ISSN: 2354-0575
Xt; X C O N G NGHE HA COC CHIM / / [^ \ BANG CACH GHEP HAI MAY RUNG
\ '^J TECHNOLOGY FOR SUBSIDENCING OF THE PILE '^'^ INTO THE GROUND BY COUPLING TWO VIBRATORS
K h i n g Doan Dien'-^ Nguyen Dac H u n g \ Vu Xuan Trudng', Nguyen T h i Doan'' 1 Trudng Dgi hpe Supham Ky thudt Hung Yin
2 Hdi Co hgc Hd Ndi 3 Ban Tuyen gido Trung Uong 4 Truong THPT An Thi, Hung Yin Tom tdt;
Mdt trong nhung cdng nghi hg cpc chim Id su dung rung dpng [I] bdng cdch ghep hai mdy rung.
Trin ca s& ke thira vd phdt tnin md hinh bdi todn trong [5], [6] vd cdc kit qud nghien ciru dd dugc trinh bdy trong [2], [3], bdi bdo trinh bdy viic xdy dung md hinh hg cgc chim sir dung rung dpng bdng edch ghep hai mdy rung. Bdng viec sir dung phuong phdp tach cdu tnic, phuang trinh Lagrange loai II, nguyen ly d'Alembert, bdi bdo da thiit lap dugc he phucmg trinh dao ddng cua md hinh hg cgc ehim. Tir do sudung cdc phuang phdp sd [4]. cdc phuang phdp gidi tich [1] de gidi he phuang trinh vi phdn dao ddng cua co he nhdm dua ra nhimg du dodn vd ede gidi phdp cdng nghi phu hgp.
Tir khda: Hg coe chim. Dao ddng, Mdy rung.
Cdc Id hiiu su dung vd thu nguyen q^. q,: Tpa dfl khoi tam ciia may rung 1 va 2 [m]
mf. Khfli lugng may rung thu nhat [kg]
m^ Khoi lugng may rung thu hai [kg]
my. Khfli lugng ciia cpc chim [kg]
a'. He sfl giam chan nhot ciia dat [KNs/m]
a'. He so giam ehan nhdt cua hen ket dan hfli [KNs/m]
C'. He so dan hfli cua dat [KN/m]
Cy. He so dan hfli eua Ifl xo hen ket hai may rung [KN/m]
C^y. He sfl dan hoi ciia tdm d i m [KN/m]
P,, /",: Bien dp lye kieh dpng cua hai may rung [N]
co: Tan sfl gfle ciia bg phdn gdy kieh dgng mng cua bai may rung [5"^]
hy hy. Toa dp khoi tam cua may rung 1 va 2 tai vj tri can bang [m]
Qgi, Q^y. Mflmen khdi lugng leeh tam cua hai may rung [KNm]
e^ ey Dp lech tdm [m]
X'. Toa dp trpng tam ciia coc tai vi tri cdn bang tinh so vol goc tpa dfl O [m]
\. Dat van de
Hien nay, cflng nghe ha cgc chira vao ddt dang duge ap dung rflng rai trong ITnh vue xay dyng giao thflng, thuy Igi, dau khi.
Ngufli ta da su dung nhieu phuang phap ha chim cgc vao dat, trong dfl phuong phap ha cgc chim vao dat bdng rung dgng dang dugc su dung phfl bien.
LTU diem ciia phuang phap nay la khi thi cong trong nen ddt yeu va dat cat, gidm thdi gian thi
cflng, giam cflng suat tieu thy eua may, cpc khong bi pha buy, co the ha chim nhieu loai coc co kich thudc va hinh dang khac nhau.
Tuy vay, cho den nay mflt sfl nha khoa hpc mdi chd yeu nghien euu bai toan ha chim cpc vao dat bang each ghep mgt may rung va kit qua nghien eiiu con han che. [1]
Vdi ly do tren, bai bao nay tiep tuc nghien euu bai toan ha chim epe vao dat bang rung dpng, dac biet bai toan ghep hai may rung cfl y nghia rat quan trgng cd ve ly thuyit va thye tien.
