3.2. 1

3.1.

3.1.1. , . , (), (), , . : 1. (. 31.1,) 2. () (. 31.1,) 3. (. 31.1,) 4. (. 31.1,) 5. (. 31.1,) 6. (. 31.1,) 7. (. 31.2,) 8. (. 31.2,) 9. (. 31.2,) 10. (. 31.3,) 11. (. 31.3,) 12. (. 31.3,) 13. (. 31.3,) :

- (. 31.1),

- (. 31.2),

(. 31.3).

2 3.

, , . , , .

. 31.1. : ) , ) , )

, ) , )

.

3.2. 3

. 31.2.

) , ) , )

. 31.3. ; )

) , ) , ) .

, , , ( ). , . .

4 3.

3.1.2. . , (. 31.4) . - . . . (. 31.4), . . ( ) ( ). , , , . d p z :

= =O p z d (31.1) :

= =pd z m z

(31.2)

(31.2) m . , . 31-1 m SRPS .C1.015. . I . II . - . . . . , . , . , . . . , .

3.2. 5

. .

. 31.4. :

b - ; d - ; df - ; d - ; h - ; h - ; hf - ; s - ; e - ; p - ; - . . , . . , . (. 31.5)

1 1 2 2= =w wv r r

6 3.

. 31.5.

:

2 21 1

2 2 1 1

= = = =w ww w

d rnin d r

(31.3)

1, 2 - , n1, n2 - , dw1, dw2 (rw1, rw2) - () .

1 1 1w wd z p 2 2 2w wd z p pw1 = pw2 = pw,

21 2

2 1 1

= = =ww

dn zin d z

(31.4)

(31.4) m

2 2 2

1 1 1

= = =z m z diz m z d

(31.5)

:

22 2 1

1 1 1 2

= = = =ww

dz d nuz d d n

(31.6)

3.2. 7

, i , u u 1. , u = i. u = 1/i i 1. . . . .

3.1.3. () . u=1/2 . . 12 C (. 31.6). , . . 31.6. . b1 1, b2 2. B tB nB. B . nB C w. B nB 1 1 1= TO T r 2 2 2= TO T r rB1 rB2 1 2. :

1 1 1=T Br r cos

2 2 2=T Br r cos B 1 vB1 = rB11, 2 vB2 = rB22, 1 2 1 2. :

1 1 1 1 1 1= =Bn B Bv v cos r cos

2 2 2 2 2 2= =Bn B Bv v cos r cos

8 3.

. 31.6.

vBn1 vBn2 . vBn1 > vBn2 b1 1 b2 2, . vBn1 < vBn2 b1 b2, , 1 . vBn1 = vBn2 :

3.2. 9

1 1 1 2 2 2=B Br cos r cos

1 2 2 2

2 1 1 1

= =B TB T

r cos rr cos r

11C 22C

22

1 1

= wTT w

rrr r

:

1 1 2 2= =w w Cr r v (31.7) (31.7) C , rw1 rw2 . (31.7) , . C . :

1 1 1 1 1 1 1 1 1 1

1 1 1 11 1

2 2 2 1 2 2 2 2 2 2

2 2 2 22

Bt B B

w w w w c ww w

Bt B B

w w w w c ww

v v sin r sin T B T C CB

CB CBr sin CB r sin v sinr r

v v sin r sin T B T C CB

CBr sin CB r sin v sinr

2w

CBr

:

1 21 2 1

1= = = 1Ckl Bt Bt Cw w w

v CBCB CBv v v vr r r u

(31.8)

(31.8) CB B vC, rw1 rw2. C 0CB , . . . . 31.6.

10 3.

2 =wr , rw2 < 0, . :

1 2 2 11 2

1 1 2 2

= = ; = =kl t t kl t tt t t t

v v v v v vv v v v

(31.9)

. .

3.1.4. , . 31.7 (Reuleaux) .

. 31.7.

1 2O O C, 1 B1 tB nB. nB 1 B'1. 1 1

3.2. 11

1B' C , B'1 C. B1 1, 1 1B' B C B. B B1 1 B2 2, C. 1 1B' C , , 2 1 2B' C B' C 2. B2 2 2. 1 1B' B CB B'2 B2 2.

