Кафедра ДМ 09 04 2013 / Киреев - Расчёт И Проектирование Зуборезных Инструментов

)

K = πdao tgα

=

3, 4 2

tg 2$ = 5,3

;

4. (2.

z0

ɜ

4

ɉɪɢɧɢɦɚɟɦ K

= 5;α

ɜ

= arctg

K z0

= arctg

5 4,0

= ,25 52$ ;

π dao

π 2

3. (2. 0)St

0

= π m − Sn

= π 3 − 4,592 = 4,833;

4. (2. )HK

= h0 +

K + K

+ 3 = 7,5 +

5 + 0

+ 3 = 8; Θ = 30$ ; rɤ = 2.

2

2

$

$

$

sinα

2 30';arctg(tg ,25 2° sin20°); 3,9

> 2,5

;

5. (2. 8)arctg tgα

ɜ

≥

w0

6. (2. 9)Dt

= dao − 2hao

− (0,4 ÷ 0,5)K = 2 − 2 3,75 − 0,4 5 = 02,5;

7. (2.20) ωt

= arcsin

m i

=

3

= ,677° = $ 40'38";

Dt

02,5

8. ɇɚɩɪɚɜɥɟɧɢɟ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ – ɩɪɚɜɨɟ; ωɤ = ωt = $ 40'38";

ɧɚ-

ɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ - ɥɟɜɨɟ;

9. (2.2 ) P

= π Dt

=

3, 4 2

= 20 2;

z

tgωɤ

tg ,677°

20. (2.22) Px0

= Pto i cosωt

= 9,425 cos ,677° = 9,429;

2 .ψ = β + ωt

= 0° + °40'= °40';

22. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɚɪɯɢɦɟɞɨɜɚ ɱɟɪɜɹɤɚ:

(2.24)αoc

= arctg

tgα wo

= arctg

tg20°

= 20,00776° ;

cos ,677°

cosωt

α

= arctg

Pz −tgαoc

= arctg

20 2−tg20,00776°

= 20,04693° = 20°3'

(2.25) xR0

Pz − kz0tgαoc

20 2−5 4 tg20,00796°

α x L0 = arctg

Pz

tgα oc

=

20 2

tg20,00776°

= 9,96877° = 9°58'

Pz

+ kz0tgαoc

4 tg20,00796°

20 2 + 5

Pt

0

9,425

23. (2.26)

Poc.o =

=

= 9,429;

cosωt

cos ,677°

24. (2.27)Soc.o

=

Sto

=

4,833

= 4,835;

cosωt

cos ,677°

27. (2.28)αa = arccos

db

= arccos

84,572

= 28,24 82° ;

da

96

α

wto

= arctg

α wo

= arctg

tg20°

= 20° ;

cosβ

cos0°

lp =[(da sinα a

−d sinαωto ) cosα wto cosψ ] cos β +2Poc.o =

ɱɚɬɵɯ ɤɨɥɟɫ

. ( . ) d =

m z

=

3 20

= 60; d2

=

m z2

=

3 40

= 20.

cosβ

cos0°

cosβ

cos0°

tgα

tg20°

m

2

2.

( .2) α t = arctg

= arctg

= 20°; mt

=

=

= 3.

cos

β

cos0

°

cos

β

cos0

°

3.

( .3) db

= d cosα t

= 60 cos20° = 56,38 ;

db

= d2 cosα t = 20 cos20° = 2,763.

2

4.

( .4) α t w

= α t

= 20° ;

Y = 0.

5.

( .5)invα t

= invα t

+

2(x + x2 )

tgα;

α t

= α w ;

w

w

z + z2

( .6) invα w = invα +

2(x

+ x2 )

tgα = inv20° +

2(0 + 0)

tg20° = inv20°

z

+ z2

60

α w = 20° ;

Y = 0;

( .8) aw = 0,5 m (z + z2 ) = 0,5 3 (20+40) = 90.

8.

( . 2) h = (2h*a + c* - y) m = (2 + 0,25 - 0) 3 = 6,75.

9.

( . 4) hf

= h - ha

= 6,75 - 3 = 3,75; hf

= 3,75.

2

df

= 26 - 2 6,75 = 2,5.

2

. ( . 6) Sn = 0,5π m − ECS = 0,5 π 3 − 0, = 4,6 2;

Sn

= 0,5 π m − ECS

= 0,5 π 3 − 0, 2 = 4,592.

