NGHIEN CUU - TRAO DOI
' P H A N TiCH DONG LlTC HOC TUONG TAG ROTOR VA O TRUC
Van Thanh Ngo, Danmei Xie
Vien Co khi Dong luc, Truang Dai hoc Vii Han, Trung Qudc
TOM TAT
Trong thiit ki, che tgo rotor, mot sd tham sd cd dnh hudmg true tiep den tinh ndng dgng luc hoc cita mdy vd thuang khdng biit mdt cdch chinh xdc. Mdt trong cdc thdng so ca bdn la dnh huang cua do citng d true tdi tdc do giai hgn vd trgng thdi dao ddng rieng cua rotor. Bdi bdo tien hdnh phdn tich dao ddng cita md hinh turbine mdy phdt dien tren ca sa phuang phdp phdn tu hiru hgn. Tdc do tdi hgn vd dgng dao ddng rieng duac phdn tich dua trin ca sd thay ddi dd cung ciia d true, tit dd cho thdy do cmg d true cd dnh hudng quan trgng din trgng thdi dao ddng cua rotor.
Tir khoa: Do cimg d true; Dao ddng ngang; Tdc do tdi han; Trgng thdi dao ddng.
1. M O DAU
Trong thiet ke may quay, 6 true la mpt trong nhimg thanh phan quan trong nhat. No anh huong true tiep den hieu suat, tuoi tho va dp tin cay cua may moc. Tham chi sau khi co cSu may dugc thiet ke va van hanh, thay doi hoac sua chiia cac tham so ciia 6 true co anh huong true tidp d i n tinh nang hieu qua, tinh kinh te va hieu suit dong cua dpng CO [1]. Dp Cling ciia 6 true khong nhimg phu thupc vao thiet ke che tao ma con phu thupc vao phuang phap lap dat cua chi tilt may [2].
Bai bao nay trinh bay trang thai dao dpng ciia mo hinh may turbine may phat dien (tai Phong Thi nghiem, Truong Dai hpc Vu Han, Trung Qu6c) bang phuang phap phkn tu huu han (Finite Element Method-FEM) [3]. Kk qua tinh toan chi ra rang, toe dp toi ban trang thai dao dpng rieng cua rotor phu thupc vao su thay d6i cac tham s6 rei TAP CHi CO KHi VIET NAM, S6 3 nam
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cua 6 true. Can tnic cua turbine may phat dien dugc bao gom dgng co dien (MOT), mo hinh true quay turbine may phat dien thiiy luc 300MW voi ty le 1: 10 [4]. True quay dugc chia thanh hai phan, rotor ap suat cao va ap suat trung binh HP-IP (high pressure and intermediate pressure), rotor ap suat thap LP (low pressure) dupe lien ket voi nhau bang khop noi cung. True may dugc lap dat tren 4 6 true dugc ki hieu la Brg 1, Brg2, Brg3, Brg4. True may co tong chieu dai 2.77ni vai nhieu bac co duang kinh khac nhau duoc mo ta nhu hinh 1.
Hinh I: Md phdng he thdng true quay, 6 true ciia turbine mdy phdt diin.
2014
NGHIEN ciru-TRAODOI
2. PHAN TICH MO HINHThong thuang, phuang frinh dao dpng cua he true nhieu bac tu do dugc vilt duoi dang sau:
Mq + (QG + C)q + Kq = F(t) (I)
Trong do: M la ma tran kh6i lugng, K la ma tran dp cung, C la ma tran can, G la ma tran Gysroscopic, Cl la toe dp quay ciia true, F(t) la vec ta luc suy rgng, q la vec ta chua cac tga dp suy rgng.
2.1. Dao dong tu do
Dao dgng tu do la la dac trung dpng luc hgc CO ban ciia he thong rotor va 6 true. Doi voi dao dgng tu do (F(t)=0), phuang trinh 1 dugc viet trong khong gian trang thai nhu sau:
2.2. Tham so 6 true
C + QG M M 0
dM^
dt\qi
K 0
0 "
-M (2)
He phuong trinh vi phan bac nhat viet trong khong gian trang thai ^ = {(7^} nhu sau:
AX + BX^0(3)
Thong thuang, nghiem cua he dugc viet duoi dang:
X{t) = X,e- ("f)
Hinh 2: Md phdng d true.
Thong thuong, 6 true dugc mo phong bang ma tran dp cung va ma tran do nhatnhu hinh 2.
