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Design and experimental evaluation of a novel stepping linear piezoelectric actuator
Sensors and Actuators A 276 (2018) 259–266
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Design and experimental evaluation of a novel stepping linear piezoelectric actuator Weishan Chen, Yuyang Liu, Yingxiang Liu ∗ , Xinqi Tian, Xiaobiao Shan, Liang Wang State Key Laboratory of Robotics and System, Harbin Institute of Technology, No.92, West Da-Zhi Street, Harbin, 150001, Heilongjiang Province, China
a r t i c l e
i n f o
Article history: Received 4 November 2017 Received in revised form 9 April 2018 Accepted 16 April 2018 Available online 23 April 2018 Keywords: Stepping piezoelectric actuator Equivalent model U-shape Precision driving Long stroke
a b s t r a c t A novel stepping piezoelectric actuator is proposed and tested in this work to achieve the linear driving with long stroke and high resolution. The proposed piezoelectric actuator contains four piezoelectric stacks located in U-shape: two of them are set horizontally, whereas the other two are placed vertically. The actuating principle of the U-shaped actuator is analyzed: two piezoelectric stacks are used to control the clamping state of the runner, while the linear stepping motion is achieved by the other two stacks. A double-level screws structure, which not only gives enough preload, but also protects the piezoelectric stacks from lateral forces, is proposed and used to make the piezoelectric stacks work under a reliable condition. An equivalent model is developed for the calculation of the clamping force of the piezoelectric actuator. The equivalent model is based on a concept of converting structures related to clamping forces into springs with certain elastic coefficients. Static analysis is performed by finite element method (FEM) to get the equivalent coefficients of the structures. A prototype is fabricated and the experimental studies are carried out to validate the actuating principle and obtain the mechanical output performances. Experimental results show that the maximum driving force of the prototype is 13.2 N and the maximum velocity is 47.6 m/s. © 2018 Elsevier B.V. All rights reserved.
1. Introduction With the rapid developments of precision machining, robots, optical instruments, MEMS and cell manipulations, the researches of precision motion platforms have become more and more urgent [1–2]. A variety of new type actuators have been invented to meet different driving requirements of precision motion platforms, such as the piezoelectric actuators, shape memory alloy actuators, magnetostrictive actuators, electrostrictive actuators and so on [3–6]. The piezoelectric actuators have attracted a lot of attentions by their merits of simple structure, high power weight ratio, high displacement resolution, no electromagnetic interference, quick response within a few milliseconds, self-lock when power off, etc [7–8]. Piezoelectric actuators usually convert the electrical energies into the mechanical energies of the linear or rotary motions of the runners by the inverse piezoelectric effect of the ceramics [9–10]. They can be classified into four types by the drive mechanisms: ultrasonic piezoelectric actuators, micro-displacement piezoelectric actuators, inertial piezoelectric actuators and stepping piezoelectric actuators [11–16]. The ultrasonic piezoelectric
∗ Corresponding author. E-mail address: [email protected] (Y. Liu). https://doi.org/10.1016/j.sna.2018.04.026 0924-4247/© 2018 Elsevier B.V. All rights reserved.
actuators can achieve higher speeds by comparing with the other three types, but their displacement resolutions are in micrometer scale [17–19]. The micro-displacement piezoelectric actuators are very suitable for platforms with nanometer resolutions and short strokes [20–22]. The inertial piezoelectric actuators can produce long stroke motions with nanometer resolution by using the difference between the inertial force and the frictional force, but their thrust forces are usually smaller than the other three types [23–26]. The stepping piezoelectric actuators mainly imitate the movement of the inchworm in nature: they usually use the cycle of the clamping and pushing movements to drive the runner step-by-step and achieve a long travel range by accumulating single steps. They can obtain larger thrust forces by comparing with the inertial piezoelectric actuators. Furthermore, they are easy to obtain different stepping displacements by varying the amplitude of the exciting voltage as the output displacement of the piezoelectric element has an approximately linear relationship with the applied voltage. Therefore, the stepping piezoelectric actuators are very popular for applications in precision platforms with requirements of long stroke and high resolution, and it becomes the research hotspot in this field. Most of the previous designs of the stepping piezoelectric actuators have used the flexible hinge displacement amplification mechanisms to amplify the output displacements [27,28]. However, these hinges are always complicated in structures as they have
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121 mm and the distance between the two axes of the two clamping packages is about 170 mm. Four piezoelectric stacks, with outer diameter of 25 mm, inner diameter of 15 mm and length of 30 mm are set in the four packages separately. The assembly of the piezoelectric stack package is realized by the double-level screws among the output shaft, the cap and the shell. The double-level screws structure not only applies preload on the piezoelectric stack, but also can reduce the effects caused by the lateral forces by transmitting them to the shell. Therefore, these packages with double-level screws structures can protect the piezoelectric stacks from shear forces, which is very likely to damage the piezoelectric stacks. Meanwhile, the packages can provide reliable preloads on the piezoelectric stacks, which will ensure the piezoelectric elements work under effective and safe states. Moreover, the deformations of the double-level screws ensure that the output shaft will have large displacement when the piezoelectric stack is energized. Generally speaking, the proposed double-level screws structure has merits of simple structure and low cost by comparing with the flexible hinges used in the previous inchworm piezoelectric actuators. The total stiffness of the piezoelectric actuator can be improved since there is no thin beam like the flexible hinges, which means that it will be less sensitive to the low frequency noises from the environment. 3. Actuating principle
Fig. 1. The basic structure of the proposed stepping piezoelectric actuator: (a) the outline structure (unit: mm), (b) the section view of the package for the piezoelectric stack.
