Dynamic control of the resonant frequency of ultrasonic transducer

Accepted Manuscript Title: Dynamic control of the resonant frequency of ultrasonic transducer Author: Hiroki Yokozawa PII: DOI: Reference:

S0924-4247(16)30861-5 http://dx.doi.org/doi:10.1016/j.sna.2017.04.052 SNA 10108

To appear in:

Sensors and Actuators A

Authors: Jens Twiefel, Michael Weinstein PII: DOI: Reference:

S0924-4247(16)30861-5 http://dx.doi.org/doi:10.1016/j.sna.2017.04.052 SNA 10108

To appear in:

Sensors and Actuators A

Authors: Hiroshi Hosaka, Takeshi Morita PII: DOI: Reference:

S0924-4247(16)30861-5 http://dx.doi.org/doi:10.1016/j.sna.2017.04.052 SNA 10108

To appear in:

Sensors and Actuators A

Received date: Revised date: Accepted date:

4-11-2016 3-4-2017 30-4-2017

Please cite this article as: Hiroshi Hosaka, Takeshi Morita, Dynamic control of the resonant frequency of ultrasonic transducer, Sensors and Actuators: A Physicalhttp://dx.doi.org/10.1016/j.sna.2017.04.052 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights     

Resonant frequency control during operation is attempted. Passive piezoelectric materials are inserted to the transducer Stiffness of passive piezoelectric materials is varied by electric boundary condition The electric boundary condition is controlled by using FET switch. The resonant frequency was modified from 30.42 to 30.55 kHz dynamically.

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Dynamic control of the resonant frequency of ultrasonic transducer Hiroki YOKOZAWA,1* Jens TWIEFEL,2) Michael WEINSTEIN,2) Hiroshi HOSAKA1) and Takeshi MORITA1)

Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, 277-8563, Japan 2 Institute of Dynamics and Vibration Research, Leibniz University of Hannover, 30167, Hannover, Germany * Corresponding author, [email protected]

This letter proposes a method for dynamic control of the resonant frequency of an ultrasonic transducer. A high-power ultrasonic transducer is often operated at its resonant frequency for efficiency. In particular, ultrasonic motors often require that the resonant frequency ratio be controlled between specific vibration modes or mode numbers. For example, typical standing wave type ultrasonic motors require synchronization between the resonant frequency of two vibration modes, such as longitudinal and bending modes. In other cases, such as resonant-type smooth impact drive mechanisms, actuators are driven by a saw-shaped displacement excited by the superposition of two longitudinal resonant vibrations whose ratio is controlled to be 1:2. In these transducers, the resonant frequency is controlled through careful design of structure and material properties. However, even if the transducer is well-designed, its resonant frequencies can shift due to nonlinear effects during high-power operation. To compensate for such shift during driving, dynamic resonant frequency control is necessary. In the present study, a transducer was developed using two piezoelectric element components; active and passive components. Generally, the stiffness of the piezoelectric materials can be varied by controlling their electric boundary condition owing to their piezoelectric effect. To achieve this, a field-effect transistor (FET) switch was connected to the passive piezoelectric elements. As expected, the resonant frequency of the transducer could be controlled by varying the switching duty ratio during operation.

Keywords: Resonant frequency control during operation; FET switching; passive piezoelectric parts

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Efficient operation of high-power ultrasonic transducers often requires to control the resonant frequency ratio between specific vibration modes or mode numbers.[1,2] For example, typical ultrasonic motors are driven by transducers that combine two vibration modes, such as longitudinal and bending modes.[3,4] For these devices, the resonant frequency of the vibration modes must be synchronized. Other devices, such as resonant-type smooth impact drive mechanism actuators [5,6], utilize a saw shaped displacement excited by two longitudinal resonant vibrations whose frequency ratio is 1:2. To obtain high performance in such ultrasonic motors, the resonant frequency has to be controlled precisely by careful design of mechanical structure and material properties. However, even if the transducer is well-designed, the resonant frequency can change due to nonlinear effects during its high-power operation. [7-9] The resonant frequency can also shift due to variations in the boundary condition such as the preload on the ultrasonic motor or the temperature influence. To compensate for such shifts, dynamic resonant frequency control during operation is required. Kim and Chubachi [10] proposed a static resonant frequency control method for a Langevin transducer, which excited longitudinal vibration by connecting inductors to passive piezoelectric parts as shown in the left of Fig. 1. Inductor changed the electric boundary condition for the passive piezoelectric elements, and acted as an equivalent mass. As a result, the mechanical resonant frequency could be reduced as indicated. Although, it is impossible to realize the dynamic control using this method, and the electrical energy loss due to the resistance of the inductor element is also a problem.

The present study followed the method of Kim and Chubachi of controlling the electric boundary condition for the passive piezoelectric elements in the transducer. The fabricated transducer used here, shown in Fig. 2, had a total length of 70 mm and a diameter of 15 mm. The driving lead zirconate titanate (PZT) element was located at the center, and the passive PZT elements were 17.5 mm away from the center. The former was composed of four hard-type PZT rings (C203, FujiCeramics, thickness: 1.5 mm, outer diameter: 15 mm, inner diameter: 8 mm), and the latter were composed of two rings for each position. The polarization of the PZT rings was along the thickness direction in order to excite the longitudinal vibration mode. These PZT rings were bolt-clamped with two duralumin rods with lengths of 17.5 and 11.5 mm.

