Design and Experimental Research of a Novel

micromachines Article

Design and Experimental Research of a Novel Stick-Slip Type Piezoelectric Actuator Mingxing Zhou, Zunqiang Fan *, Zhichao Ma, Hongwei Zhao, Yue Guo, Kun Hong, Yuanshang Li, Hang Liu and Di Wu School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China; [email protected] (M.Z.); [email protected] (Z.M.); [email protected] (H.Z.); [email protected] (Y.G.); [email protected] (K.H.); [email protected] (Y.L.); [email protected] (H.L.); [email protected] (D.W.) * Correspondence: [email protected]; Tel./Fax: +86-431-8509-4594 Academic Editors: Hiroshi Toshiyoshi and Nam-Trung Nguyen Received: 4 March 2017; Accepted: 5 May 2017; Published: 8 May 2017

Abstract: A linear piezoelectric actuator based on the stick-slip principle is presented and tested in this paper. With the help of changeable vertical preload force flexure hinge, the designed linear actuator can achieve both large travel stick-slip motion and high-resolution stepping displacement. The developed actuator mainly consists of a bridge-type flexure hinge mechanism, a compound parallelogram flexure hinge mechanism, and two piezoelectric stacks. The mechanical structure and motion principle of the linear actuator were illustrated, and the finite element method (FEM) is adopted. An optimal parametric study of the flexure hinge is performed by a finite element analysis-based response surface methodology. In order to investigate the actuator’s working performance, a prototype was manufactured and a series of experiments were carried out. The results indicate that the maximum motion speed is about 3.27 mm/s and the minimum stepping displacement is 0.29 µm. Finally, a vibration test was carried out to obtain the first natural frequency of the actuator, and an in situ observation was conducted to investigate actuator’s stick-slip working condition. The experimental results confirm the feasibility of the proposed actuator, and the motion speed and displacement are both improved compared with the traditional stick-slip motion actuator. Keywords: piezoelectric; actuator; flexure hinge; stick-slip

1. Introduction With the rapidly-growing demand for high accuracy in micro-nano fabrication and optical systems, designing high-accuracy nanopositioning systems has become more and more significant. Given the advantages of high-resolution, large output force, and rapid response, the piezoelectric nanopositioning stage has attracted widespread attention from researchers all over the world. In addition, many types of piezoelectric driven actuators have been successfully developed in the field of precision nanopositioning [1–3]. Regarding their working principles, piezoelectric actuators can be mainly divided into ultrasonic actuators, direct driving actuators, inchworm actuators, stick-slip actuators and so on. Nevertheless, all kinds of these piezoelectric-driven actuators have both advantages and disadvantages. Ultrasonic actuators have high-speed motion and rapid response, but the stability of the motion and heat generation are still problematic [4–6]. Direct-driving actuators have large output force and displacement and, furthermore, their structure can be compact and can achieve rapid responses with high resolutions; however, their operating stroke is limited [7–9]. Inchworm actuators have large motion ranges by stepping motions, and the output force is large, but the control system and mechanical structure are relatively complex [10–12]. A large amount of

Micromachines 2017, 8, 150; doi:10.3390/mi8050150

www.mdpi.com/journal/micromachines

Micromachines 2017, 8, 150

2 of 14

research still needs to be accomplished to overcome all of these actuators’ shortcomings and to develop new types of piezoelectric actuators. Nanopositioning actuators have been used in many applications. A number of applications need both nanoscale resolutions and large travel. Stick-slip actuators present the advantage to allow long displacements (several centimeters or even more) at a high speed (several mm/s) with an ultra-high resolution. Moreover, they are simple, compact, and offer a high stiffness. They are, therefore, perfectly well adapted to challenging applications, such as nanopositioning [13–15]. For example, Zhang et al. [16] presented a two-DOF (degree of freedom) rotary-linear actuator based on the stick-slip principle, which could achieve both linear displacement and angular displacement with the sequential coordination of three piezoelectric stacks. Nevertheless, when the coaxiality between actuator shaft and friction piece is not ideal, the vertically-distributed preload screw cannot provide a steady tightening force to balance the actuator shaft, implying that in order to achieve steady stick-slip motion, relatively high assembly accuracy is needed. Stieg et al. [17] proposed an inertial drive actuator for coarse and fine approaches in scanning probe microscopy, and it could perform clamping action by magnetic force without generating mechanical wear. However, the normal force between the slider element and drive body is constant, thus, the acceleration effects of gravity would lead to the slider element’s displacement loss in each working circle, so the stepping resolution and the stability of the stepping motion is limited. Li et al. [18] developed a stick-slip type linear actuator based on the lateral motion principle, it can realize fine linear motion by the flexure hinge’s parasitic movement, but there will be serious hysteresis and creep phenomena when the flexure hinge working under the high-frequency condition. So far, existing techniques in the design of piezo-driven stick slip actuators still cannot ensure high resolution, while meeting the requirements of achieving large stroke motion. Seldom have researchers paid attention to the unadjustable normal force between the mover and stator, which would restrict stepping resolution and motion speed of a stick-slip actuator to a great extent. Inspired by the above studies and the need for advanced stick-slip actuators, this paper proposes an actuator that can achieve both stable large-stroke and high-resolution linear motion, and the normal force between the stator and mover can be effectively adjusted with the help of adjusting an adjustable stage. The developed actuator mainly consists of a bridge-type flexure hinge mechanism, a compound parallelogram flexure hinge mechanism, and two piezoelectric stacks. Two kinds of working modes of this designed actuator are presented to realize different functions When the piezo-stack that nested in the bridge-type flexure hinge mechanism works alone, the parasitic motion of the bridge-type flexure hinge mechanism enables the slider mover to achieve high-resolution fine motion, which can be applied in precise compensation for the position error. On the other hand, when two piezo-stacks that are nested in different flexure hinge mechanisms work together, the slider mover will achieve large stepping displacement motion due to the action of the compound parallelogram flexure hinge. This working mode can be brought into the adjustment of coarse positioning. This means the combination of two kinds of flexure hinge mechanisms enable the actuator to have a significant enhancement both in resolution of the stepping motion and the working stroke. Additionally, a series of experiments and finite element analysis methods were carried out to test the performance of the designed piezoelectric actuator. The proposed actuator may have some significance for designing stick-slip actuators and potential applications for a high-precision micro/nano-system. 2. Design and Analysis The structure of designed stick-slip piezoelectric actuator is illustrated in Figure 1. It can be clearly seen that the actuator mainly consists of a base, an adjusting stage, a slider mover, two piezoelectric stacks, a bridge-type flexure hinge, and a compound parallelogram flexure hinge. The adjusting stage (TSM13-2A from Zolix Company, Beijing, China) is made up of a linear spherical guide, an adjusting micrometer-knob and a moving platform. The flexure hinge mechanism is assembled on the top of the moving platform, and the moving platform is mounted on linear spherical guide. When turning the