variable cross-sections, which make their fabrications difficult and expensive. Furthermore, the uses of these hinges will reduce the total stiffness of the actuator, and it will be sensitive to the low frequency noises from the environment. A U-shaped stepping piezoelectric actuator is proposed in this work, in which a double-level screws structure is used to make the piezoelectric stacks work in a reliable condition. The proposed actuator has the similar operating principle with the previous stepping piezoelectric actuators operated by inchworm-like motions, and the runner is pushed step-by-step by the alternating motions of several piezoelectric stacks. But the elements in this actuator are easy to be fabricated and low cost by comparing with the flexible hinge, and the stiffness of the actuator will also be improved. The basic structure of the proposed U-shaped stepping piezoelectric actuator is discussed in Section 2. Section 3 gives the detail explanation about the actuating principle. An equivalent model is developed for the calculation of the clamping force in Section 4. A prototype is fabricated and tested in Section 5, which is followed by a conclusion in Section 6. 2. Structure of the proposed actuator The basic structure of the proposed U-shaped stepping piezoelectric actuator is shown in Fig. 1; it consists of four similar piezoelectric stack packages, which are divided into two groups according to their functions: the two clamping packages and the two pushing packages. The two pushing packages are set horizontally and coaxially, whereas the two clamping packages are placed vertically and parallel, and they are located in U-shape. The two end tips of the two clamping packages are used as the driving feet. There are certain differences in the structures of shells and displacement output shafts between the clamping packages and the pushing packages, but these four packages have exactly the same internal structure, as shown in Fig. 1(b). The two pushing packages have a total length of 230 mm, the clamping package has a length of
The actuating principle of the U-shaped stepping piezoelectric actuator is shown in Fig. 2, in which arrows in are used to illustrate the motion of the four stacks and the runner. There are six sub-steps in each actuating cycle. The four piezoelectric stacks in the actuator are named as stack-a, stack-b, stack-c and stack-d for the identification, respectively. The operating sequences of the stepping piezoelectric actuator can be described as follows. (1) Stack-a is energized, stack-b, stack-c and stack-d are deenergized. Due to the elongation of the piezoelectric stack caused by voltage, the output shaft connected with stack-a is pushed forward. The frictional force f1 between the left foot and the runner increases, and it will exceed the frictional force f2 between the right foot and the runner. The action of the left clamping package is called “clamping”. (2) Stack-b and stack-c are energized, while the status of stack-a and stack-d are maintained as sub-step (1). The output shafts connected with stack-b and stack-c are pushed forward, which result that the left foot is moved leftward and the right foot is moved rightward. The runner will be moved leftward by the left foot for one step as the f1 is bigger than f2 . The action of the left pushing package is called “pushing”. (3) Stack-d is energized and the status of stack-a, stack-b and stackc are maintained as sub-step (2). The right clamping package clamps the runner, which is a preparation for the switch to the next sub-step. (4) Stack-a is de-energized, while the status of stack-b, stack-c and stack-d are maintained as sub-step (3). The left foot departs from the runner and the f1 becomes smaller than f2 . (5) Stack-b and stack-c are de-energized, the left foot is moved rightward and the right foot is moved leftward. The right foot pushes the runner leftward for another step. (6) Stack-a is energized and the left clamping package clamps the runner again, which is a preparation for the switching to substep (1) in the next cycle. According to the actuating principle, the signals applied on the four piezoelectric stacks are plotted in Fig. 3. T is the period; a, b, c and d represent the actuating signals applied on the corresponding
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Fig. 2. The actuating principle of the stepper piezoelectric actuator in one circle.
certain elastic coefficients, as shown in Fig. 4. k1 , k2 , k3 , k4 and k5 are the elastic coefficients of the piezoelectric stack, positioning block, output shaft, cap and shell, respectively. K1 is the equivalent elastic coefficients of k1 , k2 and k3 , while K2 is the equivalent elastic coefficients of k4 and k5 . K3 is the elastic coefficient of the pushing package under the bending deformation and K4 is the elastic coefficient of the system contained the base, guider, runner and fixture block. K1 and K2 can be calculated by the following equations based on the principle of series springs:
Fig. 3. The exciting signals applied on the piezoelectric stacks.
piezoelectric stacks, respectively. The four signals are rectangular waves and the voltages are switching between 0 and U (U is the amplitude). The duty cycle of signal-a is two-thirds; the duty cycle of signal-b and signal-c are a half, and they have a temporal delay of 120◦ with signal-a; the duty cycle of signal-d is two-thirds, its phase behinds signal-a with 180◦ . In one cycle from sub-step (1) to sub-step (6), the actuator will push the runner leftward for two steps. The stepping piezoelectric actuator can drive the runner to cover a long travel by accumulating the cycles. Meanwhile, the direction of the movement can be reversed by exchanging the exciting signals applied on stack-a and stack-d. Different step displacements can be easily achieved by changing the amplitude of the applied voltage as the deformation of the piezoelectric stack is approximately proportional to the voltage. Since the actuating progress is a periodic motion, the more actuating cycles take place in a certain time, the longer distance can be accomplished. Therefore, the direction, resolution and velocity can be controlled easily by adjusting the exciting signals. 4. Calculation of the clamping force For a piezoelectric actuator, it is really very significant to calculate its clamping force between the driving foot and the runner since the output thrust force is decided by this clamping force directly. A lot of elements, whose elasticity coefficients are different, may affect the clamping force. Therefore, we can convert these elements related to the clamping force into separated springs with
K1 =
k1 k2 k3 k1 k2 + k2 k3 + k1 k3
(1)
K2 =
k4 k4 k4 + k5
(2)
According to the conditions of static equilibrium, we can obtain the following equations: K1 (D − X3 − X4 ) = K2 (X3 + X4 ) + K4 X4
(3)
K1 (D − X3 − X4 ) = K2 (X3 + X4 ) + K3 X3
(4)
Where D is the axial deformation of the piezoelectric stack under a certain voltage and free condition. Thus, the clamping force Fq can be calculated as following: Fq = K3 X3 = K4 X4 =
DK1 K3 (K1 + K2 )(1 +
K3 K4
) + K3
=
DK1 (K1 + K2 )( K1 + 3
1 K4
)+1
(5)
Therefore, we can obtain the accurate clamping force if parameters of k1 , k2 , k3 , k4 , k5 , K3 , K4 and D are known. These elastic coefficients are calculated by the static analysis in ANSYS software since they are complicated to be measured. From Eq. (5), we can see that the increasing of K2 may cause a slight decrease of the clamping force, whereas the increasing K1 , K3 and K4 show the promoting effects. Fig. 5 shows the simulation result of the clamping package. The materials of the positioning block, output shaft, cap and shell are all set as steel with density of 7800 kg/m3 , Poisson ratio of 0.30 and modulus of elasticity of 206 GPa. The frictional coefficient between the screws is set as 0.1, and the axial force f applied on the lower surface of the positioning block is set as 1000 N (the stress P is about 3.183 MPa). The displacement of points a and b are calculated to be about 1.21 m and 2.03 m, respectively. The elastic coefficients of the piezoelectric stack is k1 = 300 N/m. Therefore, K1 and K2 can
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Fig. 4. The equivalent model of the whole linear motion system.
Fig. 6. Simulation model and displacement nephogram of the driving package: (a) the FEM model, (b) the deformation (unit: m).
