Development of a Rotary Ultrasonic Motor with Double-Sided Staggered Teeth

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Article Development of a Rotary Ultrasonic Motor with Double-Sided Staggered Teeth

Xiaohui Yang * , Dongdong Zhang, Rujun Song, Chongqiu Yang and Zonggao Mu

School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China; [email protected] (D.Z.); [email protected] (R.S.); [email protected] (C.Y.); [email protected] (Z.M.) * Correspondence: [email protected]

Abstract: Based on the conventional structure of traveling wave ultrasonic motor, a rotary ultrasonic motor with double-sided staggered teeth was proposed. Both sides of the stator could be used to actuate the rotors to rotate and output torque. Moreover, the staggered teeth in the stator could be dedicated to accommodating the piezoelectric ceramic chips. Under the excitation of two alternating voltages with a 90◦ phase difference, a traveling wave could be generated in the ring-like stator. Then, a rotary motion could be realized by means of the friction between the rotors and the driving teeth of the stator. The ﬁnite element method was adopted to analyze the motion trajectories of the driving tips. Moreover, the experimental results showed that the load-free maximum speed and maximum output torque of the prototype were 99 rpm and 0.19 N·m at a voltage of 150 Vp with a frequency of 28.25 kHz.

Keywords: bonded-type; double-sided staggered teeth; traveling wave; ultrasonic motor

Citation: Yang, X.; Zhang, D.; Song, R.; Yang, C.; Mu, Z. Development of a Rotary Ultrasonic Motor with 1. Introduction Double-Sided Staggered Teeth. The ultrasonic motor (USM) is a new type of actuator based on the converse piezo- Micromachines 2021, 12, 824. https:// electric effect [1–3], which has attracted a lot of attention due to its excellent features, doi.org/10.3390/mi12070824 such as being lightweight, its instant reaction, low-noise, higher position accuracy and self-locking [4–7]. The stator is usually a composite elastomer of metal and piezoelectric Academic Editor: Jose Luis ceramics in a special structure conﬁguration. The driving nodes on the frictional contact Sanchez-Rojas surfaces of the stator vibrate in an elliptic trajectory, which drives the rotor by the frictional force [8–12]. Received: 11 June 2021 According to the vibration form of the stator, the USM can be classiﬁed into standing Accepted: 13 July 2021 Published: 14 July 2021 wave motors [13,14], traveling wave motors [15–17] and composite vibration modes motors [18–20]. The standing wave motors usually have merits of simple structure and large

Publisher’s Note: MDPI stays neutral output force; its disadvantages are large velocity perturbation and difficulty of bidirec- with regard to jurisdictional claims in tional driving [21,22]. The composite vibration modes motors exhibit high speed and large published maps and institutional affil- torque but usually have the problem of frequency degeneration [23]. The traveling wave iations. motors have better control performance than the above two types [24–26]. Furthermore, the bonded-type ring motor may be the most typical traveling wave ultrasonic motor, which is widely used in many fields such as camera auto-focus systems and medical instru- ments [27]. Moreover, generally, the flexural mode of a metal ring is used to excite the axial vibration of the stator. However, one side of the stator in the conventional traveling wave Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. ultrasonic motor is piezoelectric ceramics, another side of which is the driving teeth. In This article is an open access article other words, only one side of the stator is used to drive the rotor, while the traveling wave distributed under the terms and energy on the other side is wasted. conditions of the Creative Commons A rotary traveling wave ultrasonic motor with double-sided staggered teeth is pro- Attribution (CC BY) license (https:// posed in this study. The teeth are staggered on both sides of the stator ring, and every creativecommons.org/licenses/by/ piezoelectric ceramic chip is placed between the two groups of teeth. If two alternating ◦ 4.0/). voltages with a 90 phase difference are applied to the top and the bottom ceramic chips,

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voltages with a 90° phase difference are applied to the top and the bottom ceramic chips, respectively, a traveling wave could be generated in the stator, which can drive the two respectively,rotors to rotate a travelingin the same wave direction. could If be the generated phase difference in the stator, of the which two alternating can drive voltages the two rotorsis change to rotated to be in −90°, the same the dual direction.-rotor system If the phase will be difference rotated ofin the tworeverse alternating direction. voltages In this ◦ isstudy, changed the structure to be −90 and, the operating dual-rotor principle system willof the be proposed rotated in ultrasonic the reverse motor direction. are pre- In thissented. study, Then, the the structure vibration and characteristics operating principle of the stator, of the proposedincluding ultrasonicresonant frequen motorcies are presented.and motion Then, of the the driving vibration nodes, characteristics are analyzed of theby way stator, of including the finite resonantelement frequenciesmethod. Fi- andnally, motion an experimental of the driving prototype nodes, are is assembled analyzed by and way tested. of the ﬁnite element method. Finally, an experimental prototype is assembled and tested. 2. Structure of The Motor 2. Structure of The Motor Figure 1 shows the overall structure of the proposed motor, which is composed of Figure1 shows the overall structure of the proposed motor, which is composed of ﬁve five main parts: the stator, the dual-rotor system, the ball bearing, the base and the shell. main parts: the stator, the dual-rotor system, the ball bearing, the base and the shell.

