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 t,z 0F... : rz * r/ : .., : Gz
* * lz : Iz * r,z
aggs 'JiuJpep rolererunu
eurns';npourr6epcene apfeuer'uee+"o+
ur;i"?ilx
oV... :oy:...
:"V:ty
r$eaarear; es afeuar8uerolsace-epxe_arlurp
eze+r^ ep rarlnr e1e axe p eiuelsrp ec pcrldurr
fnop arlur afeuar8ue :olinui i"ur'e"r*1.rontr .I
, aurr_rdroJnicer; roirrr"ra*"
",:n::_15_
€erlsoroJElrqezqr+nur Juepace:d
adeorde ryf,q..el
Jey alrrigm -u1p ap bznec'gnop .r6n1o;
rur8rio

:j1y:g1.Tp:'-41!1!JJarerFurrerlur"::illfi;$tr;"-"H,iX"3,,t.?%
rollralnd a.reolgzundsaroc,arur_rdaprice_rjaleluaiaid
iri1, i:g Flaqel uJ
poderJsepce
pul^:-'-'*:yylov1
:ootlzrt:stlvg:oE/qs
-eunu ullqo as 'n rll ep lrgrg,rd1p niiuaa .,
"f"#3lH;T#
,
!zl,!z flurp ap
Inrqlunu ISeluazardaraleid durrf iSepceu! :r__: " ,prijiapr.uo,
e-recg71$7 ap:a'yuuderlr.,rl prlpe
qg gz
: og ool
'V s z ts :a l:
- :
z l' r : 1 ?
BruJoJqns ro6n euriqo as
ZI,I :ozb - tI!

'ereosn Ar+eFI
elsaeuarqo,u
;'ijjf;"iJJ" "3"#[TSfi JIT:r,r#j
"t+"o
'esndrarirpuo,p,,,d..,oJ:"iJy:ffJ#fl
,"ffJlJ:3]$";fi#xtii,,,iirl'JiLT
'sap pqeue^uor
n n_r'earerrrdry,i:-
l:j:l?:l q glsuoj 'euralqo-rd
eurJd raricer; ear€urrrrelep jr6d.ls;i r, e1":",sl,y
Trjdreisare' ee're^rozat.rcap rs
tlg qgn
tt- l,z
.
!:- :- - - :-

aV rvn i,
ar-tx aleod- n? .l_lllrd
*r,tl leJise ecr;gdurrs aleod as ee
'ptrtur.t{ agicn$ o e}se nu y,zfiz
ir;{p;" erfce_ry,rrnzer itrpur a}reoJ uIEf,rpe
'e,at'us
?t?utnu ,;;::f; :{rf:r':,Trf;
,rr"rr;*ir'Ki::;:;:i1;H'o:;:f :;#hf
zlz
ttl,1
:
g

e'rozet ? uI elsuo3 liu1p ep ererrrnurolsef,e ,"rn*int""lr*t"

Be_r'urrrrralao

1o{ttwr.,r,{ ttlotuau@ Tniuof

0tI
 Mecanisrne pentru rcglarea iliscontinud, a twaliei 141

Tabelul 3.5
11
; < eio<t
Fracfii prime penttu

Atc ll I Atc
ilF
Bt' | -t' Bk
ll
5
8
9 5
5 -5 9

! -6
I
5 2

L I 25
5 .' r^ 56
5
1
-8
I
2,50
z5
28 I 5
25 2"90 t1
1 20
3J5 63
25 20
-l 28 7I
I I
I
5 Z 4

5
-3
7

2. Gabaritul economic al unei cutii de viteze depinde de gabaritul angre-

najelor pe care le confine, ceeace inseamni cl pentru un acelagiraport de trans-
milere,iste de preferat angrenajul a cdrui sume a numerelor de df1!i este_Tai
nici. Astfel, referitor la exemplul studiat, angrenajul avind zLl?I:28125'
fui )z : 53 este, pentru acelagi modul, de doui ori mai mic decit angre-
:56/50 cu lz : 106.
'rajul avind z'elzi
Criteriul gabaritului economic, a condus pe baze experimentale la limi-
terea sumei nimlrului de dinli al angrenajelor din cutiile de viteze la limita

