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NGHIEN CUU ^ ^'m Mot nghien eitu md^i v e phan phdi tdi ifu ti so t r u y e n eho hop giant t o e banh rang tru rang nghien hai e a p khai t r i e n (*) NGUYEN THI THANH NGA VU NGOC PI TOM TAT Bai bao gioi thieu mot ket qua moi ve phan phoi toi iru ti so truyen cho cac cap ciia hop giam toe banh rang try rang nghieng hai cap khai trien, nham dat chi tieu khoi lirong cua hop giam tdc la nho nhat Dya tren dieu kien can bang mo men cua cc he gom cac bo truyen banh rang hop va dieu kien sirc ben deu ciia chung, bai toan va chirong trinh toi mi nham xac dinh ti so truyen toi iru cua cac cap banh rang da du-yc thilt lap Tir ket qua ciia chirong trinh toi iru, cong thirc tinh toan ti so truyen ciia cac cap da diryc de xuat nhtr irng dung phirong phap hoi quy Bang viec dira cong thirc nay, viec xac dinh ti so truyen cua cac cap trff nen don gian va chinh xac Gioi thieu Trong thiet ke toi uu hop giam toe, viec xac dinh ti s6 truyen cua cac cap ciia hop la mpt nhiem vu rat quan trpng Nguyen nhan la vi kich thuae, kh6i lupng va gia eua hop giam toe phu thupe rat lon vao ti s6 truyen ciia cae cap Do vay, bai toan xac dinh ti so truyen toi uu ciia cae cap da, dang va se la van de dugc cac nghien ciru va ngoai nuae quan tam Doi voi viec xac dinh ti s6 truyen cae cap cua hop giam t6c banh rang try rang nghieng hai cap khai trien, cho den nay, co kha nhieu nghien cuu de cap den Voi dang hop nay, ti so truyen ciia eac cap co the xac dinh bang d6 thi ([1, 2]), bang phuang phap "thyc tien" dya tren phan tich cac so lieu thue tien [3] hoac bang cae c6ng thirc toi uu [4, 5] Vai bai toan toi uu phan phoi ti so truyen eho hop giam t6c khai trien, nhieu ham muc tieu khac da dugc dua Vi du, ham tiet dien ngang ciia hop la nho nhat [5], ham kh6i lupng ciia hop giam toe la nho nhat [6], hoac ham da muc tieu [2] Din nay, da co kha nhieu nghien cim de xac dinh ti s6 truyin eac cap eho dang hop da neu Tuy nhien, chua CO nghien cim nao de cap den bai toan t6i uu ve gia eua hop De giai bai toan ve gia thi bai toan khoi lugng ciia toan hop la nho nhat se la bai toan quan trpng nhSt Vai bai toan nay, nhu da neu tren, eac (*) Kiioa Co khi, Dai hoc Ky thuat Cong nghiep, Dai hoc Thai Nguyen TAP CHi c a KHi VIET NAM V tac gia [6] da dua mpt eong thirc eho phep tinh toan ti so truyen toi uu cua cae cap hop Tuy nhien, ham khoi lugng ciia hop mai ehi gom khoi lupng banh rang va vo hop chir chua ke den khoi lugng cac true (true chiem ti trpng khong nho ve khoi lugng va gia voi mpt hop giam toe banh rang) Ben canh do, anh huong eiia m6 men xoan cho phep ciia hop den ket qua phan phoi ti so truyen ehua dugc ke den Bai bao trinh bay mgt ket qua moi cua viec tinh toan toi uu ti s6 truyen cac cap cho loai hop nham dat chi tieu khoi lupng eiia hop (bao gom khoi lugng cac banh rang, eac true va khoi lugng vo hop) la nho nhat Them vao do, anh huong eua m6 men xoan da dugc ke den c6ng thirc tinh toan ti so truyen toi uu cho cac cap cua hop r r Xac dinh Idioi lirong cua hop giam toe Khoi lugng cua hop giam toe duge xac dinh nhu sau: (1)G,=G,,+G,.