NGHIEN CLTU-TRAO061
NGHIEN CLFU OONG HOC NGl/QC MAY XUC THUY LU'C L A P T H l i T B I C A T
STUDY ON INVERSE KINEMATIC MODEL OF A HYDRAULIC EXCAVATOR ATTACHED CUTTING EQUIPMENT
TS. Lfi Trgng Cuirng Hgc vien Ky thuat Quan sy TOM TAT
Bdi bdo trinh bdy mo hinh dong hgc thiet bi cdt lap tren mdy xuc tren ca sa van dung lj thuyet ca hgc he nhieu vgt Dong thai, xdy dung thugt todn de xdc dinh cdc ddc trung chuyen dong cua khdu ddn de dgt duac quy dao chuyen dgng mong muon cua dta cat. Ket qud dieu khien deu dat dugc sai so a mice khong lan han 10'", vol bon quy dgo cdt thudng gap trong thyc tien ldm viec cua thiit bi. Ket qud nghien eieu Id casa khoa hgc di tinh todn thiet ke tich hgp dgng thiet bi ndy.
Tu khoa: Dong hgc ngugc; Mo hinh dgng hgc; Mdy xuc thuy luc, dia cdt.
ABSTRACT
The present paper proposes a kinematic model of cutting equipment based on a hydraulic excavator by applying the theory of multi-body system dynamics. An algorithm for estimating the moving characteristics of driven links to achieve a desired trajectory of the cutting disc is also reconstructed. The control result has an error lower than 10"'for all 4 cases of cutting trajectory that experience regularly in the working process. The found results provide the basis for designing calculation and attaching this cutting equipment.
Keywords: Inverse kinematic, kinematic model, hydraulic excavator, cutting disc.
1. DAT VAN DE dn dinh chifiu day ck, dam bao an toan cho ngudi va thifit bi frong qua trinh lam viec thi Thifit bi ck ISp frfin may xiic thuy lyc v4n dfi dat ra la phai xac dinh quy luat chuyen cd dac difim lam vific va difiu khifin hoan toan dgng cua khau din fren co sd thifit lap va giai khac so vdi dia ck lap frfin may cdng cu hoac bai toan difiu khifin thifit bi cdng tac dfi dia clt dac diem thao tac ciia may xiic, may ck thuin di chuyfin theo quy dao mong mufin vdi tdc do tiiy. Khac vdi cac bd cdng tac khac, dfi cit pha cho phep. Ndi dung bai bao frinh bay nghien dugc da, bfi tdng, bfi tdng cdt thep,.. .thi dia ck cmi dgng hgc ngugc cua thifit bi nay dfi dap can cd tdc do chuyfin ddng rat ldn, mat khac dfi iing cac yfiu cau frong khai thac sir dung.
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NGHIEN CLfU-TRAOOOl
Hinh 1. Thiel bi dia cdt lap trin mdy xuc thtiy luc [lj.
2. MO HINH DONG HOC Bdng 1. Thdng sd ddng hoc ca he mdy xiic Xem may xiic la co he (hinh 2) gdm 5
vat (khau) ran tuyfit ddi; Khung gSm-cabin (0);
Can may (1); Tay gau (2); Gia thifit bi cat (3) va ^ a cat (4). Cac khau lien ket vdi nhau bang khdp ban le O^ ,(khau i-1 va i). Gan vao co he mdt he toa do de cac cd dinh O^jX^y^Zj, cd gdc tai true san quay cua may xuc. Cac he toa dp 0 Xjy|Z|, OjX-y^z^, OjX-yjZj va O^x^y^z^cd gdc gan tai c^c difim lifin kfit giira cac khau va thifit bi cat (cac trye O^z^ vudng gdc vdi mat phang hinh chifiu dling).
1;v^
Hinh 2. Mo hinh ddng hpc mdy xiic thuy luc lap thiet bi cdt
Khau i 1 2 3 4
a 0 0 0 0
a, a,(0.0,) 2^(0,0,)
^3(0,0,) a,(0,0^
d, 0 0 0 0
q.
