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ឡ⥲◊࣭◊✲ሗ࿌
愛総研・研究報告
➨ 16 号　2014
ྕ 2014 年
ᖺ
第
49
⩚ࡤࡓࡁ㣕⾜ᶵࡢ⩚ࡤࡓࡁ᫬ࡢὶయຊィ Measurement of aerodynamic forces for flapping Micro air vehicle
໭ᕝ୍ᩗ͊㸪㔝ᮧ㐩ஓ͊͊㸪㫽ᒃ♸ኴ͊͊
Kazutaka Kitagawa͊, Tatsuya Nomura͊͊, Yuuta Torii͊͊
Abstract
Unmanned micro aerial vehicles(UMAV) have carried out unmanned missions the natural disaster
and a forest fire on airborne survey, and direct sowing on farmland. Development of automatic and radio
controlled pilot flight system of MAV have focused on an aerodynamic behavior of low Reynolds number effect
for biofluid in unsteady regime. The motivation of present study is to design the beetle-like flapping micro air
vehicle for disaster investigating and planetary exploring. To explain the outline of flapping mechanism, the
results of the visualization of the flap motion and the experiment on little aerodynamic force measurement using
the cantilever system.
1㸬⥴ゝ
࢔ࢫ࣌ࢡࢺẚࡣ⩼ᖜࡢ஧஌࡜୧⩼㠃✚ࡢၟ㸪⩼㠃Ⲵ㔜ࡣ༢
ࢺࣥ࣎㸪⼖㸪ࣁࢳࢻࣜࡸ࢝ࣈࢺ࣒ࢩࢆᶍೌࡋࡓ⩚ࡤࡓࡁ
