The experimental research of piezoelectric actuator with two vectors of polarization direction/Eksperimentinis dviem kryptimis poliarizuoto pjezoelektrinio keitiklio tyrimas.

Lucinskis, R. ; Mazeika, D. ; Hemsel, T. 等

1. Introduction

One of the trends of mechatronics system development is reducing the size of the systems. This feature can be achieved by employing multi-degree of freedom (multi-DOF) piezoelectric actuators [1-7]. Development of multi-DOF actuator is complex engineering problem. Usually two design principles are used to build this type of actuator i.e. complex design of the oscillator is used or specific electrode pattern of piezoelectric transducer is applied. Authors introduce another way to build a multi-DOF actuator that is to use transducer with two vectors of polarization and appropriate pattern of electrodes respectively [1, 7, 8]. Independent oscillations of contact point in three directions can be achieved applying different control schemes of the electrodes.

Several multi-DOF piezoelectric motors are developed till now as well as actuators that have different design and operating principles [6-16]. One of the most frequently used principles is based on superposition of longitudinal and flexural oscillations of a beam. This paper presents study of beam type piezoelectric actuator with two perpendicular vectors of polarization. Applying different excitation schemes of the actuator, 3-DOF movement of the positioned object can be achieved.

2. Design of piezoelectric actuator

Introduced beam type piezoelectric is build so that one half of the actuator is polarized towards Ox axis while another half is polarized towards Oy axis (Fig. 1, a) [8]. It means that vectors of polarization are perpendicular. The electrodes of each half of the actuator are divided into two sections: one section of the electrode is seamless and designed for excitation of longitudinal oscillations while the other section is divided into two equal units along actuator's axis and is used for excitation of the flexural oscillations. The length of the seamless section is equal to 1/6 of piezoactuator length whereas the length of divided section is equal to 1/3 of piezoactuator length. The excited and grounded electrodes are divided symmetrically.

In order to excite flexural oscillations in desirable plane one of the sections of divided electrodes and both seamless electrodes are excited. For example oscillations in yOz plane are achieved when electrode No. 1, No. 5 and No. 6 (Fig. 1, b) are excited. Different phase of oscillation is obtained depending on the selected electrode (No. 1 or No. 2). This type of electrode excitation allows achieving reverse motion of the elliptical motion. The similar principle is used to excite flexural oscillation in xOz plane (Fig. 1, c). To perform rotational movement of the slider the electrodes No. 1, No. 3, No. 5 and No. 6 are excited (Fig. 1, d). 3-DOF movements of the slider can be achieved combining different electrodes into various excitation schemes.

[FIGURE 1 OMITTED]

3. Numerical modeling with FEM

ANSYS v.11 software was used for numerical modeling and simulation. Finite element model (FEM) was made of SOLID5 finite elements [17]. It was assumed in the model that piezoactuator is monolithic and has ideal polarization. The SP6 piezoceramics was used for the modeling. The following dimensions of piezoactuator model were used b = h = 4.6 mm and L = 46 mm (Fig. 1). No mechanical constrains were applied in the model. Electrodes were created by grouping surface nodes of the FEM model and harmonic voltage of excitation U = 100 V was applied. The grounding voltage was set to 0 V.

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The two excitation cases were used for numerical simulation and experimental study (Fig. 2, a, b). 1st case of excitation: the electrode No.1 is excited and oscillations in the xOz plane are expected. 2nd case of excitation is when the electrode No. 3 is excited and oscillations in the yOz plane are expected.

Modal shapes and resonant frequencies of the actuator were calculated. Harmonic response analysis of the actuator was done when the excitation frequency has range from 0 kHz to 100 kHz with 100 Hz frequency step. The 1st scheme was used for excitation (Fig. 1, b). The oscillations of the piezoactuator contact point were analyzed. It has elliptical type trajectory during one period of the oscillation.

[FIGURE 3 OMITTED]

Fig. 3 shows the dependence of the length of major and minor semiaxes of elliptical motion of the actuator contact point from the excitation frequency. Peaks can be noticed in the graphs where the first three peaks represent 1st, 2nd and 3rd flexural modes and the fourth peak corresponds to 1st longitudinal resonance oscillations.

