Design and experimental tests of a dual-servo piezoelectric nanopositioning stage for rotary motion Jianping Li, Xiaoqin Zhou, Hongwei Zhao, Mingkun Shao, Zunqiang Fan, and Hui Liu Citation: Review of Scientific Instruments 86, 045002 (2015); doi: 10.1063/1.4918295 View online: http://dx.doi.org/10.1063/1.4918295 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/86/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in An experimental comparison of proportional-integral, sliding mode, and robust adaptive control for piezoactuated nanopositioning stages Rev. Sci. Instrum. 85, 055112 (2014); 10.1063/1.4876596 Design, analysis and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage Rev. Sci. Instrum. 84, 125111 (2013); 10.1063/1.4848876 Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues Rev. Sci. Instrum. 83, 121101 (2012); 10.1063/1.4765048 Development of a compact and long range XYθz nano-positioning stage Rev. Sci. Instrum. 83, 085102 (2012); 10.1063/1.4740254 Design and performance of a piezoelectric actuated precise rotary positioner Rev. Sci. Instrum. 77, 105101 (2006); 10.1063/1.2336760
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REVIEW OF SCIENTIFIC INSTRUMENTS 86, 045002 (2015)
Design and experimental tests of a dual-servo piezoelectric nanopositioning stage for rotary motion Jianping Li, Xiaoqin Zhou, Hongwei Zhao,a) Mingkun Shao, Zunqiang Fan, and Hui Liu School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China
(Received 25 December 2014; accepted 5 April 2015; published online 15 April 2015) A dual-servo nanopositioning stage for high-accuracy rotary motion is presented in this article. A piezoelectric actuator is employed to achieve both the coarse motion and fine motion. By the coarse motion and fine motion, the designed dual-servo nanopositioning stage can obtain large-range rotary motion and high resolution simultaneously. The configuration and motion principle of the dual-servo nanopositioning stage were illustrated and discussed. A prototype was fabricated to test the working performance and the results demonstrate that the maximum speed of the presented dual-servo nanopositioning stage is 32 000 µrad/s and the rotary resolution is about 1.54 µrad. The working performance confirms the feasibility of the dual-servo nanopositioning stage. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4918295]
I. INTRODUCTION
With the rapid advancement in nanotechnology, the ability of nanopositioning stage has become more and more significant in the fields of nanofabrication, nanoposition, and so on. Recent years, the piezoelectric nanopositioning stage has gained extensive attention from researchers all over the world; this is caused by its great advantages: high resolution, large output force, high stiffness, rapid response, and so on.1–3 Nevertheless, the working range of piezoelectric nanopositioning stages is generally less than hundreds of micrometers, which has greatly influenced further applications of piezoelectric nanopositioning stages. Many studies are focusing on solving this problem.4–7 The dual-servo nanopositioning stage (DSNS) is widely used in the fields, which have high requirements for both the high positioning accuracy and the long working stroke.8–11 By the use of one coarse actuator and one fine actuator, dualservo nanopositioning stages can achieve high positioning accuracy and long working stroke simultaneously. For a dual-servo piezoelectric nanopositioning stage (DSPNS), the piezoelectric actuator is exploited as the fine actuator to obtain nanometer accuracy.12–15 In view of the utilization of different types of coarse actuators, dual-servo nanopositioning stages can be divided into several kinds. The stepping motor (SM) is one of the most used coarse actuators in a dual-servo nanopositioning stage. In many scanning probe microscopies and atomic force microscopies, stepping motors and piezoelectric actuators are employed to get large motion range and high positioning accuracy. For example, a permanent magnet stepping motor (PMSM) and a piezoelectric actuator were exploited as the coarse actuator and the fine actuator in a dual-servo nanopositioning stage,14 respectively. The voice coil motor (VCM) is another widely used actuator for coarse motion in a dual-servo nanopositioning stage. For instance, a VCM
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected].