lz < 120dinfi.
 'rnpo.'' r$epce pu'Ap aleuarSue ap
adnrS raJB]erJpcJlde es sns
rrunle 'elrJeJrpe1nporunc efeuer8ue pIIe es exe *"ur ep erirpuoc
gnop epc orlui
EJeCI
#
-a33ne a1afeua-r'ue e]€o]gJ .gleluauqdns.eeJe^Jesqo
F
;
ay y.a,rafipyV.'1sy1icu il{ ps adqot:
n3 ,rrrrr*ffiTr'.ilI
,axopnopapca,qug ,tauathup
l::::!::
?ruprx,,o,tolaio,tap piul,pap ,topntunu 7o1{a
buins gt gz&azr|arft glseerv
ffi
ry
'i ,,+r ,,- z(
"rrnrJ*"

tE:' lelou e-s eJeJ rrt

'zK ;:(X z-fr ,r ) #:V

praua8 uJ nes
C,+'A + : "' : (Iz*,,4+ : ...: (l;z + g + : (,",2 * ir)* : v
;j:-:11T" ESrlrurlapse .areuat*ue b"Fl"*:_ol-"q 3iJiji,fij:ilT
: 'pluetsuoo o pUIIJ aze+r^ef rarlnc ap'a"e IjlSl#A
pnop alal arlurp Elue+srg
h! ts
b/

r:'u
id :
4z
t/- lto
_

l-

lz-.u

"*
pu;rn'rse.areuar'ueu:"Jtfi
{,1;T,1.8fi1b_!.:l**:,."idXT1i.i:,H*;:
ex* qnop arlu1 .ax' Fnop erlurp roiafbiardue gurp ,'1i'i1nr"*g .q
.II .Io^ uI gl"p elsa
"1i
Inf,IBrep epoleul o
l*c
e-1;unrduraxe ep,epola.',
€l1,'yrrc.,,rsesoroJ-
TlurFpurgleido-rde T AT:Jrrffi#fif 1filljiJ.:l
nes ppFa-'ogirv eurud iarirejy
nrlued
"rrd,ri*rl"1np
j3_tli"rnlBaf,r+?ruaurJ ,rp o-pujae jJ
w
eS
llreJlp elsa eralnusuerllriT" _"j31.:o
ep 1:oder rorgj __"r::l_1
p "r"J{j,r.";"f;rX
-np 'Iruralqord earenlozer pLrrJJlpape6y "r",r"*ii"'lo.rri"""rr.o1o1 eI pulr
IjlJ_"_, ur reJ _ Ilu5p ep roJar
-J(unu rerunselJurll 16axe arlui[-gluelsuoc "rrn*_ azner pnop
eiuelsrp e]serv

7o{ g.tuc,t( t! Iaul.au?r p i wo-l

zvl
 Meoanisme pentru reglarea discontinud a turaliei 143

Numlrul de dinli al unei roli a angrenajului se poate exprima func-

lie de lz ;i de raportul de transmitere ir, pleclnd de la expresia acestuia
din urmi
',
-j : t*,
'k

clreia i se aduni la numitori, numlrltorii

,'
ok qc
_:
z|+ z'i ixl I
de unde

z'*: (z'r+ zi;) .

Ltc+ r
sau inci
-:+

z'o: 2z --J!- '

xvf L

Avlnd in vedere ci raportul de transmitere se poate exprima prin fracfia

primi

ir:#,
rezultd cd

,L : zr# nr.
Deci daci se poate determina zi cu expresia de mai sus (in care nu se
cunoagte )e) atunci se poate gisi gi
zi:lz-z'0.
Determinarea lui lz. Analizind expresia lui zi. se constatl cu ugurinf i
ci toli termenii sint num,ereintregi gi ca urmare A*nu se poate divide prin
A* * Bu, cici toate sint numere prime intre ele ;i, ca urmare, cltul zecimal
obfinut gi multiplicat apoi cu ! z, care este tot un intreg, nu va da un ei nu-
rnir lntreg.
Scriind din nou aceea;i expresie sub forma

ak- Ar,
A*+'Br

rezulti imediat c6. lz trebuie sd fie un num5r carese divide prin sumele de
formi. A* * B* (h : 1 ... n). Pentru indeplinirea acestei condilii de divizibi-
 3 u l w z :" # t tz _ snpuoc lnxe ad
zu?w! - lnuoluld - Q jJolpcnpuoc Inxe ad lnuorurd _ ,
F9 : r+urp op
lm;nF ?x*a :y1:
reur loc nc rnlnuorurd rerirzod
"Iur
,,u[ aleod as eftr nrlued (:epurrsp^5f,;l#;
Eareururrelepnrlued eruaqcs .0g., .CI.1I

os ee[op 1e nrluad) .2ec prurrd u1 v D ntu

t
xDu, u.