3 of 14


3 of 14

spherical guide. When turning adjusting fine motion of the moving Micromachines 2017, 8, 150 3 of normal 14 adjusting micrometer-knob, the finethe motion of themicrometer-knob, moving platformthe is used to change preload platform is used to change preload normal force between slider mover and flexure hinge. Two force between slider mover and flexure hinge. Two piezoelectric stacks, nested in the bridge-type spherical guide. Whennested turning micrometer-knob, fine motion moving piezoelectric stacks, in the the adjusting bridge-type flexure hinge the mechanism andofa the compound flexure hinge mechanism and a compound parallelogram, respectively, are exploited to deform the platform is used to change preload normal force between slider mover and flexure hinge. Two parallelogram, respectively, are exploited to deform the flexure hinge. A linear guide and a slider flexure hinge.from A stacks, linear guide a slider (SRS-9M from Company, Tokyo, are used piezoelectric nested and inTokyo, the bridge-type flexure hinge mechanism and a Japan) compound (SRS-9M THK Company, Japan) are used as theTHK mover for their high-carrying capacity as the mover for their high-carrying capacity and small-friction coefficient. All of the components parallelogram, respectively, to deform the hinge. A linear guide andSince a slider and small-friction coefficient.are Allexploited of the components are flexure assembled on the base carefully. the are assembled on themay base carefully. the assembling may influence preload (SRS-9M from THK Company, Tokyo, Japan) are used as adjustment the errors mover for their high-carrying capacity assembling errors influence the Since preload force, some work needs to bethe done to keepforce, small-friction coefficient. All of components are assembled on smooth the base after carefully. Since the the working motion smoothtoafter thethe assembly. someand adjustment work needs be done to keep the working motion the assembly. assembling errors may influence the preload force, some adjustment work needs to be done to keep the working motion smooth after the assembly.

Figure 1. Mechanical structure of the designed actuator.

Figure 1. Mechanical structure of the designed actuator.

The geometric model of the bridge-type flexure hinge and compound parallelogram flexure Figure 1. Mechanical structure of the designed actuator.

The geometric model the bridge-type flexure hinge and compound flexure hinge mechanism are of shown in Figure 2. The key parameters of the parallelogram designed flexure hingehinge Theare geometric model of the bridge-type flexure hinge compound parallelogram flexure mechanism are listed in Table As key the piezoelectric stack Adesigned receives power, it will deform the are mechanism shown in Figure 2.1.The parameters of theand flexure hinge mechanism hinge mechanism are shown in Figure 2. The key parameters of the designed flexure hinge bridge-type flexure hinge both in y direction and x direction. The displacement l ay is the motion listed in Table 1. As the piezoelectric stack A receives power, it will deform the bridge-type flexure are listed and in along Table 1. As theThe piezoelectric stack A is receives power, it will deform the displacement generated the elongation direction of piezoelectric stack A,displacement The displacement lax hingemechanism both in y direction x direction. displacement lay the motion generated bridge-type flexure bothtoinpush y direction and x direction. displacement lay isAdditionally, the motion is lateral motion, andhinge it is used the slider mover to moveThe along the x direction. along the elongation direction of piezoelectric stack A, The displacement lax is lateral motion, and it displacement generatedstack alongBthe elongation direction of piezoelectric A, The displacement lax when the piezoelectric gets charged, it will extend along the xstack direction, then it pushes the is used to push the slider mover to move along the x direction. Additionally, when the piezoelectric is lateral motion, and it is used to push mover along the x direction. Additionally, compound parallelogram flexure hingethe to slider deform both to in move the x and y directions, as well. However, stackwhen B gets charged, it will extend along the xitdirection, then it pushes thewill compound parallelogram piezoelectric stack B gets charged, will extend along the hinge x direction, thendeform it pushes the due tothe the structural stiffness, the compound parallelogram flexure only a very flexure hinge toparallelogram deform in the xhinge and ytodirections, as in well. due to the structural stiffness, compound flexure both xHowever, and when y directions, as well. small distance in theboth y direction, namely ldeform by, and it can bethe ignored compared withHowever, the large the compound parallelogram flexure hinge only a very smallBwill distance in theused ya direction, due to the structural the parallelogram flexure hinge deform very displacement in the xstiffness, direction lax.compound That is will to say, thedeform elongation of stack canonly be entirely to small in the yignored direction, namely lby, and itwith caninbe when compared large lax . namely lbydistance , and it can bedisplacement when compared the displacement in with the xthe direction enlarge the stepping of the slider mover theignored xlarge direction. in the x direction lax.BThat say, theused elongation of stack B can be entirely used toof the That displacement is to say, the elongation of stack can is betoentirely to enlarge the stepping displacement enlarge the stepping displacement of the slider mover in the x direction. slider mover in the x direction.

Figure 2. The designed flexure hinge: (a) structure; and (b) linkage model. Figure 2. The designedflexure flexure hinge: hinge: (a) (b)(b) linkage model. Figure 2. The designed (a)structure; structure;and and linkage model.


4 of 14


4 of 14

Table 1. Key parameters of bridge-type flexure hinge and the compound parallelogram flexure hinge. Table 1. Key parameters of bridge-type flexure hinge and the compound parallelogram flexure hinge.

Parameters α Value Parameters α45° Value

45◦

r 0.6r mm

b 6 mm b

w 0.8wmm

t 0.8t mm

d 6 dmm

l 4 mm l

0.6 mm

6 mm

0.8 mm

0.8 mm

6 mm

4 mm

Based on the stick-slip principle, an asymmetrical sawtooth-wave voltage is applied to drive the piezoelectric stack, and the percentage of stacks’ charging time in a working circle is set to be 80%. Based on the stick-slip principle, an asymmetrical sawtooth-wave voltage is applied to drive the The working process of a working circle about this designed actuator can be divided into two steps, piezoelectric stack, and the percentage of stacks’ charging time in a working circle is set to be 80%. as shown in Figure 3. From time t0 to t1, both piezoelectric stack A and B slowly obtain power, the The working process of a working circle about this designed actuator can be divided into two steps, piezoelectric stack A will push the bridge-type flexure hinge to move a certain distance both in the x as shown in Figure 3. From time t0 to t1 , both piezoelectric stack A and B slowly obtain power, and y directions, and the stack B extends slowly to push the compound parallelogram flexure hinge the piezoelectric stack A will push the bridge-type flexure hinge to move a certain distance both in in the x direction as well. Since the bridge-type flexure hinge is holding the slider through the the x and y directions, and the stack B extends slowly to push the compound parallelogram flexure preload force, theoretically, the friction force between the slider mover and bridge-type flexure hinge in the x direction as well. Since the bridge-type flexure hinge is holding the slider through hinge is a static friction force, thus, under the deformation action of compound parallelogram the preload force, theoretically, the friction force between the slider mover and bridge-type flexure flexure hinge, the piezoelectric stack B will push both the slider mover and piezoelectric stack A to hinge is a static friction force, thus, under the deformation action of compound parallelogram flexure move a small displacement ∆L, which is shown in Figure 3b; From time t1 to t2, piezoelectric stack A hinge, the piezoelectric stack B will push both the slider mover and piezoelectric stack A to move a and B discharge quickly, resulting in the swift retraction of both the bridge-type flexure hinge and small displacement ∆L, which is shown in Figure 3b; From time t1 to t2 , piezoelectric stack A and B compound parallelogram flexure hinge to their initial position. The friction force between the flexure discharge quickly, resulting in the swift retraction of both the bridge-type flexure hinge and compound hinge and slider mover changes to be the sliding friction force. Nevertheless, due to the action of parallelogram flexure hinge to their initial position. The friction force between the flexure hinge and inertial force, the slider mover will stay nearly at the same position as in Figure 3b. Consequently, slider mover changes to be the sliding friction force. Nevertheless, due to the action of inertial force, the slider moves forward one step displacement unit ∆L while the flexure hinge return to its initial the slider mover will stay nearly at the same position as in Figure 3b. Consequently, the slider moves position. As the sawtooth driving voltage increases and decreases cyclically, stick and slippage of forward one step displacement unit ∆L while the flexure hinge return to its initial position. As the the slider occur iteratively; hence, the slider is driven through an extended travel range, which is sawtooth driving voltage increases and decreases cyclically, stick and slippage of the slider occur shown in Figure 3c. iteratively; hence, the slider is driven through an extended travel range, which is shown in Figure 3c.

