“Dane do projektu”

≔

M

2

⋅

19.9

=

M

2

⎛⎝

⋅

19.9 10

3

⎞⎠

⋅

“M2 - moment skr

ęcający”

≔

z

3

35

“z3 - liczba z

ębów koła 3 ”

≔

m

3

1.5

“m3 - moduł koła 3 ”

≔

ψ

3

17.7

“z2 - liczba z

ębów koła 2”

≔

z

2

58

“m2 - moduł koła 2”

≔

m

2

1

“Lh - godznowa trwało

ść łożyska”

≔

ψ

2

14.8

“α - k

ąt zarysu”

“β - k

ąt linii śrubowej ”

≔

L

h

11000

≔

β

°

20

≔

α

°

20

1

Created with Mathcad Express. See www.mathcad.com for more information.

“1.0. Obliczenia wst

ępne”

“1.1.

Średnica podziałowa koła z2 i z3”

=

m

2

1

=

z

2

58

=

β

20

=

m

3

1.5

=

z

3

35

≔

d

2

=

―――

⋅

m

2

z

2

cos ((β))

61.72

≔

d

3

=

―――

⋅

m

3

z

3

cos ((β))

55.87

=

d

2

61.722

=

d

3

55.869

“1.2. Siły obwodowe”

=

M

2

19.9

=

d

2

61.722

=

d

3

55.869

≔

P

2

=

――

⋅

2 M

2

d

2

644.824

≔

P

3

=

――

⋅

2 M

2

d

3

712.377

=

P

2

644.824

=

P

3

712.377

“1.3. Siły promieniowe”

=

P

2

644.824

=

P

3

712.377

=

α

20

≔

P

r2

=

⋅

P

2

―――

tan ((α))

tan ((β))

644.824

≔

P

r3

=

⋅

P

3

―――

tan ((α))

tan ((β))

712.377

=

P

r2

644.824

=

P

r3

712.377

“1.4. Siły osiowe”

≔

P

x2

=

⋅

P

2

tan ((β))

234.697

≔

P

x3

=

⋅

P

3

tan ((β))

259.284

=

P

x2

234.697

=

P

x3

259.284

“1.5. Szeroko

ści więców zębatych”

=

ψ

2

14.8

=

ψ

3

17.7

≔

b

2

=

⋅

m

2

ψ

2

14.8

≔

b

3

=

⋅

m

3

ψ

3

26.55

=

b

2

14.8

=

b

3

26.55

“2.0. Kryterium napr

ężeń dopuszczalnych”

“2.1. Długo

ści wału”

≔

Ł

20

=

b

2

14.8

=

b

3

26.55

≔

a

=

+

―――

⎛⎝ +

Ł

b

2

⎞⎠

2

25

42.4

≔

a

45

≔

b

=

+

―――

⎛⎝ +

b

2

b

3

⎞⎠

2

10

30.675

≔

b

35

≔

c

=

+

―――

⎛⎝ +

b

3

Ł⎞⎠

2

25

48.275

≔

c

50

2

Created with Mathcad Express. See www.mathcad.com for more information.

“2.2. Reakcje w w

ęzłach łożyskowych”

“2.2.1. W płaszczy

źnie x-y”

=

P

x2

234.697

=

P

r2

644.824

=

P

x3

259.284

=

P

r3

712.377

=

d

2

61.722

=

d

3

55.869

=

a

45

=

b

35

=

c

50

“-w punkcie 1, w

ęzeł łożyskowy C”

≔

R

y1

=

――――――――――――

−

+

+

⋅

P

x2

―

d

2

2

⋅

P

r2

(( +

b

c))

⋅

P

x3

―

d

3

2

⋅

P

r3

c

+

+

a

b

c

259.1

=

R

y1

259.055

“-w punkcie 4, w

ęzeł łożyskowy D”

≔

R

y4

=

――――――――――――

+

+

−

⋅

P

x2

―

d

2

2

⋅

P

r2

a

⋅

P

x3

―

d

3

2

⋅

P

r3

(( +

a

b))

+

+

a

b

c

326.6

=

R

y4

326.608

“2.2.2. W płaszczy

źnie x-z”

