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Characteristics of a V-type ultrasonic rotary motor
Current Applied Physics 11 (2011) S364eS367
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Characteristics of a V-type ultrasonic rotary motor Seong-Su Jeong a, Tae-Gone Park a, *, Myong-Ho Kim b, Tae-Kwon Song b a b
Department of Electrical Engineering, Changwon National University, 9 Sarim-dong, Changwon 641-773, Republic of Korea School of Nano and Advanced Materials Engineering, Changwon National University, Changwon 641-773, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 June 2010 Received in revised form 28 January 2011 Accepted 7 March 2011 Available online 13 April 2011
In this study, a novel structured V-type ultrasonic rotary motor has been proposed to enable use in small precision machines. A thin metal plate was used as a V-shaped vibrator and four ceramic plates were attached on the upper and bottom sides of the metal plate. By applying two electric fields having a 90 phase difference on the ceramics, rotational displacement occurs at the contact point. A finite element analysis was used to simulate the motional pattern dependent on the angle between the legs of the stator. The motor was fabricated on the basis of the results of the FEM analysis. The rotor and stator were connected to a push-pull gauge and the pre-load between them was controlled with this gauge. Characteristics of the motor such as pre-load, speed, torque, and temperature were measured by using a driver and measurement equipment. The difference of resonance frequency of each model was lower than 5[Hz] and driving frequencies were applied equally to each model. As a result, when the angle of the leg decreased, torque increased. On the contrary, when the angle increased, speed increased. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: V-type ultrasonic motor USM Piezo motor Piezo actuator FEM
1. Introduction
2. V-type ultrasonic rotary motor
Demand for small size ultrasonic motors is currently increasing in various fields such as medical treatment and robotics. The minimum size of an electromagnetic motor is generally constrained to about 1 cm. In order to enhance the torque and reduce the speed of the motor, a gearbox must be used [1e6]. However, this significantly reduces the efficiency of the motor. Since electromagnetic motors are limited in terms of possible miniaturization, ultrasonic motors can be an alternative for applications involved restricted space. Furthermore, ultrasonic motors produce no electromagnetic interference [7e10]. Ultrasonic motors offer outstanding response speed, accuracy, and high efficiency. However, they are expensive and have a complex structure. The V-type ultrasonic rotary motor proposed in this paper can be applied to small precision instruments and it also has a simple structure and is economical [11,12]. It is possible to fabricate a V-type ultrasonic rotary motor by using a simple punching technique [1,9]. A finite element analysis (ATILA 5.2.4) was used to simulate the motional pattern of the stator. Displacement characteristics relative to changes of the frequency, impedance, and angle of legs were analyzed through a FEM analysis, and then optimal model was determined and fabricated. Characteristics of speed and torque according to changes of pre-load, voltage, and frequency were measured by using the fabricated ultrasonic motor.
Fig. 1 shows the structure of the stator of the V-type ultrasonic motor and the motional pattern depending on the applied voltage at the contact tip. The stator is configured such that four ceramics polarized in each direction are attached to the upper and bottom areas of the elastic body; the polarization directions and applied voltages are represented in Fig. 1. When two harmonic voltages having a 90 phase difference were applied to the ceramics, symmetric and anti-symmetric displacements were generated at the tip, resulting in elliptical motion. The rotation direction of the rotor is determined through the motion of the contact tip. Inverse motion can be realized by applying inverse phase of the applied voltage to the stator. Fig. 1 shows the motion of the contact tip. The horizontal direction of the motion is defined as y axis and the vertical direction of y axis is defined as x axis. Table 1 shows the stator composed of the ceramics and elastic body. The thickness of elastic body is 0.1[mm] and the length of the body is 15[mm]. The length, width and thickness of the ceramics are 11[mm], 2[mm] and 0.2[mm], respectively. The material and size of stator are defined to generate maximum vibration mode of longitudinal direction [13]. The ceramics used here is NEPC-6 of TOKIN Ltd., the elastic body is brass. Each physical property of the material is shown as in Table 2.
* Corresponding author. Tel.: þ82 55 213 3631; fax: þ82 55 263 9956. E-mail address: [email protected] (T.-G. Park). 1567-1739/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2011.03.013
3. FEM simulations A finite element analysis (ATILA 5.2.4) was used to simulate the motional pattern and stress of the contact tip of the stator. Brass is
S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
S365
Fig. 2. Characteristic of impedance.