఩⩼㠃✚ᙜࡓࡾࡢⲴ㔜࡛࠶ࡿ㸬ヨసᶵࡢ࢔ࢫ࣌ࢡࢺẚࡣ࡯
㣕⾜ᶵࡢ◊✲㛤Ⓨࡣ࢜ࣛࣥࢲ㸪⡿ᅜ㸪᪥ᮏࢆࡣࡌࡵ┒ࢇ࡟
ࡰྠࡌ⩚ࡤࡓࡁ࿘Ἴᩘࡢ⼖࡟ᑐࡋ࡚኱ࡁࡃ࡞ࡿ㸬㉁㔞ࡣᶵ
⾜ࢃࢀ࡚࠸ࡿ㸬
య඲యࡢ㉁㔞࡛࠶ࡾ㸪࢝ࢼࣈࣥ࡟㏆࠸⩼㠃Ⲵ㔜࡟㏆࡙ࡅࡿ
≉࡟㸪⏥⹸ࡣ⬗య㒊ࡢᐜ✚ࡀ௚᪻⹸࡜ẚࡋ࡚኱ࡁࡃ㸪ྛ
✀ᶵჾࡢᦚ㍕࡟᭷฼࡜࡞ࡿሙྜࡀ࠶ࡿ㸬ᮏ◊✲ᐊ࡟᪊࠸࡚㸪
ᖺ࠿ࡽࢥ࢞ࢿ࣒ࢩ⛉⏥⹸ࡢࢻ࢘࢞ࢿ࡜࢝ࢼࣈࣥࡢ⩚ࡤ
ࡓࡁ㣕⾜࡟ࡘ࠸࡚㸪ὶࢀሙࡸὶయຊィ ࢆ⾜࠸㸪㣕⾜≉ᚩ
࡟ὀ┠ࡋ◊✲ࢆ⾜ࡗ࡚࠸ࡿ㸬
ᮏ◊✲࡛ࡣ⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢ〇సࡢ➨ Ṍ࡜ࡋ࡚㸪
ࣇࣛࢵࣆࣥࢢ㐠ືࢆ⾜࠺⩚ࡤࡓࡁᶵᵓࢆタィ࣭〇సࡋࡓ㸬
⩚ࡤࡓࡁ㣕⾜ᶵࡢタィ᮲௳㸪ㅖඖ㸪⩚ࡤࡓࡁᶵᵓࡢᴫせ࡜
⩚ࡤࡓࡁ㐠ືࡢྍど໬࡜ὶయຊィ ࢆ⾜࠸㸪㣕⾜ᶵࡢᛶ⬟
ࢆㄪᰝࡋࡓ㸬
2㸬⩚ࡤࡓࡁ㣕⾜ᶵ
⏥⹸ࡢ⩚ࡤࡓࡁࡣࣇࣛࢵࣆࣥࢢ㐠ື㸪࣮ࣜࢹ࢕ࣥࢢ㐠ື㸪
ࡓࡵ࡟㸪㍍㔞໬ࡀᚲせ࡛࠶ࡿ㸬⩚ࡤࡓࡁ࿘Ἴᩘࡣ㸪ᑡ࡞ࡃ
࡜ࡶ 20㹼30[Hz]࡟ࡍࡿᚲせࡀ࠶ࡿ㸬ࣞ࢖ࣀࣝࢬᩘࡣ௦⾲㏿
ᗘࢆ㢼Ὕฟཱྀࡢὶ㏿㸪௦⾲㛗ࡉࢆ᭱኱⩼ᘻ㸪ື⢓ᗘࢆ✵Ẽ
20[Υ]ࡢ᫬ࡢ್࡜ࡋࡓ㸬↓ḟඖ࿘Ἴᩘࡣ௦⾲㏿ᗘࢆ㢼Ὕฟ
ཱྀࡢὶ㏿㸪௦⾲㛗ࡉࢆ᭱኱⩼ᘻ㸪࿘Ἴᩘࢆ⩚ࡤࡓࡁ࿘Ἴᩘ
࡜ࡋࡓ್࡛࠶ࡿ㸬
⾲1 Dimensional of the flapping air vehicle
Wing span[mm]
160.6
Chord length[mm]
45.0
Wing thickness[μm]
8.0
2
Wing area[mm ]
5242
Aspect ratio[-]
4.9
Mass[g]
4.86
ࣇ࢙ࢨࣜࣥࢢ㐠ືࡢ 3 ✀㢮ࢆྲྀࡾධࢀ㸪⩟ࡢᙎᛶࢆ฼⏝ࡋ
Wing loading[N/m2]
9.09
ຠ⋡ࡼࡃ㣕⩧ࡋ࡚࠸ࡿ㸬タィࡍࡿ⩚ࡤࡓࡁ㣕⾜ᶵࡣ㸪࢝ࢼ
Beating frequency[Hz]
9.3
ࣈࣥࢆᶍೌᑐ㇟࡜ࡋ㸪
ձ㉁㔞 1[g]㸪
ղ⩚ࡤࡓࡁ࿘Ἴᩘ 90[Hz]㸪
Reynolds number[-]
4345
ճ⩚ࡤࡓࡁ㐠ື㸦ࣇࣛࢵࣆࣥࢢ㸪࣮ࣜࢹ࢕ࣥࢢ㸪ࣇ࢙ࢨࣜ
Reduced frequency[-]
0.9
