1
DANH MUC CAC
K^
HIEU
0
a Toe do
am
thanh trong dong
khong
nhieu, (m/s).
b
D6
dai dac
tnmg,
(m).
b^.3^
Day
eung
khi
dong trung binh
cua
canh,
(m).
bjjj
Day cung
ddu
mtit canh,
(m).
b Day eung g6'c
cua
canh,
(N/m^).
Y Luc nang eiia
khi
cu
bay,
(N).
X
Luc can
chinh
dien eiia
khi
cu
bay,
(N).
Y
c
= —
H6 sd lire
nang eiia canh
khi
cu
bay.
^^
Cy
Dao ham
h6
s6'
luc
nang theo goe
t^n
=
i-;
^ zz —
Toa do khong thur nguyen cua mot
diem,
b b b ' *
a Goe
t&i,
(do).
p
X
r.
r
=
o
A
=
Tl
=
m
J'
' s
K
2
Goe
trucrt
canh,
(d6).
Goe mui
tSn
He true
toa d6
8
1.2
Canh eiia
khi
cu bay, cac tham so hinh hoc 9
1.3 Cac dac
tinh
khi
dong eiia canh
khi
cu bay 12
1.4
T6ng
quan cac
phuofng
phap xac dinh dac
tinh
khi
dong 14
cua canh
khi
cu bay trong dong
khi
dudri
am
1.4.1
Phudng
phap
AM
2.1
Trudng
van toe cam
ling
boi
doan xoay 18
2.2
van
toe cam
utig
bcri
he xoay xien hinh
mong
ngUa 21
2.3
van
toe cam
ling
bcri
xoay xien hinh mong ngua trong 27
cac
trudng
hdp
rieng
2.3.1
van
toe cam
utig
bcri he xoay xien hinh mong ngua 27
canh eo sai
hihi
han 31
3.2 Bai toan xac dinh cac dac
tinh khi
dong cua canh 34
3.3
Di^u ki6n bi6n
35
3.4
M6 hinh
xoay 38
3.5
H^
phudng
trinh xac dinh cudng
d6
eiia eae xoay 44
3.6 Xac dinh eae dac
tinh khi
dong cua canh 46
3.7 Cac dac
tinh khi
dong eiia canh trong dong
khi chiu
nen 47
dudfi
am
CHUONG
IV:
thdi khi
dong 59
duciamOT-l
4.3.1 M6 ta
thi
nghiem 59
4.3.2
Che'
d6 thdi
va cac ket qua do 60
4.4 Xac dinh va khao sat cac dac
tinh khi
dong cua canh 64
4.4.1 Su phan bo he so dao ham
C "^
theo sai canh
^^
4.4.2 Su phan bo ap sua't theo day cung cua canh 66
5
4.4.3 Su phu
thu6c
cac dao ham
khi d6ng
vao hinh dang 69
^
cua canh
4.4.4 Su phu thuoc eae dao ham
khi
dong vao so M 80
•K^TLUAN
bao noi chung va vol cac
phSn tii
cua
khi
cu bay noi rieng.
Cac luc
tijr
dong
khi
tac dung
len
b^
mat cua eae
ph^n tijf khi
cu bay nhu:
canh, duoi, than khong
nhihig ehi
phu thuoc vao
che
do bay dac trung bcri cac
tham so nhu: van
t6e,
do cao bay va cac goe xac dinh vi
tri eiia khi
cu bay so
vcri
dong
khi
ma eon phu thuoc vao hinh dang ben ngoai,
kich
vi
thd',
xu
hudtig
hoan thien va cai tien cac dac
tinh khi
dong cua canh
a
mot dai
r6ng thu6e
cac
ehS'
do bay,
thucfng
xua't phat
tir
nhung ket qua nghien curu ve
sir
thay d6i hinh dang ben ngoai cua canh.
Lich six
phat
tri^n
eiia nganh hang khong cho tha'y rang eiing
vofi
su ra
dori
cua cac the he dong
ecf
hang khong tien tien, su thay
ddi
sir
sang tao cua cac nha bac hoc ve cac
phuong
phap
tinh
toan va
phuong
phap
xijf
ly cac so lieu thuc nghiem da giai quyet thanh cong nhieu bai
toan ve hop ly va toi
uu
hoa hinh dang ben ngoai cua canh va cac phan tu khac
eiia
khi
cu bay.