b,L
'utws - e^+InzeJ
lz
T <t? IT
n_rlued JPr
I
u l a g :r,z !,r,
pllnzar
t

_ap pp1.,oder rnsre^ur" #Tfr ,j#;l,i.x*1

urrurur eJelrursu'Jl ap {:,_[l=
rnppode: i?i !,.$ii ;;;;Q
eerereduror ui plsuoJ eaJeurruJelao
plsee)e .Flt snpuor
;:]:-:l e
'lroFg "Brj._t^1. ^ nes iolernpuor.;. xe aree ad
^(OE.g
aleod es gr gliirzar (t
"ulluJelap
IrLzer)-.esnpuor "., ,.1".,"q-'[, ,'u!wr' _ i; : i
puyllz ,t <r? nrlujd ",*1j],,,"r.".r"o1{r1p;-
a 'l > "? arelltuslrerl ": purr;,{eeleor
?p^tj!.g"r'^:-r:.lt Fzer uI reurnri ,&*z:!z wnl
strr-;
c3
il u : u,-z
epsndnrr u\"ffi:;'ty,"gd!:jfifiT.
q-nopeJaf,erlul arelJe..rior..ep Jr".:'",.:",f"3l,dife5:;
InJq.'esu' Farlu! uip ep r'runu rrru reru
IaJ nr el€or purrJulwz.u!,az:.\i-:aV nes,utw,J- liulp iis ',"iOf:*lrr#"i"fr
'''nzer ra4 nrluad rsrunu a.triqo aieod as l)
"r*e, i'ii)" ,ur lurpr^e ,apun
pde m d uluw

aq;+T; -;fr:
uSuhl
u'*0
EJ puruf,s af,eJ as "o*0 ?nI Denuuuot4ae
1i

I
FO tluryuluQ- Zuu*K
q s?+
EteE 5J
d €r pllnzer (a:errldrl-1nur_pldurl:o_rluyg__"I{eo
+od as z( alie acareoep)
z'!-K 'liulp ep ro$raiunu e^lruns g'rrr reru
trI eer eurruJarape purJgru{}
luoi :s - z(
"r'tr410
pf, rrrnle arrcs aleod es ,aJeuun
e3
rPlrrnu1nllr 'A re1,qg* {y au-ro1ap rolauns .f,.ru.u.ur.r
Ie e}sa"*;"##"
t raFse u lu L4f
.1
({9.+ {t').r.ur.u,u.c
U: ---:E-:

EUerer pruroJep rore.,'ns

Ie'r'ru'.','ru'cur.rdgpr^p asgs e( ,"StinJ";g {Jr[
",
1o{rcutl,{ e?taLuaulc piuvT
?w
 hfecanisme pentru reglarea disocntinud, a turaliei 145

brml rezultd c6

Z^ aoz : z ^ ro j4 L ,
aL

astfel incit, inlocuind in expresia lui Q*ro,

F*it Ar+Br
n
! vm tn - -L*nr-- - emi n
M ^* A rM^*
i
i
se poate afla- mirimea lui Qqio, toti factorii din dreapta, fiind cunoscufi.
Efectuind operalia, se ob{ine in general Qm, srtb forma unui numer
E-ioz cu zecimale; cum el trebuie sl fie numir intreg, se rotunjegte, in plus (rotun-
F jirea in minus, conducela urr z*rn mai mic decit cel ales).-
Odati Q6o determinat, se gdsegte imediat
i

I
I
zl:Q*trM^lnL
Ar+ Br
t gr apoi
t.
Fzurl, zi: )*rrz - zi.
!u cel
i doul Ca exemplificare, si considerdm patru angrenaje avind rapoartele de
ls de transmitere 'i1...ia, indicate in tabelul 3.6.,
I
!
Tabelal, 3.6
l/a
I vr Determinarea numerelor de dinti

priori, Att
Bk
hoatd.
a- .
Fmrm
t s de z r : 9z it s : 7
I
r*2:3
20
40
I 105 25
iz : gztn: - -:- 5+7:12:22.3
1A 11 7 35
I
I 30
; -^o
"3 - Y2 o /3 -
r+ l:2
1 1 30
. 1 ,4 147
7+5:12:22.3 35
tt: 9 zo tz :
, 105 25

