NGHIEN Ctfu - TRAO D O I
yx
/XAC OjNH CHUYEN DONG CUA CAC KHAU DAN KHI DINH TRU'O'C QUY DAO CHUYEN DONG OTA CATTRONG TO HOP MAY XUC THUY LyC-THIET Bj CAT BE TONG COT THEP
DETERMINING THE MOTION OF DRIVEN LINKS FOR THE PREDETERMINED MOVING OF CUTTING DISC IN A HYDRAULIC EXCAVATOR INTEGRATED CUTTING EQUIPMENT
OF REINFORCED CONCRETE
PGS.TS. Tran Quang Himg, NCS,ThS. Le Anh Son Khoa Dpng luc, Hpc vien Ky thuat Quan sU
T O M TAT
Ygn dung ly thuyet cd hgc hi nhieu vgt, bdi bdo trinh bdy phUdng phdp thiet lap md hinh dgng hgc thiet bi cat bi tong cot thep (BTCT), phUdng phdp xdy dung chuong trinh tinh todn dexdc dinh cdc dgc trUng chuyen dgng cua khdu ddn de dgt dUdc quy dgo chuyen ddng cua dig cdt theo mong muon. Ket qud nghiin cUu Id cd sd khoa hgc de tinh todn thiet ke cdng nhu dieu khien, lUa chgn che do ldm viic cho thiet bi cdt BTCT.
Tii khoa: May xUc thuy luc.
ABSTRACT
Applying the dynamic theory of multi-body systems, this paper presents method of modeling of a hydraulic excavator integrated cutting disc reinforced concrete. The research also figure out a calculating program to determine the motion of driven links for the predetermined moving of cutting disc in the excavator. The found results are scientific basis for designing calculation, controlling and selecting of working mode for concrete cutting equipment
Keywords: Hydrauhc excavators.
ISSN 0866 - 7056
TAP CHi CO KHi VIET NAM, Sfi 11 nam 2014 www.cokhivietnam.vn
NGHIEN cufu-TRAO D O I
1. DAT VAN DE
Cd sd ly thuyet de tinh toan dieu khien cac may va thiet hi ndi chung deu dUa tren k^t qua giai bai toan ddng hoc ngUdc. La dang thiet hi da nang, do vay dac diem lam viec va dieu khi^n thiet bi cat lap tr^n may xiic hoan toan khac vdi dta cat lap tren may cdng cu cung nhU dac di^m thao tac eua cac may xay dUng thuan tuy. De dam bao van hanh dia cat theo che do cat yeu cau, hoac dn dinh chieu day phoi cat de an toan cho ngUdi va thiet bi trong qua trinh lam viec thi xac dinh quy luat hay dac tinh chuydn ddng ciia khdu ddn la mdt v ^ d^ c^n thiet.
gia thiet bi cat (3); Khau can nang thiet bi cat (4); Khau dia cat (5). Cac khau lien ket vdi nhau bang khdp ban le O, (khau 2 vdi khau 1), khdp ban le O^ (khau 3 vdi khau 2), khdp ban le O3 (khau 4 vdi khau 3); Khdp ban le O^ (khau 5 vdi khau 4). De quan sat chuyen ddng cua cac c0 cau may xiic va thiet bi cat, ta gan vao cd he mdt he toa dp de cac cd dinh O^x^y^z^ cd gdc tai true quay toa cua may xiic. Cac he toa do O^x^y^z^, O^xjjZj, 03X3y3Z3, O^xj^z^ va O^x^Jsh ^^ S^c gan tai cac diem lien ket gifla cac khau cua may va thiet hi cat.
Hmh 2. Mo hinh to hpp mdy xue tich hop thiet bi cdt BTCT Bdng thong so dong hgc cdc khdu Khaui
1 2 3 4 5
a.
0 0 0 0 0
a a, a.
a.
a^
a.
d 0 0 0 0 0
q, q.
q.
q.
q.
q.
