HAL Id: hal-01851630
https://hal.archives-ouvertes.fr/hal-01851630
Submitted on 30 Jul 2018
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Numerical and experimental study on flexible blade for
tilt-body drones
Fazila Mohd Zawawi, Sebastien Prothin, Peng Lv, Emmanuel Bénard, Joseph
Morlier, Jean-Marc Moschetta
To cite this version:
Fazila Mohd Zawawi, Sebastien Prothin, Peng Lv, Emmanuel Bénard, Joseph Morlier, et al.. Nu-merical and experimental study on flexible blade for tilt-body drones. 21ème Congrès Français de Mécanique - CFM 2013, Aug 2013, Bordeaux, France. pp.0. �hal-01851630�
To cite this document:
Mohd Zawawi, Fazila and Prothin, Sebastien and Lv, Peng and
Benard, Emmanuel and Morlier, Joseph and Moschetta, Jean-Marc Numerical and
experimental study on flexible blade for tilt-body drones. (2013) In: 21ème Congrès
Français de Mécanique - CFM 2013, 26-30 Aug 2013, Bordeaux, France.
O
pen
A
rchive
T
oulouse
A
rchive
O
uverte (
OATAO
)
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.
This is an author-deposited version published in: http://oatao.univ-toulouse.fr/
Eprints ID: 9318
Any correspondence concerning this service should be sent to the repository
!"#$%&'( ')* #+,#$%"#)-'( .-!*/ 0) 1#+%2(# 2('*# 30$
-%(-420*/ *$0)#.
!"#$! %&'()*+,+,- !". /01!23#04 56&7'-8 . 5049 :; . <==!4>0$ ?<8+6( . @A20BC %&6:-<6". @0!4)%!DE %&/F'<77+ ! <=>?6 @$(;,;3; A3B0&,.3& -. CD=0&#$*3;,23. .; -. CD>(B*1. "! </A/6 @$(;,;3; A3B0&,.3& -. CD=0&#$*3;,23. .; -. CD>(B*1.!"#$! %
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
&'"()*+( %
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
,-(" +./0" %
!"#$%&'( ')&*+, - ./"+ 0+1!%"+ - 23/**+) #)!'!4+*,!&**+" - 5*#6)/3#!&* 7"8!'+,$,#)83#8)+1 23()-4#+(5-3
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
!"#$%&'() *+,$)
-. /$%+,01(#&' *+,$) 2345647