(a)

(b) (c)

FigureFigure 1.1. TheThe structurestructure of of the the proposed proposed motor: motor: (a ()a assembly) assembly view; view; (b )(b internal) internal structure structure view; view; (c) explosive(c) explosive view view of the of stator.the stator. In Figure1a, the dual-rotor system mainly comprises the disc rotor, the cylindric rotor and theIn Fig shaft.ureThe 1a, the shaft dual and-rotor disc rotorsystem are mainly integrated comprises to realize the thedisc mechanical rotor, the cylindric output. The ro- disctor and rotor the and shaft. the The cylindric shaft rotorand disc are connectedrotor are integrated with each to other realize through the mechanical the thread, output. which canThe adjustdisc rotor the pre-pressureand the cylindric applied rotor on are the connected driving teeth. with Twoeach screwother holesthrough are the set thread on the, cylindricwhich can rotor. adjust After the the pre pre-pressure-pressure applied is adjusted, on the the driving set screws teeth. placed Two intoscrew the holes screw are holes set canon the prevent cylindric relative rotor. rotation After betweenthe pre-pressure the two rotors.is adjusted, The ball the bearingset screws is connected placed into to thethe shaftscrew by holes interference can prevent fit. Therelative base rotation is used tobetween fix the the stator. two Additionally, rotors. The ball the bearing center hole is con- of thenected shell to makes the shaft the by dual-rotor interference system fit. andThe thebase stator is used to be to coaxial fix the viastator. the ballAdditionally, bearing. The the shellcenter is hole fixed of to the the shell base makes by four the screws. dual-rotor system and the stator to be coaxial via the ball bearing.In Figure The1b, shell the hub is fixed is fixed to the to base the cylinder by four scre of thews. base by four screws. The stator consists of the metal ring and 32 pieces of piezoelectric ceramics. The double-sided teeth are staggered on the metal ring, which has the hub and supporting plate. The supporting

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In Figure 1b, the hub is fixed to the cylinder of the base by four screws. The stator consists of the metal ring and 32 pieces of piezoelectric ceramics. The double-sided teeth are staggered on the metal ring, which has the hub and supporting plate. The supporting plate can effectively reduce the bad effect of the fixed hub on the stator vibration. As shown in Figure 1c, all piezoelectric ceramics (PZT) are polarized along the thickness and Micromachines 2021, 12, 824 3 of 10 divided into two groups, PZT-A and PZT-B, according to the location on the metal ring. In PZT-A or PZT-B, polarization directions of two adjacent ceramics are opposite. The staggered configuration of the piezoelectric ceramics and the driving teeth achieves the doubleplate can-sided effectively driving reduce function the of bad the effect stator of with the ﬁxed a compac hub ont structure. the stator vibration. As shown in FigureThe material1c, all piezoelectric of PZT-A and ceramics PZT-B (PZT) are PZT are- polarized4, and the along relevant the thicknessparameters and are divided listed ininto Table two 1. groups, The material PZT-A of and the PZT-B, metal accordingring is a hard to the aluminum location on alloy the metal(2A12), ring. the Indensity, PZT-A elasticor PZT-B, modulus polarization and Poisson’s directions ratio of which two adjacent are 2810 ceramics kg/m3, 66 are GPa opposite. and 0.33 The, respectively. staggered conﬁguration of the piezoelectric ceramics and the driving teeth achieves the double-sided Tabledriving 1. The function material of parameters the stator withof PZT a- compact4. structure. The material of PZT-A and PZT-B are PZT-4, and the relevant parameters are listed in Properties Values Table1. The material of the metal ring is a hard aluminum alloy (2A12), the density, elastic 3 modulus and Poisson’sdensity (kg/m ratio of) which are 2810 kg/m3, 66 GPa and7624.8 0.33, respectively. 0 0 − 5.6   Table 1. The material parameters of PZT-4. 0 0− 5.6 0 0 14.8 piezoelectricProperties stress matrix (C/m2)  Values 0 0 0 density (kg/m3) 7624.8  0 12.7 0  0 0 −5.6  12.70 0 0−5.6 0     0 0 14.8  piezoelectric stress matrix (C/m2)   14.7 8.50 7.9 0 0 0 0 0   8.5 14.70 7.912.7 0 0 0 0 7.9 7.912.7 11.9 0 0 0 0 0 anisotropic stiffness matrix (1010N/m2) 14.7 8.5 7.9 0 0 0  0 0 0 3.1 0 0 8.5 14.7 7.9 0 0 0    7.90 7.9 0 11.9 0 0 0 2.60 0 0  anisotropic stiffness matrix (1010 N/m2)   0 0 0 3.1 0 0  0 0 0 0 0 2.6  0 0 0 0 2.6 0  0762.6 0 0 0 0 0 0 2.6 762.6 0 0  relative permittivity matrix 0 762.6 0 relative permittivity matrix 0 762.6 0  0 0 0 523.9 523.9