ࣥࢢ㸧࡛࠶ࡿ㸬⾲.1 ࡣヨసᶵࡢタィ௙ᵝࢆ♧ࡍ㸬⩼ᖜࡣ୧
࢝ࢼࣈࣥࡣ⩼㠃✚ 269[mm ]㸪㉁㔞 0.9[g]㸪⩼㠃Ⲵ㔜
⩼ࡢ⩼ᖜ㸪⩼ᘻࡣ᭱኱⩼ᘻ㸪⩼㠃✚ࡣ୧⩼ࡢ⩼㠃✚࡛࠶ࡿ㸬
3.3[N/m2]㸪ヨసᶵࡢタィⅬࡣ⩼㠃✚ 5242[mm2]㸪㉁㔞 7[g]㸪
2
͊
ឡ▱ᕤᴗ኱Ꮫ ᕤᏛ㒊 ᶵᲔᏛ⛉㸦㇏⏣ᕷ㸧
⩼㠃Ⲵ㔜 13.1[N/m2]㸪ヨసᶵࡣ⩼㠃✚ 5242[mm2]㸪㉁㔞
͊͊
ឡ▱ᕤᴗ኱Ꮫ኱Ꮫ㝔 ᕤᏛ◊✲⛉㸦㇏⏣ᕷ㸧
4.8[g]㸪⩼㠃Ⲵ㔜 9.0[N/m2]࡛㸪ࣁࢳࢻࣜ࡟㏆࠸ᛶ⬟࡛࠶ࡿ㸬
ឡ▱ᕤᴗ኱Ꮫ⥲ྜᢏ⾡◊✲ᡤ◊✲ሗ࿌㸪➨ 16 ྕ㸪2014 ᖺ
愛知工業大学総合技術研究所研究報告，第
16 号，2014 年
50
ᅗ 1a ࡣ⩚ࡤࡓࡁ㣕⾜ᶵ㸪b ࡣ⩚ࡤࡓࡁ㣕⾜ᶵࡢ 3 ḟඖ
CAD ᅗ㠃㸪c ࡣᅄ⠇࡚ࡇࢡࣛࣥࢡᶵᵓࡢᴫせ㸪d ࡣ⩚ࡤ
㸬ᐇ㦂⿦⨨ཬࡧᐇ㦂᪉ἲ
ࡓࡁ⩼ࢆ♧ࡍ㸬⩚ࡤࡓࡁ㣕⾜ᶵࡣ㸪⬗యࡀI1.2[mm]ࡢ࢝
ᅗ 2a ࡜ b ࡣὶయຊィ ᐇ㦂࡜ࢫࢺࣟ࣎ࢫࢥ࣮ࣉ࡟⩚ࡤࡓࡁ
࣮࣎ࣥࣟࢵࢻ㸪඲㛗 171[mm]㸪඲ᖜ 160.6[mm]࡛࠶ࡿ㸬
㐠ືࡢྍど໬ᐇ㦂ࡢᴫ␎ࢆ♧ࡍ㸬ᅗ 2a ࡢὶయຊィ ࡣ྿ࡁ
Indoor Airplane World ♫〇㉸ᑠᆺ㉥እ⥺ࣔࢪ࣮ࣗࣝࢆᐇ
ฟࡋᘧ࢚ࢵࣇ࢙ࣝᆺᑠᆺ㢼Ὕฟཱྀ࡟⩚ࡤࡓࡁ㣕⾜ᶵࢆタ⨨
⿦ࡋ㸪10㹼30[m]ࡢ⠊ᅖ࡛᧯⦪࣭ไᚚࡀྍ⬟࡛࠶ࡿ㸬⩼௨
ࡋ⾜ࡗࡓ㸬௒ᅇࡢィ ࡛ࡣ㸪⩚ࡤࡓࡁ㐠ື᫬ࡢࢫࢺ࣮ࣟࢡ
እࡢᶵయࡢ㉁㔞ࡣ 4.417[g]࡛࠶ࡾ㸪⩚ࡤࡓࡁ࿘Ἴᩘࡣ 7㹼
㠃ࡢゅᗘࢆ㢼Ὕὶࢀ࡜ᆶ┤ 90[deg]࡟タᐃࡋࡓ㸬ࡇࢀࡣ㸪⩼
10[Hz]࡛࠶ࡿ㸬
㠃࡟స⏝ࡍࡿὶయຊࡀ୍␒ຠ⋡ࡼࡃⓎ⏕ࡍࡿ≧ែࢆ᝿ᐃࡋ
ࡓ㸬⩚ࡤࡓࡁ㐠ື᫬࡟⏕ࡌࡿὶయຊィ ࡣ㸪ࡦࡎࡳࢤ࣮ࢪ
ࢆᨭⅬ௜㏆࡟ྲྀࡾ௜ࡅ㸪࢝ࣥࢳࣞࣂ࣮స⏝Ⅼ(➃㒊)࡟⏥⹸ᆺ
⩚ࡤࡓࡁ㣕⾜ᶵࢆᅛᐃࡋࡓ㸬࢝ࣥࢳࣞࣂ࣮࡟ࡣస⏝Ⅼ࠿ࡽ
ࡢ㛗ࡉ 11.6[mm]㸪O.D. 3[mm]㸪I.D. 1.5[mm]ࡢ࣮࢝࣎ࣥࣃ࢖
ࣉ㸪ࡦࡎࡳࢤ࣮ࢪ࡟ࡣओඹ࿴㟁ᴗ〇༙ᑟయࡦࡎࡳࢤ࣮ࢪ
KFG-5-120-C1-11 (᢬ᢠ್㸸120[Ȑ]㸪ࢤ࣮ࢪ⋡㸸2.1)ࢆ⏝࠸ࡓ㸬
a flapping air vehicle
b CAD design