+G, Trong do: G^^, G^^^ va G^^ tuong irng la khoi lugng vo hop, khoi lupng ciia cac banh rang va ciia eac true hop Hinh 1: Trinh bay cae thong so dugc sir dung de finh toan cac phan ciia (1) Viec tinh toan cac khoi lugng phan dugc trinh bay cu thi nhu c^ duoi day: So 08-Thang nam 2010 NGHIEN CUU - TRAO OOI (9) / / = < , , + , ^ , ; (mm) (10) 5, =/?„,+/?,,.+6^,^ (mm) (11) c = , 0 x Z + 4,5 (mm) Voi, d^^^j, ( A ; „ ] / ( M , + ) Trong do: (13) ^ , „ = [ v , J / ^,„ >^^„ y } Trong do, [S HJ la img suat tiep xuc cho phep ciia b6 truyen cap nhanh; Z,,,, Z^,,, Z^,, tuong irng la Hinh 1: So tinh toan khoi lugng ciia hop cac he s6 xet den anh huang cua co' tinh ciia vat lieu, hinh dang ciia be mat tiep xiic va t6ng chieu dai tiep 2.1, Xac dinh khoi lirotig cua vo hop xuc Y,,, la he s6 xac dinh theo cong thirc [61: Kh6i lugng ciia vo hop G^^ dugc tinh toan theo cong thirc sau: hell ' ' t_ L J (14)v,„=0,5>(7^,]/(v,.„>4., >{/C„,]) The tich ciia vo hop I^,^, dugc xac dinh nhu sau Ta CO [6]: (xem tren hinh 1): {3)V,=2%+2>V,,+2>V,, (16)^,,,, =y,„>t/„,,, Voi, V^, V^i va V^2 tuong img la the tich phan day hop, the tich mat ben theo chieu dai va theo chieu rpng ta duoc: ciia hop Cac phan co the xac dinh nhu sau: (4) Thay bilu thirc (14) va (15) vao (16) va bien d6i V,=LxB,.l5ySc (17) K, = llyl>(u,+inT,,]/{2ni,iK„]) Ty so truyin ciia bp truyen thir nhat dugc xac dinh (6) V,, = B, x// >^^ = (5, - 2S^)yH^S^ theo c6ng thirc: Thay cac bieu thirc (4), (5), (6) vao (3) ta dugc: (7) F;„=3>ixfi, >«^.+2>ix//^^+2(5, - 2>«c)x//>5o Trong cac c6ng thirc tren, L, H, S^ va B, dugc xac (18) H, =0?„.2, /(i„,i, Thay (15) vao (18) va bien d6i, ta dugc: dinh nhu sau [5]: (8) / = ( r / „ , , + ^ „ , , / + r/„,,,/2 + ^ „ „ + 2 , ) / , (19) ^,,„ = ^4H^.MT;,]/(>,„,>{/:„,]) (mm) Tinh toan tuong ty doi vtVi bp truyen ciip cham ta co - TAP CHi c a KHi VIET NAM V So 08 - Thang X nam 2010 c^ NGHIEN CUU - TRAO 0 ! (20) ^.,22 = ^I^^4^{^nVVZA^) (27) b^, = ijy LATMu,+u,f K2 = ^ laKu^+lf >{TuV(2niAKo2]) (21)"^'*"^^ ' ' ' ' ' ' '-'''-'' /(2>hl^liK,,]Hi:nil) (^^)d,.,=^4iT]n^J^,,>hlitl>[K,,Utl) (22) d^^.,,={l4Hil>{T,,]/(y ^AK^.j) Tir bieu thiic (24) ta eo: (^9) [T^^ J ~ [^ J/ (."2 ^br^o ) ^^^^ ^^ ^ ^^^^ ^^9) y^o cac bilu thiic (20), (21) Tir dieu kien can bang eua co he g6m bp truyin banh rang, ta co: (23) r, / 7;, = [T, ] /[T; , ] = M, >?^, ^ I >h I va (22) se duge: Va {2A)TJT,,=[T.]l[T^,] = u,^,^'>hl (30) ^„.,: = ^ >(7: ] / ^ ,,, >^,, >^ ; >(/^o, ] >%il) ' Trong T, [T], T,,, [T„], T,, va [T,J tuong iing la mo men xoan va mo men xoan cho phep tren true ra, true chu dpng cua bp truyen cap nhanh va cap cham /?j^ la hieu suat cua bp truyen banh rang hop; h^ la hieu suit ciia mpt cap lan (31)Z) = ^^T^ >fri>(w +1)V(2>A >^ " >f A^ l^^") (32) d^^.^^ - ^[T^]>ii,l(^ ^^2 ^br^^l "(^02]) Tir (23) ta co: 2.2 Xac dinh khoi liryng ciia cac banh rang j ^ ~ j jy.^g ^^^ ^^g ^j^ygj^ ^^^^ j.-j^g Q^^ ^^^^ ^^^ (25) [7; ] = [T,.]/ui,>h„^>h „ = [7;,]/u^ Hi, Ht -, ^ „ Thay bilu thirc (25) vao cac bilu thirc (15), (17), (19) vai chu y M, = I / / M , ta co: '^'"'^ * ^ ° ^°"8 t^"'^' , (26) (i,,,, I = 3^4 >t/2 >ir.] / ^fc„i>'t^^', '^t I >{^oi ] ) ^'^^^ ^Z"- " '^'"•1 "^ ^/"-z Trong do: 0^^^, va G^^^ 1^ ^^o^ lupng cua cap banh rang c^p nhanh va cip cham G,^^, co thi tinh nhu sau: (34)G,,, = r Ke, >p < , , >* ,, / + e, >p ^ ^ i *wi /4) = r ^ >?? < „ >*„,, y{e,+e, nif)/4 Vai, r^ la khoi lugng rieng cua vat lieu banh rang (kg/mm^); e^, e^ la he so ve the tieh cua cae banh rang va 2; tinh toan co the lay e^ » 1, e^ =; 0,6 [2] Thay Z?