GIAI BAI TOAN CQ B A N THUAT PHONG TRONG BANG Md HINH KHi£ONG SOLVING THE FUNDAMENTAL PROBLEM OF INTERIOR BALLISTICS BY USING GAS-DYNAMIC MODEL ThS.. Nguyin Quang Tii^n Hpc vien Ky t
Trang 1GIAI BAI TOAN CQ B A N THUAT PHONG
TRONG BANG Md HINH KHi£)ONG
SOLVING THE FUNDAMENTAL PROBLEM OF INTERIOR BALLISTICS BY
USING GAS-DYNAMIC MODEL
ThS Nguyin Quang Tii^n
Hpc vien Ky thuat Qum su
TOM TAT
Bdi bdo trinh bdy phuang phdp gidi bdi todn ca bdn thugt phong trong cua sung phdo bdng cdch su dung mo hinh khi dQng He phuang trinh md td cdc qud trinh thugt phong trong duac xdy difng tren ca sa ly thuyit mdi truamg lien t^ic vd dugrc gidi bang phuang phdp "hgt lan" (hay cdn duac goi la phuang phdp Davudov) Md hinh tinh todn dugc dp dung de gidi bdi todn ca bdn thugt phong trong cho phdo chong tdng nong tran 100 mm T12 vai dan duai ca EM2 Cac kit qud tinh todn dd khdng dinh tinh dung dan cua md hinh
Tu khda: Thugt phdng trong, md hinh khi dong, md hinh cd dien, phuangphdp hat l&n, dgn
du&i ca
ABSTRACT
The article describes a method of solving the fundamental problem of interior ballistics by using gas-dynamic model The system of equations describing the interior ballistics processes in gun barrels is built on the basis of continuum theory and solved hy using the method of "large particles" (also known as Davydov's method) The calculation model is applied to solve the fundamental problem of interior ballistics for Soviet smoothbore 100-mm anti-tank gun T12 with BM~2 APFSDS projectile Calculated result gives us confidence in the correctness of the model
Keywords: Interior ballistics, gas-dynamic model, the method of "largeparticles", APFSDS
projectile, the classical model
1 DAT VAN DE cho ket qud Idid chinh xac ddi vdi nhimg loai
dan cd so tdc khdng Idn lam, tuy nhien ddi vdi Viec giai bdi todn ca ban thudt phdng nhimg loai dan cd so tdc Idn thi md hmh nay Uong (TPT) cd y nghia quan trpng Uong thidt cho sai sd tuong ddi 1cm so vdi thuc nghiem
kd, cai tien, khai tiidc va su dung cac loai vii Nguyen nhdn la md hinh cd didn bd qua nhiSu khi CO ndng Hien nay, vdn sii dung md hinh hien tupng tiiang ddi quan trpng xdy ra ti-ong
cd didn (md hmh nhiet dgng) de giai bdi ca bdn qud tiinh ban Dd gidi quyet vdn dd ndy hien TPT Thuc td dd chi ra ring, md hmh cd didn nay ngudi ta su dung md hinh khi ddng
ISSN 0866 - 7056
TAP CHI CO KHl VIET NAM, Sd 1+2 nam 2017
Trang 22 HE PHXrONG TRINH VI P H A N CUABAI
TOAN CO BAN TPT C t A SUNG-PHAO
Bdn chat cua phuang phap nay la su
dung ly thuyet mdi trudng lien tuc dd md td su
bidn ddi cua cdc tham s6 khi thudc trong long
ndng BB thidt lap he phucmg trinh toan hpc
md ta hien tugng ban trong md hinh ktii ddng
ta ch^ nhan mgt so gid thidt nhu sau:
- Cac tiiam sd ciia khi thudc cd gia tri
nhu nhau tai mgi diem cua ciing mgt mat cat
long ndng;
- Thanh ndng dugc coi la cimg tuydt ddi;
- Thudc phdng khdng nen dugc;
- Khi thudc cd the ndn dugc, bd qua luc