Fig. 1. Structure of V-type ultrasonic motor and elliptical motions of the contact tip. Table 1 Size of the stator. Ceramic length
Ceramic width
Ceramic thickness
Elastic body thickness
11 mm
2 mm
0.2 mm
0.1 mm
used as the elastic body of the stator due to high Young’s modulus. Boundary condition is set at the both leg ends because of weak influence on elliptical displacement of the contact tip. First, a modal analysis was conducted to determine the longitudinal vibration mode required for operating the motor. Next, the resonance mode generating the maximum displacement was determined as the operating frequency. Fig. 2 shows the resonance modes depending on changes in frequency; 43 kHz was defined as the operating frequency. Displacement depending on changes in the angle of the legs was then analyzed. Each model was chosen by increasing the angle of the legs in increments of 10 from 70 to 110 . Fig. 3 shows the displacement depending on variation of the angle of the legs at the contact tip. As the angle of the legs becomes smaller, the Table 2 Material properties of ceramic and elastic body.
Ceramic (TOKIN e NEPEC 6)
Elastic body (Brass)
Fig. 3. Characteristic of elliptical displacement depending on the leg angle.
displacement of the x-axis increases. On the other hand, as the angle of the legs becomes larger, the displacement of the y-axis and the torque of the motor become larger. Displacement depending on variation of the angle of the legs affected the speed and torque of the motor. The results are described in further detail in the following section. 4. Experiments
Item
Coefficient
d31 d32 d33 g31 g33 g34 Kr K31 K33 Kt K15 Qm D Young’s modulus (E) Poisson’s ratio (s) Density (r)
133 1012[m/V] 302 1012[m/V] 419 1012[m/V] 10.4 103[Vm/N] 23.5 103[Vm/N] 45.1 103[Vm/N] 0.65 0.34 0.68 0.55 0.71 1500 7.77 103[kg/m3] 9.2 1010[N/m2] 0.33 8270[kg/m3]
Five models depending on variation of the angle of the legs were fabricated. The experiment stage was set up as shown in Fig. 4. The stator was connected to the pushepull gauge applying pre-load by moving up and down. The rotor was fixed to facilitate contact with the stator. Experiment stage was also designed so as to enable measurement of the speed and torque. Fig. 5 shows characteristics of the speed and torque depending on the angle of the legs. When the angle of the legs became larger, the speed of the motor increased and the torque decreased depending on increase in the y-axis displacement. Compared to the results of the simulation, the y-axis displacement is proportional to the torque and the x-axis displacement is proportional to the speed. Characteristics of the speed and torque depending on the frequency are shown in Fig. 6. Driving frequencies are applied to equally to each model because
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S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
Fig. 4. Experiment of the V-type ultrasonic rotary motor.
Fig. 5. Characteristic of speed and torque depending on the leg angle.
Fig. 7. Characteristic of speed and torque depending on the pre-load.
Fig. 6. Characteristic of speed and torque depending on the frequency.
Fig. 8. Characteristic of speed and torque depending on the voltage.
S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
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element analysis. Displacement characteristics of the x and y-axes are analyzed by a FEM program to define the operating characteristics depending on the angle of the legs, and the speed and torque are measured after fabricating the motor. As a result of the experiment, when the angle of the legs becomes smaller, the displacement of the y-axis increases and the torque of the motor also rises. On the other hand, when the angle becomes larger, the displacement of the x-axis and the speed of the motor respectively increase. Abrasion due to friction between the rotor and stator could be reduced by using an abrasive. Existing ultrasonic motors that consist of complex structures can be replaced with a thin V-type ultrasonic motor that can be fabricated more economically due to its simpler structure and by utilizing a simple punching technique. The motor will be highly suitable for small and accurate machinery by utilizing a stator that is thinner than 1 mm. Development of a small and thin type ultrasonic motor technique will fulfill market demand for smaller and more accurate motors.