To realize dynamic and precise control, this study examined the electric boundary condition control using an FET switch, instead of the inductors. Turning the FET on and off changes the stiffness of the passive piezoelectric elements due to the piezoelectric effect. Generally, the stiffness is In contrast, this stiffness increases to

when the piezoelectric material has shortened electric boundary condition.

when the electric boundary condition is opened. Using this phenomenon, the

resonant frequency of the transducer can be controlled by turning the FET on and off. To achieve precise control, the switching frequency was set to frequency of the driving voltage, and the duty ratio between switching on and off states was

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varied. For example, when the switching duty ratio has a low value such as 20 %, the passive piezoelectric elements spend a long time in an open-condition, which corresponds to a mechanically hard condition (the stiffness value is close to

). As a

result, the transducer has a high resonant frequency. The resonant frequency can be reduced by increasing the duty ratio, because in this situation the time spent in an electrically shortened becomes longer and the stiffness approaches

. By

controlling the duty switching ratio, the resonant frequency can be modified accurately and continuously. To confirm this principle, a circuit simulator (LT spice IV) was utilized. As shown in Fig. 3, a general LCR circuit was modified to include an additional electrical terminal (Terminal 2) in order to describe the passive piezoelectric elements [11]. Here,

, and

represent the equivalent mass, compliance, and damping factor respectively, and

,

and

,

represent the damped capacitances and the force factors of each piezoelectric parts, respectively. To obtain these equivalent parameters, the admittance curve of the fabricated transducer around the first mode was measured at one terminal using an impedance analyzer (4294A, Agilent) while the other terminal was opened. Depending on which terminal was measured, i.e., from the driving or passive piezoelectric parts, a different admittance curve was obtained. The admittance curve measured from Terminal 1 is given by:

(

)

(

)

That from terminal 2 is:

By curve fitting using these equations, the equivalent parameters were obtained as shown in Table I. The equivalent mass, compliance and damping factor were expressed in terms of the force factors, and the force factor ratio was then calculated. To obtain the actual values for these mechanical equivalent parameters and respective force factors, it is necessary to measure the vibration velocity of the transducer. However, this process is not needed to calculate the admittance curve. The fitting results showed that

is half smaller compared to

because the nodal point for the first longitudinal mode is at the center

of the transducer which corresponds to the driving piezoelectric component, not at the passive piezoelectric components.

By replacing the FET switch with an ideal switch in the equivalent circuit, the admittance curve modification was simulated. The switching duty ratio was varied in order to achieve continuous and precise resonant frequency control. The switching frequency was set to the frequency of the driving voltage applied to the driving piezoelectric component. In this

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calculation, the phase shift between the driving and switching voltage was not considered, and it was zero for all switching duty ratios. The resonant frequency for the admittance curve was successfully modified as the switching duty ratio was varied, as shown by the solid line in Fig. 4. However, the peak admittance value was reduced, as shown by the broken line due to the energy loss associated with the switching process. When the switching duty ratio was 40 %, the peak admittance value decreased to less than half of that without switching process. This energy loss is due to release of accumulated charge on the passive piezoelectric elements. During transducer operation, piezoelectric effect generates an electric charge on the passive piezoelectric elements. When the passive piezoelectric elements are electrically opened with turning the switch off, the generated charge is accumulated on the passive part. This accumulated charge is released to ground when the switch is turned, causing the energy loss. Therefore, to eliminate the energy loss, the switch must be turned on when the accumulated charge is zero.

The dependence of the peak admittance value on the switching phase shift, i.e., the timing for turning the switch on, was investigated by varying the phase in 9 deg. steps. A strong dependence was observed; for example, for a duty ratio of 30 %, the peak admittance value varied from 3.3 to 7.8 mS as the switching phase was changed. Similar results were obtained for other switching duty ratios. The optimum switching phase shift are shown in Table II for different duty ratios. Figure 5 shows the dependence of the resonant frequency and the peak admittance value on the duty ratio when the optimum switching phase shifts in Table II were used. It can be seen that the use of the optimum switching phase shift suppressed the energy loss, so that the peak admittance value is independent of the duty ratio.

To confirm the simulation results, the experiment was carried out using the transducer shown in Fig. 2 with an FET (ZVN2106A, DiodesZetex Ltd.) connected to the passive piezoelectric component as a switching element. The driving and switching voltage were generated by a two-channel function generator (WF1974, NF Corporation) and the driving voltage was amplified by a high-speed bipolar amplifier (HSA4052: NF Corporation). The driving and switching voltages were swept in a synchronized frequency using a general-purpose interface bus (GPIB) controller. The switching phase shift was varied in steps of every 18 degree, and the current was measured using a lock-in amplifier (LI5640, NF Corporation), to obtain the admittance value. The experimentally obtained optimum switching phase shifts are shown in Table III. Figure 6 shows the dependence of the resonant frequency and the peak admittance value on the switching duty ratio when the phase shifts in Table III were used. As in the simulation, the peak admittance value is seen to be almost independent of the duty ratio, and the resonant frequency could be controlled in the range 30.42 to 30.55 kHz.