Hmh 1. Thiet bi cdt BTCT tich hdp 2. JVIO H i N H NGHIEN CUtJ D O N G HOC M A Y XUC THUY LLfC-THIET BI CAT BTCT
Gia thiet may xiic tich hpp thiet bi cat BTCT la vat ran tuyet doi dupc dac trUng bfii 6 khau bao gom: Khau khung gam va ca bin (0);
Khau c&i may xue (1); Khau tay gau (2); Khau
Tinh dupc cac ma tran Denavit Hartenberg tuong dfii cua cac Idiau:
cosq. -cosa.smq, sinq, cosa^cosq^
0 sina, 0 0
sina,sinq^
-sina.cosq, cosa,
0 a^cosq, a,sinq, d,
1
"c, -s, 0 a,c, s, c, 0 a,s^
0 0 1 0 0 0 0 I _
vdii = l, 2,3,4,5 (1)
Theo do ma tran bien doi cua khau 5 (dia cat) vdi he toa do cd dinh dUdc tinh theo
cdng thiic sau: ^
ISSN 0866 - 7056
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NGHIEN C J u - TRAO D 6 |
K-mr-
c,,„ -i,,„ 0 a,c,+a,c„ + i,c,„+i,c,„
^1234 '•1234 ^ ^A^^2^12 + ^3^I23+Vl234
0 0 1 0 0 0 0 1
(2)
Vfii:
Gii sti ma tran tUa nghich dao c i a ma tran chU nhat J(q) cfi dang:
J*(q) = J ' ( q ) [ j ( q ) J " ( q ) J ' (8) Nhan hai ve bifo thde (6) vfii J+ ta n h ^ c„ ,=cos(q,-l-qj-l-....+q,);s„ ,=sin(q,+q,+....-fq,)
Nhu vay. tpa dp cua diem tam dia cat O =C, chinh la:
duac:
J*(q(t))x(t) = q(t) (9)
yK05=a,s,+a;S,j-fa3S,j3-fa,s,j„ (3) Ky hieu vec tP suy rfing cua co he i! = [<li fli flj fl, flsfva vec t a dinh vi dia cat
^^[''ROS JROS] . theo do ta cfi ket qua dpng hpc
thuan X = f (q) theo cong thUc:
flfl)-[f,(q) f2(q)r=[x,„3 y . „ , r (5) 3. THUAT T O A N GIAI B A I TOAN XAC
DJNH QUY L U A T DAN D O N G K H A U DAN
De dieu khien dia cat theo quy dao mong muon thi can phai xac dinh cac gia tri cua q de dat dupc x theo yeu cau. Nghia la fi bai toan dfing hpc ngupc can phai thiet lap duac quan hS q=f'(x). Dao ham hai ve bieu thUc theo thfii gian:
q = J(q)q (6)
Vec tp gia tfie cac tpa dp suy rpng dilgc xac dinh bang each dao ham hai ve (9):
q(t) = r ( q ( t ) ) x ( t ) - l - r ( q ( t ) ) ) t ( t ) (10) Xac dinh ma tran J*(q(t)) nhu sau:
r ( q ) J ( q ) r ( q ) = J^(q) (n) Dap ham hai ve bieu thde (11). nhan dupc:
J*(q)J(q)j'(q) + J-(q)[j(,)jT(q) + J(q)j'(,)J^jT(,)(12) Bien doi phuong trinh (12) nhiin dil(lc m a t r a n j * ( q ( t ) ) :
J*(q)-{l'(q)-I-(q)[i(q)J'(q)+J(q)J'(q)])[j(q)j'(,)]-'(j3) De xac dinh duac q(t) trong (9) va (10) ta chia khoang thfii gian lam viec cua thiet bi cat [0 T] thanh N khoang bang nhau:
T
At = —,tacfit^^, =t^-HAtvfiik=l,2,...,N-l Ap dung khai trien Taylor doi vfii quanh nhan dupc:
Trong dfi: J(q) la ma tran Jacobi cfi 3x5, " - = " ( ' ' ^ ^ ' ) = ' J ^ + q ^ ^ ' + q . « + . . . (M)
J(q) =
'df^ Sf^ dt^ dfj_ dt^
3<i: Sqj Sq, aq, dq, B. «^ sf^ at^ dt^
dl, dq, dq, dq, dq.
(7)
The bieu thiJc (9) vao (14) va bfi qua vo cung be bac >2, (14) trfi thanh:
q h i = q i , + J * ( q J X j A t
vfiik=l,2,...,N-l (15)
ISSN 0866-7056
TAP CHi CO KHi VIET NAM, Sfi 11 nam 2014 www.cokhivietnam.vn
NGHIEN Ctfu - TRAO edi
N h u vay, xac dinh quy luat chuyen dfing ciia cac khau dan theo thuat toan sau:
Hinh 3. Thugt todn gidi bdi todn ddng hoc ngUde that bi cdt
4. THONG SO DAU VAO VA CAC KET QUA DONG HOC NGUOC
Thong so kich thUfic k^t cau lien quan CLia mfi hinh may: aj=:4,332m; a2=2,067m;
a3=l,961m; aj=0,903m; 35=0; qj=7l/4; q^=5-K/i;
q,=23Tt/12; q,=237t/12; qj=237t/12.