was employed as the coarse actuator in consideration of its long stroke and high accuracy.15 And a flexure hinge amplifier with a piezoelectric actuator was used for the fine precision motion. The output displacement of it can be over 10 mm. Other actuators such as hydraulic cylinders and air cylinders are also used in some dual-servo nanopositioning stages. However, most of the dual-servo nanopositioning stages mentioned above have a relative large size, and the utilization of coarse and fine actuators makes the control system more complex. What is more, only a few of researchers paid attention to flexure-based nanopositioning stages for rotary motion. And most of the proposed flexure-based rotary stages have their own advantages and disadvantages. For example, Byung-Ju Yi et al. designed one parallel micro-mechanism based on three flexure-hinge chains.16 The rotary motion could be easily obtained, but the rotary angle was limited. Umesh Bhagat et al. proposed a novel flexure-based mechanism which was capable to perform planar motion with three degrees of freedom (X, Y, and θ); the lever based amplification was used to enhance the displacement of the mechanism, so the working angle was relatively larger.17 Qingsong Xu used one VCM and radial flexures to design a large-range compliant rotary micropositioning stage, and the maximum rotary angle could be as large as 10◦, but it was still limited to the input range of the VCM.18 Jianping Li et al. presented a piezoelectric nanopositioning stage for rotary motion using inchworm method and flexure-hinge mechanism, so it could realize unlimited large-stroke rotary motion, but the structure and control of it were complicated.5 Most of the flexure-based rotary stages paid no attention on the dual-servo function. This paper presents a dual-servo nanopositioning stage that uses only one piezoelectric actuator to realize large rotary motion range and high accuracy at the same time. That is to say, the coarse motion and fine motion are both achieved by only one piezoelectric actuator. This will make the whole nanopositioning stage compact and easy to control, and unlimited working range can be got easily. This paper may have some reference significance for the study of dual-servo nanopositioning stage.
0034-6748/2015/86(4)/045002/6/$30.00 86, 045002-1 © 2015 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 49.140.205.17 On: Sun, 26 Apr 2015 06:00:43
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II. CONFIGURATION AND WORKING PRINCIPLE
FIG. 1. Schematic of the designed dual-servo nanopositioning stage.
Fig. 1 shows the structure of the designed dual-servo nanopositioning stage for rotary motion. It is mainly made up of the base, the rotor, the flexure hinge mechanism, the piezoelectric actuator, and the wedge block. One precision bearing is used in the rotor for its small friction coefficient. The piezoelectric actuator and the flexure hinge mechanism work together to achieve both the coarse and fine motions. The wedge block is used for the preloading of the piezoelectric actuator. The material of the flexure hinge mechanism is AL7075. In this study, the coarse motion and fine motion are both achieved by the piezoelectric actuator which is nested inside the flexure hinge mechanism. When the piezoelectric actuator works in the stick-slip principle, a long-stroke motion (coarse motion) can be got. A sawtooth-wave voltage is applied to drive the piezoelectric actuator in the coarse motion. The coarse motion principle is illustrated in Fig. 2.
FIG. 2. Working process of the coarse motion. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 49.140.205.17 On: Sun, 26 Apr 2015 06:00:43
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when the target displacement is smaller than 385 µrad (the corresponding arc length is 5 µm), the control system will stop the coarse motion and apply a voltage gradually increasing from 0 V until the target displacement is achieved, and the final positioning resolution is relatively high compared with the stick-slip motion whose minimum step size is limited, as shown in Fig. 3. The Proportion-integration-Differentiation (PID) method is applied in the fine motion. The designed nanopositioning stage can achieve both coarse motion and fine motion only by using different types of input voltages, and the option is controlled automatically by the control system.
III. DESIGN AND ANALYSIS
FIG. 3. Working process of the designed dual-servo nanopositioning stage.