The detailed list of resonance frequencies and corresponding modes of oscillation is given in Table 1. Oscillation trajectories of contact point will be analyzed in more detail when 2nd and 3rd flexural and 1st longitudinal resonance frequencies are applied to electrodes of the actuator.

Trajectories of contact point movement are presented in Fig. 4 and Fig. 5 when the actuator is excited applying 1st and 2nd schemes at 2nd flexural resonance frequency. Major axis of elliptical trajectory of the contact point is parallel to x and y axis when 1st and 2nd excitation point is parallel to x and y axis when 1st and 2nd excitation schemes are used respectively. By observing these two ellipses it can be noticed that the trajectory presented in Fig. 5 has larger z direction component. This can be explained in the way that when scheme No.1 is used the contact point is in a distance of 2/3 actuator length from the excited electrode meanwhile when 2nd excitation scheme is used, the contact point is next to the electrode. Different component of z axis is obtained because of different location of contact point to the electrode.

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Oscillation trajectories of the contact point obtained at the excitation frequency equal to 35400 Hz are given in Figs. 6 and 7 when the 1st and 2nd excitation schemes are used respectively. Analyzing both ellipses it can be seen that projections of the major semiaxis to xOy plane are similar as were in the case when excitation frequency at 2nd flexural mode was used. The projections reach the angle of approximately 90[degrees]. However, there is an important note that the 3rd flexural mode is close to the 1st longitudinal mode. Therefore the major semiaxes of given trajectories have larger components in the direction of z-axis that represent direction of longitudinal oscillations of the actuator.

[FIGURE 6 OMITTED]

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Frequency of the 3rd flexural mode does not coincide exactly with the 1st longitudinal mode as it can be seen from Table 1. So trajectories of contact point motion when excitation frequency is equal to the frequency of the 1st mode of longitudinal oscillation were calculated. The 1st and 2nd excitation schemes were used as in previous cases. Results of calculations are given in Figs. 8 and 9.

[FIGURE 8 OMITTED]

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It can be seen that length of major axes of the ellipses are different because of different excitation schemes. When the electrode is located closer to the contact point (1st scheme) when larger longitudinal vibration amplitude is achieved.

4. Experimental investigation of piezoelectric actuator

Prototype piezoelectric actuator was made for the experimental investigation (Fig. 10). The same excitation schemes were used as in numerical simulation.

The sections of electrodes were created by burning off a silver layer with electric arc. Formation procedure of the electrodes was local and did not change temperature of actuator bulk. So it was assumed that it did not change the quality of piezoelectric material. Special complex measurement stand has been developed for experimental investigation.

[FIGURE 10 OMITTED]

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The principle scheme and photo of the experimental stand is shown in Fig. 11. The actuator was put on the foam and oscillations were measured. It was assumed that soft but not viscous layer of the foam will not make influence to the measured oscillations of the actuator.

Generator (Wavetek 395) was used to generate harmonic electrical signal and amplified using amplifier (Bruel&Kjaer 2713). Signal from the amplifier is transferred to the electrodes of the actuator and to an oscilloscope (Yokogawa DL716) as well. This input is needed for the calculation of phase change between the excited and measured signals of oscillations. Oscillations of the actuator contact point are measured by a laser vibrometer (Polytec CLV-3D). Forthcoming and processed signal is sent to a controller (Polytec CLV-3000) which decodes the signal to the oscillation speed component [v.sub.x], [v.sub.y] and [v.sub.z] and transfer forthcoming signal to the oscilloscope. The data transferred to the oscilloscope is written and saved for the next step of measurement.

First of all admittance of the actuator has been measured in order to find resonance frequencies. Impedance analyzer (HP 4192A) was employed for the measurement. Fig. 12 shows results of the measured and calculated impedance. By comparing these graphs it can be noticed that measurement result and the results from numerical simulation have good agreement.

[FIGURE 12 OMITTED]

Measured frequencies at the peaks of admittance values mostly coincide with the calculated resonance frequencies. The calculated and measured admittance values have small differences but do not exceed 10%. The comprehensive results of the measured impedance data are shown in Table 2 and Figs. 13-15.

By comparing data presented in the Table 1 and Table 2 it can be noticed that measured frequencies are lower than calculated. The biggest difference between the results did not exceed the error of 6%.