Acknowledgment
Fig. 9. Characteristic of temperature depending on the time.
the difference of resonance frequency of each model is lower than 5 [Hz]. The maximum speed and torque are obtained at the resonance frequency, 43 kHz. The speed and torque increase somewhat linearly below the resonance frequency and decrease sharply above the resonance frequency. Frequency control is possible in a range of 42e43 kHz. Fig. 7 shows the characteristics of speed and torque depending on the changes in the pre-load; the speed and torque are inversely proportional to increase of the pre-load. When the motor is connected to the case and fabricated as a finished product, the optimal pre-load could be determined by using the data of Fig. 7. Characteristics of the speed and torque depending on the applied voltage are represented in Fig. 8. The speed and torque increase somewhat linearly with increasing applied voltage. Accordingly, control over speed and torque depending on the applied voltage is possible. The experiment using the pushepull gauge is conducted to apply the pre-load within 30 s. For a longtime stable driving, it is necessary to apply the pre-load including spring and to consider preventing abrasion due to friction between the rotor and stator. Fig. 9 shows characteristic of the temperature depending on the operating time. From images acquired during a 120 s period using an infrared camera it is found that the initial temperature increases by 5 after stable operation is achieved without temperature change. Higher temperature is generated at the contact tip of the rotor and the fixed part of the stator. The structure to prevent wear and deformation by the friction temperature of the contact tip will be improved. 5. Conclusion In this study, a V-type ultrasonic motor is proposed and then fabricated for practical use on the basis of the results of a finite
This research was financially supported by the Ministry of Education, Science Technology (MEST) and Korea Institute for advancement of Technology (KIAT) through the Human Resource Training Project for Regional Innovation. The authors of this paper were partly supported by the Second Stage of Brain Korea21 Projects.
References [1] T.G. Park, B.J. Kim, M.H. Kim, K. Uchino, Characteristics of the first longitudinal-fourthbending mode linear ultrasonic motors, Jpn. J. Appl. Phys. 41 (2002) 7139e7143. [2] R. Lee, Lobster-auto focusing & zoom. in: Proceeding of 47th ICAT/JTTAS Joint International Smart Actuator Symposium, 2006, pp. 3e4. [3] H. Hu, Y. Fuda, M. Katsuno, T. Yoshida, A study on rectangular-bar-shaped multilayer transformer using length extensional vibration mode, Jpn. J. Appl. Phys. 38 (1999) 3208e3212. [4] H.W. Kim, S. Dong, P. Laoratanakul, K. Uchino, T.G. Park, Novel method for driving the ultrasonic motor, IEEE 49 (10) (2002) 1356e1362. [5] T. Kanda, A. Makino, K. Suzumori, T. Morita, M.K. Kurosawa, A cylindrical micro ultrasonic motor using a micro-machined bulk piezoelectric transducer, IEEE Ultrason. Symp. (2004) 1298e1301. [6] H.P. Ko, S.S. Kim, S.N. Borodinas, P.E. Vasiljev, C.Y. Kang, S.J. Yoon, A novel tiny ultrasonic linear motor using the radial mode of a bimorph, Sens. Actuators A: Phys. (2006) 125. [7] C.A. Randalli, A. Kelnberger, G.Y. Yang, R.E. Eitel, T.R. Shtout, High strain piezoelectric multilayer actuators-a material science and engineering challenge, J. Electroceram. 14 (2005) 177e191. [8] H.W. Kim, S. Priya, K. Uchino, R.E. Newnham, Piezoelectric energy harvesting under high pre-stressed cyclic vibrations, J. Electroceram. 15 (2005) 27e34. [9] H.H. Chong, T.G. Park, M.H. Kim, A study on driving characteristics of the cross type ultrasonic rotary motor, J. Electroceram. (2006) 17. [10] T. Morita, M.K. Kurosawa, T. Higuchi, Cylindrical micro ultrasonic motor utilizing bulk lead zirconate titanate (PZT), Jpn. J. Appl. Phys. 38 (1999) 3347e3350. [11] H.P. Ko, S.S. Kim, C.Y. Kang, H.J. Kim, S.J. Yoon, Optimization of a piezoelectric linear motor in terms of the contact parameters, Mater. Chem. Phys. 90 (2005) 322e326. [12] A. Hall, M. Allahverdi, E.K. Akdogan, A. Safari, Development and electromechanical properties of multimaterial piezoelectric and electrostrictive PMN-PT monomorph actuators, J. Electroceram. 15 (2005) 143e150. [13] S.S. Jeong, C.H. Park, T.G. Park, Optimal design of V-type ultrasonic motor, J. Cent. South Univ. Technol. 17 (2010) 1247e1250.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Characteristics of a V-type ultrasonic rotary motor Seong-Su Jeong a, Tae-Gone Park a, *, Myong-Ho Kim b, Tae-Kwon Song b a b