=

P

2

644.824

=

P

3

712.377

“-w punkcie 1, w

ęzeł łożyskowy C”

≔

R

z1

=

――――――

+

⋅

P

2

(( +

b

c))

⋅

P

3

c

+

+

a

b

c

695.606

=

R

z1

695.606

“-w punkcie 4, w

ęzeł łożyskowy D”

≔

R

z4

=

――――――

+

⋅

P

2

a

⋅

P

3

(( +

a

b))

+

+

a

b

c

661.594

=

R

z4

661.594

3

Created with Mathcad Express. See www.mathcad.com for more information.

“2.2.3. Siły obci

ążające węzły łożyskowe”

=

R

y1

259.055

=

R

z1

695.606

=

R

y4

326.608

=

R

z4

661.594

“-obci

ążenie promieniowe łożyska w ptk 1”

≔

F

r1

=

‾‾‾‾‾‾‾‾‾

+

R

y1

2

R

z1

2

742.279

=

F

r1

742.279

“-obci

ążenie promieniowe łożyska w ptk 4”

≔

F

r4

=

‾‾‾‾‾‾‾‾‾

+

R

y4

2

R

z4

2

737.821

=

F

r4

737.821

=

P

x2

234.697

=

P

x3

259.284

“-obci

ążenie osiowe łożyska”

≔

F

a

=

||

−

P

x2

P

x3

|| 24.59

=

F

a

24.587

“2.3. Momenty gn

ące”

“2.3.1. W płaszczy

źnie x-y”

=

a

45

=

b

35

=

P

x2

234.697

=

P

r2

644.824

=

P

x3

259.284

≔

M

gy1

0

=

M

gy1

0

≔

M

gy2

=

⋅

R

y1

a

⎛⎝

⋅

11.657 10

3

⎞⎠

=

M

gy2

⎛⎝

⋅

11.657 10

3

⎞⎠

⋅

≔

M'

gy2

=

−

M

gy2

⋅

P

x2

―

d

2

2

⎛⎝

⋅

4.414 10

3

⎞⎠

⋅

=

M'

gy2

⎛⎝

⋅

4.414 10

3

⎞⎠

⋅

≔

M

gy3

=

−

−

⋅

R

y1

(( +

a

b))

⋅

P

x2

―

d

2

2

⋅

P

r2

b

⋅

−9.087 10

3

⋅

=

M

gy3

⋅

−9.087 10

3

⋅

≔

M'

gy3

=

−

M

gy3

⋅

P

x3

―

d

3

2

⋅

−16.33 10

3

⋅

=

M'

gy3

⋅

−16.33 10

3

⋅

≔

M

gy4

0

=

M

gy4

0

“2.3.2. W płaszczy

źnie x-z”

=

R

z1

695.606

=

P

2

644.824

≔

M

gz1

0

≔

M

gz1

0

≔

M

gz2

=

⋅

R

z1

a

⎛⎝

⋅

31.302 10

3

⎞⎠

⋅

=

M

gz2

⎛⎝

⋅

31.302 10

3

⎞⎠

⋅

≔

M

gz3

=

−

⋅

R

z1

(( +

a

b))

⋅

P

2

b

⎛⎝

⋅

33.08 10

3

⎞⎠

⋅

=

M

gz3

⎛⎝

⋅

33.08 10

3

⎞⎠

⋅

≔

M

gz4

0

=

M

gz4

0

4

Created with Mathcad Express. See www.mathcad.com for more information.