„,, =y MX^MX^'^^ (^4) ta co: (35) G,,,, = r , ^ 5^ ^_^^ < , , Ke, +6, >^,')/4 Rut y irAUM+1)Ke + e, xu^)/{2>[K,,]>hI >h] Hi; Hi,) Tuang tu doi vai cap banh rang cap cham ta co: (37) G,,3 = p >r, ^ r j >4J4 Vai, r, la khoi lugng rieng cua vat lieu lam true (kg/mm'); l^ la chieu dai ciia ciia true 1; d^^^^: duong kinh sa bp ciia true 1, dugc tinh nhu sau [6]: y halmm '-y hul '•y halmax F02]_(/]) Vai, [r] la img suat xoan cho phep ([x] = 12 ^ 20) dinh Tren nhu sau: thyc u.te, cac gia tri rang buoc co the xac , , V bd I m ax y balm a.x ^0,45 [6] • ba\xr\\n y bain 5, u = , u, = 1; u, =9; hma.v ' Jmin ^ 2ma.\ [K^,,], ta' De xac dinh cac gia tri gioi han ciia [K^jJ va Thay bieu thirc (70) vao (40) ta co: bien a6i (13): (48) K,, =[s ,,p^„, (41) < „ = ^ [ ; ] / ( , > { / ] > / ? , ; > / , > , ) >*„„ xK„,(Z,„Z„,zj] Voi h6p khai trien va voi b6 truyen cap nhanh, Tinh toan tuong tu, ta co kh6i lugng ciia true va theo [6] va [7] gan dimg co the layAT,^,, * I J , A : „ , = , , Z ; l - Z - - , ; Z„=274 Ben canh do, true 3: Kfjg I = 1,02 ^ 1,28 [7] nen co thi k4y K,,^ , = , Khi {42)G„.,=p>4,/4 (43) G„.,=p XT, xdi, (13) se fro thanh: xl,/4 (49)/:,,,-5,4617-10-''-[S^, J Trong ducmg kinh (7^, ,d^ ,ciia true va la: Vai bp tmyen cap cham vi A'^^ , = 1,01 nen co the lay K^ , 1,16 [7] 1,08 Khi tinh toan tuong ty bp tmyen cap nhanh, ta co: (44)^,,„-i7:.]/(0,2>(/]>/j„,>/7>^) (50)/^^,-5,7l4-IO-"-[s,„f Tir (49) va (50) ta thay cac rang buoc ciia ( ) < „ = 3/[7-,]/(0,2>(/]) Chieu dai ciia cac true 1,2 va tuong img xac dinli nliu sau: /, = fi, + 1,2 >t/^,„ ; /, = 5, va /, = 5, +1,2 >^,„ r r 3.1 Ham muc tieu va cac rang buoc Tir ket qua tinh toiin kh6i lupng cua hop (phan 2) ta CO the bieu dien bai toan toi uu de xac dinh ti s6 truyen cac cap nham dat kh6i lugng hop giam toe la nho nhat nhu sau: (46) mine,, = , / ( „ , , , ^ , [ : ],v ,„,v , „ : , [ / ^ „ , ] , K ] ) "/,n„n £ "/, £ W/,„i.x [SH,] va [S,J: [S//,L^[S«|]^[S//,L ^^ [ s « L ^ l S / / : ] ^ f e ô : L x ã ^^^ ^'^""^ ""^"g l'^"g thep, CO the my [S/y,L = [ S « : L =300 (MPa); Bai toan toi uu va ket qua Voi eac rang bupe sau: [K|||] va [KjjJ se tro cac rang buoc ciia [s«.L=ls«dax=600 Voi hop giam t6c cap khai trien, co the khao sat [T] tir lO.lO-Mln 10.10" Nmm 3.2 Ket qua va nhan xet Sau da xay dyng dugc ham muc tieu va ciic rang bu6c, mpt chuong trinh may tinh da dugc thief lap Hinh the hien quan he giira ti so truyen toi iru cua ciie c3p voi ti so truyen chung cua hop Khi u,, tang, ti s6 tmyen cac cap tiing Tuy nhien, ti so tmyen cua ciip '^" TAP CHi c a KHi VIET NAM V So OS - Thang nam 2010 NGHIEN CUU - TRAO OOI nhanh tang nh anh hon cap cham u^ tang vi u,^ lon, sy chenh lech mo men xoan tren tren true vod true vao se Ion nen can u, lan de giam bat chenh lech kich thuac giira cac cap va giam khoi lugng eho hop Cong thire (51) diing de xac dinh ti so tmyen ciia cap nhanh theo u,^ Sau tinh duge u^ ta se tinh u^ theo cong thiie sau: (51) w, =Uj^ /M| Ket luan Khoi lugng nho nhat cua hop giam toe hai