Ứng dụng phương pháp xoáy rời rạc để xác định và khảo sát các đặc tính khí động của cánh khí cụ bay trong dòng khí dưới âm215610

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,

(m).
I
Sai
canh,
(m).
S
Di6n tieh
cua
canh
khi
cu
bay,
(m^).
p
Mat
d6
cua
khong
khi,
(kg/m^).
p
Ap
sua't
dong
khi,
(N/m^).
q
=
^^
Dong ap,

(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

a
Cy"
Dao ham he so luc nang theo goe quay
co^
m"
Dao ham he so momen doc theo goe tan a
mf
Dao ham he so momen doc theo goe quay
co^
m^'
Dao ham he so momen ngang theo goe quay
co^
M So
Mach
cua dong khong
nhilu.
Re So Reynolds.
UQ
van
toe eiia dong khong nhieu dong, (m/s).
YV
Toe do cam umg khong
thu"
nguyen.
X, y, z Toa do cua mot
di^m,
(m).
^
=_;
y]

=
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

canh, (do).
Cudng
do eiia xoay, (mVs).
Cudng do khong
thii
nguyer
The van toe, (mVs).
Do gian dai eiia canh.
D6
that eiia canh.
3
MUCLUC
DANH MUC CAC KY HIEU 1
MUC LUC 3
M6DAU
6
CHUONG
I:
TONG
QUAN
CAC
PHUONG
PHAP
XAC
DEMH
DAC 8
TINH KHI DONG CUA CANH TRONG DONG
DUCtt
AM
1.1

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

tinh
toan
ly
thuyd't
14
1.4.2
Phudng
phap
thirc
nghiem 16
1.4.3
Phuong
phap vat ly
khi
dong
17
CHUtJNG
H:
TRUONG
VAN
TOC
CAM
UNG
Bdl
CAC
HE
XOAY
18
TRONG DONG KHI
DUCil

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

khi goe
x=0
2.3.2 Van toe cam
utig
bdi
he xoay xien hinh mong ngua 28
khi goe
X'^O
, y=0
• 4
2.4 Van
tdc
cam
ung
bcri mat
phang
xoay 29
CHlTONG
m:
PHUONG
PHAP XOAY
RClI
RAC XAC DINH DAC
31
TINH KHI DONG CUA CANH KHI CU BAY TRONG DONG KHI
f.
A
DUOIAM
3.1 Dinh ly Giukovsky
cho phSn tijf

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:

KET
QUA TINH TOAN VA KHAO SAT CAC DAC 50
TINH KHI DONG CUA CANH
6
TOC Dp
DU6l
AM
4.1
Gidri
thieu
ehuong
trinh xac dinh cac dao ham
khi
dong 50
eiia canh
4.2
Ki^m nghiSm
do hoi tu va do
chinh
xac 51
4.2.1
Dohoitu
51
4.2.2 Do chinh xac 57
4.3 So sanh
vdi
ket qua
thi nghiSm
trong
6'ng

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

.83
TAI
LIEU THAM KHAO 85
6
MCJDAU
Su ra
d5i
va nhip do phat
tri^n
manh me cua nganh ky thuat Hang khong
lu6n gan
liin vdi nhflng
thanh tuu eiia
Imh
vue
khi
dong hoc,
chuydn
nghien curu
cac qui
luat ehuy^n
dong cua
eh^t khi
va su tac dung
tudng
tac giua dong
khi vdfi
*
vat
chay

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

thude cua
timg
phan
tir
cung nhu
sir
phoi
tri
chinh trong so do
e^u
thanh
khi
cu bay.
Canh cua
khi
eu bay bao gom canh nang va cac canh dieu
khi^n.
Giong
nhu
6 khi
cu bay, hinh dang eiia canh tren binh do cung la mot trong cac yeu to
anh
hudng cd
ban den cac dac
tinh khi d6ng
cua canh
6
cac che
d6
bay. Chinh