Department of Electrical Engineering, Changwon National University, 9 Sarim-dong, Changwon 641-773, Republic of Korea School of Nano and Advanced Materials Engineering, Changwon National University, Changwon 641-773, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 June 2010 Received in revised form 28 January 2011 Accepted 7 March 2011 Available online 13 April 2011
In this study, a novel structured V-type ultrasonic rotary motor has been proposed to enable use in small precision machines. A thin metal plate was used as a V-shaped vibrator and four ceramic plates were attached on the upper and bottom sides of the metal plate. By applying two electric fields having a 90 phase difference on the ceramics, rotational displacement occurs at the contact point. A finite element analysis was used to simulate the motional pattern dependent on the angle between the legs of the stator. The motor was fabricated on the basis of the results of the FEM analysis. The rotor and stator were connected to a push-pull gauge and the pre-load between them was controlled with this gauge. Characteristics of the motor such as pre-load, speed, torque, and temperature were measured by using a driver and measurement equipment. The difference of resonance frequency of each model was lower than 5[Hz] and driving frequencies were applied equally to each model. As a result, when the angle of the leg decreased, torque increased. On the contrary, when the angle increased, speed increased. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: V-type ultrasonic motor USM Piezo motor Piezo actuator FEM
1. Introduction
2. V-type ultrasonic rotary motor
Demand for small size ultrasonic motors is currently increasing in various fields such as medical treatment and robotics. The minimum size of an electromagnetic motor is generally constrained to about 1 cm. In order to enhance the torque and reduce the speed of the motor, a gearbox must be used [1e6]. However, this significantly reduces the efficiency of the motor. Since electromagnetic motors are limited in terms of possible miniaturization, ultrasonic motors can be an alternative for applications involved restricted space. Furthermore, ultrasonic motors produce no electromagnetic interference [7e10]. Ultrasonic motors offer outstanding response speed, accuracy, and high efficiency. However, they are expensive and have a complex structure. The V-type ultrasonic rotary motor proposed in this paper can be applied to small precision instruments and it also has a simple structure and is economical [11,12]. It is possible to fabricate a V-type ultrasonic rotary motor by using a simple punching technique [1,9]. A finite element analysis (ATILA 5.2.4) was used to simulate the motional pattern of the stator. Displacement characteristics relative to changes of the frequency, impedance, and angle of legs were analyzed through a FEM analysis, and then optimal model was determined and fabricated. Characteristics of speed and torque according to changes of pre-load, voltage, and frequency were measured by using the fabricated ultrasonic motor.
Fig. 1 shows the structure of the stator of the V-type ultrasonic motor and the motional pattern depending on the applied voltage at the contact tip. The stator is configured such that four ceramics polarized in each direction are attached to the upper and bottom areas of the elastic body; the polarization directions and applied voltages are represented in Fig. 1. When two harmonic voltages having a 90 phase difference were applied to the ceramics, symmetric and anti-symmetric displacements were generated at the tip, resulting in elliptical motion. The rotation direction of the rotor is determined through the motion of the contact tip. Inverse motion can be realized by applying inverse phase of the applied voltage to the stator. Fig. 1 shows the motion of the contact tip. The horizontal direction of the motion is defined as y axis and the vertical direction of y axis is defined as x axis. Table 1 shows the stator composed of the ceramics and elastic body. The thickness of elastic body is 0.1[mm] and the length of the body is 15[mm]. The length, width and thickness of the ceramics are 11[mm], 2[mm] and 0.2[mm], respectively. The material and size of stator are defined to generate maximum vibration mode of longitudinal direction [13]. The ceramics used here is NEPC-6 of TOKIN Ltd., the elastic body is brass. Each physical property of the material is shown as in Table 2.
* Corresponding author. Tel.: þ82 55 213 3631; fax: þ82 55 263 9956. E-mail address: [email protected] (T.-G. Park). 1567-1739/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2011.03.013
3. FEM simulations A finite element analysis (ATILA 5.2.4) was used to simulate the motional pattern and stress of the contact tip of the stator. Brass is
S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
S365
Fig. 2. Characteristic of impedance.
