Pham Thanh Long va Big Tap chf KHOA HOC & CONG NGHfi 176(16): 1 1 - 1 7
T I N H T O A N D U N G S A I C H U O I D A N D O N G C H O T K H O A K E T S A T B A N G P m r O N G P H A P S 6
Pham Thanh Long', Le Thi Thu Thily Trudng Dgi hgc Ky tkudi Cong nghiep - DN Thai Nguyen T O M T A T
Trong chl t£io may viec dam bao do chinh xac cua cac co ciu co khf 1^ mot trong cac noi dung co ban Q budc thiet ke, ngudi ^ su can dinh luong dugc gia tri dung sai cua cac chi tiSt may dya tren so d l lien kit dong hoc ciia chiing. Chuoi kich thudc \k m6t trong nhflng phuong phap plio bien dl lam viec nay, tuy nhien cac chuli khong gian vdi s6 lugng khSu Idn khong de c6_dugc Idi giai hgp ly. Bai bao nay gioi thieu mpt phuong phap sfi giiip x^c dinh dung sai cac ca ciu khong gian nhanh chong, chinh xac va ton trgng phan iing dong hpc tu nhiSn ciia co cau hon phuong phap chu6i kIch thudc truyin thing. Chiing toi ciing minh hpa giai thuat tren mot co ciu co khi la he thong dan dong chot khoa ket sat. Ket qua thuc nghiem tren mo hinh va mo phong cho thay tfnh dung dan cua giai thuat trong dieu kien lap lin hoan toan chi tiet may. Phuang phap nay hoan toan CO the ung dung tren cac cum chi tiet may dang chu6i dgng kin ho^c hd
Tu" khoa: dung sai; chudi ddng; ldp lan; do chinh xdc; Jacobian M O D A U
Dp chinh xac cua c o cau chap hanh la he qua ciia mflt qua trinh lu thiet k l , che tao, lap rap, dieu chinh va dieu khiln. Viec dieu khien phan hdi khong the thay the hoan toan cho chat lugng che t^o c a khf, do vay viec xac djnh d u g c dung sai ciia cac khau thanh phan tham gia vao chudi ddng hpc la mgt ngi dung CO ban cua he dan dgng c a khi.
Cd hai p h u a n g phap c a ban de lam viec nay, mdt la p h u o n g phap chudi kich thudc truyen thflng [1]. P h u a n g phap nay dupe iing dung trong n h i l u ky thuat bao gflm ca tinh toan dung sai chufli kich thudc va thiet k l dp chinh xac ciia cac phep do nhieu thu nguyen [1]. N o CO n h u g c d i l m mang nhilu nhgn dinh chu quan do trong mpt chudi ddng n khau can gan trudc ( n - l ) thanh phan ciia chudi de giai khau khep kin, each lam nay tuy dam bao dugc dung sai ciia chudi song khong tdn trpng phan ling dpng hpc t u nhien ciia c a cau.
Hai la dua vao ma tran Jacobian de tim anh xa cua cac di chuyen nhd ngo vao theo cac di c h u y i n nho ngo ra [2]. Cach nay kha phiic tap va It dugc ung dyng do phai xac dinh dugc dao ham cua cac ham lien k i t dfing hpc phii'c
Ve/, 0947 169291. Email kalongkc@gmail com
tap, mat khac nd cung chua tim dupe dung sai ciia t i t ca cac yeu tfl thiet ke bao g6m cac kich thudc dai va kich thudc gdc.
Do bai toan ddng hpc ngugc cua robot cung la mdt kenh phan anh chinh xac quan he ve chat lugng che tao cac khau thanh phan vdi dp chinh xac vi tri va hirdng khau cudi [3]. Nen hoan toan cd the su dung cdng cu nay xac dinh dung sai cho cac chufli ddng hpc neu cd mpt cflng cy giai d u g c bai toan nay vdi dp chinh xac cao [3]. Mpt so nghien ciiu khac sii dung hdi quy thuc nghiem se khdng xac djnh dugc dung sai che tgo ma se cung cap thong tin ve miic dfl anh hudng ciia cac thdng sfl khac nhau tdi c h i t lugng dieu khien khau cuoi nhu d6 chinh xac, diln hinh cho hu'dng nghien cuu nay la [4].