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

hinh dang ben ngoai
cua canh
tir
canh
diip
den canh
dofn
c6 do gian dai
Idn,
tien den canh c6 goe mui
ten
Icfn,
do gian dai nho va cuoi cung canh eo hinh dang
phiic
tap, thay ddi hinh
hoc trong khi bay da lam thay ddi
tiTng budfc
ve chat eae dac
tinh khi
dong cua
canh noi rieng va cua
khi
cu bay noi chung.
Nhihig thanh tuu
eiia llnh
vuc nghien
eun khi
dong ly thuyet va thuc
nghidm,
cu the

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

thcri
gian
ngan
eo
th^
tinh
toan
m6t s6 ludng
lorn cac
phucmg
an
thig't
ke khi dong khi cu bay. Cac
phucfng
•phap
dUde sijf
dung
phd
bien trong thuc
nghiem
so hien nay do la:
- Doi
vcfi
mo hinh khi cu bay c6
th^
tieh,
thu&ng diing
phucfng phap panen.
Theo
phudng

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

phSn
tu huu han
[16],
phuong
phap sai phan
hiJu
han [6],
phuong
phap xoay rcri
rac
[10],
[11],
[12],
[13], [14]. Trong cac phuomg phap neu tren , phucfng phap xoay
r5i
rac la
phuofng phap
duoe suf
dung rong rai, c6 hieu qua va do chinh xac cao. De tai cua
luan
van
ufng
dung phuofng phap xoay rcri rac va
sijf
dung may tinh di xac dinh va
khao sat eae dac tinh khi dong cua canh trong moi quan he phu thuoc vofi hinh
dang ben ngoai eiia no
d
cac toe do duori am. •
Luan van gom:

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

QUAN
CAC
PHUONG PHAP XAC DINH DAC TINH
KHI DONG CUA CANH TRONG DONG
DUOl
AM
I
1.1. He
true
toa
dp:
Nghien
cihi
cac loai canh cua khi cu bay, thudng su dung he true toa do
lien ket hinh 1.1.
He
true toa do OXYZ cd true OX hudng theo
chieu ehuye'n
dong eiia canh, true OY
nlm
trong mat phang doi
xiing
cua canh, true OZ hudng
theo
nira
canh phai.
My>0
Hinh
1.1:
He

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

ph^n
van toe
U^
lien he vdi goe
tifn
a va goe
trugt
p:
Uox =
U^,
cos a cos
p
U„y
= -
U„
sin a cos
P
(1.2)
U,,
= -U„sinp
Khi xet bai toan chay bao canh eae khi cu bay trong khuon kh6 tuye'n tinh thi
mdi lien he
giiia
eae thanh
ph^n van
toe cua
U^
vdi cac goe a va
P
cd dang:

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

mui ten khong
d6i
(hinh
1.2a)
hoac la
nhihig
dudng thang
gay
khiic
vdi
goe
miii ten thay d6i (hinh 1.2 b), hoac la
nhiftig dudng
cong (hinh 1.2 c).
X
Hinh 1.2a
10
Hinh 1.2b Hinh 1.2c
Hinh 1.2. Cac dang canh tren binh do.
Ky hieu: 1 - sai canh, bg- Day cung goe canh,
b^,^
- Day cung
miit
canh,
Xi
- Gdc mui ten mep canh sau canh, S - Dien tieh canh. Dang canh tren binh do
xac dinh bang cac tham so dac trUng: Do gian dai
X,
do that
r\

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

b'
va
tgXo
xac dinh bang cac bieu
thiic:
b'
=
b^
•
Z(tgXo-tgXi)
b'
Hoac:
=
i-z(i-n)
(1.5)
(1.5')
Hoac:
tgXe=tgXo-2-^(1—)9
;z
=
tgXe=tg)Co-
—
(^)
X
r\-\-\
- 2z
(1.6)
(1.6)
11
Canh eiia khi cu bay cd mep trude va sau la dudng thing gay

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)

Canh cua khi cu bay cd mep trude canh la dudng cong xac dinh bang
phucfng trinh:
Xo(z>^
;b(i).^
(1.11)
thi:
tgxe=^(^-e-^
(1.12)
1 d(z) d(z)
*
Ngoai
nhihig
tham so hinh hoc
neu
tren con cd cac tham so dac trung khac
phue
vu cho qua trinh khao sat cac dac tinh khi dong cua canh nhu:
- Tam ap sua't ky hieu toa do theo true OX la:
x^^
- diem dat eiia t6ng hcfp
lire
khi dong len canh.
- Tieu cu khi dong ky hieu toa do theo true OX la:
Xp
- diem ma momen
doc
mjj
khong phu thuoc vao gdc ta'n a khi van toe
U^
khong d6i.

