ǫǰǡǟVol. 2: )3125*Ą4:ġ57

࿲ൌळచɤાૺ༜ᆵཡ๝ക඲Ɉ࿹‫ູݷ‬౯Ʌ࠲ȳɥॸ࢞ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢ㈇Ⲵ≉ᛶ࡟㛵ࡍࡿ◊✲ᮧୖ ኳඖ*1㸪௒஭ ᗣ㈗*1㸪Ọ⏣ ಟ୍*1
A Study on Load Characteristics of Floating Type Pendulum Wave Energy Converter
Tengen MURAKAMI*1, Yasutaka IMAI*1 and Shuichi NAGATA*1*1

Institute of Ocean Energy, Saga University
1-48, Hirao, Kubara-aza, Yamashiro-cho, Imari-shi, Saga, 849-4256, JapanA floating type pendulum wave energy converter (FPWEC) with a rotary vane pump as the power take-off system
was proposed by Watabe et al. in 1998. They showed that this device had high energy conversion efficiency. In theprevious research, the authors conducted 2D wave tank tests in regular waves to evaluate the generating efficiency ofFPWEC with a power take-off system composed of pulleys, belts and a generator. As a result, the influence of theelectrical load on the generating efficiency was shown. Continuously, the load characteristics of FPWEC are pursued
experimentally by using the servo motors to change the damping coefficient in this paper. In a later part of this paper,the motions of the model with the servo motors are compared with that of the case with the same power take-off system
as the previous research. From the above experiment, it may be concluded that the maximum primary conversion
efficiency is achieved as high as 98% at the optimal load.
Key Words : Pendulum, Wave Energy Converter, Floating Type, Load Characteristics, Primary Conversion Efficiency