. 31.8. B11

2B2

12 3.

2, D2, 2 F2, 2. , B, C, D, F, . . . . . . . . . . 31.8 , 2, 1. . 1 B11 (. 31.8). B1 , 1 . 2 2B2. 1 2 2 B1 , B2 1 B2 . , , . (), (B11 2B2). . , .

3.1.5. , .

3.2. 13

, . - . . .

. 31.9.

, . . , . (. 31.9), ( ).

14 3.

3.2.

3.2.1.

3.2.1.1. 3.1.5. 1 1 1 - k1, 2 2 2 - k2 (. 32.1). k1 k2 . 1 2 . 1 2 , 1 2TT , 2 1 . 1 1 , . AE . C.

3.2.1.2. db1 db2 rb1 rb2 (. 32.1) k1 k2 k'1 k'2 . .

3.2. 15

. 32.1. ;

, . hwP = 2m (. 32.2). hw = 2h0 (. 32.3). hP = hfP+haP (. 32.2) .

16 3.

(. 32.2). :

. 32.2. DIN 867

.

p = m, m = p/.

S - S . sP = P = p/2.

P = 20, 2P = 40.

: hP = m hfP = m + cP hP = hP + hfP = 2m + cP

cP = (0,1....0,3)m ( 0,4m).

hwP = 2m.

( . 32.3.) 0 = cP /(1 - sin 0 ).

ISO DIN h0 0 P ( 32-1 32-2). .

3.2. 17

.

.32.3. .32.2.

3.2.1.3. . (. 32.4) :

=PT BT

( ) =b i i b ir r tan

=i i itan (32.1) i (32.1) i inv i ( i). 32-3. . i. . 32.4 :

= =b bii i

r dcosr d

0 0 0=a a psin c

0 0= /(1 )a pc sin

. 32.4.

18 3.

d :

= bdcosd

:

=bd d cos (32.2)

2 2= = = =i i b b i i iBT r r r tan r sin (32.3)

.

3.2.1.4. . , . , pb. pi (. 32.5) pb, p ( )

2 2= = = =b i ie b i ir r cosp p p cosz z

(32.4)

:

= bppcos

(32.5)

. 32.5.

3.2. 19

3.2.1.5. . . , . . . . w. . 32.6. C r1 r2.

1 2=da r r (32.6) .

. 32.6. ; ) C

) C . 32.6. a. C ( ) rw1 rw2.

20 3.

, w. , . 11C 22C . 32.6. :

1 2

1 2

=b b

r rr r

1 21 2

=w wb b

r rr r

2 22

1 1 1

= = =b wb w

r rr ir r r

(32.7)

(32.7) 1 2O O . (. 32.6,) :

1 2 1 21 2= = =b bw w

w w w

r r r cos r cosa r rcos cos cos

(32.8)

1 2=2 w

z z cosa mcos

(32.9)

(32.9) . . (32.7) (32.8) :

1 21= ; =

1 1w wir a r a

i i

(32.10)

3.2.1.6. P-P (. 32.7). , . p. S-S (. 32.7) . P-P S-S. . x m, xm.

3.2. 21

(. 32.7,), (. 32.7,).

. 32.7.

(S-S - ; P-P - ) . , . . . , () z = , .

22 3.

. , . . . (. 32.8) . .

. 32.8. ,

) , ) , )

3.2.1.7. P-P (. 32.9):

= 2 22 2ps x m tan m x tan

(32.11)

. . . (. 32.10):

= =2 2

ii

i

ssinv invr r

3.2. 23

. 32.9.

:

. 32.10

24 3.

=i i iss d inv invd

(32.12)

di = db i = 0 (32.12)

=b bss d invd

(32.13)

di

= =ii i idp s e

z

=i i ie p s (32.14)

di = d i = a (32.12)

=a a ass d inv invd

(32.15)

a . 32.4 : = /a b acos r r .