Fig. 1. Structure of V-type ultrasonic motor and elliptical motions of the contact tip. Table 1 Size of the stator. Ceramic length
Ceramic width
Ceramic thickness
Elastic body thickness
11 mm
2 mm
0.2 mm
0.1 mm
used as the elastic body of the stator due to high Young’s modulus. Boundary condition is set at the both leg ends because of weak influence on elliptical displacement of the contact tip. First, a modal analysis was conducted to determine the longitudinal vibration mode required for operating the motor. Next, the resonance mode generating the maximum displacement was determined as the operating frequency. Fig. 2 shows the resonance modes depending on changes in frequency; 43 kHz was defined as the operating frequency. Displacement depending on changes in the angle of the legs was then analyzed. Each model was chosen by increasing the angle of the legs in increments of 10 from 70 to 110 . Fig. 3 shows the displacement depending on variation of the angle of the legs at the contact tip. As the angle of the legs becomes smaller, the Table 2 Material properties of ceramic and elastic body.
Ceramic (TOKIN e NEPEC 6)
Elastic body (Brass)
Fig. 3. Characteristic of elliptical displacement depending on the leg angle.
displacement of the x-axis increases. On the other hand, as the angle of the legs becomes larger, the displacement of the y-axis and the torque of the motor become larger. Displacement depending on variation of the angle of the legs affected the speed and torque of the motor. The results are described in further detail in the following section. 4. Experiments
Item
Coefficient
d31 d32 d33 g31 g33 g34 Kr K31 K33 Kt K15 Qm D Young’s modulus (E) Poisson’s ratio (s) Density (r)
133 1012[m/V] 302 1012[m/V] 419 1012[m/V] 10.4 103[Vm/N] 23.5 103[Vm/N] 45.1 103[Vm/N] 0.65 0.34 0.68 0.55 0.71 1500 7.77 103[kg/m3] 9.2 1010[N/m2] 0.33 8270[kg/m3]
Five models depending on variation of the angle of the legs were fabricated. The experiment stage was set up as shown in Fig. 4. The stator was connected to the pushepull gauge applying pre-load by moving up and down. The rotor was fixed to facilitate contact with the stator. Experiment stage was also designed so as to enable measurement of the speed and torque. Fig. 5 shows characteristics of the speed and torque depending on the angle of the legs. When the angle of the legs became larger, the speed of the motor increased and the torque decreased depending on increase in the y-axis displacement. Compared to the results of the simulation, the y-axis displacement is proportional to the torque and the x-axis displacement is proportional to the speed. Characteristics of the speed and torque depending on the frequency are shown in Fig. 6. Driving frequencies are applied to equally to each model because
S366
S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
Fig. 4. Experiment of the V-type ultrasonic rotary motor.
Fig. 5. Characteristic of speed and torque depending on the leg angle.
Fig. 7. Characteristic of speed and torque depending on the pre-load.
Fig. 6. Characteristic of speed and torque depending on the frequency.
Fig. 8. Characteristic of speed and torque depending on the voltage.
S.-S. Jeong et al. / Current Applied Physics 11 (2011) S364eS367
S367
element analysis. Displacement characteristics of the x and y-axes are analyzed by a FEM program to define the operating characteristics depending on the angle of the legs, and the speed and torque are measured after fabricating the motor. As a result of the experiment, when the angle of the legs becomes smaller, the displacement of the y-axis increases and the torque of the motor also rises. On the other hand, when the angle becomes larger, the displacement of the x-axis and the speed of the motor respectively increase. Abrasion due to friction between the rotor and stator could be reduced by using an abrasive. Existing ultrasonic motors that consist of complex structures can be replaced with a thin V-type ultrasonic motor that can be fabricated more economically due to its simpler structure and by utilizing a simple punching technique. The motor will be highly suitable for small and accurate machinery by utilizing a stator that is thinner than 1 mm. Development of a small and thin type ultrasonic motor technique will fulfill market demand for smaller and more accurate motors.