Figure 3. Working process of a circle: (a) the initial position; (b) the largest displacement position; Figure 3. Working process of a circle: (a) the initial position; (b) the largest displacement position; and (c) the final position. and (c) the final position.

Regarding the the contact contact point pointPPbetween betweenthethe mover slider bridge-type flexure hinge, mover slider andand bridge-type flexure hinge, the the stepping displacement of point P can be considered as the lax and stepping displacement xp ofxppoint P can be considered as the sumsum of laxofand lbx: lbx :

+ llbx xxpp== llax ax + bx

(1)

Here, llax is the moving distance in x direction caused by piezoelectric stack A, and lbx is the Here, ax is the moving distance in x direction caused by piezoelectric stack A, and lbx is the moving distance in the the xx direction direction caused caused by by the the piezoelectric piezoelectric stack stack B. B. moving distance in According to the previous works [19–21], the relationship between motion displacement of the bridge-type flexure hinge in the x and y directions can be obtained from the following equation:


5 of 14

According to the previous works [19–21], the relationship between motion displacement of the bridge-type flexure hinge in the x and y directions can be obtained from the following equation: Micromachines 2017, 8, 150

lax

y pzt cot α = 2

5 of 14

(2)

y pzt cot α

(2) lax = stack A, and α denotes the inner angle of bridge-type Here, ypzt is the elongation of piezoelectric 2 flexure hinge, namely 45◦ . Here, ypzt is the elongation of piezoelectric stack A, and α denotes the inner angle of bridge-type Since the motion displacement in the x direction of piezoelectric stack B is fully used to push the flexure hinge, namely 45°. slider mover, the moving distance caused by stack B can be written as follows, where xpzt represents Since the motion displacement in the x direction of piezoelectric stack B is fully used to push the the elongation of piezoelectric stack B: slider mover, the moving distance caused by stack B can be written as follows, where xpzt represents lbx = x pzt (3) the elongation of piezoelectric stack B:

As above mentioned, Equation (1) can belequivalent to the following: =x bx

pzt

As above mentioned, Equation (1) can x p be = equivalent 0.5y pzt + xtopztthe following:

(3)

(4)

x p = 0.5 y pzt + x pzt (4) The finite element analysis method (FEM) is adopted to investigate the working performance of The finite element analysis method The (FEM) is adopted to investigate the working of the designed flexure hinge mechanism. software ANSYS Workbench 15.0 is performance used to simulate in the designed flexure mechanism. The software ANSYS is used to simulate inhinge. this study. The finest 3Dhinge tetrahedron element is used to meshWorkbench the model 15.0 of the designed flexure this study.the The finest 3D tetrahedron element to bodies mesh the of the designed flexure way Additionally, piezoelectric stacks used are setisasused rigid andmodel the displacement controlled hinge. Additionally, the piezoelectric stacks used are set as rigid bodies and the displacement is used for them. This is mainly due to the fact that the displacement of piezoelectric is approximately controlled way is used for them. This is mainly due to the fact that the displacement of piezoelectric proportional to the driving voltage. When the driving voltage is 100 V, the elongation of piezoelectric is approximately proportional to the driving voltage. When the driving voltage is 100 V, the stacks A and Boffrom NEC is stacks about A 10and µm.B Three screw holes 10 areμm. fully fixed during elongation piezoelectric from NEC is about Three screw holesthe aresimulation. fully The material used for the flexure hinge is Al 7075 and the main parameters are shown in fixed during the simulation. The material used for the flexure hinge is Al 7075 and theTable main2. The resultare of shown the FEM is illustrated in Figure 4, and it can be seen that the moving distance of parameters in Table 2. of the FEM is illustrated in Figure 4, and it cantobe seen thatobtained the moving distance of (4), point P inThe theresult x direction is 14.378 µm, which is nearly equal the value from Equation point in theTheoretically, x direction is 14.378 μm, which nearly to the value obtained accuracy from Equation (4), finite namely 15Pµm. the error mayisbe dueequal to the computational of the namely 15 μm. Theoretically, the error may be due to the computational accuracy of the finite element method. element method.

Table 2. Mechanical properties of the material used in the FEM. Table 2. Mechanical properties of the material used in the FEM.

Parameter Parameter Young’s modulus modulus EE Young’s Poisson’s Poisson’s ratio ratio νν Yield Yieldstress stressσσss Density Density ρρ

Mechanical Properities Mechanical Properities 72,000 (MPa) 72,000 (MPa) 0.330.33 (MPa) 505 505 (MPa) 3) (kg/m 3) 28102810 (kg/m

Figure FEMresult result of of the the flexure the working direction. Figure 4.4.FEM flexurehinge hingeinin the working direction.


6 of 14

3. Optimization Micromachines 2017, 8, 150

6 of 14

In the past decades, structural optimization has been extensively explored and successfully applied to optimize structures and mechanisms in many practical engineering designs with the use 3. Optimization of FEA [22]. The purpose of the optimization process for the flexure hinge mechanisms is to obtain In the past parameters decades, structural optimization has been extensively exploredwhile and successfully optimal design to achieve the maximum stepping displacement taking into applied to optimize structures and mechanisms in many practical engineering designs with the use account of the stress concentration occurred in the flexural hinges. Generally, the radius r, thickness of and FEAlength [22]. The purpose processstructural for the flexure mechanisms is to obtain w, of rigid linksofl the are optimization the three important factorshinge to the static performances of optimal design parameters to achieve the maximum stepping displacement while taking intothe account of the flexure hinge, and these parameters are chosen as the design variables. Thus, above the stress concentration occurred in the flexural hinges. Generally, the radius r, thickness w, and length multiple-objective optimization problem in this research is briefly described in the standard of rigid links format l are the mathematical as:three important structural factors to the static performances of the flexure hinge, and these parameters are chosen as the design variables. Thus, the above multiple-objective : r , w, l Find optimization problem in this research is briefly described in the standard mathematical format as:  Maximize displacement: x p ( r , w, l )   Find : r, w,equivalent l  Minimize stress : S ( r , w, l )     Maximize displacement: x p (r, w, l )  Opt  (5)  . Subject to constrains :   Minimize equivalent stress : S(r, w, l )  0.54 ≤ r ≤ 0.66 Opt. Subject to constrains : (5) 0.72 ≤ w ≤ 0.85    0.54 ≤ r ≤ 0.66     ≤≤ 3.6 ≤≤l w 4.20.85  0.72    3.6 ≤ l ≤ 4.2 (RSM) is a kind of mathematical and statistical Since the response surface methodology technique that can be used to explore the relationships between several explanatory variables and Since the response surface methodology (RSM) is a kind of mathematical and statistical technique one or more response variables [23], an optimization process is carried out in the commercial that can be used to explore the relationships between several explanatory variables and one or more software ANSYS Workbench 15.0 to quickly reflect effects of different parameters on performance response variables [23], an optimization process is carried out in the commercial software ANSYS characteristics of the flexure hinge mechanism. Regarding the created response charts and surfaces, Workbench 15.0 to quickly reflect effects of different parameters on performance characteristics of change trends of displacement and equivalent stress with designing parameters of flexure hinge the flexure hinge mechanism. Regarding the created response charts and surfaces, change trends of mechanism are shown in Figures 5 and 6. It can be noted that when l increases, the displacement displacement and equivalent stress with designing parameters of flexure hinge mechanism are shown and stress decrease slowly, as shown in Figure 5a,d. When r and w increase, their displacement in Figures 5 and 6. It can be noted that when l increases, the displacement and stress decrease slowly, quickly increase, as shown in Figure 5b,c. The stress will show slight increases when r increases, as as shown in Figure 5a,d. When r and w increase, their displacement quickly increase, as shown in shown in Figure 5e. Seen in Figure 6b,e, the sensitivities of both displacement and stress with w and Figure 5b,c. The stress will show slight increases when r increases, as shown in Figure 5e. Seen in l are considerately higher than with others. As illustrated in Figure 6a,c, r seems to have little Figure 6b,e, the sensitivities of both displacement and stress with w and l are considerately higher than influence on the displacement. with others. As illustrated in Figure 6a,c, r seems to have little influence on the displacement.