9,
%
8,
e.
Cac ma tran Denavit - Hartenberg tuong ddi giira 2 khau (i) va(i-l):
D'l
cos9, -cosa,sin6, sina,sin6i a,cos9, sinO, cosa^cosOj -sma,cos9j ajSinb, 0 sina, cosa, d, 0 0 0 1
vdi i=^l-^4; (1)
Ma tran bifin doi ciia khau 4 (dia cat) vdi he tga do cd djnh:
D;=nD;, ; (2)
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NGHIEN cuu-TRAO DC!)I
r(e)J(e)j^(e)=r(9); dn
Ci2_j=cos(e|-l-92-H... -t-e^); s,2 ,=sin(el-^e2+....+eJ); ' Dao ham hai ve bifiu thiic (11):
Tga do CLia tam dia cat O, dugc xac dinh:
K yosl-hci+a^c^-HajC,^ h„+a,s,+a,s„+a3S,y]; (3)
^(e)j(9)f(e)+r(0)[j(e)r(e)+j(6)j^(6)]=r(6);(i2)
Ky hifiu vec to suy rfing ciia co he Bien ddi (12) nhan dugc ma tran j"^(9(t)):
e=[e, e. e,f va vec tctoada vi tri tam dia cjt i.(e)={jT,e,_r(e)[j(6),'(9)H.,(e)j'(9)])[j(e)i'(e)]-'; (B)
x = [xo3 yoj] .Ket qua dpng hpc thuan x = r(6):
De xac dinh dugc 9(t) trong (9) va (10) r(6)^[r,(9) rj{e)] =[xoj yoj] ; (S) ta chia Idioang thai gian iam viec cua tiiiet bi cit
[0 T] tiianh N khoang b3ng nhau:
3. THUAT TOAN GIAI BAI TOAN BONG HpCNGirOC
At=T/N,tac6t|,„ =t|,+At
„-.. . . . . . . . . .1 . v6ilc=l,2,...,N-l;
Criai bai toan dpng hpc ngupc de xac
dinh cac gia tri ciia 9 de dat duac x theo yeu chu, , , . ..
Khai trien Taylor doi vai quanh nh§n tlic la thiet lap dupc quan he 0 = r"'(x). Dao duac:
ham hai ve (5) theo thoi gian:
9w=e(t,+At) = 9j+ejAt + ej(Atf+...; (14) x = — e = J(9)6; (6)
50 The (9) vao (14) va bo qua vo ciing be Trong do: J(9)- Ma tran Jacobi co 2x3, ^^' 1™ hon 1:
e,„ =6, +r(eJx^At; voi k=l, 2,..., N-1; (15) voi: 1(6) = — ; (7)
'^ Thuat toan xac dinh quy luat chuyen Gia sil ma tran tua nghich dao cua ma '''"S ™a cac khau din (hinh 3).
tran J(9) co d^ng:
r(9)=r(9)[j(9)j'(e)J'; (g)
Nhan hai ve biSu thiic (6) voi J*(6(t)):r(9(t))x(t) = 9(t); (9) Dao ham hai vi (9) xac dinh dupc vec to
gia toe cac tpa dp suy rpng:
9(t) = r(9(t))x(t) + r(9(t))is(t); (19) Xac djnh ma tran r(e(t)):
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BATBAU ) • ! rce),s(i),j(0),i„,ec,N,T |
] k:=0; t:=t(,; Q^:=e^ \
1
, , 1
1 Tinhe, 1 1^
1 k-it-l Tsai
• ^ l ~- N ^
^ f W n ,
Tinhj(ej,r(ej;j(o,) 1
I Tinh e^;e^ 1
1 1
[ KtTTHtJC 1
Hinh 3. Sa do khdi thudt todn
NGHIEN CLfU-TRAO DOI
4. T H O N G SO DAU VAO VA KET QUA TfNH TOAN
Thong so kich thuac hinh hpc ciia thigt bi: a,=4,015m; aj=l,887m; a3=0.450m; 0,=ji/6;
9j=77r/4; 83=2371/12.