Fig. 5. Simulation model and displacement nephogram of the clamping package: (a) the finite element method (FEM) model, (b) the deformation (unit: m).
be calculated by the following equations (d2 and d1 indicate the displacements of point a and b, respectively): K1 =
K2 =
k1 K1
k1 + K1
=
k1 ( d
5. Experiments
f
2 −d1
k1 + ( d
)
f
2 −d1
f = 826.4N/m d1
)
= 240.8N/m
(6)
(7)
The elastic coefficient K3 of the pushing package under the bending deformation is obtained by a similar method, see Fig. 6. The FEM model of the pushing package is established, and a lateral force of 1000 N is applied on the side surface of the end tip (the stress P is about 1.208 MPa). The materials are also set as steel with density of 7800 kg/m3 , Poisson ratio of 0.30 and modulus of elasticity of 206 GPa. The displacement d3 of point c is obtained and the elastic coefficient K3 can be calculated as following: K3 = f/d3 = 40.7N/m
force can achieve 16.4 N when the frictional coefficient between the driving foot and the runner is about 0.15. It should be noted that the elastic coefficients K3 and K4 are smaller than K1 and K2 , which means that bending stiffness of the pushing package and the total stiffness of the system contained the base, guider, runner and fixture block should be improved if we want to improve the output thrust force.
(8)
By a similar method, the other elastic coefficient K4 is calculated to be about 27.6 N/m. The piezoelectric stack has a free deformation of about 30 m under voltage of 200 V, and the clamping force is calculated to be about 109.6 N by Eq. (5). Therefore, the thrust
To validate the actuating principle and obtain the mechanical output characteristics of the proposed piezoelectric actuator, a prototype was fabricated, and a linear motion platform for the measurement was also fabricated, as shown in Fig. 7. The test platform consists of the actuator, a fixture block, a preload device, a runner, two guiders, a bracket and a base. The two guiders were fixed on the base by the bracket. A PI D-E20.200 capacitance type displacement sensor, with measuring range of 200 m, static resolution of 2 nm and dynamic resolution of 4 nm, was used to measure the displacement of the runner. Firstly, the output displacements of the prototype under different voltages were tested. Voltages of 25 V, 50 V, 75 V, 100 V, 125 V, 150 V, 175 V and 200 V were used, and the output displacements of the four packages were measured, see Fig. 8. The points for the measurement of the output displacements were selected at the end tip of each output shaft. The test results show that the maximum output displacements of package-a, b, c, d are about 6.18 m, 5.35 m, 4.84 m and 6.87 m, respectively. The output displacements rise with the increase of the applied voltages, and they have
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Fig. 9. Plot of the output displacement of the PZT stacks versus the time. Table 2 The fall times under different voltages. Fig. 7. The prototype of the proposed stepping piezoelectric actuator and the platform.
Fig. 8. Plot of the output displacement versus the exciting voltage.
Table 1 The rise times under different voltages. Voltage
Package-a (ms)
Package-b (ms)
Package-c (ms)
Package-d (ms)
50V 100V 150V 200V
20.0 21.8 25.2 29.6
20.0 21.0 24.2 27.6
19.2 21.4 24.2 29.6
19.6 21.4 24.8 27.2
approximately linear relationships. There are slight discrepancies among the output displacements of the four packages, which are mainly caused by the machining errors of the four PZT stacks and the clamping elements. According to the above actuating principle, it is known that the time of each sub-step determines the maximum working frequency of the proposed piezoelectric actuator. In each sub-step, the piezoelectric stacks either extend or shorten, which means that the maximum working frequency can be decided by measuring the transient rise time and fall time of the output displacement. The rise times and fall times of the output displacements of the four piezoelectric stack packages were measured by applying rectangular wave signals with frequency of 2 Hz and duty cycle of 50%. Fig. 9 shows the transient response of the output displacement of package-d under voltage of 200 V. The rise times and fall times of four piezoelectric stack packages under different voltages are listed in Table 1 and Table 2.
Voltage
Package-a (ms)
Package-b (ms)
Package-c (ms)
Package-d (ms)
50V 100V 150V 200V
19.2 21.6 25.2 29.8
19.6 21.8 25.6 28.2
19.4 21.6 25.2 28.6
20.2 22.0 25.4 27.4
It is found that the rise time and fall time increase gradually as the increasing of the voltage. The rise time and fall time reaches the maximum values under voltage of 200 V. The four piezoelectric stack packages have different rise times and fall times as the machining errors between the PZT stacks, but their discrepancies are quite small. The maximum value of the rise time and fall time is about 30 ms under voltage of 200 V, which means that the maximum working frequency is about 5.6 Hz as the piezoelectric stack packages are energized and de-energized six times in one circle. It should be noted that tested rise times and fall times are decided by the output power of the signal controller directly, and the controller used for the experiment has a peak power of 30 W. Theoretically speaking, that the maximum working frequency of the proposed actuator can be improved obviously by using a signal controller with higher power. The above operating principle states that the runner is driven by the difference between frictional forces f1 and f2 . The driving force was measured by the following method: a frictional force F0 was gained by force gauge when stack-a and stack-d were de-energized firstly, while another frictional force F1 was obtained when stack-a was energized, and the driving force of the left foot was Fleft =F1 F0 . The driving force of the right foot was measured by the similar method. The driving forces of the two feet under different voltages are plotted in Fig. 10, which shows that they are proportional to the voltage. The maximum driving force of the left foot is about 12.5 N under voltage of 200 V, whereas the maximum driving force of the right foot is 13.2 N. The discrepancy between these two forces are mainly caused by the differences between the output displacements of stack-a and stack-d. These two forces are smaller than the calculated one of 16.4 N, which is mainly caused by the errors between the physical parameters used in the FEM model and the true values. Then, the actuating signals shown in Fig. 3 were applied on the piezoelectric stacks respectively to test the motion of the runner. Fig. 11 shows the transient displacement curve of the runner. The frequency of the actuating signals is 1 Hz and the voltage is 200 V. T represents a movement period and (1) to (6) represents the six sub-steps shown in Fig. 2. The runner is only moved during substep (2) and (5) according to the actuating principle. But it is found that the actuator also causes displacement to the runner during
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Fig. 10. Plot of the driving force versus the voltage.
Fig. 11. Plot of the displacement of the runner versus the time.
