Paul Gonnard

Nonlinear behavior of an ultrasonic transducer

A transducer model, based on nonlinear piezoelectric constitutive equations, has been developed to describe the harmonic generation that occurs on current or velocity signal analysis when the transducer is driven at high voltage. The symmetrical Langevin transducer studied close to its resonance frequency is composed of Navy III type power ceramics. The nonlinearities create an energy spread over the frequency spectrum and consequently result in an amplitude saturation effect at the driving frequency, which can be interpreted in terms of the loss mechanism. Experiments have been carried out to measure the nonlinear losses and the harmonic amplitude evolutions. Results are given and discussed. Eventually, by experimental means, identification of the influential nonlinear coefficients permits comparison between theoretical predictions and experimental results.

Modelling of a cantilever non-symmetric piezoelectric bimorph

The aim of this paper is the modelling of a non-symmetric bimorph constituted by a piezoelectric material deposited on an alumina substrate and used either as an actuator or a sensor. Theoretical modelling based on the flexural modes of the structure is carried out and the influence of the electrode characteristics (geometrical dimensions and elastic parameters) is introduced in the modelling for calculating the bimorph bending displacement. In actuator mode, the electrical admittance of the cantilever non-symmetric bimorph is stated and the intrinsic electromechanical coupling factor linked to the bimorph bending motion is deduced and compared with that defined in IEEE Standards. The analytical modelling was used for characterizing a cantilever bimorph constituted by a piezoelectric thick film deposited on an alumina substrate. A trial and error fitting method is described for determining the elastic, piezoelectric and dielectric constants of the piezoelectric material. The influence of the electrode parameters is calculated and the measurement uncertainty is deduced. In sensor mode the open voltage delivered by the bent piezoelectric layer and the electrical equivalent circuit of the bimorph are given. Theoretical results are compared with those obtained by the finite element method, and discussed.

Frequency behaviour and speed control of piezomotors

The rotational speed of a piezomotor is directly linked to the vibration velocity of its stator. Because some drifts of the stator characteristics lead to an unwanted variation of the motor speed, a control is necessary. This paper discusses the origins of drifts in travelling wave ultrasonic motors (TWUM). The typical behaviour of this kind of motor and its consequences on speed control are presented. While control is easily achieved when the applied torque is constant, variations of this quantity make more difficult to obtain an efficient method. Finally, the basic idea of this paper is to derive a general control method by using the absorbed current, which is the only always detectable quantity.

Investigation of factors affecting the preparation of PZT thick films

Many piezoelectric applications require materials with a thickness less than 100 μm. As the manufacturing of bulk ceramics of this thickness is not very easy, thick films were deposited by screen-printing on Ag–Pd-coated alumina substrates. Deposits were about 80 μm thick. Thick films were prepared from a PZT powder and an organic vehicle. The following studies on preparation of the layers were carried out: (1) influence of the powder preparation process (dry or wet route) upon the ink quality and piezoelectric characteristics of thick films; (2) part played by two different dispersing agents in the improvement of ink composition; and (3) flux addition as PbO–PbF2 and Bi2O3–B2O3–CdO, to lower sintering temperatures while maintaining good piezoelectric coefficients. A comparison of d31 and dh coefficients for bulk and thick films is given.

PZT and PT screen-printed thick films

Abstract Thick films (40–80 μm) of modified lead zirconate titanate (PZT) and lead titanate (PT) are screen-printed on alumina substrates electroded with Ag–Pd. First the influence of the powder grain size distribution on film characteristics after sintering is studied. With regard to the powder preparation, two processes are used: a mixed-oxide method and a wet coprecipitation process. Then thick films characteristics are compared with bulk ceramics ones. Two main factors explain the observed differences: residual porosity of the film and lateral clamping effect of the substrate. Other piezoelectric and elastic films coefficients are estimated from a plane wave model.

Nonlinearities in Langevin transducers

At frequencies close to resonance, Langevin transducers exhibit strong nonlinearities at low voltage levels. First, characteristic phenomena of a nonlinear behavior, such as the resonance frequency shift and the hysteresis effect, appear. Moreover, these nonlinearities result in an electrical and mechanical energy spreading over a discrete spectrum. Experimental results for current and tail mass displacement are given for power piezomaterial. They show a saturation of the fundamental amplitude due to the increase of the overtones amplitudes. To interpret these experimental results, a nonlinear oscillator model, based on nonlinear piezoelectric relationships, has been developed. A numerical solution of this nonlinear Langevin equation is given. Simulations and experimental results are in good agreement

Properties improvement of P.Z.T. ceramics with multiple substituents

The purpose of this paper is to define an elementary principle of multiple substitutions in the A site: the average cubic radius of the substituted ions is kept unchanged in order to avoid disturbance of the initial solid solution. Substitution of barym for lead is carried out on an initial composition Pb0.90Sr0.12(Zr0.56Ti0.44Sb0.02)O3(0.233). Measurements indicate a peak value of the planar coupling factor kp and of the figure of merit d233/e between 4 and 5% Ba.

Dopant distribution between A and B sites in PbZr0.95Ti0.05O3 ceramics of type ABO3

The influence of doping PbZr0.95Ti0.05O3 is studied. A theoretical model allows the doping ion distribution between A and B sites to be determined from their ionic radii. The tolerance factor t, calculated for each doped composition, has a minimum value when the AF property is at its maximum. The experimental results agree well with theoretical calculations.

Electromechanical conversion in an ultrasonic motor using a non-axisymmetric (1,1) mode

An ultrasonic motor using a non-axisymmetric (1,1) mode has been built in our laboratory. Such motors are based on a double energy conversion: the piezoelectric material in the stator converts electrical energy into mechanical vibrations; a rotor pressed on the vibrating stator moves due to the frictional force at the interface. These two conversions have been modelled by using electromechanical circuits derived from the Mason model. The mechanical performance of the whole motor has been experimentally determined. The losses which occur during the electromechanical conversion have been studied. Our work points out that they depend on the ratio between the inner radius and the outer radius of the annular ceramic plate used for the stator and the electromechanical characteristics of the chosen ceramic material. A criterion based on an electrical model is given in order to make a better choice between different PZT materials.

Modal control of beam flexural vibration

An active control system was developed to control the flexural vibrations of a beam with a modal filtering with only one secondary actuator. Segmented piezoelectric actuators and sensors were used for driving and sensing the bending beam vibrations. The primary actuator was fed by a broadband random disturbance signal in order to excite the first five modes of the structure. However, only the second to fifth modes were controlled. The control algorithm was implemented on a DSP board and the input and output signals were filtered using high order low pass filters. These filters, implemented on the DSP board avoid the degrading effect on the control performances of the higher order modes and which are not controlled. The modal filtering was achieved by computing. To this end, it is based on a previous identification procedure. This latter models, in one step, the dynamics of the structure and also the transfer function of the electronic circuits of the controller. The identified filtered modes were then used to compute the gain matrix using a LQR technique (linear quadratic regulator). Simulations of the active control were carried out and practical implementation of the control algorithms was performed. Experimental and simulation results were then compared and discussed.