Angular rate sensor

• US 20020134156A1
• Filed: 10/09/2001
• Published: 09/26/2002
• Est. Priority Date: 12/14/1999
• Status: Active Grant

• Current Assignee: Matsushita Electric Industrial Company Limited (Panasonic Holdings Corporation)
• Original Assignee: Matsushita Electric Industrial Company Limited (Panasonic Holdings Corporation)
• Inventors: Yukawa, Junichi, Ouchi, Satoshi, Hatanaka, Masakazu, Matsubara, Katsunori
• Granted Patent: US 6,523,410 B2
• Time in Patent Office: Days
• US Class Current: 73/504.16
• CPC Class Codes: G01C 19/5607 using vibrating tuning forks double-ended tuning forks using planar vibrating masses suspended at opposite ends G01C19/5719

Abstract

An object of the present invention is to improve the efficiency of a driving operation of an angular rate sensor employing a tuning fork oscillator made of single crystalline piezoelectric material such as quartz.

In order to achieve the object of the present invention, a tuning fork oscillator (10) assembled directly has driver electrodes (1), (2) and detector electrodes (3), (4) provided on a first main surface, a second main surface, an outer surface, and an inner surface of a arm (10a), respectively. The oscillator also has a driver electrode (5), a monitor electrode (6), and detector electrodes (7) and (8) provided on a first main surface, a second main surface, an inner surface, and an outer surface of the other arm (10b) thereof, respectively. A driving voltage is supplied from a driving power source (9) so that the two driver electrodes (2) and (5) may be equal in the polarity while the polarity of the driver electrode (1) is opposite to that of the driver electrodes (2) and (5).

Claims

1. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first, second, third, and fourth electrodes provided on a first main surface, a second main surface, an outer surface, and an inner surface of one of the arms of the tuning fork oscillator, respectively;

a fifth electrode provided on one of first and second main surfaces of other arm of the arms of the tuning fork oscillator; and

sixth and seventh electrodes provided on inner and outer surfaces of the other arm of the tuning fork oscillator, respectively,

wherein, when the fifth electrode is provided on the first main surface, a driving voltage is applied to the second and fifth electrodes at a polarity identical to each other and applied to the first electrode at a polarity opposite to the second and fifth electrodes, and

wherein, when the fifth electrode is provided on the second main surface, a driving voltage is applied to the second and fifth electrodes at polarities opposite to each other and applied to the first electrode at a polarity identical to the fifth electrode.

2. The angular rate sensor according to claim 1,

wherein the third and seventh electrodes are connected to a common port, the fourth and sixth electrodes are connected to another common port, and a detection signal is detected from a differential signal between the common ports.

31. The angular rate sensor according to any of claims 1 to 30, wherein the electrodes provided on the first and second main surfaces of the arms are extended onto a surface of the base.

32. The angular rate sensor according to any of claim 1, claims 3 to 9, claims 11 to 13, and claims 15 to 29, wherein the electrodes provided on the outer surfaces of the arms are extended onto a surface of the base.

3. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first, second, third, and fourth electrodes provided on a first main surface, a second main surface, an outer surface, and an inner surface of one of the arms of the tuning fork oscillator, respectively;

fifth and sixth electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the fifth and sixth electrodes being provided on portions close to one of outer and inner surfaces of the other arm, respectively; and

a seventh electrode provided on a surface of the other arm of the tuning fork oscillator,

wherein, when the fifth and sixth electrodes are provided on the portions close to the outer surface of the other arm, respectively, the seventh electrode is provided on the outer surface,

wherein, when the fifth and sixth electrodes are provided on the portions close to the inner surface of the other arm, respectively, the seventh electrode is provided on the inner surface, and

wherein a driving voltage is applied to the first and sixth electrodes at a polarity identical to each other and applied to the second and fifth electrodes at an polarity opposite to the first and sixth electrodes.

4. The angular rate sensor according to claim 3, further comprising an eighth electrode provided on a surface opposite to the surface of the other form arm of the tuning fork oscillator on which the seventh electrode is provided,

wherein, when the seventh electrode is provided on the outer surface, the fourth and eight electrodes are connected to a common port, the third and seventh electrodes are connected to another common port, and a detection signal is detected from a differential signal between the common ports, and

wherein, when the seventh electrode is provided on the inner surface, the third and eight electrodes are connected to a common port, the fourth and seventh electrodes are connected to another common port, and a detection signal is detected from a differential signal between the common ports.

5. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first, second, third, and fourth electrodes provided on a first main surface, a second main surface, an outer surface, and an inner surface of one of the arms of the tuning fork oscillator, respectively; and

fifth, sixth, seventh, and eighth electrodes provided on a first main surface, a second main surface, an outer surface, and an inner surface of other arm of the arms of the tuning fork oscillator, respectively,

wherein, when the fifth electrode is provided on a portion close to the outer surface of the other arm, the sixth electrode is provided on a portion close to the inner surface of the other arm,

wherein, when the fifth electrode is provided on a portion close to the inner surface of the other arm, the sixth electrode is provided on a portion close to the outer surface of the other arm, and

wherein a driving voltage is applied to the first and sixth electrodes at a polarity identical to each other and applied to the second and fifth electrodes at a polarity opposite to the first and sixth electrodes.

6. The angular rate sensor according to claim 5, wherein a detection signal is detected from a differential signal between the third and fourth electrodes.

7. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively;

third and fourth electrodes provided on one of outer and inner surfaces of the one of the arms, the third and fourth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively; and

a fifth electrode provided on a surface opposite to the surface on which the third and fourth electrodes are provided,

wherein a driving voltage is applied to the first and fourth electrodes at a polarity identical to each other and applied to the second and third electrodes at a polarity opposite to the first and fourth electrodes.

8. The angular rate sensor according to claim 7, further comprising sixth and seventh electrodes provided on inner and outer surfaces of the other arm of the tuning fork oscillator, respectively,

wherein, when the fifth electrode is provided on the inner surface of the one of the arms, a detection signal is detected from a differential signal between the sixth and seventh electrodes, or the fifth and sixth electrodes are connected to a common port, and a detection signal is detected from a differential signal between the common port and the seventh electrode, and

wherein, when the fifth electrode is provided on the outer surface of the one of the arms, a detection signal is detected from a differential signal between the sixth and seventh electrodes, or the fifth and seventh electrodes are connected to a common port, and a detection signal is detected from a differential signal between the common port and the sixth electrode.

9. The angular rate sensor according to claim 7, further comprising:

a sixth electrode provided on one of first and second main surfaces of the other arm of the tuning fork oscillator; and

seventh and eighth electrodes provided on inner and outer surfaces of the other arm, respectively,

wherein, when the sixth electrode is provided on the first main surface, a driving voltage is applied to the first and sixth electrodes at polarities opposite to each other, and

wherein, when the sixth electrode is provided on the second main surface, a driving voltage is applied to the first and sixth electrodes at a polarity identical to each other.

10. The angular rate sensor according to claim 9,

wherein, when the fifth electrode is provided on the inner surface of the one of the arms, a detection signal is detected from a differential signal between the seventh and eighth electrodes, or the fifth and seventh electrodes are connected to a common port, and a detection signal is detected from a differential signal between the common port and the eighth electrode, and

wherein, when the fifth electrode is provided on the outer surface of the one of the arms, a detection signal is detected from a differential signal between the seventh and eighth electrodes, or the fifth and eight electrodes are connected to a common port, and a detection signal is detected from a differential signal between the common port and the seventh electrode.

16. The angular rate sensor according to claim 7, further comprising electrodes provided on inner surfaces of the arms of the tuning fork oscillator, respectively, wherein the electrodes being connected to a common port, and a detection signal is detected from the common port.

24. The angular rate sensor according to any of claims 16, 18, 20, and 22, further comprising:

two grounding electrodes provided on remaining portions of the first and second main surfaces of the one of the arms of the tuning fork oscillator, respectively; and

two monitor electrodes provided on remaining portions of the first and second main surfaces of the other arm.

11. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively;

third and fourth electrodes provided on an outer surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively; and

fifth and sixth electrodes provided on an inner surface of the one of the arms, the fifth and sixth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively, wherein a driving voltage is applied to the first, fourth, and sixth electrodes at a polarity identical to one another and applied to the second, third, and fifth electrodes at a polarity opposite to the first, fourth, and sixth electrodes

12. The angular rate sensor according to claim 11, further comprising seventh and eighth electrodes provided on inner and outer surfaces of the other arm of the tuning fork oscillator, respectively, wherein a detection signal is detected from a differential signal between the seventh and eighth electrodes.

13. The angular rate sensor according to claim 11, further comprising:

a seventh electrode provided on one of first and second main surfaces of other arm of the arms of the tuning fork oscillator; and

eighth and ninth electrodes provided on inner and outer surfaces of the other arm, respectively,

wherein, when the seventh electrode is provided on the first main surface, a driving voltage is applied to the first and seventh electrodes at polarities opposite to each other, and

wherein, when the seventh electrode is provided on the second main surface, a driving voltage is applied to the first and seventh electrodes at a polarity identical to each other.