ࡦࡎࡳࢤ࣮ࢪࡢᅇ㊰࡟ࡣ㸪 ᐃឤᗘྥୖࡢⅭ࡟ 2 ࢔ࢡࢸ࢕
ࣈࢤ࣮ࢪἲࢆ⏝࠸࡚࠾ࡾ㸪2 ᯛࡢࡦࡎࡳࢤ࣮ࢪࢆ౑⏝ࡋࡓ㸬
ᅛᐃࡋࡓ⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢᆶ┤᪉ྥࡢὶయຊ(Fv)࡜
Ỉᖹ᪉ྥࡢὶయຊ(Fh)ࢆྠ᫬ィ ࡍࡿⅭ࡟㸪2 ᯛ 1 ⤌ࡢࡦࡎ
ࡳࢤ࣮ࢪࢆ 2 ⟠ᡤ࡟㈞ࡾ௜ࡅࡓ㸬
c Four-bar lever crank
d Flapping wing
mechanism
ᅗ 1 Description of the beetle-like micro air vehicle(MAV)
ᅗ 1bձշ㒊ࡣI[mm]࣮࢝࣎ࣥࣟࢵࢻ㸪ղ㒊ࡣࣔࢪࣗ
࣮ࣝ 0.3㸪ࣉࣛࢫࢳࢵࢡ〇ࢠ࢔㸪࣮ࣔࢱ࠿ࡽᅄ⠇࡚ࡇࢡࣛ
a Measurements of aerodynamic force
ࣥࢡᶵᵓ㒊ࢠ࢔ࡲ࡛ࡢࢠ࢔ẚࡣ 26.7 ࡛࠶ࡿ㸬ճ㒊ࡣ 3D
ࣉࣜࣥࢱ࣮࡟ࡼࡾ㐀ᙧࡋࡓ⩼࡜ࢡࣛࣥࢡࡢ㐃⤖㒊ရ㸪մ
㒊ࡣI4[mm]ࢥ࢔ࣞࢫ࣮ࣔࢱ㸪ࢥ࢖ࣝ᢬ᢠ್ࡣ 7[ȍ]㸪࣮ࣔ
ࢱ᭱኱ฟຊࡣ 0.28[W]࡛࠶ࡿ㸬յ㒊ࡣ⩼࡛࠶ࡾ㸪⬗య࠿ࡽ
᏶඲࡟ศ㞳ࡋ࡚࠸ࡿ(ᅗ 1d ཧ↷)㸬ն㒊ࡣཷಙኚㄪ࿘Ἴᩘ
38[kHz]ࡢ㉥እ⥺ཷಙᶵ㸪㏦ಙ⠊ᅖࡣ 10㹼30[m]㸪ࢧ࢖ࢬ
7.5™9[mm]࡛࠶ࡿ㸬շ㒊ࡣ㉁㔞 1.1[g]㸪ᐃ᱁㟁ᅽ 3.7[V]㸪
ᐜ㔞 30[mAh] Li-Po ࣂࢵࢸ࣮࡛ࣜ࠶ࡿ㸬ո㒊ࡣὶయຊィ ⏝࢝ࣥࢳࣞࣂ࣮ඛ➃㒊ࡢᅛᐃ㒊ศ࡛࠶ࡿ㸬ᅄ⠇࡚ࡇࢡࣛࣥ
ࢡᶵᵓ࡟ࡼࡾ࣮ࣔࢱࡢᅇ㌿㐠ືࢆࣇࣛࢵࣆࣥࢢ㐠ື࡟ኚ
᥮ࡍࡿᶵᵓ࡜࡞ࡗ࡚࠸ࡿ㸬ᅗ 1c ࠿ࡽࣇࣛࢵࣆࣥࢢ㐠ືࡢ
b Visualization of flapping motion
ᅗ 2 Experimental setup
ࢫࢺ࣮ࣟࢡゅࡣࢥ࢞ࢿ࣒ࢩ⛉⏥⹸ࡢ࢝ࢼࣈࣥࢆᶍೌࡋ㸪
ᅗ 2b ࡢ⩚ࡤࡓࡁ㐠ື᫬ࡢྍど໬ࡣ㸪↓㢼᫬ࡢᐃᖖⓗ࡞⩚
⩼ ࢆ Ỉ ᖹ ఩ ⨨ ࠿ ࡽ ୖ Ṛ Ⅼ ࡬ (Top Dead Center : ௨ ୗ
ࡤࡓࡁ㐠ື᫬࡟㸪ࢹࢪࢱࣝࢫࢺࣟ࣎ࢫࢥ࣮ࣉ’㸦Ⳣཎ◊✲ᡤ
T.D.C) 51[deg] 㸪 ୗ Ṛ Ⅼ ࡬ (Bottom Dead Center : ௨ ୗ