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e < 70, 000N= OPQ6R= '! '1$"#1) /(,1-! '!/ '!')*,1, .#/( /(7()#0(/ 4* S$()' FTH 8', 1!%(-$'%(/ 1!%# %2( /(,1-! 1%($'%17( 0$#.(,,5 ;2( %&$4&)(!.( (?(.% 8', ()1+1!'%(/ 4* &,1!- 9'% 0)'%( FUH5 6! %21, $(,0(.%= %2( V.$1% 0'$'+(%($= &,(/ %# /(<!( %2( %&$4&)(!.( )(7() 1! OPQ6R= .'! 4( ,(% ', W5X "#$ 4#%2 91-2% +#/(,5 C YK4)'/(/ $#%#$ 81%2 $(.%'!-&)'$ 0)'!"#$+ MR = 0.1m, c = 0.02mN= 9'% 0)'%( 4)'/( 0$#<)( 81%2 %21.D!(,, t/c = 2.5% '!/ 4)'/( 01%.2 #" 25Z 8', &,(/ "#$ 7')1/'%1#!M2#7($ .',(N= 1! P1-5 XM'N5 B('!821)(= %2( 0$#0())($ C[\ ]>U 8', &,(/ %# 7')1/'%( %2( P[LQ[ "#$ "#$8'$/ 91-2% .',(5 ;2( 1!9#8 7()#.1%* 8', 16m/s5 P$#+ %2( 7')1/'%1#! $(,&)% ', ,2#8! 1! P1-5 XM4N= 1% 1, "#&!/ %2'% %2( /(7()#0(/ @AB; +(%2#/ 81%2 %2( 1!%(-$'%1#! #" OPQ6R ,2#8, 4(%%($ '-$((+(!% 81%2 %2( (>0($1+(!%') +(',&$(+(!% .#+0'$(/ %# %2( )1!('$ +#/() ^[LQ[5 C ,)1-2% 1!.$(',( 1! %#$3&( #4,($7(/ 1! %2( (>0($1+(!%') $(,&)% .'! 4( /&( %# %2( 2('7* +'%($1') M')&+1!1&+N &,(/ 1! %2( 4)'/(5
- 89%"'9"%() *+,$) 23:;/*7
;2( ,%$&.%&$') '!')*,1, 1, 4',(/ &0#! %2( &,( #" '!1,#%$#01. 4('+ <!1%( ()(+(!% +#/() %# /(%($+1!( %2( 4)'/( /(9(.%1#!, /&$1!- #0($'%1#!5 ;2( P@ACB .#!,1,%, #" '! 1!%(-$'%(/ ,(% #" 0$#-$'+,= 821.2 0($"#$+ ' %8#K/1+(!,1#!') .$#,,K,(.%1#!') '!')*,1, #" %2( 4)'/(= "#))#8(/ 4* ' #!(K/1+(!,1#!') <!1%( ()(+(!% #" ' 0$#0$#%#$ 4)'/(5 C -)#4') .##$/1!'%( ,*,%(+ 1, &,(/ "#$ %2( /(,.$10%1#! #" %2( 4)'/( -(#+(%$* '!/ %2( .').&)'%1#! #" %2( )#'/,5 @A\C_ F`H= ' .$#,,K,(.%1#!') '!')*,1, %##) 821.2 1, /(7()#0(/ '% S(!+'$D ;(.2!1.') !17($,1%* MS; N 8', 1!.#$0#$'%(/ 1! %21, ,%$&.%&$') '!')*,1, 0$#-$'+5 ;2( +#%17'%1#! #" (+0)#*1!- @A\C_ 1, /&( %# %2( "'.% %2'% @A\C_ 2', '41)1%* %# /(%($+1!( %2( .$#,, ,(.%1#! ,%1?!(,, 0$#0($%1(, 821)( '..#&!%1!- "#$ ')) %2( -(#+(%$1.') '!/ +'%($1') 1!/&.(/ .#&0)1!-,5;2( )1!('$ $()'%1#! 4(%8((! -(!($')1a(/ "#$.(, F '!/ %2( $(,&)%1!- ,%$'1!, '!/ .&$7'%&$(, q 1, 8$1%%(! 1! ' +'%$1> "#$+ ', "#))#8, b Kq = F MXN 82($( K 1, %2( ,(.%1#!') ,%1?!(,, +'%$1>5 ;2( <!') "#$+ #" ()',%1. (!($-* '!/ D1!(%1. (!($-* '$( 8$1%%(! 1! A35 Y5 Ke= Z L 0 BTSBdz; Me= Z L 0 NTMsN dz MYN 82($( Ms ,(.%1#!') +',, +'%$1>= B 1, %2( ,%$'1!K/1,0)'.(+(!% +'%$1> '!/ N 1, %2( 0#)*!