and 41.7). 41.3 Vibrations To calculate the vibration damping, we first calculate the contact stress field. This calculation will be updated by the measurements of the voltage which are in progress in our laboratory. Then we will apply the displacement field of each modes, see Fig. 41.8, as a loading of the structures. Using the Masing rules, see [7], we will simulate the energy dissipated by friction in the contact surfaces under the normal stresses that we have previously determined.
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