S-126X㸧ࢆタ⨨ࡋ㸪ࢹࢪࢱ࣓ࣝ࢝ࣛ(ࢽࢥࣥ D800)࡟ࡼࡾ᧜
B.D.C) 29 [deg]࡜ࡋࡓ㸬ᅗ 2d ࡢ⩼ࡣ㸪⩼⭷ࡢཌࡉ 8[μm]
ᙳࢆ⾜ࡗࡓ㸬
ࡢ࣏࢚ࣜࢳࣞࣥࣇ࢕࣒ࣝ㸪⩼ᖜ 80.3[mm]㸪᭱኱⩼ᘻ㛗
45[mm]࡛࠶ࡿ㸬⩼㦵ཬࡧ⩟⬦࡟ࡣI0.5[mm]ࡢ࣮࢝࣎ࣥࣟ
㸬ᐇ㦂⿦⨨ཬࡧᐇ㦂᪉ἲ
ࢵࢻࢆ౑⏝ࡋ㸪⩼➃࠿ࡽ⩼᰿᪉ྥ࡬㛗ࡉ 46[mm]ࡢ࣮࢝࣎
ࣥࣟࢵࢻࡢ⩟⬦ࢆ㈞ࡾ௜ࡅࡓ㸬
ᅗ 3a ࡜ 3b ࡣ⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢ T.D.C ࠿ࡽ୍࿘ᮇ
⩚ࡤࡓࡁ㣕⾜ᶵࡢ⩚ࡤࡓࡁ᫬ࡢὶయຊィ 羽ばたき飛行機の羽ばたき時の流体力計測
ศࡢࣇࣛࢵࣆࣥࢢ࣮ࣔࢩࣙࣥࢆ♧ࡍ㸬ᅗ 3a ࡣ T.D.C ࠿ࡽ
51
࡚㸪ࣇ࢙ࢨࣜࣥࢢ㐠ື࡟ࡼࡗ࡚㸪ྤฟ ࢆⓎ⏕ࡋ࡚࠸ࡿ
B.D.C ࡲ࡛㸪ᅗ 3b ࡣ B.D.C ࠿ࡽ T.D.C ࡲ࡛ࡢࢫࢺࣟ࣎᧜ᙳ
ࡀ㸪Fv ࡜ Fh ࡣṤ࡝ྠࡌ኱ࡁࡉࡢὶయຊࢆⓎ⏕ࡋ࡚࠸ࡿ㸬
ࡢ⤖ᯝࢆ♧ࡋ㸪ྛ෗┿ࡢ᫬㛫㛫㝸ࡣǼt = 1.00msec ࡛࠶ࡿ㸬
T*=0.18 ௜㏆ࡲ࡛㸪Fv ࡣቑຍ㸪Fh ࡣ᢬ᢠࢆ⏕ࡌῶᑡࡍࡿ㸬
ᅗ 3a ࠿ࡽ⩼ࡣ㸪T.D.C ࠿ࡽࡢ᣺ࡾୗࡆ㐠ື࡛㸪ὶయຊࡢᙳ
㡪ཬࡧ⩟⬦ࡢ⮬㔜࡟ࡼࡾࣇ࢙ࢨࣜࣥࢢ㐠ືࢆ⾜ࡗ࡚࠸ࡿ㸬
B.D.C ࡟ྥ࠿ࡗ࡚㸪㏄ゅࡢᑠࡉ࠸ࡲࡲ㸪㝆ࡾୗࡆືసࢆ⾜࠸㸪
ୗṚⅬ㏆ࡃ࡛኱㏄ゅ≧ែ࡬ࡢኚ᭦ࡍࡿ㸬ᅗ 3b ࠿ࡽ⩼ࡣ኱
㏄ゅ≧ែ࠿ࡽ㸪᣺ࡾୖࡆ㐠ື࡜ࣇ࢙ࢨࣜࣥࢢ㐠ືࢆ⾜ࡗ࡚
࠸ࡿ㸬T.D.C ࡟ྥ࠿࠺࡟ࡘࢀ࡚㸪኱㏄ゅ≧ែࢆᑠࡉ࠸㏄ゅ࡬
ኚ᭦ࡋ࡚࠸ࡿ㸬T.D.C ௜㏆࡛ࡣ㸪኱㏄ゅ࡟ኚ໬ࡋ㸪⩟⬦ࡢᙳ
㡪ࡀฟጞࡵࡿ㸬௨ୖࡢࡼ࠺࡞୍㐃ࡢືసࢆ⧞ࡾ㏉ࡍࡇ࡜࡛㸪
⩚ࡤࡓࡁ㣕⾜ࢆ⾜ࡗ࡚࠸ࡿ㸬
ᅗ 4 Time histories of vertical and horizontal force for
the beetle-like MAV (Stroke face angle = 90 [deg])
T*=0.18 ࡛๓⦕๤㞳 ࡢⓎ⏕࡟ࡼࡗ࡚㸪Fv ࡣῶᑡ㐣⛬㸪
Fh ࡣቑຍ㐣⛬࡟⛣ࡗ࡚࠸ࡿ㸬T*=0.33 ࡟࠾࠸࡚㸪๓⦕๤㞳
ࡢⓎ⏕ࡢ☜ㄆࡀ࡛ࡁࡿ㸬ࡋ࠿ࡋ㸪Fv ࡣ᭱ᑡ࡜࡞ࡗ࡚㸪ቑ