3.2.1.8. . . (. 32.11),

sw1 = w2 ; sw2 = w1

pw = sw1 + w1 = w2 + sw2 = sw1 + sw2 (32.16) (32.16) . (32.11) (32.12) i = w :

11 1 11

= 22

ww w

ds x tg z inv invz

22 2 22

= 22

ww w

ds x tg z inv invz

3.2. 25

. 32.11.

1

1

= wwdp

z

(32.16)

1 2

1 2

= 2wx xinv tan invz z

(32.17)

(32.17) . x1 x2 :

(x1 = x2 = 0), V- (x1 + x2 = 0), V- (x1 + x2 0).

26 3.

. 32.12. V- p ;

) ; )

. 32.13. V- ; ) ; )

3.2.1.9. V- , .

3.2. 27

P (. 32.13,). ( ) (. 32.12). ( ) . . P (. 32.13,). . . :

1 2 1 2= =Pk m a a r r m x x a (32.18) k - . .

3.2.1.10. . (31.2) :

1 1 2 2= ; =d m z d m z (32.19) (32.2) :

1 1 2 2= =b bd d cos ; d d cos (32.20) 32.6 :

b w wr r cos r cos :

1 1 2 2= ; =w ww w

cos cosd d d dcos cos

(32.21)

. 32.13, : r1 = r1 + m(1 + x1); r2 = r2 + m(1 + x2)

(. 32.13,) :

1 1 1 2 2 21 1a ar r m x k m; r r m x k m km (32.18) :

1 2 2 2 1 12 2a ad a m m x d ; d a m m x d (32.22) c (. 32.13,):

28 3.

1 2 2 1f a f aa r c r r c r

:

1 2 2 12 2 2 2a f a fd a d c; d a d c (32.23)

:

1 1 1 2 2 22 2 2 2f fP f fPd d mx h ; d d mx h (32.24)

d0 0 :

1 01 01 2 02 022 2f a f ad a d ; d a d (32.25)

h (. 31.2) h hf ,

h = h + hf hw h1 h2 , .:

1 21 2= = 2

a aw a a

d dh h h a

h (h = m), hf hf = (1,1 ...1,3)m. :

1 2 2 11 1 2 2= = = =2 2

a f a fw w

d d d dc h h a ; c h h a

(32.26)

3.2.1.11. . 2 1 (. 32.1). 1 ( 1), 1. 1 . 1 (. 32.14). , . , 1 2TT .

3.2. 29

. 32.14.

. . . , , .

. 32.15.

30 3.

(. 32.15). . . . 32.16 . TDC :

= =DC m x mTCsin sin

OTC TC

= =2

m zTC r sin sin

:

21 =2

m zm x sin (32.27)

22= = 1Gz z x sin

= 20 zG = 17,1(1 - x)

. 32.16.

3.2. 31

x= 0 zG = 17,1. :

17= =17

G

G

z z zxz (32.28)

:

14=17

zx (32.29)

" ". ( ) " " . s 0,2m, , s 0,4m . - . 32.29.

3.2.1.12. AE . , p . D (. 32.17,). B. B D . B , . p, D . B D , . () (. 32.17,) B , D . () . B , D .

. 32.17.

32 3.

. 32.14.

. 32.18. l A' E'

3.2.1.13.

, . l pw l > pw. :

= 1w

lp

l E'A' (. 32.18) :

=

' '

b w

E A lr r

3.2. 33

, E'A' EA = g, (. 32.6,) :

= =wb w

r gl gr cos

(32.30)

(32.4)

e b w wp p p cos m cos :

= = = =w w w e

g g glp p cos p m cos

(32.31)

(32.31) g p. (g) (gf) 1 :

1 21 2= = =

fa

e e e e

gg g gp p p p

(32.32)

. 32.19 g = 1 1T E T C 2 2

1 1 1 1= =a a b b wg g r r r tan (32.33)

:

2

11 1

1

1= = 12

aa b w

b

dg g d tand

(32.34)

2

22 2

2

1= = 12

af b w

b

dg g d tand

(32.35)

(32.34) (32.35) (32.32) :

2 2

1 21

1 2

= 1 1 12

a aw

b b

d dz u u tand d

(32.36)

32.1.