Figure 5. The dependence of the stepping displacement x and maximum equivalent stress S on each Figure 5. The dependence of the stepping displacement xpp and maximum equivalent stress S on each of the design parameters: the change trend of stepping displacement with (a) l; (b) r; (c) w; and the of the design parameters: the change trend of stepping displacement with (a) l; (b) r; (c) w; and the change trend of maximum stress S with (d) l; (e) r; and (f) w. change trend of maximum stress S with (d) l; (e) r; and (f) w.

Micromachines 2017, 8, 150 Micromachines 2017, 8, 150

7 of 14 7 of 14

Figure Figure 6. 6. Stepping Steppingdisplacement displacementxxppplot plotin interms termsof of(a) (a)lland andr,r,(b) (b)w wand andl;l; (c) (c) rr and and w; w; the the maximum maximum equivalent equivalent stress stress SS plot plot in in terms terms of of (d) (d) ll and and r;r; (e) (e) w w and and l;l; and and (f) (f) rr and w.

After After computational computationalanalysis, analysis,the thepotential potentialcandidates candidatesare arecompared comparedand andestimated estimatedto to find find the the best candidate, which can be seen in Table 3. According to Table 3, Candidate 1 was selected as best the best candidate, which can be seen in Table 3. According to Table 3, Candidate 1 was selected as the best optimal because it completely satisfies the first design the objectives: the maximum optimal designdesign because it completely satisfies the first design objectives: maximum displacement displacement x p was the highest among the candidates, and the maximum equivalent stress was xp was the highest among the candidates, and the maximum equivalent stress was still well below the still belowofthe strength of the Compared material (505 MPa). Compared the initial design, the yieldwell strength theyield material (505 MPa). with the initial design,with the static characteristics of static characteristics of the actuator was relatively improved, as seen in Table 3: (i) the stepping the actuator was relatively improved, as seen in Table 3: (i) the stepping displacement was increased displacement was up stress to 2.99%; and (ii) by theapproximately maximum stress up to 2.99%; and (ii)increased the maximum was decreased 4.95%.was decreased by approximately 4.95%. Table 3. Comparisons among candidates. Table 3. Comparisons among candidates. Candidate Points l (mm)l (mm) w (mm) w (mm) r (mm) Candidate Points Candidate 1 3.6765 0.8491 0.5909 Candidate 2 1 3.73413.6765 0.8473 0.8491 0.6107 Candidate Candidate 3 2 3.79173.7341 0.8482 0.8473 0.6054 Candidate

Candidate 3

3.7917

0.8482

Displacement xp S (MPa) Stress S Improvement Improvement of Stress of xp and S (MPa) x and S p 38.56 2.99%, 4.95%

Displacement xp (μm) r (mm) (µm) 14.85 0.5909 14.63 14.85 0.6107 14.79 14.63

0.6054

14.79

37.82 38.56 39.18 37.82

1.75%, 6.78% 2.99%, 4.95% 2.86%, 3.42% 1.75%, 6.78%

39.18

2.86%, 3.42%

4. Experiment 4. Experiment 4.1. Experimental Setup 4.1. Experimental Setup A prototype of this stator has been constructed for the purpose of studying its performance, and A prototype of this stator has been constructed forsize the of purpose studying itsmm. performance, the actuator possesses a compact structure with a whole 80 mm of × 65 mm × 16 Both the and the actuator possesses a compact structure with a whole size of 80 mm × 65 mm 16high mm. flexure hinge mechanism and the slider mover are fabricated from Al 7075 material due to×its Both the flexure hinge mechanismlarger and the slider mover are fabricated Al 7075 material due to its elastic modulus and relatively stiffness. The prototype wasfrom manufactured by low-speed high elastic modulus and relatively larger stiffness. The prototype was manufactured by low-speed wire-cut electric discharge machining (WEDM) technique with the wire diameter being 0.4 mm, and wire-cut electric discharge machining with wire diameter 0.4 mm, the machining tolerances were specified(WEDM) as ±5 μm technique throughout. Thethe experiment systembeing is established and the machining tolerances were specified as ± 5 µm throughout. The experiment system is as shown in Figure 7, and it mainly consists of one personal computer, one signal controller, one established as shown in Figure 7, and it mainly consists of one personal computer, one signal controller, signal amplifier, one laser sensor, and the prototype. When the experimental system works, the one signal amplifier, one laser sensor, andTechnologies, the prototype.Beijing, WhenChina) the experimental system works, signal generator DG3121A (from RIGOL will provide the needed the signal generator DG3121A (from RIGOL Technologies, Beijing, China) will provide the needed sawtooth wave voltage signal, then the voltage signal will be amplified by the signal amplifier sawtooth wave signal, then the voltage signalChina), will bethe amplified the signal RH1500D/1 (fromvoltage SOLUBLE CORE Technology, Harbin, enlargedby voltage is thenamplifier used to RH1500D/1 (from SOLUBLE Technology, Harbin, China), the enlarged voltage is channels) then used is to drive the piezoelectric stacks. CORE The maximum power of the RH1500D/1 amplifier (three 300 W. A laser sensor LK-G10 (from Keyence Corporation, Osaka, Japan) with a resolution of 10 nm


8 of 14

2017, 8, 150stacks. The maximum power of the RH1500D/1 amplifier (three channels) 8 of 14 driveMicromachines the piezoelectric is 300 W. A laser sensor LK-G10 (from Keyence Corporation, Osaka, Japan) with a resolution of 10 nm is is used to measure the moving displacement of the slider. The piezoelectric stack (AE0505D16) is used to measure the moving displacement of the slider. The piezoelectric stack (AE0505D16) is from from NEC-Tokin and the size is 5 mm × 5 mm × 20 mm. NEC-Tokin and the size is 5 mm × 5 mm × 20 mm.

Figure 7. Experimental system and the prototype of the designed actuator. Figure 7. Experimental system and the prototype of the designed actuator.