quan tinh vd luc cdn nhdt cua Idii thudc;
- Bd qua cac phdn ijmg hda nhiet xdy ra
Uong qua trinh tao tiianh, dan nd vd ngudi khi
thudc;
- Thdnh phdn khi thudc, luc thudc phdng,
hang sd chdt khi va chi sd miz doan nhiet coi
nhu khdng ddi trong toan bd thai gian xdy ra
hidn tugng bdn
Gid su rang khdng khi va cac sdn pham
chay Id mdt hdn hgp ddng nhdt Khi dd, su
bien ddi ciia ddng khi thudc trong Idng ndng
dugc md td bdi he phuang trinh vi phan sau:
- Phuang trinh bdo toan khdi lugng:
dt + div(pW) = 0;
- Phuong trinh bao toan dong luong:
^^^^divipu-W)+^ = 0;
dt dx
- Phuang trinh bdo todn ndng lugng:
d{pE)^
dt +• divipEW) + div{pW) = 0;
0 e tim dp suat khi thudc ta sii dung
jdnrang liinh trang Ihai dudi dang p = £p(k-\), trong d6£ = E-u 12 la ndi nang rieng cua
chat khi
Cdc phuong trinh md ta qua trinh ehdy
va tao khi cua thudc phong:
dz _ p
Cac phuang trinh md ta chuyen ddng cua dan:
dl^_ dv _Sp
dt ' dt tpm
3 FHirONG PHAP "HAT LCfN" DE GIAI
HE PHlTONG TRINH VI P H A N CUA BAI TOANCOBANTPT
Trong phucmg phap nay mdi trudng lien tuc dugc mo hinh hda bdi mpt hd cdc hat Idn, cdc hat nay tai thdi diem ddu tien trimg vdi cac
d mang cua ludi Ole (hinh 1)
rU'7""T
(Say ' - 6 m^g (W- "ff^I"
(aw
Hinh 1 Cdu true ludi tinh todn Ole
Qua trinh tinh toan gdm nhieu budc lap
di lap lai ve thdi gian Mdi budc tinh bao gdm
ba giai doan nhu sau: ^
ISSN 0866 - 7056
Trang 31) Giai doan Ole: Trong giai doan nay,
ta se bd qua cdc hieu img lien quan tdi su dich
chuyen ciia d mang (mdi trudng vat chdt dugc
coi nhu tam thdi dung j^en), chi tinh tdi cac
liỉu ling tang tdc ciia chat khi nhd vao luc ap
suat Trong giai doan nay se xac dinh cac gia
tri trung gian ciia cac tham sd cdn tim ^{U,E)
cho mdi d mang:
r.n _ ,,n pf+\l2 'p"-\n , Af
Ạ p
-O day, nhung dai luong voi chi so khong
nguyen la gia tri cua cac tham s6 tai bien cac
6 mang:
""+""+1 n uf+uU
"Mn^ ^"^'; ""-1/2 = ^ ' ' ;
2) Giai doan Lagrange: Trong giai doan
nay se tmh toan cac dong v§t chit di chuySn
qua bien cac 6 mang Ole:
P'^MIlSAt, khiS?n,2>0,
.A"+1«J°+1/2'5Ă, khiiỉ^,/2 <0
3) Giai doan cuoi cung: Trong giai doan
nay xay ra sy phln ph6i 1^ vat chit, dgng
lu(mg va nang luong trong khong gian tren co
so cic dinh luat bao toan d6i vol m6i 6 mang
noi rieng va cho toan bp he noi chung KSt qua
cuoi cung cua giai doan nay la gia tri eia cac
tham sa cua dong tfii thai diSm mm cho m6i o
mang yr(p,u,E,p)
Co sd ii tinh toan trong giai doan nay la
cac dinh lutt bao toan kh6i lugng, dgng lugng
va nang lugng toan phin Cac dinh luat bao
toan nay dugc vi6t duoi dang sai phln cho
timg 6 mang:
Af"+i=M"+2;AM|;+AM3„
d day AMj - Kh6i lugng khi dich
chuyen qua mgt bien nao do ciia 6 mang trong khoang thai gian At,XAWj- T6ng kh6i lugng khi dich chuyen qua tit ca cac Men cua 6
mang Cac dai lugng Alf va AÊ dugc hiSu tuong tu nhu d6i vai AM^ Cac dai lugng voi
