A Study on the Mode Shape Piezoelectric Motor

Transcription

1 Ope Joural of Acoustcs, 015, 5, 5-65 Publshe Ole Jue 015 ScRes. A Stuy o the Moe Shape Pezoelectrc Motor Jwo Mg Jou Departmet of Mechacal Egeerg, Cheg Shu Uversty, Kaohsug Cty, Tawa Emal: k0556@gclou.csu.eu.tw Receve 17 Aprl 015; accepte 5 Jue 015; publshe 9 Jue 015 Copyrght 015 by author a Scetfc Research Publshg Ic. Ths work s lcese uer the Creatve Commos Attrbuto Iteratoal Lcese (CC BY). Abstract I ths paper, we try to use the coatg of effectve electroe surface a chage the recto of polarzato to esg the moe shape pezoelectrc motors of the frst three moes. We also compare the ga of the moe shape pezoelectrc motors wth respect to the ormal shape pezoelectrc motor, clug rotatoal spee, loag ablty, torque, phase agle coverso a effcecy. Accorg to the results of theoretcal a smulato aalyss, we have fou that the ga of the moe shape pezoelectrc stators are larger tha the ormal shape pezoelectrc stator o average. Accorg to the results of expermets, we fou that the ga of the rotatoal spee, loag ablty, torque, rvg phase agle coverso a effcecy of the moe shape (1-3) pezoelectrc motors are hgher tha the ormal shape pezoelectrc motor () uer rvg coto of the seco vbrato moe. Also, the ga of the rotatoal spee a loag ablty of the moe shape () pezoelectrc motor are hgher tha other shapes pezoelectrc motors (, 1 a 3) uer rvg coto of the seco vbrato moe. The use maxmum rotatoal spee of the moe shape () pezoelectrc motor s up to 96 rpm uer cotos of 180 V p-p rvg voltage, 10.7 khz rvg frequecy, 0 rvg phase agle a 13.0 gw et weght. The maxmum loag ablty a torque of the moe shape () pezoelectrc motor s respectvely 51 gw a 0.91 mkgw-m uer cotos of 180 V p-p rvg voltage, 10.7 khz rvg frequecy, 0 rvg phase agle a 173 rpm rotatoal spee. A the ga of effcecy (output power) a maxmum loag ablty (torque) of the moe shape () pezoelectrc motor are respectvely.8 a 1.5 wth respect to the ormal shape pezoelectrc motor uer cotos of 180 V p-p rvg voltage, 10.7 khz rvg frequecy a 0 rvg phase agle. Accorg to the results of the expermets, we have fally fou that the pezoelectrc motors ( a 1-3) ca be rve oly by the seco vbrato moe because the stator ca prouce ellptcal moto a allows the rotor to geerate oretato rotato. However, the frst vbrato moe ca allow the rotor to be rotate very fast but t ca t make the rotato of the rotor oretato. Furthermore, we also fou that the rotor ca t rotate by the thr vbrato moe because ts vbrato eergy s absorbe by the structure tself, so causg the rotor stagato. How to cte ths paper: Jou, J.M. (015) A Stuy o the Moe Shape Pezoelectrc Motor. Ope Joural of Acoustcs, 5,