“2.4. Moment gn

ący maksymalny”

=

M

gy1

0

=

M

gz1

0

=

M

gy2

⎛⎝

⋅

11.657 10

3

⎞⎠

⋅

=

M'

gy2

⎛⎝

⋅

4.414 10

3

⎞⎠

⋅

=

M

gz2

⎛⎝

⋅

31.302 10

3

⎞⎠

⋅

=

M

gy3

⋅

−9.087 10

3

⋅

=

M

gz3

⎛⎝

⋅

33.08 10

3

⎞⎠

⋅

=

M'

gy3

⋅

−16.33 10

3

⋅

=

M

gy4

0

=

M

gz4

0

≔

M

g1

=

‾‾‾‾‾‾‾‾‾‾‾

+

M

gy1

2

M

gz1

2

0

=

M

g1

0

≔

M

g2

=

‾‾‾‾‾‾‾‾‾‾‾

+

M

gy2

2

M

gz2

2

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

=

M

g2

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

≔

M'

g2

=

‾‾‾‾‾‾‾‾‾‾‾‾

+

M'

gy2

2

M

gz2

2

⎛⎝

⋅

31.612 10

3

⎞⎠

⋅

=

M'

g2

⎛⎝

⋅

31.612 10

3

⎞⎠

⋅

≔

M

g3

=

‾‾‾‾‾‾‾‾‾‾‾

+

M

gy3

2

M

gz3

2

⎛⎝

⋅

34.305 10

3

⎞⎠

⋅

=

M

g3

⎛⎝

⋅

34.305 10

3

⎞⎠

⋅

≔

M'

g3

=

‾‾‾‾‾‾‾‾‾‾‾‾

+

M'

gy3

2

M

gz3

2

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

=

M'

g3

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

≔

M

g4

=

‾‾‾‾‾‾‾‾‾‾‾

+

M

gy4

2

M

gz4

2

0

=

M

g4

0

“2.5. Momenty redukowane”

=

M

g2

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

=

M'

g2

⎛⎝

⋅

31.612 10

3

⎞⎠

⋅

=

M

2

⎛⎝

⋅

19.9 10

3

⎞⎠

⋅

=

M

g3

⎛⎝

⋅

34.305 10

3

⎞⎠

⋅

=

M'

g3

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

≔

M

z1

0

=

M

z1

0

≔

M

z2g

=

M

g2

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

=

M

z2g

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

≔

M'

z2s

=

‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+

M'

g2

2

⋅

0.19 M

2

2

⎛⎝

⋅

32.781 10

3

⎞⎠

⋅

=

M'

z2s

⎛⎝

⋅

32.781 10

3

⎞⎠

⋅

≔

M

z3s

=

‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+

M

g3

2

⋅

0.19 M

2

2

⎛⎝

⋅

35.385 10

3

⎞⎠

⋅

=

M

z3s

⎛⎝

⋅

35.385 10

3

⎞⎠

⋅

≔

M'

z3g

=

M'

g3

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

=

M'

z3g

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

≔

M

z4

0

=

M

z4

0

5

Created with Mathcad Express. See www.mathcad.com for more information.

“2.6.

Średnice powierzchni funkcjonalnych”

“2.6.1. Napr

ężenia dopuszczalne”

“Przyj

ęto stal węglową E335”

≔

R

m

600 ――

2

“Rm - wytrzymało

ść doraźna na rozciąganie mat. E335”

“wg. PN-88/H-84020”

≔

x

z

3.5

“xz - współczynnik bezpiecze

ństwa”

≔

k

go

=

―――

⋅

0.42 R

m

x

z

72 ――

2

“kgo - przy wachadłowym zginaniu”

=

k

go

72 ――

2

≔

k

sj

=

―――

⋅

0.56 R

m

x

z

96 ――

2

“ksj - przy t

ętniącym skręcaniu”

=

k

sj

96 ――

2

“2.6.2. Obliczenieniowe

średnice pod łożyskiem C”

=

M

z2g

⎛⎝

⋅

33.403 10

3

⎞⎠

⋅

=

Ł

20

=

a

⎛⎝ ⋅

45 10

−3

⎞⎠

=

k

go

72 ――

2

≔

d'

1

=

‾‾‾‾‾‾‾‾‾

3

――――

⋅

⋅

32 M

z2g

Ł

⋅

⋅

⋅

2

a k

go

10.164

=

d'

1

10.164

“2.6.3. Obliczeniowa

średnica pod kołem zębatym z2”

=

M'

z2s

⎛⎝

⋅

32.781 10

3

⎞⎠

⋅

≔

d'

2

=

‾‾‾‾‾‾‾‾

3

―――

⋅

32 M'

z2s

⋅ k

go

16.676

=

d'