Xet 4 truong hop (hinh 4): Quy dao c^t xien (I), c5t ngang (II), cat dung (III) va cat cong (IV) tuong ling voi bi§u thiic toan hoc (16).
' v
N
/
1 i Ill j
\ 1
^
H(«/i 4. Quy dcio dinh trwac ciia tam dia cat O^
(I) " ; (n) " ; ly„,.U941+O,035. |yo,-l,2Ml ( | g )
fxn,=5,6895; fxn,=5,3395.0,35cos(tit/T) (IU) °= ; (IV) " ;
[yoj.1,2941+0,0351 [y„j.l.294140,3Siin(te/T) Ket qua tinh toan nhan dupc quy luat dpng hpc Clia cac khau din:
v-\~'"'
"•""-A ..,
1
"
y
\ 'T
' y<y
J
V '
_,/'
\ ~v
'y<y
Hinh 6. Quy lugt vgn toe chuyin dpng aia cdc khdu
Trfin h i n h 5, dfi thi g d c q u a y ciia c a c khau ling vdi trudng hgp (IV) cd bifin do thay ddi it nhSt, tuy nhifin bien thifin bien dg l^ii khdng tuyfin tinh, do dd van tdc va gia tdc cua cac khau d trudng nay thay ddi phuc tap hon so vdi 3 trudng hgp cdn lai (hinh 6, 7).
Hinh 7. Quy ludt gia loc chuyen dpng cua cdc khdu Trudng hgp (I), (II) va (III) thi van tdc chuyen ddng ciia cac khau cd xu hudng dn dinh (hinh 6), gia tdc lai cd xu hudng giam dan theo thdi gian khao sat (hinh 7).
Htnh 5. Quy ludt dich chuyen cua cdc khdu ddn
Hinh 8. Sai so vi tri cda tdm dta cdl theo thdi gian khdo sdt
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NGHIEN c u u - T R A O D 6 | Sai sd vi tri tam dia cat cho ca 4 trudng hgp dfiu khdng vugt qua gia tri 10"'' (hinh 8).
Do dac difim phi tuyfin nfin sai sd vi tri bifin ddi khi cat cong (IV) rat khd hifiu chinh, sai sd nay cd difim khac bifit giira tung do va hoanh do Clia OJ, d khoang giira ciia vet cfit hoanh do x^^
cd sai sd ldn, cdn tung do y^^ lai cd sai sd nhd.
Khi cat theo dudng thang sai sd thay ddi tuyfin tinh, do do cd the hieu chinh de khu sai sd nay.
ling dugc yen cau ciia cac chfi do ck.
Kfit qua nghien ciiu la co sd khoa hgc dfi tinh toan thifit kfi he difiu khien khi tich hgp thiet bi cat Ifin may xiic thuy luc.*;*
Ngay nhan bai: OS/6/2017 Ngay phan bifin: 15/6/2017
5. KET L U A N Tai lieu tham khao:
Bai bao da xay dung dugc thuat toan giai bai toan ddng hgc ngugc cua thifit bi cit lap trfin may xuc. Xac dinh dugc quy luat ddng hgc cua 3 khau din: Cin, tay can va gia nang thifit bi cat de dap ung tga do tam dia ck dat dugc quy dao cho trudc.
Sai sd vi tri tga do tam dia ck phy thufie vao phuong phap cat. Vdi bon quy dao cat thudng gap trong thuc tifin lam viec ciia thiet bi, gia hi nay nhd hon 10"^ hoan toan dap
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[2]. NguySn Van Khang (2007); Dpng luc hoc hi nhiiu vdt, NXB. Khoa hoc va Ky thuat, Ha Noi.
[3]. Nguyen Doan Phuoc (2005); Ly thuySl dieu khiin ndng cao, NXB. Khoa hoc va Ky thuat, HaNdi.
[4]. TR. 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.
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