Fig. 13. Plot of the output speed versus the frequency.
output speed are tested to be about 2.4 m/s, 6.4 m/s, 12.8 m/s, 15.7 m/s, 19.2 m/s, 23.5 m/s, 26.6 m/s and 30.1 m/s, respectively. The tested speed of the runner has approximately a linear relationship with the voltage. At last, the output speed was tested under different working frequencies by setting the voltage as 200 V. Frequencies of 1 Hz, 2 Hz, 4 Hz, 5 Hz, 6 Hz, 8 Hz, 10 Hz, 12 Hz, 14 Hz, 16 Hz and 20 Hz were used, and the measured speeds were about 6.0 m/s, 12.0 m/s, 23.4 m/s, 30.4 m/s, 35.4 m/s, 42.5 m/s, 43.2 m/s, 47.7 m/s, 44.2 m/s, 25.5 m/s and 3.6 m/s, respectively, as shown in Fig. 13. The speed rises firstly with the increase of the frequency, and reaches the maximum value of 47.7 m/s at the frequency of 12 Hz; then, it decreases rapidly. The relationship between the speed and the frequency has a good linearity when the frequency is less than 6 Hz. The speed still increases when the frequency is between 6 Hz to 12 Hz, but the rise slope reduces. According to measurement result of the rise times and fall times, the maximum frequency of the actuator is 5.6 Hz at 200 V, which make the prototype have nearly linear performance of speed versus frequency in the range of 1 Hz to 6 Hz. The actuator cannot follow the desired motions strictly when the frequency is higher than 6 Hz, and there are partial overlaps among the sub-steps. These overlaps increase with the increase of the frequency, which makes the step displacement decrease gradually. The speed turns to decrease when the negative influence caused by the overlaps is greater than the positive influence caused by the frequency. 6. Conclusion
Fig. 12. Plot of the output speed versus the voltage.
sub-step (1), (3), (4) and (6). This phenomenon is caused by the reaction of the clamping force when the foot clamps the runner: the reaction force bends the pushing package (especially for the output shaft) at a certain angle, which leads to the rotation of the clamping package and the displacement of the runner. Surely, this motion coupling can be decreased by improving of the bending stiffness of the pushing package. However, the actual effective displacement of the runner caused by the clamping is equal to zero in a whole cycle as the two clamping packages complete the clamping and lessening in every actuating cycle. The output speed of the runner is decided by the voltage and the frequency of the exciting signals, and their relationships are plotted in Fig. 12. The frequency of the exciting signals is 5 Hz, and voltages of 25 V, 50 V, 75 V, 100 V, 125 V, 150 V, 175 V and 200 V are used; the
A U-shaped stepping piezoelectric actuator consisted of four piezoelectric stack packages with double-level screws structures was presented and analyzed. An equivalent model was developed for the calculation of the clamping force. A prototype was fabricated to test its mechanical characteristics based on the analysis of the actuating principle. The experimental results showed that the step displacement and average velocity could be controlled by the exciting signals. The voltage was used to change the step displacement and the speed, and the frequency was also used to change the speed. The maximum working frequency of the actuator was tested to be about 5.6 Hz under the voltage of 200 V if the actuating principle was followed strictly. The prototype achieved the maximum speed of 47.6 m/s and the maximum thrust force of 13.2 N. The future works will focus on the improvement on the mechanical output ability since the working frequency and the output speed can be improved obviously by using a controller with higher power; the bending stiffness of the pushing package and the total stiffness of the system contained the base, guider, runner and fixture block need to be improved to increase the output thrust force and
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decrease the fluctuation of the output displacement. The application of this actuator in a linear platform and the control problems will also be developed in the following works. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (No. 51622502 and No. 51475112), in part by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 201428), in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 51521003), and in part by the Fok Ying Tung Education Foundation (No. 151053).
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Weishan Chen was born in Hebei, China, in 1965. He received the B.E. and the M.E. degrees in precision instrumentation engineering, and the Ph.D. degree in Mechatronics engineering from Harbin Institute of Technology, China, in 1986, 1989, and 1997, respectively. Since 1999, he is a professor with the School of Mechatronics Engineering, Harbin Institute of Technology. His research interests include ultrasonic driving, smart materials and structures, bio-robotics. Email: [email protected].
Yuyang Liu was born in Sichuan province, China, in 1992. He received his B.E. degree and M.E. degree from the School of Mechatronics Engineering, Harbin Institute of Technology, China, in 2015 and 2017, respectively. His research interests include piezoelectric actuator. E-mail: [email protected].
Yingxiang Liu was born in Hebei province, China, in 1982. He received the B.E. degree, M.E. degree and Ph.D. degrees from the School of Mechatronics Engineering at Harbin Institute of Technology, China, in 2005, 2007 and 2011, respectively. He is currently a professor of the School of Mechatronics Engineering at the Harbin Institute of Technology. He is the vice director of the Department of Mechatronic Control and Automation. He is also a member of the State Key Laboratory of Robotics and System at Harbin Institute of Technology. He joined the School of Mechatronics Engineering, Harbin Institute of Technology in 2011, where he has been a professor since December 2013. He was a Visiting Scholar at the Mechanical Engineering Department, University of California, Berkeley, from August 2013 to August 2014. He has served as an Associate Editor of IEEE Access. His research interests include piezoelectric actuating, ultrasonic motor, piezoelectric actuator, precision actuating, piezoelectric micro jet, bionic robot, fish robot and soft robot. Email: [email protected]. Xinqi Tian was born in Inner Mongolia province, China, in 1992. He received his B.E. degree and M.E. degree from the School of Mechatronics Engineering, Harbin Institute of Technology, China, in 2014 and 2016, respectively. He is currently a Ph.D. candidate in the Harbin Institute of Technology, China. His research interests include ultrasonic motor and precision piezoelectric actuating. Email: [email protected].
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Xiaobiao Shan was born in Jiangxi, China, in 1977. He received the B.E. degree in Mechanical Design, Manufacturing and Automation, the M.E. and Ph.D. degrees in Mechatronics Engineering from Harbin Institute of Technology, China, in 2001, 2004 and 2008, respectively. He is currently an associate professor with the School of Mechatronics Engineering, Harbin Institute of Technology. His research interests include ultrasonic application, energy harvesting, smart materials and structures. Email: [email protected].
Liang Wang was born in Jilin province, China, in 1990. He received the B.E. degree from the Jilin Agricultural Science and Technology University, China, in 2013. He received the M.E. degree from the Changchun University of Technology, China, in 2016. He is currently a Ph.D. candidate in the Harbin Institute of Technology, China. His research interests include ultrasonic motor and precision piezoelectric actuating. Email:[email protected].