As shown in Fig. 2(b), from the time t 0 to t 1, the piezoelectric actuator gets power slowly, so the flexure hinge mechanism will extend for a small distance ∆L slowly. Because of the friction force between the flexure hinge mechanism and the rotor, the rotor will rotate for a small angle ∆θ. From time t 1 to t 2, the piezoelectric actuator loses power quickly, so the flexure hinge mechanism will move back quickly, seen in Fig. 2(c). Due to the inertia force, the rotor cannot rotate back quickly, so the rotor stays in the place similar to the place in Fig. 2(b). After the two steps, one coarse motion cycle is completed, and by repeating this cycle, a long-stroke coarse motion will be achieved. The fine motion can be achieved by changing the type of the input voltage for the piezoelectric actuator. When the target displacement is too large, the control system will make the piezoelectric actuator work in the coarse motion. Then,
One of the functions of the flexure hinge mechanism is to amplify the working stroke of the piezoelectric actuator, and another more significant function is to produce the motions both in the x-axis and y-axis (see Fig. 4). Right-circular flexure hinges are used in this mechanism, and the flexure hinge mechanism is in a special symmetrical bridge-type, so point A (the contacting point between the flexure hinge and the rotor) will move both in the x direction and the y direction when the piezoelectric actuator extends. The motion in x direction is used to push the rotor to rotate and the motion in y direction will enhance the preloading force between the flexure hinge and the rotor; thus, a better performance can be achieved. According to Ref. 19, the relationship between the motion displacement in x and y directions can be got from the following equation: l x = l y cot α =
ypzt cot α , 2
(1)
where l x is the motion displacement of contacting point A in x direction, l y is the motion displacement of contacting point A in y direction, ypzt is the elongation of the piezoelectric stack, and α is the angle of the bridge-type amplification and the value of it is 30◦. Dimensions of the flexure hinge mechanism and the working principle of it are illustrated in Fig. 4. The material of the flexure hinge mechanism is Al7075 for the good performance of elastic property, and the electrical discharge machining (EDM) method is applied to manufacture it. The stiffness of rotation around the fixing point will influence the
FIG. 4. Schematics of the bridge-type flexure hinge mechanism. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 49.140.205.17 On: Sun, 26 Apr 2015 06:00:43
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FIG. 5. Experimental system for the designed nanopositioning stage.
performance of the designed device, especially for the output force. The contact force between the rotor and the flexure hinge mechanism will generate one torque around the fixing point; when the stiffness of the rotation around the fixing point is small, the contact force will be small as well, and so does the output force. Thus, the value of the rotational stiffness should be appropriate. In this paper, according to the dimensions in Fig. 4, the rotational stiffness around the fixing point is about 32.59 Nm/rad measured by finite element method (FEM) for the difficulty of experimental measurement.
IV. EXPERIMENTS
In order to obtain some preliminary knowledge of the feasibility and the behavior of the proposed linear actuator concept, a prototype was fabricated. A series of experiments were carried out to test the working performances of the designed piezo-driven linear actuator. A. Experiment system
Fig. 5 shows the established experimental system and it mainly consists of one industry personal computer (IPC), one signal controller, one signal amplifier, one laser sensor,
and the prototype. When the dual-servo nanopositioning stage works, the IPC will inform the signal controller to produce an appropriate type of input voltage according to the value of the displacement between the target position and the real position. When the value is larger than 385 µrad, the system works in the coarse motion, otherwise it works in the fine motion (see Fig. 3). The input voltage will be amplified to a suitable value by the signal controller (E-500) which is from PI Company to drive the piezoelectric actuator. The laser sensor LK-G10 from Keyence Company with a resolution of 10 nm is applied to measure the moving displacement. The piezoelectric actuator is from Tokin Company (AE0505D16, 5 × 5 × 20 mm), and when the driving voltage is 100 V, its elongation is about 10 ± 2 µm. The piezoelectric actuator is considered as the ideal one, so the hysteresis is ignored for the small influence on the designed device. For the reason that the rotary angle in one working cycle is rather small, the rotary angle can be got from the following equation: ∆S , (2) R where ∆θ is the stepping angle of the rotor, ∆S is the stepping displacement measured by the laser sensor, and R is the radius of the rotor and the value of it is 13 mm. ∆θ ≈
B. Motion performance
The coarse motion is based on the stick-slip principle and it is significant for the dual-servo nanopositioning stage to achieve rapid speed and long-stroke. A series of experiments are taken to test its performance. Fig. 6(a) shows the working performance of coarse motion when the driving voltage is 100 V and the driving frequency is 1 Hz. A backward motion can be seen in each working circle, and the stepping displacement ∆S can be got from the following equation: ∆S = S − S0.