Hau het cac dang 6 true, moi quan he giiia tai trpng va do dich chuyen la moi quan he phi tuyen tinh va phan tich phiic tap hon rat nhieu he tuyen tinh. Tuy nhien, de don gian trong phan tich 6 true, phan tich tuyen tinh van dugc sii dung rgng rai. Vi vay, quan he giiia luc tac dung len ngong true la phu thupc vao va toe va do dich chuyen ciia ngong true ttong 6 true va dugc uac lugng theo phuang trinh sau[l,2].
(6)
Trong do, X^ Id vec ta phirc, s tri rieng (dual dgng so phuc).
Trong do: o),,,.<^d,'f,: La t§n s6 dao dgng tu do, tSn s6 dao dgng tu do c6 can, ty so can doi voi trang thai dao dgng thu i.
TAP
Trong do: f^f la cac luc dgng theo phuong X va phuong y, x,y,x,y la cac tham so dp dich chuyen va van toe ciia ngong true theo phuang x va phuong y.
2.3. Phan tich do nhay cam ciia he true Ham so tinh toan do nhay cam dugc cho boi cong thiic sau [4].
LA- AJ/Xl
LS'^^ = (7)
I ' ^YiY\ ' ^
Trong do: S^ la dp nhay cam cua tham so X ^ CHi CO KHi VIET NAM, S6 3 nam 2014 ffj\
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NGHIEN cuu-TRAO001
d6i vol tham s6 Y. Trong bai bao nay, biln X la tan s6 dao dpng tu do, biln Y la do ciing cua 6 fruc.
2.4. T6C do toi han va trang thai dao dong rieng Trang thai dao dgng rieng tai toe do tai ban CO vai fro quan frpng. No phan anh he thong dao dpng khi trang thai cpng huong dugc kich thich.
Trang thai dao dgng rieng nay dugc xac dinh boi t6c do quay ciia he true bang vai toe dp tai han, dugc tinh theo cong thuc sau [1].
[Ms^+(C + aG)s + K]u^=0 (S)
3. KET QUA TINH TOAN
3.1. Do nhay cam ciia tan s6 dao dgng rieng Do nhay cam ciia t i n s6 dao dgng rieng cua he thong true quay-6 true dugc tinh toan dira tren su thay doi do cimg ciia 6 true tir frang thai
"mem" sang frang thai "cimg". O true duoc gia thilt la d6i ximg va nam tai cac nut 10, 30,32,49 voi do Cling ban dau la k^^-k^=10''N/m. Ket qua tinh toan 4 tan so dao dgng tu do dau tien va do nhay cam doi voi su thay doi dp cimg 6 true dugc cho trong bang 1 va bang 2.
Bdng 1. Bdn tdn sd dao ddng tu do ddu tien a/Hz) phu thudc do cung d true (k^ A ^, (N/m))
I0«
20.20 26.24 35.12 71.04
2.10' 27.61 34.72 41.47 74.44
3.10' 32.49 39.45 47.67 78.29
5.10' 38.38 45.38 57.81 86.87
8.10' 42.72 50.71 69.11 100.15
10' 44.34
52.98 75.24 108.5
10"
50.97 64.01 152.7 257.3
10»
52.23 65.75 201.4 336.3
Bdng 2. Go nhgy cdm ciia bdn tdn so dao dgng tu do ddu tten phu thugc do cung d true (kxx, kyy (N/m)
10' ro.(Hz) 20.20 26.24 35.12 71.04
2.10' S%
36.74 32.31 18.08 4.78
3.10' S%
35.34 27.29 29.92 10.35
5.10' S%
54.33 45.06 63.79 32.85
8.10' S%
11.32 11.75 19.54 15.29
10'
s%
15.16 17.90 35.50 33.67
10"
S%
1.66 2.31 11.38 15.22
10»
S%
0.28 0.30 3.59 3.41
*Tdt cd cdc truang hop do nhat Idy bdng C ^2x10-^ N-s/m C ^2>^ 10^ N-s/m.
Co the thay rang, khi do cirng 6 true thay d6i tir lO^N/m den 5.10^N/m, tan so dao dgng tu do tang nhanh va do nhay cam ciia no dat d i n 54,33%. Boi vi, khi tang do ciing 6 true d i n den toan bo dp ciirng cua he thSng dugc tang len trong khi kh6i lugng ciia he thong khong thay doi. Khi dp cung h
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NGHIEN cuu-TRAO DO!
true tang cao, true quay duoc coi la bi chOt chat y ring, cac quy tich ciia tat ca cac diSm doc theo tai 6 true, vi vay tan s6 dao dong tu do se tijn true la hinh tron vi he true -6 true la mot he co tinh den gia tri cO dinh. chit ddi xung.