- 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)'

^cax ^^tgXo(Y]+2)
b_
12
n
(1.15)
(1.16)
L3.
Cac dac
tinh khi
dong
ciia
canh khi cu bay.
Cac tham so dac trung cho
chuydn
dong
diimg
(khong phj thuoc vao thdi
gian) cua canh vdi tdc do
U^
dudi am nhu trong 1.1 la:
q^
=
(a,p,(Ox,
cOy,
(o^)
1=1,2 n
Dac tinh khi
d6ng
cua canh khi cu bay la tap hop cac dai
ludng

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

ling
khong
thii
nguyen :
c^^,
Cy,
c^,
m^^,
my,
m^.
Moi lien he giua cac luc, momen khi dong vdi cac he so khong
thii
nguyen
tucfng
utig:
X=c,^S;M,=m,^S.b
Y =c
§-^S
•
Y
Cy
^ ^
,
Z
=
c^S;
M,=my^^
S.b
M,=m,^^S.b
(1.13)

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

d6ng
va tieu cu khi dong
Xp:
K=
^
;(1.15)
c
X
m
Xp =
(1.16)
Khac vdi cac luc va momen, cac he so khi dong khong thur nguyen khong
phu thuoc vao
d6ng
ap
(-—-
) va kich thude hinh hoe eiia canh (S, b, 1) ma lai
phu
thu6c
vao hinh dang eiia canh tren binh do (x,
A,,
r\
). Cac tham
s6'
chuyen
dong (a,
P,
0)^,
co ,
co^) sd

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)

M^=
JJ
APzdxdz (1.19)
S t6ng dien
tieh
eiia canh.
Sijf
dung do chenh ap va eae toa do
khdng thiJ
nguyen:
AP -
^' 'f
2
^=b^
^=^
^
b'
- 2z
z = —
I
Khi dd he so luc nang va eae he so momen doc va ngang ducfe xac dinh:
b
2
l/2b5|
S
=2^
J
jAPd?d!:
(1.18)
S

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

dirdi
am.
Xac dinh, khao sat cac dac tinh khi dong cua khi cu bay noi chung va ciia
canh noi rieng cd cac phucfng phap nghien
cihi
chinh sau:
1.4.1
Phirong
phap tinh toan ly thuyet
15
Bao gom phucfng phap giai tieh va phucfng phap so. Rieng phucfng phap
s6 trong nhung nam gin day vdi su phat
tri^n
nhanh va manh cua
Imh
vue cong
nghe thong tin, ket hop vdi may tinh da hinh thanh phucfng phap
thix
nghiem so
«
[15] trong nghien
euti
khao sat eae dac tinh khi dong cua canh va khi cu bay.
Bai toan chay bao cac vat trong moi trudng khi thuc (khi cd do nhdt) tren
cd sd cac mo hinh toan hoe ve
Idp
bien roi, cac phucfng phap so va ket hcfp vdi
may tinh cd
th^
giai quyet ducfe

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

khi hoac
cha^t
long ly tudng va
Idp
bien. Bai toan chay bao vat
(canh)
CO
hinh dang khong gian
phiJc
tap,
eiing
vdi viec
lira
chon cac hinh dang
t6'i uu, cac
phuong
phap tinh toan ly thuyet cd xu hudng hoan thien doi vdi cac
mo hinh toan hoe.
Gia thuyet ve dong chay the' va ve
sir
thay
the*
vat chay bao bang cac dac
trung thuy khi dong (xoay, nguon, hut, ludng cue ) la nhirng giai phap hieu qua
de'
hoan thien mo hinh dong chay bao chat khi hoac chat long ly tudng. Mo
hinh
chay bao cd
luu
sd van tdc ciia Giukovsky, Traplugin lam ro co che tao ra