34 3.

3.2.2.

3.2.2.1. , . . 31.9 32.1. .

. , . , , . . b (. 32.20). . , , . , () . . .

3.2.2.2. . 32.21

. 32.20.

3.2. 35

. 32.21. :

) 1 ; ) 2

. . 1 (. 32.21,) , 2 (. 32.21,) -. 1 2, . . : - - - . (. 32.2). t. n. . . 32.21, :

36 3.

= = =n n nt t t

p m m cosp m m

(32.37)

mn mt . mn 31-1. (32.37)

=wn wwt

p cosp

(32.38)

. 32.22 . , , . :

= =n tCB ABtan ; tanBD BD

:

= =nt

tan CB costan AB

= nttantancos

32.39)

(32.39)

= wnwtw

tantancos

(32.40)

(. 32.20).

. 32.22.

3.2. 37

di,

, . pz, . . b, w. 32.23 :

= = = =i b wzi b w

d d ddptan tan tan tan

= = ; = =b b b bt wtw w

tan d tan dcos costan d tan d

= ; = =b tb t wwt wt

tan costan tan cos tan tancos cos

(32.41)

. . . . , . . . .

. 32.23.

38 3.

. , (. 32.24). , , . , .

. 32.24. . . (. 32.24). . . . 32.25 . (. 32.25) =en et bp p cos :

1 2 1 22 2= =

n nn

en en et b et b

g g g gp p p cos p cos

(32.31) :

1 22 2 2= =n

b b bcos cos cos

(32.42)

3.2. 39

(32.42) .

. 32.25.

. 32.26.

, . b , . (. 32.25), .

40 3.

, . (. 32.26) :

= bg b tan

:

= = =t t n

g b tan b sinp m m

(32.43)

:

= (32.44)

. .

3.2.2.3. (N-N) , d (. 32.27). . , C.

:

= bbnb

ddcos cos

(32.45)

2=nb

ddcos

(32.46)

2 3=nb b

z zzcos cos cos

(32.47)

. 32.27.

3.2. 41

32.1. (: n- ; t- ; t n t= t = ; : - , - ; : - +, -, , - ; , z2 )

.

1 - p, hP, hfP, c JUS .C1.016

2 =d cost /coswt=mn(z1+z2)cos t /(2cos coswt)

2 d=(d1+d2)/2=mt (z1+z2)/2=mn (z1+z2)/(2cos )

3 tan t =t n /cos cos t =db /d tan n = t cos

n=P

4 cos wt=db/dw=mt (z1+z2) cos t /(2)=d cos t / inv wt = inv t + 2 (x1+x2) tan n /(z1+z2)

5 x1+x2 = (inv wt - inv t)(z1+z2)/(2tan n)

6 sin b = sin cos n ; tan b = tan cos t cos b = cos cos n /cos t = sin n / sin t

7 mt=mn /cos mn mn - JUS .C1.015 8 z zn=z/cos2bcos) z/cos3

9 d=z mt = z mn /cos dn=d/cos2

dn=

10 db=d cos t dbn=dn cos n

11

dw1 = 2z1 / (z1+z2)=2/(u+1)=d1 cos t /cos wt dw2=udw1

u=z2/z1

12 d1=2 - df2 2c=d1 + 2h1 d1 + 2mn(1+x1) d2=2 - df1 2c=d2 + 2h2 d2 + 2mn(1+x2)

; c=(0.1-0.3)mn , h-

13

df1=d1-2hf1=d1+2x1mn-2hfP df2=d2-2hf2=d2+2x2mn-2hfP

hf- hfP=kPmn

(kP=1.2;1.25;1.3;1.4..)

14 pt = mt = mn /cos pn= mn = pt cos

15 =

pt = pbt = pt cos t pn= pbn= pn cos n =

= pbt cos b

16 st= mt ( /2+2xtg n)+s sn= st cos s -

17

211 1 1

22

2 2 2

12

12

a b wt

a b wt

z d / d tan

zd / d tan

18 =1+2=

2 211 1 1 2 21 1 12 a b a b wtz d / d u d / d tan u

19 = b tan /pt= b sin /(mn )

20 g = +

42 3.