4.2. Motion Performance Tests 4.2. Motion Performance Tests Figure 8 illustrates comparison of of motion motion performance about twotwo kinds of working modes, Figure 8 illustrates thethe comparison performance about kinds of working modes, namely stack A and B working together and stack A working alone. The given input voltages and namely stack A and B working together and stack A working alone. The given input voltages and driving frequency of two working modes are 100VVand and11Hz, Hz,respectively. respectively. It driving frequency of two working modes are 100 It can canbe beseen seenthat thatwhen when the the sawtooth wave voltage is applied to the piezoelectric stacks, the slider mover will move stepwise sawtooth wave voltage is applied to the piezoelectric stacks, the slider mover will move stepwise in a in a working circle, that is, even if the slider reaches the maximum displacement L2 at time t1, it will working circle, that is, even if the slider reaches the maximum displacement L2 at time t1 , it will retract retract a slight distance L1 during time of t2. This may be caused by the condition that when flexure a slight distance L1 during of t2 . This may be the caused that the when flexure hinges hinges reverting back to time their undeformed shape, sliderby is the still condition in contact with flexure hinge reverting the slider still in contact with the during duringback timetot1 their to t2. undeformed Then the slidershape, will move back aissmall distance L1 under the flexure action ofhinge sliding timefriction t1 to t2 .force. ThenTherefore, the sliderthe will move backdisplacement a small distance under action of sliding friction real stepping of theL1slider in the a working circle can be force.calculated Therefore, thethe real stepping displacement of the slider in a working circle can be calculated from from following equation:

the following equation:

ΔL = L − L

∆L = L22 − L1 1

(6)

(6)

Here, ∆L is the stepping displacement, L2 is the maximum displacement of forward motion and Here, ∆L is the stepping displacement, L is the maximum displacement of forward motion and L1 is the displacement of backward motion in2a working circle. L1 is the displacement backward a working Additionally, itofcan be notedmotion that theinwhen stack Acircle. and stack B work together, the stepping Additionally,is itobviously can be noted thatthat the when whenstack stack A andalone. stackSeen B work stepping displacement larger than A works from together, the Figure the 8, when displacement isAobviously than that whenvoltage stack and A works alone.frequency, Seen from the Figure 8, piezo stacks and B worklarger together at 100 V input 1 Hz driving the stepping of the slidertogether can reach μm. Similarly, stepping displacement is 2.68 whendisplacement piezo stacks∆L A and B work at 9.39 100 V input voltagethe and 1 Hz driving frequency, the μm stepping when piezo A works These results thatthe thestepping combination of two kinds flexure displacement ∆Lstack of the slider alone. can reach 9.39 µm.confirm Similarly, displacement is of 2.68 µm when enablesThese the actuator toconfirm have a great both in resolution stepping motionhinge piezohinge stackmechanism A works alone. results thatenhance the combination of twoof kinds of flexure and working stroke, and so does the motion speed of it, the motion speed can be written as follows:

mechanism enables the actuator to have a great enhance both in resolution of stepping motion and working stroke, and so does the motion speedVof= it, theLmotion speed can be written as follows: f ×Δ (7)

where V is the motion speed of slider mover, f is the driving frequency, and ∆L is the stepping V = f × ∆L (7) displacement in a working circle. Figure 9 illustrates the motion displacement of the slider under different input voltages when where V is the motion speed of slider mover, f is the driving frequency, and ∆L is the stepping stack A and stack B work together. Obviously, the motion displacement of the slider mover in one displacement in a working circle. working circle varies with the input voltage. When the input frequency is relatively low, such as 1 Figure 9 illustrates the motion displacement of the theinput slidervoltage understably. different input voltages Hz, the motion displacement will increase along with Figure 10 presents thewhen stackrelationship A and stack B work together. Obviously, motion displacement of the modes. slider mover between stepping displacement andthe input voltage about two working It can bein one working circle with the input voltage. increases When the input frequency is relatively low, such as 1 Hz, clearly seenvaries that the stepping displacement along with the enlargement of input voltage

the motion displacement will increase along with the input voltage stably. Figure 10 presents the relationship between stepping displacement and input voltage about two working modes. It can be


9 of 14

Micromachines 150 9 of 14 clearly seen that2017, the8, displacement increases along with the enlargement of input voltage as Micromachines 2017, 8,stepping 150 9 of 14 Micromachines 2017, 8, 150 9 of 14 well, and it agrees with the fact that the extension of piezoelectric stack will becomes greater when its well, and it agrees with the fact that the extension of piezoelectric stack will becomes greater when well, and itit agrees agrees withmaximum the fact fact that thatstepping the extension extension of piezoelectric piezoelectric becomes greater when driving voltage rises. The displacement is 9.37stack µm will when the stack A and stack B well, and the when its driving voltagewith rises.the The maximum stepping of displacement isstack 9.37 will μm becomes when thegreater stack A and its driving voltage rises. The maximum stepping displacement is 9.37 μm when the stack A and than workits together at 100 V input voltage. Considering the fact that when the input voltage is less driving voltage rises. The maximum stepping displacement is 9.37 μm when the stack A and stack B work together at 100 V input voltage. Considering the fact that when the input voltage is less stack work together together at 100 100 V V input voltage. voltage. Considering the fact fact that that when the the input voltage voltage is less less BB at input Considering the when input is 20 V,stack the actuator cannot move forward smoothly, sosmoothly, the effective minimum stepping displacement of than 20work V, the actuator cannot move forward so the effective minimum stepping than 20 20 V, V, the the actuator actuator cannot cannot move move forward forward smoothly, smoothly, so so the the effective effective minimum minimum stepping stepping than the actuator is 0.29ofµm. is, the of this actuator can beofequivalent to the displacement theThat actuator is motion 0.29 μm.resolution That is, the motion resolution this actuator caneffective be displacement of of the the actuator actuator is is 0.29 0.29 μm. μm. That That is, is, the motion resolution resolution of of this this actuator actuator can can be be displacement minimum stepping namely 0.29 displacement, µm. the motion equivalent to thedisplacement, effective minimum stepping namely 0.29 μm.

equivalent to to the the effective effective minimum minimum stepping stepping displacement, displacement, namely namely 0.29 0.29 μm. μm. equivalent

Figure 8. Motion displacement of two kinds working modes: stack A working alone, and stack A and

Figure 8. Motion displacement of of two kinds working stack Aworking workingalone, alone, and stack A and B Figure 8. Motion Motion displacement of two kinds workingmodes: modes: stack stack A A working alone, and stack A and and Figure 8. displacement two kinds working modes: and stack A B working together. B working together. working together. B working together.

Figure 9. Motion displacement under different input voltages.

Figure 9. Motiondisplacement displacement under under different input voltages. Figure Motion displacement input voltages. Figure 9. 9. Motion underdifferent different input voltages.

Figure 10. Stepping displacement under two working modes at different input voltages. Figure 10. Stepping displacement under two working modes at different input voltages.

Figure 10. Stepping displacement under two working modes at different input voltages. Figure 10. Stepping displacement under two working modes at different input voltages.