3.3. Principle Principle of of the the Stator Stator Vibration Vibration FigFigureure 22 showsshows two two sinusoidal sinusoidal alternating alternating voltages voltages applied applied to PZT to PZT-A-A and and PZT PZT-B-B respectively,respectively, which which have have a phase a phase difference difference of of 90°. 90 ◦Each. Each group group of of the the piezoelectric piezoelectric ceramics, ceramics, PZTPZT-A-A or or PZT PZT-B,-B, can can generate generate a a standing standing wave wave in in the the stator stator under under the the excitation excitation of of one one alternatingalternating voltage. voltage.

FigureFigure 2. 2. TwoTwo sinusoidal sinusoidal alternating alternating voltages voltages with with 90° 90◦ phasephase difference. difference.

The following equations represent two standing waves obtained via exciting PZT-A and PZT-B in the stator: Y1 = ξ cos kx · cos ωt 0 0 (1) Y2 = ξ cos kx · cos ωt

where ξ is the amplitude, k is the wave vector (k = 2π/λ, λ is the wavelength), x and x0 are space angles, ω is the angular frequency of vibration, and t and t0 are the vibration times. According to the layout of PZT-A and PZT-B, x0 = x−λ/4. Because of the 90◦ phase Micromachines 2021, 12, x FOR PEER REVIEW 4 of 11

The following equations represent two standing waves obtained via exciting PZT-A and PZT-B in the stator:

Y1 =cos kx cos t  (1) Y=cos kx cos t  2 Micromachines 2021, 12, 824 4 of 10 where ξ is the amplitude, k is the wave vector (k=2π/λ, λ is the wavelength), x and x' are space angles, ω is the angular frequency of vibration, and t and t' are the vibration times. According to the layout of PZT-A and PZT-B, x'=x−λ/4. Because of the 90° phase difference differencebetween two between voltages, two t voltages,'=t−T/4 (Tt0 is= thet−T cycle)./4 (T is Therefore, the cycle). the Therefore, second standing the second wave standing equa- wavetion is equation also as follows: is also as follows: Y=sin kx sin t (2) Y2 =2 ξ sin kx · sin ωt (2) The two standing waves are superposed to form a flexural traveling wave under the The two standing waves are superposed to form a ﬂexural traveling wave under the above conditions. The traveling wave equation is presented as follows: above conditions. The traveling wave equation is presented as follows: Y= Y + Y =cos( t − kx ) 12 (3) Y = Y1 + Y2 = ξ cos(ωt − kx) (3) Figure 3 shows the movement process of any node P on the surface of driving teeth. h representsFigure3 showsthe distance the movement from point process P to the of anyneutral node surface P on the of surfacethe stator. of driving When the teeth. trav-h representseling wave the moves distance in the from stator, point the P stator to the ring neutral produces surface a of bending the stator. vibration. When the β is traveling the rota- wavetion angle moves of inthe the section stator, where the stator node ringP is located, produces and a bendingnode P moves vibration. from βpoiisnt the P0 rotation to point angleP1. of the section where node P is located, and node P moves from point P0 to point P1.

FigureFigure 3.3. TheThe movementmovement processprocess onon thethe surfacesurface ofof drivingdriving teeth.teeth.

AccordingAccording toto FigureFigure3 ,3, the the displacement displacement equations equations of of node node P P in in ZZ-axis-axis andandX X-axis-axis directionsdirections couldcould bebe obtainedobtained asas follows:follows: WZW=Z Y=− Y −h( h1(1− −cos β)  ((4)4) WhWX= =sinh sin β  X

TheThe bendingbending angle ββ isis tiny. tiny. Thus, Thus, the the axial axial vibration vibration displacement displacement WZW couldZ could be ap- be approximatedproximated as asfollows: follows: WZ ≈ Y = ξ cos(ωt − kx) (5) W Y =cos( t − kx ) Z (5) The beam deforms slightly, so the tangential vibration displacement WX could be expressedThe beam as follows: deforms slightly, so the tangential vibration displacement WX could be ex- pressed as follows: dY W ≈ hβ ≈ h = hξk sin(ωt − kx) (6) X dx dY W h  h = h  ksin(  t − kx ) The relationship between WXX and WZ satisﬁes the following equation: (6) dx 2 2 The relationship between WX Wand WZ satisfiesW the following equation: Z + X = 1 (7) ξ 22hkξ WWZX     +=   1 (7) Therefore, the ellipse trajectories on the surfacehk nodes of driving teeth are formed.     In Figure3, two ellipse trajectories in the top and bottom surfaces of the stator have reverseTherefore, directions the clockwise ellipse trajectories and anticlockwise, on the surface respectively. nodes of In driving this way, teeth the are two formed. rotors inIn contactFigure 3, with two the ellipse stator trajectories rotate in thein the same top direction and bottom under surfaces the friction of the stator force. ha If theve reverse phase difference of two alternating voltages is altered to be −90◦, two rotors will rotate in the opposite direction.