1. ⥴   ゝἼຊⓎ㟁ࢩࢫࢸ࣒(1)࡟࠾࠸࡚㸪᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡣ࢚ࢿࣝࢠ࣮ኚ᥮㐣⛬ࡀᑡ࡞ࡃ㸪Ⓨ㟁ຠ⋡ࡀ㧗࠸ࡇ࡜ࡀ♧ࡉࢀ࡚࠸ࡿ㸬Ώ㒊ࡽ(2)ࡣἢᓊᅛᐃᘧࡢ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࢆᥦ᱌ࡋ㸪ࡇࡢ⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࡣ᭱኱࡛ 82 %࡜࡞ࡿࡇ࡜ࢆ♧ࡋ㸪஧ḟኚ᥮⿦⨨࡜ࡋ࡚࣮ࣟࢱ࣮࣮࣏ࣜ࣋ࣥࣥࣉࢆ㛤Ⓨࡋ࡚࠸ࡿ㸬ࡇࡢ࣮ࣟࢱ࣮࣮࣏ࣜ࣋ࣥࣥࣉࡣ㸪ᅇ㌿ࢺࣝࢡࢆἜᅽ࡟ኚ᥮ࡍࡿ⿦⨨࡛࠶ࡾ㸪ࡇࡢ⿦⨨࡜Ⓨ㟁ᶵࢆ⤌ࡳྜࢃࡏ࡚⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪஧ḟኚ᥮ຠ⋡ࡀ 68㹼74 %࡜࡞ࡿࡇ࡜㸪࠾ࡼࡧⓎ㟁ຠ⋡ࡣ 40㹼60 %⛬ᗘ࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬୍᪉㸪ἢᓊᅛᐃᘧࡣᘓタࢥࢫࢺࡢ⣙ 70 %ࡀࢣ࣮ࢯࣥࢥࢫࢺ࡛࠶ࡿࡇ࡜ࡸᘓタሙᡤࡢไ⣙ࡀ࠶ࡿࡇ࡜࡞࡝ࡢ㞴Ⅼࡀ࠶ࡿ㸬ࡇࡢἢᓊᅛᐃᘧࡢ㞴ⅬࢆゎỴࡍࡿᡭἲ࡜ࡋ࡚㸪Ώ㒊(2)ࡣἈྜ࡟タ⨨ࡍࡿᾋయᆺ⿦⨨ࢆᥦ᱌ࡋ࡚㸪Ἴᾉ࢚ࢿࣝࢠ࣮࠿ࡽ᣺ࡾᏊࡢ྾཰࢚ࢿࣝࢠ࣮࡬ࡢኚ᥮ຠ⋡㸦୍ḟኚ᥮ຠ⋡㸧࡟㛵ࡍࡿணഛⓗ࡞ᐇ㦂ࢆ⾜ࡗ࡚࠸ࡿ㸬ᾋయᆺ⿦⨨ࡣ㸪Ἴ㧗ࡢ㧗࠸Ἀྜ࡟タ⨨ࡍࡿࡓࡵⓎ㟁㔞ࡢቑຍࡀぢ㎸ࡵࡿࡇ࡜㸪⿦⨨ࢆ㐀⯪ᡤ࡛▷ᮇ㛫࡟ᘓ㐀࡛ࡁࡿࡇ࡜࠿ࡽ㸪ึᮇࢥࢫࢺࢆ኱ࡁࡃపῶ࡛ࡁࡿࡇ࡜࡞࡝ࡢ฼Ⅼࡀ࠶ࡿ㸬ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨࡟㛵ࡋ࡚㸪ⴭ⪅ࡽ(3)ࡣ஧ḟኚ᥮⿦⨨࡜ࡋ࡚ࣉ࣮ࣜ࡜࣋ࣝࢺ࡟ࡼࡿቑ㏿ᶵᵓࢆ⏝࠸ࡓⓎ㟁ࣘࢽࢵࢺ㸪ࡲࡓ㸪ࡇࢀࢆᶍᨃࡋࡓࢲࣥࣆࣥࢢࢆẁ㝵ⓗ࡟ኚ໬ࡉࡏࡿࢺࣝࢡࢲࣥࣃ࣮ࡢ 2 ✀㢮ࢆྲྀࡾ௜ࡅࡓ
ᶍᆺࢆ⏝࠸ࡓỈᵴᐇ㦂ࢆ⾜࠸㸪Ⓨ㟁ຠ⋡ࡢ᭱኱್ 26 %࠾ࡼࡧ୍ḟኚ᥮ຠ⋡ࡢ᭱኱್ 80%ࢆᚓࡓ㸬㏆ᖺ㸪Park ࡽ(4)ࡶ㟁ື࣮ࣔࢱࢆᦚ㍕ࡋࡓ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࢆᐇ㦂ⓗ࡟ồࡵ࡚࠸ࡿࡀ㸪ᅇ㌿㏿ᗘ࡟ẚ౛ࡋࡓࢺࣝࢡࢲࣥࣆࣥࢢࡢ⢭ᗘࡀ୙༑ศ࡛࠶ࡿ㸬ࡲࡓ㸪Nam ࡽ(5)ࡣ㸪㧗ḟቃ⏺せ⣲ἲࢆ⏝࠸࡚つ๎Ἴ࠾ࡼࡧ୙つ๎Ἴ୰࡛ࡢ㸪ᾋయࡢࢧ࣮ࢪ㸪ࣄ࣮ࣈ࠾ࡼࡧࣆࢵࢳࡢ⦪㐠ືࢆィ⟬ࡋ㸪ᐇ㦂್࡜ẚ㍑ࡋ࡚࠸ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ࡇࡢィ⟬࡛ࡣ୍ḟኚ᥮ຠ⋡࡟㛵ࡍࡿィ⟬್࡜ᐇ㦂್ࡢẚ㍑ࡣ⾜ࢃࢀ࡚࠸࡞࠸㸬ᮏ◊✲࡛ࡣ㸪ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢⓎ㟁ຠ⋡ࢆࡉࡽ࡟㧗ࡵࡿࡓࡵ࡟㸪⿦⨨ࡢ࢚ࢿࣝࢠ࣮྾཰≉ᛶࡢྍ*ཎ✏ཷ௜ 2014 ᖺ 07 ᭶ 31 ᪥
బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮㸦ࠛ849-4256 ఀ୓㔛ᕷᒣ௦⏫ஂཎᏐᖹᑿ 1-48㸧
E-mail: murakami@ioes.saga-u.ac.jp