Micromachines 2017, 8, 150 Micromachines 2017, 2017, 8, 8, 150 150 Micromachines

10 of 14 10 of of 14 14 10

As shown in Figure 11, when the input voltages of piezo piezo stacks A and and are both 100 V, V, the As input voltages of stacks A BB are 100 As shown shownin inFigure Figure11, 11,when whenthe the input voltages of piezo stacks A and B both are both 100the V, motion displacement varies greatly with different driving frequency. Figure 11a illustrates the motion displacement varies greatly with different driving frequency. the motion displacement varies greatly with different driving frequency.Figure Figure11a 11aillustrates illustrates the the motion displacement of the slider when the piezo stacks are working under low frequency: 1, 2, 4, motion motion displacement displacementof ofthe the slider slider when when the the piezo piezo stacks stacks are are working working under under low low frequency: frequency:1, 1,2, 2,4, 4, and 8 Hz. Figure 11b shows the motion displacement at the high frequency: 10, 20, 40, 80, and 100 and 8 Hz. Figure 11b shows the motion displacement at the high frequency: 10, 20, 40, 80, and 100 and 8 Hz. Figure 11b shows the motion displacement at the high frequency: 10, 20, 40, 80, and 100 Hz. Hz. These results indicate that, with the increases increases of driving driving frequency, the backward backward motion of the Hz. These results indicate the of frequency, the motion the These results indicate that,that, withwith the increases of driving frequency, the backward motion of theof slider slider is and more anddifficult more difficult difficult to observe observe in aa working working circle. This is is caused caused by the the fact that the slider is more and more to in circle. by the is more more to observe in a working circle. This is This caused by the fact thatfact thethat flexible flexible part of the flexure hinge cannot recover to its undeformed shape in a limited response flexible part of the flexure hinge cannot recover to its undeformed shape in a limited response part of the flexure hinge cannot recover to its undeformed shape in a limited response interval time interval time before beforethe undergoing the next next working circle. circle. interval time undergoing the working before undergoing next working circle.

Figure11. 11.Motion Motiondisplacement displacementunder underdifferent different driving driving frequencies: frequencies: (a) (a) 1–8 1–8 Hz; Hz; and and (b) (b) 10–100 10–100 Hz. Hz. Figure 11. Motion displacement under different Figure

Accordingly, the motion speed speed is is also also considered considered to to be another another performance performance indicator indicator of the Accordingly, Accordingly, the the motion motion speed is also considered to be be another performance indicator of of the the designed actuator. Figure 12 presents the relationship between motion speed and driving frequency designed designedactuator. actuator. Figure Figure 12 12 presents presents the the relationship relationship between between motion motion speed speed and and driving drivingfrequency frequency when the input voltages of stack A and stack are both 100 V. It can can be be found found in in Figure 12a that the when when the the input input voltages voltagesof ofstack stackA Aand andstack stackBB Bare areboth both100 100V. V. It It can be found in Figure Figure 12a 12a that that the the piezoelectric actuator would work stably when the driving frequency is below 510 Hz. However, the piezoelectric when thethe driving frequency is below 510 510 Hz. Hz. However, the piezoelectricactuator actuatorwould wouldwork workstably stably when driving frequency is below However, stepping displacement will sharply sharply decrease when the driving driving frequency is higher higher than than 510 Hz, Hz, and stepping displacement will decrease when the frequency is than 510 the stepping displacement will sharply decrease when the driving frequency is higher 510and Hz, this may be caused by the fact that due to the flexure hinges’ mechanical inertia, the elastic this may be caused by the fact that due to the flexure hinges’ mechanical inertia, the elastic and this may be caused by the fact that due to the flexure hinges’ mechanical inertia, the elastic deformation offlexure flexurehinges hinges cannot be synchronized synchronized with the elongation elongation of stacks stacksthe when the deformation flexure hinges cannot the of when the deformation of cannot be be synchronized withwith the elongation of stacks when driving driving frequency is quiteInhigh. high. Inwords, other words, words, the piezoelectric piezoelectric stack is unable unable to accomplish accomplish driving frequency quite In other the is to aa frequency is quite is high. other the piezoelectric stack isstack unable to accomplish a stable stable performance at fairly high driving frequency. According to the Equation (7), when the input stable performance at high fairlydriving high driving frequency. According to the Equation (7),the when thevoltage input performance at fairly frequency. According to the Equation (7), when input voltage for both stackstack A and and stack is 100 100 with V, along along with the the driving frequency frequency being 510 Hz, the the voltage both A BB along is V, with driving Hz, for bothfor stack A stack and B isstack 100 V, the driving frequency being 510 being Hz, the510 maximum maximum motion speed of the slider is 3.27 mm/s. maximum motion speed of the slider is 3.27 mm/s. motion speed of the slider is 3.27 mm/s.

Figure 12. (a) Illustration of the motion speed under various driving frequencies; (b) illustration of the Figure Figure12. 12.(a) (a)Illustration Illustrationof ofthe themotion motionspeed speedunder undervarious variousdriving drivingfrequencies; frequencies;(b) (b)illustration illustrationof ofthe the partial enlarged drawing of motion speed under low driving frequency: 1–100 Hz. partial frequency: 1–100 Hz. partialenlarged enlargeddrawing drawingof ofmotion motionspeed speedunder underlow lowdriving driving frequency: 1–100 Hz.

In order order to to quantitatively quantitatively explain explain the the correlation correlation between between motion motion speed speed and and driving driving frequency, frequency, In two linear equations of speed and driving frequency are given in Figure 12b by applying the least least two linear equations of speed and driving frequency are given in Figure 12b by applying the


11 of 14


11 of 14

In order to quantitatively explain the correlation between motion speed and driving frequency, square method. Obviously, when the driving frequency is less than 100 Hz, the linear relationship two linear equations of speed and driving frequency are given in Figure 12b by applying the least can be approximately written as follows with the piezoelectric stacks A and B working together: square method. Obviously, when the driving frequency is less than 100 Hz, the linear relationship can be approximately written as follows with ythe piezoelectric = 8.15 x +12.85stacks A and B working together: (8)

On the other hand, when piezoelectric stack+A is working alone, the relationship can (8) be y = 8.15x 12.85 approximately written as follows: On the other hand, when piezoelectric stack A is working alone, the relationship can be y = 4.58x − 3.46 (9) approximately written as follows: y = 4.58x − 3.46 where y is the motion speed of the slider mover (μm/s), and x denotes the driving frequency (Hz).(9) In summary, the input voltage and driving frequency both can considerably influence the where y is the motion speed of the slider mover (µm/s), and x denotes the driving frequency (Hz). motion performance of the designed piezoelectric actuator. In summary, the input voltage and driving frequency both can considerably influence the motion performance of the designed piezoelectric actuator. 4.3. First Resonance Frequency Tests 4.3. First Resonance Frequency In order to verify that theTests stator will not show obvious vibration when it working under the low driving frequency, the first resonance frequency of obvious the statorvibration were measured a vibration In order to verify that the stator will not show when it by working underanalyzer the low (INV3018C from China Orient Institute of Noise and Vibration). When conducting the test, analyzer a model driving frequency, the first resonance frequency of the stator were measured by a vibration hammer (Coinv MSC-3)Orient is utilized to of provide impulse force excitation, then the was (INV3018C from China Institute Noise and Vibration). When conducting thetest test,data a model collected and analyzed in a modal analyzer softer (Coinv DASP v10). Figure 13 illustrates the hammer (Coinv MSC-3) is utilized to provide impulse force excitation, then the test data was collected experimental result when the flexure hinge mechanism is actuated by the model hammer in the x and analyzed in a modal analyzer softer (Coinv DASP v10). Figure 13 illustrates the experimental result direction. Similarhinge results in the y direction canby bethe obtained via the same but not illustrated when the flexure mechanism is actuated model hammer in themethod, x direction. Similar results herein. It can be found that the first resonance frequency of the designed actuator is 706.1 Hz, and in the y direction can be obtained via the same method, but not illustrated herein. It can be found that there will be noticeable vibration only when the stator is operating at the highvibration driving the first resonance frequency of the designed actuator is 706.1 Hz, and there willrelatively be noticeable frequency. That is, the stator canatachieve stable high linear motion when the piezo stacks arecan driven at only when the stator is operating the relatively driving frequency. That is, the stator achieve the conventional testing frequencies. stable linear motion when the piezo stacks are driven at the conventional testing frequencies.