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Design and experimental evaluation of a novel stepping linear piezoelectric actuator Weishan Chen, Yuyang Liu, Yingxiang Liu ∗ , Xinqi Tian, Xiaobiao Shan, Liang Wang State Key Laboratory of Robotics and System, Harbin Institute of Technology, No.92, West Da-Zhi Street, Harbin, 150001, Heilongjiang Province, China
a r t i c l e
i n f o
Article history: Received 4 November 2017 Received in revised form 9 April 2018 Accepted 16 April 2018 Available online 23 April 2018 Keywords: Stepping piezoelectric actuator Equivalent model U-shape Precision driving Long stroke
a b s t r a c t A novel stepping piezoelectric actuator is proposed and tested in this work to achieve the linear driving with long stroke and high resolution. The proposed piezoelectric actuator contains four piezoelectric stacks located in U-shape: two of them are set horizontally, whereas the other two are placed vertically. The actuating principle of the U-shaped actuator is analyzed: two piezoelectric stacks are used to control the clamping state of the runner, while the linear stepping motion is achieved by the other two stacks. A double-level screws structure, which not only gives enough preload, but also protects the piezoelectric stacks from lateral forces, is proposed and used to make the piezoelectric stacks work under a reliable condition. An equivalent model is developed for the calculation of the clamping force of the piezoelectric actuator. The equivalent model is based on a concept of converting structures related to clamping forces into springs with certain elastic coefficients. Static analysis is performed by finite element method (FEM) to get the equivalent coefficients of the structures. A prototype is fabricated and the experimental studies are carried out to validate the actuating principle and obtain the mechanical output performances. Experimental results show that the maximum driving force of the prototype is 13.2 N and the maximum velocity is 47.6 m/s. © 2018 Elsevier B.V. All rights reserved.
1. Introduction With the rapid developments of precision machining, robots, optical instruments, MEMS and cell manipulations, the researches of precision motion platforms have become more and more urgent [1–2]. A variety of new type actuators have been invented to meet different driving requirements of precision motion platforms, such as the piezoelectric actuators, shape memory alloy actuators, magnetostrictive actuators, electrostrictive actuators and so on [3–6]. The piezoelectric actuators have attracted a lot of attentions by their merits of simple structure, high power weight ratio, high displacement resolution, no electromagnetic interference, quick response within a few milliseconds, self-lock when power off, etc [7–8]. Piezoelectric actuators usually convert the electrical energies into the mechanical energies of the linear or rotary motions of the runners by the inverse piezoelectric effect of the ceramics [9–10]. They can be classified into four types by the drive mechanisms: ultrasonic piezoelectric actuators, micro-displacement piezoelectric actuators, inertial piezoelectric actuators and stepping piezoelectric actuators [11–16]. The ultrasonic piezoelectric
∗ Corresponding author. E-mail address: [email protected] (Y. Liu). https://doi.org/10.1016/j.sna.2018.04.026 0924-4247/© 2018 Elsevier B.V. All rights reserved.
actuators can achieve higher speeds by comparing with the other three types, but their displacement resolutions are in micrometer scale [17–19]. The micro-displacement piezoelectric actuators are very suitable for platforms with nanometer resolutions and short strokes [20–22]. The inertial piezoelectric actuators can produce long stroke motions with nanometer resolution by using the difference between the inertial force and the frictional force, but their thrust forces are usually smaller than the other three types [23–26]. The stepping piezoelectric actuators mainly imitate the movement of the inchworm in nature: they usually use the cycle of the clamping and pushing movements to drive the runner step-by-step and achieve a long travel range by accumulating single steps. They can obtain larger thrust forces by comparing with the inertial piezoelectric actuators. Furthermore, they are easy to obtain different stepping displacements by varying the amplitude of the exciting voltage as the output displacement of the piezoelectric element has an approximately linear relationship with the applied voltage. Therefore, the stepping piezoelectric actuators are very popular for applications in precision platforms with requirements of long stroke and high resolution, and it becomes the research hotspot in this field. Most of the previous designs of the stepping piezoelectric actuators have used the flexible hinge displacement amplification mechanisms to amplify the output displacements [27,28]. However, these hinges are always complicated in structures as they have
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121 mm and the distance between the two axes of the two clamping packages is about 170 mm. Four piezoelectric stacks, with outer diameter of 25 mm, inner diameter of 15 mm and length of 30 mm are set in the four packages separately. The assembly of the piezoelectric stack package is realized by the double-level screws among the output shaft, the cap and the shell. The double-level screws structure not only applies preload on the piezoelectric stack, but also can reduce the effects caused by the lateral forces by transmitting them to the shell. Therefore, these packages with double-level screws structures can protect the piezoelectric stacks from shear forces, which is very likely to damage the piezoelectric stacks. Meanwhile, the packages can provide reliable preloads on the piezoelectric stacks, which will ensure the piezoelectric elements work under effective and safe states. Moreover, the deformations of the double-level screws ensure that the output shaft will have large displacement when the piezoelectric stack is energized. Generally speaking, the proposed double-level screws structure has merits of simple structure and low cost by comparing with the flexible hinges used in the previous inchworm piezoelectric actuators. The total stiffness of the piezoelectric actuator can be improved since there is no thin beam like the flexible hinges, which means that it will be less sensitive to the low frequency noises from the environment. 3. Actuating principle
Fig. 1. The basic structure of the proposed stepping piezoelectric actuator: (a) the outline structure (unit: mm), (b) the section view of the package for the piezoelectric stack.