f" ." in coloana a treia se indici fracliile prime AolBr, iar in a patra - sumele
!Poate
-t de forma A* * Bz, descompuseln factori primi.
Cel mai mic multiplu comun al acestor sume este
M -1 n :22' 3:12.
 l ff+1 F
trM#)
erle esereradrnlnxeeaurrso;F_ rttd:ffi#j
:y_rjg 1.-"re
unzer eleunuI .Erlpe rcap .$u1p : "Jt:1lT,1r""T""n
1elrror 9l lz rurururinuoirira
"i.J;t;;;;
'8h: zK
rJunle 'g ap co1uJ ep .ereoi:agur+erparureaJeoI"Aer as fl n.rluadeceg
'
g-rpysapiureurq.p]"p eurelqo:dn-r1uadrrinlos,rr'urr!Tt::Hr"#Jt";rf;t;
ilarryilr
0Zl : zK of :0
-eryus 80I : zK 6 :0
B sq[E
96 :zK 8 :0
"s rl u$
IBf ,g -z( L:0
m pep LL
_
-
d|2
&\\ g :0
+lJdp uuur lyLu q a1lers
o rrole^ elle a:ale10d
rse;ele es.{urp
1odes #rLr.":;?
I^r:t ll:5
aleod ryy
ezatt^ ryore^ "p 0zl'l:;[
ta liq) '{urp ep 0zr Burrxeur ea:eoprr
ee.te ep egprn irrluad p11qls1urp; ikrir;;;pe"
J tm) uI pu;^y
s+sa giyry Zt er?ef,nuI"T, eleor r$Eruru1ru
alsa99.- e(
-a.rd:f,i;e"f
ri:f -""r
EUrorrp 'er1edeH;H":,,:::lx:,r*"1*:*r-";:*:ir"*i_:]gii:;;
€ueoloru'n ,iu'o ep elererun,.or'.;id:;;;;ii;h"ili
'pqe1 r6ernlef,eE pueolof, eruq1n ur alnf,eJl ."1"ur*rr1"p
1og,
T"J "'z-Og:;',2
4 g *'r v
0g : o,z
.lopior a1eliurp ep elararxnu J"r
'Ag : ZI X g : "r*W"r*,o: zu!*K
r; e.r liurp ep JoleJeunu e prururru etuns
.E : u?*0
urruilu plgc .rcag
L u?uJltr
' E! : 'v
LI , LI k +r b - '- u t u - : '? : 0
rJ eA rururur plIJ 'liup ,I : u?w,pJ pulJeprsuo3
a-rrnu4 .!z : aluz nap 16n?lt rz
< eo elelsuor as
lsoI ns
,L,a
: +: + 16s,s
: L:,,
rres Fttrl
ut
Ier l]l
'f ,
.furpepr:#,f
fi :ffiilTl"ii*"il;u"1";f
f ::,,niiilff"",?,.u
azezlcetd es ES JesecSu elsa- ',o,*s unutw mlnlJr
seJe'rruJalap nJlusd
||-
7o{acutt( ctgawawzt 7m/ua7
9pI
 Xlecanisnte pemtru reglarea discontinui a turaliei 147

t c. Rezolvarea problemei in cazuri dificile. ApariJia factor.ilor primi mari,.

ln cel mai mic multiplu comun M*ro de naFtere la operalii laborioase 9i
la solulion[ri. in care-rapoartele de"tiansmitere sint rcalizate cu erori mai
marl sau mal mrcl.
Astfel, si considerdmci pe lingi cele patru lapoarte de.transmitere,care
au fost solulionate dupl cum-s-av:6zut, niai sint necesare,inci doui ln con-
tinuare (tabelul 3.7).
I aOetU t J ./
Determinarea numerelor de dinfi
(in completarea tabelului 3.6)