2 Keywors Moe Shape (), Normal Shape (), Pezoelectrc Motor, Pezoelectrc Stator, Ga 1. Itroucto The ma object for stuy s a moe shape pezoelectrc motor a ts comparso object s the ormal shape pezoelectrc motor ths paper. Its appearace s smlar to the tubular pezoelectrc motors or ultrasoc motors. For comparso, the fou expermetal ata are lste Table 1 [1]-[10]. The ma fferece betwee the ormal shape a moe shape pezoelectrc motor les the fferet coatg metho of effectve electroe surface. Due to the ormal shape, the tubular pezoelectrc motors have may avatages, clug small sze, fast rotatoal or movemet spee a respose, hgh torque or hgh loag ablty. So they are very useful for optcal a electro-mechacal systems. For example, they may be apple to autofocus system of the optcal les, a let them to be embee wth the camera or moble phoes. Also, they are the ma trasmsso moe geerate by the actuatg force or frctoal force of the pezoelectrc stator to rve the rotor orer to rotate or sle movemet. The sze of the actuatg force or frctoal force epes o the composto of the stator a motor, the coatg of effectve electroe surface, a rvg cotos. The tubular pezoelectrc motor was frst escrbe 00 [1]. It s prmarly a metal tube o both ses of two pezoelectrc ceramc affxe. The stator sze s D. mm L10 mm. The maxmum agular or rotatoal spee of tubular pezoelectrc motor s 60 ra/s or 573 rpm uer cotos of 10 V p-p rvg voltage a 69.5 khz rvg frequecy. A the maxmum torque, output power a effcecy are 1.8 mnm, 60 mw, a 5% respectvely. The followg year, a smaller tubular pezoelectrc motor has bee propose for publcato [], whch sze of the stator s D1.6 mm L6 mm. But the maxmum agular or rotatoal spee s oly 5 ra/s or 30 rpm uer cotos of 100 V p-p rvg voltage a khz rvg frequecy. A the maxmum torque, output power a effcecy are 0.5 mnm, 5 mw a 16% respectvely. The aga the ext year, aother smaller tubular pezoelectrc motor s propose [3], whch sze of the stator s D0.8 mm L. mm. The maxmum rotatoal spee s up to 3850 rpm uer cotos of 0 V p-p rvg voltage a 70.0 khz rvg frequecy. But the maxmum torque a loag are oly 5 Nm a 0.5 mn respectvely. I 005, a mature tubular pezoelectrc motor s publshe [], whch sze of the stator s D.0 mm L5.0 mm. The maxmum rotatoal spee s up to 000 rpm uer cotos of 5 V p-p rvg voltage a 67.0 khz rvg frequecy. But the maxmum torque s oly 1.6 μnm. I 006, aother mature tubular pezoelectrc motor s propose [5], whch sze rato of L/D of the stator s The maxmum rotatoal spee s oly 385 rpm uer cotos of 00 V p-p rvg voltage a 9. khz rvg frequecy. A the maxmum torque s 3.1 Nm. I 007, aother oe mature tubular pezoelectrc motor s publshe [6], whch sze of the stator s D.0 mm L5.0 mm. The maxmum rotatoal Table 1. The performace comparso of the tubular pezoelectrc motors [1]-[10]. Refereces Spee (rpm or mm/s) Torque (mnm) or Loag (mn) Voltage (V p-p) Frequecy (khz) Sze (mm) [1] D. L10.0 [] D1.6 x L6.0 [3] E 5 or D0.8 L. [] E D.0 L5.0 [5] L/D = 3.5 [6] E D.0 L5.0 [7] D3.0 L1 [8] D6.6 L5. [9] D1.0 L55.0 [10] E 3 or D5.0 L15.0 6

3 spee s up to 9600 rpm uer cotos of 30 V p-p rvg voltage a 31.5 khz rvg frequecy. But the maxmum torque s 5.5 μnm. I 009, a metal tube type pezoelectrc motor s apple to push the optcal les [7], whch sze of the stator s D3.0 mm L1.0 mm. The maxmum rotatoal spee s 075 rpm uer cotos of 10 V p-p rvg voltage a 6.0 khz rvg frequecy. A the maxmum loag s 0 mn. I 011, a sgle vbrato moe tubular pezoelectrc motor s publshe [8], whch sze of the stator s D6.6 mm L5. mm. The maxmum rotatoal spee s 00 rpm uer cotos of 100 V p-p rvg voltage a 3.5 khz rvg frequecy. But the maxmum torque s oly 0.3 mnm. Next year, a rotary-lear pezoelectrc motor s propose [9], whch sze of the stator s D1.0 mm L55.0 mm. The maxmum movemet spee s oly 11 mm/s uer cotos of 150 V p-p rvg voltage a 19.7 khz rvg frequecy. But the maxmum torque s up to 500 mn. Recetly, a tubular pezoelectrc motor s propose [10], whch sze of the stator s D5.0 mm L15.0 mm. The maxmum rotatoal spee s oly 08 rpm uer cotos of 100 V p-p rvg voltage a 97.0 khz rvg frequecy. But the maxmum torque a loag are oly 3.6 μnm a 5.0 mn. At ths pot, we ca f that the tubular pezoelectrc motors have characterstcs of hgh spee a low torque or low spee a hgh torque. However, f the torque or loag of the tubular pezoelectrc motor s too small, the a bg spee s stll ot beg apple to for optcal or electro-mechacal systems. Therefore, the approprate composto, sze, torque, loag ablty a rotatoal or movemet spee of the tubular pezoelectrc motor must be carefully cosere.. The Composto a Operato Prcple I ths paper, the composto a operato prcple of the ormal shape a moe shape pezoelectrc motors as show Fgures 1-3. Where the composto of the ormal shape or moe shape pezoelectrc motors whch clues a pezoelectrc stator a a rotor. The pezoelectrc stator s compose of a metal tube a four pezoelectrc ceramcs whch have the ormal shape a moe shape effectve electroe surface, as show Fgure 1 a Fgure 3. A the full sze of the stator pezoelectrc s 50 mm 7. mm 7. mm. I operato, as log as to rve the pezoelectrc stator by approprate frequecy a voltage, to make the free e of stator geerate ellptcal trajectory, thereby to push the rotor rotates, as show Fgure. As for the coatg metho of effectve electroe surface of the moe shape pezoelectrc ceramcs are base o the vbrato moes of the catlever beam or pezoelectrc stator, show as Fgure. I whch the equato φ x as follows: of mesoless vbrato moes φ x = cosh λ x cos λ x σ sh λ x s λ x, 0 x 1; = 1,, 3,,. (1) where the mesoless egevalues a λ a parameters As for the effectve electroe surfaces FP ca be efe as: σ are efe as: cosh λ cos λ + 1 = 0. () sh λ s λ σ =. (3) cosh λ + cos λ x of the ormal shape a moe shape pezoelectrc ceramcs ( x ) FP = 0 FP x = 1 φ x FP ( x ) = λ x. () Because of the hgh frequecy vbratos are easly absorbe by the structure tself, so we oly focus o the frst three vbrato moes a effectve electroe surfaces of the moe shape pezoelectrc ceramcs, as show Table a Fgure Equato of Moto The equato of moto of the ormal shape a moe shape pezoelectrc stator ca be obtae from the prevous paper as follows [11]: 7

