- Trudng hop canh cd sai hiru ban, mdng va gdc v^nh v|y thi :•
3.4. Mo hinh xoay:
Canh cua khf cu bay duoc coi la mdng va cd do cong dudng trung binh profin canh khong Idn, hinh dang tren binh đ la bat ky cd the la hinh chir nhat, hinh thang va tam giaẹ.. Mep canh trudc va sau cua canh cd the la nhimg dudng thang hoac dudng thang cd cac diem gay, hoac dudng cong va thay doi hinh hoc khi baỵ
M6 hinh xoay cua canh duoc xay dung tren mat phang trung binh cua canh [12] hay cdn goi la mat phang gdc cua canh. Su dung he true toa do OXYZ lien ket vdi mat phang gdc canh. Xem hinh 3.3. Di^m gdc he true toa
^ đ O trung vdi diim dSu day cung gdc canh. True OX theo true đi xumg ciia
canh hudng theo đng chay bao, true OZ theo sai canh hudng ben phai cdn Uuc OY vuong gdc vdi mat phang gdc canh. Neu mep canh trudc cua canh la dudng cong thi cd th^ thay the thanh dudng gay khiic gom nhirng doan thang nhd.
Mat phang gdc canh chia thanh nhiJng viing f(h) blng each qua cac diim gay ciia mep trudc canh ke cac ti^'t didn song song vdi true OX. Sd thu* tu vung tfnh tir day cung miit den day cung gdc canh. Ky hieu viing cd xoay la f, cdn viing chiJa diim tfnh toan la h:
l < f < a ; l < h < a (3.22) Trong mdi viing chia thanh cac dai song song vdi true OX cd do rong Trong mdi viing chia thanh cac dai song song vdi true OX cd do rong
bang nhau theo sai canh. Tuy nhien do rong cua mdi dai thuoc cac viing khac nhau dam bao sao cho chiing xap xi bang nhaụ Ky hieu tiet dien Kf, thuoc viing f, cdn tiet difin P,, thuoc viing h. Sd thu* tu cua K^, P^ tfnh la khong la ti^'t dien bien trai cua viing, cdn Kf = N^; P,, = N,^ la tiet dien bien phai cua viing.
Hmh 3.3: So đ xoay cua canh cd sai hihi ban
Trong mdi dai chura xoay va diem tfnh toan (xem tren hinh 3.4) ky hieu
day cung tutimg dtig tiet dien bien Kf la bKf, K^.j la h^.ị Tuong tu day cung
tuong ling tiet dien bien P,, la bpi,, P,,.i la bp,,.ị Chia cac cap dai cung tren thanh
3a
Xi
fV^^M^-^^^^
Hinh 3.4:
r;^;,^.,- Cudng do xoay tai mep sau canh
Rdi ndi cac diim chia tuong utig vdi nhau duoc Uf (n^) d hinh thang. Tuong tu nhu vay d tat ca cac dai trong cac viing f va h deu cd Uf (n^) d hinh thang. Tiep tuc trSn cac canh day cua cac d hinh thang trong dai Kf, K^., va (P,,, P^.i) chia thanh 4 ph^n bang nhaụ Cach mep trudc ciia mdi 6 1/4 dat dai xoay lien két, cdn diim tfnh toan nam tren dudng trung binh ciia hinh thang va each
mep trudc 6 la 3/4. Dai xoay lien ket theo sai canh ky hieu la \i, dudng ndi cac* diim tfnh toan theo sai canh ky hiSu la v. Thii tu tfnh \i (v) tir mep trudc den
mep sau canh:
1 < ( ! < % ; 1< v < nh
Ky hieu i la sd xoay lien két, j la sd diim tfnh toan:
(3.24) l < i < I l < i < I f Z n (3.25) f = 1 K^ =1 N, 1 <j < Z Zn (3.26) h = l P.
42
Sir dung cac toa do khdng thii nguyen đi vdi cac diim tren mo hinh xoay ciia canh.
^=z— ; T I = 7 — ; C =
cax cax cax
bcAx " Day cung khf đng trung binh ciia canh.
Toa do diim tfnh toan trdn md hinh xoay duoc xac dinh:
^rv.=^(^op.+^op.-,H ^ ( b p - b p ^ , ) ^ 2 n , — h ^ h 2 n , — h ^ h nV.=^(nvP,-TịP,-.) Sv\-1 ố^^Ph "*"SvP,-l) > (3.26) (3.27) v=I,2...n,; P,=1,2...N,; h=l,2...a J
Toa do diim giiia cua xoay lien ket, sai va gdc xien cua xoay tUOng tU xac dinh bang cac bilu thiic sau:
S[iKf-Ĩ"T(SOKf'*"SOKf-l)"'" - (^Kf " b R f - l ) 2n ^ (1 Kf-1 *~ ^ I ^ OKf ' * " n OKf-1 / S j i K f - l " - ( SoKf "'"SOKf-1 ) (3.28) (3.28) ' Kf-\ ~ ^ ( ^)OKf-l "4)0Kf / [^ - ^EX\i Kf-\ ^oK,+^oK,-M -z^^iKr^K.-i) 2n SjiKf-l'SuKf
^=l,2...nf; K^l,2...Nf; f=l,2...a
Trfin hinh 3.3. md hinh xoay ciia canh mdi cho niia canh ben phai, cdn nufa canh ben trai đi xihig qua mat phang OXY, sd xoay va su bd tri chiing
irtn mat phing gdc tuong tu nhu nua canh ben phaị
Toa do diim giiia ciia xoay lien ket, sai va gdc xien ciia xoay tuong tu xac dinh nhu sau:
oc^^Kf-i S;.Kf-í OL,^Kf-1 - Sj.K,-ị or\^ j.^_i-r|^ j,^_, ,
K
Sli;-.=lt.;8x^Kf^_,V,-r (3.29) Md hinh xoay đ'i vdi canh cd mep canh trudc va sau la dudng thing, Md hinh xoay đ'i vdi canh cd mep canh trudc va sau la dudng thing, gdc mui ten Xc cd' dinh. Mdi dai xoay lien két cung la dudng thing cd gdc xien Xx ciia xoay cd dinh, cdn đi vdi canh cd cac mep canh la dudng gay hoac dudng cong thi cac dai xoay lien két cung la dudng gay khiic va dudng cong. O trudng hop dai xoay lien két la dudng cong, gdc xien cua xoay xac dinh bang gdc nghieng cua tiep tuyén vdi dudng cong trong dai chiia xoay (Kf,Kf -1). Md hinh xoay cua canh hinh chii nhat, cac xoay xien se la cac xoay thing hinh mdng nguạ
>fhu vay tren toan bo mat gdc cua canh da duoc thay the mot Idp xoay lien tuc, phan bd rdi rac theo day cung canh. Su bien thien lien tuc cua luu sd van tdc r hay la cua cudng do xoay theo sai canh duoc xem nhu gan vdi qui luat bien thien bac thang. Phuong phap xac dinh dac tinh khf dong cua canh dua tren mo hinh xoay rdi rac, ap dung rat hieu qua vdi sir tro giiip ciia cac thiet bi cong nghe thong tin. Dieu nay ly giai mot mat la do phuong phap dua trfin loai dac tnmg thuy khf dong xoay don gian de md ta đng chay bao phai tim, mat khac rat quan trong la he cac phuong trinh dai sd d l xac dinh cudng do xoay, cd Idi giai rat 6n dinh đ'i vdi cac diJ kien đu vao cua bai toan.
44