2. Doi tugng vd phuong phap nghien cuu Ddi tup^g nghien cim: Hai may rung cfl tin sfl gflc 03 lien ket vdi nhau bing 16 xo cfl dfl eiing tuong duong la C^ va bp giam chdn co he sfl can nhdt la a^.
Giiia cpc va may rung thu nhat dupe ghep voi nhau thflng qua mgt tdm d i m dan hfli eo dfl eung la Cj^. Phan lyc ciia dat d dau cgc cfl dp cimg dan hdi C^ va he sfl can nhdt a,. Lye raa sdt mat ben giiia cgc va nen dat la F^^;
_ m^ m^. m^. a,, a „ C^, C^, P,, P^, k. m. A,, h^\k cac hang sd duong.
Phuang phap nghien ciru: Mfl hinh hoa cflng nghe h^ cpe ehim (hinh I) va su dung phuang phap tach cau tnic, tach rao hinh ha cgc chim (su dung rung dgng tren co sd ghep hai may rung) thanh hai CO he con va dp dung phuang trinh Lagrange loai II dang giai tich, nguyen ly d'Alembert (dli vdi CO he) d l thiet lap he eac phuang trinh vi phan chuyen dgng rao ta dao dflng cua mfl hinh ba cgc chim. Tu do su dung phuang phap sfl d l gidi he cac
Khoa hoc & Cong nghg - S6 3/2014 Journal of Science and Technology
ISSN: 2354-0575 trinh vi phan chuyen dgng da thilt lap vdi diiu kiln
ban dau xde djnh nhdm mue dich dua ra cdc nhan xet, du doan va eac bien phap cflng ngh| phii hgp eho bai toan ha cgc chim sd dung rung dgng hi hai may rung.
pi C0SC3t I
Hinh 1. Md hinh hg coc chim
3. Cac kit quaTrudc khi tien hdnh tinh toan, ta dua ra rapt sfl gia thilt sau:
- Cac phan tu tiet dien ehi djeh chuyen theo phuang dgc.
- Kit can dich chuyen theo phuong thang diing.
- Cac may rung gay ra lyc kich dgng theo phuang thang dung la hdm cosin cua thdi gian / tan sfl 0) eua bg phan gay kich dgng rung cua hai may rung la nhu nhau va cac lye kich dflng eua chung efl cung pha vdi pha ban dau bang khflng.
- Kit ciu dich chuyen theo huong ha chim.
- Chilu dai ciia kit cau khdng Idn.
- Ddt eoi nhu moi truflng dan nhot.
- Kit cau ngap hoan toan trong dat.
- Mat dat khflng djeh ehuyen trong khi ha chim kit cdu.
- Lye tae dung len mat dau ket cau ha ehim dugc thay bdng Ifl xo dan hfli co do cirng c^, he so giam chan nhfltctj.
- V^n tflc dich chuyen ciia ket cau khong ldn, lyc ma sat giiia mat bin eua ket cau va dat phu thugc bac nhat vao van tflc ehuyen dflng.
- it la he sfl ma sat ciia dat no phu thuge vao dat nen va kieh thudc cua kit cau, dupe xae dinh bang thyc nghiem.
3.1. Thilt lap he phirong trinh vi phln dao dgng bdng phuong phap tach cau true
Tach he ehinh ban dau (mfl hinh ha cpc chim, hinh 1) thanh hai he con (hinh 2 va hinh 3).
Thay lien kit giua hai may rung va cgc chim bang phan lue dflng \ucp(q,t).
p2 cosrot i t
Hinh 2. Hi con thir nhdt P(q.t>
Hinh 3. Hi con thir hai
Xet he con thir nhdt (gdm hai mdy rung) nhu hinh 2.
Chgn gfle tpa dp he hai may rung 0 | trung vdi mep dudi cua tam dim dan hfli khi hai may rung d tr^ng thai can bdng tmh. q^, q^ la toa dp trpng tam cua may rung thu nhat vd may rung thir hai khi chiing dao dflng so vdi gflc tga dp 0|.
