Cylindrical piezoelectric element

Abstract

To provide a cylindrical piezoelectric element capable of obtaining more uniform residual polarization by a more uniform electric field in polarization processing, and capable of uniformizing force generated by piezoelectric effect due to a more uniform electric field even when being used as a drive mechanism.SOLUTION: A cylindrical piezoelectric element includes a cylindrical piezoelectric body and a plurality of electrodes arranged in a circumferential direction on an outer peripheral surface of the piezoelectric body, and no electrode is disposed on an inner peripheral surface of the piezoelectric body.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a cylindrical piezoelectric element. [Background technology]

[0002] Since cylindrical piezoelectric elements are hollow, they are expected to be used as scanners by passing an optical fiber through the hollow portion, or as ultrasonic motors by passing a shaft through the hollow portion.

[0003] As an example of a cylindrical piezoelectric element, Patent Document 1 discloses a cylindrical piezoelectric element comprising a plurality of driving electrodes arranged at approximately equal intervals in the circumferential direction on the outer peripheral surface of the cylindrical piezoelectric element, a reference electrode arranged on the inner peripheral surface of the cylindrical piezoelectric element, a folded electrode arranged on the outer peripheral surface near one end in the axial direction of the cylindrical piezoelectric element and electrically connected to the reference electrode on the inner peripheral surface, and a plurality of piezoelectric activation regions which are polarized regions between the driving electrode and the reference electrode. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2013-80774 A Summary of the Invention [Problem to be solved by the invention]

[0005] A cylindrical piezoelectric element having electrodes on its inner circumferential surface is polarized by applying a voltage between the electrodes on the inner circumferential surface and the electrodes on the outer circumferential surface. After the polarization process, the piezoelectric element is driven as an actuator (driving mechanism) by applying a voltage to the electrodes on the outer circumferential surface and the inner circumferential surface. However, the present inventors have found that as cylindrical piezoelectric elements become smaller, the strength of the electric field generated in the piezoelectric body during the polarization process is uneven in conventional piezoelectric elements having electrodes on their inner circumferential surface. In particular, it was found that the electric field strength is large on the inner circumferential surface and small on the outer circumferential surface. In this case, if the voltage applied during the polarization process is increased in order to increase the electric field strength on the outer circumferential surface, dielectric breakdown may occur within the piezoelectric element.

[0006] In addition, when a conventional cylindrical micro-piezoelectric element having electrodes on its inner circumferential surface is used as an actuator, the electric field strength becomes large on the inner circumferential side of the actuator, which may cause the remanent polarization to be reversed. Thus, in the case of a micro-piezoelectric element having electrodes on its inner circumferential surface, there is a limit to the driving voltage so that the inner circumferential side is not repolarized.

[0007] The present invention has been made in consideration of the above circumstances, and aims to provide a cylindrical piezoelectric element that can obtain a more uniform residual polarization by a more uniform electric field in a polarization process, and that can also make the force generated by the piezoelectric effect due to the more uniform electric field uniform when used as a driving mechanism. [Means for solving the problem]

[0008] The present inventors have studied the reason why unevenness in electric field strength occurs after polarization processing in a piezoelectric element having an electrode on its inner peripheral surface as the piezoelectric element is miniaturized, and have found that the influence of unevenness in electric field strength in the radial direction becomes large because the thickness of the piezoelectric element increases relative to the distance from its central axis to its outer peripheral surface as the piezoelectric element is miniaturized. The present inventors have further studied ways to suppress unevenness in electric field strength in the radial direction, and have found that polarization is possible by providing multiple electrodes on the outer peripheral surface of the piezoelectric body without providing electrodes on the inner peripheral surface, and performing polarization processing using the multiple electrodes provided on the outer peripheral surface, and further that such polarization processing can suppress variation in the polarization direction.

[0009] The present invention has been made based on these findings, and the gist of the present invention is as follows. [1] A cylindrical piezoelectric element according to one embodiment of the present invention comprises a cylindrical piezoelectric body and a plurality of electrodes extending longitudinally on the outer peripheral surface of the piezoelectric body, and no electrodes are arranged on the inner peripheral surface of the piezoelectric body. [2] In the cylindrical piezoelectric element described in [1] above, it is preferable that a dimensional ratio d1 / d2, which is a ratio of the outer dimension d1 to the inner dimension d2 of the piezoelectric body, is 1.5 or more. [3] In the cylindrical piezoelectric element according to the above [1] or [2], the number of the electrodes is preferably three or more. [4] In the cylindrical piezoelectric element according to the above [1] or [2], the number of the electrodes is preferably two. [5] In the cylindrical piezoelectric element described in any one of [1] to [4] above, it is preferable that the outer periphery of the piezoelectric body in a cross section perpendicular to a central axis along the longitudinal direction of the piezoelectric body has a polygonal shape, and the multiple electrodes are arranged on multiple planes that constitute the outer periphery. [6] In the cylindrical piezoelectric element described in any one of [1] to [5] above, it is preferable that the outer peripheral surface of the piezoelectric body has a plurality of recesses extending in the longitudinal direction of the piezoelectric body, and that the plurality of electrodes are arranged in at least any of the plurality of recesses. [7] In the cylindrical piezoelectric element according to any one of the above items [1] to [6], it is preferable that the plurality of electrodes are arranged at approximately equal intervals in the circumferential direction. Effect of the Invention

[0010] According to the cylindrical piezoelectric element of the above aspect, it is possible to obtain a more uniform residual polarization by a more uniform electric field in the polarization process, and when used as a driving mechanism, it is also possible to make the force generated by the piezoelectric effect due to the more uniform electric field uniform. [Brief description of the drawings]