ຍ㐣⛬࡟ධࡾ㸪Fh ࡣῶᑡ㐣⛬࡟ධࡿ㸬T*=0.50 ࡢ B.D.C ࡛
⩚ࡤࡓࡁ㐠ືࡣ᣺ࡾୖࡆ㐠ື࡜࡞ࡿ㸬ࡇࡢ᫬ Fv ࡣῶᑡࡋጞ
ࡵ㸪Fh ࡣቑຍࡋጞࡵࡿ㸬T*=0.65 ࡢ᣺ࡾୖࡆ㐠ື࡛ࣇ࢙ࢨ
ࣜࣥࢢ㐠ືࢆ⾜ࡗࡓᚋ࡟㸪Fv ࡣቑຍࡋ㸪Fh ࡣῶᑡࡋጞࡵࡿ㸬
a Down stroke motion
T*=0.81 ࡢ᣺ࡾୖࡆ㐠ື࡛⩼ୗ㠃࡟๓⦕๤㞳 ࡀ☜ㄆ࡛ࡁ㸪
Fv ࡣῶᑡࡋጞࡵ㸪Fh ࡣቑຍࡋጞࡵࡿ㸬T*=1.00 ࡛ T.D.C ࡟
ᡠࡾ㸪ྠࡌὶయຊᙧᡂࡀ⧞ࡾ㏉ࡉࢀࡿ㸬
⩚ࡤࡓࡁ㣕⾜ᶵࡢືຊ࡟ࡼࡗ࡚㸪ὶయຊィ ୰࡟࢝ࣥࢳ
ࣞࣂ࣮ࡀ᣺ືࡋࡓ㸬ᶵయᚋ᪉࡬ࣂࢵࢸ࣮ࣜࢆ⛣ືࡋ㸪✵ຊ
୰ᚰࡣ࢝ࣥࢳࣞࣂ࣮స⏝Ⅼ௜㏆࡟⛣ືࡉࡏࡓ㸬ࡑࡢ⤖ᯝ㸪
ᅄ⠇࡚ࡇࢡࣛࣥࢡᶵᵓ࠿ࡽࡢ᣺ືࡀఏࢃࡾ㸪ࣂࢵࢸ࣮ࣜ௜
㏆࠿ࡽࡶ⮬㔜࡟ࡼࡾ᣺ືࡋ࡚ࡋࡲࡗࡓ㸬ࡲࡓ⩼⭷ࢆ௜ࡅ࡚
࠸࡞࠸≧ែ࡛⩚ࡤࡓࡁ㐠ືࢆ⾜ࡗࡓ࡜ࡇࢁ㸪ᅄ⠇࡚ࡇࢡࣛ
ࣥࢡᶵᵓ࡜ࣂࢵࢸ࣮ࣜ࠿ࡽࡢ᣺ືࡀࡦࡎࡳࢭࣥࢧ࡟ఏࢃࡗ
࡚࠸ࡿࡇ࡜ࢆ☜ㄆࡋࡓ㸬௒ᅇࡢὶయຊィ ⤖ᯝ࡟ࡣ㸪⩚ࡤ
b Up stroke motion
ᅗ 3 Flapping motion
ᅗ 4 ࡣ⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢࢫࢺ࣮ࣟࢡ㠃ࡢゅᗘ
90[deg]ࡢ᫬ࡢὶయຊィ ࡢ 1 ࿘ᮇศࡢ⤖ᯝࢆ♧ࡍ㸬ᶓ㍈ࡣ
⩚ࡤࡓࡁ㐠ື 1 ࿘ᮇศࡢ᫬㛫࡛↓ḟඖ໬ࡋࡓ↓ḟඖ᫬㛫 T*
ཬࡧᐇ ᫬㛫࡛࠶ࡿ㸬⦪㍈ࡣ㸪 ᐃࡋࡓྛ᪉ྥࡢὶయຊ(Ỉ
ᖹ᪉ྥࡢὶయຊ Fh㸪ᆶ┤᪉ྥࡢὶయຊ Fv)ࢆ♧ࡍ㸬ࢢࣛࣇ
୰ࡢ◚⥺ࡀ Fh㸪ᐇ⥺ࡀ Fv ࢆ⾲ࡋ㸪Fh ࡣ౪ヨయࢆᢲࡍ᪉ྥ
ࡢຊࢆṇ㸪Fv ࡣୖ᪉ྥࡢຊࢆṇ࡜ࡋࡓ㸬
T*=0.00 ࡢ T.D.C ࠿ࡽ᣺ࡾୗࢁࡋ㐠ືࢆ⾜࠸ጞࡵࡿ㸬ࡑࡢ
᫬ࡢ Fv ࡣቑຍࡋጞࡵ㸪Fh ࡣῶᑡࡋጞࡵࡿ㸬⏥⹸ᆺ⩚ࡤࡓ
ࡁ㣕⾜ᶵࡣ⩼➃௜㏆ࡢࡳ⩟⬦ࢆ᭷ࡍࡿ⩼࡛࠶ࡾ㸪ᅗ 3 ࡢ
T*=0.09 ཬࡧ T*=0.64 ࠿ࡽ㸪⩼ࡣὶయຊࡢᙳ㡪ཬࡧ⩟⬦ࡢ⮬
㔜࡟ࡼࡾࣇ࢙ࢨࣜࣥࢢ㐠ືࢆ⾜ࡗ࡚࠸ࡿ㸬T*=0.09 ࡟࠾࠸
ࡓࡁ㐠ື࡟ࡼࡿ⩼ࡢ័ᛶຊ㸪ᅄ⠇࡚ࡇࢡࣛࣥࢡᶵᵓ࡜ࣂࢵ
ࢸ࣮ࣜ࠿ࡽࡢ᣺ືࡶྠ᫬ィ ࡋ࡚࠸ࡿྍ⬟ᛶࡀ࠶ࡿ㸬
ࡼࡗ࡚㸪࢝ࣥࢳࣞࣂ࣮ࡀὶయຊ࡟ࡼࡿຊ௨እ࡛᣺ືࡋ࡞