Thiet lap phuang trinh viphdn chuyen ddng cua he hai mdy rung
Ap dung phuang trinh Lagrange loai II dang giai tieh ta efl:
dt dq, dq.
= a ii= 1,2) T Id dflng ndng cua he con thu nhat:
miqi + 2 ''^lio.-i 9i)
(1)
(2)
Khoa hoc & Cong nghf - So 3/2014 Journal of Science and Technology
Tinh cac dao ham:
l(lr)=<"'•'•""''''"""''
d / 3T \
- § = - [ C , A - a (,.-„)]
"•f^^'^'^"""'
3^ / . - 1 -^T - a2 {qi - qi}
dqi
(7) (8)
(9)
(10) ISSN: 2354-0575
Q (i^l, 2) la cdc lue suy rflng (gom lye efl thi, lue can, luc kieh dflng ngoai):
n la hara thi nang eua he hai may rung:
^-\c^^q'i + \cAq.-q.Y (4)
"t" la ham hao tdn cua he con thii nhat:
4>i ^ 'i'2 = y tt2 (92 ~ g i ) f5j Q'' (i= I. 2) la cae luc suy rgng tae dung vao
hai may rung;
Qi = {P1+P2) cos U)t-p{q,t) ,.. 34) V- • N
^'^f - - ^ = - 0 2 ( 9 2 - 9 1 ) (32^-p2COsa)f '^Si Thay cac kit qua tu (2) d i n (10) vao (I) ta thu dugc be hai phuang trinh vi pban chuyen dgng mo ta dao dgng ciia he hai may rung:
i
(pi + P2) cos coi - (mi + 7712)91 "^ "1292 + 02 (92 - 91) + C's (92 ~ 91) - Cj^li ^ pU^ 0 (11)^2(92 - 91) + a2 (92 - 91) + C2 (92 ^ 91) = P2Cosa)i (12) Xet ea he con thir hai (hg coc chim, hinh 3) Xdc dinh phdn luc dpng luc (luc Ide dung
Gid thiet rdng: Cgc la vat ran tuyet dfli; Lyc vdo ddu cpc) p(q,t) p(q.t) dat d vj tri trgng tam ciia cgc. Theo [5] ta cd:
Chpn he hTic tpa dp nhu hinh 3, tryc X di __ Qmei 2. __ ^02^2 2 qua trgng tdm cua vat, luc nay ta coi vat la chat ^ "119 '^'^ w.2{/
diem va efl phuang theo phuong chuyen dflng cua „ . , , . ,,,^ ^ , . - . , u .L- i - i • • L-- J L • Dat V = 9 , - fl, va thay vao (11) ta duoc he vat (phuong thang dune) va eo chieu duong huong , '. . ^ '
• ; phuang trmh sau:
xuong. ^ ^
Tai thdi diim khao sat dilm M i a dilm thuflc \{p^+p2)cQ?.(iit + m,y +a^y + C,y +
dat vd nam sat vdi dauraut cpe. Xet vi tri can bang <—mig, — C^^g, ~p{q,t) (15) tai trgng tam eua vat. [7ra.y + ff,y + C2j/ = 3?,cos(o(
Gpi X la tpa do tnmg tam eua cgc tai vi tri
can bang tmh so vdi gflc tga dp O. Ap dung nguyen ly d'Alembert vdi he hai Tai thdi diem t^ (mflc thdi gian ban dau) vat may rung ta cfl:
CO tga dp la x^. Tai thoi diem (thi vdt eo tga dp la x. p(q^t) =(p^+p^) cos coi + my +
Tu mfl hinh nhu trin, ap dung nguyen ly .. _ • _^ __ r- (^^^
d'Alembert, t a c o : ^- mi 9: — a^y — C2I/ — C^qj
•mx + (k + a\)x + Cix — p{q,t) (13) K e t h g p v d i p h u o n g trinh(15) va (16) taco:
md + tk + a,)i-^ax-Acoscot + Bsmwt (14) PM= ^'+P')<^oso^t + ^^y-^^>''^' t^^) Trong phuang trinh (14): ^ ^ ^ u vay, bdng vile sir dung phuang phap
A-P1+P2 nhGiCO + a-iHiu) + taeh ciu tnic va su dyng phuang trinh Lagrange loai + c 1 laiHi _|_ c;Gi\ II, nguyen ly d'Alembert, ta da thilt lap dugc he 03
•" mi \ CO o j M phuang trinh vi phan ehuyln dgng md td dao dgng B ^ - TibiH^tji' - c - L / ' ^ ' G _ Czffi) ciia mfl hinh ca he ha cpc ehim va 01 phuong trinh
'^^ m, \ CO t o M xac dinh phan lyc ddng lyc p(q,t).