*14:

51

ഺ௫๏ই -!਱‫ۈ‬য়ࡦ -!‫܊‬๜ୌ‫ێ‬⬟ᛶࢆ᫂ࡽ࠿࡟ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡋ࡚࠸ࡿ㸬ලయⓗ࡟ࡣ㸪ᐇᶵࡢ㈇Ⲵ≉ᛶࢆᶍᨃࡍࡿࡇ࡜ࡀ࡛ࡁࡿࢧ࣮࣮࣎ࣔࢱ
ࢆ⿦ഛࡋࡓᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ᶍᆺࢆ〇సࡋ㸪஧ḟඖỈᵴᐇ㦂ࢆ⾜࠸㸪୍ḟኚ᥮ຠ⋡࠾ࡼࡧᾋయࡢ㐠ືࢆồࡵࡓ㸬ࡉࡽ࡟㸪ࣉ࣮ࣜ࡜࣋ࣝࢺ࡟ࡼࡿቑ㏿ᶵᵓࢆ᭷ࡍࡿ஧ḟኚ᥮⿦⨨ࢆᦚ㍕ࡋ࡚Ⓨ㟁ຠ⋡ࢆồࡵࡓ㸬
2. ᐇ㦂⿦⨨2࣭1 ౪ヨయᶍᆺᅗ 1 ࡣ౪ヨయᶍᆺࡢᴫ␎ᅗࢆ♧ࡍ㸬ᶍᆺࡣ㸪᣺ࡾᏊᯈ㸪Ỉᐊᗏ㠃㸪Ỉᐊഃ㠃㸪Ỉᐊᚋቨ㸪ῶᦂᯈ㸪ᾋຊయ㸪ࣂࣛࢫࢺ㸪ࢧ࣮࣮࣎ࣔࢱ࠾ࡼࡧ࢔࣑ࣝࣇ࣮࣒࡛ࣞᵓᡂࡉࢀ࡚࠸ࡿ㸬ᾋయࡢ඲㛗ࡣ 1340 mm ࡛࠶ࡾ㸪඲㛗ࡢἼୖഃ
1/2 ࢆ᣺ࡾᏊỈᐊ㸪Ἴୗഃࢆ㐟Ỉ㒊࡜ࡋ㸪ῶᦂᯈࡣỈᐊᚋቨ࠿ࡽ 665 mm ࡢ఩⨨࡟タ⨨ࡋ㸪ධᑕἼࢆࢫ࣒࣮ࢬ࡟᣺ࡾᏊỈᐊ࡟ᑟࡃࡓࡵ㸪᣺ࡾᏊỈᐊࡢࡳࢆἼୖഃ࡟ 5 mm ᘏ㛗ࡋࡓࠋᾋయࡢႚỈ d ࡣ 216 mm ࡛࠶ࡿ㸬ࡲࡓ㸪ᅗ 2࡟♧ࡍࡼ࠺࡟᣺ࡾᏊᯈ୰ኸ㒊࠿ࡽἼୗഃ 40 mm ࡢ఩⨨࡜Ỉᐊᚋቨ୰ኸ㒊࠿ࡽἼୖഃ 40 mm ࡢ఩⨨ࡢ 2 ⟠ᡤ࡟Ἴ㧗ィࢆタ⨨ࡋࡓ㸬2࣭2 ᐇ㦂⿦⨨㓄⨨
ᅗ 3 ࡣ஧ḟඖỈᵴෆ࡟࠾ࡅࡿ౪ヨయᶍᆺ㸪Ἴ㧗ィ➼ࡢ㓄⨨ᅗࢆ♧ࡍ㸬Ỉᵴࡢ୧➃࡟ࡣ྾཰ᘧࡢ㐀Ἴ⿦⨨ࡀタ⨨ࡋ࡚࠶ࡾ㸪㏱㐣ഃࡢ㐀ἼᶵࡣἼࡢ྾཰ࡢࡳ࡟⏝࠸ࡓ㸬Ἴࡣᅗࡢྑഃ࠿ࡽᕥഃ࡟㐍⾜ࡍࡿ㸬Ỉᵴࡢ඲㛗ࡣ 18.5 m㸪
Ỉ῝ࡣ 1.0 m ࡛࠶ࡿࠋᶍᆺࡣ㸪Ỉᵴ୰ኸ㒊࡟⦆ಀ␃ࡉࢀ࡚࠾ࡾ㸪Ἴୖഃಀ␃⣴ࡢඛ࡟ࡣ᳨ຊィࡀタ⨨ࡋ࡚࠶ࡿ㸬ࡲࡓ㸪ᶍᆺࢆᖹ⾮≧ែ࡟ಖࡘࡓࡵ࡟㸪Ἴୗഃࡣࢼ࢖ࣟࣥ⣒ࢆ⏝࠸࡚ึᮇᙇຊ 1 N ࡛ᘬࡗᙇࡗࡓ㸬࡞࠾㸪᣺ࡾᏊᯈࡣ㸪ᅗ 4 ࡟♧ࡍࡼ࠺࡟Ỉᐊᚋቨ࠿ࡽ P = 0.650 m ࡢ఩⨨ࢆᇶ‽࡜ࡋ㸪P = 0.490 m ࠾ࡼࡧ P = 0.325 m ࡢ఩⨨࡟ኚ᭦ࡋ࡚ᐇ㦂ࢆ⾜ࡗࡓ㸬ィ ⠊ᅖࡣ㸪Ἴ㛗OࢆỈᐊ㛗ࡉ L ࡛㝖ࡋࡓ್ࡀ 0.6㹼7.0 ࡢ⠊ᅖ࡜ࡋ㸪ධᑕἼࡣἼ㧗 0.015 m ࡢつ๎Ἴ࡛࠶ࡿ㸬ᾋయືᦂࡣ MVTec ♫〇⏬ീゎᯒࣉࣟࢢ࣒ࣛ HALCON ࡟ࡼࡾィ ࡋࡓ㸬Ballast

Wave height gauge

Servo motor

Fig. 1 Experimental model with servo motors

Fig. 2 Configuration of wave height gauges

Fig. 3 Experimental equipment configuration in wave tank52࿲ൌळచɤાૺ༜ᆵཡ๝ക඲Ɉ࿹‫ູݷ‬౯Ʌ࠲ȳɥॸ࢞

160.5

30.5

300
TorqueTorque-3-0.5
40

4100

Rotational speed
424344

N rpm

6Q Nm

1N rpmQ NmFig. 4 Location of pendulum

Rotational speed-3-0.54041

42t sec.

t sec.