variable cross-sections, which make their fabrications difficult and expensive. Furthermore, the uses of these hinges will reduce the total stiffness of the actuator, and it will be sensitive to the low frequency noises from the environment. A U-shaped stepping piezoelectric actuator is proposed in this work, in which a double-level screws structure is used to make the piezoelectric stacks work in a reliable condition. The proposed actuator has the similar operating principle with the previous stepping piezoelectric actuators operated by inchworm-like motions, and the runner is pushed step-by-step by the alternating motions of several piezoelectric stacks. But the elements in this actuator are easy to be fabricated and low cost by comparing with the flexible hinge, and the stiffness of the actuator will also be improved. The basic structure of the proposed U-shaped stepping piezoelectric actuator is discussed in Section 2. Section 3 gives the detail explanation about the actuating principle. An equivalent model is developed for the calculation of the clamping force in Section 4. A prototype is fabricated and tested in Section 5, which is followed by a conclusion in Section 6. 2. Structure of the proposed actuator The basic structure of the proposed U-shaped stepping piezoelectric actuator is shown in Fig. 1; it consists of four similar piezoelectric stack packages, which are divided into two groups according to their functions: the two clamping packages and the two pushing packages. The two pushing packages are set horizontally and coaxially, whereas the two clamping packages are placed vertically and parallel, and they are located in U-shape. The two end tips of the two clamping packages are used as the driving feet. There are certain differences in the structures of shells and displacement output shafts between the clamping packages and the pushing packages, but these four packages have exactly the same internal structure, as shown in Fig. 1(b). The two pushing packages have a total length of 230 mm, the clamping package has a length of
The actuating principle of the U-shaped stepping piezoelectric actuator is shown in Fig. 2, in which arrows in are used to illustrate the motion of the four stacks and the runner. There are six sub-steps in each actuating cycle. The four piezoelectric stacks in the actuator are named as stack-a, stack-b, stack-c and stack-d for the identification, respectively. The operating sequences of the stepping piezoelectric actuator can be described as follows. (1) Stack-a is energized, stack-b, stack-c and stack-d are deenergized. Due to the elongation of the piezoelectric stack caused by voltage, the output shaft connected with stack-a is pushed forward. The frictional force f1 between the left foot and the runner increases, and it will exceed the frictional force f2 between the right foot and the runner. The action of the left clamping package is called “clamping”. (2) Stack-b and stack-c are energized, while the status of stack-a and stack-d are maintained as sub-step (1). The output shafts connected with stack-b and stack-c are pushed forward, which result that the left foot is moved leftward and the right foot is moved rightward. The runner will be moved leftward by the left foot for one step as the f1 is bigger than f2 . The action of the left pushing package is called “pushing”. (3) Stack-d is energized and the status of stack-a, stack-b and stackc are maintained as sub-step (2). The right clamping package clamps the runner, which is a preparation for the switch to the next sub-step. (4) Stack-a is de-energized, while the status of stack-b, stack-c and stack-d are maintained as sub-step (3). The left foot departs from the runner and the f1 becomes smaller than f2 . (5) Stack-b and stack-c are de-energized, the left foot is moved rightward and the right foot is moved leftward. The right foot pushes the runner leftward for another step. (6) Stack-a is energized and the left clamping package clamps the runner again, which is a preparation for the switching to substep (1) in the next cycle. According to the actuating principle, the signals applied on the four piezoelectric stacks are plotted in Fig. 3. T is the period; a, b, c and d represent the actuating signals applied on the corresponding
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Fig. 2. The actuating principle of the stepper piezoelectric actuator in one circle.
certain elastic coefficients, as shown in Fig. 4. k1 , k2 , k3 , k4 and k5 are the elastic coefficients of the piezoelectric stack, positioning block, output shaft, cap and shell, respectively. K1 is the equivalent elastic coefficients of k1 , k2 and k3 , while K2 is the equivalent elastic coefficients of k4 and k5 . K3 is the elastic coefficient of the pushing package under the bending deformation and K4 is the elastic coefficient of the system contained the base, guider, runner and fixture block. K1 and K2 can be calculated by the following equations based on the principle of series springs:
Fig. 3. The exciting signals applied on the piezoelectric stacks.
piezoelectric stacks, respectively. The four signals are rectangular waves and the voltages are switching between 0 and U (U is the amplitude). The duty cycle of signal-a is two-thirds; the duty cycle of signal-b and signal-c are a half, and they have a temporal delay of 120◦ with signal-a; the duty cycle of signal-d is two-thirds, its phase behinds signal-a with 180◦ . In one cycle from sub-step (1) to sub-step (6), the actuator will push the runner leftward for two steps. The stepping piezoelectric actuator can drive the runner to cover a long travel by accumulating the cycles. Meanwhile, the direction of the movement can be reversed by exchanging the exciting signals applied on stack-a and stack-d. Different step displacements can be easily achieved by changing the amplitude of the applied voltage as the deformation of the piezoelectric stack is approximately proportional to the voltage. Since the actuating progress is a periodic motion, the more actuating cycles take place in a certain time, the longer distance can be accomplished. Therefore, the direction, resolution and velocity can be controlled easily by adjusting the exciting signals. 4. Calculation of the clamping force For a piezoelectric actuator, it is really very significant to calculate its clamping force between the driving foot and the runner since the output thrust force is decided by this clamping force directly. A lot of elements, whose elasticity coefficients are different, may affect the clamping force. Therefore, we can convert these elements related to the clamping force into separated springs with
K1 =
k1 k2 k3 k1 k2 + k2 k3 + k1 k3
(1)
K2 =
k4 k4 k4 + k5
(2)
According to the conditions of static equilibrium, we can obtain the following equations: K1 (D − X3 − X4 ) = K2 (X3 + X4 ) + K4 X4
(3)
K1 (D − X3 − X4 ) = K2 (X3 + X4 ) + K3 X3
(4)
Where D is the axial deformation of the piezoelectric stack under a certain voltage and free condition. Thus, the clamping force Fq can be calculated as following: Fq = K3 X3 = K4 X4 =
DK1 K3 (K1 + K2 )(1 +
K3 K4
) + K3
=
DK1 (K1 + K2 )( K1 + 3
1 K4
)+1
(5)
Therefore, we can obtain the accurate clamping force if parameters of k1 , k2 , k3 , k4 , k5 , K3 , K4 and D are known. These elastic coefficients are calculated by the static analysis in ANSYS software since they are complicated to be measured. From Eq. (5), we can see that the increasing of K2 may cause a slight decrease of the clamping force, whereas the increasing K1 , K3 and K4 show the promoting effects. Fig. 5 shows the simulation result of the clamping package. The materials of the positioning block, output shaft, cap and shell are all set as steel with density of 7800 kg/m3 , Poisson ratio of 0.30 and modulus of elasticity of 206 GPa. The frictional coefficient between the screws is set as 0.1, and the axial force f applied on the lower surface of the positioning block is set as 1000 N (the stress P is about 3.183 MPa). The displacement of points a and b are calculated to be about 1.21 m and 2.03 m, respectively. The elastic coefficients of the piezoelectric stack is k1 = 300 N/m. Therefore, K1 and K2 can
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Fig. 4. The equivalent model of the whole linear motion system.
Fig. 6. Simulation model and displacement nephogram of the driving package: (a) the FEM model, (b) the deformation (unit: m).