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

miit
canh tien
v^
v6 cue).
Phucfng phap sd
d^
giai bai toan chay bao cac loai canh ciia khi cu bay cd
hinh dang
phufc
tap va trong eae t6 hcfp
giiJa
canh vdi cac
phin tiJf
khac eiia khi cu
bay la phucfng phap xoay rdi rac [10 ] ,[11],[12],[16].
Ph^n Idn
mo hinh toan hoc trong cac phucfng phap tinh toan ly thuyet
thudng
dUde
tuye'n tinh hoa
d^
cd
nhutig
ket qua giai tieh. Ngoai ra eon nhan
tha^y
rang tuyen tinh hoa cac bai toan chay bao khi cd nhirng nhieu dong nhd
trong dong khi eon tao ra cd sd
d^
xac dinh cac dac tinh khi dong ciia canh cd
sai

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

lira
chon cac ke't qua nhan dudc trong qua trinh nghiep
cihi
khao sat.
Phudng phap thuc nghiem
phSn Idn dude tie'n
hanh tren cac mo hinh trong
cac dng th6i khi dong cd cac kha nang dieu chinh dUdc mot sd tham sd cua dong
khi nhu van tdc, mat do
Nghien
cuti
khao sat cac dac tinh khi dong ciia canh va khi cu bay tren cac
mo hinh eiia vat thuc, ddi hoi phai dap
utig
cac tieu chuan cua ly thuyet dong
dang nhu: ve hinh hoe, dong hoc va dong
lire
hoc. Thuc te cho tha'y rang dam
bao tieu
chu^n
dong
lire
hoc mot each tuyet ddi la viec ra't khd khan. Chinh vi
vay, tuy thuoc vao ban chat ciia hien tucfng vat ly, phucfng phap thuc nghiem tren
cac md hinh chi dam bao mot each cd ban hoac mot phan nao dd cua tieu chuan
dong dang ve dong
lire
hoe ddi vdi vat chay bao kich thude thuc ma thoi.
Nhin chung xac dinh, khao sat cac dac tinh khi dong cua canh, cung nhu
cua khi cu bay bang phucmg phap thuc nghiem ddi hdi phai dau tu nhieu.

• 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

dong chay bao
canh va khi cu bay nhu: Phucfng phap khdi, phUdng phap mang chat long,
phudng phap quang hoc
18
CHl/ONG
n
TRl/CJNG
V^N
T6C
CAM
IDNG
B6I
CAC HE XOAY
TRONG DONG KHI
Dl/Cfl
AM
• -
Phucfng phap ap dung di xac dinh va khao sat cac dac tinh khi ddng cua
canh cac khi cu bay dude xay dung tren cd sd ly thuyet xoay trong ddng khi dudi
am.
Trong cac cong tnnh [10], [11], [12],
[13]
tren cd sd cong
thirc
xac dinh
van
tdc cam
dug
cua Bioxavara, cac tac gia da nghien
cihi

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,,

di^m A2
cd toa do tUdng umg
X2,
y2,
^-
Chon
di^m
M(xo, yo, zo) bat ky trong
khong gian, la
di^m
d^
tinh van tdc W cam umg bdi doan xoay
A^Aj.
Dung mat phang di qua doan thang
A1A2
va diem M. Ndi
A^,
A2
vdi diem
M. Gdc d cac
dinh Ai
va
A2
ky hieu la
cp^
va
(p2 '
khoang each
tir
diem M den

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

bat ky trong khong gian, tao ra tai cac
di^m Ian
can.
Ky hieu phap tuyen cua mat phang
A^
A2
M la OK vdi vec td ddn vi la n,
chieu dudng ciia phap tuyen
la'y
theo chieu dudng eiia xoay
7~^.
Gdc
giira
phap
tuyen n vdi cac true toa do la
P^
P2
va
P3.
Khi dd hinh chieu
ciia
vec td van tdc
cam umg W tren cac true toa do Ox, Oy, Oz xac dinh bang cac bieu thufc:
W,=
W
cospi;
Wy=
W
C0SP2;
W,=