Cac quy dao cho trufic cua tam dia cat dupc mfi ta bfii cac ham phu thupc thep thfii gian t va dUpc minh hpa tren hinh 4:
TrUfing hpp 1 (thi) - cat cong:
x„,=7,3965-0,4sin(0,lt) y,„,=0,9092-l-0,2sin(0,4t) TrUfing hpp 2 (th2) - cat xien:
„ =7,3965-0,051 ly»o!-0.90924-0.05t TrUfing h a p 3 (th3) - cat ngang;
x „ , =7,3965-0,051 y.o,-0.9092
Triidng hdp 4 (th4) - cat diing:
x . „ =7,3965;
y , „ =0,9092+0,051
Do t hi quy dao tam d<a cat t h l
- - - tn2
— — in3 Ih4
• ] - - - -
- i - - - f - - f - -f ••
•••r K - - - - : • i
; ; / ; ; ;
i ; ' ; ; ; ;
e s 6 9 7 7 1 7 2 7 3 7 4 7 ? xCm>
Hmh 4. Quy dao dinh trUdc c^a tdm dia cdt Sfi dung cac bildc tinh toan da md ta d tren nhan dddc ket qua nhan diidc la cac quy luat ddng hpc tiidng iing ciia cac khau dan de tam dia cat chuyen ddng theo cac quy dao dinh trUdc trong thdi gian khao sat T-lOgiay: "^
ISSN 0866 - 7056
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NGHIEN cufu - TRAO D(!)l
K'TlKr-
\m 'hm ^ ^i'^i"''^2'^i2 •'•^3'^i23 •'•^4'^i2:
'1234 ^23J ^ 3 l S l " ^ 2 S | 3 +33^123 +34S123 0 0 1 0 0 0 0 1
(2)
Gi^ sii ma tran tiia nghich dao ciia ma tran chii nhat J(q) cd dang:
J*(q) = J ^ ( q ) [ j ( q ) j " ( q ) J ' (8) Nhan hai ve bieu thUc (6) vfii J* ta nhan c,j ,=cos(q,+q,-i-....+q); s„ ,=sin(q,+q;+....-l-q,)
Nhu vay, tpa dp cita diem tam dia cat O =C, chinh la:
duoc:
r(q(t))x(t) = q(t) (9)
= a,c,-fa;C,j-fa,c„,+ajC,23,
= a,s,-i-ajS,j-i-a,s,„-i-a.s,„, (3)
Ky hieu vec td suy rdng ciia ca he q = [qi q, q, q^ q j ' v a vec td dinh vi dia cat
^ ^ [^R05 yRos] ' t^heo dd ta cd ket qua ddng hpc thuan X = f (q) theo cdng thiic:
fl:D=[f,(q) f.(q)r = [x,„ y „ f (5) 3. THUAT T O A N GIAI BAI T O A N XAC DINH QUY L U A T DAN DONG K H A U DAN
De dieu khien dia cat theo quy dao mong muon thi can phai xac dinh cac gia tri cila q de dat dupc x theo yeu cau. Nghia la fi bai toan dfing hpc ngupc can phai thiet lap dupc quan he q=f'(x). Dap hiun hai ve b i & thde theo thfii gian:
Vec tP gia toe cac tpa dp suy rang dupc xac dinh bang each dao ham hai ve (9):
q(t) = r ( q ( t ) ) x ( t ) - H * ( q ( t ) ) i t ( t ) (10) Xac dinh ma tran J*(q(t)) n h u sau:
J*(q)J(q)J^(q) = J^(q) ( n ) Dao ham hai ve bieu thilc (11), nhan dupc:
J*(q)J(q)J'(q) + r(q)[j(q)j'(q) + J(q)j'(,)] = j'(q)(12) Bien dfii phuong trinh (12) nhan dupc m a t r a n j * ( q ( t ) ) :
i'(q) = {i'(q)-r(q)[i(q)J'(q) + J(q)j'(q)]}[l(,)r(,)]-'(j3) De xac dinh duac q(t) trong (9) va (10) ta chia khaang thfii gian lam vific cua thiet bi cat [0 T] thanh N khaang bang nhau:
. df x = — q = J ( q ) q
5q (6)
^ ' = ^ ' ' a c 6 t ^ ^ , = t ^ - F A t v 6 i k = l , 2 N-I Ap dung khai trien Taylor doi vfii quanh nhan duoc;
Trong dfi: J(q) la ma tran Jacobi Cfi 3x5, ' ' * ' = ' ' ( ' ^ ^ ^ ' ) = ^^ ^ - l ^ ^ ' + q. K + . . • (H)
J(q) = Bf, oq, c f . dq,
dt, dq,_
df.