Fig. 5. Simulation model and displacement nephogram of the clamping package: (a) the finite element method (FEM) model, (b) the deformation (unit: m).
be calculated by the following equations (d2 and d1 indicate the displacements of point a and b, respectively): K1 =
K2 =
k1 K1
k1 + K1
=
k1 ( d
5. Experiments
f
2 −d1
k1 + ( d
)
f
2 −d1
f = 826.4N/m d1
)
= 240.8N/m
(6)
(7)
The elastic coefficient K3 of the pushing package under the bending deformation is obtained by a similar method, see Fig. 6. The FEM model of the pushing package is established, and a lateral force of 1000 N is applied on the side surface of the end tip (the stress P is about 1.208 MPa). The materials are also set as steel with density of 7800 kg/m3 , Poisson ratio of 0.30 and modulus of elasticity of 206 GPa. The displacement d3 of point c is obtained and the elastic coefficient K3 can be calculated as following: K3 = f/d3 = 40.7N/m
force can achieve 16.4 N when the frictional coefficient between the driving foot and the runner is about 0.15. It should be noted that the elastic coefficients K3 and K4 are smaller than K1 and K2 , which means that bending stiffness of the pushing package and the total stiffness of the system contained the base, guider, runner and fixture block should be improved if we want to improve the output thrust force.
(8)
By a similar method, the other elastic coefficient K4 is calculated to be about 27.6 N/m. The piezoelectric stack has a free deformation of about 30 m under voltage of 200 V, and the clamping force is calculated to be about 109.6 N by Eq. (5). Therefore, the thrust
To validate the actuating principle and obtain the mechanical output characteristics of the proposed piezoelectric actuator, a prototype was fabricated, and a linear motion platform for the measurement was also fabricated, as shown in Fig. 7. The test platform consists of the actuator, a fixture block, a preload device, a runner, two guiders, a bracket and a base. The two guiders were fixed on the base by the bracket. A PI D-E20.200 capacitance type displacement sensor, with measuring range of 200 m, static resolution of 2 nm and dynamic resolution of 4 nm, was used to measure the displacement of the runner. Firstly, the output displacements of the prototype under different voltages were tested. Voltages of 25 V, 50 V, 75 V, 100 V, 125 V, 150 V, 175 V and 200 V were used, and the output displacements of the four packages were measured, see Fig. 8. The points for the measurement of the output displacements were selected at the end tip of each output shaft. The test results show that the maximum output displacements of package-a, b, c, d are about 6.18 m, 5.35 m, 4.84 m and 6.87 m, respectively. The output displacements rise with the increase of the applied voltages, and they have
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Fig. 9. Plot of the output displacement of the PZT stacks versus the time. Table 2 The fall times under different voltages. Fig. 7. The prototype of the proposed stepping piezoelectric actuator and the platform.
Fig. 8. Plot of the output displacement versus the exciting voltage.
Table 1 The rise times under different voltages. Voltage
Package-a (ms)
Package-b (ms)
Package-c (ms)
Package-d (ms)
50V 100V 150V 200V
20.0 21.8 25.2 29.6
20.0 21.0 24.2 27.6
19.2 21.4 24.2 29.6
19.6 21.4 24.8 27.2
approximately linear relationships. There are slight discrepancies among the output displacements of the four packages, which are mainly caused by the machining errors of the four PZT stacks and the clamping elements. According to the above actuating principle, it is known that the time of each sub-step determines the maximum working frequency of the proposed piezoelectric actuator. In each sub-step, the piezoelectric stacks either extend or shorten, which means that the maximum working frequency can be decided by measuring the transient rise time and fall time of the output displacement. The rise times and fall times of the output displacements of the four piezoelectric stack packages were measured by applying rectangular wave signals with frequency of 2 Hz and duty cycle of 50%. Fig. 9 shows the transient response of the output displacement of package-d under voltage of 200 V. The rise times and fall times of four piezoelectric stack packages under different voltages are listed in Table 1 and Table 2.
Voltage
Package-a (ms)
Package-b (ms)
Package-c (ms)
Package-d (ms)
50V 100V 150V 200V
19.2 21.6 25.2 29.8
19.6 21.8 25.6 28.2
19.4 21.6 25.2 28.6
20.2 22.0 25.4 27.4
It is found that the rise time and fall time increase gradually as the increasing of the voltage. The rise time and fall time reaches the maximum values under voltage of 200 V. The four piezoelectric stack packages have different rise times and fall times as the machining errors between the PZT stacks, but their discrepancies are quite small. The maximum value of the rise time and fall time is about 30 ms under voltage of 200 V, which means that the maximum working frequency is about 5.6 Hz as the piezoelectric stack packages are energized and de-energized six times in one circle. It should be noted that tested rise times and fall times are decided by the output power of the signal controller directly, and the controller used for the experiment has a peak power of 30 W. Theoretically speaking, that the maximum working frequency of the proposed actuator can be improved obviously by using a signal controller with higher power. The above operating principle states that the runner is driven by the difference between frictional forces f1 and f2 . The driving force was measured by the following method: a frictional force F0 was gained by force gauge when stack-a and stack-d were de-energized firstly, while another frictional force F1 was obtained when stack-a was energized, and the driving force of the left foot was Fleft =F1 F0 . The driving force of the right foot was measured by the similar method. The driving forces of the two feet under different voltages are plotted in Fig. 10, which shows that they are proportional to the voltage. The maximum driving force of the left foot is about 12.5 N under voltage of 200 V, whereas the maximum driving force of the right foot is 13.2 N. The discrepancy between these two forces are mainly caused by the differences between the output displacements of stack-a and stack-d. These two forces are smaller than the calculated one of 16.4 N, which is mainly caused by the errors between the physical parameters used in the FEM model and the true values. Then, the actuating signals shown in Fig. 3 were applied on the piezoelectric stacks respectively to test the motion of the runner. Fig. 11 shows the transient displacement curve of the runner. The frequency of the actuating signals is 1 Hz and the voltage is 200 V. T represents a movement period and (1) to (6) represents the six sub-steps shown in Fig. 2. The runner is only moved during substep (2) and (5) according to the actuating principle. But it is found that the actuator also causes displacement to the runner during
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Fig. 10. Plot of the driving force versus the voltage.
Fig. 11. Plot of the displacement of the runner versus the time.