(a) Motor a(b) Motor b

4344Fig. 5 Torque and rotational speed of pendulum shaft

3. ୍ḟኚ᥮ᐇ㦂⤖ᯝ3࣭1 ୍ḟኚ᥮ຠ⋡ᅗ 5 ࡣᐇ㦂࡛ᚓࡽࢀࡓ᣺ࡾᏊ㍈ࡢࢺࣝࢡ Q ࠾ࡼࡧᅇ㌿㏿ᗘ N ࡢ᫬㛫ኚ໬ࢆ♧ࡋ㸪㸦a㸧࠾ࡼࡧ㸦b㸧ࡣࡑࢀࡒࢀ
᣺ࡾᏊ㍈୧➃࡟タ⨨ࡋࡓࢧ࣮࣮࣎ࣔࢱࢆ⾲ࡍ㸬ᮏᐇ㦂࡛ࡣ㸪᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘࢆ 1 msec.ẖ࡟ィ ࡋ㸪ῶ⾶ಀᩘ
CP㸦= Q/Z㸸Nm࣭s/rad.㸪Z㸸ゅ㏿ᗘ㸧ࡀ᪤ᐃ್࡜࡞ࡿࡼ࠺࡟ࢺࣝࢡไᚚࢆ⾜ࡗࡓ㸬ධᑕἼ࢚ࢿࣝࢠ࣮Ein㸪ྲྀᚓ࢚ࢿࣝࢠ࣮Eout ࠾ࡼࡧ୍ḟኚ᥮ຠ⋡K1 ࡣ㸪௨ୗࡢᘧ㸦1㸧㸪ᘧ㸦2㸧࠾ࡼࡧᘧ㸦3㸧࡛୚࠼ࡽࢀࡿ㸬

S2

Ein

2kh ·§H·§B ¨ ¸ U g ¨1 ¸                               㸦1㸧
2kT © 2 ¹
© sinh 2kh ¹

Eout

1 T
Pout (t )dt                                      㸦2㸧
T ³0K1

Eout / Ein                                       㸦3㸧ࡇࡇ࡛㸪B㸦= 0.735 m㸧ࡣ᣺ࡾᏊᯈᖜ㸪H ࡣධᑕἼἼ㧗㸪T ࡣἼ࿘ᮇ㸪k ࡣἼᩘ㸪Uࡣᐦᗘ㸪g ࡣ㔜ຊຍ㏿ᗘ㸪hࡣỈ῝㸪Pout㸦= QZ㸧ࡣฟຊࢆ⾲ࡍ㸬
ᅗ 6 ࠾ࡼࡧᅗ 7 ࡣ୍ḟኚ᥮ຠ⋡ࢆ♧ࡋ㸪ᅗ 6 ࡣἼ㛗O/L ࡟ࡼࡿኚ໬㸪ᅗ 7 ࡣῶ⾶ಀᩘ CP ࡟ࡼࡿኚ໬ࢆ♧ࡍ㸬ࡲࡓ㸪
㸦a㸧ࡣ᣺ࡾᏊᯈ఩⨨ P = 0.650 m ࡢሙྜ㸪㸦b㸧ࡣ P = 0.490 m ࡢሙྜ㸪㸦c㸧ࡣ P = 0.325 m ࡢሙྜࢆ♧ࡍ㸬ᅗ 7࡟࠾࠸࡚᣺ࡾᏊᯈ఩⨨ P ࠾ࡼࡧO/L ࡟ࡼࡽࡎ CP ࡀ 1.8 Nm࣭s/rad.࠿ࡽ 5.2 Nm࣭s/rad.࡬ቑຍࡍࡿ࡟ࡘࢀ୍࡚ḟኚ᥮ຠ⋡ࡣ༢ㄪቑຍࡋࡓ㸬P = 0.650 m ࡢሙྜ㸪ῶ⾶ಀᩘ CP = 6.0 Nm࣭s/rad.࠾ࡼࡧO/L = 1.5 ࡟࠾࠸୍࡚ḟኚ᥮ຠ⋡ࡢ
᭱኱್ 0.98 ࡀᚓࡽࢀࡓ㸬ࡲࡓ㸪P = 0.490 m ࡢሙྜࡣ㸪CP = 5.2 Nm࣭s/rad.࠾ࡼࡧO/L = 3.0 ࡟࠾࠸࡚᭱኱ࡢ୍ḟኚ᥮ຠ⋡ 0.91 ࡀᚓࡽࢀ㸪P = 0.325 m ࡢሙྜࡣ㸪CP = 5.2 Nm࣭s/rad.࠾ࡼࡧO/L = 2.5 ࡟࠾࠸࡚᭱኱ࡢ୍ḟኚ᥮ຠ⋡ 0.90ࡀᚓࡽࢀࡓ㸬
3࣭2 ỈᐊෆỈ఩
ᅗ 8 ࡣỈᐊෆỈ఩ࡢ᫬㛫ኚ໬ࢆ♧ࡋ㸪]1 ࡣ᣺ࡾᏊᯈ࠿ࡽ 40 mm ἼୗഃࡢỈ఩㸪]2 ࡣᚋቨ࠿ࡽ 40 mm ἼୖഃࡢỈ఩ࢆ⾲ࡋ㸪ࡑࢀࡒࢀධᑕἼ᣺ᖜ]i ࡛↓ḟඖ໬ࡋࡓ㸬ᅗ 8㸦a㸧ࡢ P = 0.650 m ࡢሙྜ㸪O/L = 1.5 ࡟࠾ࡅࡿ]1 ࡢ᣺ᖜ53ഺ௫๏ই -!਱‫ۈ‬য়ࡦ -!‫܊‬๜ୌ‫ێ‬

1

1C = 1.8 Nm䞉s/rad.
P

C = 3.5 Nm䞉s/rad.

0.80.8P

O/L = 0.6
O/L = 1.0
O/L = 1.5O/L = 2.0
O/L = 2.5
O/L = 3.0
O/L = 3.5O/L = 4.0
O/L = 5.0
O/L = 6.0
O/L = 7.0

C = 5.2 Nm䞉s/rad.
P

C = 6.0 Nm䞉s/rad.
P

0.6

0.6

K1

P

C = 7.4 Nm䞉s/rad.
PK1

C = 6.7 Nm䞉s/rad.