2

16.676

“2.6.4. Obliczeniowa

średnica pod kołęm zębatym z3”

=

M'

z3g

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

≔

d'

3

=

‾‾‾‾‾‾‾‾

3

―――

⋅

32 M'

z3g

⋅ k

go

17.346

=

d'

3

17.346

“2.6.5. Obliczeniowa

średnica pod łożyskiem D (4)”

=

M'

z3g

⎛⎝

⋅

36.891 10

3

⎞⎠

⋅

=

Ł

20

=

c

50

≔

d'

4

=

‾‾‾‾‾‾‾‾‾‾

3

――――

⋅

⋅

32 M'

z3g

Ł

⋅

⋅

⋅

2

c k

go

10.144

=

d'

4

10.144

6

Created with Mathcad Express. See www.mathcad.com for more information.

“3.0. Kryterium dopuszczalnego ugi

ęcia”

“3.1. Ugi

ęcie w płaszczyźnie x-y”

“3.1.1. Stałe całkowania”

=

a

45

=

b

35

=

c

50

=

R

y1

259.055

=

P

x2

234.697

=

P

r2

644.824

=

P

x3

259.284

=

P

r3

712.377

=

d'

2

16.676

=

d'

3

17.346

≔

L

=

+

+

a

b

c

130

“- odległo

ść między węzłami łożyskowymi”

=

L

130

=

L

130

≔

C

y

⋅

――

1

⋅

6 L

⎛
⎜
⎜⎝

−

−

+

−

⋅

R

y1

L

3

⋅

P

r2

(( +

b

c))

3

⋅

P

r3

c

3

⋅

3 ――――――

⋅

⋅

P

x2

d'

2

(( +

b

c))

2

2

⋅

3 ――――

⋅

⋅

P

x3

d'

3

c

2

2

⎞
⎟
⎟⎠

=

C

y

⎛⎝

⋅

260.138 10

3

⎞⎠

⋅

2

“3.1.2.

Średnia średnica wału”

=

d'

1

10.164

=

d'

4

10.144

=

Ł

20

=

d'

2

16.676

=

d'

3

17.346

≔

d

so

=

⋅

―

1

L

⎛
⎜

⎝

+

⋅

―

Ł

2

⎛⎝

+

d'

1

d'

4

⎞⎠

⋅

――

−

L

Ł

2

⎛⎝

+

d'

2

d'

3

⎞⎠

⎞
⎟

⎠

15.956

=

d

so

15.956

“3.1.3. Ugi

ęcie pod kołem z2”

≔

E

⋅

2.1 10

5

――

2

“- stała Younga”

=

d

so

15.956

=

C

y

⎛⎝

⋅

260.138 10

3

⎞⎠

⋅

2

=

a

45

=

R

y1

259.055

≔

f

y2

=

⋅

――――

64

⋅

⋅ d

so

4

E

⎛
⎜
⎝

−

⋅

C

y

a

―――

⋅

R

y1

a

3

6

⎞
⎟
⎠

⎛⎝

⋅

11.631 10

−3

⎞⎠

=

f

y2

⎛⎝

⋅

11.631 10

−3

⎞⎠

7

Created with Mathcad Express. See www.mathcad.com for more information.

“3.1.4. Ugi

ęcie pod kołem z3”

=

d

so

15.956

=

E

⎛⎝

⋅

210 10

3

⎞⎠ ――

2

=

C

y

⎛⎝

⋅

260.138 10

3

⎞⎠

⋅

2

=

a

45

=

b

35

=

P

r2

644.824

=

P

x2

234.697

=

d'

2

16.676

=

R

y1

259.055

≔

f

y3

=

⋅

――――

64

⋅

⋅ d

so

4

E

⎛
⎜
⎜⎝

−

+

+

⋅

C

y

(( +

a

b))

―――

⋅

P

r2

b

3

6

――――

⋅

⋅

P

x2

d'

2

b

2

4

――――

⋅

R

y1

(( +

a

b))