[0011] [Figure 1] 1 is a schematic diagram of a conventional piezoelectric element in which electrodes are arranged on the outer and inner peripheral surfaces of a cylindrical piezoelectric body. [Diagram 2] 1 is a perspective view of a cylindrical piezoelectric element according to an embodiment of the present invention; [Diagram 3] FIG. 2 is a plan view of a cylindrical piezoelectric element according to the same embodiment. [Figure 4] 1A is a plan view illustrating another aspect of the cylindrical piezoelectric element according to the same embodiment, where (A) is a plan view of a cylindrical piezoelectric element having an outer periphery shape that is a regular octagon, and (B) is a plan view of a cylindrical piezoelectric element having a recess on its outer periphery. [Diagram 5] FIG. 4 is a partial plan view for explaining the shape of a recess according to the embodiment. [Figure 6] FIG. 2A is a schematic diagram for explaining a method of polarization processing of a cylindrical piezoelectric element according to the embodiment, and FIG. 2B is a vector diagram of an electric field generated during polarization processing. [Figure 7] FIG. 2A is a plan view of the cylindrical piezoelectric element for explaining an example of the operation of the cylindrical piezoelectric element according to the embodiment, and FIG. [Figure 8] FIG. 1A is a plan view illustrating the structure of a cylindrical piezoelectric element according to a first example of the present invention, and FIG. 1B is a perspective view of the cylindrical piezoelectric element according to the first example of the present invention. [Figure 9] 1A is a plan view for explaining the structure of a cylindrical piezoelectric element according to Comparative Example 1, and FIG. 1B is a perspective view of the cylindrical piezoelectric element according to Comparative Example 1. FIG. [Figure 10]1A is a vector diagram of the electric field generated in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 1 of the present invention during polarization processing, and FIG. 1B is a vector diagram of the electric field generated in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Comparative Example 1 during polarization processing. [Figure 11] 1A is a contour diagram showing the distribution of electric field strength in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 1 of the present invention; FIG. 1B is a contour diagram showing the distribution of electric field strength in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Comparative Example 1; FIG. 1C is a graph showing the area ratio of each section of electric field strength in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 1 of the present invention; and FIG. 1D is a graph showing the area ratio of each section of electric field strength in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Comparative Example 1. [Figure 12] FIG. 10(A) is a plan view illustrating the structure of a cylindrical piezoelectric element according to a second example of the present invention, and FIG. 10(B) is a perspective view of the cylindrical piezoelectric element according to the second example of the present invention. [Figure 13] 10A is a plan view illustrating the structure of a cylindrical piezoelectric element according to a third example of the present invention, and FIG. 10B is a perspective view of the cylindrical piezoelectric element according to the third example of the present invention. [Figure 14] FIG. 13(A) is a plan view illustrating the structure of a cylindrical piezoelectric element according to a fourth example of the present invention, and FIG. 13(B) is a perspective view of the cylindrical piezoelectric element according to the fourth example of the present invention. [Figure 15] FIG. 1A is a vector diagram of the electric field generated in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 2 of the present invention during polarization processing; FIG. 1B is a vector diagram of the electric field generated in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 3 of the present invention during polarization processing; and FIG. 1C is a vector diagram of the electric field generated in the XY cross section at the longitudinal center of a cylindrical piezoelectric element according to Example 4 of the present invention during polarization processing. [Figure 16](A) is a graph showing the area ratio for each section of the electric field strength generated in the XY cross-section at the central position in the longitudinal direction of the cylindrical piezoelectric element of Invention Example 2, (B) is a graph showing the area ratio for each section of the electric field strength generated in the XY cross-section at the central position in the longitudinal direction of the cylindrical piezoelectric element of Invention Example 3, and (C) is a graph showing the area ratio for each section of the electric field strength generated in the XY cross-section at the central position in the longitudinal direction of the cylindrical piezoelectric element of Invention Example 4. [Figure 17] It is a plan view for explaining the structure of the cylindrical piezoelectric element according to Invention Example 8. [Figure 18] It is a graph showing the relationship between the magnitude of the deviation between the center of the outer circumference and the center of the inner circumference of the cylindrical piezoelectric element in the XY cross-section and the uniformity of the electric field strength. [Figure 19] It is a plan view for explaining another aspect of the cylindrical piezoelectric element according to an embodiment of the present invention. [Figure 20] It is a plan view for explaining another aspect of the cylindrical piezoelectric element according to an embodiment of the present invention.

Mode for Carrying Out the Invention

[0012] First, prior to the description of the cylindrical piezoelectric element according to an embodiment of the present invention, with reference to FIG. 1, when a conventional cylindrical piezoelectric element having electrodes on its inner peripheral surface and outer peripheral surface is miniaturized, the reason why the unevenness of the electric field strength becomes large in the cross-section perpendicular to the central axis in the longitudinal direction of the piezoelectric element during the polarization process using these electrodes will be explained. FIG. 1 is a schematic diagram of a conventional piezoelectric element in which electrodes are arranged on the outer peripheral surface and the inner peripheral surface of a cylindrical piezoelectric body.

[0013] Consider a piezoelectric element in which electrodes are arranged on each of the outer peripheral surface and the inner peripheral surface of a cylindrical piezoelectric body. Here, as shown in FIG. 1, let the inner diameter of the piezoelectric body be a and the outer diameter be b. When a charge of +Q [C] per unit length is applied to the electrode on the inner peripheral surface and a charge of -Q [C] per unit length is applied to the electrode on the outer peripheral surface, the magnitude Et of the electric field generated at a position radially away from the central axis by t (a <t <b) in the piezoelectric body is expressed by the following equation (1) from Gauss's theorem. Note that ε is the dielectric constant of the piezoelectric body.

[0014]

number

[0015] The potential difference V0 generated between the electrode on the inner circumferential surface and the electrode on the outer circumferential surface at this time is the integral value of the electric field magnitude Et from the inner circumferential surface to the outer circumferential surface of the piezoelectric body, and is expressed by the following equation (2).

[0016]

number

[0017] The capacitance C per unit length of the piezoelectric body is expressed by the following formula (3) from the above formula (2).

[0018]

number

[0019] From the above formulas (1) and (3), the magnitude Et of the electric field generated at a position t away from the central axis of the piezoelectric body in the radial direction is expressed by the following formula (4).

[0020]

number

[0021] Assuming a miniaturized piezoelectric body, substituting a = 200 μm and b = 400 μm into the above formula (4), calculating the magnitude of the electric field on the inner circumferential surface (t = 200 μm) and the magnitude of the electric field on the outer circumferential surface (t = 400 μm), and comparing these, the magnitude of the electric field generated on the inner circumferential surface E a is the magnitude of the electric field generated on the outer surface E b This is about twice as much.

[0022] On the other hand, a relatively large cylindrical piezoelectric element has a small wall thickness relative to its outer dimensions. For example, in a cylindrical piezoelectric element with an inner dimension a = 9 mm and an outer dimension b = 10 mm, the magnitude of the electric field on the inner circumferential surface E a is the electric field strength E on the outer surface bIt is about 1.1 times as large as the piezoelectric element. Thus, when the difference between the outer and inner dimensions is small relative to the outer dimensions, in other words, when the thickness is small relative to the outer dimensions, the difference in the magnitude of the electric field between the inner and outer circumferential surfaces of the piezoelectric element is small. However, as described above, as the piezoelectric element becomes smaller, the thickness becomes larger relative to the outer dimensions, and the difference in the magnitude of the electric field between the inner and outer circumferential surfaces of the piezoelectric element becomes larger. As a result, the inside is polarized by a high electric field, but the electric field required for polarization is not applied to the outside, resulting in insufficient polarization. So far, we have explained the reasons why the unevenness of the electric field strength increases when a conventional cylindrical piezoelectric element having electrodes on its inner circumferential surface is miniaturized.