Figure 13. 13. Experimental Experimental results results of of the the first first resonance resonance frequency tests. Figure

4.4. Electrical Electrical Loading Loading Rates Rates Tests Tests Electrical Electrical loading loading rates rates can can considerably considerably influence influence the the responses responses of of the the structure structure with with PZT PZT actuators [24,25]. When When the the driving driving frequency frequency and and amplitude amplitude of of the the input input voltage voltage are are unchangeable, unchangeable, the electrical loading loading rate rate is affected by the symmetry of sawtooth input voltage. Thus, Thus, five kinds of typical symmetry symmetryofof sawtooth voltage are applied piezo stacks to the thisthis sawtooth wavewave voltage are applied to piezo to stacks to compare thecompare performance performance of the actuator. of the actuator. Figure 14 illustrates the motion displacement of the slider in a working circle when piezo stacks are subjected subjected to toVVmax max = 100 (V) (V)with withdifferent differentloading/unloading loading/unloadingrates, rates,and and driving frequency of thethe driving frequency of the the sawtooth wave voltage is 1 Hz. It can be clearly seen that when the percentage of the stacks’ charging time in a working circle is less than 80%, the retraction displacement of slider are significant, and it will seriously reduce the effective stepping displacement of the actuator.


12 of 14


12 of 14

Micromachines 2017,voltage 8, 150 sawtooth wave

12 of 14 is 1 Hz. It can be clearly seen that when the percentage of the stacks’ charging However, when the percentage of stacks’ charging time in a working circle is too high, for instance time in a working circle is less than 80%, the retraction displacement of slider are significant, and it will 85% or higher, hysteresis of of thestacks’ displacement more easily. That say, when the input However, whenthe the chargingoccurs time in aactuator. working circleisistotoo high, instance seriously reduce the percentage effective stepping displacement of the However, when thefor percentage voltage is abruptly unloading (Vmax →0), piezo occurs stacks more cannot be fully duethe to input their 85% or higher, the hysteresis of the displacement easily. Thatordischarged ishigher, to say,the when of stacks’ charging time in a working circle is too high, for instance 85% hysteresis of capacitance characteristics. voltage is abruptly unloading (Vmax→0), stacks cannot be fully discharged due to their the displacement occurs more easily. That piezo is to say, when the input voltage is abruptly unloading capacitance characteristics. (V max →0), piezo stacks cannot be fully discharged due to their capacitance characteristics.

Figure 14. Displacement of the slider in a working circle with different percentages of stacks’ charging time.14. 14. Figure Displacement of the slider a working circle with different percentages stacks’ charging Figure Displacement of the slider in ainworking circle with different percentages of of stacks’ charging time. time.

4.5. In Situ Observation of the Stick-Slip Process 4.5. In Situ Observation of the Stick-Slip Process 4.5. InASitu Observation ofdevice the Stick-Slip charge-coupled (CCD) Process camera (Nikon SMZ25, Tokyo, Japan) is used to record the A charge-coupled device (CCD) camera (Nikon SMZ25, Tokyo, Japan) is used to record the stick-slip process in real-time. As shown in Figure 15a,SMZ25, a dark line is marked the contact A charge-coupled device (CCD) camera (Nikon Japan) isnearly used to to the record the stick-slip process in real-time. As shown in Figure 15a, a darkTokyo, line is marked nearly to contact region in process the slider, and it is As used as a in reference to measure the motion displacement. Since the stick-slip in real-time. shown Figure 15a, a dark line is marked nearly to the contact region in the slider, and it is used as a reference to measure the motion displacement. Since the bridge-type flexure hinge is holding the slider through the preload force, it can push the slider to move region in the slider,hinge and isit holding is used the as slider a reference to the measure motion the bridge-type flexure through preloadthe force, it candisplacement. push the sliderSince to move along the x direction. By applying a continued 20 s driving voltageforce, of 100itVcan and the driving frequency bridge-type flexure hinge is holding the slider through the preload push the slider to move along the x direction. By applying a continued 20 s driving voltage of 100 V and the driving frequency of 10 Hz sawtooth signal to the piezo-stacks, piezoelectric stack B will push the slider and along the sawtooth x direction. By applying a continued the 20 driving voltage of 100 V and theboth driving frequency of 10 Hz signal to the piezo-stacks, thes piezoelectric stack B will push both the slider and piezo-stack A to move a large-stroke displacement ∆S of 2.04 mm, as shown in Figure 15b. It is verified of 10 Hz sawtooth signal to the piezo-stacks, the piezoelectric stack B will in push both theItslider and piezo-stack A to move a large-stroke displacement ∆S of 2.04 mm, as shown Figure 15b. is verified that the combination ofa two kinds ofdisplacement flexure hinges∆Sand an adjustable-normal-force mechanism gains piezo-stack A to move large-stroke of 2.04 mm, as shown in Figure 15b. It is verified that the combination of two kinds of flexure hinges and an adjustable-normal-force mechanism gains the advantage in enhancing stroke for the nanopositioning systems. Moreover, for a video of that the combination of two working kinds of flexure hinges and an adjustable-normal-force mechanism gains the advantage in enhancing working stroke for the nanopositioning systems. Moreover, for a video of the in situ observation of the stick-slip please see the Supplementary Information. the in enhancing stroke forsee thethe nanopositioning systems. Moreover, for a video of the advantage in situ observation of theworking stick-slip please Supplementary Information. the in situ observation of the stick-slip please see the Supplementary Information.

Figure 15. In In situ situ observation observation of the stick-slip process: (a) initial initial position; and (b) ending position. Figure 15. In situ observation of the stick-slip process: (a) initial position; and (b) ending position.

5. 5. Conclusions Conclusions 5. Conclusions A piezo-driven linear A novel novel piezo-driven linear actuator actuator based based on on the the stick-slip stick-slip principle principleisisproposed proposedin inthis thispaper. paper. It can achieve both large-stroke and high-resolution linear motion by using only two piezo novel piezo-driven linear and actuator based on thelinear stick-slip principle is proposed this stacks. paper. It canAachieve both large-stroke high-resolution motion by using only twoin piezo stacks. The actuator mainly consistsofof a bridge-type flexure hinge, a compound parallelogram It can achievemainly both large-stroke high-resolution linear by using only two flexure piezo flexure stacks. The actuator consists a and bridge-type flexure hinge, amotion compound parallelogram hinge, hinge, and a linear motion module. The working principle and optimization of geometry are The mainly module. consists of bridge-type flexureand hinge, a compound parallelogram flexure and actuator a linear motion Thea working principle optimization of geometry are discussed. discussed. working performance of the actuator, prototype is fabricated and a series hinge, andTo a verify linear the motion module. The working principle aand optimization of geometry are of experiments are conducted. Furthermore, the variations in step sizes and velocities are observed discussed. To verify the working performance of the actuator, a prototype is fabricated and a series of experiments are conducted. Furthermore, the variations in step sizes and velocities are observed