Ngay nay, trong
linh
vue nghien curu
khi
dong cac khi cu bay, mot hudng
di mdi da va dang hinh thanh, do la thuc nghiem tinh toan so tren eo so cac mo
7
hinh
toan hoc
vdi
su trcr giup hieu qua cua cac thiet bi cong nghe thong tin.
Hudng
nghidn
curu nay cho phep trong mot khoang
phap nay, be mat khi cu bay
dUde
thay the bang nhieu eae panen
phing, hinh
chiJ
nhat.
Viee
tinh toan
dude
tien hanh doi
vdri
timg panen sau do
t6ng
hofp
lai.
PhUdng
phap nay thuat toan
phlJc
tap , do chinh xac khong cao ma
khS'i lucmg
tinh toan lai qua 1cm.
- Di don gian hoa trong qua trinh tinh toan, mo hinh tinh toan doi vofi khi
cu bay cd thi tieh
duoe
thay the bang mo hinh mat nang mong. Doi vdi
loai
mo
hinh nay ton tai ph6 bien eo eae phucfng phap nhu:
Phuong
phap
Chuofng
I:
Tdng
quan cac phucfng phap xac dinh dac tinh khi dong cua canh
trong dong khi
dudfi
am.
Chucmg
II:
Trudfng van
toe cam
utig
bcri cac he xoay trong dong khi dudi am.
Chuc^g
III: Phucfng phap xoay rcri rac xac dinh cac dinh dac tinh khi dong cua
canh trong dong khi dudi am.
Chucmg
IV: Ket qua tinh toan va khao sat cac dac tinh khi dong cua canh khi cu
bay.
Tac gia luan van xin
chan
thanh bay to long biet ofn
sau sac
den cac thay
va cac dong nghiep da tan tinh giup dd tac gia hoan thanh cac noi dung cua luan
van nay.
8
CHirONG
I
T6NG
true
toa do xac dinh cac dac tinh khi dong canh khi cu
bay.
Ky hieu:
U^
- Vec tcf van toe tuyet doi, goe toa do O,
Q
- Vec tcr van toe cua
canh quay quanh cac true toa do. Cac thong so chuyen dong tuyet doi cua canh
tren cac true eiia he
true
toa do dong OXYZ:
Uo =
iU„,+jU„^
+
kU„,
(11)
Q
= i
Q,
+
jQy
+
kQ,
Vi tri
eiia
canh ddi vdi dong chay bao dac tnmg bang eae goe: Goe ta'n a
va goe trucrt
p.
Cac thanh
u„,
=
u.
a
=
^^
P
=
u,
u.
(1.3)
1.2. Canh cua
khf
cu bay, cac tham so
hinh
hoc:
Canh cua
khi
cu bay
phd
bien la canh doi
xiing
tren
binh
do c6 mep canh
tnrdc
va sau la nhihig doan
thSng
vdi
goe
va goe mui ten
mep canh
trude
Xo-
S
-^
(1.4)
Doi vdi canh cd mep canh trude la doan
thang,
khi thay
d6i
cac tham so
X,
T],
Xo
s^
nhan
duoc
nhieu dang canh tren binh do khac
nhau.
Ky hieu b' - Day cung canh cua tie't dien Z theo sai canh va
Xe
gdc mui ten
eiia
ducmg
thang chia day cung theo
ti le
9 tren hinh
1.2a
Dai lucfng
khiic.
Cac diem gay
eiia mep canh chia canh thanh cac viing 8=1,2 n (tren hinh
1.2b).
Gia su cac
tham
s6
dac trung trong moi vung
Sj
da biet:
Tis=
^;tgXoe;i>^
(1.7)
6
day:
U
- Sai cua vung canh
e^,
b'^
- Day cung canh
a
diem gay. Khi dd:
S=^Z(—+ —K)
(1.8)
'- '
(—-^)(^-l)
(1.9)
tgXec=tgXoe-
2^(-L-±)l
(1.10)
- Day cung khi dong trung binh ky hieu
(b^a^) la
day cung eiia canh thuc
hien phep trung binh hoa theo dien
tieh
canh:
b,,,=A|b=dz
(1.13)
L2
Xcax=^
jxb
dz (1.14)
S :
12
d
day:
X(au^
- Toa do theo true OX
di^m ddu
eiia day cung khi dong
trung binh.