, . 32.1. ( 3.2.1.11), zn. 3.2.4.

3.2.2.4. :

. . ( ).

. b (. 32.24).

, . , . . .

( ) . .

. . .

zG ( 32.39) .

3.2.3. .

3.2. 43

z2 = . z2 - . z2, d2 a , . () (. 32.28). . , . :

, , .

, .

.

.

, . .

: .

.

.

.

, . . z2 ( 32.1). , . :

df2 = 20 - d0 (32.48) : 0 - ,

44 3.

d0 - .

. 32.28.

( ) . . . , ( 3.2.4).

3.2.4. 3.2.1.11. . , . . .

3.2.4.1. , . 32.29, .

1 5. 1,

3.2. 45

(32.49)

5. 0,2mn. (32.15). 1 , 5 .

. 32.29. . : 1 - ; 2 - ; 3,4 - ; 5 - .

3 4. . :

( 3) d db + 2mn ( 4) a bd d

( 3), ( 4).

2. 1 (. 32.14). P.

46 3.

. (. 32.14) (32.27) (. 32.16) :

2 2

0 = =2 2t n t

Na

d sin m z sinh x mcos

:

0 002 2

1= 2 = 2 a a n nNa nG

n t n t

h sin x mh x mz cos cosm sin m sin

(32.50)

, ( ) . ( 2) hN0 = mn :

2 2

= 1 = 12 2

t n tz sin z sinxcos

(32.51)

zn (32.47).

3.2.4.2. . . P rNf1(0) rNf2(0) ( "0" ). P . P , . (. 32.17,) , rNf1(2) rNf2(1). :

1 2 1 0Nf ( ) Nf ( )r r 2 1 2 0Nf ( ) Nf ( )r r (32.52)

(32.52) . P . h0 = 1,25m .

3.2. 47

. 32.30.

(32.52). . (. 32.30). rNf1(2):

2

2 2 21(2) 1 2 2=Nf b a b wtr r r r a sin (32.53)

P rNf1(0) :

2

2 01(0) 1 1= Na nNf b t

t

h x mr r r sinsin

(32.54)

:

2

2 2 21(0) 1 0 0 0 0=Nf b wt Na br r a sin r r (32.55)

(. 32.31).

48 3.

rNf2(1), :

2

2 2 22(1) 2 1 1=Nf b a b wtr r r r a sin (32.56)

P rNf2(0) :

2

2 2 22(0) 2 0 0 0 0=Nf b wt Na br r a sin r r (32.57)

. 32.31.

(32.53) (32.56), ( 3.2.3), rb2 . (32.52). , . . (.32.32). . .

3.2. 49

10 .

3.2.5.

, , . , . . , , . . JUS .C1.030...036 ISO 1328-1975. JUS ISO- . DIN 3960...70, ISO . . 12 1 , 12 . , , , , , DIN, 32-5...32-11.

. 32.32.

50 3.

3.2.5.1. ( , ), ( , ), ( , , ) . (s < e)

jt=e-s .

. 32.33. (t ) (n)

t n (. 32.33). :

n t nj j cos cos (32.58)

3.2. 51

, As Asn (. 32.34). t

1 22= a n sn sntA tan A A

jcos

(32.59)

(32.58). (snd) (ag), (sng) (ad). , . , .

. 32.34.

52 3.

:

m mm 0,8...1,75 2...3 3,25...5 6...10 12...25 t m 50...100 80...130 100...230 180...400 250...1000

3.2.5.2.

. (. 32.35) . s . . - . W (. 32.36,) sb (zw-1) :

1w e bW z p s (32.60)

. 32.36. () () .

(32.4) (32.13) (32.11) :

. 32.35.

3.2. 53

= 0.5 2wW m cos z z inv x m sin (32.61) :

= 0.5 2n n w t n nW m cos z z inv x m sin (32.62) x ( x ) z (zn) zw 32-4. (. 32.36,):

b > Wsinb (32.63) zw2

54 3.