4 Fgure 1. The composto of the ormal shape or moe shape pezoelectrc motor. Fgure. The operato prcple of the ormal shape or moe shape pezoelectrc motor. Fgure 3. The oblque vew of the ormal shape a moe shape pezoelectrc motors. 8

5 Fgure. The frst three vbrato moes a effectve electroe surface of moe shape pezoelectrc stator. Fgure 5. The frst three vbrato moes a effectve electroe surfaces of the moe shape pezoelectrc ceramcs. 9

6 Table. The frst three vbrato moes a effectve electroe surfaces of the moe shape pezoelectrc ceramcs. x/l φ φ φ 1 3 FP 1 FP FP where λ = , λ =.691, λ = 7.858; σ = 0.731, σ = , σ = a wxt x (, ) wxt (, ) + = 0 t λ φ wxt, wxt, Λ3 t x + λ = x t λ x where the efto of costats the above Equato (5)-(6) as follow: k 1 3 k = 1. (5). (6) D = ( c ) ( z z k k ). (7) k = 1 ( ρ h ) ρh =. (8) k k hk = zk zk 1. (9) ρhl ω ρhl π f λ = =. (10) D D ρhl ω ρhl π f λ = =. (11) D D where above the symbols of c 11, D 11, e 31, f, f, h, V 3, W, t, x, z, ω, ω, λ a λ are efe as the Youg s moulus, beg stffess costat per ut wth, a arbtrary frequecy, the resoace frequecy, thckess, pezoelectrc charge costat, trasverse rvg voltage, trasverse splacemet, tme, logtual coorate, trasverse coorate, esty, the agle velocty of arbtrary frequecy, the agle velocty of resoace frequecy, the egevalues of arbtrary frequecy a the egevalues of resoace frequecy. Furthermore we ca f the geeral soluto of moe shape a ormal shape pezoelectrc stator from the prevous paper as follow [11]: a = jω, sh cosh s cos e t w x t C λ x C λ x C λ x C λ x. (1) 50

7 = λ + λ + λ + λ + φ jω, 1sh cosh 3s cos e t w x t C x C x C x C x A x. (13) where above costats ca be eterme by the followg electro-mechacal bouary cotos: a jωt Π3e w( 0, t) = w ( 0, t) = 0; w ( 1, t) = ; w ( 1, t) = 0 λ ( x) Π φ w( 0, t) = w ( 0, t) = 0; w ( 1, t) = ; w 1, t = λ. (1) φ ( x) jωt jωt 3 3e Π3e 3 x λ x 1 x = x= 1. (15) Let Equato (1) a Equato (13) are substtute to Equato (1) a Equato (15), we ca get the trasverse splacemet soluto of the frst three vbrato moes of free e of the ormal shape a moe shape pezoelectrc stators o xz-plae as follow: a jωt 3, = φ 1 λ λ λ wxt wxt Π e cosh λ + cos λ Π e ( 1+ cosh cos ) jωt 3 = φ 1 λ λ λ λ ( ). (16). (17) where the egevalues λ λ φ 1 φ 1 a R a I. Smlarly, we ca get the soluto of vertcal splacemet of the frst three vbrato moes of the ormal shape a moe shape pezoelectrc stators at of free e o xy-plae as follow: a a, jωt 3 = φ 1 λ λ λ v xt v xt Π e cosh λ + cos λ Π e ( 1+ cosh cos ) jωt 3, = φ 1 λ λ λ λ ( ) Uer steay-state operatg moe, above Equato (16-19) ca be rewrtte as follow: 3 cos cos λ λ λ ( 1+ cosh cos ). (18). (19) Π φ 1 cosh λ + cos λ wxt = ( ωt+φ ) = W ( ωt+φ). (0) ( 1) Π φ λ wxt = ( ωt+φ ) = W ( ωt+φ). (1) 3 cos cos λ λ λ ( ) Π φ 1 cosh λ + cos λ v ( xt) = ( ωt+φ ) = V ( ωt+φ). () 3 cos cos λ λ λ ( 1+ cosh cos ) ( 1) Π φ λ v ( xt) = ( ωt+φ ) = V ( ωt+φ). (3) 3 cos cos λ λ λ ( ) where Φ s efe as rvg phase agle. A,, a W W V V represetatve ampltue of the ormal shape a moe shape pezoelectrc stators at the trasverse a vertcal recto respectvely. I orer to get a ellptcal trajectory of the ormal shape a moe shape pezoelectrc stators at the free e, we ca make rvg phase agle fferece 90 or use a fferet rvg waveforms uer fferet ses of 51