Si, dt, 3q, 8f, Sq,
Sf, Sq^
S f Sq.
flf Sq, Sf, Sq,
(7)
The bieu thttc (9) vao (14) va bfi qua vo ciing be b | c >2, (14) trfi thanh:
q k , i = q k + r ( q ^ ) X j A t
vfiik=1.2,...,N-l (15)
ISSN 0866-7056
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NGHIEN cufu - TRAO D 6 |
N h u vay, xac dinh quy luat chuyen ddng cua cac khau dan theo thuat toan sau:
Tinh q^
k=k+1 Sai
BATDAU
i f(q);!L(t);J(q);t..q.,N;T
i
h=At = T/N i lt:=0; t:=t,; q,:=q,
i
Tinli J(q,);J'(q,);J(q,)
I
Tinh q^;q^.
i
In <ltAA
^ ^^^^^ ^^t
I Dung KET THUC
Hinh 3. Thudt todn gidi bdi todn dgng hgc ngUdc thiet bi cdt
4. THONG SO DAU VAO VA CAC KET QUA DONG HOC NGUOC
Thdng sd kich thiidc ket cau lien quan cua md hinh may: a|=:4,332m; a^=2,067m;
a3=l,961m; a^=0.903m; d.=Q\ q,=7i/4; qj=5Tr/3, qj=237r/12; q^=237r/12; q5=23Tt/12.
Cac quy dao cho tnidc cua tam dia cat diidc md ta bdi cac ham phu thudc theo thdi gian t va diidc minh hpa tren hinh 4:
Tnidng hdp 1 (thl) - cat cong:
|x^„^=7,3965-0,4sin(0,lt) I y R05 =0,9092+0,2sin(0,4t) Tnidng hdp 2 (th2) - cat xien:
rx^„^=7,3965-0,05t lyRo. =0,9092+0,051 Tnidng hdp 3 (th3) - cat ngang:
| x „ =7,3965-0,051
| y . „ - 0 , 9 0 9 2
Tnidng hdp 4 (th4) - cat diing:
/ x . „ =7,3965;
| y , „ . 0 , 9 0 9 2 + 0 . 0 5 t
Do thl quy dfto tftm dia cat
---
- t h l ' th2 - t h 3 th4 --1-1 '
/ • >
^ r ] •'
68 6 9 7 71 7 2 73 7* 75
Hmh 4. Quy dao dmh trUdc cda tdm dia eat Svf dung cac biidc tinh toan da md ta d tren nhan dUdc ket qua nhan diidc la cac quy luat ddng hpc tiidng iing cua cac khau dan de tam (Ka cat chuyen ddng theo cac quy dao dinh tnidc trong thdi gian khao sat T-lOgiay: ^
ISSN 0866 • 7056
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NGHIEN cufu - TRAO D O I
Da tit 9u)tn li {t t«i 3 tf Uw t
Cb h ctk^an • ft tAi 3 g3 it«Dt
LIU eo:
- 0 0 1
i =
sse
Oamtt%t/ir* t*wu'iq*ir^D\
ttfl th3
"• th«
Hinh 5. Quy luat dich chuyin cda cdc khdu ddn
Ket qua the hien tren hinh 5 cho thay bien dd thay ddi cac gdc quay cua cac khau iing vdi trudng hop cat diing (th4) la nhd nhat. Vdi tnidng hdp cat cong (thl) quy Iuat dich chuyen ctia cac khau cd xu hUdng phiic tap hdn so vdi cac tnidng hdp cat cdn lai. Dac diem bi^n ddi nay cdn the hien rat rd tren cac do thi d hinh 6 va hinh 7.
, fQ Ds:^i«n|DC|khM>i)a' tfMot
" • • • = k " " " 1 — 1 ~ "
— * - - ini th2 ms IM
• " - - - - i
0 : 4 6 8
K 10* [)OiN«nlK|ki«u3}Q3lt>toi
, f g ' Oolhlw^loc.'^h>2)q2lhMt
-.-.-.•.ir..-.':^!*\br->^"-
- • - m 2 Iti3
\M
0 ! 4 J J ,0
1 " ' x i o Di>ItilwnlocEtrw4)q4»i«ot
4 ! I
'• .