QUAN HE DICH C H U Y E N KHAU CUOI v e i l DUNG SAI K H A U T H A N H PHAN Xet mdt chu6i ddng hpc n thanh phan gdm cac yeu to kich thudc dai va kich thudc gdc khi khdng ke den dung sai cd dang nhu ( I ) :
f(d„..,d„)^p,; i = \^m ( I ) Trong do d, la kich thudc (dai hoac gdc) khao sat, m la sfl lugng diem khao sat;
Mfl hinh ( I ) the hien quan he ly tudng khi cac tham so d, che tao chinh xac va p, la diem
Pham Thanh Long vd Big Tiip chi KHOA HOC & CONG NGHf 176(16): 11-17 mong muon. Khi ke dgn dung sai cua !<ich
thu-ac d„ vi tri va huang cua diem cuoi CO sir thay doi va ducrc bieu dien boi phuang trinh (2):
/(d,±Sd„..,d,±Sd,) = p, ±Sp,;
(2)
•(3)
•(4)
Do trong (2) chiia ca kich thudc dai va kich thudc gdc nen bai toan nay rat khd de khao sat chung, tien hanh chia nhd bai toan (2) thanh hai bai toan dudi dang dan gian hon bang each chi nhin nhgn mpt logi tham so co dung sai trong mdi lan khao sat trong khi cac tham sfl khac giu efl djnh gia tn danh nghTa ciia nd:
f{d,±Sd^,..,d^±Sd^di^^,..,d„) = p,±Sp,;^
i = \-m
f{d„..,djd^^,±Sdj^^,..,d„±dd„) = p,±5p, ;^^
i = \-m
Trong (3,4) d|...d, dugc coi la kich thudc dai, dj+|...dn dugc coi la kich thudc goc.
Trong cac bai toan nay p, \h tga dp cac dilm khao sat dugc ngudi thiet ke lira chpn, ±<5p, the hien chat lugng djnh vj hoac djnh hudng khau cuoi mong muon. Toan bp cac ki'ch thudc danh nghTa di..dn lay theo thiit kl, phuang trinh (3) chuay in so la cac dung sai tu Sdi..Sdj, phuang trinh (4) chua cac in sd la dd^^y.dd„.
Nlu giai dupe cac phuang trinh (3) va (4) se xac djnh dugc miln dung sai cua cac khau thanh phan tham gia vao chudi kich thudc tai cac diem khao sat, viee cac gia tri nay cd diing cho ca miln gia trj ciia cac tham sd do hay kh6ng cin dupe chiing minh ddc lgp dl CO ket qua cuoi ciing, viec chung minh nay dupe trinh bay trong muc tiep theo.
PHUONG PHAP SO CHO BAI TOAN DUNG SAI De giai bai toan (3) va (4) vdi dac tnmg ciia chudi kich thudc tdng quat thi chiing co dac dilm phi tuyin, si6u vi?t [3], vi (3) va (4) cd dang nhu nhau, d day trinh bay each giai vdi (3) la vidu.
Bien doi so cip (3) vl dang tuang duung nhu sau:
M/l[/(rf, ±Sd„..,dj ±Sdjd^^„..,d„)-{p, ±Sp,)];
i = l-?-/M
Khi bilu diln cho mdt chufli khflng gian, phuang trinh (5) dudi dang khai trien thudng dudi dgng cac toa dp thanh phan vdi dang khai trien nhu sau:
l^in[lf{d,±gd,,..,d^±Sdjdj^ d„),-(p,±SpXf-\- (fid,±sd„..,d^±sdj^,„.,d„),-(p,±dp,\f+ ; {fi.d^±Sd^,..,d^±dd^dj,,,..,dX-{p.±Sp,\f];
(6) Ham toan d (6) gpi la ham Banana, ttxmg [3] ban den each giai bai toan nay bang phuang phap GRG va hieu qua thuc te da dugc chiing minh.