cap khai trien CO the dat dugc nha phan phoi t6i uu ti so tmyen cho cac cap ciia hop Anh huong cua cac thong so nhu mo men xoan eho phep tren true ra, he so chieu rpng banh rang vv den ti s6 tmyen toi uu cua cae cap da duge khao sat Hinh 2: Quan he ti so truyen cac cap va ti so truyen cua hop Dua tren dieu kien can bang eua ca he gom hai cap banh rang va dieu kien sire ben deu ciia cac cap, cong thirc tinh toan ti so truyen toi uu cua cac cap eua hop da dugc de xuat Bang viec dua cong thuc hoi quy duoi dang ham hien, viec tinh toan ti so tmyen toi uu cua eac cap nham dat kh6i lugng hop nho nhat tra nen don gian va chinh xac *> 12 10 10 20 30 40 50 Tai lieu ttiam l^hao: Uh [1| B.H KyApneuee lO.A /tep^Kaeeu E.T Diyapee, • Tr=10 Nm - • — Tr=100 Nm - * — Tr=1000 Mm KoHCmpyKijuu u pacnem dyOntbix pedyKtopoe, HsflaxejibCXBO Hinh 3: Anh hucmg cua mo men xoan tren true den ti so truyen cac cap "MaiuMHOCTpoeHHe" JlenuHrpa/i, (1971) |2] Trinh Chat, Tinli todn toi iru ti so Iruyen he truyen Ket qua khao sat chuong trinh cho thay, mo men xoan cho phep tren true ciing anh huong den phan ph6i ti s6 tmyen cho cac cap (hinh 3) Nhu tren hinh ve mo ta, mo men xoan tang, ti so tmyen toi uu eua cap nhanh giam So dT nhu vay la vi, tmong hgp ehiu mo men xoan lon, bp tmyen cap cham can kich thuoc lon hon nen can tang ti so tmyen eua cap Ben canh do, kit qua ciing cho thay anh huong ciia cac he so y ^^i, y ha2' [K^,] va [Kj,,] den ti so tmyen t6i uu eua cac cap la khong dang ke dong bdnh rdng, Hoi nghi Khoa hoc, Dai hoc Bach khoa Ha Npi, Tir cac kit qua cua chuong trinh, phan tich hoi quy da dugc tiln hanh va mpt cong thire (vai he so xac dinh R-=0.9998) dl tinh toan ti so tmyen eua cap nhanh cua hop da duge de nghi: Berechnungsverfahren, Konstruktion 44, 229- 236, (1992) -0.0068 (51)^,,lop = , 6 < " ' V J , TAP CHi c a KHi VIET NAM V 74-79,(1996) [3] G Milou; G Dobre; F Visa; H Vitila, Optimal Design of Two Step Gear Units, regarding the Main Parameters, VDI Berichte No 1230, 227-244, (1996) [4] Vu Ngoc Pi, A new method for optimal calculation of total transmission ratio of two step helical gearboxes The Nation Conference on Engineering Mechanics, Hanoi, 133- 136, (2001) |5| Romhild I , Linlie H., Gezielte Auslegung Von Zatmradgetrieben mit minimaler Masse auf der Basis neuer [6| Trjnh ChSt, Le Van Uyen, Tinh lodn ihiit ki he ddn dong ca khi, Nha xuat ban Giao due, (1998) |7| B.H KyApHBueB lO.A .ZlepiKaseu u flp., Kypcoeoe npoeKmupoeauue demaneu MUWUH, HsflaxejibCTBO "MaiuHHOCTpoeHHe" JleHHHrpafl, (1984) S6 08-Thang nam 2010 ... (51) w, =Uj^ /M| Ket luan Khoi lugng nho nhat cua hop giam toe hai cap khai trien CO the dat dugc nha phan phoi t6i uu ti so tmyen cho cac cap ciia hop Anh huong cua cac thong so nhu mo men xoan... >^; >t^,^) 2.3 Xac djnh khoi luyng cua cac true Kh6i lugng ciia cac true G^^ cua hop giam toe hai cap khai trien dugc xac dinh nhu sau: TAP CHi c a KHi VIET NAM *l* S6 08 - Thang nam 2010 NGHIEN... iru ti so Iruyen he truyen Ket qua khao sat chuong trinh cho thay, mo men xoan cho phep tren true ciing anh huong den phan ph6i ti s6 tmyen cho cac cap (hinh 3) Nhu tren hinh ve mo ta, mo men xoan
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