࠸࢝ࣥࢳࣞࣂ࣮ࡢᮦᩱ㸪ᵓ㐀ࡢ㑅ᐃ࡜ࡑࡢ๛ᛶࢆቑࡋ㸪ᶵ
యࡢ㔜ᚰ࡟࢝ࣥࢳࣞࣂ࣮ࢆྲྀࡾ௜ࡅࡿ࡞࡝ࡋ࡚ᨵၿࡍࡿᚲ
せࡀ࠶ࡿ㸬ࡲࡓ㸪ᅄ⠇࡚ࡇࢡࣛࣥࢡᶵᵓࡸ⩼ࡢ័ᛶຊ࡟ࡼ
ࡿ᣺ືࢆᢚไࡍࡿࡓࡵ࡟㸪ࡑࢀࡽࡢ᣺ືࢆᡴࡕᾘࡍᶵᵓࡀ
ᚲせ࡛࠶ࡿ㸬
5㸬⤖ゝ
⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢタィ᮲௳㸪ㅖඖ㸪⩚ࡤࡓࡁᶵᵓ
ࡢᴫせ㸪⩚ࡤࡓࡁ㐠ືࡢྍど໬࡜ὶయຊィ ࢆ⾜࠸㸪௨ୗ
ࡢ⤖ᯝࢆᚓࡓ㸬
52
ឡ▱ᕤᴗ኱Ꮫ⥲ྜᢏ⾡◊✲ᡤ◊✲ሗ࿌㸪➨ 16 ྕ㸪2014 ᖺ
愛知工業大学総合技術研究所研究報告，第 16 号，2014 年
(1)ᅄ⠇࡚ࡇࢡࣛࣥࢡᶵᵓ࡟ࡼࡾࠊ⩚ࡤࡓࡁ࿘Ἴᩘ9.3[Hz]
࡛ࣇࣛࢵࣆࣥࢢ㐠ືࢆ⾜࠺⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡀ᏶ᡂ
ࡋࡓ㸬
(2)⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢ⩼࿘ࡾࡢྍど໬⤖ᯝ࠿ࡽ㸪⩼⭷
ࡢ⩼➃௜㏆࡟⩟⬦ࢆ᭷ࡍࡿ⩼ࡣ㸪T.D.CཬࡧB.D.C฿㐩┤
ᚋ࡟ࣇ࢙ࢨࣜࣥࢢ㐠ືࢆ⾜࠸㸪ࡑࢀ࡟ࡼࡾ⩼ᚋ⦕࠿ࡽྤ
ฟ ࡀⓎ⏕ࡋ࡚࠸ࡿ㸬
(3)⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢὶయຊィ ࠿ࡽ㸪㸯࿘ᮇࡢ⩚
ࡤࡓࡁ㐠ືࡢ୰࡛Fh㸪Fvඹ࡟ቑຍ࡜ῶᑡࡢኚ᭤Ⅼࡀ6⟠ᡤ
ࡶ࠶ࡾ㸪ࢫ࣒࣮ࢬ࡟ὶయຊࢆⓎ⏕ฟ᮶࡚࠸࡞࠸ࡇ࡜ࡀࢃ
࠿ࡗࡓ㸬
(4)⏥⹸ᆺ⩚ࡤࡓࡁ㣕⾜ᶵࡢὶయຊィ ࡣ⩚ࡤࡓࡁ㐠ືᶵ
ᵓ࡟ࡼࡿ᣺ືࡸ⩚ࡤࡓࡁ㐠ືࡢ័ᛶຊࡶィ ࡋ࡚ࡋࡲ࠺
ࡓࡵ㸪ࡑࢀࡽࡢ᣺ືࢆᡴࡕᾘࡍᶵᵓࢆ⏝࠸࡚ィ ࡍࡿᚲせ
ࡀ࠶ࡿ㸬
ཧ⪃ᩥ⊩
(1) Sir J. Lighthill, "Mathematical Biofluid dynamics", SIAM
(1975)
(2) C. P. Ellington, "The aerodynamics of hovering insect
flight, III. Kinematics", Phi. Trans. of the R. Soc. of
London, Vol. 305, No. 1122 , 41-78 (1984)
