Internal and External Spline Teeth - Gears - Internal and External Spline Teeth, Spline Connections With Involute Flanks, Spline Connections With Straight Flanks [PDF]

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Internal and external spline teeth The tool machines and extensive hobbing and cutting tools available to us, allow us to achieve external and internal spline connections according to the standards NBN-DIN – BS-AGMA or NF on gear blanks of which the dimensions fall within the limits of our manufacturing capabilities. This applies both to spline connections with involute anks as for spline connections with straight anks. Spline connections with straight anks:

A: Pro le of the nave B: Pro le of the shaft The form of the slots as indicated above is closely linked to the nish method. For choosing the number of keys depending on the diameters and of the load, as also for indicating the tolerances according to the desired t (loose, sliding, straining) we refer to the tables published by the various standardization organizations: NBN 90.01 / 02 / 03 DIN 5462 / 63 / 64 / 65 SAE Standard Splines We only present a part of the DIN-tables. d1

Light sequence DIN 5462

Average sequence DIN 5463

Heavy sequence DIN 5464

DIN 5472

DIN 5471

z

d2

d3min

b

z

d2

d3min

b

z

d2

d3min

b

z d2

d3min b

z d2 d3min b

21

–

–

–

–

6

25

19,5

5

10

26

18,44

3

6 25

–

5

4 25 –

8

23

6

26

22,1

6

6

28

21,3

6

11

29

20,3

4

6 28

–

6

– –

–

–

26

6

30

24,6

6

6

32

23,4

6

12

32

23

4

6 32

–

6

– –

–

–

28

6

32

26,7

7

6

34

25,9

7

13

35

24,4

4

6 34

–

7

4 32 –

10

32

8

36

30,42

6

8

38

29,4

6

14

40

28

5

6 38

–

8

4 38 –

10

36

8

40

34,5

7

8

42

33,5

7

15

45

31,3

5

6 42

–

8

4 42 –

12

42

8

46

40,4

8

8

48

39,5

8

16

52

36,9

6

6 48

–

10 4 48 –

12

46

8

50

44,62

9

8

54

42,7

9

17

56

40,9

7

6 52

–

12 4 52 –

14

52

8

58

49,7

10

8

60

48,7

10

18

60

47

5

6 60

–

14 4 60 –

14

56

8

62

53,6

10

8

65

52,2

10

19

65

50,6

5

6 –

–

–

–

58

–

–

–

–

–

–

–

–

20

–

–

–

– 65

–

14 4 65 –

16

62

8

68

59,82

12

8

72

57,8

12

21

72

56,1

6

6 70

–

16 4 70 –

16

68

–

–

–

–

–

–

–

22

–

–

–

6 78

–

16 4 78 –

16

72

10

78

69,6

12

10

82

67,4

12

23

82

65,9

7

6 82

–

16 – –

–

–

78

–

–

–

–

–

–

–

–

24

–

–

–

6 90

–

16 – –

–

–

82

–

–

–

–

10

92

–

12

25

–

–

–

6 95

–

16 – –

–

–

88

–

–

–

–

–

–

–

–

26

–

–

–

6 100 –

16 – –

–

–

92

–

–

–

–

10

102

–

14

–

–

–

–

6 105 –

20 – –

–

–

98

–

–

–

–

–

–

–

–

–

–

–

–

6 110 –

20 – –

–

–

105 –

–

–

–

–

–

–

–

–

–

–

–

6 120 –

20 – –

–

–

115 –

–

–

–

–

–

–

–

–

–

–

–

6 130 –

20 – –

–

–

130 –

–

–

–

–

–

–

–

–

–

–

–

6 145 –

24 – –

–

–

– –

–

The tolerances are depending on mounting conditions, shaft (Iz) or tooth ank centering (Fz). b nave

d1

d2

Soft

Hardened

Nave Iz + Fz

D9

F10

H7

H11

Shaft Iz sliding

h8

e8

f7

a11

Shaft Iz sliding

p6

h6

j6

Shaft Fz sliding

h8

e8

–

Shaft Fz tight

u6

k6

–

Indication : B DIN 5462 – B 6x28x32 Spline connections with involute anks

The increased use of spline connections with involute tooth anks has brought us to purchase a wide variety of hobbing and tools and this is in accordance with the various standardization systems. These connections can be “sliding” or “ xed”, and with “centering” on the tooth anks or on the external diameter of the axle (tooth tip) or on the inner diameter. The involute spline connections are similar to the classic teeth for gears, with a pressure angle of 20° or 30° depending on the standard used. The intention which is the basis of this idea is: external spline connections manufactured in the same way (same machines and similar tools), as for the classic gears, by hobbing (hobbing and cutting tools). The corresponding internal spline connections manufactured by the gear generating proces at tooth hobbing machines (Fellows &-Lorenz) or by broaching machines (for larger series). Certain systems are even equipped to use the same milling tools as for normal teeth. The most common pressure angles are 20° (with adjusted positive addendum modi cation to obtain an e ective pressure angle of ± 30 °in the area of the pitch circle; i.e. NBN 270 or PN-E 22-141) and 30° (DIN 5480, 5482 and AISIB92-1-1970). Recently the Americans added to the standard used pressure angle 30°, the standardization of the pressure angles 37°30′ and 45°. For choosing the tooth numbers, the module, the type of centering and tting, we are referring to the tables published by the various standardization organizations. Hereafter, we present the characteristics of the main spline connections. DIN 5480