4. Analysis of the Stator In order to validate the effectiveness of the proposed motor, the ﬁnite element method was adopted to analyze the stator model in this study. Figure4a shows the main structural parameters of the ceramic chip. The thickness, width L and central angle α of the ceramic chip are 0.5mm, 10mm and 10◦, respectively. Figure4b shows the main structural parameters of the metal ring. H1 and R are the Micromachines 2021, 12, x FOR PEER REVIEW 5 of 11

directions clockwise and anticlockwise, respectively. In this way, the two rotors in contact with the stator rotate in the same direction under the friction force. If the phase difference of two alternating voltages is altered to be −90°, two rotors will rotate in the opposite direction.

4. Analysis of the Stator In order to validate the effectiveness of the proposed motor, the finite element method was adopted to analyze the stator model in this study. Micromachines 2021, 12, 824 5 of 10 Figure 4a shows the main structural parameters of the ceramic chip. The thickness, width L and central angle α of the ceramic chip are 0.5mm, 10mm and 10°, respectively. Figure 4b shows the main structural parameters of the metal ring. H1 and R are the dimen- sionsdimensions of the hub, of which the hub, are which determined are determined by the cylinder by the of cylinder the base. of Moreover, the base. the Moreover, hub was the fixedhub during was ﬁxed analysis, during which analysis, might which have mightlittle effect have on little the effect stator on vibration. the stator H vibration.1 is also theH 1 thicknessis also theof the thickness metal ring of the without metal regard ring without to the regardteeth, which to the determines teeth, which the determines axial bend- the ingaxial strength bending of the strength stator ofring. the L stator2 is the ring. widthL2 isof thethe widthteeth. ofH4 the is the teeth. heightH4 is of the the height teeth, of whichthe teeth,should which be a shouldlittle larger be a littlethan largerthe thickness than the of thickness the ceramic of the chip ceramic to prevent chip to contact prevent betweencontact the between rotor a thend the rotor ceramics. and the H ceramics.2 is the thicknessH2 is the of thickness the supporting of the supporting plate to hold plate the to statorhold ring, the which stator ring,should which be thinner should than be thinnerH1. L1 is thanthe lengthH1. L 1ofis the the supporting length of the plate, supporting which is determinedplate, which by is determinedthe outer diameter by the outerof thediameter stator ring. of the stator ring.

(a) (b)

FigureFigure 4. The 4. The main main structural structural parameters parameters of the of the stator: stator: (a) (Ceramica) Ceramic chip; chip; (b) ( bMetal) Metal ring. ring.

In Inthis this study, study, the the outer outer diameter diameter of the of thestator stator ring ring is 80 is mm, 80 mm, the other the other dimensions dimensions of whichof which are listed are listed in Table in Table 2. Additionally,2. Additionally, the the model model of ofstator stator without without the the hub hub and and the the supportingsupporting plate plate was was established established and and analyzed analyzed in infinite ﬁnite element element software software firstly. ﬁrstly. Modal Modal analysisanalysis was was carried carried out out to toextract extract the the resonant resonant frequencies frequencies of ofB(0,8) B(0,8) vibration vibration modes modes of of thethe stator, stator, which which were were 29.061 29.061 kHz kHz and and 29.074 29.074 kHz, kHz, respectively. respectively. Then, Then, the the model model of ofthe the entireentire stator stator was was established. established. Fig Figureure 5 shows5 shows the the vibration vibration shapes shapes of ofthe the stator, stator, Mode Mode-A-A andand Mode Mode-B,-B, where where B(0,8) B(0,8) bending bending vibration vibration modes modes can can be be recognized. recognized. B(0,8) B(0,8) bending bending vibrationvibration mode mode has has eight eight antinodes antinodes on on either either side side of ofthe the ring. ring. Mode Mode-A-A is isgenerated generated by by excitingexciting PZT PZT-A-A on on the the bottom bottom surface, surface, and and Mode Mode-B-B is generated is generated by by exciting exciting PZT PZT-B-B on on the the toptop surface. surface.

TableTable 2. 2.TheThe dimensions dimensions of ofthe the stator stator (unit: (unit: mm). mm).

Micromachines 2021, 12, x FOR PEER REVIEWL1 L2 RH1 H2 H3 H46 of 11 L1 L2 R H1 H2 H3 H4 10 5 15 3 1 1 2 10 5 15 3 1 1 2

(a) (b)

FigureFigure 5.5. Vibration modemode shapesshapes ofof thethe stator:stator: ((aa)) Mode-A;Mode-A; ((bb)) Mode-B.Mode-B.

