Reestablishing the dimensional parameters of helical gear trains

Purpose of the work Reestablishing the dimensional parameters of helical gear trains damaged during the gearing process.

Necessity of the work If a gear train is damaged or worn and it must be replaced with a new one, the dimensional parameters must be reestablished in order to maintain the initial geometrical and kinematical parameters.

Theoretical considerations

Compared to cylindrical spur gear trains, helical gear trains have the following advantages:

Lower noise and leaner functioning Higher gear ratio and bearing capacity

Use of helical gear trains has the following inconveniences:

Axial thrust loads Radial-axial bearings must be used

When using helical gears more teeth are in contact simultaneously and, as a result, the load is transferred gradually and uniformly as successive teeth come into engagement. These gears operate smoother and can carry larger loads at higher speeds. Also, the line of contact extends diagonally across the face of mating teeth.

For helical gear trains several planes can be defined:

a) Normal plane = plane perpendicular to tooth direction and defined on the pitch cylinder (or on the operating pitch cylinder)

a. The helical rack has its elements standardized in the section normal to the tooth, section which is the same as the reference rack (STAS 821);

b. The module is standardized in the normal plane, mn. b) Frontal plane = plane perpendicular to the gear axis

a. The tooth has an involute profile in this plane. c) Axial plane = the plane containing the gear train axis

Lets consider a general use gear train with involute teeth flanks, generated by a standardized tool with the reference profile in the normal plane according to STAS 821:

Reference rack profile: geometric parameters pressure angle n 20 [] addendum coefficient han* 1 [-] tip and root clearance cn* 0,25 [-]

Geometrical elements of the gear train MEASURED VALUES

Not. Designation Value w Center distance z1 Number of teeth in pinion z2 Number of teeth in gear Width of face $ Helix angle on the outside circle Reference helix angle of the rack a1 Addendum diameter of pinion a2 Addendum diameter of gear f1 Dedendum diameter of pinion f2 Dedendum diameter of gear '((*) Dimension over N teeth (pinion) ',(*) Dimension over N teeth (gear) '(-.(*) Dimension over N+1 teeth (pinion) ',-.(*) Dimension over N+1 teeth (gear)

CALCULATED VALUES Not. Designation Formula Value N1 Number of teeth to

measure over .,1 = .,1cos7 $ *180 + 0,5 N2 mn Module in normal plane

(Circular pitch) * = 1,2+1() D1()EFGHIJ * = KL(,,HMN OP(,,QRNOL

mt Module in frontal plane (Circular pitch) S = TJFGHO

Helix angle = arcsin TJP(,,KL(,, tan $ a Reference center

distance = TJ(P(-P,)1FGHO t Pressure angle (frontal

plane) S = arctan QRNIJFGHO wt Operating pressure

angle (frontal plane) ZS = arccos $FGHI[$\ xns Sum of profile shift

coefficients *^ = MN_I\[DMN_I[1QRNIJ . + 1 yn Center distance

variation coefficient * = $\D$TJ yn Specific depth

correction * = *^ * or * = 2 $* + * KL(,,DKf(,,1TJ

xn1

Profile shift coefficient (normal plane)

*( = *, = 0 or *(,, = Kf(,,1T P(,,1FGHO + $* +

xn2

xt1

Profile shift coefficient (frontal plane)

S(,, = *.,1 cos xt2 d1 Pitch circle diameter .,1 = .,1 = * P(,,FGHO d2 db1 Base diameter h(,, = .,1 cos S db2 dw1

Operating pitch diameter Z(,, = .,1 FGHI[FGHI\[

Z(,, = S .,1 FGHI[FGHI\[ Z(,, = TJFGHO .,1 FGHI[FGHI\[

dw2

aw Operating center distance (calculated) Z = K\(-K\,1

da1 Outside diameter

$(,, = cos .,1 + 2 $* + *(,, * cos da2 df1 Root diameter i(,, = cos .,1 2 $* + * 1,2 df2 h Whole depth = 2 $* + * * '((*) Dimension over N teeth (calculated) '(,,(*) = 1,2 0,5 + 1,2 inv cos + 2 1,2 sin cos ',(*) Conclusions The following topics must be covered: ascertaining of the defined gear train planes, helix direction, wear of teeth flanks, main particularities of the gear train, differences between the measured and calculated values as well as the possible reasons for their occurrence.

Desfurarea lucrrii 1. Se numr dinii roilor dinate z1 i z2 i se msoar urmtoarele elemente:

a. Distana dintre axe b. Diametrele cercurilor de cap i de picior ale pinionului, respectiv ale roii c. Cotele peste N i N+1 dini d. Limea roilor

2. Se determin modulul prin una din metodele prezentate 3. Se calculeaz distana axial de referin 4. Se stabilesc coeficienii deplasrilor de profil x1 i x2 i a scurtrii specifice a nlimii dinilor

y: a. Dac Z = , atunci

*^ = S. + S1 = *. + *1 = 0 i * = 0

i. Dac

i(,, = TJFGHO .,1 2 + cos atunci *^ = S. = S1 = *. = *1 = 0, *^ = S^, * = 0

ii. n caz contrar S. = S1 , *. = *1, *^ = S^ = 0, yn = 0 i se determin cu relaiile

*(,, = Kf(,,1T P(,,1FGHO + $* +

b. Dac Z , atunci *^ = *. + *1 0, S^ = S. + S1 0, S. S1 , *. *1 i 0 n acest caz, se vor calcula:

Simbol Denumire Relaia de calcul Valoare

t Unghiul de angrenare de referin n plan frontal Z = arctan tan *cos

wt Unghiul de angrenare real n plan frontal

ZS = arccos cos SZ inv S Involuta unghiului de angrenare de referin inv S = tanS 180 inv ZS Involuta unghiului de angrenare real inv ZS = tanZS ZS 180 xns

Suma coeficienilor deplasrilor de profil *^ = inv ZS inv S2 tan * . + 1

yn Coeficientul de varianie a distanei axiale

* = $\D$TJ yn

Scurtarea specific a nlimii dinilor

* = *^ * sau * = 2 $* + * $(,, i(,,2 *

xn1 Coeficienii deplasrilor

de profil *(,, = i(,,2 .,12 cos + $* + * xn2

Observaie: Valorile involutelor se determin cu cel puin 6 zecimale.

5. Cu valorile coeficienilor deplasrilor de profil i a scurtrii specifice a nlimii dinilor se calculeaz elementele geometrice ale angrenajului.

6. Valorile obinute se trec n tabel.