8 pezoelectrc stators. Therefore, above Equatos (3)-() ca be rewrtte aga as follow: a Π φ 1 cosh λ + cos λ v ( xt) = ( ωt+φ ) = V ( ωt+φ). () 3 s s λ λ λ ( 1) ( 1+ cosh cos ) Π φ λ v ( xt) = ( ωt+φ ) = V ( ωt+φ). (5) 3 s s λ λ λ ( ) Follow by, we ca get a ellptcal trajectory of the ormal shape a moe shape pezoelectrc stators at the free e o the zy-plae from Equatos (0)-(1) a Equatos ()-(5), show as Fgure 6. If we further coser the effect of axal or horzotal vbrato o the ormal shape a moe shape pezoelectrc stators, the above equatos ca be rewrtte as aga: a Π φ 1 cosh λ + cos λ wxt ( ωt ) W ( ωt ) ωt. (6) 3 = cos cos s +Φ = +Φ λ λ λ ( 1) ( 1+ cosh cos ) Π φ λ wxt ωt W ωt ωt. (7) 3 = cos cos s +Φ = +Φ λ λ λ ( ) Π φ 1 cosh λ + cos λ v ( xt) ( ωt ) V ( ωt ) ωt. (8) 3 = s s s +Φ = +Φ λ λ λ ( 1+ cosh cos ) ( 1) Π φ λ v ( xt) ωt V ωt ωt. (9) 3 = s s s +Φ = +Φ λ λ λ ( ) Fgure 6. The ellptcal trajectory of the ormal shape or moe shape pezoelectrc stator o xz-plae a xy-plae. 5

9 where the axal or horzotal vbrato splacemet of the ormal shape a moe shape pezoelectrc stators as follow: a u xt = U cosωt. (30) u xt = U cosωt. (31) where U a U represetatve ampltue of the ormal shape a moe shape pezoelectrc stators at axal or horzotal recto respectvely. So far, we ca get a oval ball of the ormal shape a moe shape pezoelectrc stators at the free e, as follow: a u v w + + = 1. (3) U V W u v w + + = 1. (33) U V W I fact, U V W a U V W for 3D pezoelectrc stators.. Ga a Effcecy I ths paper, we ca get the ga of vertcal a trasverse splacemet or velocty ( V or or W or ) of the ormal shape a moe shape pezoelectrc stators or motors from Equatos ()-(7) uer the same rvg cotos, as follow: or a or ( cosh λ + cos λ) ( 1 cosh cos ) 1 λ G = V 1 ( λ ) : V ( λ) φ ( 1 ) : φ ( 1 V ) = λ λ λ λ + λ λ ( cosh λ + cos λ) ( 1 cosh cos ) 1 λ G = V 1 ( λ ) : V ( λ) ( 1 ) : ( 1 V = φ φ ) λ λ λ λ + λ λ ( cosh λ + cos λ) ( 1 cosh cos ) 1 λ G = W 1 ( λ ) : W( λ) φ ( 1 ) : φ ( 1 W ) = λ λ λ λ + λ λ ( cosh λ + cos λ) ( 1 cosh cos ) 1 λ G : ( 1 ) : ( 1) W = W λ 1 W λ φ φ = λ λ λ λ + λ λ. (3). (35). (36). (37) So for, we ca prect the ga of the ormal shape a moe shape pezoelectrc stators from Equatos (3)-(37) uer the same rvg cotos. I ato, the coverso effcecy of the ormal shape a moe shape pezoelectrc stators or motors ca be efe as: POut η = 1.0. (38) P where the efto of the put power as: 53

