円環状電気ひずみ磁器を円周方向に分極する際の電気力線分布と電界集中

概要

論文の詳細を見る
In the preceding paper, the authors showed the Bolt-clamped electrostrictive torsional vibrator for ultrasonic power applications (Fig. 1). The electrostrictive ceramics of the vibrator were polarized circumferentially in one body by dividing it into n portions (in Fig. 2, n=8) and by sequential polarization ; polarizing conditions of the ceramics, such as ratios of [electrodes gap]/[thickness of ceramics](which is 2a/2t in Fig. 3) or [width of electrode]/[thickness of ceramics](which is (e-a)/2t in Fig. 3), were chosen without any definite basis. In the present paper, the authors determined the electric lines of force and equipotential lines of inner portion of the ceramics by means of conformal mapping. Assuming a thin pipe within the ceramic, the authors expanded it (Fig. 3), and reduced the problem to a two-dimensional one as shown in Fig. 4, by neglecting the radial component of the electric field. Because they are symmetrical as to the GHG' line in Fig. 4, the authors considered only half of the ceramics(hatched portion in Fig. 4), and converted it into the half-infinite-plane as shown in Fig. 5 . The transformation function here used is eq. (1). This half-infinite-plane can be converted into the internal area of the rectangle shown in Fig. 6 by eq. (5), which is an elliptic-integral of the first kind, and the size of the rectangle is given by K and K' which are the complete-elliptic-integrals of the first kind. In Fig. 6, electric lines of force are horizotal, and equipotential lines are vertical, because two electrodes are in parallel. These lines are inversely transformed into the half-infinite-plane as shown in Fig. 5, by means of eq. (6) or eq. (7) which is Jacobi's elliptic function. Fig. 7 is an example of the chart showing the lines of electric force and equipotential lines. Fig. 8-11 show the group of charts showing the distribution of these lines within a ceramics. From these charts, the assumptions the authors adopted in the preceding paper are shown to be valid. The concentration of the electric field near the surface of ceramic is evaluated as shown in Fig. 12. In this figure, ratios of [maximum value of the mean potential gradient between the electrodes and the equipotential surface the potential of which is 19/20 of the voltage across the electrodes]/[mean electric field between electrodes given as (potential difference)/(electrodes gap)] are shown in the letters Z, Y, X or W which means 26 times, 25 times, 24 times or 23 times etc. For example, in the region we utilized to polarized ceramics (a/t=1. 5〜2. 0 and e/t=2. 0〜3. 0), the letters are shown in B or C, which means the ratio mentioned above is 2 or 3.
社団法人日本音響学会の論文
1973-07-01

円環状電気ひずみ磁器を円周方向に分極する際の電気力線分布と電界集中

スポンサーリンク

概要

著者

関連論文

スポンサーリンク