v i n dl cdn lai d day la khi (3) vk (4) giai rieng, dap iing rieng le ciia cac nghiem dgt dugc tu (3) hoac (4) duang nhien thoa man cac phuang trinh nay. Tuy nhien chiing co thi thda man (2) hay khdng mdi la dilu kien du de chap nhan ldi giai cd tu each iing dung vao che tgo. Sir dieu chinh mien dung sai dat du^
tren co sd phuang phap kiem tra phfli hop nhu sau:
Ggi dj E(dj^^,dj^^^y, j=\...,i la miln dung sai tinh toan dgc lgp ctia dj theo (3) va (4), chia khoang nay lam k phin deu nhau, vdi k dil nho. Chudi gia trj khao sat vdi moi mdt kich thudc danh nghTa sg lit mflt chuoi cdng cd dgng:
d -d, d -d
* k (7) Nhu vgy vdi mdt chudi dgng hpc cd n khau dgng, so td hpp can kiem tra dung sai theo phuang trinh (2) tren quan diem lap lan hoan toan cac chi tiet may se la n td hgp.
Trong trudng hgp mdt phuang an ngau nhien nao dd that bai, tiic (2) khdng thoa man, viec dieu chinh cd the dien ra nhu sau:
- Di chuyen mgt can xa han so vdi gia tri
danh nghia ciia dj vl phia trung tam, bo di
mgt bu'dc chia theo (7), luc nay gia trj mdi
ciia mien la:
Ph9m Thanh Long vo Big Tjp chl KHOA HOC & CONG NGHfi 176(16): 11-17
'','^C''.™.+- , . ) ; y = l - '
- Di chuyen ca hai c^n ve phia trung tam ciia mien bo di mpt b u a c chia a moi dSu:
7 = 1
+ ( * - l ) . -
");
(9) Can lap mdt c h u o n g trinh de lam vice nay vi kh6i lupng tinh toan khi kiem tra toan bfl n^ tfl
hgp la rat Idn, tuy cac bai toan (3) va (4) dugc giai rieng re nhung den day ket qua da dugc hop nhat khi su dung mfl hinh (2) de kiem tra anh hudng phfli hgp ciia tat ca cac dung sai thanh phan.
TINH TOAN DUNG SAT CHUOI DAN D O N G CHOT KHOA KET SAT
D I minh hga quan diem ly thuyet neu tren, trong muc nay chiing tfli trinh bay mgt tinh toan va kiem chiing bang md phdng sd cung nhu thuc nghiem vdi chufli canh cua tren ket sat.
(a) Mat dung cdnh (b) Khai trien mdt cdt ngang cdnh cira
Hinh 1. Kit cdu he thdng chdl khda cdnh ctta kit sdt gom muai nhdnh doc lap vd cdc kich I hudc danh nghTa khi chua tinh todn dung sai
Can Cli vito s o do ddng ciia chu6i dan dpng ehdt khda, xay dung s o dd tuong duong de tinh toan dung sai cho mot nhanh nhu hinh 2
1. Ban le ciia 2. Canh ciia 3 DTa trung tam 4 Thanh song phing 5. C^ng ngang 6. Con trupt bi 7. Ch6t khoa 8 Lokhda
Hinh 2. Sa do hda mol nhdnh dgc lgp he thdng chot khda cdnh cda kit sdt
Khau I: la ban le cita dudi cung ciia cSnh ciia {ctVa gom hai ban le, dong tryc, doi xung qua dudng nam ngang di qua tam cdnh ctia);
Khau 2: tugng tnmg cho mpt nua chieu cao, mpt niia chieu rflng cua canh cua, tinh tfr gdc dudi ben trai den tam canh cua;
Khau 3: Tupng tnmg cho ban kfnh tdc dong ciia dta dan dfing trung tam ciia khoa, no gan vol cac khau song phing so 4 co hai diu sir dung khdp R;
KhSu 5: cang ngang cd chiic nang truyen dfing tap trung cho cac chot cung phia;
13
Pham Thanh Long va Dtg Tap chf KHOA HQC & CONG NGHE Khau 6: Con truot bi dugc so do hoa thdnh o truot;
Khau 7: chflt khda vdi dudng tam di dong theo vj trf cdnh cira (gom 6 bgc tir do khi tinh dung sai).