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

ZQ
— Z]
_
z-z.
Z2-Z0
>
(2.3)
y
Tiir
(2.3) xac dinh cac
goe
<p,,
^9,
va khoang
each
r
A:
COSrp,
=
(2.4)
r.r,:
20
COS'f
r =
VA*'+B*^+C''
(2.5)
(2.6)
Vdi;
A;
=

(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-

Zo);
(2-8)
Fi
=
V(x,
-Xo)'
+(y,
-Yo)'
+(z,
-Zo)'
;
(2.9)
(2.10)
(2.11)
(2.12)
(2.13)
(2.14)
^2= V(x2
-Xo)'
+(y2
-yo)'
+(z2
-ZQ)'
;
ri2
=
V(x2-x,)'+(y2-y,)'+(z2-z,)'
;
A*=
(Xo-

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
+

BY
+
CZ
+ D =
0.
(2.15)
Khi
do:
A
cospi=
cosp2
=
COSP3
=
VA^
VA^
B
+
B^
C
+
C^
+c'
(2.16)
VA'+B'
+C'
Cac he
sd
A,B,C
trong phucfng trinh (2.15)

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

cac he so nhan duoc:
A
=
(Y2-
yi)(Zi
-
Zo)-
(Zj
-
Zi)(Y,-Yo);
"^
B
=
(Z2-
Z,)(X,-
Xo)-
(X2-
Xi)(Zi-
Zo);
«
C =
(Xj
-X,)(Y,
-YO)
-(Y2-YI)(XI-XO).
Theo
bi^u thiic
(2.19) va
bi^u thiic
(2.12),(2.13) va (2.14) nhan tha'y

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
-(^
+ ^)

•)
(2.20)
(2.21)
(2.22)
Trong
d6'
A*,B*,C*,ri,r2
duoc xac dinh theo cac
bi^u thiJc
til (2.7) den (2.14).
2.2
V$n toe
cam umg
bdi
he xoay xien
hinh
mong ngua.
Xet mot he xoay gom 1 doan xoay lien ket
AjAj
va 2 soi xoay tu do song
song vdi van
toe
Uo, xua't phat
tir
diem
d^u
va cuoi cua xoay lien ket
AjAj.
Xoay
lien ke't lech 1 goe

%
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)

r.
00
F7
(^
00
Hmh 2.2: He xoay xien hinh mong ngua
22
Xac dinh
van
toe cam umg
bdi
he xoay tai diem M trong khong gian.
Di^m
M
CO
toa do
(x^,
yo,
z^).
Van
tdc
cam
ihig
do he xoay gay ra la tdng cac
van
tdc cam
ihig
xoay lien ket
AjAj
va 2 xoay tu do

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

ta cd:
V2=
^(l
+
cos^3)
(2.25)
471
r
6
day r+: cudng do xoay va dung bang cudng do xoay lien ke't
AjA^.
r: Khoang each tir M tdi true
soi
xoay.
(Py
Gdc tao bdi
giffa
MA2
va
Ajoo-
Bie't toa do
di^m
M(\^,
yo^^o),
ta cd:
r =
VYO+(22-^0)'
(2.25)
Cos
(p3

=
. '''"''
(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

bien ddi
tuong
tu doi vdi
soi
xoay tu do
Ajoo
ta co van
tdc
cam umg.
Vu=
0;
V
=
-^
(^1
"^°^
(1
+
^"
"'^i
)
(2 29)
"
47i(y-+(z,-z„)=
4{x,-xS-^z,-z„f+yl
4;t(y„+(z,-zJ
^{x xJ'Hz zJ'+yl
Cuoi Cling
cd:
23

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

^^*^+B*^+C*^^
r,
r,
y:+(z,-z„y
*il +
hZ^).^IlZl^
y^+(z,-zj
(,
+ ^iili^)
(2.33)
r
>i*
A* A*
7-7
\V
-
^
(
/^l
•
^2
X
•
^1
^o
»
^
4;r^^*^+B-+C*^^,
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„.