2

2. ( . 7)ρa = 0,5

da2

− db2 = 0,5 662 − 56,38 2 = 7, 55.

3.

( . 8) ρp = aw

sinα t

w

− 0,5

da2

− db2

= 90 sin20° −

2

2

− 0,5

262 − 2,7632

= 2,673.

4.

( . 9)

L = 0,5(

da2

− db2 +

da2

− db2

)− aw sinα tw =

2

2

= 0,5(

662 − 56,3 2

+ 262

− 2,7632 )− 90 sin 20° = 4,482 .

5.

( .20)

L = 0, 5 m sinα tw = 0, 5 3 sin 20° = ,3 6.

6.

( .22)

Ε = (L + 0, 5L) π m sinσ cosα =

K = πdao tgα

ɜ

=

3, 4 80

tg9° = 3,98

, ɩɪɢɧɢɦɚɟɦ Ʉ

= 4,0; ɬɨɝɞɚ

z0

0

α

= arctg

kz0

= arctg

4 0

= 9,04°

; K =

K =

4

= 6.

ɜ

πdao

π 80

,5

,5

d

< d

df

52,5

Ɍ ɤ

f

b

,

ɬɨ

(2.62)

α wo

= arccos

= arccos

2. . .

min

= 2 ,38° .

db

56,38

0

Ⱦɨɥɠɧɨ

ɛɵɬɶ αwo >α

womin

(2.63). Ɋɚɡɧɢɰɚ ɜ

ɭɝɥɚɯ

α wo ɢ

3. (2.65)

S = 0,0 7 m + 0,08 = 0,007 3 + 0,08 = 0, 3 ; ɩɪɢɧɢɦɚɟɦ S = 0, 4 ;

(2.66)

δ = S =

0, 4

= 0,07.

Pb

8,856

5.

(2.68) Pwo =

=

= 9,425.

cosα wo

cos20°

6.

(2.69)βwo

= arcsin

sinβ cosα

= arcsin

sin0° cos20°

= 0° .

cos20°

cosα wo

7.

(2.70)α wt

= arctg

tgα wo

= arctg

tg20°

= 20° .

0

cosβwo

cos0°

8.

(2.7 ) dw

=

d cosα

=

60 cos20°

= 60 .

cosα wto

cos20°

9.

(2.72) Sw

Sn

+

S

=

= dw

+ invα t − invα wto

d cosβ

4,6 2 + 0, 4

= 60

+ invα t − inv20° − inv20° = 4,752.

60 cos0°

0.

(2.73)

Sno = Pw0

− Sw

= 9,425 − 4,752 = 4,673.

. (2.74)

hno

=

dw

− df

=

60

− 52,5

= 3,75.

2

2

2.

(2.75)

h0 = h + 0,3m = 6,75 + 0,3 3 = 7,65 .

3.

(2.76)

hy = hno − [(0,5 dw sinα wto − ρp − δ) sinα wto ]=

= 3,75 −

[(

60

sin20° − 2,673 − 0,007

)

sin20°

]

=

, 7

≈ , 8

;

0,5

h

y

(2.77) c =

=

, 8

= ,25;

cosα wo

cos20°

a = δ + 0,05 = 0,07 + 0,005 = 0, 2;

a

0, 2

b = c –

= ,25 –

= 0,8;

tg(20° −

5°)

tg α

−

5

°

w o

r =

0, m

=

0, 3

= 0,4.

− sin20°

2

− sinα wo

Ɍ.ɤ. b > 0,5, ɬɨ ɩɪɢɧɢɦɚɸ ɮɨɪɦɭ ɭɫɢɤɚ ȼ.

4. ɉɪɨɜɟɪɤɚ ɜɟɥɢɱɢɧɵ ɭɬɨɥɳɟɧɢɹ ɭ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɧɚ ɜɨɡɦɨɠ-

ɧɨɫɬɶ ɱɪɟɡɦɟɪɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɟɤ ɡɭɛɚ ɤɨɥɟɫɚ.