[0023] As described above, when a voltage is applied to the electrodes on the outer circumferential surface and the electrodes on the inner circumferential surface, an electric field with a large variation in strength is generated in the piezoelectric body. As a result of studies by the present inventors, it was found that by applying a voltage only to the electrodes on the outer circumferential surface, an electric field with excellent uniformity in electric field strength can be generated in the piezoelectric body, and a more uniform remanent polarization can be obtained compared to conventional microscopic piezoelectric elements.

[0024] A piezoelectric element according to one embodiment of the present invention will be described below with reference to Figs. 2 to 5. Fig. 2 is a perspective view of a cylindrical piezoelectric element 1 according to one embodiment of the present invention. Fig. 3 is a plan view of the cylindrical piezoelectric element 1 according to this embodiment. Fig. 4 is a plan view for explaining another aspect of the cylindrical piezoelectric element 1 according to this embodiment, where (A) is a plan view of a piezoelectric element whose outer periphery has a regular octagonal shape, and (B) is a plan view of a cylindrical piezoelectric element having a recess on the outer periphery. Fig. 5 is a partial plan view for explaining the shape of the recess 13 according to this embodiment. It should be noted that the dimensions and ratios of each component in the drawings do not necessarily represent the actual dimensions and ratios of each component.

[0025] In the following, the direction in which the central axis of the piezoelectric element extends along the longitudinal direction is sometimes referred to as the axial direction, and the direction along the outer periphery of the piezoelectric element in a plane perpendicular to the central axis is sometimes referred to as the circumferential direction. Furthermore, in the plane perpendicular to the central axis of the piezoelectric element, two directions that are perpendicular to each other are sometimes referred to as the X-axis direction and the Y-axis direction, respectively, and the direction in which the central axis of the piezoelectric element extends is sometimes referred to as the Z-axis direction. Furthermore, a surface of the piezoelectric element cut by a plane perpendicular to the central axis of the piezoelectric element is sometimes referred to as the XY cross section.

[0026] [Cylindrical piezoelectric element 1] As shown in FIGS. 2 and 3, the cylindrical piezoelectric element 1 according to this embodiment includes a cylindrical piezoelectric body 11 and a plurality of electrodes 12 extending in the axial direction on the outer circumferential surface of the piezoelectric body 11.

[0027] The piezoelectric body 11 is made of a material having piezoelectricity. The piezoelectric material is, for example, ceramics having a perovskite structure. The ceramics having the perovskite structure are, for example, barium titanate, lead zirconate titanate, potassium niobate, lithium niobate, lithium tantalate, and lead zirconate titanate (PZT) doped with nickel, bismuth, lanthanum, neodymium, niobium, or the like. The material of the piezoelectric body 11 is preferably a material having a high relative dielectric constant in order to form a more uniform electric field. In addition, the polarization process is performed between the external electrodes, but since the distance is greater than that of conventional electrode arrangements, it is preferable to use a material that is easily polarized, such as PZT.

[0028] The piezoelectric body 11 is cylindrical and has an outer circumferential surface 111 and an inner circumferential surface 112 . The shape of the outer periphery 111 of the piezoelectric body 11 in the XY cross section (hereinafter, the shape of the outer periphery of the piezoelectric body 11 in the XY cross section will be simply referred to as the outer periphery shape of the piezoelectric body 11) can be, for example, a rotationally symmetric shape. Specifically, the outer periphery shape of the piezoelectric body 11 can be, for example, a circle as shown in FIG. 3, or a regular octagon as shown in FIG. 4(A) in which the shape of the outer periphery 111B is a regular octagon. The outer periphery shape is not limited to FIG. 3 and FIG. 4(A), and can be, for example, an ellipse, a polygon, or the like. The polygon includes a regular polygon in which all sides are equal in length and all interior angles are equal in size, a polygon in which at least one of the multiple sides forming the polygon has a different length, and a polygon in which at least one of the multiple interior angles has a different size. When the shape of the outer periphery 111 in the XY cross section is polygonal, the electrodes 12 are arranged on the planes that form the outer periphery surface 111, but the number of electrodes 12 does not have to be the same as the number of planes that form the outer periphery surface 111, and the number of electrodes 12 may be less than the number of planes that form the outer periphery surface 111. When the number of electrodes 12 is less than the number of planes that form the outer periphery surface 111, it is sufficient that the electrodes 12 are provided on multiple planes so as to be arranged at approximately equal intervals in the circumferential direction.

[0029] The outer dimension d1 of the piezoelectric body 11 is, for example, more than 200 μm and not more than 800 μm. The outer dimension d1 of the piezoelectric body 11 can be determined depending on the application. There is no particular lower limit to the outer dimension d1 of the piezoelectric body 11, but from the viewpoint of manufacturability, it is preferable that the outer dimension d1 is 400 μm or more. Note that the outer dimension d1 referred to here refers to the longest length when connecting two points on the outer periphery of the piezoelectric body 11 in the XY cross section.

[0030] The shape of the inner circumference of the piezoelectric body 11 in the XY cross section is not particularly limited, and may be, for example, a rotationally symmetric shape, such as a circle, an ellipse, a polygon, etc. In order to make the electric field more uniform, it is preferable that the shape of the inner circumference of the piezoelectric body is a circle.

[0031] The inner dimension d2 of the piezoelectric body 11 is, for example, 125 μm or more. If the inner dimension d2 of the piezoelectric body 11 is 125 μm or more, the core and clad of an optical fiber can be provided inside the piezoelectric body 11, and the cylindrical piezoelectric element 1 can be applied to an optical fiber. There is no particular upper limit to the inner dimension d2 of the piezoelectric body 11, and it can be determined according to the size of a member to be inserted inside the piezoelectric body 11 depending on the application of the cylindrical piezoelectric element 1. The inner dimension d2 of the piezoelectric body 11 is, for example, 200 μm or less. The inner dimension d2 referred to here refers to the shortest length when connecting two points on the inner circumference of the piezoelectric body 11 in the XY cross section.

[0032] The thickness t of the piezoelectric body 11 is not particularly limited and may be determined according to the outer dimension d1 and the inner dimension d2, but from the viewpoint of the internal pressure during extrusion molding, the thickness t of the piezoelectric body 11 is preferably 125 μm or more. Note that the thickness t here is a value calculated by (d1-d2) / 2.

[0033] In the piezoelectric body 11, the dimensional ratio d1 / d2, which is the ratio of the outer dimension d1 to the inner dimension d2, is not particularly limited, but is, for example, 1.5 or more. If the dimensional ratio d1 / d2 is 1.5 or more, a more uniform polarization state can be obtained compared to a conventional cylindrical piezoelectric element having the same dimensional ratio d1 / d2 and electrodes on the inner peripheral surface. The dimensional ratio d1 / d2 is preferably 1.6 or more, and more preferably 2.0 or more. On the other hand, the upper limit of the dimensional ratio d1 / d2 is not particularly limited, but can be, for example, 6.4 or less.