tg
X
-
(Xo
+
l„/2
tg
X).
lo
=
Zo
•
lo tg
X
- Xo
•
lo
r,=
j(^tgx+xJ^+y^+(V2 +
zJ^
r.=
,&x-xj'+y„^+(L/2-zJ^
(2.36)
(2.37)
(2.38)
(2.39)
(2.40)
A,* =
lo.
tgx

(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
.
(-
+

x^sinx
+z„cosx
)
2.Cosy
Cosy
A,*
=
lo.
tgx
(lo/2
tg
X -Xo)
+
lo (lo/2
-
z„)=
(2.41)
1.
1
2.Cos
X
Cosx
24
x„sinx -z„cosx
)
(2.42)
Thay
th^
cac hiiu thiic
tir

(2.36) den (2.42) vao (2.32) nhan duoc
W. =
loY,
47r
l„(y:
+
y„Vx+(z„tgx-xJ-
/^
"
(TTT—+
x,Sinx+z,Cosx)
-i^(-A___x^Sinx-ZoCosx)
COSY
2COSY
ft
vay:
w.
=
I
COSY 2COSY
L2
, 2
tgX+x„)^+(^+zJ^+y^
'(^tgx-xJ^+(^-zJ^+y;
"\
>
Yo
4;r
yo+yotgx+(Zntgx-xJ'
r

(—-—
+
x^Sinx
+
ZoCosy)
Cosx__2Cosx Cosx
2Cosx
i-Z^r
x,Sinx-z„Cosx)
>^
(~iBx
+ ^y + (k+^of + yl j
(YtgX-xJ^+(^-zJ^+y„^
K2.43)
W = -
il r ^otg;ir-Xo
^
4;r
Jy„'
+
y^'tg'x
+
(z„tgx
- x
J'
(—i—+
x„Sinx +z„Cosx)
COSY
2COSY
'

( '
Cosy
ZCosy
x^Sinx
-z^Cosy)
J(Ytgx+xJ^+(^
+
zJ^+y;
^(^tgy-xJ^+(^-zJ^+y;
+
z.
x„+-rtgx
(1
+
0 +
yl+i^
+ ^oY
J(^tgx+xJ^+(-^
+
zJ^
+
y^
•\
-z.
x„-:rt8X
.2
.1.
(1
+
yo+(^-Zo)

'(^tgx-xj=+(|-zj=+y^
•)
(2.44)
w,
=
4;r
-
Yo tgZ
.2*_2
yo + yotgx
+(z„tgx-xj'
25
X
(r:r^—+ x„Sinx+z„Cosx)
COSY
2COSY
'
(:'
I
COSY
ZCOSY
XoSinx
-
z^Cosx)
(ftgx+x„)^+(^
+
zJ^
+
y„^
'(^tgx-xJ^+(^-zJ^+y;

Yo
y\+<k+^j
(1+
x„+ytgx
(|tgx+xJ^+(^
+
zJ^+y^
0 +
y^+(^-0^
(1
+
x„+^tgx
(^tgx-xJ^+(^-zJ^+y^
•)
Chuyen
qua toa do khong
thii
nguyen
Datr+
=
u„br;
^0=^;
Tio=^;
Co=^;
b
b
D
d
day
r

la hang sd khong ddi nao dd, b: do dai dac tnmg.
Khi dd
bidu thiic
(
2.43) viet lai thanh:
(2.45)
(2.46)
W
=
Uor
4K
llo
(^o+^;tgx+(^otgx-?o)"
'
(:
'"
Cosy
2b.CosY
+? ,Sinx +C oCosy)
>
(.
lo
^^
j
COSY
2b.Cosy
-? „Sinx -^ oCosx)
j(^.gx*«.)=*(^H.)" ;
J(5*-l.)'+(^-c.)".,;
>2.47)

^J
B\i\x
thiic
(2.44) trd thanh:
^
471
1
(_
lo
? o tgx -?
COSY
2b.COSY
(il'+il'tg'x +CotgX -?o)
+? „Sinx +C „Cosx)
'
(-^^
? „Sinx-? „Cosx)
^(^tgx.?J^.(^HJ ^
j
I
COSY
zbCosy
(^tgx-?J^+(^-?J^+r,|