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

2. ( . 8) ρp = aw sinα wt

− 0,5 da2 − db2

= 6 ,78 sin2 ,4327° −

2

2

ɪɚɫɫɬɨɹɧɢɹ ɡɭɛɨɪɟɡɧɨɝɨ ɞɨɥɛɹɤɚ». ɉɪɢɦɟɦ z0 =

3 . Ɍɨɝɞɚ d0 = 00,92996;

db

0

= 93,87 927; Dɤ = 00; α ɭɫɬ = 20, 6; β = 22,8638 ° = 22° 5 '50" = 0,3990487

ɪɚɞ; α t = 2 ,55428° = 0,376 93 ɪɚɞ.

ɇɨɜɵɟ ɡɧɚɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚ-

ɬɵɯ ɤɨɥɟɫ ɛɭɞɭɬ

d

=

mz

=

3 25

= 8 ,395;

d

=

mz2

=

3 75

= 244, 85;

cosβ

cos22,8638 °

2

cosβ

cos22,8638 °

α t

= arctg

tgα

= arctg

tg20°

=

2 ,55427° = 0,376 929 ɪɚɞ;

cosβ

cos22,8638 °

mt = m / cosβ = 3 / cos 22,8638 ° = 3,2558;

db

= d cosα t

= 8 ,395 cos2 ,55427° = 75,703;

db

2

= d2 cosα t = 244, 85 cos2 ,55427° = 227, 09;

α tw

= α t = 2 ,55427° ; aw

= [0,5 m (z + z2 ) cosα t ] (cosα tw cosβ)=

h = (2h*a + c* −

y) m = (2 + 0,25 − 0) 3= 6,75;

df

= da

− 2h = 87,395 − 2 6,75=

73,895; df

= da

− 2h = 250, 85 − 2 6,75 =

2

2

= 236,685;

Sn

= 0,5 π m + 2 x m tgα − Ecs

= 0,5 π 3 + 2 0,3 tg20° − 0,07 = 4,642;

Sn

2

= 0,5 π m + 2 x2 m tgα − Ecs

= 0,5 π 3 + 2 0,3 tg20° − 0,08 = 4,632;

2

ρ

a

= 0,5 d 2

− d 2 = 0,5 87,3952

− 75,7032 = 2 ,834

a

b

ρp

= aw sinα tw

− 0,5 da2

− db2

= 62,790 sin 2 ,55427° −

2

2

− 0,5

250, 852 − 227, 092 = 7,332.

9. (3. 3)

S

'

= d

'

'

(d

+(tgα

'

'

ato

a0

S

no

0

cosβ)

t

−α

t

)− tgα

ato

−α

=

ato

0. (3. 4) Sato

= ( 0,2594 m − 0,0375)cosβ =

min

= ( 0,2594 3 − 0,0375)cos0,3990487° = 0,934.

. (3. 5) γ = 5° ; α ɜ = 6° ;

(3. 6)α n = arctg tgα

ɜ

sinα = arctg(tg6° sin 20°)= 2,058°;2,058° < 2°30.

ɉɪɢɧɢɦɚɟɦ α n = 2,5° .

Ɍɨɝɞɚ αɜ = arctg(tgα n

sinα)= arctg(tg6° /sin20°)= 7° 6'= 7, 275°

4, 5.

S

=d

''

'

+2x

'

(d

cosβ )+(tgα

−d

)−

atomin

ao

S

no

m tgα

t

t

0

0

''

−α

''

− tgα

ato

ato

.

ɪɟɡɭɥɶɬɚɬ ɏ0' = 0,7656.

6. (3.23)

a'H = (x0'

m

tgα b )cosβ = (0,7656 3 tg7,275°) cos 22,8638 =

= 6,578.

S

ato

min

d'

S'

−

cosβ

'

ato

ao

aH

=

=

7. (3.24)

'

'

'

′

2

(dao )

2 d

ao

tgα

ato

− S

tgα

ɜ

−

C

ato

d0

9. (3.26)

α'tw' = arccos

2(db

+ db0 )(df

− 2ρp sinα t )

=

)2 + df2 − db2 − 4ρp2

(db

+d

b0

0

= arccos

2(75,703 + 93,872)(73,895 − 2 7,332 sin2 ,55427°) =

(75, 03 + 93,72)2 + 73,8952 − 93,8722 − 4 7,3322

= 22,7 563°

= 0,3964625 ɪɚɞ.

20. (3.27)

a'H' =

(tgα'tw'

− α'tw'

− tgα t + α t )(d + d0 )− 2 x tgα t m

=

c

=

(tg0,3964625 − 0,3964625 − tg0,376 929 + 0,376 929)

= 5,523.

0, 073

2 . Ɍɚɤ ɤɚɤ a'H − a'H' > 0, ɬɨ aH

= a'H'

= 5,52.

22. (3.28) α'tw''

= arctg[2(ρa

+ ρ 0 )/(db

+ db

0

)]; ρ10 = 5 ;

= arctg [2(2 ,834 + 5)/(75,703 + 93,872)] = 7,56 8 ° = 0,3065 4 ɪɚɞ.