TheThe resonanceresonance frequencies of thethe B(0,8)B(0,8) bendingbending vibrationvibration modemode ofof thethe entireentire statorstator werewere 28.99228.992 kHzkHz andand 28.998 kHz,kHz, respectively, whichwhich werewere 6969 HzHz andand 7676 HzHz different fromfrom thatthat withoutwithout thethe supportingsupporting plateplate andand thethe hub.hub. ItIt cancan bebe seenseen thatthat the supporting plateplate andand thethe hubhub playplay anan essentialessential rolerole inin thethe vibrationvibration characteristicscharacteristics ofof thethe stator.stator. Secondly,Secondly, transienttransient analysisanalysis usingusing thethe ﬁnitefinite elementelement methodmethod waswas analyzedanalyzed toto studystudy thethe travelingtraveling wavewave inin thethe stator.stator. Additionally,Additionally, thethe calculationcalculation waswas carriedcarried outout underunder thethe excitationexcitation of twotwo sinusoidalsinusoidal alternatingalternating voltages.voltages. The frequenciesfrequencies ofof thethe twotwo alternatingalternating voltages were both 28.995 kHz with the same value of 150 Vp. Three nodes, M1–M3, were selected to study the movement of one driving tooth, as shown in Figure 6.

Figure 6. The selection of nodes.

Figure 7a shows the motion trajectories of three nodes on one driving tooth in one cycle. In Figure 7a, the circumferential vibration displacements of three nodes are approximately equal, but the axial vibration displacements are different. The larger the radius of the node is, the stronger the axial vibration is. Then, eight center nodes of outer edges on eight evenly distributing teeth of the top surface were selected, T1–T8, as shown in Figure 6. There were another eight nodes selected, N1–N8, on the bottom surface in the same way. The motion trajectories of the 16 center nodes mentioned above are shown in Figure 7b,c. The motion trajectory consistency indicates that the traveling wave was generated in the stator ring, and rotation directions of the ellipse trajectories on the top and bottom surfaces were opposite. Overall, finite element simulations of the proposed stator model validate that the two rotors could rotate in the same direction.

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(a) (b)

Figure 5. Vibration mode shapes of the stator: (a) Mode-A; (b) Mode-B.

The resonance frequencies of the B(0,8) bending vibration mode of the entire stator were 28.992 kHz and 28.998 kHz, respectively, which were 69 Hz and 76 Hz different from that without the supporting plate and the hub. It can be seen that the supporting plate and

Micromachines 2021, 12, 824 the hub play an essential role in the vibration characteristics of the stator. 6 of 10 Secondly, transient analysis using the finite element method was analyzed to study the traveling wave in the stator. Additionally, the calculation was carried out under the excitation of two sinusoidal alternating voltages. The frequencies of the two alternating voltages were both 28.995 kHzkHz withwith thethe samesame valuevalue ofof 150150 VVpp.. ThreeThree nodes,nodes, MM11–M–M33, were selected to study the movement of one driving tooth, as shown in FigureFigure6 6..

Figure 6. The selection of nodes.

FigFigureure7 7aa shows shows the the motion motion trajectories trajectories of threeof three nodes nodes on one on drivingone driving tooth tooth in one in cycle. one cycle.In Figure In Fig7a,ure the 7a, circumferential the circumferential vibration vibration displacements displacements of three of nodes three arenodes approximately are approx- imatelyequal, but equal, the axialbut the vibration axial vibration displacements displacements are different. are different. The larger The the larger radius the of radius the node of theis, thenode stronger is, the stronger the axial the vibration axial vibration is. Then, is. eight Then, center eight center nodes nodes of outer of edgesouter edges on eight on eightevenly evenly distributing distributing teeth teeth of the of topthe surfacetop surface were were selected, selected, T1–T T18–,T as8, as shown shown in in Figure Figure6. There were another eight nodes selected, N –N , on the bottom surface in the same way. 6. There were another eight nodes selected, N1 1–N88, on the bottom surface in the same way. The motion trajectories of the 16 center nodes nodes mentioned mentioned above above are are shown shown in in Fig Figureure 77bb,c.,c. The motion trajectory consistency indicates that the traveling wave was generated in the Micromachines 2021, 12, x FOR PEER REVIEWThe motion trajectory consistency indicates that the traveling wave was generated7 in of the 11 stator ring, and rotation rotation directions of the ellipse trajectories on the top and bottom surfaces were opposite. Overall, finite ﬁnite element simulations of the proposed statorstator model validate that the two rotors could rotate in the same direction. that the two rotors could rotate in the same direction.

(a) (b) (c)

FigureFigure 7. 7. MotionMotion trajectories trajectories of of nodes: nodes: (a ()a three) three nodes nodes on on one one tooth; tooth; (b) ( eightb) eight center center nodes nodes on the on thetop topsurface; surface; (c) eight (c) eight centercenter nodes nodes on on the the bottom bottom surface. surface.