Hinh 3. Mo hinh hda ddng hoc hi Ihdng chot khda cdnh cua kit sdt theo kp thugt robot Bang thdng sd D-H:
Bang 1. Bdng thdng so D-H
R(z,-..ot,) T(2,.„d.) T(x„ai) R(x„a,) 1
2 3 4 5 6
m w m m
0W
dl
0 0 0 (d,) 0
9<f 0 50°
Xay dung ma tran truyen
" , J , P,
Tien hanh khao sat su xe dich ve hirang cua ch6t Ithoa xung quanh vi tri dong:
o^-EE^^x.
Hinh 4. Vi tri ddng khoa chinh xdc
Hinh 5. a) Suxe djch hudng cua chot vai true ndm trong hinh Hinh 5. b) 8 diem khdo sdt ndm non cho phip tren dirdng sinh mdt non
Pham Thanh Long vd Dtg Tap chi KHOA HpC & CONG NGHE 176(16): : Ket qud khdo sdt bdi loan kich thu&c goc:
Vdi d u d n g kinh Id va chot da chpn, ta cd khe h d huong kinh la 0,5mm, n h u vay, su lech hudng cho phep ciia true X^ se nam trong hinh non nhu hinh tren, vdi gdc a,na,=0,0393 rad, dinh non tgi d i l m P(610,0,363)
Khao sat 8 diem tren d u d n g sinh (hinh 5.b) cho ra sai sfl cho phep cua cac bien khdp dugc ket qua the hien trong biing sau:
B^ng 2. Kit qua khdo sdt sai sd cdc biin khdp qi nx
1 0,999228 0,999228 0,999228 0,999228 0.999228 0,999228 0,999228 0,999228
0 -0,03929 0,0392899 -0,019649 0,0196487 0.0196487 -0,019649
• 1
-1 -0,999228 -0,999228 -0,999807 -0,999807 -0,999807 -0,999807
ql
-1,056E-07 1,056E-07 5,3E-08 5,28E-08 5,28E-08
q2 -0,3914889
•0,4062307 -0,4062307 -0,4058793
•0,4038704 -0,4010218 -0,399034 -0,4062307 -0.4062307
q3 0,7715775 0,7776914 0,7776914 0,7775117 0,7777601 0,7767342 0,7666561 0,7776914 0,7776914
q 4 1,1462471 1,1507832 1,1507832 1,1507461 1,1487591 1,1480985 1.1543436 1.1507832 1,1507832
q5 26 25,956184 25,956184 25,956208 25,987616 25,999177 25,780797 25,956184 25,956184
q6 -1,5707963 -1,5615439 -1,5615439 -1,5617971 -1,5630315 -1,5652816 -1,5612657 -1,5615439 -1,5615439
Theo ket qua khao sat d bang 2, gia trj cua bien khdp q, thdng ke theo tirng cdt vdi i= I -6 se bien dflng trong mdt gidi han nhat dinh khi so s^nh cac gia trj Idn nhat va nho nhat ctia chiing trong cac cot dd se dinh ra dung sai ciia tung khdp.
Vgy dung sai cho phep ciia cac bien khdp la:
5q2 = - 0 . 0 1 5 - 0 . 0 0 (rad) 5q3 = - 0.0036 - 0.006 (rad)
5q^ = 0.00 - 0.005 (rad) Sqs = - 0 . 1 5 - ^ 0 . 0 0 (mm) 5q6 = 0.00 - 0.0088 (rad) Kiem tra ket qua tren phan mem:
Ket qua md phdng tren phan mem khi quan sat cac giao diem ciia d u d n g thang tugng trung true ciia chflt vdi mat phang day cua hlnh non. Cac diem cham deu da roi vao trong mat non gidi han.
Theo hinh 5, viec kiem tra mdt p h u a n g an dinh hudng nao d o cd rai vao trong ndn huong chap nhan d u g c hay khdng cd the thuc hien Ihdng qua vi$c kiem tra diem cat cua p h u o n g ^n do vdi mgt d i y cua ndn. N l u diem nay roi vao phia trong v d n g trdn b i l u thj day cua ndn thi p h u a n g an do chap nhan dupe va n g u p c lgi.