23. Ɍɚɤ ɤɚɤ df < db , ɬɨ (3.29)

IV

2df (db

+ db0 )

α tw = arscos

=

(d

+ d

)2 + d2 − d2

b

b0

f

b

0

2

73,895(75,703 + 93,872)

= arccos

= 9,42 866° = 0, 64443 ɪɚɞ.

(75,703 + 93,872)2 + 73,8922 − 93,8722

24. Ɍɚɤ ɤɚɤ α IIItw − α IVtw > 0, ɬɨ α twc

= α twIII

= 0,3065 4 ɪɚɞ.

25. (3.30) ac =

tgαtwc − αtwc − tgαt + αt

d

+ d0 − 2x tgα ɜ m

=

C

Ɉɩɪɟɞɟɥɟɧɢɟ ɱɟɪɬɟɠɧɵɯ ɪɚɡɦɟɪɨɜ ɞɨɥɛɹɤɚ

28. (3.32) invα

twɧ

= invα

t

+

2tgα x + x2

;

z

+ z2

x0

= A tgα ɜ

(m cos β )= 5,5 tg7,275°

(3 cos22,8638 °)= 0,254;

invαtwH = tg0,376 929 – 0,376 929 +

2 tg0,3490658(0 + 0,254)/(25 + 3 ) =

= 0,022 38; αtwH = 0,396 6.

29. Ɍɚɤ ɤɚɤ H > Bp , ɬɨ B= ȼ′Ɋ = 2.

(3.33) xoc = (A – Bp/ ) tgα B /(m cosβ)=

=(5,5 − 2) tg7,275° /(3 cos22,8638°)= – 0,3.

invαtwcɮɚɤɬ

=invαt + 2 tgα (x + xoc ) (z + z2 )= tg0,376 929 −0,376 929 +

+ 2 tg0,3490658° (0 − 0,3) (25 + 3 )= 0,0 49 25;

αtwcɮɚɤɬ = 0,3499 25 ɪɚɞ = 20,003389°.

30. Ɍɚɤ ɤɚɤ ɇ > Bp , ɬɨ ȼ = ȼp/ + ȼɢɡɧ= 2 + 8 = 20.

3 . (3.35) Sno = Sno/ + A c cosβ = 4,783 + 5,5 0, 073 cos22,8638 ° = 5,344.

32. (3.36)

d

=

db + db

0

− d

=

75,703

+ 93,872

− 73,895 = 09,9 6.

ao

cos

α

cos0,396 6

twɧ

f

d0 cosαt

=arccos

00,93 cos2 ,55428°

33.(3.37)αato

= 0,547 06 ɪɚɞ.

=arccos

dao

09,9 6

Sno

dao tgβ

5,344

S

=d

+invα −invα cos arctg

=

+

ano

ao

cosβ

t

ato

d0

00,93

cos22,8638 °

d0

+ tg0,3766 929 − 0,376 929 − tg0,547 06 − 0,547 06)

09,9 6

tg0,3990487

cos arctg

= ,4439 ≈ ,44 ɦɦ.

00,93

34.

(3.38)

hao =

dao − d0

=

09,9 6 − 00,93

= 4,5 0 ɦɦ.

2 cosγ

2 cos5°

35.

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

36.

(3.40)

α ɛɨɤ

= arctg

tgα ɜ tgα

= arctg

tg7,275° tg20°

= 2,69° = 2° 4 '.

− tgγ tgα

ɜ

− tg5° tg7,275°

37.

(3.42)

α min

= arctg

(tgα + tgγ tgα ɛɨɤ )cos αɛɨɤ

=

cos(β − αɛɨɤ )

= arctg

(

° +

°

°)

°

=

° = ° 0'23".

(

° +

°)

(3.43) α =

(

α +

γ

α ) α

=

(β − α )

= arctg =

(

° +

°

°)

°

=

° = ° 23'26".

° −

(

°)

38.

(3.45)

=

α =

° = 93,977.

39.

(3.47)

α = α

β = ( ° °)= ° =

= ° 53'.

δ

= αρχτγτγα −

4(ηλ− ηα− ξ0) χοσβ

0

τ

40.

(3.48)

ζ0 σιν2ατ

=

Λ

= arctg

=

(3.49)

=

=

= 2,448.

4 . (3.50)

= (tg 0,25948 – 0,259482 +

+ 0,259482)

2'.

42. (3.5 )

9'.

= 2,75829

45';

(3.55)

= 2,66576

40'.

0,7 d

% &&' ( ) = 75.

$

, m = 3, z

= 25, h

= ; h

= ,25, h

= 2,

, x = 0,7

z2= 75, x= 0 , h

= , h

= ,25, h

= 2.

. ( . )

;

2.

( .2)

% 8 "39 " #

3.

( .3)

= 74,425;

= 223,277.

4.

( .4) x = x = 0;

= 0,3695352.

5.

( .7)

=

=

= 59,626.

6.

( .9) x = x

= 0: y = 0.

7.

( . 0)

= 3;

= 3.

8.

( . 3) h =

= 6,75.

9.

( . )

= 85,8 3;

= 245,44.

0. ( . 5)

= 72,3 3;