3

6

⎞
⎟
⎟⎠

⎛⎝

⋅

6.752 10

−3

⎞⎠

=

f

y3

⎛⎝

⋅

6.752 10

−3

⎞⎠

“3.2. Ugi

ęcie w płaszczyźnie x-z”

“3.2.1. Stałe całkowania”

=

R

z1

695.606

=

P

2

644.824

=

P

3

712.377

=

c

50

=

L

130

≔

C

z

=

⋅

――

1

⋅

6 L

⎛
⎝

−

−

⋅

R

z1

L

3

⋅

P

2

(( +

b

c))

3

⋅

P

3

c

3

⎞
⎠

⎛⎝

⋅

1.337 10

6

⎞⎠

⋅

2

=

C

z

⎛⎝

⋅

1.337 10

6

⎞⎠

⋅

2

“3.2.2. Ugi

ęcie pod kołem z2”

=

C

z

⎛⎝

⋅

1.337 10

6

⎞⎠

⋅

2

≔

f

z2

=

⋅

――――

64

⋅

⋅ d

so

4

E

⎛
⎜
⎝

−

⋅

C

z

a

―――

⋅

R

z1

a

3

6

⎞
⎟
⎠

⎛⎝

⋅

74.261 10

−3

⎞⎠

=

f

z2

⎛⎝

⋅

74.261 10

−3

⎞⎠

“3.2.3. Ugi

ęcie pod kołem z3”

≔

f

z3

=

⋅

――――

64

⋅

⋅ d

so

4

E

⎛
⎜
⎜⎝

−

+

⋅

C

z

(( +

a

b))

―――

⋅

P

2

b

3

6

――――

⋅

R

z1

(( +

a

b))

3

6

⎞
⎟
⎟⎠

⎛⎝

⋅

78.188 10

−3

⎞⎠

=

f

z3

⎛⎝

⋅

78.188 10

−3

⎞⎠

“3.3 Max. strzałki ugi

ęcia”

“3.3.1. Pod kołem z2”

=

f

y2

⎛⎝

⋅

11.631 10

−3

⎞⎠

=

f

z2

⎛⎝

⋅

74.261 10

−3

⎞⎠

≔

f

2

=

‾‾‾‾‾‾‾‾

+

f

y2

2

f

z2

2

⎛⎝

⋅

75.167 10

−3

⎞⎠

=

f

2

⎛⎝

⋅

75.167 10

−3

⎞⎠

“3.3.2. Pod kołem z3”

=

f

y3

⎛⎝

⋅

6.752 10

−3

⎞⎠

≔

f

3

=

‾‾‾‾‾‾‾‾

+

f

y3

2

f

z3

2

⎛⎝

⋅

78.479 10

−3

⎞⎠

=

f

3

⎛⎝

⋅

78.479 10

−3

⎞⎠

8

Created with Mathcad Express. See www.mathcad.com for more information.

“3.4. Dopuszczalne ugi

ęcie”

=

L

130

≔

f

dop

=

⋅

⋅

2 10

−4

L

⎛⎝ ⋅

26 10

−3

⎞⎠

=

f

dop

⎛⎝ ⋅

26 10

−3

⎞⎠

=

f

2

⎛⎝

⋅

75.167 10

−3

⎞⎠

=

f

3

⎛⎝

⋅

78.479 10

−3

⎞⎠

“Stosujemy współczynnik poprawkowy

średnicy , ponieważ fdop<f2 oraz fdop<f3”

“3.5. Współczynniki poprawkowe

średnicy”

“3.5.1. Pod kołem z2”

=

f

dop

⎛⎝ ⋅

26 10

−3

⎞⎠

≔

k

12

=

‾‾‾‾

4

――

f

2

f

dop

1.304

=

k

12

1.304

“3.5.2. Pod kołem z3”

≔

k

13

=

‾‾‾‾

4

――

f

3

f

dop

1.318

=

k

13

1.318

“3.5.3. Współczynnik poprawkowy”

“k1=max(k12 u k13) = k13”

≔

k

1

k

13

=

k

1

1.318

“4.0. Kryterium dopuszczalnego k

ąta skręcenia”

“4.1. Wzgl

ędny kąt skręcenia wału”