ky hieu "ch" la khoi lugng khi, dgng lugng va nang lugng ma 6 mang nhan dugc tu su chiy ciia thuoc phong Khi tinh toan nang lugng khi thuoc trong cac 6 m ^ g ta can phai tinh toi ca cong ma khi thuoc da thirc hien d6 dich chuyin dan trong long nong, cong nay dugc ky hieu 11
AỆ Ta nhin dugc cac biju thiic ii xac dinh
gia tri cudi cung cua cac tham s6 cua dong khi t^ thoi diSm mai t"*' = t" + At co dang nhu sau:
^«+i
' SAx " Six
r - t l - P, B .^tlxA*^,"-! -g'<™»i/;t(g'm;,.u-Mj
Nhu vay, ta da nhto dugc gii tri ciia cic tham s6: p (mat do), u (van tSc) va E (nang lugng toan phin) cua khi tai thai diSm t " = f + At D6 tim ap suit ta lam nhu sau:
- Trudc tien thay u va E vua tun dugc
vaobiSuthiic ê^E-ip-12 dSttoiẹ
ISSN 0866-7056
TAP CHi CO KHI VIET NAM, S6 1+2 nam 2017
Trang 4- Tidp tiieo thay p va e vao phuong trinh
ang thdi p = Ep{k -1) dd tim dp sudt
Chuydn ddng cua dan dugc giai bdng
huong phap sai phdn hiiu han theo sa do sau:
i H + i - v " pS
= •£— Tir dd suy ra:
M <pq
, « + l = v " + — ; S
tpq
Tuong ty ta ciing xac dinh dugc quang
ucmg chuyen dgng cua dan tir phuang trinh:
dl
f Theo so do sai phan huu han dang Ole ta g_ KET LUAN
- Luc Ihuoc phdng; / = 1200000 [KG.dm/kg];
- Mat do thudc phong; iJ = 1,52 [kg/dm^ ] ;
-Xunglugngtoanphan; 7^ = 1143 ATG-y/rf/K ;
- Cac dac tnmg hitih dang cua thuoc phong
;!r = l,0016; 2 = -0,0016;
KSt qua nhan dugc va so sanh vai so hSu trong bang ban thyc nghiem:
Theo bang bdn Theo tinh toan
Dp chenh lech
Ap suat trung binh Ion nhat, kG/cm^
335
3361 0,3%
Van toe dkn
nong, m/s
1575
1579 0,2%
6:1 zL=v".Suyra/"'^^=/"+v"Af
A(
Nhu vdy, chu trinh tinh todn da kdt thiic
^a dd tim dugc tat cd cdc tham sd ciia khi tiiudc
ho mgi d mang ciing nhu van tdc ciia dan tai
tdi didm t"*' =t" + At
i KIEM NGHIEM MO HINH TINH TOAN
Sii dung md hinh tmh toan vira dugc
rhih bay d tren de giai bai toan ca bdn TPT
ho phao chdng tang 100 mm T12 vd dan dudi
5 BM2 vdi cdc sd lieu ban ddu dugc lay tir tai
ieu [2]:
Didn tich tidt dien Idng ndng; s = 0,7S6[dm^];
The tich budng ddt; WQ=9,1 [dm^];
Quang duong chuyen ddng Idn nhat cua dan
rang ndng; l^ = 57 \dm\;
Trpng lugng dau dan; g = 4,35 {kgl;
Ap sudt tdng dan; p^ - 7000[i;:G / dm^ ]
Trgng lugng thudc phdng; {D = 6,7 [kg];
Ta thay rang, do chenh Idch giua kdt qua tinh toan so vdi sd lidu trong bang ban ve dp sudt trung binh Idn nhdt Id 0,3% vd vd van tdc dau ndng la 0,2% Dp chdnh Idch nay Id hodn todn chap nhdn dugc, do dd ta cd the nit ra ket luan rang md hinh khi ddng la mdt md hinh ddng tin cdy de khdo sdt bdi toan ca ban TPT cho cac h? vii khi cd ndng.'t*
Ngay nhan bai: 05/01/2017 Ngay phdn bidn: 16/02/2017
Tai lifu tham kbao:
[1] Nghiem Xuan Trinh, Nguyen Quang Lucmg;
Thugt phong trong, HQC vi$n Ky thuat QuSn su,
(2015)
[2] Nguyin Quang Luang, Tran Quoc Trinh; So li$u
VM AAi - dgn, Hpc vien Ky thuat Quan s\r, 2009
[3] A A KopojieB, EajuracTHKa paKeTHoro H CTBOJibHOro opyacHs, Bojirorpafl, 2010 [4] A BerexHH, rasoflKHaMH^ecKHe OCHOBM BHyrpeHHeii 6ajuiHCTHKH, MocKBa, 1957 [5] Ta6inmbi cTpejii.6H 1 00-MM npoTHBOTanKOBOH nymKHT12,MocKBa, 1980
ISSN 0866-7056