10 a the efto of the output power as: P = IV = IV = IV. (39) p p rms P = FV FW = µ Wr ω = T ω Out f or f or R or q or N π = µ Wr πf = µ Wr π µ rw N or = R R R or or. (0) where f, Ff, I, r, N, Tq, V, WR, ω, µ a η represetatve the moal resoace frequecy, frctoal force, put rvg curret, raus of rotor, rotatoal spee, torque, put rvg voltage, weght or loag of rotor, the moal agle velocty, yamc frcto coeffcet a effcecy of the ormal shape a moe shape pezoelectrc stators or motors. 5. Case Stuy Theoretcal Aalyss, Smulato Aalyss a Expermets I ths paper, we have to uersta the ffereces a ga betwee the ormal shape a moe shape pezoelectrc motors or stators, partcular, through theoretcal aalyss, smulato aalyss a expermets to valate. A the materal propertes are use the aalyss a the expermetal proceure, as show Table 3. where the step of the theoretcal aalyss s as follows: (5-1-1) Usg the smple approxmate soluto of oe-mesoal spatal structure to o aalyss, a oly o a comparatve aalyss of mesoless vbrato splacemet or velocty by Equatos (38-39). (5-1-) Usg the mmum frequecy spacg ( f = 1 Hz ) to aalyze the ga of the frst three moes of the moe shape a ormal shape pezoelectrc stators from 1 khz to 0 khz. As for the smulato aalyss proceure s as follows: (5--1) Moelg of the moe shape a ormal shape pezoelectrc stators respectvely, clug select elemet type, eter the physcal propertes, as well as coorate system coverso, as show Fgure 7. (5--) Meshg of the moe shape a ormal shape pezoelectrc stators respectvely, clug select the most sophstcate cuttg of mesh or select the smart sze 1, as show Fgure 8. (5--3) Smulato Aalyss: Solvg of the moe shape a ormal shape pezoelectrc stators respectvely, clug settg bouary cotos of electro-mechacal, as show Fgure 9. All of whch rvg voltage o the effectve electroe surface s 1.0 V. (5--) Post-processg of the moe shape a ormal shape pezoelectrc stators respectvely, clues processg the frst three moes, the maxmum eformato or electrc potetal, as show Fgures As regars the expermetal step s as follows: (5-3-1) Cuttg the pezoelectrc ceramcs wth the effectve electroe surface, a makg the pezoelectrc stators of ormal shape a moe shape, show as Fgure 1. (5-3-) Usg the ual chael arbtrary fucto geerator (Moel: A-303, AA Lab. Systems Lt. Co.) a Table 3. The materal propertes a sze of pezoelectrc stator. Dmeso _ Materal Name Relatve Permttvty (N.A.) Pezoelectrc Stress Costat (V/Nm) 1D_PZT D_PZT 3D_PZT 1D_Al D_Al 3D_Al ε11 = 1730 ε11 = ε = 1730, ε33 = 1700 e31 = 5.3 e31 = e3 = 5.3 ε11 = ε = 1730, ε33 = 1700 e31 = e3 = 5.3, e33 = 15.8, e = e15 = 1.3. c11 = c = 1.e11, c1 = c1 = 7.5e10, c13 = c31 = Youg's Moulus (Pa) c11 = 1.e11 c11 = c = 1.e11 c3 = c3 = 7.51e10, c33 = c11 = 7E10c11 = c = 7E e11, c = 3.0e10, c55 = c66 =.6e10 c11 = c = c33 = 7E10 Desty (kg/m 3 ) Posso Rato (N.A.) Sze (mm 3 )

11 Fgure 7. Moelg a settg the materal propertes of the ormal shape a moe shape pezoelectrc stators. Fgure 8. Meshg the materal propertes of the ormal shape a moe shape pezoelectrc stators usg the most fe mesh. the power amplfer (Moel: AFG-30, Tektrox Co.) to rve the ormal shape a moe shape pezoelectrc motors, show as Fgure 15. (5-3-3) Usg the gtal tachometer (Moel: RM-1501, TES Electrcal Electroc Co.) a the sou level meter (Moel: TES 1350A, TES Electrcal Electroc Co.) to measure the rotatoal spee a ose of the ormal shape a moe shape pezoelectrc motors, show as Fgure 15. (5-3-) Usg the loag test weght a rotors to test the loag ablty of the ormal shape a moe shape pezoelectrc motors, show as Fgure 16. Whch the materal of the loag test weght or mass s alumum a copper. Ther sze a weght are D50 mm H10 mm a 53 gw or 165 gw. A the materal of the rotor s 55

12 Fgure 9. Defe loas or settg bouary cotos of electroe-mechacal of the ormal shape a moe shape pezoelectrc stators uer clampefree mechacal bouary cotos a 1.0 V p-p rvg voltage electrcal bouary cotos. Fgure 10. The frst three vbrato moes of the ormal shape pezoelectrc stators o the yz plae usg 3D Materals. copper. Its sze a weght are D15 mm H10 mm a 13 gw. Due to the materal of metal tube of the pezoelectrc stator s alumum, a the materal of rotor s copper. So the yamc frcto coeffcet of metal tube a rotor s about or µ = As for the trasform coeffcet of Equato () must Al Cu be eterme after the expermet, t s usually much less tha 1.0 or µ T

13 Fgure 11. The frst three vbrato moes of the moe shape 1 pezoelectrc stators o the yz plae usg 3D Materals. Fgure 1. The frst three vbrato moes of the moe shape pezoelectrc stators o the yz plae usg 3D Materals. 6. Results a Dscusso Accorg to the results of theoretcal aalyss, smulato aalyss a expermets, we fou: 1) Uer cotos of theoretcal aalyss of oe-mesoal (1D) approxmato soluto a usg the 57

14 Fgure 13. The frst three vbrato moes of the moe shape 3 pezoelectrc stators o the yz plae usg 3D Materals. Fgure 1. The pezoelectrc ceramcs a stators of the ormal shape a moe shape. mmum frequecy spacg of 1Hz, the ga of the maxmum mesoless vbrato splacemet or velocty of the all moe shape 1-3 (1-3) pezoelectrc stators are far tha the ormal shape () pezoelectrc stator, as show Fgure 17 a Table. Where the moe shape 3 (3) pezoelectrc stator has 58