3.2. Su- thay do! cua t6c do toi h?n d6i vol do
cung 6 true " " ^ ^
Hinh 3: Thay ddi tdc do tai hgn Id hdm cua do cung d true.
Sir thay doi cua toe do toi han va do cimg 6 true thay doi tir lO'N/m din lO'N/m dugc chi ra nhu hinh 3. Hai trang thai tOc dp toi han dSu co do doc ve ben trai, trang thai toe dp tai han thii ba co do doc o doan giua. Nhu vay, toe dp toi han ciia he truc-6 true co the thay doi tang hoac giam. Doi voi phiin ben phai eua hinh ve, do cung eiia 6 true eo gia tri rat loTl so vai dp cirng ciia true, vi vay, thay doi dp ciing a true trong truang hpp nay eo anh huang rat it den su thay doi toe dp tai han ciia he true. Do do, eo the eoi dp cung 6 true co giai han tren doi vai su thay doi ciia toe dp tai han.
So sanh trang thai dao dpng rieng ciia ba trang thai rieng dSu tien Idii 6 true Brg4 thay doi din gia tri lO^N/m duac chi ra nhu hinh 4. Dp lan quy tich cua t4t ca cac diem mit doc theo true quay thay ddi dpc theo true. Trang thai dap dpng rieng nay phan anh trang thai dao dpng ciia he truc-6 true khi gia tri dp ciing 6 true thay doi tir
"mim" sang "cimg". T6c dp tai han co gia tri nho han khi 6 true co gia tn dp ciing thap hon. Luu TAP
Hinh 4; Hai trgng thdi dao ddng rieng ddu tien thay ddi theo do cung d true.
3.3: DS thi lien he tic do toi ban va trang thai dao dong rieng
Do thi trang thai dao dong va tie dp tai han eiia he true khi thay doi tham si do cimg cua 6 true nhu hmh 5. Co the thSy ring, khi dp ciing I true CP gia trj thjp, (10'^5.10'N/m), trang thai dap dgng rieng cp nhieu biln dli. Tai gia tri cap cua dp cimg 6 true, 6 true duge eoi nhu chit chat, trang thai dao dpng rieng thay dli rit it. Nhu vay, CO the eoi 6 true co dp ciing tuyet dli sp vai true quay.
4. MET LUAN
Su thay dli eiia do eiing I true ciia he dap dpng true quay 6 true cp thi lam thay dli tin si dao dpng tir do. Tan si dao dpng diu tien thutmg ep dp nhay cam Ion hon so vai cac tin s6 khac.
Trong tinh toan dpng lire hpe rotor, dl thi anh huang cua dp cirng I true dli voi tic do tai han va trang thai dao dpng rieng la mpt trpng nhung ®"
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NGHIEN cuu-TRAODOI
tham s6 ca ban nh4t. No dugc tmh toan phan tich bang phuong phap phin tir huru ban va phan mem Matlab. D6 thi nay cung cap cho nguai ky su mgt each tdng quat ve su thay d6i cua t6c dp toi han va trang thai dao dpng rieng ciia he true - 6 true khi thay doi dp cung cua 6 true.
Hinh 5: Dd thi thay ddi trgng thdi dao ddng rieng khi thay ddi do citng d truc.*>
Ngay nhan bai: 19/02/2014 Ngay phan bien: 15/3/2014
Tai lieu tham khao:
[1]. Friswell M I, Penny J E T , Garvey S D, Lees AW, ^'Dynamics of Rotating Machines", Cambridge University Press, New York, (2010).
[2]. Vance J, Zeidan F, Murphy B, "Machinery vibration and Rotordynamics", John wiley & Songs, INC, Hoboken, (2010).
[3]. Van Thanh Ngo, Danmei Xie, Hengliang Zhang, Yangheng Xiong, Yi Yang, "Dynamic analysis of a ng shafting vibration based on finite element". Front. Mech. Eng. 2013, 8(3): 244-251.
[4]. Xie D, Liu Z, Zhang H, Yang Z, Dong C, "Sensitivity analysis of torsional vibration behavior of the shafting of a turbo-generator set to changes of its mechanical parameters". Power Engineering, 25(4): 462-465 ^ 2005.
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