(pi + P ; ) c o s c o i - ( m + rrh)qi + ithfji + ff? ( 9 2 - 9i) + G ( g j - g,) - C ^ q , = p{q,t)
•nh(q2-q,) + a-i (92 - 91) + G (9:; - gi) ^ p-j cos coi . m a f + (A; + ffi)i + CiZ - Acosti)(+Ssincoi
V^q-i^ ~ (fl +j^)coscoi + 77t;T/ + m!9i —ff^y —C5?/— C^,,?,
Khoa hoc & Cong nghe - S6 3/2014 Journal of Science and Technology
ISSN: 2354-0575
He phuong trinh (18) co 04 phucmg trinh vi phdn du d i giai 04 dn nghiem cdn tim laq^.q^.x va p(q.t). Trong bai bao nay, tac gia su dyng phuang phap sfl d l gidi be cac phucmg trinh vi phan vdi lap binh tinh todn b-ln p h i n m i m Maple 18 (mue 3.3) voi cac so lieu thue nghiem dugc xac dinh trong bang 1.
3.2. Xac dmh cac thdng so d^u vao va dilu kien ban dau
Vdi luc tac dyng vao d i u cpe la p(q,t), tao ra vdn tflc chuyin dflng cua cpc la
iit) =-GiQ)smwt+H,Q)cos(ot.
Vi vay, ta di tinh chgn eac thong sfl ciia mdy de ha chim cpc b l tflng cfl tilt d i | n hmh vuong 0.3 X 0.3 (m^) efl chiiu dai la 10m, cpc mac be tong 200 cfl khfli lugng rieng la 2500kg/m^ dugc dflng tren nen cat cfl can.
Tinh todn cdc thdng sd co bdn:
Bdng phuong phdp giai tich ta xac dinh duge phuang trmh dao dflng eiia cpc la:
x^Gicosajt+HiSincot [fl].
Ta cd b i l n dp dao ddng eua cgc:
X--
^fa'+Hi
, _ A{ci — m3(ii^)^Bk(n Vdi i
a-
k^(ii^ + (ci-m3(£l^fB{ci — Tn3(li^) +k(£iA ["'~ kW + {c^-m,(ii'f Trong dd:
A —pi+p2 — m2Gi(ii^ + a2Hi(£i + + c,l(a2H^.BGL\
•"• mi \ CO fo /
- (I)- tan sd goc cua bd ph^n gdy kich dpng rung cua hai may rung (rad/s).
Ggi n la so vong quay trong mgt phiit cua
qua lech tam n = 420 vong/phut.
Nhu vay oi = ^ = 44 (Rad/s) - ay he sfl gidm chan cua lien k i t ddn hdi (KNs/m); ehgn a, =10 (KNs/m).
- Cy he sfl dan hfli eiia 16 xo lien k i t hai may rung (N/m); Theo kinh nghi|m chon C^ = 300N/m
= 30000 kg/m.
- C^^: he sfl dan hfli cua tdm d i m liln kit may mflt voi cpe; chgn C^^ = 50000 kg/ra.
- C,: he sfl dan hfli cua ddt (KN/m); Chgn C^
= 50N/m = 5000 kg/m.
- e: Tam sai (dp lech tam); chgn e =150 (rara) Voi ege be tflng da chpn thi khdi lugng eiia cgc se la: m, = 0.3 x 0.3 x 10 x 2500 = 2250 (kg).
- m: khfli lugng qua lech tim eiia may rung Tim m= ?