[0034] In the XY cross section, the center of the inner circumference 112 of the piezoelectric body 11 does not have to coincide with the center of the outer circumference 111 of the piezoelectric body 11. Although details will be described in Example 4 below, in the cylindrical piezoelectric element 1 according to this embodiment, even if the center of the inner circumference 112 of the piezoelectric body 11 and the center of the outer circumference 111 of the piezoelectric body 11 are misaligned from each other, highly uniform polarization processing is possible. On the other hand, if the center of the inner circumference 112 of the piezoelectric body 11 and the center of the outer circumference 111 of the piezoelectric body 11 are significantly misaligned, when the cylindrical piezoelectric element 1 is driven as an actuator, the force applied to the piezoelectric body 11 becomes non-uniform within the piezoelectric body 11, and the driving direction of the cylindrical piezoelectric element 1 may change from when the centers of the respective centers coincide with each other. In order to suppress changes in the behavior of the cylindrical piezoelectric element 1 when driven as an actuator, the distance between the center of the inner circumference 112 of the piezoelectric body 11 and the center of the outer circumference 111 of the piezoelectric body 11 in the XY cross section is preferably 20 μm or less.

[0035] The piezoelectric body 11 may have a plurality of recesses 13 extending in the axial direction on the outer peripheral surface 111 as shown in FIG. 4(B), for example. When the piezoelectric body 11 has a plurality of recesses 13 extending in the axial direction, the plurality of recesses 13 are preferably arranged at approximately equal intervals in the circumferential direction. The electrode 12 is formed in the recesses 13. The plurality of electrodes 12 are preferably arranged in at least one of the plurality of recesses 13. By forming the electrode 12 in the recesses 13, it is possible to prevent the electrode paste from spreading during the manufacture of the electrode 12, and the electrode 12 can be thinned. In addition, in a piezoelectric body 11 that does not have the recesses 13 on the outer peripheral surface 111, it may be difficult to specify the formation position of the electrode 12, and the formation position of the electrode 12 may be shifted from the desired position. However, by having the recesses 13 on the outer peripheral surface 111 of the piezoelectric body 11, it is easy to specify the formation position of the electrode 12, and it is easy to form the electrode 12 at the desired position. Furthermore, by disposing the electrode 12 in the recess 13, the electric field that tends to concentrate in the vicinity of the circumferential end of the electrode 12 can be alleviated. The electrodes 12 are disposed in the recesses 13, but the number of the electrodes 12 and the number of the recesses 13 do not have to be the same, and there may be more recesses 13 than electrodes 12. When there are more recesses 13 than electrodes 12, the electrodes 12 may be disposed in a plurality of recesses 13 so as to be disposed at approximately equal intervals in the circumferential direction.

[0036] The cross-sectional shape of the recess 13 is not particularly limited, and may be, for example, an arc shape having a predetermined radius of curvature with the center of the circle of curvature outside the piezoelectric body 11 as shown in Fig. 5(A), or may be a rectangle with the center outside the piezoelectric body 11 as shown in Fig. 5(B). The width of the recess 13 (the distance between the two ridges between the recess 13 and the outer circumferential surface 111) may be, for example, 50 µm or more. From the viewpoint of the formability of the electrode 12, the width of the recess 13 is preferably 100 µm or more. Also, as shown in FIG. 5(C), it is preferable that the ridge between the recess 13 and the outer peripheral surface 111 is chamfered. When the piezoelectric body 11 is manufactured by extrusion molding, the ridge between the recess 13 and the outer peripheral surface 111 is rounded and chamfered. In this way, from the viewpoint of manufacturability, it is preferable that the ridge between the recess 13 and the outer peripheral surface 111 is chamfered. By chamfering the ridge, for example, when the electrode 12 is formed by applying electrode paste to the narrow recess 13 by an inkjet method, the tip of the nozzle for ejecting the electrode paste can be easily inserted into the recess 13, and the electrode 12 can be easily formed. In addition, by chamfering the ridge, it is possible to suppress the concentration of the electric field, and also to suppress the occurrence of cracks and breaks at the ridge. The chamfering of the ridge between the recess 13 and the outer peripheral surface 111 may be R-chamfered or C-chamfered. 5(D), the bottom surface of the recess 13 may be an arc shape having a predetermined radius of curvature with the center of the circle of curvature inside the piezoelectric body 11. The bottom surface of the recess 13 is preferably an arc shape with the center of the circle of curvature at the central axis C. If the bottom surface of the recess 13 is an arc shape with the center of the circle of curvature at the central axis C, it is possible to allow for a twist error during the manufacture of the electrode.

[0037] The electrodes 12 are made of a conductive material, such as gold, silver, copper, nickel, or a silver-palladium alloy.

[0038] The electrode 12 is formed from one end to the other end in the axial direction of the piezoelectric body 11. However, the length of the electrode 12 along the axial direction can be appropriately changed, and may be, for example, 90% or less of the length of the piezoelectric body 11 in the axial direction, 75% or less, or 50% or less.

[0039] The width (length in the circumferential direction) of the electrode 12 is determined according to the outer dimension d1 and the outer peripheral shape of the piezoelectric body 11, but when a voltage is applied between the electrodes 12 provided on the outer peripheral surface 111 of the piezoelectric body 11, it is preferable that the width of the electrode 12 is small. The width of the electrode 12 is, for example, 150 μm or less. On the other hand, the width of the electrode 12 can be, for example, 50 μm or more, but from the viewpoint of manufacturability, the width of the electrode 12 is preferably 70 μm or more. The thickness of electrode 12 (the maximum distance from outer peripheral surface 111 of piezoelectric body 11 to the surface of electrode 12) is preferably 1 μm or more. If the thickness of electrode 12 is 1 μm, the resistance of electrode 12 can be sufficiently small. The thickness of electrode 12 is more preferably 2 μm or more.

[0040] In the cylindrical piezoelectric element 1, a plurality of electrodes 12 are arranged on the outer peripheral surface 111 of the piezoelectric body 11, extending in the longitudinal direction. For example, in FIG. 3, four electrodes extending in the longitudinal direction are arranged at equal intervals in the circumferential direction on the outer peripheral surface 111. The number of electrodes 12 is not limited to four, and two or more may be arranged. For example, in FIG. 19, two electrodes 12 are arranged on the outer peripheral surface 111 of the piezoelectric body 11 symmetrically with respect to a line L that passes through the central axis C of the piezoelectric body 11 and is parallel to the X-axis. If two or more electrodes 12 are arranged, the variation in polarization of the piezoelectric body 11 polarized by these electrodes 12 can be reduced.

[0041] When two electrodes 12 are arranged on the outer circumferential surface 111, by arranging the two electrodes 12 symmetrically, when the cylindrical piezoelectric element 1 after polarization processing is used as an actuator, it can be deformed in the direction in which the two electrodes 12 are arranged. In addition, by arranging the two electrodes 12 not symmetrically but with an appropriate offset, it is possible to control the deformation of the piezoelectric element.