#+1') +'%$1>5 ;2( /(%'1), #" (3&'%1#! &,(/ 1! %2(,( $()'%1#!,210, '$( /(,.$14(/ 1! F]H5 c)#4') ,%1?!(,, #" %2( 4)'/( 1, #4%'1!(/ %2$#&-2 ,0'!81,( 1!%(-$'%1#!5 C, "#$ %2( #!(K/1+(!,1#!') <!1%( ()(+(!%= %2( .)',,1.') ;1+#K ,2(!D# 4('+ %2(#$* 1, &,(/ "#$ .#!,1/($1!- <!1%( ()(+(!% '!')*,1,5 d1%2 %2( #4%'1!(/ ,2'0( "&!.%1#!= %2( 0$1!.10)( #" 71$%&') /1,0)'.(+(!%, 1, &,(/ %# /($17( %2( ()(+(!%') ,%1?!(,,5 P#$ ,%$&.%&$') +#/() 7')1/'%1#!= ' ,%'%1. '!')*,1, #! ' $(.%'!-&)'$ 0)'!"#$+ 81%2 /1+(!,1#! MXeW5T++>XY5`++>G5X`T++N 8', 0($"#$+(/5 B'%($1') 0$#0($%1(, #" -$'021%(K(0#>* '$( b
µ = 0.3 and ρ = 1550kg/m3
!"# $%& '()%# *+," -#.$#/, ,0 $+,/" '1+. *'. 234 !"# -#.5%, 06,'+(#7 +( 89:;< *'. ='%+7',#7 6& <>/ ?'.,-'(@ +( 8+) 2
!" #$%&'()*+(,$*-.,%/.%,( 01234
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
" 35&(,67(8.+' 9(.%&
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`3K !"# 7+.,'(/# 0C -#C#-#(/# +. `33BB@ '(7 ,"# -'()# 0C B#'.5-+() /'( 6# 6#,*##( DK`3BB ,0 `33BB !"# .'B$%+() C-#J5#(/& 0C ,"+. %'.#- *'. .#%#/,#7 '. M3@333PH A( 0-7#- ,0 7#,#-D B+(# ,"# 0=#-'%% 5(/#-,'+(,& Ulaser 0C ,"# #1$#-+B#(,'% -#.5%,@ ,"# 6+'. '(7 $-#/+.+0( %+B+,.@ Blaser '(7
Plaser@ B5., 6# /0B6+(#7 !"+. +. '//0B$%+."#7 5.+() ,"# a00,D>5BD>J5'-# Ea>>G B#,"07@
Ulaser = (Blaser+ Plaser)1/2 E2G
; -#C#-#(/# .5-C'/# *'. B#'.5-#7 [-., ,0 7#,#-B+(# ,"# $-#/+.+0( %+B+,.@ ,"#( ,"# ,0,'% 5(/#-,'+(,& +. 06,'+(#7@ ± 0.1% \U> -#/0-7. ,"# b /00-7+(',#. *"+/" +. ,"# 7+.,'(/# C-0B ,"# $0.+,+0( 7#,#/,#7 0( 6%'7# .5-C'/# ,0 -#C#-#(/# $%'(# <#'(*"+%#@ .J5'-# *'=# +( ,+B# 70B'+( +. B#'.5-#7 6& aR< .#(.0- !"#(@ '=#-')# aR< '(7 '()5%'- .$##7 ', #'/" 6%'7# .#/,+0( /'( 6# #1,-'/,#7 C-0B ,"# .J5'-# *'=# 85-,"#-B0-#@ *+," ,"# 'H+B5," 0C C#',"#-+()@ $0%'- /00-7+(',#. +. $0..+6%# ,0 6# ,-'(.C#--#7 ,0 F'-,#.+'( /00-7+(',#. c '(7 ^ F0B6+(+() /00-7+(',#. c@ ^ '(7 b@ ' $0%&(0B+'% .5-C'/# [,,+() +. $#-C0-B#7 ,0 06,'+( ,"# 6#(7+() '(7 ,0-.+0( 0C -0,',+() 6%'7# !0 #='%5',# ,"# I#1+6%# 6%'7# $#-C0-B'(/#@ ,"# ,"-5., '(7 ,0-J5# *#-# B#'.5-#7 5.+() ,*0 ,-'(.75/#-.