15 Fgure 15. The expermetal structure of the ormal shape or moe shape pezoelectrc motor. Fgure 16. The ormal shape a moe shape pezoelectrc motors. 59

16 Fgure 17. The ga a mesoless vbrato splacemet or velocty of the frst three moes of the ormal shape a moe shape pezoelectrc stators by 1D approxmate soluto. Table. The ga of the maxmum mesoless vbrato splacemet or rotatoal spee of the ormal shape a moe shape pezoelectrc stators uer cotos of theory aalyss, smulato aalyss a expermets. Moe G1_Th. G_Th. G3_Th. G1_1D_S. G_1D_S. G3_1D_S. G1_D_S. G_D_S. G3_D_S. G1_3D_S. G_3D_S. G3_3D_S. G1_Ex. G_Ex. G3_Ex N.A. N.A. N.A Note: Th.: Theoretcal Aalyss; S.: Smulato Aalyss; Ex.: Expermets; N.A.: Represets the rotato recto of the rotor ca ot be eterme. the largest ga whch s about Followe by, the ga of the moe shape 1 (1) pezoelectrc stator s about Furthermore s the ga of the moe shape () pezoelectrc stator s about ) Uer cotos of usg the 1D materal propertes to smulate the 3D pezoelectrc stators, the ga of the maxmum mesoless vbrato splacemet or velocty of the frst three moes of the moe shape 1 (1) pezoelectrc stator s larger tha other type (, a 3) pezoelectrc stators. Where the ga of the thr vbrato moe of the moe shape 1 (1) pezoelectrc stator wth respect to the ormal shape () pezoelectrc stator s about 1.0, as show Table. 3) Uer cotos of usg the D materal propertes to smulate the 3D pezoelectrc stators, the ga of the maxmum mesoless vbrato splacemet or velocty of the all moe shape 1-3 (1-3) pezoelectrc stators are larger tha the ormal shape () pezoelectrc stator. Where the ga of the orthogoal moes of the moe shape 1-3 (1-3) pezoelectrc stators wth respect to the ormal shape () pezoelectrc stator are 1.30, 1.0 a 1.50, as show Table. ) Uer cotos of usg the 3D materal propertes to smulate the 3D pezoelectrc stators, the ga of the maxmum mesoless vbrato splacemet or velocty of the all moe shape 1-3 (1-3) pezoelectrc stators are larger tha the ormal shape () pezoelectrc stator o average. Where the ga of the orthogoal moes of the moe shape 1-3 (1-3) pezoelectrc stators wth respect to the ormal shape () pezoelectrc stator are 1.0, 1.30 a 1.50, as show Table. 5) Accorg to the results of expermets, show as Fgure 18 a Fgure 19 a Table, we fou the ormal shape () a moe shape 1-3 (1-3) pezoelectrc motors ca be rve by the seco vbrato moe oly, because the seco vbrato moe ca allow the stator to prouce ellptcal moto, a allow the rotor to geerate oretato rotato. A we also fou the ga of rotatoal spee of the moe shape () pezoelectrc motor s hgher tha other shapes pezoelectrc motors (, 1 a 3) uer rvg coto of the seco vbrato moe. Where the ga of rotatoal spee of the seco vbra- 60

17 Fgure 18. The ga a the rotatoal spee of the ormal shape a moe shape pezoelectrc motors uer cotos of 180 V p-p rvg voltage, khz rvg frequecy a 13 gw et weght. Fgure 19. The real moto state of the ormal shape a moe shape pezoelectrc motors. to moe of the moe shape 1-3 (1-3) pezoelectrc stators wth respect to the ormal shape () pezoelectrc stator are 1.19, 1.31 a 1.9, as show Table. I ato, the ga of rotatoal spee of the frst vbrato moe ca t be eterme. Although we observe that the rotatoal spee of rotor s very fast, but we also fou that the recto of rotato of the rotor to be volatle. Therefore, the rotatoal spee of rotor of all type ( a 1-3) pezoelectrc stators s treate as zero uer rvg coto of the frst vbrato moe. Furthermore, the ga of rotatoal spee of all type ( a 1-3) pezoelectrc stators are zero uer rvg coto of the thr vbrato moe. Because ts vbrato eergy s absorbe by the structure tself, so causg the rotor stagat. 6) Show as Table 5, we ca f the output power a effcecy of the moe shape () pezoelectrc motor s hgher tha other type (, 1 a 3) pezoelectrc motors uer cotos of 0 rvg phase agle, 180 V p-p rvg voltage, 13 gw et weght, maxmum loag a fferet yamc frcto coeffcet ( µ = 0. a µ = 0.7 ) a the rvg frequecy of the seco vbrato moe. Where the maxmum output power of the pezoelectrc motors (, 1, a 3) s respectvely mw, 3.5 mw, 3.6 mw a mw. A where the effcecy of the pezoelectrc motors (, 1, a 3) s respectvely 0.0%, 0.09%, 0.09% a 0.07%. I ato, the ga of the maxmum output power or effcecy of the moe shape pezoelectrc motors (1-3) s respectvely.8,.8 a