D6i vdi dang canh
dd'i xihig
tren binh do vdi cac mep canh la dudng thing
•c6:
^ = ^
—1_
b,
3'
ri(ri+l)'
xac dinh
sir
tac dung tucfng
h6 giira
canh vdi khong khi trong cac
ehuye'n
dong cu the' cua
canh. Dac tinh khi dong cho phep xac dinh cac luc va momen khi tac dung len
canh eung nhu cac moi quan he phu thuoc giua
chiing
vdi nhau, giua
chiing
vdi
hinh dang cac tham so hinh hoc, cac tham so chuyen dong cua canh. Dac tinh
khi dong eiia canh
th^
hien qua:
- Cac luc va momen khi dong:
lire
can X, luc nang Y, luc canh Z va
momen
lieng
M^^,
momen hudng
My
va momen
chiic
ngdc
M^.
- Cac he so khi dong tucfng
13
Cac he so khi dong khong
thiJ
nguyen cd the bieu thi qua cac he
so
dao
ham khi
d6ng
nhu sau:
i=I
n
(1.14)
(1.14')
i=l
6
day:
c?'
=
5c.
;m?'
=
9m
5qi dq\
- Quan he
giffa
cac he so khi dong khong
thu*
nguyen nhu: chat
lugng
khi
mach M
U.
00
va so Reynol Re =
Uo.b
Luc nang Y, momen doc
M^
va momen ngang
M^
sinh ra do cd do chenh
ap
giiJa
mat dudi va mat tren canh (AP =
P^
-
Px^).
Cac bieu
thiic
d^
tinh luc nang
va cac momen tren hinh 1.3 la:
Y
14
Hinh 1,3: Sa do tinh luc va cac momen canh khi cu bay,
Y= JJ
APdxdz (1.17)
h
M^=
Jj
APxdxdz (1.18)
0.
b
2
l/2b?
m,
=-2^
J
jAP?d?d!:
(1.19)
S
0.
b
2
l'2bi:
m,
=-2^
J
JAPCdgdC
(1.20)
O day:
^o,
^1
toa do khong
thu"
nguyen eiia diem thuoc mep trude va sau
c^nh.
1.4. Tong quan cac
phir0ng
phap xac dinh dac tinh khi dong cua canh khi
cu bay trong dong khi
hdu
het cac van de cua bai toan chay bao dat ra.
Tuy nhien, doi vdi bai toan chay bao cac vat cd hinh dang khong gian
phiic
tap,
con
nhi^u
v^n
de chua giai quyet. Vi du d so' Reynoil
Idn
tUcfng
umg
vdi dieu
kien dong khi ciia canh va cac khi cu bay khi
chuyen
dong,
d^
xac dinh cac dac
tinh khi dong, thuc
te'
cho tha'y khong
e^n
doi hoi phai giai bai toan chay bao vat
trong dieu kien khi thuc ma
chi edn
giai bai toan chay bao vat (canh) tren
cof
sd
m6 hinh ciia
chSii
lire
nang
ciia
canh va khi cu bay.
Phuong
phap bien
d6i
bao giae cua Giukovsky da giai quye't bai toan chay
bao cac profil canh dcfn gian, cac bai toan
luong
phut trong chat khi ly tudng
khdng
chiu nen. Hudng chung va
ph6
bien de giai cac bai toan chay bao vat
trong dong chat khf khong chiu nen la quan niem thay
the'
dudng thang hoac mat
phang bao quanh vat bang cac dac trUng trong thuy khi dong hoc, khi dd bai toan
chay bao dua ve giai cac phucfng trinh tieh phan.
Ddi vdi bai toan chay bao canh cd sai huu han, do gian dai canh X nhd.