DiJiDBivcijty diycAibmlng Cbip ntita ia^'
-K^
V -.^
,^ Huftng chlnh n*c
Hinh 5. Kiem tra do chinh xdc dinh hitdng cita chot khda qua diem chgm tren mgt day ndn huang
chdp nhgn dugc
Tren hinh 6, chiing tdi md ta ket qua kiem tra toan bd cac tfl hpp dupe lap lan theo quan diem noi tren. Cd the thay rang tat ca cac tfl hpp cd the cd da rai vao trong vdng trdn gidi hgn.
\
Hinh 6. Cdc diem chgm khi ldp lan cdc khdu bieu diin tren ddy mat ndn sai sd hudng gidi hgn
Pham Thanh Long vd Big Tap chl KHOA HpC & CONG NGHg 176(16): 1 1 - n
.^ O c l K l i a n Calculi
r'fu
* • = « • » ™ ™ I H n s Z M iPM OOOOOOI)
J M CCOCOX!
/ I n n a E M
^ u orooDO Xngls q i M l )
An^eqZtBd) J M OCIHBO / n ^ s q S t a l ) J M OHnccc j An>^e <H WH) , ^** " • ™ ^ J A n q S ^ i m
^ M • 0160000
1
i A 4 e q S » a d ) J M OEOoooa
U.Sa-,m,
r v . , .
^ V . l ^
. ^ v ^
._ y ^
^ v*»
, v « .
:- Vduo
: vjiu*
-^-—-_
''^ • i i
jMoowBo^:
298000000^:
" M 5 0 0 0 0 0 >
G05(XKK»4
M O M T O M ^
o.ooonoo^:
• o » i H » :
1 W{2M
ieoiKi»a>
-MTDSW
_ . ^ . _ „
»».
.^
i ^
*w
JmKi
' • • "
,„
STIBW
J I K H 1 •
—
o.oooood^
ooooooo^
ooooooo—
O M O M O :
OOMBOO^-.
DIKWGOO:
oooeooo-;^
0005000-;
" • "
Spllnumbsr
S B K ™ * ^
S o » . u * * .
Sptrunbt.
SpHnumMr
SlAruntiw
Scttrunbor
SlAiuriier
SpHrunlw
Spttumlwf
Splrunbn-
„
TX'
•V Swce
^ 9 « =
-;- Sups
4 - S w e
; ' 9 M I
....
: a s > t
.J. Stcpc
: s i « =
.; s i » s
: Steps
r -ZZ"
0
"
*
0 Da
.»,
0IXI12S
05375
awd
::„..
C S u o F I .
Z A « . R .
: ( U s f h
LJflUoRil
,^ila!«
- ' ftisfn
lM„fy.
! "• " 11H =•-
UnffBTSn) OKO-;-
r . c . i ^ w . Pu P,)
fe*j|*-J
:
»VSh™ VKIm V) W B lim:
5 M M 3 ! i . « i t ^
kJ6.W^~<ht=D ZM.BJOjwthj.O
).(ii^ht-D h 0<K5-0J915|Mlhe^KI3rai ITtTOB 0777H1 v«ic^DOJ»i IH6;i!S121»U>t-0.(XI125 . l57C9-16KUlht=0.002 i 'oial HIDOOOlemi '-^
f«lK=Py5l>Sfl01!''A
Hinh 7. Gftio (//e« va kel qud Theo ket qua kiem tra tren hinh 7, cd 500000 kha nang da dugc thir nghiem xung quanh diem tinh toan, tat ca deu da dat yen cau ve dung sai.
Ket qua thuc nghiem tren 03 san pham that bao gflm ket sat trong de tai ma sd T 2016-31 [5] do trudng DHKT Cflng nghiep quan ly, ket sat trong luan van Thac sy cua hpc vien Nguyen Manh Tuan [6], va ket sat ma tic gia che tao cho cflng ty Nam Viet (hinh I) cung cho thay cac chi tiet dugc ISp ngau nhien khflng qua lya chon sau khi khang djnh chiing dap mig dung sai theo tinh toan, he thflng ludn vgn hanh on dinh khflng bi hoc, k?t. Dieu nay chung td dp tin cay ciia phuang phap tinh toan dung sai mdi ma chiing tfli gidi thieu.