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This letter proposed a method for dynamically controlling the resonant frequency for an ultrasonic transducers. In the proposed method, the stiffness of passive piezoelectric elements was controlled using a switch to open and shorten the electrical boundary condition. The switching duty ratio was used to tune the resonant frequency. Simulations were performed in order to evaluate the effectiveness of this approach, and the results indicated that the switching phase shift should also be taken into consideration in order to suppress energy loss. To achieve zero energy loss, the accumulated charge on the passive piezoelectric components must be zero when the switch is turned on. The resonant frequency can then be shifted without affecting the peak admittance value. To verify the simulation results, an experiment was carried out using an FET as a switching element. The results were found to be in good agreement with those of the simulations. It was shown to be possible to precisely vary the resonant frequency from 30.42 to 30.55 kHz. In future work, other vibration modes such as the third longitudinal mode will be considered. To expand the controllable resonant frequency range, the larger stiffness change of the passive piezoelectric parts between the electric open and short condition is required. Considering the transducer’s design the passive piezoelectric parts should be located at the nodal position for the larger force factor. At present, we are studying on the resonant frequency control system, by placing the passive piezoelectric parts at the nodal point of the 3 rd mode, which enlarge the resonant frequency control range. Moreover, the development of a practical system for fixing the resonant frequency or its ratio at specific value will be attempted.

This work was supported by JSPS KAKENHI Grant Number 16J07294 and NSK Foundation for the Advancement of Mechatronics.

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References [1] T. Morita, Miniature piezoelectric motors, Sensors and Actuators A 103, 291-300. [2] Uchino, Piezoelectric ultrasonic motors: overview, Smart Materials and Structures 7, 273-285. [3] K. Nakamura, M. Kurosawa and S. Ueha, Design of a Hybrid Transducer Type Ultrasonic Motor, IEEE Transactions of Ultrasonics, Ferroelectrics and Frequency Control 40(4), 395-401. [4] M. Takano, K. Hirosaki, M. Takimoto and K. Nakamura, Improvements in Controllability of Ultrasonic Linear Motors by Longitudinal-Bending Multilayered Transducers with Independent Electrodes, Japanese Journal of Applied Physics 50, 07HE25. [5] H. Yokozawa and T. Morita, Wireguide driving actuator using resonant-type smooth impact drive mechanism, Sensors and Actuators A 230, 40-44. [6] T. Yokose, H. Hosaka, R. Yoshida and T. Morita, Resonance frequency ratio control with an additional inductor for a miniaturized resonant-type SIDM actuator, Sensors and Actuators A 214, 142-148. [7] Y. Liu, R. Ozaki and T. Morita, Investigation of nonlinearity in piezoelectric transducers, Sensors and Actuators A 227, 31-38. [8] Y. Liu and T. Morita, Nonlinear coefficients in lead-free CuO-(K,Na)NbO3 transducers, Japanese Journal of Applied Physics 54(7), 07HC01. [9] Y. Liu and T. Morita, Simplified determination of nonlinear coefficients in piezoelectric transducers, Japanese Journal of Applied Physics 54(10), 10ND01. [10] M. J. Kim, N. Chubachi, Frequency Controllable Multilayer Piezoelectric Transducers by the Control of Electrical Terminal Impedance, Electronics C 115(7), 893-900 [in Japanese]. [11] L. Petit and P. Gonnard, Inter-phases mechanical coupling in ultrasonic motors, Sensors and Actuators A 116, 492-500.

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Figure captions Fig. 1 Langevin transducer with a passive piezoelectric elements Fig. 2 Fabricated transducer with the passive piezoelectric parts Fig. 3 The equivalent circuit of the transducer with the passive piezoelectric part Fig. 4 Dependence of resonant frequency (solid line) and peak admittance value (broken line) on switching duty ratio Fig. 5 Dependence of resonant frequency (solid line) and peak admittance value (broken line) on switching duty ratio using optimum switching phase shifts Fig. 6 Measured dependence of resonant frequency (solid line) and peak admittance value (broken line) on switching duty ratio

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Fig. 1

9

Fig. 2

10

Fig. 3

11

Fig. 4

12

Fig. 5

13

Fig. 6

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Table captions Table I. The obtained equivalent parameters Table II. Calculated optimum phase shift between driving and switching voltages Table III. Experimentally obtained optimum phase shift between driving and switching voltages

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Table I

791 [mH]

43.8 [pF]

3.96 [nF]

483 [

16

4.18 [nF]

⁄ 1.94

Table II Duty ratio [%] Optimum phase [deg.]

10 -18

20 -36

30 -54

17

40 -72

50 -90

60 -108

70 -126

80 -144

90 -180

Table III Duty ratio [%] Optimum phase [deg.]

10 -27

20 -45

30 -72

18

40 -90

50 -117

60 -126

70 -144

80 -153

90 -171