(3) R. Dudley, "The Biomechanics of Insect Flight", Princeton
Univ. Press (2000)
(4) M. Azhar, et al, “Mimicking unfolding motion of a beetle
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Exp. Bio, 54, 575-585 (1971)
(6) H. V. Phan, et al, "Stable Vertical Takeoff of an
Insect-Mimicking Flapping-Wing System Without Guide
Implementing Inherent Pitching Stability", J. Bio. Eng.
9,391–401, (2012)
(7) A. J. Burton, "Nervous control of flight orientation in a
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wings and body of a dragonfly", J. Exp. Bio., 199,
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(9) S. Sunada, et al, "Airfoil characteristics at a low rey-nolds
number", J. Flow Visualization & Image Processing, Vol.
7, 207-215 (2000)
(10) K. Kitagawa, et al, "Visualization of flapping wing of the
drone beetle", J. Visualization, Vol. 12, No. 4, 393-400
(2009)
(11) ῝℩㸪໭ᕝ, "ࢥ࢞ࢿ࣒ࢩ⛉⏥⹸ࡢ㣕⩧᫬ࡢ㠀ᐃᖖὶయ
ຊࡢィ ", ➨ 25 ᅇ࢚࢔࣭ࣟ࢔ࢡ࢔ࣂ࢖࣓࢜࢝ࢽࢬ࣒◊✲
఍ㅮ₇఍㈨ᩱ㞟, 17-18(2010)