18 wth respect to the ormal shape pezoelectrc motor () uer cotos of 0 rvg phase agle, 180 V p-p rvg voltage, maxmum loag, µ = 0.7 fferet yamc frcto coeffcet a the rvg frequecy of the seco vbrato moe. 7) Show as Table 6, we have fou that the maxmum torque a ga of the moe shape () pezoelectrc motor s hgher tha other type (, 1 a 3) pezoelectrc motors uer cotos of 180 V p-p rvg voltage, maxmum loag, fferet yamc frcto coeffcet ( µ = 0. a µ = 0.7 ) a the rvg frequecy of the seco vbrato moe. Where the maxmum torque of the pezoelectrc motors (, 1, a 3) s respectvely 0.59 mkgw-m, 0.81 mkgw-m, 0.91 mkgw-m a 0.70 mkgw-m. A where the ga of the maxmum torque or loag of the moe shape pezoelectrc motors (1-3) s respectvely 1.36, 1.5 a 1.18 wth respect to the ormal shape pezoelectrc motor () uer cotos of 0 rvg phase agle, 180 V p-p rvg voltage, maxmum loag, µ = 0.7 fferet yamc frcto coeffcet a the rvg frequecy of the seco vbrato moe. 8) Show as Fgure 0, we fou the ose level crease, represets the pezoelectrc motors are eterg to best vbrato moe. Oe of the bggest ose level the seco vbrato moe are about B. 9) Show as Fgure 1, we ca f the coverso effcecy of rvg phase agle of the moe shape () pezoelectrc motor s hgher tha other type (, 1 a 3) pezoelectrc motors. O the whole, the coverso effcecy of rvg phase agle of the moe shape 1-3 (1-3) pezoelectrc motor s hgher tha the ormal shape () pezoelectrc motor. 10) Show as Fgure, we ca f the loag ablty of the moe shape () pezoelectrc motor s hgher tha other type (, 1 a 3) pezoelectrc motors. A loag ablty of the moe shape1-3 (1-3) pezoelectrc motor s hgher tha the ormal shape () pezoelectrc motor. 11) Show as Fgure 3, we ca f the rotatoal spee of the moe shape () pezoelectrc motor s hgher tha other type pezoelectrc motors uer cotos of fferet rvg voltage ( V p-p ) a 13gw et weght. A rotatoal spee of the moe shape pezoelectrc motor s hgher tha the ormal shape pezoelectrc motor o average. Where the r maxmum rotatoal spee of the moe shape () pezoelectrc motor s about 96 rmp uer cotos of 180 V p-p rvg voltage a 13gw et weght. Table 5. The output power, effcecy a ga of the ormal shape a moe shape pezoelectrc stators uer cotos of 0 0 rvg phase agle, 180 V p-p rvg voltage, 13 gw et weght, maxmum loag a the rvg frequecy of the seco vrbrato moe. Pout of Net Weght (mw) Pout of Maxmum Loag (mw) Effcecy (η ) Ga Items µ = 0. µ = 0.7 µ = 0. µ = 0.7 µ = 0. µ = 0.7 µ = 0. µ = % 0.0% % 0.09% % 0.09% % 0.07% Note: Iput Power_P I = 6 Watts Uer Coto of 180 V p-p Drvg Voltage. The Maxmum Loag of the, 1, a 3 s 9 gw, 398 gw, 51 gw a 35 gw respectvely. The Drvg Frequecy of the Seco Vrbrato Moe of the, 1, a 3 s 10.3 khz, 10.3 khz, 10.7 khz a 10.8 khz respectvely. Table 6. The torque a ga of the ormal shape a moe shape pezoelectrc stators uer cotos of 0 0 rvg phase agle, 180 V p-p, maxmum loag a the rvg frequecy of the seco vrbrato moe. Torque (mkgw-m) Ga of Torque (mkgw-m/mkgw-m) ITE 0. µ = µ = 0.7 µ = 0. µ =

