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1984.10 1986.7 1995 60 1991 Piezoelectric Actuators and Ultrasonic Motors Kluwer Academic Publishers 1996 6 Jayne Giniewicz 1) 1 2 4 5 6 7 8 10 3 8 9 10 11 75 30 1) Dr. Jayne Giniewicz i
NEC Ben K. Wada J. L. Fanson and M. A. Ealey Xinξtics H. B. Strock Strock Technology Associates A. B. Flatau Iowa State University A. E. Clark Clark Associates Nesbit Hagood Masachussets Institute of Technology Mark R. Jolly and J. David Carlson Lord Corporation Philippe Bouchilloux Magsoft Corporation 1995 2004 Robert E. Newnham L. E. Cross 2002 5 State Collete, PA Kenji Uchino Indiana, PA Jayne Giniewicz ii
1 1 1.1 1 1.2 3 1.3 6 1.4 24 1 26 1 27 2... 29 2.1 29 2.2 37 2.3 39 2.4 49 2.5 64 2.6 65 2.7 73 2 78 2 80 3... 81 3.1 81 3.2 102 3.3 108 3.4 111 3.5 113 3 127 3 127 4... 130 4.1 130 iii
4.2 135 4.3 160 4.4 / 163 4 166 4 167 5... 170 5.1 170 5.2 172 5.3 187 5.4 199 5.5 206 5 219 5 220 6... 222 6.1 222 6.2 242 6.3 248 6 254 6 254 7... 256 7.1 256 7.2 257 7.3 259 7 268 7 268 8... 269 8.1 269 8.2 275 8.3 276 8.4 278 8.5 VTR 284 8.6 286 8 287 iv
8 288 9... 289 9.1 289 9.2 292 9.3 295 9.4 301 9.5 305 9.6 307 9 309 9 309 10... 311 10.1 311 10.2 317 10.3 320 10.4 323 10.5 332 10.6 333 10.7 334 10.8 336 10.9 341 10.10 346 10.11 348 10.12 349 10 354 10 354 11... 356 11.1 356 11.2 357 11.3 360 11 371 11 371... 372 v
D (Electric Displacement) E (Electric Field) P (Dielectric Polarization) P s α γ (Spontaneous Polarization) (Ionic Polarizability) (Lorentz Factor) µ (Dipole Moment) ε 0 ε K κ χ C T 0 T c G A F x x s X s c v d h g (Dielectric Permittivity of Free Space) (Dielectric Permittivity) (Relative Permittivity or Dielectric Constant) K χ = K 1 (Inverse Dielectric Constant) (Electric Susceptibility) (Curie-Weiss Constant) (Curie-Weiss Temperature) (Curie Temperature (Phase Transition Temperature)) (Gibbs Free Energy) (Helmholtz Free Energy) (Landau Free Energy Density) (Strain) (Spontaneous Strain) (Stress) (Elastic Compliance) (Elastic Stiffness) (Sound velocity) (Piezoelectric Charge Coefficients) (Inverse Piezoelectric Charge Coefficient) (Piezoelectric Voltage Coefficient) M, Q (Electrostrictive Coefficients) k (Electromechanical Coupling Factor) η (Energy Transmission Coefficient) Y (Young s Modulus) tan δ (tan δ ) (Dielectric Loss) tan φ (tan φ ) (Elastic Loss) tan θ (tan θ (Piezoelectric Loss) vi
1 2 c s X x X 4 x 4 1 1 3 4 5 6 7 ρ s E v l v f 0 ( cos kx cos ωt +cos kx π ) ( cos ωt π ) [ ] =cos 2 2 S t K C 2 2 8 [δ(t)] 9 Z 0 Z 1 10 d X P vii
10 60 1 2 X=cx x=sx x 4 =2x 23 =2φ 1 1 3 v = 1 5 ρs E ρse 4 f = v 2L 5 (kx ωt) 6 C = ε 0 K S t C = K S 5 t 1 7 f = 2π LC 8 1 9 Z 1 = Z 0 ( Z 1 = Z0 * ) Z 1 V Z 1 V Z 0 + Z 1 Z 0 + Z 1 P V 2 Z 1 P = (Z 0 + Z 1 ) 2 = V 2 1 V 2 ( Z0 + ) 2 4 Z 0 Z 1 Z1 P max Z 0 Z1 = Z 1 Z 1 = Z 0 10 P = dx viii
1 1.1 1.1 [1] 1.1 1nm 1 µm 1
1 0.01 µm [2] NASA [3] 10 m 1.2 1.2 2
1.2 1 cm 10 1.2 1.1 1.1 1 50 Nm 10 s 100 mm 100 µm 10 1 N/mm 2 10 s 1 100 Nm 1s 1,000 mm 10 µm 100 N/mm 2 1s AC 1 30 Nm 100 ms DC 1 200 Nm 10 ms 1,000 mm 10 µm 300 N 100 ms 1mm 0.1 µm 300 N 1ms 100 µm 0.01 µm 30 N/mm 2 0.1 ms 100 µm 0.01 µm 100 N/mm 2 0.1 ms 1 1Nm 1ms 3 [4] 1. 2. 3. 1.2.1 1.3 3
3 3.1 3.1.1 1880 1921 1940 KDP 2 1940 1943 BaTiO 3 Wainer Salmon Ogawa Wul Golman 1950 Jaffe PZT PZT PZT 3 1969 Kawai PVDF 1978 Newnham 81