(2.78) hk = hno − [r2 ( − sinα wo )]= 3,75 − [0,4( − sin 20°)]= 3,486;

(2.79) rB

=

(0,5db )2 + (ρ p + δ )2 =

(0,5 56,38 )2 + (2,673+ 0,07)2

= 28,323 ;

(2.80) αB = arccos

db

= arccos

56,38

= 0,359328 ɪɚɞ

2 rB

2

28,323

(2.8 )ϕ = λ + invαwto − invα B

= 0,359338+ inv20° − inv5,5443 8° =

0,3739398

(2.82) et = [(0,5 dw

– hk ) tgλ ] - (0,5 dw ϕ – hk tgα wto ) =

(2.86)

dA = da − 2hf

= 66 − 2 0,6 = 64,8 ;

α A = arccos

dw

cosα wo

= arccos

60 cos20°

(2.87)

= 29,53 35°;

dA

64,8

(2.88)

αɮ

= arccos

dw cosdɮɨ

= arccos

60

cos30°

A

= 36,69038°;

dA

64,8

(2.89)

hɮo =

d (invα wo − invαA − invαɮɨ + invαɮȺ )

+ hno =

2(tgαɮɨ − tgα wo )

=

60(inv20° − inv29,53 35° − inv30° + inv36,69038)

+ 3,75 = 5,834

2(tg30° − tg20°)

(2.90)

αaɨɫɧ

= arccos

dw cosα wo

= arccos

60 cos20°

= 3 ,32 23°

da

66

(2.9 ) Saɨɫɧ

= da

Sw

+ invα wo

− invαaɨɫɧ

=

dw

4,752

= 66

+ inv20° − inv3 ,32 23° = 2, 28

60

(2.92)

Sw

4,752

SA

= dA

+ invα w

0

− invαA

= 64,8

+ inv20° − inv29,53 35° =

60

dw

=2,788;

(2.93) αɚɮ = arccos

dw cosαɮɨ

= arccos

60

cos30°

= 38,06644° ;

da

66

(2.94)Sɚɮ = da

SA

=

+ invαɮɚ − invαɚɮ

dA

2,788

= 66

+ inv36,903° − inv38,06644° = ,9 4;

64,8

S

− Sɚɮ

−

4

(2.95) q =

aɨɫɧ

=

2, 28

,9

= 0, 06;

2

2

Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɣ ɪɚɫɱɟɬ

ɩɨɤɚɡɚɥ, ɱɬɨ ɮɥɚɧɤ ɫ ɪɚɡɦɟɪɚɦɢ αɮɨ = 35° ɢ

hɮɨ = 5,9 ɨɛɟɫɩɟɱɢɬ ɫɪɟɡ ɭɝɨɥɨɜɤɢ ɡɭɛɚ ɤɨɥɟɫɚ hf = 0,6 ɢ f = 0, 5.

6. (2. 3)

hao

= hf = 3,75.

7. (2. 4)

Dt

= dao − 2hao − 0,4K = 80 − 2 3,75 − 0,4 5,5= 70,3

8. (2. 5)

ωt

= arcsin

m i

= arcsin

3

= 2,44579 ° = 2° 26'45".

Dt

70,3

9. (2. 6) Hɤ

= h0

+

K + K

+ 2 = 7,65 +

4 + 6

+ 2 = 3,65.

2

2

ɉɪɢɧɢɦɚɸ ɇɤ = 4.

20.

Θ = 30°

2 . (2. 7) r = π (dao − 2Hɤ ) 0z = 3, 4 (80 − 2 8) 0 0 = ,38.

ɉɪɢɧɢɦɚɸ r = ,5.

22.

ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ɧɨɪɦɚɥɶɧɨɟ ɤ

ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡ-

ɤɟ, ɬ.ɟ. ɥɟɜɨɟ ɢ (2. 8) ωɤ = ωt

= 2° 26'.

P = π Dt

=

3, 4 70,3

tg2°26' = 5

(2.

9)

z

tgωɤ

68.

23.

(2. 20) Dw

= dao − 2hno − 0,4 K = 80 − 3,75 − 0,4 5,5= 70,3.

o

Dt

70,3

24.

tg2,44579 ° = 2°

26'45".

(2. 2 ) ω = arctg

tgωt = arctg

70,3

Dwo

(2. 22) Pxo

Pwo i

9,425

25.

=

=

= 9,433.

cosω

cos 2,44579 °

4,673.

30. (2. 26)

P

=

Pwo

=

9,425

= 9,433.

cosω

cos2,244579 °

oc.o