-3 .4
•rr:::'r.r.r
L •
'Zr:
!
'"V"
Ih2 Bd
^ — I h 4
Itl)
Hinh 6. Quy ludt van tde chuyen ddng cua cdc khdu
ISSN 0 8 6 6 - 7 0 5 6
TAP CHi CO KHi VIET NAM. S6 11 nam 2014 www.cokhivietnam.vn
NGHIEN cufu - TRAO D O I
MglBMo»tMu1)q1 tnv)t
_ -2
I.
1 ! j — ' - - - l h 2
ms IW4
10'* Do(hlelaloe(lihK2)
K id'* Do IN Bia too n tmj 3) Q3 ttwo I
iS|;H;i:4-^
r "^^-;.llt;j;
Ui3
:;i::;;
e a 10 x 10"
7 ^
OolH gM tosarwu 4) q4 Vmo 1 -!• 4- 4 - - - -
.|::;.~;.i::r..-.i:.^.
—.K- u,i - - - » i 2 013 [_"-»... [ i_ • — j — —
Hinh 7. Quy ludt gia toe chuyin dgng cua edc khdu
Van tdc chuyen ddng cila cac khau gan nhU cd xu hiidng dn dinh vdi cac triidng hdp quy dao dia cat la diidng thang (ket qua triidng hdp th2, th3,th4 tren hinh 6: Cac gia tri cd xu hiidng di ngang). Gia tdc cila cac khau (hinh 7) lai cd xu hiidng giam dan theo thdi gian khao sat.
- - • — I M M IW
• tut
• — " 1 "
• 4 -
^ r r T
.1^:::
^Nr 1 ? • • • ? •
e 8 10
Hmh 8. Sai sd vi tri cua tdm dia cdt theo thdi gian khdo sdt
Ket qua sai sd vi tri tam dia cat tren hinh 8 cho thay: Do sai sd bien ddi lien tuc khi cat cong rat kho de hieu chinh sai sd vi tri. Ngiidc Iai khi cat theo diidng thang thi sai sd lai nam d gia tri dn dinh, do vay de dang hieu chinh de khC( sai sd nay.
5. KET LUAN
Ket qua giai bai toan ddng hgc ngiidc thiet hi cat BTCT the hien tren cac hinh 5 (ket qua dich chuyen), hinh 6 (van toe) va hinh 7 (gia toe). Bang viec xay diing thuat toan bai bao da tim ra cac ma tran chuyen trung gian va quy luat ddng hoc cua 4 khau dan: Can, tay can, gia nang va '^
ISSN 0866 - 7056
TAP CHi CO KHI VIET NAM, Sd 11 nam 2014 www.cokh ivietn a m. vn
NGHIEN cufu-TRAO D 6 I
can nang de dap ling toa do diem cdng tac (tam dia cat) dat diidc quy dao cho tnidc vdi cac trUdng hdp cat cong, diing, ngang va cat xien.
Sai sd vi tri the hien trong hinh 8 cho thay tuy theo phiidng phap cat ma gia tri sai sd cd sii bien thien khac nhau, nhin chung cac gia tri nay khdng ldn hdn l,6.10"'(m), gia tri nay nam trong gidi ban sai so cho phep cua thiet bi cat BTCT.
Cac ket qua ve ddng hoc ngif dc chinh la dau vao cho bai toan ddng liic hpc ngiidc d^ xac dinh quy luat dan ddng cac khau dan, thiet ke he dieu khien cho thiet hi cat va cac may, thiet bi cd ket cau tiidng tii.*!*
Ngay nhan bai: 12/9/2014 Ngiiy phin bien: 22/10/2014
Tai lieu tham khao:
[1]. Nguyen Van Khang (2007), Ddng lUc hgc he nhiiu vdt, NXB. Khoa hpc va Ky thuat, Ha Ngi.
[2]. E Holzweissig, H. Dresig (2001), Gido trinh dgng lUe hgc mdy, NXB. Khoa hoc Ky thuat, Ha Npi, (ngiidi dich: Nguyen Wan Khang, Vu Liem Chinh, Phan Nguyen Di).
[3]. Nguyen Doan PhUdc, Ly thuyet dieu khiin ndng cao, NXB. Khoa hpc va Ky thuat (2005).
[4]. T.R. Kurfess (Editor), (2005), Robotics and Automation Handbook, CRC Press.
[5]. J.J. Craig, (2005), Introduction to Robotics: Mechanics and Control. Pearson Prentice Hall, New Jersey
ISSN 0866 - 7056
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