[FIGURE 13 OMITTED]

Figs. 12-14 demonstrate the impedance peaks at the frequency close to 1st, 2nd and 3rd flexural modes respectively. Two peaks can be seen in each figure. These peaks represent symmetrical modes of flexural oscillations in two perpendicular directions. From Figs. 12-14 it can be seen that difference between two symmetrical resonant frequencies increases when the mode number of flexural oscillations increases as well. For example difference between the resonances at 2nd flexural mode is approximately equal to 300 Hz while the difference at the 3rd flexural mode is equal to 400 Hz.

[FIGURE 14 OMITTED]

Measurement of contact point trajectories were done in order to compare it with the trajectories calculated in numerical modeling. All the measurements were done by exciting the actuator with the same excitation voltage 100 V and using the same excitation schemes as was done in numerical simulation. Linear speed components [v.sub.x], [v.sub.y] and [v.sub.z] of the contact point were measured with laser vibrometer. Speed values were coded by the voltage amplitudes at the controller output.

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The accuracy of 25 mm/s/V was used during the measurements. The coordinates of the contact point were calculated from the given data. Measured trajectories are shown in Figs. 16-21 where each curve is composed of 1000 measured points.

Figs. 16, 17 show the trajectories when 1st and 2nd excitation schemes are applied at the frequency equal to the 2nd flexural mode. The excitation frequency was set to 18.7 kHz. It can be noticed that parameters of the ellipses differ because of different excitation schemes. Comparing results from numerical modeling (Figs. 4, 5) and experimental investigation it can be seen that they slightly differ because off the influence of two symmetrical flexural modes into measured vibrations of the contact point.

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

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Figs. 18 and 19 show measured elliptical trajectories of the contact point, when excitation frequency is close to 3rd flexural mode was used. This frequency closed to 1st longitudinal mode as well, so vibration components into z axis are bigger than in previous cases. It can be seen; parameters of the ellipses in Figs. 18 and 19 weakly depend on excitation schemes. This can be explained as damping influence of the foam on oscillations of the actuator.

[FIGURE 20 OMITTED]

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The last measurement was done when the excitation frequency 35.5 kHz was used. This frequency is very close to 1st longitudinal resonance, so in this case longitudinal component of the oscillation is considerably larger than others and the contact point moves towards a very spiky elliptical trajectory (Figs. 20 and 21).

5. Conclusion

Numerical and experimental investigation of the piezoelectric actuator with two polarization vectors confirm that elliptical trajectory of motion can be achieved in two perpendicular directions. Parameters and direction of elliptical motion of contact point can be controlled when different excitation schemes are applied. Results of numerical and experimental investigation are in good agreement.

Experimental investigation highlighted the problems with symmetrical flexural modes in the analyzed piezoelectric actuator that had square cross-sectional area. It was clarified that small changes in excitation frequency make considerable influence on orientation and parameters of elliptical motion of the contact point. So in order to obtain more stable trajectory it is recommended to use beam with non square cross-section.

Acknowledgement

This work has been supported by Lithuanian State Science and Studies Foundation, Project No. B-07017, "PiezoAdapt", Contract No. K-B16/2009-1.

Received December 29, 2009 Accepted March 25, 2010

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R. Lucinskis *, D. Mazeika **, T. Hemsel ***, R. Bansevicius ****

* Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: Raimundas.Lucinskis@fm.vgtu.lt

** Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: Dalius.Mazeika@fm.vgtu.lt

*** Paderborn University, Furstenallee 11, 33102 Paderborn, Germany, E-mail: Tobias.Hemsel@uni-paderborn.de

**** Kaunas University of Technology, Kestucio 27, 44312 Kaunas, Lithuania, E-mail: Ramutis.Bansevicius@ktu.lt

Table 1

Oscillation modes of the piezoelectric actuator

Mode type           Frequency, Hz

1st flexural             7400
2nd flexural            19300
3rd flexural            35400
1st longitudinal        36800
1st lexural             54200
2nd longitudinal        73400

Table 2

Measured resonance frequencies of the actuator

Mode               Frequency, Hz

1st flexural            7050
2nd flexural           18650
3rd flexural           33300
1st longitudinal       35900
2nd longitudinal       73500