Ta da biit luc kieh dpng/j chinh la lyc qudn tinh Ii tam. Hay p = 2mecij^, tu dfl suy ra:
"•= 2 ^ ( = | - " = ) Nhu ta da biet anh huflng ciia rung dpng toi qua trinh dong coc thi lyc kich dgng p phai dii ldn so vdi trgng lupng cpc, nd phai n i m trong khoang 0.2 < - ^ < I (do gin 2 may mng).
- > P = 2 Q = 2 x 2 2 5 0 =22500 (kg).
Thay vao ta dugc m = 420 (kg).
Khfli luong dau may ta lay xdp xi m^ = mj = 5586 (kg).
- k la he sfl raa sat dgng ciia d i t cat va ege, ta chpn k = 30000 (kgs/m).
- Uj la he sfl can nhdt cua ddt, ta ehon a ^ 2000 (kgs/m).
Do dfl ta chgn cac thong sfl gia dinh d i tinh cho bai toan (bang l).[7]
">i = nij (kg) 5586 P,(kg) 22500 Q,iKN 10
Bang 1. Cac thong so cong nghe cita tn ni, (kg)
2250 P2(kg) 22500 Q.,KN 10
a^ (kgs/m) 10 K = k + a, (kgs/m)
32000 Cl (mm)
150
0 hinh ha coc chim C, (kg/m)
30000 to (rad/s)
44 Cj (mm)
150
C . ( k g / m ) 50000 C, (kg/m)
5000 g(m/s')
10
Khoa hoc & Cong nghe - So 3/2014 Journal of Science and Technology
ISSN: 2354-0575
3.3. Phdn tich dao dgng bdng phuwng p h a p so Su dung phucmg phap Runge-Kutta- Nystrom [4] lap trinh tren phln mem toan hgc Maple 18 (trinh bay chi tiit tai Phu lyc I [7]) ta thu duae cac ket qua nhu sau:
x(ms'')
Hinh 4. Dd thi pha ciia cgc chim
,
s 2 ••
1 \
! t(s)^ ^ Toc do khoi iam may nmg 1 Toe do khoi nm may ning 2
Hinh 5. Van tdc cgc, mdy rung 1 vd2 ,£•
-i -i
.
^ \
<(»)
1 ^a^^ 3 4 J
11 1 li s
S E'E
>>> II I
iii¥lHinh 6. Vi tri cgc. mdy rung 1 vd 2
Hinh 7. Luc tdc dung tgi ddu coc Tir cdc ket qud trin ta nhdn thdy:
Vi tri khfli tam cgc chun giam theo thoi gian;
Toc dp dong cgc trong khoang 2 giay dau k l tu khi ha epe tang rat nhanh va thay doi dot ngpt, do do lyc qudn tinh tac dung vao cpc rat Ion co tac dung ha cpc ehim rat nhanh, mat khae ehieu dai tiep xiic ciia cgc ngap ttong dat con nho nen ma sat nin dit tac dyng vao cpc la yeu, trong khi luc cuong buc dieu hfla dp he phu (hai may rung) dao dflng theo xu huong tdng dan theo thoi gian (vl phia chiiu am).
Khao sat dfl thi pha cua cgc (hinh 4) ta nhan thdy toc dg cgc ty l l nghieh voi ehieu sau cgc (phan tiep xde giira cgc voi dat), nghTa la khi chiiu sau cgc tang, thi tflc do cpe giara theo chieu am.
Mflt dieu dac biet quan trpng do Id dfl thi tflc dp ha cgc chim dao dflng theo huong giam dan, dilu nay ehung tfl ngoai vile ha cgc thi he phu (gflm hai may rung) con gay ra hien tugng nhfl eoc do lyc kieh dpng diiu hfla thay ddi ehiiu theo thdi gian, tuy nhiin chieu sdu ha cpc Ion hon khoang nhfl ege nin cpc van dan dugc ha sau trong dit. Diiu nay la CO lgi cho cflng nghe ha epe chim. Ban chit eiia hi|n tupng nay cung giflng nhu viec taro ren trong nganh co khi chi tao, niu thuin tiiy chi quay tay quay cila ban taro theo rapt chiiu quay nhdt dmh, thi se khong the taro duge ren, do ma sat tiip xuc gida vat li?u tarfl voi mui taro Ifln, nhiet sinh ra tai viing cat rat ldn, thong thudng khi quay duoc mpt sfl vflng, ngudi ta se quay ngupe lai d i be phoi va giam ma sat cat.