[0042] Furthermore, when three or more electrodes 12 are arranged on the outer circumferential surface 111, it is preferable that the electrodes 12 are arranged at approximately equal intervals. By arranging three or more electrodes 12 at approximately equal intervals in the circumferential direction, when the cylindrical piezoelectric element 1 is used as an actuator, the cylindrical piezoelectric element 1 can be deformed arbitrarily by controlling the magnitude and phase of the voltage applied to each electrode 12. For example, when one end of the cylindrical piezoelectric element 1 is fixed and the cylindrical piezoelectric element 1 is driven, the end opposite to the fixed end can be displaced arbitrarily on the XY plane.

[0043] As described above, in the cylindrical piezoelectric element 1 according to this embodiment, the electrodes 12 are arranged only on the outer peripheral surface 111 of the piezoelectric body 11, and are not arranged on the inner peripheral surface 112. By performing a polarization process on the piezoelectric body 11 using the multiple electrodes 12 arranged on the outer peripheral surface 111, the polarization state of the piezoelectric body 11 can be made more uniform. Furthermore, when a voltage is applied to the cylindrical piezoelectric element 1 after the polarization process to drive it, the residual polarization of the piezoelectric body 11 is more uniform, so that a high voltage can be applied when used as a drive mechanism. In addition, since there is no need to provide electrodes on the inner peripheral surface 112, the manufacturing process is easier and the manufacturing costs can be reduced compared to conventional piezoelectric elements in which electrodes are provided on the inner peripheral surface. So far, the cylindrical piezoelectric element 1 according to this embodiment has been described.

[0044] Although the present invention has been described above based on one embodiment of the present invention, the present invention is not limited thereto. The above is merely an example, and anything that has substantially the same configuration as the technical idea described in the claims of the present invention and exhibits similar effects is included in the technical scope of the present invention.

[0045] The piezoelectric body in the cylindrical piezoelectric element described above has a point-symmetric shape in a plan view, but the shape of the piezoelectric body is not limited to point symmetry and may be line-symmetric. For example, as shown in FIG. 20, the piezoelectric body may be a piezoelectric body 11A having an outer peripheral surface 111A and an inner peripheral surface 112A that are elliptical in a plan view. In FIG. 20, the long axis coincides with the X-axis direction, the short axis coincides with the Y-axis direction, and two electrodes 12 are arranged symmetrically on the outer peripheral surface 111A of the piezoelectric body 11A with respect to a line L that passes through the central axis C of the piezoelectric body 11A and is parallel to the X-axis. The cylindrical piezoelectric element 1A shown in FIG. 20 has different shapes in the X-axis direction and the Y-axis direction, so that when it is operated as an actuator, it may have a resonance frequency that bends and deforms in the X-axis direction and a resonance frequency that bends and deforms in the Y-axis direction. In order to operate the cylindrical piezoelectric element 1A as an actuator, a polarization process is performed, an AC voltage is applied to the electrodes 12, 12, and a potential difference is applied between the electrodes 12, 12 to generate an electric field due to the potential difference. By setting the frequency of the AC voltage to one of the resonance frequencies, the tip of the cylindrical piezoelectric element 1A can be displaced in a direction corresponding to the resonance frequency. In addition, by controlling the frequency of the AC voltage, the cylindrical piezoelectric element 1A can be displaced in any direction.

[0046] The shape of the piezoelectric body is not limited to the above-mentioned shapes, and when it is operated as an actuator, an AC voltage having a frequency according to the shape of the piezoelectric body may be applied.

[0047] Even when the piezoelectric body has an axisymmetric shape, the piezoelectric body may have a plurality of recesses, and a plurality of electrodes may be disposed in any of the plurality of recesses. Also, the plurality of electrodes may be disposed at approximately equal intervals in the circumferential direction.

[0048] [Method of manufacturing cylindrical piezoelectric element 1 and actuator] Next, an example of a method for manufacturing the cylindrical piezoelectric element 1 will be described. First, a powdered piezoelectric material is molded into a cylindrical shape using a press or the like. The molding is performed, for example, by extrusion molding or injection molding. After that, the cylindrical molded body is heated to a temperature of about 1000°C to sinter the molded body and produce the piezoelectric body 11. Next, a plurality of electrodes 12 are formed on the outer circumferential surface 111 of the piezoelectric body 11. The electrodes 12 are formed, for example, by applying an electrode paste using a plating process or an inkjet method, and then baking the electrode paste if necessary. So far, one example of the manufacturing method for the cylindrical piezoelectric element 1 has been described.

[0049] The cylindrical piezoelectric element 1 is polarized by applying a voltage between the electrodes 12. FIG. 6(A) is a schematic diagram for explaining a method of polarization processing of the cylindrical piezoelectric element 1 according to this embodiment, and FIG. 6(B) is a vector diagram of an electric field generated during polarization processing. FIG. 6(A) shows a schematic diagram of a cylindrical piezoelectric element 1 having four electrodes 12 arranged at equal intervals in the circumferential direction on the outer peripheral surface 111. For example, the electrodes 12B and 12D are set to 0V (ground voltage), and a voltage V is applied to the electrode 12A and the electrode 12C which is point-symmetrical to the electrode 12A with respect to the central axis C. The voltage V to be applied is, for example, a voltage such that the intensity of the electric field generated by the voltage V is about 50V / mm to 3kV / mm, and the application time is about 30 minutes to 2 hours. If necessary, heat of about 100°C to 300°C is applied to perform polarization processing. 6(B), an electric field from electrode 12A to electrode 12B and an electric field from electrode 12A to electrode 12D are generated between electrodes 12A and 12B and between electrodes 12A and 12D, respectively. In addition, an electric field from electrode 12C to electrode 12B and an electric field from electrode 12C to electrode 12D are generated between electrodes 12C and 12B and between electrodes 12C and 12D, respectively. Due to the generated electric field, the polarization direction is aligned in the direction indicated by the arrows, and residual polarization remains in piezoelectric body 11 after the voltage V applied to electrodes 12A and 12C is removed.

[0050] [Actuator operation] Next, the operation of the cylindrical piezoelectric element 1 as an actuator will be described with reference to Fig. 7. Fig. 7(A) is a plan view of the cylindrical piezoelectric element 1 according to this embodiment for explaining an example of the operation of the piezoelectric element, and (B) is a perspective view. In the cylindrical piezoelectric element 1 shown in Fig. 7, four electrodes 12 are arranged at equal intervals in the circumferential direction on the outer circumferential surface 111, and the cylindrical piezoelectric element 1 is polarized in the direction of the dashed arrow.