≔

G

⋅

8.1 10

4

――

2

“- wspolczynnik sztywnosci postaciowej”

=

M

2

⎛⎝

⋅

19.9 10

3

⎞⎠

⋅

=

d

so

15.956

≔

φ

sr

=

―――――

⋅

32 M

2

⋅

⋅ G ⎛⎝ ⋅

k

1

d

so

⎞⎠

4

⎛⎝

⋅

12.79 10

−6

⎞⎠ ――

1

“-podatnosc skretna walu”

=

φ

sr

⎛⎝

⋅

12.79 10

−6

⎞⎠ ――

1

“4.2. Dopouszczalny k

ąt skręcania”

≔

φ

dop

⋅

4 10

−6

――

1

>

φ

sr

φ

dop

“Informacja ta mówi nam,

że musimy dodatkowo policzyć punkt 4.3.”

9

Created with Mathcad Express. See www.mathcad.com for more information.

“4.3. Współczynnik poprawkowy

średniej średnicy”

=

φ

sr

⎛⎝

⋅

12.79 10

−6

⎞⎠ ――

1

=

φ

dop

⎛⎝ ⋅

4 10

−6

⎞⎠ ――

1

≔

k

2

=

‾‾‾‾

4

――

φ

sr

φ

dop

1.337

=

k

2

1.337

“4.4.

Średnica wału po korekcie”

=

d'

1

10.164

=

d'

2

16.676

=

d'

3

17.346

=

d'

4

10.144

=

k

1

1.318

=

k

2

1.337

≔

d

1

=

⋅

⋅

d'

1

k

1

k

2

17.916

=

d

1

17.916

≔

d

2w

=

⋅

⋅

d'

2

k

1

k

2

29.393

=

d

2w

29.393

≔

d

3w

=

⋅

⋅

d'

3

k

1

k

2

30.574

=

d

3w

30.574

≔

d

4

=

⋅

⋅

d'

4

k

1

k

2

17.88

=

d

4

17.88

“Po poprawkach przyj

ęto:”

≔

d

1

20

≔

d

2w

30

≔

d

3w

32

≔

d

4

20

“4.4.1. Koło z2 - nasadzane?”

=

d

2

61.722

=

m

2

1

≔

d

f2

=

−

d

2

⋅

2.5 m

2

59.222

=

d

f2

59.222

=

d

f2

59.222

=

M

2

19.9

⋅

≔

d

d2

=

−

d

f2

⋅

⋅

2 3.45

‾‾‾‾

3

19.9

40.524

=

d

d2

40.524

=

d

2w

30

=

d

d2

40.524

“kolo 2 nasadzane bo d2w<dd2”

10

Created with Mathcad Express. See www.mathcad.com for more information.

“4.4.2. Koło z3 - nasadzane?”

=

d

3

55.869

=

m

3

1.5

≔

d

f3

=

−

d

3

⋅

2.5 m

3

52.119

=

d

f3

52.119

=

d

f3

52.119

=

M

2

19.9

⋅

≔

d

d3

=

−

d

f3

⋅

⋅

2 3.45

‾‾‾‾

3

19.9

33.421

=

d

d3

33.421

=

d

3w

32

=

d

d3

33.421

“kolo 3 nasadzane bo d3w<dd3”

“4.5. Długo

ść rowka wspustowego”

“4.5.1. Koło 2”

≔

t

22

3.3

“-gł

ębokość piasty”

≔

z

2

1

“-liczba wpustów”

≔

k

dw

100 ――

2

“-dopuszczalne naciski powierzchniowe”

=

d

2w

30

≔

b

w2

8

“-szeroko

ść wpustu”

=

M

2

⎛⎝

⋅

19.9 10

3

⎞⎠

⋅

≔

l

2

=

+

―――――

⋅

2 M

2

⋅

⋅

⋅

d

2w

k

dw

t

22

z

2

b

w2

12.02

=

l

2

12.02

“Przyj

ęto wpust A8x7x18 ”

“wg PN-70/M-85005”

“4.5.2. Koło 3”

≔

t

22

3.3

“-gł

ębokość piasty”

≔

z

3

1

“-liczba wpustów”

=

d

3w

32

≔

b

w3

8

“-szeroko

ść wpustu”

≔

l

2

=

+

―――――

⋅

2 M

2

⋅

⋅

⋅

d

3w

k

dw

t

22

z

3

b

w3

11.769

=

l

2

11.769

“Przyj

ęto wpust A10x8x22 ”

“wg PN-70/M-85005”

11

Created with Mathcad Express. See www.mathcad.com for more information.