19 Fgure 0. The vbrato ose of the ormal shape a moe shape pezoelectrc motors uer cotos of 180 V p-p rvg voltage, khz rvg frequecy a 13 gw et weght. 7. Cocluso Fgure 1. The rotatoal spee versus rvg phase agle of the ormal shape a moe shape pezoelectrc motors uer cotos of 180 V p-p rvg voltage, the seco vbrato moe a 13 gw et weght. Accorg to the results of theoretcal aalyss, we have fou that the gas of the moe shape pezoelectrc stators are larger tha the ormal shape pezoelectrc stator. A we also fou that the moe shape pezoelectrc stators ca be effectvely separate from the moal vbrato. However, we have also fou that the ormal shape pezoelectrc stator oes ot have ths ablty theory. Accorg to the results of smulato aalyss, we have also fou the ga of the moe shape pezoelectrc stators ca stll appear oorthogoal vbrato moes. Because the results of theoretcal aalyss are solutos a eal approxmato, the results of smulato aalyss are closer to realty. Therefore, the real results evetually must be cofrme through expermets. Accorg to the expermetal results, we have moreover fou that the rotor ca be rotate oly by the seco vbrato moe. Here the ga of the rotatoal spee, loag ablty a torque of the moe shape () pezoelectrc motor s hgher tha other shapes pezoelectrc motors (, 1 a 3) uer rvg coto of the seco vbrato moe. A the gas of the rotatoal spee, loag ablty, torque, rvg phase agle coverso a effcecy of the moe shape (1-3) pezoelectrc motors are hgher tha the ormal shape pezoelectrc motor () uer rvg coto of the seco vbrato moe. I ato, we have also fou that the frst vbrato moe allows the rotor to rotate very fast, but we ca t eterme the recto of rotato of the rotor. However, t ca t make the rotato of the rotor oretato. Furthermore, we also fou 63

20 Fgure. The rotatoal spee versus loag of the ormal shape a moe shape pezoelectrc motors uer cotos of 180 V p-p rvg voltage a the seco vbrato moe. Fgure 3. The rotatoal spee versus rvg voltage of the ormal shape a moe shape pezoelectrc motors uer cotos of 13 gw et weght a the seco vbrato moe. that the rotor caot be rotate by the thr vbrato moe because ts vbrato eergy s absorbe by the structure tself, so causg the rotor stagato. At last, we have also fou that the ose spectrum ca help us quckly f the best vbrato moe posto of the ormal shape a moe shape pezoelectrc motors. Whe the ose level or ecbel creases, the pezoelectrc motors are eterg to best vbrato moe. Ackowlegemets Ths stuy ca be fshe smoothly, I especally wat to thak MOST of Tawa of ROC sposor o fug, (Project No.: MOST103-1-E ). Refereces [1] Koc, B., Cagatay, S. a Ucho, K. (00) A Pezoelectrc Motor Usg Two Orthogoal Beg Moes of a Hollow Cyler. IEEE Trasactos o Ultrasocs, Ferroelectrcs a Frequecy Cotrol, 9, [] Cagatay, S., Koc, B. a Ucho, K. (003) A 1.6-mm, Metal Tube Ultrasoc Motor. IEEE Trasactos o Ultrasocs, Ferroelectrcs a Frequecy Cotrol, 50,

21 [3] Kaa, T., Mako, A., Suzumor, K., Morta, T. a Kurosawa, M.K. (00) A Cylrcal Mcro Ultrasoc Motor Usg a Mcro-Mache Bulk Pezoelectrc Trasucer. IEEE Ultrasocs Symposum,, [] Kaa, T., Oomor, Y., Mako, A., Suzumor, K. a Kobayash, A. (005) Desg a Testg of Rotors for a Cylrcal Mcro-Mache Mcro Ultrasoc Motor. IEEE Ultrasocs Symposum, 1, [5] Zhu, H. a Zhao, C.S. (006) Dyamc a Ketc Aalyses of the Stator of a Cylrcal Ultrasoc Motor. Proceegs of the 006 IEEE Iteratoal Coferece o Robotcs a Bommetcs, Kumg, 17-0 December 006, [6] Kobayash, A. a Kaa, T. (007) Drvg Performace of a Cylrcal Mcro Ultrasoc Motor. Proceegs of the 007 IEEE/RSJ Iteratoal Coferece o Itellget Robots a Systems, Sa Dego, 9 October- November 007, [7] Jou, J.M. (009) A Stuy o the Metal Tube Type Ultrasoc Motor (MTTUSM). Proceegs of the Europea Frequecy a Tme Forum Iteratoal Frequecy Cotrol Symposum, [8] He, S.Y., Charot, P.R. a Park, S. (011) A Sgle Vbrato Moe Tubular Pezoelectrc Ultrasoc Motor. IEEE Trasactos o Ultrasocs, Ferroelectrcs, a Frequecy Cotrol, 58, [9] Cheg, T.-H., Guo, X.-D., Bao, G., Gao, H. a Xao, C.F. (01) Aalyss a Developmet of Plate-Attache Cylrcal Rotary-Lear Ultrasoc Motor. Proceegs of the 01 Symposum o Pezoelectrcty, Acoustc Waves a Devce Applcatos (SPAWDA), Shagha, 3-5 November 01, [10] Guo, M.S., Hu, J.H., Zhu, H., Zhao, C.S. a Dog, S.X. (013) Three-Degree-of-Freeom Ultrasoc Motor Usg a 5-mm-Dameter Pezoelectrc Ceramc Tube. Ultrasocs, Ferroelectrcs a Frequecy Cotrol, IEEE Jourals & Magazes, 60, [11] Jou, J.-M. (01) Theory a Smulato Aalyss of the Moe Shape a Normal Shape Actuators a Sesors. Ope Joural of Acoustcs,,