0.4

0.4

0.2

0.2

0002

4

6803O/L6912

C Nm䞉s/rad.
P(a) P = 0.650 m(a) P = 0.650 m
11
C = 1.8 Nm䞉s/rad.
P

C = 3.5 Nm䞉s/rad.

0.80.8PO/L = 0.6
O/L = 1.0
O/L = 1.5
O/L = 2.0
O/L = 2.5
O/L = 3.0
O/L = 3.5O/L = 4.0
O/L = 5.0
O/L = 6.0
O/L = 7.0

C = 5.2 Nm䞉s/rad.
P

C = 6.0 Nm䞉s/rad.
P

0.6

0.6K1PC = 7.4 Nm䞉s/rad.
PK1

C = 6.7 Nm䞉s/rad.

0.4

0.4

0.2

0.2

000246803O/L(b) P = 0.490 m

6912C Nm䞉s/rad.
P(b) P = 0.490 m
11
C = 1.8 Nm䞉s/rad.
P

C = 3.5 Nm䞉s/rad.

0.80.8P

O/L = 0.6
O/L = 1.0
O/L = 1.5
O/L = 2.0
O/L = 2.5
O/L = 3.0
O/L = 3.5
O/L = 4.0
O/L = 5.0
O/L = 6.0
O/L = 7.0

C = 5.2 Nm䞉s/rad.
P

C = 6.0 Nm䞉s/rad.
P

0.6

0.6

K1

P

C = 7.4 Nm䞉s/rad.
PK1

C = 6.7 Nm䞉s/rad.

0.4

0.4

0.2

0.2

0002468

O/L(c) P = 0.325 m
Fig. 6 Changes in primary conversion efficiency dueto wave length036912C Nm䞉s/rad.
P(c) P = 0.325 m
Fig. 7 Changes in primary conversion efficiency dueto damping coefficientࡀO/L = 2.0 ࡢሙྜ࡜ẚ࡭࡚ᴟࡵ࡚ᑠࡉࡃ࡞ࡗ࡚࠸ࡿ㸬ࡇࡢࡇ࡜࠿ࡽ㸪O/L = 1.5 ࡛ࡣ Second mode ࡢᐃᅾἼ㸪ࡍ࡞
ࢃࡕᅗ 9㸦b㸧࡟♧ࡍࡼ࠺࡟Ἴ㛗ࡀ P = 0.650 m ࡢ 4/3 ಸࡢἼࡢ⠇㒊࡜᣺ࡾᏊᯈ఩⨨ࡀ࡯ࡰ୍⮴ࡋ࡚࠸ࡿࡶࡢ࡜᥎
࡛ࡁ㸪ࡇࡢࡇ࡜ࡀᴟࡵ࡚㧗࠸୍ḟኚ᥮ຠ⋡ࢆᚓࡽࢀࡿせᅉ࡛࠶ࡿ㸬୍᪉㸪O/L = 2.0 ࡛ࡣ᣺ࡾᏊᯈ఩⨨࡟ᐃᅾἼࡢ
⭡㒊ࡀ࠶ࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪P = 0.650 m ࡢሙྜ㸪O/L = 3.5 ࡟࠾࠸࡚ࡶ]1 ࡢ᣺ᖜࡣᑠࡉ࠸㸬ࡇࢀࡣᚋ㏙ࡢ
First mode ࡢᐃᅾἼࡢⓎ⏕ࢆព࿡ࡋ࡚࠸ࡿ㸬ᅗ 8㸦b㸧ࡢ P = 0.490 m ࡢሙྜࡣO/L = 3.0㸪㸦c㸧ࡢ P = 0.325 m ࡢሙྜ
ࡣO/L = 2.5 ࡟࠾࠸࡚]1 ࡢ᣺ᖜࡣᑠࡉ࠸㸬ࡇࢀࡣ First mode ࡢᐃᅾἼ㸪ࡍ࡞ࢃࡕᅗ 9㸦a㸧࡟♧ࡍࡼ࠺࡟᣺ࡾᏊᯈ࡜ᚋቨ࡜ࡢ㊥㞳 P ࡢ 4 ಸࡢἼ㛗ࡢἼࡢ⠇㒊࡜᣺ࡾᏊᯈ఩⨨ࡀ୍⮴ࡋ࡚࠸ࡿࡇ࡜ࢆព࿡ࡋ࡚࠾ࡾ㸪ࡇࢀࡀ㧗࠸ຠ⋡ࢆᚓࡽࢀࡿせᅉ࡛࠶ࡿ㸬ࡲࡓ㸪᣺ࡾᏊᯈ఩⨨ P = 0.650 m ࡀ 0.490 m ࠾ࡼࡧ 0.325 m ࡬࡜ᚋቨ࡟㏆࡙ࡃ࡟ࡘࢀ࡚㸪First54࿲ൌळచɤાૺ༜ᆵཡ๝ക඲Ɉ࿹‫ູݷ‬౯Ʌ࠲ȳɥॸ࢞44]1/]i0-2]2/]-440424446

i0-2i]2/]-44850404244t sec.