5.5. Experiments Experiments TheThe metal metal ring ring of of the the stator stator w wasas machined machined by by a a high high-precision-precision CNC CNC (computer (computer nu- nu- mericalmerical control) control) milling milling machine. machine. Then, Then, the the PZT PZT chips chips were were bonded bonded on on the the metal metal ring ring with with epoxy resin. Both bottom and top sides of the stator are shown in Figure 8a,b with welded wires. The whole prototype was assembled completely, as shown in Figure 8c.

(a) (b) (c)

Figure 8. The prototype of the proposed motor: (a) the bottom of the stator; (b) the top of the stator; (c) assembly view with shell and assembly view with no shell.

The admittance characteristics of the stator fixed on the base were measured by using an impedance analyzer (E4990A, Keysight Inc, Santa Rosa, CA, USA). Figure 9 shows the admittance test results of the prototype under the excitations of two modes. While PZT-A on the bottom of the stator was connected with the HIGH terminal via the red wire and the metal ring was connected with the LOW terminal via the yellow wire, the test results of Mode-A are shown in Figure 9a. While PZT-B on the top of the stator was connected with the HIGH terminal via the blue wire and the metal ring was connected with the LOW terminal via the yellow wire, the test results of Mode-B are shown in Figure 9b. The resonant frequencies of the two modes were 28.353 kHz and 28.171 kHz, respectively. The admittance test results of the prototype were different from the finite element simulation

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(a) (b) (c)

Figure 7. Motion trajectories of nodes: (a) three nodes on one tooth; (b) eight center nodes on the top surface; (c) eight center nodes on the bottom surface. Micromachines 2021, 12, 824 7 of 10 5. Experiments The metal ring of the stator was machined by a high-precision CNC (computer nu- merical control) milling machine. Then, the PZT chips were bonded on the metal ring with epoxyepoxy resin.resin. BothBoth bottombottom and top sides of the stator stator are are shown shown in in Fig Figureure 8a,8a,bb with welded welded wires.wires. TheThe wholewhole prototypeprototype waswas assembled completely completely,, as shown in Fig Figureure 88cc..

(a) (b) (c)

FigureFigure 8. 8.The The prototype prototype of of the the proposed proposed motor: motor: ( a()a) the the bottom bottom of of the the stator; stator; ( b(b)) the the top top of of the the stator; stator; ( c()c) assembly assembly view view with shellwith and shell assembly and assembly view withview no with shell. no shell.

TheThe admittanceadmittance characteristicscharacteristics of the stator fixed ﬁxed on on the the base base were were measured measured by by using using anan impedanceimpedance analyzeranalyzer (E4990A, Keysight Inc Inc,, Santa Rosa, Rosa, CA, CA, USA USA).). Fig Figureure 9 showshowss the the admittanceadmittance testtest resultsresults ofof the prototype under the excitations excitations of of two two modes. modes. While While PZT PZT-A-A onon thethe bottombottom ofof thethe statorstator was connected with the the HIGH HIGH terminal terminal via via the the red red wire wire and and thethe metalmetal ringring waswas connectedconnected with the LOW terminal terminal via via the the yellow yellow wire, wire, the the test test results results ofof Mode-AMode-A areare shownshown inin FigureFigure9 9a.a. WhileWhile PZT-BPZT-B onon thethe toptop ofof thethe statorstator was connected withwith thethe HIGH terminal terminal via via the the blue blue wire wire and and the metal the metal ring was ring connected was connected with the with LOW the Micromachines 2021, 12, x FOR PEER REVIEWLOWterminal terminal via the via yellow the yellow wire, the wire, test the results test results of Mode of- Mode-BB are shown are shown in Figure in Figure 9b. The9b. 8reso- Theof 11

resonantnant frequencies frequencies of the of the two two modes modes were were 28.353 28.353 kHz kHz and and 28.171 28.171 kHz, kHz, respectively. respectively. The The admittanceadmittance testtest resultsresults of the prototype were different from from the the finite ﬁnite element element simulation simulation results, which might result from the manufacturing and assembling process, oror neglectneglect of solder joints and epoxide resin, etc.

(a) (b)

Figure 9. Conductance and susceptance response spectrums under twotwo modesmodes excitations:excitations: (aa)) Mode-A;Mode-A; ((bb)) Mode-B.Mode-B.

Then,Then, the vibration modes of the stator were measured by the use of a scanning laser Doppler vibrometer (PSV-400-M2,(PSV-400-M2, Polytec, Waldbronn, Germany).Germany). The vibrationvibration shapesshapes and vibration velocity response spectrums of the prototype are shown in FigureFigure 1010,, whilewhile wires connection methods were the samesame asas thethe admittanceadmittance characteristicscharacteristics test.test. The top ◦ vibration shapes of Mode-AMode-A andand Mode-BMode-B were bothboth standingstanding waves, which have aa 9090° phase difference in space. The mode shape test results were consistent with FigureFigure5 5,, butbut the measuredmeasured resonantresonant frequencies frequencies in in Figure Figure 10 c10c were were also also different different from from ﬁnite finite element element sim- simulation results. However, the resonant frequencies measured in admittance and vibration characteristics tests were almost exactly the same.