KET LUAN
Vdi cac he thong kit cSu ca khi cd chuyin dflng khdng gian viec chuyen sang tinh dung sai theo hudng sfl hda la cin thiet. Khi do cac gia tri dung sai ciia tiing khSu khdng cSn chpn trudc theo quan diem chu quan nhu phuang phap truyen thdng, t5t ca cac gia tri nay hinh thanh dong thdi va khong cd khau kh^p kin chufli nOa. Do bai toan khdng khao sat dugc dong thdi hai nhdm biin 1^ biin kich thudc 16
kiim tra tai diem tinh todn
gdc va bien kich thudc dai nen da dupe chia lam hai bai toan nhd. Viec hcrp nhat ket qua sau do bang each kiem tra dap irng 13p lan hoan toan tren phuang trinh ddng hpc thuan cho thiy cac chi tiet may da xae djnh dupe gia tri dung sai cho phep cua tung kich thudc.
Vdi each tiep can tong quan nhu chiing toi trinh bay d tren, phuang phap thiet ke dung sai nay cd the ap dung dugc cho nhieu kieu dSn dflng khac nhau tir robot cflng nghiep, cac cum may, cac ca cau khdng gian nhieu bac tir do noi chung deu rat hieu qua.
LCII CAlVI ON
Nhdm tac gia xin tran trpng cam an Dgi hpc Thai Nguyen da tai trg kinh phi cho bai bao nay thdng qua de tai ma sfl DH2017-TN02- 01 .DH, do Dgi hpc Thai Nguyen dat hang.
TAI LIEU THAM KHAO 1. Nguyen HOu Cong (2002), Gido trinh ky lhu$l do lu&ng, Nxb Dgi hpc Quflc Gia H^ Nfli, Ha N$i._
2. Nguyin Thien Ph(ic(2006), Nghien cuu, thiit ki. chi tgo cdc robot Ihdng minh phuc vif cho cdc ung dung quan trgng, D I tai cap Nha niroc, mas6KC.03.08.
3. Pham Thanh Long (2012), A New Method to
Sohe the Reverse Kinematic Robot Problem,
ISTS,ThaiLandp 43-46, 10-2012.
Pham Thanh Long vo Org Tap chi KHOA HOC & CONG NQHE 176(16), 11 - 17 4. Son Duy Dao, and Kazem Abhaiy (2012), tdy chpn bao mat va bao ve ciia ca nhan ngiroi Delermmalion of the Significance of Tolerance diing, dS tai cdp CO so ma so T2016-31.
Parameters on Robot Performance Using Taguchi's 6. Nguyin Manh Tuan, Thia k6, chl tao ket sat Tolertmce Design Experiment. Applied Mechamcs ^. ^ ^ j |^^^ ^^ ^ Luan van Thac
and Materials, Vols 229-231, pp. 2100-2105. . . 6 „ , ' 5. Pham Thanh Long. Wghien ciu, phat triSn '^ ^ * * BHKT CN Thj, NguySn, 2017.
phien ban ket sat ccr dien tu theo hudng nang cao A B S T R A C T
C A L C U L A T I N G T O L E R A N C E O F T H E A C T U A T O R I N G C H A I N OF T H E L A T C H L O C K OF T H E S A F E BY N U M E R I C A L M E T H O D
Pham Thanh Long', Le Thi Thu Thuy University ofTeclinology - TNU In the manulacture of machines, ensuring the precision of the mechanical structure is one of the basic contents At the design stage, the engineer needs to quantify the tolerance values ofthe machine parts based on their kinematic linkage scheme. Size chains are one of the common methods to do this, however spatial sequences with large numbers of strings are not easy to come up with This paper introduces a numerical method that helps to define the tolerances of spatial structures more accurately and respects the natural dynamic response of the structure than the traditional dimension chain method. We also illustrate the algorithm on a mechanical mechanism is the key system locking the safe. Experimental results on the model and the simulation showed the correctness of the algorithm in terms of fully assembled and assembled components. This method can be applied on clusters of closed or open kinematic chain.
Keywords: Tolerance, Kinematic chain; interchangeabihty; Precision; Jacobian
Ngdy nhdn bdi: 01/11/2017; Ngdy phdn biin: 30/11/2017; Ngdy duyitdang: 05/01/2018 'Tel: 0947 169291. Email: [email protected]