13 of 14

To verify the working performance of the actuator, a prototype is fabricated and a series of experiments are conducted. Furthermore, the variations in step sizes and velocities are observed by changing the driving voltage and frequency, respectively. The minimum step size for the linear motion is 0.29 µm when the input voltage is 20 V. Moreover, the actuator has maximum linear velocity of 3.27 mm/s when all driving voltages and the frequency are 100 V and 510 Hz, respectively. The experiment results confirm that the combination of two kinds of flexure hinges and an adjustable-normal-force mechanism is valid in enhancing positioning accuracy and working stroke for nanopositioning systems. Further studies will be performed to investigate the relationship between stepping displacement and roughness of the contacting surface in the future. Supplementary Materials: The following are available online at www.mdpi.com/2072-666X/8/5/150/s1. Video S1: In situ observation of the stick-slip process in the CCD camera. Acknowledgments: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: this research is funded by The National Natural Science Foundation of China (51422503, 51505180), Fund Guiding on Strategic Adjustment of the Jilin Provincial Economic Structure Project (2014Z045), Major Project of Jilin Province Science and Technology Development Plan (20150203014GX, 20150520108JH, 20170101134JC), the Jilin Provincial Industrial Innovation Special Fund Project (2016C030), and the Fundamental Research Funds for Central Universities. Author Contributions: Zunqiang Fan is responsible for the main composition and modification of the work; Mingxing Zhou designed and conducted the experiments and drafted the manuscript; Zhichao Ma and Hongwei Zhao are responsible for the task assignment and the overall planning; Yue Guo and Kun Hong are responsible for analyzing the experiment data; Yuanshang Li and Hang Liu prepared the figures and the deduction of the formula; and Di Wu assembled the protype and supervised the research. Conflicts of Interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References 1.

2. 3. 4.

5. 6.

7. 8. 9.

10. 11.

Yong, Y.K.; Moheimani, S.O.R.; Kenton, B.J.; Leang, K.K. Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues. Rev. Sci. Instrum. 2012, 83, 802–843. [CrossRef] [PubMed] Tian, Y.; Zhang, D.; Shirinzadeh, B. Dynamic modelling of a flexure-based mechanism for ultra-precision grinding operation. Precis. Eng. 2011, 35, 554–565. [CrossRef] Polit, S.; Dong, J. Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing. IEEE/ASME Trans. Mechatron. 2011, 16, 724–733. [CrossRef] Hou, X.; Lee, H.P.; Ong, C.J.; Lim, S.P. Development and numerical characterization of a new standing wave ultrasonic motor operating in the 30–40 kHz frequency range. Ultrasonics 2013, 53, 928–934. [CrossRef] [PubMed] Lim, K.J.; Lee, J.S.; Park, S.H.; Kang, S.H.; Kim, H.H. Fabrication and characteristics of impact type ultrasonic motor. J. Eur. Ceram. Soc. 2007, 27, 4159–4162. [CrossRef] Fernandez, J.M.; Perriard, Y. Comparative analysis and modeling of both standing and travelling wave ultrasonic linear motor. In Proceedings of the 2003 IEEE Symposium on Ultrasonics, Honolulu, HI, USA, 5–8 October 2003; Volume 2, pp. 1770–1773. Park, K.H.; Lee, J.H.; Kim, S.H.; Kwark, Y.K. High speed micro positioning system based on coarse/fine pair control. Mechatronics 1995, 5, 645–663. [CrossRef] Wu, Z.; Li, Y. Design, Modeling, and Analysis of a Novel Microgripper Based on Flexure Hinges. Adv. Mech. Eng. 2014, 8, 1–11. [CrossRef] Li, C.; Gu, G.; Zhu, L.; Su, C. Odd-harmonic repetitive control for high-speed raster scanning of piezo-actuated nanopositioning stages with hysteresis nonlinearity. Sens. Actuators A 2016, 244, 95–105. [CrossRef] Park, J.; Keller, S.; Carman, G.P.; Hahn, H.T. Development of a compact displacement accumulation actuator device for both large force and large displacement. Sens. Actuators A 2001, 90, 191–202. [CrossRef] Peng, Y.; Peng, Y.; Gu, X.; Wang, J.; Yu, J. A review of long range piezoelectric motors using frequency leveraged method. Sens. Actuators A 2015, 235, 240–255. [CrossRef]


12. 13. 14.

15. 16.

17. 18. 19.

20. 21. 22. 23. 24. 25.

14 of 14

Den Heijer, M.; Fokkema, V.; Saedi, A.; Schakel, P. Improving the accuracy of walking piezo motors. Rev. Sci. Instrum. 2014, 85, 31–736. [CrossRef] [PubMed] Chen, T.; Wang, Y.; Yang, Z.; Liu, H.; Liu, J.; Sun, L. A PZT Actuated Triple-Finger Gripper for Multi-Target Micromanipulation. Micromachines 2017, 8, 33. [CrossRef] Breguet, J.-M.; Clavel, R. Stick and slip actuators: Design, control, performances and applications. In Proceedings of the 1998 International Symposium on Micromechatronics and Human Science (1998 MHS’98), Nagoya, Japan, 25–28 November 1998. Pan, P.; Yang, F.; Wang, Z.; Zhong, B.; Sun, L.; Ru, C. A Review of Stick—Slip Nanopositioning Actuators. In Nanopositioning Technologies; Springer International Publishing: Basel, Switzerland, 2016; pp. 1–32. Zhang, Y.; Zhang, W.; Hesselbach, J.; Kerle, H. Development of a two-degree-of-freedom piezoelectric rotary-linear actuator with high driving force and unlimited linear movement. Rev. Sci. Instrum. 2006, 77, 465–481. [CrossRef] Stieg, A.Z.; Wilkinson, P.; Gimzewski, J.K. Vertical inertial sliding drive for coarse and fine approaches in scanning probe microscopy. Rev. Sci. Instrum. 2007, 78, 036110. [CrossRef] [PubMed] Li, J.; Zhou, X.; Zhao, H.; Shao, M.; Hou, P.; Xu, X. Design and experimental performances of a piezoelectric linear actuator by means of lateral motion. Smart Mater. Struct. 2015, 24, 065007. [CrossRef] Hao, G.; Kong, X. Conceptual Design and Modelling of a Self-Adaptive Compliant Parallel Gripper for High-Precision Manipulation. In Proceedings of the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, IL, USA, 12–15 August 2012; pp. 161–167. Hao, G.; Hand, R.B. Design and static testing of a compact distributed-compliance gripper based on flexure motion. Arch. Civ. Mech. Eng. 2016, 16, 708–716. [CrossRef] Hao, G.; Li, H. Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multi-beam Parallelogram Mechanisms. J. Mech. Robot. 2015, 7, 041016. [CrossRef] Hao, G.; Kong, X.; Reuben, R.L. A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules. Mech. Mach. Theory 2011, 46, 680–706. [CrossRef] Khuri, A.I.; Mukhopadhyay, S. Response surface methodology. Wiley Interdiscip. Rev. Comput. Stat. 2010, 2, 128–149. [CrossRef] Hunstig, M. Piezoelectric Inertia Motors—A Critical Review of History, Concepts, Design, Applications, and Perspectives. Actuators 2017, 6, 7. [CrossRef] Luo, Q.; Tong, L. Design and testing for shape control of piezoelectric structures using topology optimization. Eng. Struct. 2015, 97, 90–104. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).