(a) (b) (c)

Figure 10. The vibration scanning result of the stator: (a) the vibration shape of Mode-A; (b) the vibration shape of Mode-B; (c) the vibration velocity response spectra under two mode excitations.

The mechanical output performances of the prototype were tested by the experimental set-up, as shown in Figure 11.

Micromachines 2021, 12, x FOR PEER REVIEW 8 of 11

results, which might result from the manufacturing and assembling process, or neglect of solder joints and epoxide resin, etc.

(a) (b)

Figure 9. Conductance and susceptance response spectrums under two modes excitations: (a) Mode-A; (b) Mode-B.

Then, the vibration modes of the stator were measured by the use of a scanning laser Doppler vibrometer (PSV-400-M2, Polytec, Waldbronn, Germany). The vibration shapes and vibration velocity response spectrums of the prototype are shown in Figure 10, while Micromachines 2021, 12, 824 wires connection methods were the same as the admittance characteristics test. The8 of top 10 vibration shapes of Mode-A and Mode-B were both standing waves, which have a 90° phase difference in space. The mode shape test results were consistent with Figure 5, but the measured resonant frequencies in Figure 10c were also different from finite element ulationsimulation results. results. However, Howeve ther, resonantthe resonant frequencies frequencies measured measured in admittance in admittance and and vibration vibra- characteristicstion characteristics tests tests were were almost almost exactly exactly the same. the same.

(a) (b) (c)

FigureFigure 10.10. TheThe vibrationvibrationscanning scanning result result of of the the stator: stator: ( a()a the) the vibration vibration shape shape of of Mode-A; Mode-A; (b ()b the) the vibration vibration shape shape of of Mode-B; (Modec) the- vibrationB; (c) the velocityvibration response velocity spectraresponse under spectr twoa under mode two excitations. mode excitations.

Micromachines 2021, 12, x FOR PEER REVIEWThe mechanical output performances of the prototype were tested by the experi-9 of 11 The mechanical output performances of the prototype were tested by the experimental set-up,mental asset shown-up, as inshown Figure in 11 Fig. ure 11.

Figure 11. The experiment set-up of the prototype. Figure 11. The experiment set-up of the prototype.

IfIf thethe Phase-APhase-A voltage led led the the Phase Phase-B-B voltage voltage by by 90°, 90 ◦and, and the the dual dual-rotor-rotor system system ro- rotatedtated clockwise, clockwise, then then when when the the Phase Phase-A-A voltage voltage lagged the Phase-BPhase-B voltagevoltage byby 9090°,◦, thethe dual-rotordual-rotor system system rotated rotated counterclockwise. counterclockwise. The The experiment experiment of of the the prototype prototype showed showed that that whetherwhether thethe dual-rotordual-rotor systemsystem rotatedrotated clockwiseclockwise oror counterclockwise,counterclockwise, thethe testtest resultsresults ofof mechanicalmechanical outputoutput performanceperformance werewere almostalmost consistent.consistent. WhenWhen thethe voltagesvoltages werewere 150150 VVpp,, thethe phasephase difference was was 90° 90◦ (whether(whether the the Phase Phase-A-A voltage voltage led led or lagged or lagged the Phase the Phase-B-B volt- voltageage by 90°), by 90 and◦), andFigure Figure 12 shows 12 shows the plot the of plot the of speed the speed versus versus the frequency the frequency of the ofexcita- the excitationtion voltage voltage without without the weight the weight loaded. loaded. The maximum The maximum speed speedof the prototype of the prototype was 99 wasrpm 99when rpm the when excitation the excitation frequency frequency was 28.25 was 28.25kHz. kHz.Figure Figure 13 shows 13 shows the p thelot plotof the of speed the speed and andpower power versus versus the theoutput output torque torque when when the thefrequency frequency was was set setto be to 28.25 be 28.25 kHz. kHz. With With the theexcitation excitation voltage voltage of of150 150 Vp V, thep, the motor motor achieved achieved its its maximum maximum torque torque of of 0.19 0.19 N·m N·m and and a amaximum maximum mechanical mechanical power power of of 0.64 0.64 W. W. Compared with Li’sLi’s travelingtraveling wavewave ultrasonicultrasonic motormotor [ 27[27],], the the weight weight of of the the ceramics ceramics decreased decreased from from 0.039 0.039 kg tokg 0.007 to 0.007 kg, andkg, and the load-freethe load- speedfree speed was increasedwas increased from from 76 rpm 76 torpm 99 to rpm. 99 rpm.

Figure 12. Plot of the speed versus the excitation frequency.

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Figure 11. The experiment set-up of the prototype.