3 PMN 10 % PT [18] [22] ZnO PZT MEMS 3.1.2 / ABO 3 3.1 BaTiO 3 PbZrO 3 A(B,B )O 3 A 2+ (B 3+ 1/2 B 5+ 1/2 )O 3 A 2+ (B 2+ 1/3 B 5+ 2/3 )O 3 3.1 ABO 3 3.2 B 82
3.1 3.2 B B B 3.1.3 3.1 3.1 [1, 2] BaTiO 3 PZT4 PZT5H (Pb,Sm)TiO 3 PVDF-TrFE d 33 (pc/n) 2.3 190 289 593 65 33 g 33 (10 3 Vm/N) 57.8 12.6 26.1 19.7 42 380 k t 0.09 0.38 0.51 0.50 0.50 0.30 k p 0.33 0.58 0.65 0.03 K 33 T 5 1700 1300 3400 175 6 Q m > 10 5 500 65 900 3-10 T c( C) 120 328 193 355 ( 1 ) SAW LiNbO 3 LiTaO 3 α- 32 537 C β AT ST X 10 5 Q m 1210 C 660 C 3m c 83
6 3 tan δ tan φ Q m 6.1 Q m Q m Q m T. Ikeda [1] [2] Q m 222
6.1.1 6.1 [3] (1) (2) (3) (4) (1) [4] 6.1 Pb 0.9 La 0.1 (Zr 0.5 Ti 0.5 ) 1 x Me x O 3 tan φ tan δ Me Mn Fe Al x 0 0.09 f 520 khz 5mm 0.4 mm 520 khz Mn 1% Fe 1-2 % Al 3% 6.1 tan φ =0.32 tan δ (6.1) 90 [ mx 2 tan φ = s ε 0 K X ] Ps 2 s E tan δ (6.2) 6.1 tan φ tan δ [4] Pb 0.9 La 0.1 (Zr 0.5 Ti 0.5 ) 1 x Me xo 3 Me Mn, Fe, Al x 0 0.09 f 520 khz 223
6 m 0.7-0.8 x s K X P s s E x s = QP 2 s (6.3) d =2Qε 0 K X P s (6.4) Q (6.2) 2 k 2 6.1.2 P -E ( 1 ) D P E D E 6.2 6.2 D E D E E ω = 2πf E = E 0 e jωt (6.5) D δ D = D 0 e j(ωt δ) (6.6) E D D = K ε 0 E (6.7) K K 224
E 0 6.1 K = K jk (6.8) K K =tanδ (6.9) (6.8) K ε 0 = ( ) ( ) D0 cos δ K D0 ε 0 = sin δ E 0 6.2 w e 2π ω w e = DdE = D de dt (6.10) dt 0 (6.5) (6.6) (6.10) w e = 2π ω 0 D 0 cos(ωt δ)[e 0 ω sin(ωt)] dt = E 0 D 0 ω sin(δ) 2π ω 0 sin 2 (ωt) dt = πe 0 D 0 sin(δ) (6.11) w e = πk ε 0 E 2 0 = πk ε 0 E 2 0 tan δ (6.12) δ =0 w e =0 1 100 % tan δ 1/2 4U e U e 6.2 1/4 K ε 0 = ( D0 4U e = 1 2 (2E 0)(2D 0 cos δ) =2(E 0 D 0 )cosδ E 0 ) cos δ (6.13a) 4U e =2K ε 0 E 2 0 (6.13b) (6.12) ( )( ) 1 we tan δ = 2π U e (6.13a) (6.13b) (6.14) 225
3 162 BaTiO 3 81 C m 188 C v 188 ER 20 Känzig region 89 LIGA 8 MEMS 7, 8 MR 20 PPP 303 PTCR 161 PVDF 81, 95 PVF2 95 PWM 197 PZT 81 π 319 SAW 83 Transinforgration 369 Zernike 271 262 1, 3 123 256 23 199 30 210 102 16 212 99 188 38, 102 256 131 130 116 29 32 134 1 51 158 138 159 24 6, 367 210 208 111 103 17 348 259 117 12 182 178 256 262 107 124 207 314 138 372
146 284 130 223 1 231 231 106 172 12 315 7, 16, 19, 38, 55, 65 55, 210 34-34 - 34-34 256 192 311 130, 131, 361 116 30, 39 31 100 363 361 311 349 111 138, 139 178 256, 260 11, 12 23 63 12, 94 7, 99 86 176 76 6, 19 298 2 65, 66 103, 105 352 1 7 3 271 131 210 113 113 249 297 208 316 172 170 130 208 20 7 233 227, 229 222 222, 226 229 348 112 30 68 146 209 68 133 271 30 192 150 373
8 233 229 222 229 81 7, 64 14 100 7 7, 10 184 315 152 175 368 285 24 6 6, 367 2 138 141 55 349 352 134 75 116 137 16 177 311 207 138 160 256 161 111 32 280 203 113 204 361 93 31 361 315, 316 189 203 65 37 348 65 74 81 148 311 12 131 207 161 94 181 178 202 2, 269 138 197 87 37 134 361 56, 103, 199, 232 204 232 232 20 7 29 256 374
29 176 29 23 7, 38, 55 94 203 239 180 139 250 6, 367 180 50 37 7, 37, 184 62 29 146 210 131 138 117, 361 349 361 93 8 175 170 197 117 259 36 36 207 209 209 19 19 7 89 208 298 38 177 29 316 83 8 177-209 178 321, 363 224 280 125 173 303 141 251 87 186 39 138 175 16, 159 256 19 259 66 5 321 64, 65 256 133 185 81, 95 17 17 87 375
272 155 209 349 280 12 152 182, 210 117 256 150 84 289 159 256 363 76 74 225 29 223 224 146, 166 207 138 259 306 117 173 314 116, 133 361 116, 133 89 111, 298, 361 249 74 153 151 81 32 24 7, 367 119 162 119 376
2005 JCLS Printed in Japan ISBN978-4-627-77331-8