O/L = 1.548504024042]1/]

48] /]i

04446485040]1/]i4850]1/]

20-2

4648

50

4850O/L = 2.5]2/]

ii0-2]2/]i-444464i-44244t sec.

] /]i] /]i]2/]
4042O/L = 3.02-2i04050-442O/L = 2.0]1/]i]2/]

it sec.

448-2]2/]i4050]1/]2-44646O/L = 1.0

it sec.

244t sec.

-2i444242] /]i] /]ii] /]-4] /]i

46O/L = 1.50-2]2/]i-44]1/]0-2iit sec.

42]1/]

2] /]i2] /]i] /]i24]1/]-440424446485040424446t sec.

t sec.

t sec.

O/L = 3.5O/L = 3.5O/L = 3.0(a) P = 0.650 m, CP = 6.0 Nm࣭s/rad.

(b) P = 0.490 m, CP = 5.2 Nm࣭s/rad.

(c) P = 0.325 m, CP = 5.2 Nm࣭s/rad.

Fig. 8 Water displacement in water chamber

Back wall

Back wall(b) Second mode(a) First mode
Fig. 9 Standing waves in water chambermode ࡢᐃᅾἼࡀⓎ⏕ࡍࡿἼ㛗O/L ࡣ 3.5㸪3.0㸪2.5 ࡜ῶᑡࡋ࡚࠾ࡾ㸪ྠᵝ࡟ Second mode ࡀⓎ⏕ࡍࡿἼ㛗O/L ࡶ᣺ࡾᏊᯈ࡜ᚋቨ࡜ࡢ㊥㞳 P ࡢῶᑡ࡟కࡗ࡚ᑠࡉࡃ࡞ࡿ㸬3࣭3 ᾋయࡢືᦂ
ᅗ 10 ࡣࢧ࣮ࢪ᪉ྥ᣺ᖜ X/]i㸪ࣄ࣮ࣈ᪉ྥ᣺ᖜ Z/]i ࠾ࡼࡧࣆࢵࢳ᪉ྥ᣺ᖜ4/k]i ࢆ♧ࡋ㸪㸦a㸧ࡀ First mode ࡢሙྜ㸪㸦b㸧ࡀ Second mode ࡢሙྜࢆ♧ࡍ㸬ᅗ 10㸦b㸧ࡢ Second mode ࡢሙྜ㸪ᾋయࡢືᦂࡣṤ࡝ぢࡽࢀ࡞࠿ࡗࡓ㸬୍᪉㸪ᅗ 10㸦a㸧ࡢ First mode ࡢሙྜ㸪ᾋయࡢືᦂࡣ᣺ࡾᏊᯈ఩⨨ P ࡟࠿࠿ࢃࡽࡎ Second mode ࡢሙྜࡼࡾ㢧ⴭ࡟࡞ࡗࡓ㸬ࡲࡓ㸪First mode ࡢሙྜ㸪CP ࡢቑຍ࡟కࡗ࡚ᾋయࡢືᦂࡣపῶࡉࢀ㸪᣺ࡾᏊᯈ఩⨨ P = 0.325 m ࡢሙྜ࡟᭱ࡶືᦂࡣᑠࡉࡃ࡞ࡗࡓ㸬ࡇࢀࡣ㸪P = 0.325 m ࡢሙྜ࡟࠾࠸࡚ᾋయࡢືᦂ࡟㉳ᅉࡍࡿ ࡢⓎ⏕ࢆ᭱ࡶᢚไ࡛ࡁࡿࡇ࡜ࢆព࿡ࡋ࡚࠸ࡿ㸬
4. Ⓨ㟁ᐇ㦂⤖ᯝ4࣭1 Ⓨ㟁ᐇ㦂⿦⨨

55ഺ௫๏ই -!਱‫ۈ‬য়ࡦ -!‫܊‬๜ୌ‫ێ‬22
P = 0.650 m (O/L = 3.5)
P = 0.490 m (O/L = 3.0)
P = 0.325 m (O/L = 2.5)

1i0.5

10.500036

9120C Nm䞉s/rad.

2

P
P = 0.650 m
P = 0.490 m

36

P = 0.325 m

912C Nm䞉s/rad.

2

P

P = 0.650 m (O/L = 1.5)

Z/]

Z/]

i1.5i1.510.5

10.5000369120C Nm䞉s/rad.
P

P = 0.650 m (O/L = 3.5)
P = 0.490 m (O/L = 3.0)
P = 0.325 m (O/L = 2.5)

16912C Nm䞉s/rad.
P

P = 0.650 m (O/L = 1.5)

1.5
i

i

1.5

324/k]

24/k]

P = 0.650 m (O/L = 1.5)

1.5

X/]

X/]

i

1.5

0.5
0

1
0.5
003

6

9120

36C Nm䞉s/rad.

912C Nm䞉s/rad.

