Research of rotary piezotable driven by two harmonic signals

I. Grybas*, A. Bubulis**, R. Bansevičius***, V. Jūrėnas**** *Kaunas University of Technology, Kęstučio 27, 44025 Kaunas, Lithuania, E-mail: ignas.grybas@ktu.lt **Kaunas University of Technology, Kęstučio 27, 44025 Kaunas, Lithuania, E-mail: algimantas.bubulis@ktu.lt ***Kaunas University of Technology, Kęstučio 27, 44025 Kaunas, Lithuania, E-mail: ramutis.bansevicius@ktu.lt ****Kaunas University of Technology, Kęstučio 27, 44025 Kaunas, Lithuania, E-mail: vytautas.jurenas@ktu.lt


Introduction
Rotary piezoelectric stages and motors exploiting ultrasonic vibrations are found in many mechatronical applications including positioning, metrology, manufacturing process control, pick-and-place assembly, consumer electronics, medicine, aerospace systems, etc [1][2][3][4][5].This tendency is governed by such prevalent benefits over conventional electromagnetic actuators as high precision and accuracy, compactness, high torque output at low speed, simple structure, nearly zero noise level, insensitivity to magnetic field and high efficiency [1,[6][7][8].Despite piezopositioning stages mostly make use of standing and/or travelling waves there is a very limited amount of information about rotational oscillations and their positive impacts.

System construction and operation principle
Schematic construction of the system to be analysed is given in Fig. 1, while relevant operation principle is explained in the subsequent text.
This table structure contains rotor 1 contacting with ring shaped piezoelement 3 via five frictional elements 2 (three units) and 5 (two units), what ensures precise positioning of the rotor with respect to its axis of rotation.When rotational motion takes place these five supporting points become vibroactive, and this significantly reduces resisting moment of friction forces.Ring-shaped piezoelectric transducer is composed of two groups of con-trol electrodes, with one group inducing rotation of the rotor, while the other initiates motion of opposite direction under operational regime voltage supply.
In order to excite specific rotational type oscillations within the rotor two harmonic signals (U1 and U2) of different frequency and amplitude are supplied to both groups of control electrodes.Signal expressions are presented in Eqs. ( 1) and (2) [9]: . In the presence of such conditions the moving member (i.e.rotor) performs a periodic motion, which is defined by the following law [9]: is the maximal amplitude and t is time of rotational type vibrations.
In this case harmonic oscillations are excited in frequency range from 0 Hz at

Experimental setup and investigation
A prototype of the piezotable researched has the piezoelectric ring-shaped transducer, in which the alternating strain is excited by an AC electrical field, preferably operating at the mechanical resonance frequency.In order to determine the resonance frequency of the designed piezoelectric ring-shaped transducer, an impedance analyzer Wayne Kerr 6500B (Fig. 2) is used to measure the impedance characteristics of the prototype, and the measurement plot of electric impedance within the measured frequencies is shown in Fig. 4.
So as to measure the dynamic characteristics of the piezotable, an experimental setup, which includes two function generators and high voltage amplifiers, the laser Doppler interferometer, vibrometer, oscilloscope and PC, was used.A simplified structural scheme can be seen in Fig. 3, a and its actual components are shown in Fig. 3, b.A prototype of the piezotable was built and tested.In order to determine the operational AC frequency of the researched piezotable the measurement plot of electric impedance and phase of the ring-shaped piezoelectric transducer within the measured frequencies is shown in Fig. 4.
By observing the measured impedance vs. frequency characteristic, shown in Fig. 4, there are three resonant frequencies (around 44 kHz, 92 kHz and 132 kHz) at which the impedance reaches The operation frequency of the piezotable is 44.1 kHz, and it was determined experimentally.
However, it should be noted that rotary piezotable can also operate in a slightly wider frequency range, which is determined by width of the characteristic impedance curve in the peak zone.
Two oscillation regimes of investigated piezotable rotor were obtained with one of them exhibiting maximal vibration amplitudes (0.2 rad) and another one featured by minimal vibration amplitudes (~10 µrad).Respective plots are given in Figs. 5 and 6.In each case rotating motion of the rotor is absent, i.e. rotor just vibrates rotationally forth and back.Two harmonic signals (U1 and U2) of different frequencies and equal amplitudes are supplied to both groups of control electrodes.On the contrary, a possibility to combine rotational motion with rotational oscillations of the rotor is presented in Fig. 7.It has to be pointed that the latter opportunity implementation is only feasible, if two harmonic excitation frequencies are not the same and their voltage amplitudes are different (i.e.f1 ≠ f2, U1 ≠ ≠U2).Furthermore, although measured rotor angular speed was 3.5 µrad/s, it can be increased/decreased by setting higher/ lower values of voltage amplitudes.Emphasis should also be placed on capability of bidirectional rotational motion in this case too.Despite this characteristic is not shown in the paper it will definitely be discussed more in details in future work.

Conclusions
Developed piezoelectric rotary table driven by two harmonic signals was discussed and analysed in this article.The following conclusions are formed.
1.A new design and operation principle of the rotary piezotable was described.
2. Experimental setup for determination of rotary piezotable resonant frequencies and investigation of major dynamic characteristics was presented.
4. Specific regime combining ordinary rotational motion with rotational oscillations was demonstrated to be possible (rotor angular speed 3.5 µrad/s).