14. The angular rate sensor according to claim 13, wherein a detection signal is detected from a differential signal between the eighth and ninth electrodes.

18. The angular rate sensor according to claim 17, further comprising electrodes provided on outer surfaces of the arms of the tuning fork oscillator, respectively, wherein the electrodes are connected to a common port, and a detection signal is detected from the common port.

20. The angular rate sensor according to claim 19, further comprising:

a ninth electrode provided on an inner surface of the one of the arms of the tuning fork oscillator; and

a tenth electrode provided on an outer surface of the other arm, wherein a detection signal is detected from a differential signal between the ninth and tenth electrodes.

15. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively, the first and second electrodes being provided on portions close to an outer surface of the one of the arms, respectively;

third and fourth electrodes provided on the outer surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first main surface of the one of the arms and a portion close to the second main surface of the one of the arms, respectively;

fifth and sixth electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, the fifth and sixth electrodes being provided on portions close to an outer surface of the other arm of the tuning fork oscillator, respectively; and

seventh and eighth electrodes provided on the outer surface of the other arm, the seventh and eighth electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively,

wherein a driving voltage is applied to the first, fourth, sixth, and seventh electrodes at a polarity identical to one another and applied to the second, third, fifth, and eighth electrodes at a polarity opposite to the first, fourth, sixth, and seventh electrodes.

23. The angular rate sensor according to any of claims 15 to 22, further comprising four monitor electrodes provided on remaining portions of the first and second main surfaces of the arms of the tuning fork oscillator, respectively.

17. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively, the first and second electrodes being provided on portions close to an inner surface of the one of the arms, respectively;

third and fourth electrodes provided on the inner surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first main surface of the one of the arms and a portion close to the second main surface of the one of the arms, respectively;

fifth and sixth electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the fifth and sixth electrodes being provided on portions close to an inner surface of the other arm, respectively; and

seventh and eighth electrodes provided on the inner surface of the other arm, the seventh and eighth electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively,

wherein a driving voltage is applied to the first, fourth, sixth, and seventh electrodes at a polarity identical to one another and applied to the second, third, fifth, and eighth electrodes at a polarity opposite to the first, fourth, sixth, and seventh electrodes.

19. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively, the first and second electrodes being provided on portions close to an outer surface of the one of the arms, respectively;

third and fourth electrodes provided on the outer surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first main surface of the one of the arms and a portion close to the second main surface of the one of the arms, respectively;

fifth and sixth electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the fifth and sixth electrodes being provided on portions close to an inner surface of the other arm, respectively; and

seventh and eighth electrodes provided on the inner surface of the other arm, the seventh and eighth electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively,

wherein a driving voltage is applied to the first, fourth, sixth, and seventh electrodes at a polarity identical to one another and applied to the second, third, fifth, and eighth electrodes at a polarity opposite to the first, fourth, sixth, and seventh electrodes.

21. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively, the first and second electrodes being provided on portions close to an inner surface of the one of the arms, respectively;

third and fourth electrodes provided on the inner surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first main surface of the one of the arms and a portion close to the second main surface of the one of the arms, respectively;

fifth and sixth electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the fifth and sixth electrodes being provided on portions close to an outer surface of the other arm, respectively; and

seventh and eighth electrodes provided on the outer surface of the other arm, the seventh and eighth electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively,

wherein a driving voltage is applied to the first, fourth, sixth, and seventh electrodes at a polarity identical to one another and applied to the second, third, fifth, and eighth electrodes at a polarity opposite to the first, fourth, sixth, and seventh electrodes.

22. The angular rate sensor according to claim 21, further comprising:

a ninth electrode provided on an outer surface of the one of the arms of the tuning fork oscillator; and

a tenth electrode provided on an inner surface of the other arm, wherein a detection signal is detected from a differential signal between the ninth and tenth electrodes.

26. The angular rate sensor according to claim 25, further comprising:

a tenth electrode provided on an inner surface of the other arm of the tuning fork oscillator; and

two monitor electrodes provided on remaining portions of the first and second main surfaces of the other arm, respectively,

wherein, when the fifth electrode is provided on the inner surface of the one of the arms, the fifth and tenth electrodes are connected to a common port from which a detection signal is detected, and

wherein, when the fifth electrode is provided on the outer surface of the one of the arms, a detection signal is detected from a differential signal between the fifth and tenth electrodes.