Fig. 13. Plot of the output speed versus the frequency.
output speed are tested to be about 2.4 m/s, 6.4 m/s, 12.8 m/s, 15.7 m/s, 19.2 m/s, 23.5 m/s, 26.6 m/s and 30.1 m/s, respectively. The tested speed of the runner has approximately a linear relationship with the voltage. At last, the output speed was tested under different working frequencies by setting the voltage as 200 V. Frequencies of 1 Hz, 2 Hz, 4 Hz, 5 Hz, 6 Hz, 8 Hz, 10 Hz, 12 Hz, 14 Hz, 16 Hz and 20 Hz were used, and the measured speeds were about 6.0 m/s, 12.0 m/s, 23.4 m/s, 30.4 m/s, 35.4 m/s, 42.5 m/s, 43.2 m/s, 47.7 m/s, 44.2 m/s, 25.5 m/s and 3.6 m/s, respectively, as shown in Fig. 13. The speed rises firstly with the increase of the frequency, and reaches the maximum value of 47.7 m/s at the frequency of 12 Hz; then, it decreases rapidly. The relationship between the speed and the frequency has a good linearity when the frequency is less than 6 Hz. The speed still increases when the frequency is between 6 Hz to 12 Hz, but the rise slope reduces. According to measurement result of the rise times and fall times, the maximum frequency of the actuator is 5.6 Hz at 200 V, which make the prototype have nearly linear performance of speed versus frequency in the range of 1 Hz to 6 Hz. The actuator cannot follow the desired motions strictly when the frequency is higher than 6 Hz, and there are partial overlaps among the sub-steps. These overlaps increase with the increase of the frequency, which makes the step displacement decrease gradually. The speed turns to decrease when the negative influence caused by the overlaps is greater than the positive influence caused by the frequency. 6. Conclusion
Fig. 12. Plot of the output speed versus the voltage.
sub-step (1), (3), (4) and (6). This phenomenon is caused by the reaction of the clamping force when the foot clamps the runner: the reaction force bends the pushing package (especially for the output shaft) at a certain angle, which leads to the rotation of the clamping package and the displacement of the runner. Surely, this motion coupling can be decreased by improving of the bending stiffness of the pushing package. However, the actual effective displacement of the runner caused by the clamping is equal to zero in a whole cycle as the two clamping packages complete the clamping and lessening in every actuating cycle. The output speed of the runner is decided by the voltage and the frequency of the exciting signals, and their relationships are plotted in Fig. 12. The frequency of the exciting signals is 5 Hz, and voltages of 25 V, 50 V, 75 V, 100 V, 125 V, 150 V, 175 V and 200 V are used; the
A U-shaped stepping piezoelectric actuator consisted of four piezoelectric stack packages with double-level screws structures was presented and analyzed. An equivalent model was developed for the calculation of the clamping force. A prototype was fabricated to test its mechanical characteristics based on the analysis of the actuating principle. The experimental results showed that the step displacement and average velocity could be controlled by the exciting signals. The voltage was used to change the step displacement and the speed, and the frequency was also used to change the speed. The maximum working frequency of the actuator was tested to be about 5.6 Hz under the voltage of 200 V if the actuating principle was followed strictly. The prototype achieved the maximum speed of 47.6 m/s and the maximum thrust force of 13.2 N. The future works will focus on the improvement on the mechanical output ability since the working frequency and the output speed can be improved obviously by using a controller with higher power; the bending stiffness of the pushing package and the total stiffness of the system contained the base, guider, runner and fixture block need to be improved to increase the output thrust force and
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decrease the fluctuation of the output displacement. The application of this actuator in a linear platform and the control problems will also be developed in the following works. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (No. 51622502 and No. 51475112), in part by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 201428), in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 51521003), and in part by the Fok Ying Tung Education Foundation (No. 151053).
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Weishan Chen was born in Hebei, China, in 1965. He received the B.E. and the M.E. degrees in precision instrumentation engineering, and the Ph.D. degree in Mechatronics engineering from Harbin Institute of Technology, China, in 1986, 1989, and 1997, respectively. Since 1999, he is a professor with the School of Mechatronics Engineering, Harbin Institute of Technology. His research interests include ultrasonic driving, smart materials and structures, bio-robotics. Email: [email protected].
Yuyang Liu was born in Sichuan province, China, in 1992. He received his B.E. degree and M.E. degree from the School of Mechatronics Engineering, Harbin Institute of Technology, China, in 2015 and 2017, respectively. His research interests include piezoelectric actuator. E-mail: [email protected].
Yingxiang Liu was born in Hebei province, China, in 1982. He received the B.E. degree, M.E. degree and Ph.D. degrees from the School of Mechatronics Engineering at Harbin Institute of Technology, China, in 2005, 2007 and 2011, respectively. He is currently a professor of the School of Mechatronics Engineering at the Harbin Institute of Technology. He is the vice director of the Department of Mechatronic Control and Automation. He is also a member of the State Key Laboratory of Robotics and System at Harbin Institute of Technology. He joined the School of Mechatronics Engineering, Harbin Institute of Technology in 2011, where he has been a professor since December 2013. He was a Visiting Scholar at the Mechanical Engineering Department, University of California, Berkeley, from August 2013 to August 2014. He has served as an Associate Editor of IEEE Access. His research interests include piezoelectric actuating, ultrasonic motor, piezoelectric actuator, precision actuating, piezoelectric micro jet, bionic robot, fish robot and soft robot. Email: [email protected]. Xinqi Tian was born in Inner Mongolia province, China, in 1992. He received his B.E. degree and M.E. degree from the School of Mechatronics Engineering, Harbin Institute of Technology, China, in 2014 and 2016, respectively. He is currently a Ph.D. candidate in the Harbin Institute of Technology, China. His research interests include ultrasonic motor and precision piezoelectric actuating. Email: [email protected].
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Xiaobiao Shan was born in Jiangxi, China, in 1977. He received the B.E. degree in Mechanical Design, Manufacturing and Automation, the M.E. and Ph.D. degrees in Mechatronics Engineering from Harbin Institute of Technology, China, in 2001, 2004 and 2008, respectively. He is currently an associate professor with the School of Mechatronics Engineering, Harbin Institute of Technology. His research interests include ultrasonic application, energy harvesting, smart materials and structures. Email: [email protected].
Liang Wang was born in Jilin province, China, in 1990. He received the B.E. degree from the Jilin Agricultural Science and Technology University, China, in 2013. He received the M.E. degree from the Changchun University of Technology, China, in 2016. He is currently a Ph.D. candidate in the Harbin Institute of Technology, China. His research interests include ultrasonic motor and precision piezoelectric actuating. Email:[email protected].