L L 56
4 : 97.ors: 2 + r: 3
1 1 28

2, 8 28 14 61
Ls: 91ors: -:- 1445:19
1 105 23

CeI mai mic multiplu comun, in acest caz' va fi

M^in:22 '3 ' 19 - 228,
fB- datoritl apariliei factorului prim 19 provenit de la raportul detransmitere iu.
nti Este inutili continuarea operatiei de determinare a cituiui minim Q*0,
cdci chiar daci ar avea cea mai mice valoare (unitatea) suma minim6 de
rca dinli va fi
Iit
deci cu mult mai mare decit aceeaadmisibild.
Ca urmare, raportul de transmit:r: i6, a cirui mdrime este datl de frac-
tia 1415,nu va pulea lirealizat; fraclia in cauzl trebuie s6 fie inlocuitl cu
alta a'cirei valoire va fi diferitl de aceeaa lui i6, insl in limitele erorii admi-
sibile.
Folosind metoda indicatd in anexl, se gesesc citurile parliale gi apoi
redusele respective
era 1tl
"l
10 llr 5
lnci t-
01 213 T4
+1 | -t 0

ETTrl
x)n, Cea mai apropiate redus6, care poate inlocui fraclia. 14f5,este 3/1. Fn*
'deci
Au * Bu este ?, 22, astfel incil cel mai mic multiplu comun at ti 17,
I E ilililii
t" Tl
Khd
i,
psre' ,g *,v e..,ns
urrderereralrrur""r;':fl"FriJ:Hr'TliJ:"f;ffi:*
ap aricerlsqe aJBI as 'dols lsaJe uI 'apolaru a1p rd eJs"esolo; es es rBSeJeu
l- nil irlr,
else ]rcur IeIlsE 'ElrqeualuoJ arinios o rsg8 aleod as Bun€eplolur n\i
G,0fu)rhfri
'1aqe1 rSelaf,e uI alnJorl luts
r* luapaca;d InzeJ ul r$ ec gunuJelep as -ropfo,r a1e riurp ep elaraunN
'liutp pS : F8 X | : z1Llutg
W'
16I : "oT\pev
tg ng u?ul N
ll
wriu-Tr, | > ;' --- : : " i0
w' $ r" " s = r b . -- e
elnrurol nJ Ezealnllel as urrurur 1n1rr 'areur-rn 'snpuor Inxe
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 Meeanisme pentru reglarea disccntittud a turatiet 149

ii foarte Se determind, pentru rest, numerele de dinli dupi cum s-a arltat, iar
pentru rapoartele de transmitere eliminate se determinl, prin una din meto-
dele urmitoare, angrenajul sau angrenajele care sI satisfacd, cu eroare mai
micd sau mai mare, mirimea rapoartelor de transmitere.
In acestscop,se poate folosi metoda prin:
Qind cu - lncerclri;
- angrenaje cu dantur5-corijatS;
iritorilor - angrenaje cu module diferite;
- angrenaje cu danturl inclinatd.
Prin tncercdri. Rapartul de transmitere care introduce factori primi
mari fiind i, (in cazul exempluiui ii : iu) nu se ia in considerare gi se deter-
mini rolile pentru celelalte rapoarte de transmitere. Cunoscindu-seastfel
mare va 2*r^2, una din rofile angrenajului eliminat se va determina cu expresia
:$ei l4/5, z'i : E-inz .a-'
t1 *|

Totdeauna z| rezultl ca un numer fracfionar. El se rotunjegte pini la

mlrimea intreagi apropiat5, apoi se determinS.zi prin scidere din l*ooz.
)rul prim In_cal,;il exemplului ultim, ii : iu: t415. Prin eliminarea sa, penrru
restul de rapoarte se gesegteM*io: i2 gi ! minz:60 de dinli. Ca urmare

z 'a: Z* nz uo 4 4 ,x2 4 4
entual de
#:
r ql
Y' ^h:
z'i: 60 - 44 : 16 dinli.
Angrenajul va avea raportul de transmitere
zi, _44:)1\
_ p,tJ ,
z ,{ to
ri este pe
deci cu o eroare de *0,05 sau de -1,8o/o, ceea ce este admisibil. Pinionul
cu 16 dinli fiind poate prea mic, se poate lua in considerare2z :72, imediat
urmS.toare.In acest caz. rezultb,
z6 : 53,05c 53 $i z'i: 19.
Angrenajul

5 _ 53 :2J9
recedent ;i z'u' 19
asiguri u_qraport de transmitere cu eroare maimici decit precedentul(-0,01
incit este sau -0,53o/o).
straclie de
- B, fac sl _ Prin angrenaje cu d,anturdcorijatd.. Pentru angrenajui defectuos se alege
o xzt apropiatd d"^F-q,ior.^celorlalte angrenaje. Caurmare distanJa / dintie
axe a acestuia va fi diferiti de distanJa,4'dintre axe a celorlalte'angrenaje-
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