If the Phase-A voltage led the Phase-B voltage by 90°, and the dual-rotor system rotated clockwise, then when the Phase-A voltage lagged the Phase-B voltage by 90°, the dual-rotor system rotated counterclockwise. The experiment of the prototype showed that whether the dual-rotor system rotated clockwise or counterclockwise, the test results of mechanical output performance were almost consistent. When the voltages were 150 Vp, the phase difference was 90° (whether the Phase-A voltage led or lagged the Phase-B voltage by 90°), and Figure 12 shows the plot of the speed versus the frequency of the excitation voltage without the weight loaded. The maximum speed of the prototype was 99 rpm when the excitation frequency was 28.25 kHz. Figure 13 shows the plot of the speed and power versus the output torque when the frequency was set to be 28.25 kHz. With the excitation voltage of 150 Vp, the motor achieved its maximum torque of 0.19 N·m and a

Micromachines 2021, 12, 824 maximum mechanical power of 0.64 W. Compared with Li’s traveling wave ultrasonic9 of 10 motor [27], the weight of the ceramics decreased from 0.039 kg to 0.007 kg, and the load- free speed was increased from 76 rpm to 99 rpm.

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FigureFigure 12. 12. PlotPlot of of the the speed speed versus versus the the excitation excitation frequency. frequency.

Figure 13. Plot of the speed and power versus the output torque. 6. Conclusions 6. Conclusions A rotary traveling wave ultrasonic motor with double-sided staggered teeth was A rotary traveling wave ultrasonic motor with double-sided staggered teeth was pro- proposed. The stator of the motor was constructed by bonding thirty-two pieces of ceramic posed. The stator of the motor was constructed by bonding thirty-two pieces of ceramic chips on a metal ring with double-sided staggered teeth. The dual-rotor system was chips on a metal ring with double-sided staggered teeth. The dual-rotor system was in- intended to utilize all the traveling wave energies on both sides of the stator, which avoided tended to utilize all the traveling wave energies on both sides of the stator, which avoided the energy waste problem of the conventional traveling wave ultrasonic motor. In addition, the energy waste problem of the conventional traveling wave ultrasonic motor. In addi- the corresponding load capacity could be improved efficiently. The modal and transient tion, the corresponding load capacity could be improved efficiently. The modal and tran- simulations showed that both sides of the stator could generate the traveling wave to rotate sient simulations showed that both sides of the stator could generate the traveling wave two rotors. The admittance and vibration characteristics tests verified the rationality of the to rotate two rotors. The admittance and vibration characteristics tests verified the ration- structural design and the simulation results. Additionally, the assembled prototype could ality of the structural design and the simulation results. Additionally, the assembled pro- achieve double-sided driving stably. Under excitation voltage of 150 Vp, the prototype achievedtotype could a load-free achieve speeddouble of-sided 99 rpm driving and astably. maximum Under output excitation torque voltage of 0.19 of N150·m. Vp This, the studyprototype provides achieved a new a load method-free speed to achieve of 99double-sided rpm and a maximum driving ofoutput the traveling torque of wave 0.19 ultrasonicN·m. This motor.study provides a new method to achieve double-sided driving of the traveling wave ultrasonic motor. Author Contributions: Conceptualization, X.Y.; data curation, D.Z. and X.Y.; formal analysis, D.Z. andAuthor X.Y.; Contribution funding acquisition,s: Conceptualization, X.Y. and Z.M.; X.Y.; investigation, data curation, D.Z.; D.Z. methodology, and X.Y.; formal D.Z. and analysis, X.Y.; project D.Z. administration,and X.Y.; funding X.Y. acquisition, and R.S.; resources, X.Y. and X.Y.;Z.M.; software, investigation, D.Z. and D.Z.; X.Y.; method supervision,ology, D.Z. X.Y., and R.S. X.Y.; and Z.M.; validation,project administration D.Z. and X.Y.;, X.Y. visualization, and R.S.; resources, D.Z.; writing—original X.Y.; software, D.Z. draft, and D.Z.; X.Y.; writing supervision, —review X.Y., and editing,R.S. and X.Y.Z.M.; and validation, C.Y. All authorsD.Z. and have X.Y.; read visualization, and agreed D.Z.; to the writing published—original version draft, of the D.Z.; manuscript. writing —review and editing, X.Y. and C.Y. All authors have read and agreed to the published version of Funding:the manuscript.This work was supported by the National Natural Science Foundation of China (Grant No. 51905316 and 61903100), Shandong Province Higher Educational Science and Technology Program (GrantFunding: No. This 2019KJB031). work was supported by the National Natural Science Foundation of China (Grant No. 51905316 and 61903100), Shandong Province Higher Educational Science and Technology Pro- Datagram Availability(Grant No. 2019KJB031). Statement: Not applicable. Acknowledgments: The authors would like like to to thank thank the the anonymous anonymous reviewers reviewers for for their their valuable valuable comments and suggestions. ConflictsConflicts ofof Interest:Interest: TheThe authorsauthors declaredeclare nono conflictconflict ofof interest.interest.

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