Addendum modi cation nave

x1.m = – 0,05.m tot + 0,45.m

Addendum modi cation shaft

x2.m = = – x1.m = + 0,05.m tot – 0,45.m

Nominal diameter

dB = m.z1 + 2.x1.m + 1,1.m

Nave tip diameter

da2 = m.z2 + 2.x2.m + 0,9.m

Shaft tip diameter

da2 = m.z1 + 2.x1.m + 0,9.m

Nave root diameter

df1 = m.z2 + 2.x2.m – 2.hfp

Shaft root diameter

df1 = m.z1 + 2.x1.m – 2.hfp

Pitch circle diameter

d = m.z

Base circle

db = m.z.cosa

Addendum

hap = 0,45.m

Dedendum

hfp = 0,60.m

Tooth depth

hp = hap + hfp

Nave tooth thickness Shaft tooth thickness

s2 = m.

+ 2.x2.m.tana

s1 = m.

+ 2.x1.m.tana

The following is the table of normalized dimensions according to DIN 5480. The dimensions and modules in brackets ( ) are avoidable values. Summary table – shaft diameter – module – number of teeth DIN 5480 dB

0,5 (0,6) (0,75) 0,8 (1) 1,25 (1,5) (1,75) 2

(2,5)

3

(4)

5

(6)

8

(10)