Cung tuong ty eho md hinh ha cgc chim, vile h£i cgc rdi nhd cgc, ldm eho viec dflng cpe trd nin de dang ban, lyc quan tmh tdng nhanh, giam ma sat giiia nen dat va epe, tfln it nang lugng cho viec dflng cgc.
4. Ket l u l n
Dya tren c a sd k l thua md hinh bai toan
Khoa hoc & Cong nghe - So 3/2014 Journal of Science and Technology
ISSN: 2354-0575
trong, cac tac gia da md rgng khd nang cflng nghe cho phep ha rapt s6 loai cpe, flng, van eu thep trong ciia mfl hinh va su dyng cac phuang phap giai tieh xay dyng nha ddn dyng, nha cflng nghiep,... trong toan hgc, cdc phuang phap sfl d l xac dinh cdc dai diiu kien dit la moi trudng dan nhflt bdng each lugng hinh hgc, dgng hgc, dgng lyc hgc va eac ghep thim rapt hay nhiiu may mng d l kit cdu cfl thflng sfl cflng nghe. _ the dat duoe do sdu ha ehim ma ta mong mufln ma Dya^ tren eo sd phan tich cac kit qua thu khflng nhit thiit phai thay thi may rung co cong dugc, ta thdy rang k i t qua bai todn cfl thi dp dyng suit Idn ban.
Tdi lilu t h a m khdo
[1]. Nguyen Thiic An, Nguyin Dinh Chiiu, Khflng Doan Diin, Ly thuyit dao ddng, NXB Nong Nghiep, Ha Ngi 2006.
[2]. Khong Doan Dien, Nguyen Duy Chinh, Optimal parameters of vibration reduction system TMD-D and DVA for an inverted pendulum type structure, Vietnam Joumal of Mechanis, VAST, Vol. 32, No I (2010), pp.59-69.
[3]. Khong Doan Dien, Vu Xuan Truong, Nguyen Duy Chinh, Research to reduce vibration for shaft of machine using the reduced vibration TMD, Proceedings Of The Regional Conference on Mechanical and Manufacturing Engineering 2014 (RCMME2014).
[4]. Khflng Doan Diln, Nguyen Duy Chinh, Vii Xuan Trudng, Phuong phdp sd trong Co hgc ky thugt, NXB Khoa hpe va Ky thuat, Ha Npi 2014.
[5]. Nguyin Dinh Chieu, Nguyen Dac Hung, Dao ddng cua kit ciu dugc hg chim vdo d&t bang hai mdy rung. Tap chi Khoa hpe ky thuat thiiy lgi va mfli truong so 9/2005.
[6]. Nguyen Dac Hung, Nghien cuu bdi todn hg chim coc vdo ddt bdng hai thiet bi rung ddng, Luan an Tiln si ky thuat.
[7], Nguyin The Doan, Lua« vdn r/iac sf, Trudng Dai hpe Su pham Ky thuat Hung Yin, 2014.
Abstract:
One of the technology for subsideneing of pile into the ground is used vibrations by coupling two vibrators. On the basis of inheriting and developing a model in [5]. [6] and the research results were presented in [2], [3]. The article present model for subcidencing pile into the ground that used vibrations by coupling two vibrators. By using the method of separation of structure, Lagrangian equations, d 'Alembert principle lo set the system of vibration equations of the modeling for subsideneing of pile into the ground.
From then, we use numerical methods to solve a system ofvibrations equations of the model for subsideneing of pile into the ground, to predict and propose appropriate technological solutions.
Keywords: Subsidence of pile into the ground, Vibration. Vibrators
Ngirdi phdn b i l n : G S . T S K H . Vu Duy Q u a n g