PP(b) Second mode(a) First mode
Fig. 10 Motion amplitude of floating body஧ḟኚ᥮⿦⨨ࡢዲ㐺໬ࡀ୙༑ศ࡛ࡣ࠶ࡿࡀ㸪ᅗ 11 ࡟♧ࡍ࣋ࣝࢺ࡜ࣉ࣮ࣜ࡟ࡼࡿቑ㏿ᶵᵓࢆ᭷ࡍࡿࣃ࣮࣡ࢸ࢖ࢡ
࢜ࣇࢩࢫࢸ࣒ࢆᾋయ࡟ᦚ㍕ࡋ࡚Ⓨ㟁ᐇ㦂ࢆ⾜ࡗࡓ㸬᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘࡣ࣋ࣝࢺ࡜ࣉ࣮ࣜ࡟ࡼࡗ࡚ 28.8 ಸ࡟ቑ㏿ࡉࢀࡿ㸬Ⓨ㟁ᶵ࡟ࡣ㸪SKY-denshi ♫〇 SKY-HR㸦600 rpm㸪ฟຊ 36W㸧ࢆ⏝࠸ࡓ㸬ࡲࡓ㸪ᩚὶჾ㸦Shindengen ♫〇S10VTA60㸧ࢆ⏝࠸࡚Ⓨ㟁ᶵ࠿ࡽࡢ஺ὶฟຊࢆ඲Ἴᩚὶࡋ㸪ࡑࡢᚋࢭ࣓ࣥࢺ᢬ᢠࢆ⏝࠸࡚⇕࢚ࢿࣝࢠ࣮࡟ኚ᥮ࡋࡓ㸬ᮏⓎ㟁ᐇ㦂࡛ࡣ㸪᣺ࡾᏊᯈ఩⨨ࢆ P = 0.650 m ࡜ࡋ࡚㸪᢬ᢠ R ࢆ 50:㸪100:㸪200:㸪300:࠾ࡼࡧ 400:࡟ኚ᭦ࡋࡓ㸬Ⓨ㟁ᶵฟຊ Pout ࡣᘧ㸦4㸧࡛୚࠼ࡽࢀࡿ㸬

Pout      

V2 / R

㸦4㸧ࡇࡇ࡛ V ࡣ㉳㟁ᅽࢆ⾲ࡍ㸬4࣭2 Ⓨ㟁ຠ⋡ᅗ 12 ࠾ࡼࡧᅗ 13 ࡣⓎ㟁ຠ⋡ࢆ♧ࡋ㸪ᅗ 12 ࡣἼ㛗OL ࡟ࡼࡿኚ໬㸪ᅗ 13 ࡣ᢬ᢠ R ࡟ࡼࡿኚ໬ࢆ♧ࡍ㸬ᅗ 12 ࡟♧ࡍⓎ㟁ຠ⋡ࡣ㸪ᅗ 6㸦a㸧ࡢ୍ḟኚ᥮ຠ⋡࡜ẚ࡭࡚ᴟ➃࡟ᑠࡉࡃ࡞ࡗ࡚ࡣ࠸ࡿࡀ㸪ຠ⋡ࡢࣆ࣮ࢡࡣ࡯ࡰྠࡌἼ㛗OL ࡛⾲ࢀࡓ㸬ࡲࡓ㸪ᅗ 13 ࡟♧ࡍࡼ࠺࡟᢬ᢠ R = 300 :ࡢሙྜ࡟᭱ࡶ㧗࠸Ⓨ㟁ຠ⋡ࡀᚓࡽࢀࡓ㸬
Generator

4࣭3 ᾋయ࠾ࡼࡧ᣺ࡾᏊᯈࡢ㐠ືḟ࡟㸪
ᅗ 14 ࡣࢧ࣮࣮࣎ࣔࢱ࠾ࡼࡧⓎ㟁ᶵࢆᦚ㍕ࡋࡓᶍᆺヨ㦂࡟࠾࠸࡚㸪ࡑࢀࡒࢀ㧗ຠ⋡ࡀᚓࡽࢀࡓሙྜࡢᾋయࡢ㐠ືࢆẚ㍑
ࡋ࡚࠸ࡿ㸬ᅗ 14 ࠿ࡽศ࠿ࡿࡼ࠺࡟㸪ࢧ࣮ࢪ㸪ࣄ࣮ࣈ࠾ࡼࡧࣆࢵࢳࡢ࠸ࡎࢀ࡟࠾࠸࡚ࡶᾋయࡢ㐠ື࡟㢧ⴭ࡞㐪࠸ࡣぢࡽࢀ࡞࠿ࡗࡓ㸬ࡉࡽ࡟㸪ᅗ 15 ࡣ First mode ࡀⓎ⏕ࡍࡿO/L = 3.5 ࠾ࡼࡧ Secondmode ࡀⓎ⏕ࡍࡿO/L = 1.5 ࡟࠾ࡅࡿ᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘ N ࢆ♧ࡋ㸪㸦a㸧ࡀࢧ࣮࣮࣎ࣔࢱࡢሙྜ㸪㸦b㸧ࡀⓎ㟁ᶵࡢሙྜࢆ♧ࡍ㸬

Fig. 11 Power take-off system᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘ N ࡣἼ 1 ࿘ᮇศࢆᖹᆒࡋࡓ᫬㛫ᖹᆒ್࡛࠶

56࿲ൌळచɤાૺ༜ᆵཡ๝ക඲Ɉ࿹‫ູݷ‬౯Ʌ࠲ȳɥॸ࢞

0.4

0.4

R = 50 :R = 100 :0.3

R = 400 :KK

0.3

R = 200 :R = 300 :

0.2

0.1

2468O/L
Fig. 12 Changes in generating efficiency due towave length

0200

300

4005002.5

Servo motor (C = 6.0 Nm䞉s/rad. )N rpm

P2Generator (R = 300 :)

iX/]

100

R:
Fig. 13 Changes in generating efficiency due to electric
resistor

31O/L = 1.5
O/L = 3.5

2
1.5
1
0.5

002

4

6082O/L

36810P(a) Servo motor

P

Generator (R = 300 :)i4C Nm䞉s/rad.