Hien tucfng tach dong va chay tran tren cac mep canh anh hudng ro ret den dac
tinh ciia dong chay bao. Mo hinh dong chay bao ddi vdi trudng hop nay
vln
la
•
16
dong the ne'u mat canh ducfe tiep tue la mot mat phang xoay tu do (eae dai xoay
xu^t
phat tir mep sau va
hffu
han trong dong khi
vudt
am.
1.4.2
Phuong
phap thuc nghiem
Phudng phap thuc nghiem cd vai trd quan trong trong qua trinh tie'p can,
nhan biet
v^
ban cha't cua hien tUdng va cac dac trung cua dac tinh khi dong cua
khi cu bay. Mae du phucfng phap tinh toan giai tieh va phudng phap sd da dat
dude
nhi^u
thanh tuu, nhung phUdng phap thuc nghiem
d^
nghien
cihi,
khao sat
eae dac tinh khi dong cua canh va khi cu bay
vln
la nhu
cSu cSn
thiet
nhlm
cung
ca'p
nhiJng
ket qua de tham dinh cac phudng phap tinh toan ly thuyet eung nhu
lam cd sd di so sanh va
• 17
1.4.3 Phuong phap vat ly khi dong:
Phudng phap vat
1^
khi
ddng
canh va cac khi cu bay nham nghien
cihi,
khao sat
cSiu
tnic dong chay bao canh va khi cu bay, cac trudng
van
tdc, ap suat,
nhiet do va mat do eiia dong khi. Phudng phap quan sat cac ph6 ciia dong chay
bao canh va khi cu bay cho phep tim
hi^u
cac qua trinh vat ly xay ra, ly giai cac
d^u
hieu dac biet, dong thdi eung
c^p
cac sd lieu
dSu
vao cho viec xay dung cac
mo hinh toan hoe eiia bai toan dat ra.
Hien nay ton tai rat
nhi^u
phudng phap
d^
quan sat
phd
ve trudng van tdc cam
umg
bdi cac he xoay khac nhau trong ddng khi dudi am. Dudi day tien hanh khao
sat, he thong nhutig ket qua nghien curu ve trudng van tdc cam ling bdi cac he
xoay trong ddng khi dudi am, dac biet dua ra nhirng
hiiu thiie
tdng quat
d^
xac
dinh cac thanh
ph^n
van toe cam umg eiia he xoay xien hinh mdng ngua.
2.1 Trudng van tdc cam umg bdi doan xoay:
Trong
th^
tieh khong khi gidi han, cd mot doan xoay
A^
A2
bat ky cd
cudng do
r+
khong ddi tren chieu dai ciia doan xoay (xem hinh 2.1).
«
Trong he
true
toa do de cac OXYZ,
diim Aj
cd toa do tUdng umg x,,
y,,
z,,
doan thang
A1A2
ky hieu la r. Theo cong
thiic
cua Bioxavara [20], van tdc cam
umg bdi doan xoay
dude
xac dinh.
W =
^
(Cos^,
+Cos^2)
(2.1)
4m
CJ
day van tdc cam umg W cd phUdng vuong gdc vdi mat phang
A1MA2,
hudng theo chieu tucfng umg vdi chieu quay cua cudng do xoay r+.
19
Ky hieu cac thanh
phin
van tdc cam
ling
W theo cac true toa do OX, OY,
OZ la Wx, Wy va Wz. Xay dung cac
bi^u thiic
di xac dinh Wx, Wy va Wz.
Hinh
2.1
Xac dinh tdc do do doan xoay cd hudng
W
cosp3.
. (2.2)
Viet phudng trinh cac canh eiia tam giae
A^
A2
M khi biet toa do cac
dinh
x
-X
y-Yi
z-z,
>
x^-x,
X -x,
XQ
—
X|
X-XQ
^2 ~ ^0
Y2-YI
y-Yi
_
Yo-Yi
Y-Yo
Y2-Y0
Z2-Z,
'
z-z,
9
(Xi-
X2)
(xi-
Xo)
+
(Yi-
y^)
(Yi-
Yo)
+
(z,-
Zj)
(z,-
ZQ);
(2.7)
A;
=
(X2-
Xi)
(Xj-
Xo)
+
(y2-
Yi)
(Y2-
yo)
+
(Z2-
Zi)
(Z2-
X,)(Y2-Y,)-
(YO-YI)(X2-
XI);
B*=
(yo-yi)(z2-Zi)
-(vzi)(Y2-yi);
C*=
(ZO-Z,)(X2-XI)-
(XO-X,)(Z2-ZI).