Acknowledgment
Fig. 9. Characteristic of temperature depending on the time.
the difference of resonance frequency of each model is lower than 5 [Hz]. The maximum speed and torque are obtained at the resonance frequency, 43 kHz. The speed and torque increase somewhat linearly below the resonance frequency and decrease sharply above the resonance frequency. Frequency control is possible in a range of 42e43 kHz. Fig. 7 shows the characteristics of speed and torque depending on the changes in the pre-load; the speed and torque are inversely proportional to increase of the pre-load. When the motor is connected to the case and fabricated as a finished product, the optimal pre-load could be determined by using the data of Fig. 7. Characteristics of the speed and torque depending on the applied voltage are represented in Fig. 8. The speed and torque increase somewhat linearly with increasing applied voltage. Accordingly, control over speed and torque depending on the applied voltage is possible. The experiment using the pushepull gauge is conducted to apply the pre-load within 30 s. For a longtime stable driving, it is necessary to apply the pre-load including spring and to consider preventing abrasion due to friction between the rotor and stator. Fig. 9 shows characteristic of the temperature depending on the operating time. From images acquired during a 120 s period using an infrared camera it is found that the initial temperature increases by 5 after stable operation is achieved without temperature change. Higher temperature is generated at the contact tip of the rotor and the fixed part of the stator. The structure to prevent wear and deformation by the friction temperature of the contact tip will be improved. 5. Conclusion In this study, a V-type ultrasonic motor is proposed and then fabricated for practical use on the basis of the results of a finite
This research was financially supported by the Ministry of Education, Science Technology (MEST) and Korea Institute for advancement of Technology (KIAT) through the Human Resource Training Project for Regional Innovation. The authors of this paper were partly supported by the Second Stage of Brain Korea21 Projects.
References [1] T.G. Park, B.J. Kim, M.H. Kim, K. Uchino, Characteristics of the first longitudinal-fourthbending mode linear ultrasonic motors, Jpn. J. Appl. Phys. 41 (2002) 7139e7143. [2] R. Lee, Lobster-auto focusing & zoom. in: Proceeding of 47th ICAT/JTTAS Joint International Smart Actuator Symposium, 2006, pp. 3e4. [3] H. Hu, Y. Fuda, M. Katsuno, T. Yoshida, A study on rectangular-bar-shaped multilayer transformer using length extensional vibration mode, Jpn. J. Appl. Phys. 38 (1999) 3208e3212. [4] H.W. Kim, S. Dong, P. Laoratanakul, K. Uchino, T.G. Park, Novel method for driving the ultrasonic motor, IEEE 49 (10) (2002) 1356e1362. [5] T. Kanda, A. Makino, K. Suzumori, T. Morita, M.K. Kurosawa, A cylindrical micro ultrasonic motor using a micro-machined bulk piezoelectric transducer, IEEE Ultrason. Symp. (2004) 1298e1301. [6] H.P. Ko, S.S. Kim, S.N. Borodinas, P.E. Vasiljev, C.Y. Kang, S.J. Yoon, A novel tiny ultrasonic linear motor using the radial mode of a bimorph, Sens. Actuators A: Phys. (2006) 125. [7] C.A. Randalli, A. Kelnberger, G.Y. Yang, R.E. Eitel, T.R. Shtout, High strain piezoelectric multilayer actuators-a material science and engineering challenge, J. Electroceram. 14 (2005) 177e191. [8] H.W. Kim, S. Priya, K. Uchino, R.E. Newnham, Piezoelectric energy harvesting under high pre-stressed cyclic vibrations, J. Electroceram. 15 (2005) 27e34. [9] H.H. Chong, T.G. Park, M.H. Kim, A study on driving characteristics of the cross type ultrasonic rotary motor, J. Electroceram. (2006) 17. [10] T. Morita, M.K. Kurosawa, T. Higuchi, Cylindrical micro ultrasonic motor utilizing bulk lead zirconate titanate (PZT), Jpn. J. Appl. Phys. 38 (1999) 3347e3350. [11] H.P. Ko, S.S. Kim, C.Y. Kang, H.J. Kim, S.J. Yoon, Optimization of a piezoelectric linear motor in terms of the contact parameters, Mater. Chem. Phys. 90 (2005) 322e326. [12] A. Hall, M. Allahverdi, E.K. Akdogan, A. Safari, Development and electromechanical properties of multimaterial piezoelectric and electrostrictive PMN-PT monomorph actuators, J. Electroceram. 15 (2005) 143e150. [13] S.S. Jeong, C.H. Park, T.G. Park, Optimal design of V-type ultrasonic motor, J. Cent. South Univ. Technol. 17 (2010) 1247e1250.