Servo motor (C = 6.0 Nm䞉s/rad. )

2Z/]

0.200

2.5

002

4

68O/L

6N rpm1Servo motor (C = 6.0 Nm䞉s/rad. )iO/L = 3.5
O/L = 4.0
O/L = 5.0
O/L = 6.0
O/L = 7.0

0.104/k]O/L = 0.6O/L = 1.0
O/L = 1.5
O/L = 2.0
O/L = 2.5
O/L = 3.0

1.5
10.5

P4O/L = 1.5
O/L = 3.5

2Generator (R = 300 :)

0100

200

300

400

500

R:(b) Generator

2002468Fig. 15 Rotational speed of pendulum shaft in firstand second modes

O/LFig. 14 Comparison between servo motor andgenerator on motion amplitudeࡿ㸬᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘ N ࡣ㸪ῶ⾶ಀᩘ CP ࠾ࡼࡧ᢬ᢠ R ࡢቑຍ࡟కࡗ࡚ῶᑡࡋࡓ㸬ࡲࡓ㸪᭱኱ࡢ୍ḟኚ᥮ຠ⋡ࡀᚓࡽࢀࡓῶ⾶ಀᩘ CP = 6.0 Nm࣭s/rad.࠾ࡼࡧ᭱኱ࡢⓎ㟁ຠ⋡ࡀᚓࡽࢀࡓ᢬ᢠ R = 300 :࡟࠾ࡅࡿ᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘࡣ࠸ࡎࢀࡶ⣙ 1.2 rpm ࡛࠶ࡗࡓ㸬௒ᚋ㸪᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘࡀ⣙ 1.2 rpm ࡜ప㏿࡛࠶ࡗ࡚ࡶ㧗ຠ⋡ࡀᚓࡽࢀࡿࡼ࠺஧ḟኚ᥮⿦⨨ࢆᨵⰋࡍࡿணᐃ࡛࠶ࡿ㸬
5. ⤖   ゝᮏ◊✲ࡣ㸪ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢつ๎Ἴ୰࡟࠾ࡅࡿ㈇Ⲵ≉ᛶࢆ㏣✲ࡋ㸪௨ୗࡢࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓ㸬1.

Ỉᐊෆ࡟ Second mode ࡢᐃᅾἼࡀⓎ⏕ࡋࡓ࡜ࡁ࡟᭱኱ࡢ୍ḟኚ᥮ຠ⋡ 98 %ࡀᚓࡽࢀࡓ㸬

2.

First mode Ⓨ⏕᫬࡛࠶ࡗ࡚ࡶ㧗࠸୍ḟኚ᥮ຠ⋡ 91 %ࡀᚓࡽࢀࡓ㸬

3.

First mode Ⓨ⏕᫬㸪ᾋయࡢືᦂࡣῶ⾶ಀᩘࡢቑຍ࡟కࡗ࡚ῶᑡࡍࡿ㸬4.

㧗ຠ⋡ࡀᚓࡽࢀࡿ࡜ࡁࡢ᣺ࡾᏊ㍈ᅇ㌿㏿ᗘࡣ⣙ 1.2 rpm ࡛࠶ࡗࡓ㸬ᩥ   ⊩57ഺ௫๏ই -!਱‫ۈ‬য়ࡦ -!‫܊‬๜ୌ‫ێ‬(1) Ώ㒊ᐩ἞㸪͆ᐇ⏝໬࡟ྥ࠿࠺ἼຊⓎ㟁͇㸪ࣃ࣮࣡♫(2009)㸬
(2) Watabe, T., “Utilization of the Ocean Wave Energy͇
㸪Fuji Print Press(2008)㸬
(3) ㇏⏣࿴㝯㸪Ọ⏣ಟ୍㸪௒஭ᗣ㈗㸪℩ᡞཱྀಇ᫂㸪ᑠ㔝ᆂ௓㸪͆ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢ◊✲㸦➨୍ሗ㸧-つ๎Ἴ୰Ⓨ㟁≉ᛶヨ㦂-͇㸪᪥ᮏ⯪⯧ᾏὒᕤᏛ఍ㄽᩥ㞟㸪Vol.13, (2010), pp. 67-74.
(4) Park, J. Y.㸪Shin, S. H.㸪Hong, K. Y. and Kim, S. H., “A Study on the Wave Response and Efficiency of a Pendulum Wave
Energy Converter͇㸪Proceedings of the Twenty-second International Offshore and Polar Engineering Conference㸪(2012), pp.
601-606.
(5) Nam, B. W.㸪Hong, S. Y.㸪Shin, S. H., “A Study on Wave-induced Motion of Floating Pendulum Wave Energy Converter͇㸪
Asian Wave and Tidal Conference Series㸪(2012), pp. 124-128.