D^
tinh
cac thanh
ph^n
W^
,Wy
va
W^
cua vec to cam
iJng
W can thiet xac dinh
gia tri cac cosin
chi
phuong ciia phap tuyen vdi mat phang
A,A2
M. Phuong trinh
ciia mat
phSng AjA2
Mc6 dang:
AX
+
diroe
xac dinh bang phucfng
trinh
mat phang
AjA^
M di qua 3
di^m
Ai(Xj,yi,Zi);
A2(x2,y2,Z2) ^^ M(^o'yo'Zo) ^6
dang sau:
x-x,
y-y,
z-z,
^0
^i
Yo
Yi
^
X:
-X,
y y,
z
=
0.
(2.17)
y
(2.18)
21
Dong
nhlft thlic
A*=A;B*=B;C*=C
Suy ra:
VA'+B'+C'
=
VA''+B*'+C*'
(2.19)
Thay (2.3),(2.4),(2.5) vao (2.1) va ket hop
vdd
cac
bi^u thiJc (2.18),(2.19)
ta co:
W_=
B*
An (A''+B'^+C*')
r.
•2
)
r
c*
'
47r(A'^+B*^+r^)^
r
W
=
A*
4n
(A'^+B'^+C*') r
*2
-(^
+ ^)
%
so vdi
true
OZ. Khoang each
giiJa
2 xoay:
1^.
Hai xoay tu do
va xoay lien ke't nam tren
eiing
mat phang XOZ. (Xem
hinh
ve 2.2.) Cac xoay
trong he xoay
cucmg
do khong
d6i
duoc the hien:
r+=Uo
IQ
F,
f eucfng
do xoay
khong
thii
nguyen.
U,
Ai(Xi,0,Zi)
.
M(Xo,yo,Zo)
A,oo
va
A2X
•
W
=
U+V (2.23)
Trong dd U la
van
tdc cam dug do xoay lien ke't
A,A2.
Van tdc nay
duoc xac dinh theo hiiu
ihxic
(2.20); (2.21); (2.22) vdi luu y cac toa do
yj
=
y,
= 0.
Xet van tdc cam
thig
do 2 xoay tu do gay ra.
V=V,+V2
(2.24)
Ap dung cong
thiie
Bioxavara ddi vdi
sdi
xoay
A2ao
=
. '''"''
(2.26)
V(x2-Xo)'+(z2-Zo)'+yo
Tijf
day suy ra:
V.x=
0;
^2y=
- .
y^-
^"^°\.
(1
+
, ^""^ , ,
)
(2.27)
\^=
—^;
^'y°^
^
(1+
.
^°'^^
)
(2.28)
47c(y„+(z,-z„)
^-x^y+z^-z^f+yl
Bang
each
w,
=
u,
+
v,,+v
2x
(2.31)
Khai
tri^n
cu thi hiiu thurc (2.31) ta co:
W
=-^(
B
(^
+ ^))
4;r
\4*'+B*'+C*'
r,
r
(2.32)
1
*2
w,
=
-^
(__^____(AL+AL)
+^—
*
c
4;r
y^+(z,-zj^
^(1 +
Xo-Xi
-)+ , '? '° ,, (1 + ^^^^^)
y:+(z2-Zo)"
(2.34)
Bidu
thi cac gia tri
Xj
=
-
—tgx,
Zj
=
-\J2
ma
X2=YtgX.
Z2 = lo/2
(2.35)
Tinh
duoc:
A*= -l„yotgx
B*=
yo-l„
C*
=
(z,
+
1^2)
1„.
(lo/2
tg
X
+
x„)
+
1„ (lo/2
+
Zo)=
=
% tg^x
+
lo Xo
tgx +
Y + 'o^o
=
TT!^^
+
lo x„
tgx
+loZo=
2
2
2.Cos
y
L ,
lo
.
(-
+
(2.36) den (2.42) vao (2.32) nhan duoc
W. =
loY,
47r
l„(y:
+
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