(3)
The stepping angle can be got from Eq. (2), and relationship between the stepping angle and the driving voltage in the coarse motion is shown in Fig. 6(b). It can be seen that the stepping angle will increase when the driving voltage goes up, and the maximum stepping angle is
FIG. 6. Experimental results for the coarse motion: (a) working performance under 100 V, 1 Hz and (b) relationship between the driving voltage and the stepping angle. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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FIG. 7. Relationship between the driving frequency and the moving velocity.
24.62 µrad when the voltage is 100 V and the frequency is 1 Hz; the minimum stepping angle is 6.92 µrad with a driving voltage of 35 V. The slope of curve in Fig. 6 varies; this may be coursed by the preloading gap of the bearing used in the rotor and the asymmetry of the assembly. The relationship between the driving frequency and the velocity in the coarse motion is shown in Fig. 7. The velocity is got from the following equation: v = f ∆θ,
(4)
where v is the moving velocity of the rotor and f is the driving frequency. The moving velocity goes up while the driving frequency increasing, and after 70 Hz, the increasing rate of velocity becomes slow. It can also be seen that the slope in Fig. 7 is not the same when the driving frequency increases, and this is because that the stepping angle ∆θ cannot keep the same. When the driving frequency is high enough, the stepping angle will become small, and this is the reason why the moving velocity cannot go up all the way. The maximum velocity is about 32 000 µrad/s with a constant driving frequency of 100 Hz, and the driving voltage is 100 V.
FIG. 9. Working performance of the dual-servo motion.
The standard weight was used to measure the output vertical force of the designed nanopositioning stage and the relationship between the stepping angle and the output vertical force is illustrated in Fig. 8. The standard weight was put on the upper surface of the rotor during the experiments. It can be seen that the stepping angle decreases when the output vertical force becomes large, and when the vertical force is larger than 1200 g, the designed nanopositioning stage cannot work stably, so the maximum output vertical force is 11.76 N. The relationship between the stepping angle and the vertical force is not linear, and this may also be caused by the influence of the preloading gap and the assembly errors. The coarse motion is used to achieve large-stroke and high speed, and the fine motion is applied to achieve a high resolution motion. As shown in Sec. II, the system will work in the coarse motion until the difference between the target and real displacements is smaller than 385 µrad. Here, 385 µrad is used for the reason that the moving displacement of the rotor measured by the laser sensor in one working circle is about 5 µm, so the corresponding stepping angle got from Eq. (2) is about 385 µrad. The closed-loop control is from the software Labview, the PID module of Labview is used, and the PID control gains are given as 1000, 0.01, and 0, after a series of tries. Then, the fine motion will be applied to realize a high positioning accuracy. Fig. 9 shows the experimental result when the target displacement is 3850 µrad (the corresponding arc length is about 50 µm), and the driving frequency of the coarse motion is 1 Hz for it is easy to control and convenient to observe. The positioning resolution of the fine motion is about 20 nm (about 1.54 µrad) according to the used laser sensor. The resolution in coarse motion described above is about 6.92 µrad. It can be seen that the resolution is much smaller by using the dual-servo method than that only using the stick-slip motion. V. CONCLUSIONS
A dual-servo nanopositioning stage is proposed in this paper and it can achieve both the long-stroke and high accuracy rotary motion by using only one piezoelectric actuator. Coarse motion and fine motion are used in the working process of the designed dual-servo nanopositioning
FIG. 8. Relationship between the stepping angle and the vertical output force. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
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stage. The experimental results indicated that the maximum velocity is 32 000 µrad/s with a constant driving voltage of 100 V and frequency of 100 Hz; the positioning resolution is about 1.54 µrad when the driving voltage and frequency are 100 V and 1 Hz; and the maximum output vertical force is about 11.76 N. The designed dual-servo nanopositioning stage may have some significance for the applications of piezoelectric stages. More work will be done to improve the performance and the control accuracy. ACKNOWLEDGMENTS
This research is funded by the National Natural Science Foundation of China (NSFC) (Grant Nos. 51275198, 51105163, and 51422503), National Hi-tech Research and Development Program of China (863 Program) (Grant No. 2012AA041206), and Program for New Century Excellent Talents in University (Grant No.NCET-12-0238), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130061110026), Patent Demonstration Project for Research Team in Jilin Province (Grant No. 20130416015ZG).
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