[0051] A voltage is applied to electrodes 12A and 12B to set the potential of electrodes 12A and 12B to a positive potential V, and electrodes 12C and 12D are grounded to a potential of 0 V. At this time, since there is no potential difference between electrodes 12A and 12B and between electrodes 12C and 12D, no electric field is generated between electrodes 12A and 12B and between electrodes 12C and 12D, and no distortion is generated in the above-mentioned region of piezoelectric body 11. Between the electrodes 12B and 12C, an electric field E B-C An electric field E is generated by the potential difference V between the electrodes 12B and 12C. B-C is the opposite direction to the polarization direction (from electrode 12C to electrode 12B) indicated by the dashed arrow. Therefore, in the XY cross section, contraction deformation occurs between electrode 12B and electrode 12C. As a result, expansion deformation occurs in the axial direction between electrode 12B and electrode 12C. Between the electrodes 12D and 12A, an electric field E A-D An electric field E is generated by the potential difference V between the electrodes 12A and 12D. A-D is the same as the polarization direction indicated by the dashed arrow (the direction from electrode 12A to electrode 12D). Therefore, in the XY cross section, expansion deformation occurs between electrode 12D and electrode 12A. As a result, contraction deformation occurs in the axial direction between electrode 12D and electrode 12A. When one end of the cylindrical piezoelectric element 1 is fixed, an expansion deformation occurs between electrodes 12B and 12C in the direction along the central axis C, and a contraction deformation occurs between electrodes 12D and 12A in the direction along the central axis C, so that the tip of the cylindrical piezoelectric element 1 is displaced toward the space between electrodes 12D and 12A (in the negative direction of the X-axis), as shown in Figure 7(B).

[0052] The voltage applied to the electrodes when the cylindrical piezoelectric element 1 is driven as an actuator may be adjusted as appropriate.

[0053] The piezoelectric element according to this embodiment can be applied to a scanner or an ultrasonic motor. EXAMPLES

[0054] The present invention will be described in more detail below with reference to examples, although the present invention is not limited to these examples.

[0055] [Example 1] An analysis of the electric field assuming a polarization process was performed using the finite element method for a cylindrical piezoelectric element according to the present invention (Invention Example 1) and a conventional cylindrical piezoelectric element (Comparative Example 1) having electrodes on the inner and outer circumferential surfaces of a piezoelectric body. Fig. 8(A) is a plan view for explaining the structure of the cylindrical piezoelectric element according to Inventive Example 1, and (B) is a perspective view of the cylindrical piezoelectric element according to Inventive Example 1. Fig. 9(A) is a plan view for explaining the structure of the cylindrical piezoelectric element according to Comparative Example 1, and (B) is a perspective view of the cylindrical piezoelectric element according to Comparative Example 1.

[0056] (Example 1 of the present invention) In the present invention example 1, a cylindrical piezoelectric body with an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm was used, and four electrodes A to D were arranged in this order on the outer circumferential surface of the piezoelectric body at approximately equal intervals in the circumferential direction as shown in FIG. 8(A). The width of each electrode was 80 μm, and as shown in FIG. 8(B), they were arranged in the axial direction from one end of the piezoelectric body to the other end. A voltage was applied to electrodes A and C, and the potential of these electrodes was set to 300 V. Electrodes B and D were grounded, and the potential of these electrodes was set to 0 V. FIG. 10(A) shows electric field vectors in the XY cross section at the center position in the length direction of the cylindrical piezoelectric element of the present invention example 1, and FIG. 11(A) shows a contour diagram showing the distribution of electric field intensity in the XY cross section at the center position in the length direction of the cylindrical piezoelectric element of the present invention example 1. Table 1 shows the distribution of electric field strength when the electric field strength is divided equally into 30 parts from the minimum to maximum in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Example 1. Fig. 11(C) shows a graph showing the area ratio for each division of the electric field strength in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Example 1.

[0057] [Table 1]

[0058] Comparative Example 1 In Comparative Example 1, a cylindrical piezoelectric body having an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm was used. As shown in FIG. 9(A), four electrodes A to D were arranged in this order on the outer peripheral surface of the piezoelectric body at approximately equal intervals in the circumferential direction, and an electrode E was arranged on the inner peripheral surface over the entire circumferential direction. The width of each of the electrodes A to D on the outer peripheral surface was 200 μm. As shown in FIG. 9(B), the electrodes A to D on the outer peripheral surface and the electrode E on the inner peripheral surface were arranged from one end to the other end of the piezoelectric body in the axial direction. A voltage was applied to the electrodes A to D, and the potential of these electrodes was set to 300 V. The electrode E on the inner peripheral surface was grounded, and the potential of these electrodes was set to 0 V. FIG. 10(B) shows electric field vectors in the XY cross section at the center position in the length direction of the cylindrical piezoelectric element of Comparative Example 1, and FIG. 11(B) shows a contour diagram showing the distribution of the electric field strength in the XY cross section at the center position in the length direction of the cylindrical piezoelectric element of Comparative Example 1. Table 2 shows the distribution of electric field strength when the electric field strength generated in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Comparative Example 1 is divided into 30 equal parts from the minimum to the maximum. Fig. 11(D) shows a graph showing the area ratio for each division of the electric field strength in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Comparative Example 1.

[0059] [Table 2]

[0060] (result) In the present invention example 1, as shown in FIG. 10(A), it was found that the electric field direction was uniform in the direction of the arrow. It was also found that an electric field was generated on the outer peripheral surface side between each electrode. In addition, by comparing FIG. 11(A) with FIG. 11(B) and FIG. 11(C) with FIG. 11(D), it was found that the variation in the electric field strength of the piezoelectric element of the present invention example 1 was smaller than that of the piezoelectric element of Comparative Example 1. As shown in Table 1 and FIG. 11(C), the area ratio of the region having an electric field strength of rank 10 was the largest at 28.6%, and the area ratio of the region having an electric field strength within 10% of the whole (rank 9 to 11) based on the electric field strength with the largest area ratio (rank 10) was 57.5% with respect to the whole area of ​​the XY cross section. Thus, it was found that the piezoelectric element of the present invention example 1 has an electric field direction uniform and the variation in the electric field strength is small, so that it can be polarized uniformly in the direction of the arrow. On the other hand, in Comparative Example 1, as shown in FIG. 10(B), it was found that the direction of the electric field was from the electrodes A to D on the outer peripheral surface toward the electrode E on the inner peripheral surface. In Comparative Example 1, as shown in FIG. 10(B), it was found that a large electric field was generated at the end of each electrode arranged on the outer peripheral surface, but there was a portion on the outer peripheral surface between each electrode where no electric field was generated. In addition, as shown in Table 2 and FIG. 11(D), the area ratio of the area having the electric field strength of rank 19 was the largest at 13.1%, and the area ratio of the area of ​​the area having the electric field strength within 10% of the whole (ranks 18 to 20) based on the electric field strength with the largest area ratio (rank 19) was 34.6% with respect to the whole area of ​​the XY cross section. In Comparative Example 1, the difference in electric field strength was large between the outer peripheral surface and the inner peripheral surface, and while a strong electric field was applied near the inner peripheral surface, the electric field was weak in many parts near the outer peripheral surface. As a result, as shown in FIG. 11(D), it was found that the electric field generated in the piezoelectric element of Comparative Example 1 was non-uniform, resulting in non-uniform polarization. Thus, it was found that the electric field strength was more uniform in Inventive Example 1 compared to Comparative Example 1. Therefore, it was found that Inventive Example 1 could be polarized more uniformly than Comparative Example 1.