: ;(-%'.- <+'6)+.6$8
!"# ='%+7',+0( -#.5%,. +( $#-C0-B'(/# '-# ."0*( +( 8+) ` ;. /'( 6# .##(@ ,"# 8RaOR ')-##. *#%% *+," #1$#-+B#(,'% 7',' 0C ,"-5., P0*#=#-@ +, 0=#-D$-#7+/,. ,"# ,0-J5# 8+) d ."0*. ,"# )007 ')-##B#(, 6#,*##( ,"# 8;: .+B5%',+0( '(7 ,"# #1$#-+B#(,'% 7',' '. 06,'+(#7 C-0B \U> B#'.5-#B#(,. !"+. +. ,"# -#.5%, 06,'+(#7 C0- ,"# 6%'7#. /%'B$#7 ', /0%%#/,+=# $+,/" 2`4 !"# I5/,5',+0(. ,"', /'( 6# 06.#-=#7 2!"#$%! &'( )")* +,# #- *)-#".( /#0& (") !) ")&$, & 12 !) +"),/./0("2 +#& 3+"#')&&/0% .) !#*4 50 !/& .) !#*6 !) *)-#".( /#0 7(& )8 "(' )* !"#$%! !) *( ( /0 )"+#,( /#0 ( )('! &)' /#04 9/0') !) :/1"( /#0 #- "# ( /0% 1,(*) +"#1(1,2 %)0)"( )* $0')" (/0 2 # !) ;<9 *( ( /0 &+(07/&)6 !)0')6 !) *)-#".( /#0 )8!/1/ & $0&.## !0)&& /0 !) +,# &4
!"#$%&'("#'
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
)**+#,(-20000 2500 3000 3500 4000 0.2 0.4 0.6 0.8 1 1.2 Rotational speed, Ω (rpm) Thrust, T (N) Experimental QPROP FPROP !" #$%&'( 20000 2500 3000 3500 4000 1 2 3 4 5 Rotational speed, Ω (rpm) Torque, Q (N.cm) Experimental QPROP FPROP )" #*%+&,!"#$% G H I#.+("/� #- JKL@ &/.$,( /#0 (0* '#"")&+#0*/0% .)(&$").)0 & -#" !#:)" MNOPQ
4000 6000 8000 10000 12000 −0.5 0 0.5 1 1.5 2 2.5 3 Rotational Speed, RPM Thrust, T (N) FPROP QPROP Experimental !" #$%&'( 40000 6000 8000 10000 12000 2 4 6 8 10 Rotational Speed, RPM Current, I (Amp) FPROP QPROP Experimental )" #*%+&,
0 0.05 0.1 0.15 0.2 −14 −12 −10 −8 −6 −4 −2 0 2x 10 −3 Spanwise position (m) Flapwise deflection, u y (m) MSc.NASTRAN FBEAM !" #$%&'%( 0 0.05 0.1 0.15 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 Spanwise position (m) Torsion, θz (°) MSc.NASTRAN FBEAM )" *+,-'+% !"#$% ! "#$%& '()*+(,*-. /0 &123 4%156%4 0 0.05 0.1 0.15 0.2 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Spanwise position (m) Flapwise deflection, u y (m) Single−step Coupled−aero−structure !" #$%&'%( 0 0.05 0.1 0.15 0.2 −6 −5 −4 −3 −2 −1 0 Spanwise position (m) Torsion, θz (°) Single−step Coupled−aero−structure )" *+,-'+% !"#$% 7 ! 589 9:92, -; 11 (.+ <%1 =*>?)(,*-. -. ,89 /)(+9 +9;-@>(,*-.= 1000 1200 1400 1600 0 0.5 1 1.5 2 RPM Thrust, N Experiment FPROP !" *.,/-0 1000 1200 1400 1600 0 2 4 6 8 10 RPM Torque, N.cm Experiment FPROP )" *+,1/$ !"#$% A ! 58@?=, (.+ ,-@B?9 -; @*C*+ (.+ D9E*/)9 F@-F@-,-@ (, +*:9@9., @-,(,*-.() =F99+ GHIJK A