“5.0. Ło

żyskowanie toczne”

“5.1. W

ęzeł ustalony”

=

F

r1

742.279

=

F

r4

737.821

=

F

a

24.587

=

d

1

20

=

d

4

20

≔

n

2

1000

“Fr1>Fr4”

“5.1.1. Parametry konstrukcyjne”

“Wst

ępnie założono łożysko nr 16004”

≔

C

01

4050

“- nominalna no

śność statycza”

≔

C

1

7000

“- nominalna no

śność dynamiczna”

=

――

F

a

C

01

⋅

6.071 10

−3

≔

e

0.19

≔

X

1

≔

Y

0

“przyjmujemy Fa/C01=0.014”

=

――

F

a

F

r4

⋅

33.324 10

−3

“5.1.2. Siła zast

ępcza”

≔

P

1

=

F

r4

737.821

=

P

1

737.821

“5.1.3. Wska

źnik prędkości i trwałości łożyska”

=

L

h

⎛⎝ ⋅

11 10

3

⎞⎠

≔

W

=

‾‾‾‾‾‾‾‾‾‾‾‾‾

3

―――――

⋅

L

h

n

2

⋅

⋅

16660

8.708

=

W

8.708

“5.1.4. Obliczeniowa no

śność ruchowa”

=

W

8.708

=

P

1

737.821

≔

C'

1

=

⋅

W P

1

⎛⎝

⋅

6.425 10

3

⎞⎠

=

C'

1

⎛⎝

⋅

6.425 10

3

⎞⎠

=

C

1

⎛⎝ ⋅

7 10

3

⎞⎠

=

C'

1

⎛⎝

⋅

6.425 10

3

⎞⎠

“C '1<C1”

“przyj

ęt łożysko kulkowe zwykłe nr 16004, gdzie śrenica wewnętrzna d=20 mm”

“

średnica zewnętrzna D=42mm; szerokość B=8mm; nominalna nośność dynamiczna Cu=7000N”

“5.2. W

ęzeł pływający”

≔

C'

4

=

⋅

W F

r4

⎛⎝

⋅

6.425 10

3

⎞⎠

≔

d

amin

20

=

C'

4

⎛⎝

⋅

6.425 10

3

⎞⎠

“C '4<C1”

“przyj

ęt łożysko kulkowe zwykłe nr 16004, gdzie śrenica wewnętrzna d=20 mm”

“

średnica zewnętrzna D=42mm; szerokość B=8mm; nominalna nośność dynamiczna Cu=7000N”

12

Created with Mathcad Express. See www.mathcad.com for more information.

“6.0. Elementy mocowania i technologiczne”

“6.1. Pier

ścienie osadcze sprężyste”

“

Średnica”

“Oznaczenie”

“Szerokow

ść rowka” “Średnica wew. rowka” “Odl. od końca czopa”

d

4

=

d

1

20

20 z

1.3 H13

19 h12

1.5

=

d

2w

30

30 z

1.6 H13

28.6 h12

2.1

=

d

3w

32

32 z

1.6 H13

30.3 h12

2.6

“6.2. Nakiełki”

“

Średnia średnica wału”

=

k

1

1.318

=

k

2

1.337

=

d

so

15.956

≔

d

sr

=

⋅

⋅

k

1

k

2

d

so

28.124

=

d

sr

28.124

“Oznaczenie”

“Nakiełek A2,5 wg PN-EN ISO 6411:2002”

“6.3. Podci

ęcie obróbkowe”

“

Średnica wału”

“Oznaczenie”

“d1=d4=20mm”

“C1,6 wg. PN-58/M-02043”

13

Created with Mathcad Express. See www.mathcad.com for more information.