[0061] [Example 2] In this example, an analysis of an electric field assuming a polarization process was performed by the finite element method for a piezoelectric element with a modified outer peripheral shape. Fig. 12(A) is a plan view for explaining the structure of a cylindrical piezoelectric element according to a second example of the present invention, and (B) is a perspective view of the cylindrical piezoelectric element according to the second example of the present invention. Fig. 13(A) is a plan view for explaining the structure of a cylindrical piezoelectric element according to a third example of the present invention, and (B) is a perspective view of the cylindrical piezoelectric element according to the third example of the present invention. Fig. 14(A) is a plan view for explaining the structure of a cylindrical piezoelectric element according to a fourth example of the present invention, and (B) is a perspective view of the cylindrical piezoelectric element according to the fourth example of the present invention.

[0062] (Example 2 of the present invention) In the present invention example 2, the piezoelectric element has an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm. As shown in FIG. 12(A), the outer peripheral shape is a regular octagon and the inner peripheral shape is a circle. Four electrodes A to D are arranged in this order on the outer peripheral surface of the piezoelectric element at approximately equal intervals in the circumferential direction. The width of each electrode is 100 μm, and as shown in FIG. 12(B), they are arranged in the axial direction from one end of the piezoelectric element to the other end. A voltage is applied to electrodes A and C, and the potential of these electrodes is set to 300 V. Electrodes B and D are grounded, and the potential of these electrodes is set to 0 V. FIG. 15(A) shows the electric field vectors generated in the XY cross section at the center position in the longitudinal direction of the piezoelectric element of the present invention example 2. Table 3 shows the distribution of electric field strength when the electric field strength generated in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Example 2 of the present invention is divided into 30 equal parts from the minimum to the maximum, and Figure 16(A) shows a graph showing the area ratio for each electric field strength division.

[0063] [Table 3]

[0064] (Example 3 of the present invention) In the third example of the present invention, the piezoelectric element had an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm. As shown in FIG. 13(A), four recesses were arranged at equal intervals on the circular outer peripheral surface, and the shape of the inner periphery was circular. The depth of each recess was 25 μm and the width was 50 μm. Electrodes A to D were arranged in this order in the four recesses on the outer peripheral surface of the piezoelectric element. The width of each electrode was 50 μm, and they were arranged from one end of the piezoelectric element to the other end in the axial longitudinal direction as shown in FIG. 13(B). A voltage was applied to electrodes A and C, and the potential of these electrodes was set to 410 V. Electrodes B and D were grounded, and the potential of these electrodes was set to 0 V. FIG. 15(B) shows electric field vectors generated in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of the third example of the present invention. Table 4 shows the distribution of electric field strength when the electric field strength generated in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Example 3 of the present invention is divided into 30 equal parts from the minimum to the maximum, and Figure 16 (B) shows a graph showing the area ratio for each electric field strength division.

[0065] [Table 4]

[0066] (Example 4 of the present invention) In the fourth example of the present invention, the piezoelectric element had an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm. As shown in FIG. 14(A), four recesses were arranged at equal intervals on the circular outer peripheral surface, and the shape of the inner periphery was circular. Each recess had a depth of 10 μm and a width of 150 μm. Electrodes A to D were arranged in this order in the four recesses on the outer peripheral surface of the piezoelectric element. Each electrode had a width of 150 μm, and was arranged from one end of the piezoelectric element to the other end in the axial direction as shown in FIG. 14(B). A voltage was applied to electrodes A and C, and the potential of these electrodes was set to 300 V. Electrodes B and D were grounded, and the potential of these electrodes was set to 0 V. FIG. 15(C) shows electric field vectors generated in the XY cross section at the center position in the length direction of the cylindrical piezoelectric element of the fourth example of the present invention. Table 5 shows the distribution of electric field strength when the electric field strength generated in the XY cross section at the center position in the longitudinal direction of the cylindrical piezoelectric element of Example 4 is divided into 30 equal parts from the minimum to the maximum. Fig. 16(C) shows a graph showing the area ratio for each electric field strength division.

[0067] [Table 5]

[0068] (result) In the present invention examples 2 to 4, it was found that the electric field was oriented in the direction of the arrow as shown in Fig. 15. Therefore, it was found that the piezoelectric elements of the present invention examples 2 to 4 could be polarized in the direction of the arrow.

[0069] In Example 2 of the present invention, as shown in Table 3 and FIG. 16(A), the area ratio of the region having an electric field strength of rank 11 was the largest, at 33.5%. In Example 3 of the present invention, as shown in Table 4 and FIG. 16(B), the area ratio of the region having an electric field strength of rank 13 was the largest, at 23.4%. In Example 4 of the present invention, as shown in Table 5 and FIG. 16(C), the area ratio of the region having an electric field strength of rank 14 was the largest, at 19.3%. Thus, it was found that even when the shape of the outer periphery of the piezoelectric element was changed, the electric field strength was more uniform and uniform polarization was possible.

[0070] [Example 3] In this example, the driving of the piezoelectric element according to the present invention was simulated. Fig. 17 is a plan view for explaining the structure of the piezoelectric element according to Example 8 of the present invention.

[0071] (Example 5 of the invention) In Invention Example 5, one end of the piezoelectric element of Invention Example 1 was fixed, and voltage was applied to electrodes A and C shown in Fig. 8(A) to set the potential of electrode A to 10 V and the potential of electrode C to -10 V. Electrodes B and D were grounded, and the potentials of these electrodes were set to 0 V. As a result, the other end of the piezoelectric element was displaced 462 nm between electrodes A and D (X-axis negative direction).

[0072] (Example 6) In Invention Example 6, one end of the piezoelectric element of Invention Example 2 was fixed, and voltage was applied to electrodes A and C shown in Fig. 12(A) to set the potential of electrode A to -10 V and the potential of electrode C to 10 V. Electrodes B and D were grounded, and the potentials of these electrodes were set to 0 V. As a result, the other end of the piezoelectric element was displaced 592 nm toward the space between electrodes A and D (X-axis negative direction).