0 0.05 0.1 0.15 0.2 0 0.01 0.02 0.03 0.04 0.05 0.06 Spanwise position (m) Flapwise bending, u y (m) Experimental Fit (Experimental) FAE !" #$%&'%( 0 0.05 0.1 0.15 0.2 −8 −7 −6 −5 −4 −3 −2 −1 0 Spanwise position (m) Torsion, θz (°) Experimental Fit (Experimental) FAE )" *+,-'+%
!"#$% ! "#$%&'()#* #+ ,-. )($/0&1(#* 2(13 134 5#''4)%#*6(*7 $4&)/'4$4*1)
!"!#$%&$'
89: ;3<&'&=4>? ;@? A#)53411& B@A@? C&1&(004? C@ DEEF -4'#6=*&$(5 64)(7* #+ $(5'# &(' >43(504) +#' >4'1(5&0 G(731@ <#3&$*= #> ?,&1&*>; ! 9H9IJ9HDK
8D: L(M#*? A@N@ 9OFF P$%'#>4$4*1) 1# 1(01J'#1#' %4'+#'$&*54 13'#/73 %&))(>4 Q&064 12()1 5#*1'#0@ @?A? B.1C$,1*= /.D#&*$-3D !99EF8 9JO
8R: S4()3$&*? T@ DEE U40(5#%14' &4'#6=*&$(5)@ "*DG&,-%. ?.&#(H*1. A.&,.(6 $- .-,;,#$
8K: -6<(*)? "@L@ 9OOE V4)(7* #+ #%1($/$ %'#%4004')@ <#3&$*= #> I&#H3=(,#$ *$- I#J.& "# H J FD 8I: V'40&? A@ 9OFO -* &*&0=)() &*6 64)(7* )=)14$ +#' 0#2 W4=*#06) */$Q4' &('+#(0? 0#2 W4=*#06)
*/$Q4' &4'#6=*&$(5@ AH&,$%.&K.&=*%6 @.J L#&M 9J9D
8 : U4(*? C@ W@?"3#%'&? P@ DEEH U#>4' %4'+#'$&*54 #+ & $(5'# &(' >43(504 X '#1#' &1 0#2 W4=*#06) */$Q4'@ <#3&$*= #> ?D.&,1*$ N.=,1#H;.& A#1,.;O !$ DIKJD D
8H: C0&)Y/4)? B@Z@? S&[&'#>? C@ DE9D C."-; \D? - 5'#))J)451(#* &*&0=)() 1##0 +#' &*()#1'#%(5 &*6 (*3#$#74*4#/) Q4&$ )451(#*) #+ &'Q(1'&'= 74#$41'=@ P,(QB.1C$,1*=P.H#&;P,(QRP !SFE6B.1C$,1*=TR $,U.&(,;O #> V.$D*&M
8F: ]($? ^@? C'&**4'? ]@? U&*)4*? -@ A@ DE99 V4>40#%(*7 &*()#1'#%(5 Q4&$ 404$4*1 +#' 64)(7* 5#$%#J )(14 2(*6 1/'Q(*4 Q0&64)@ W$ I..-,$%( #> ;C. !F;C W$;.&$*;,#$*= "#$>.&.$1. #$ "#DH#(,;. /*;.&,*=6 <.X36 Y#&.*
8O: N(00(&$)? V@ "@ 9OOR _%1(5&0 A413#6) (* .*7(*44'(*7 A41'#0#7=@ "C*HD*$ *$- N*==
89E: ,04$(*7? T@ -@? T#'1#* ;@ 9OOF A4&)/'4$4*1 #+ W#1#'5'&+1 C0&64 V4+#'$&1(#* `)(*7 Z'#a451(#* A#('4 P*14'+4'#$41'=@ I..-,$%( #> ;C. BC,&- W$;.&$*;,#$*= "#$>.&.$1. #$ K,G&*;,#$ /.*(3&.D.$;( GO Z*(.& B.1C$,23.( [ ?-U*$1.( *$- ?HH=,1*;,#$(6 AIW\];C. W$;.&$*;,#$*= A#1,.;O >#& ^H;,1*= \$%,R $..&,$%6 ?$1#$*6 W;*=O I9KJIDH
899: ;53$(61? ^@? ^=)#*? B@? T&0&*/0()? ]@ DEER ,/00J,(406 V=*&$(5 V()%0&54$4*1 &*6 ;1'&(* A4&)/J '4$4*1 `)(*7 -6>&*546 RV P$&74 "#''40&1(#* Z3#1#7'&$$41'= X Z&'1 9@ \5H.&,D.$;*= B.1C$,23.( $% KHJIE
89D: A(53&40? ;@? S&2)#*? B&=&*1? ;@ DE99 A4&)/'4$4*1 #+ V4+#'$&1(#* #+ W#1&1(*7 C0&64) `)(*7 V(7(1&0 P$&74 "#''40&1(#*@ E $- ?W??_?A/\_?A"\_?NA_?A" A;&31;3&.(6 A;&31;3&*= VO$*D,1( *$- /*;.&,*=( "#$>.&.$1.6 V.$U.&6 "#=#&*-# &'&& $#""(")%* 9J9I