28. The angular rate sensor according to claim 27, further comprising:

a tenth electrode provided on an outer surface of the other arm of the tuning fork oscillator; and

two monitor electrodes provided on remaining portions of the first and second main surfaces of the other arm,

wherein, when the fifth electrode is provided on the inner surface of the one of the arms, a detection signal is detected from a differential signal between the fifth and tenth electrodes, and

wherein, when the fifth electrode is provided on the outer surface of the one of the arms, the fifth and tenth electrodes are connected to a common port from which a detection signal is detected.

30. The angular rate sensor according to claim 29,

wherein, when the seventh electrode is provided on the first main surface, the fourth and ninth electrodes are connected to a common port, the sixth and eleventh electrodes are connected to another common port, and a detection signal is detected from a differential signal between the common ports, and

wherein, when the seventh electrode is provided on the second main surface, the fourth and eighth electrodes are connected to a common port, the sixth and tenth electrodes are connected to another common port, and a detection signal is detected from a differential signal between the common ports.

25. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively;

third and fourth electrodes provided on one of outer and inner surfaces of the one of the arms, the third and fourth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively;

a fifth electrode provided on one of the inner and outer surfaces of the one of the arms, the fifth electrodes being provided on a surface opposite to the surface on which the third and fourth electrodes are provided;

sixth and seventh electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the sixth and seventh electrodes being provided on portions close to an outer surface of the other arm, respectively; and

eighth and ninth electrodes provided on the outer surface of the other arm, the eighth and ninth electrodes being provided on a portion close to the sixth electrode and a portion close to the seventh electrode, respectively, wherein a driving voltage is applied to the first, fourth, seventh, and eighth electrodes at a polarity identical to one another and applied to the second, third, sixth, and ninth electrodes at a polarity opposite to the first, fourth, seventh, and eighth electrodes.

27. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively;

third and fourth electrodes provided on one of outer and inner surfaces of the one of the arms, the third and fourth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively;

a fifth electrode provided on one of the inner and outer surfaces of the one of the arms, the fifth electrode being disposed a surface opposite to the surface on which the third and fourth electrodes are provided;

sixth and seventh electrodes provided on first and second main surfaces of other arm of the arms of the tuning fork oscillator, respectively, the sixth and seventh electrodes being provided on portions close to an inner surface of the other arm, respectively; and

eighth and ninth electrodes provided on the inner surface of the other arm, the eighth and ninth electrodes being provided on a portion close to the sixth electrode and a portion close to the seventh electrode, respectively, wherein a driving voltage is applied to the first, fourth, seventh, and eighth electrodes at a polarity identical to one another and applied to the second, third, sixth, and ninth electrodes at a polarity opposite to the first, fourth, seventh, and eighth electrodes.

29. An angular rate sensor comprising:

a tuning fork oscillator having at least two arms and a base, including;

a first oscillator member of a single crystalline piezoelectric material having at least two arms and a base joining the two arms; and

a second oscillator member of the single crystalline piezoelectric material having a shape substantially identical to a shape of the first oscillator member, the first and second oscillator members being bonded directly to each other in a direction of a thickness and in a direction of a crystallographic axis so that opposite polarities of a piezoelectric effect may be developed along a widthwise direction of the first and second oscillator members;

first and second electrodes provided on first and second main surfaces of one of the arms of the tuning fork oscillator, respectively;

third and fourth electrodes provided on an outer surface of the one of the arms, the third and fourth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively;

fifth and sixth electrodes provided on an inner surface of the one of the arms, the fifth and sixth electrodes being provided on a portion close to the first electrode and a portion close to the second electrode, respectively;

a seventh electrode provided on one of first and second main surfaces of other arm of the arms of the tuning fork oscillator;

eighth and ninth electrodes provided on an outer surface of the other arm, the eighth and ninth electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively; and

tenth and eleventh electrodes provided on an inner surface of the other arm, the tenth and eleventh electrodes being provided on a portion close to the first main surface of the other arm and a portion close to the second main surface of the other arm, respectively,

wherein, when the seventh electrode is provided on the first main surface, a driving voltage is applied to the first, eighth, and tenth electrodes at a polarity identical to one another and applied to the second, third, fifth, and seventh electrodes at a polarity opposite to the first, eighth, and tenth electrodes, and

wherein, when the seventh electrode is provided on the second main surface, a driving voltage is applied to the first and seventh electrodes at a polarity identical to each other and applied to the second, third, fifth, ninth, and eleventh electrodes at a polarity opposite to the first and seventh electrodes.