[0073] (Example 7) In Invention Example 7, one end of the piezoelectric element of Invention Example 3 was fixed, and a voltage was applied to electrodes A and C shown in Fig. 13(A) to set the potential of electrode A and the potential of electrode C to 10 V. Electrodes B and D were grounded, and the potential of these electrodes was set to 0 V. As a result, the other end of the piezoelectric element was displaced 516 nm toward the space between electrodes A and D (X-axis negative direction).

[0074] (Example 8) In the eighth example of the present invention, the piezoelectric element has an outer dimension of 400 μm, an inner dimension of 200 μm, and a length of 5 mm. As shown in FIG. 17, a recess is arranged on every other face of the eight faces constituting the outer peripheral face of a regular octagon, for a total of four recesses. The shape of the inner circumference is circular. The shape of each recess is semicircular, the depth of the recess is 35 μm, and the width of the recess is 70 μm. Electrodes A to D are arranged in this order in these four recesses. Each of the electrodes A to D is arranged so as to fill the recess, and is arranged from one end of the piezoelectric body to the other end in the longitudinal direction. The potentials of the electrodes A and C are each set to 300 V, the electrodes B and D are grounded, and the potentials of these electrodes are set to 0 V, and the polarization process is performed. One end of this piezoelectric element was fixed, and a voltage was applied to electrodes A and C to set the potential of electrode A to -10 V and the potential of electrode C to 10 V. Electrodes B and D were grounded, and the potentials of these electrodes were set to 0 V. As a result, the other end of the piezoelectric element was displaced 650 nm toward the space between electrodes A and D (the negative direction of the X-axis).

[0075] As described above, it has been found that the piezoelectric element according to the present invention can be used as an actuator.

[0076] [Example 4] In this embodiment, the electric field generated when a voltage is applied to the electrodes of a cylindrical piezoelectric element in which the center of the outer circumference and the center of the inner circumference are shifted from each other in the XY cross section was investigated. Specifically, in the cylindrical piezoelectric element of the present invention example 1 and the cylindrical piezoelectric element of the comparative example 1, the electric field change was analyzed by the finite element method when the center of the inner circumference in the XY cross section is shifted from the center of the outer circumference by 5 μm, 7.5 μm, 10 μm, and 20 μm in the positive direction of the X axis, and when it is shifted by 5 μm, 7.5 μm, 10 μm, and 20 μm in the direction of 45 degrees from the positive direction of the X axis to the positive direction of the Y axis. In the cylindrical piezoelectric element of Example 1, an example in which the center of the inner circumference of the XY cross section is shifted in the positive direction of the X-axis relative to the center of the outer circumference is Example 9, and an example in which the center is shifted 45 degrees in the positive direction of the Y-axis relative to the positive direction of the X-axis is Example 10. In the cylindrical piezoelectric element of Comparative Example 1, an example in which the center of the inner circumference of the XY cross section is shifted in the positive direction of the X-axis relative to the center of the outer circumference was taken as Comparative Example 2, and an example in which the center is shifted 45 degrees in the positive direction of the Y-axis relative to the positive direction of the X-axis was taken as Comparative Example 3. The voltage was applied in the same manner as in invention example 1 and comparative example 1. That is, in invention examples 9 and 10, a voltage was applied to electrodes A and C, and the potential of these electrodes was set to 300V. Electrodes B and D were grounded, and the potential of these electrodes was set to 0V. In comparative examples 2 and 3, a voltage was applied to electrodes A to D, and the potential of these electrodes was set to 300V. Electrode E on the inner circumferential surface was grounded, and the potential of this electrode was set to 0V.

[0077] In the electric field generated in the XY plane at the center of the cylindrical piezoelectric element in the longitudinal direction, the minimum to maximum electric field strength was divided equally into 30 equal parts called ranks 1 to 30, and the area ratio of the region having an electric field strength of 10% was calculated around the rank showing the largest ratio. The results are shown in FIG. 18. FIG. 18 is a graph showing the relationship between the magnitude of deviation between the center of the outer circumference and the center of the inner circumference of the cylindrical piezoelectric element in the XY cross section and the uniformity of the electric field strength, with the vertical axis showing the area ratio (%) of the region where the electric field strength is within 10% of the total, based on the rank of electric field strength with the largest area ratio, and the horizontal axis showing the deviation (μm) of the center of the inner circumference from the center of the outer circumference in the XY cross section.

[0078] When the center of the inner circumferential surface was shifted laterally, the decrease in uniformity of the electric field strength due to the shift of the center of the inner circumferential surface was smaller in Example 9 of the present invention, and the uniformity of the electric field strength was maintained at a high level, compared to Comparative Example 2. Similarly, when the center of the inner circumferential surface was shifted diagonally, the decrease in uniformity of the electric field strength due to the shift of the center of the inner circumferential surface was smaller in Example 10 of the present invention, and the uniformity of the electric field strength was maintained at a high level, compared to Comparative Example 3. Therefore, even if the center of the outer peripheral surface and the center of the inner peripheral surface of the cylindrical piezoelectric element according to the present invention are misaligned due to an error during manufacturing, the effect on the polarization process is small, and the cylindrical piezoelectric element according to the present invention can be stably driven when used as an actuator. Therefore, even when the cylindrical piezoelectric elements according to the present invention are mass-produced, the performance variation between cylindrical piezoelectric elements is suppressed compared to conventional cylindrical piezoelectric elements. [Explanation of symbols]

[0079] 1. 1A cylindrical piezoelectric element 11, 11A Piezoelectric 12, 12A, 12B, 12C, 12D electrodes 13 Recess 111, 111A Outer surface (outer periphery) 112, 112A Inner surface (inner circumference)

Claims

1. A cylindrical piezoelectric body; a plurality of electrodes extending in a longitudinal direction on an outer peripheral surface of the piezoelectric body; The electrodes are not disposed on the inner peripheral surface of the piezoelectric body, The piezoelectric body has a cylindrical shape with an outer dimension of more than 200 μm and not more than 800 μm, The cylindrical piezoelectric element, wherein the piezoelectric body is a ceramic having piezoelectric properties.

2. 2. The cylindrical piezoelectric element according to claim 1, wherein a dimensional ratio d1 / d2, which is a ratio of an outer dimension d1 to an inner dimension d2 of the piezoelectric body, is 1.5 or more.

3. The cylindrical piezoelectric element according to claim 1 , wherein the number of the electrodes is three or more.

4. The cylindrical piezoelectric element according to claim 1 , wherein the number of the electrodes is two.

5. The outer peripheral surface of the piezoelectric body is provided with a plurality of recesses extending in the longitudinal direction of the piezoelectric body, The cylindrical piezoelectric element according to claim 1 , wherein the plurality of electrodes are disposed in at least one of the plurality of recesses.

6. The cylindrical piezoelectric element according to claim 1 , wherein the plurality of electrodes are arranged at approximately equal intervals in the circumferential direction.

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