6

10

8

6

6

–

–

–

–

–

–

–

–

–

–

–

–

7

12

10

8

7

–

–

–

–

–

–

–

–

–

–

–

–

8

14

12

9

8

6

–

–

–

–

–

–

–

–

–

–

–

9

16

13

10

10

7

–

–

–

–

–

–

–

–

–

–

–

10

18

15

12

11

8

6

–

–

–

–

–

–

–

–

–

–

11

20

17

13

12

9

7

–

–

–

–

–

–

–

–

–

–

12

22

18

14

13

10 8

6

–

–

–

–

–

–

–

–

–

13

24

20

16

15

11 9

7

–

–

–

–

–

–

–

–

–

14

26

22

17

16

12 10

8

6

–

–

–

–

–

–

–

–

15

28

23

18

17

13 10

8

7

6

–

–

–

–

–

–

–

16

30

25

20

18

14 11

9

8

6

–

–

–

–

–

–

–

17

32

27

21

20

15 12

10

8

7

–

–

–

–

–

–

–

18

34

28

22

21

16 13

10

9

7

–

–

–

–

–

–

–

19

36

30

24

22

17 14

11

9

–

–

–

–

–

–

–

20

38

32

25

24

18 14

12

10

6

–

–

–

–

–

–

8

21

40

34

26

25

19 15

12

10

–

–

–

–

–

–

22

42

35

28

26

20 16

13

11

6

–

–

–

–

–

23

44

37

29

27

22 17

14

12

–

–

–

–

–

24

46

38

30

28

22 18

14

12

–

–

–

–

–

25

48

40

32

30

24 18

15

13

–

–

–

–

–

26

50

42

33

31

24 19

16

13

–

–

–

–

–

27

52

44

34

32

26 20

16

14

–

–

–

–

–

28

54

45

36

34

26 21

17

14

–

–

–

–

–

29

56

47

37

35

28 22

18

15

–

–

–

–

–

30

58

48

38

36

28 22

18

16

–

–

–

–

–

31

60

50

40

37

30 23

19

16

–

–

–

–

–

32

62

52

41

38

30 24

20

17

6

–

–

–

–

33

64

54

42

40

32 25

20

17

–

–

–

–

34

66

55

44

41

32 26

21

18

–

–

–

–

35

68

57

45

42

34 26

22

18

–

–

–

–

36

70

58

46

44

34 27

22

19

–

–

–

–

37

72

60

48

45

36 28

23

20

17

13

11

8

–

–

–

–

38

74

62

49

46

36 29

24

20

18

14

11

8

–

–

–

–

39

76

64

50

47

38 30

24

21

–

–

–

–

40

78

64

52

48

38 30

25

21

18

14

12

8

6

–

–

–

42

–

68

54

51

40 32

26

22

20

15

12

9

7

–

–

–

45

–

74

58

55

44 34

28

24

21

16

13,14 10

7

–

–

–

47

–

76

60

57

46 36

30

25

22

17

14

10

8

–

–

–

48

–

78

62

58

46 37

30

26

22

18

14

10

8

6

–

–

50

–

–

64

60

48 38

32

27

24

18

15

11

8

7

–

–

(52) –

–

68

64

50 40

33

28

24

19

16

11

9

7

–

–

55

–

–

72

66

54 42

35

30

26

20

17

12

9

8

–

–

(58) –

–

–

70

56 45

37

32

28

22

18

13

10

8

–

–

60

–

–

–

74

58 46

38

33

28

22

18

13,14

10

8

6

–

(62) –

–

–

–

–

48

40

34

30

23

19

14

11

9

65

–

–

–

–

–

50

42

36

31

24

20

15

11

9

(68) –

–

–

–

–

53

44

37

32

26

21

15,16

12

10

70

–

–

–

–

–

54

45

38

34

26

22

16

12

10

(72) –

–

–

–

–

56

46

40

34

27

22

16

13

10

75

–

–

–

–

–

58

48

41

36

28

24

17

13,14

11

(78) –

–

–

–

–

60

50

43

38

30

24

18

14

11,12

80

–

–

–

–

–

62

52

44

38

30

25

18

14

12

(82) –

–

–

–

–

–

53

45

40

31

26

19

15

12

85

–

–

–

–

–

–

55

47

41

32

27

20

15,16

13

(88) –

–

–

–

–

–

57

49

42

34

28

20

16

13

90

–

–

–

–

–

–

58

50

44

34

28

21

16

13,14

(92) –

–

–

–

–

–

60

51

44

35

29

22

17

14

95

–

–

–

–

–

62

53

46

36

30

22

18

14

–

9

11

12

7

8

10

13,14 10

14

16

11

12

7

8

8

9

10

7

– 7

– –

7

– –

8

– –

8

6

9

7

10

7

10

8

(98

–

–

–

–

–

–

64

54

48

38

31

23

18

15

100

–

–

–

–

–

–

64

56

48

38

32

24

18

15

11

8

105

–

–

–

–

–

–

68

58

51

40

34

25

20

16

12

9

110

–

–

–

–

–

–

72

60,61

54

42

35

26

20

17

12

9

120

–

–

–

–

–

–

–

66,67

58

46

38

28

22

18

13,14

10

130

–

–

–

–

–

–

–

–

64

50

42

31

24

20

15

11,12

140

–

–

–

–

–

–

–

–

68

54

45

34

26

22

16

12

150

–

–

–

–

–

–

–

–

74

58

48

36

28

24

17

13,14

160

–

–

–

–

–

–

–

–

–

–

52

38

30

25

18

14

170

–

–

–

–

–

–

–

–

–

–

55

41

32

27

20

15,16

180

–

–

–

–

–

–

–

–

–

–

58

44

34

28

21

16

190

–

–

–

–

–

–

–

–

–

–

62

46

36

30

22

17,18

200

–

–

–

–

–

–

–

–

–

–

65

48

38

32

24

18

210

–

–

–

–

–

–

–

–

–

–

68,69 51

40

34

25

20

220

–

–

–

–

–

–

–

–

–

–

–

–

42

35

26

20

240

–

–

–

–

–

–

–

–

–

–

–

–

46

38

28

22

250

–

–

–

–

–

–

–

–

–

–

–

–

48

40

30

24

260

–

–

–

–

–

–

–

–

–

–

–

–

50

42

31

24

280

–

–

–

–

–

–

–

–

–

–

–

–

54

45

34

26

300

–

–

–

–

–

–

–

–

–

–

–

–

58

48

36

28

320

–

–

–

–

–

–

–

–

–

–

–

–

62

52

38

30

340

–

–

–

–

–

–

–

–

–

–

–

–

–

55

41

32

360

–

–

–

–

–

–

–

–

–

–

–

–

–

58

44

34

380

–

–

–

–

–

–

–

–

–

–

–

–

–

62

46

36

400

–

–

–

–

–

–

–

–

–

–

–

–

–

65

48

38

420

–

–

–

–

–

–

–

–

–

–

–

–

–

68

51

40

440

–

–

–

–

–

–

–

–

–

–

–

–

–

72

54

42

450

–

–

–

–

–

–

–

–

–

–

–

–

–

74

55

44

460

–

–

–

–

–

–

–

–

–

–

–

–

–

75

56

44

480

–

–

–

–

–

–

–

–

–

–

–

–

–

78

58

46

500

–

–

–

–

–

–

–

–

–

–

–

–

–

82

61

48

DIN 5482

For further information, we refer to the relevant standard. DIN 5481

For further information, we refer to the relevant standard. ANSI B92.1 – 1970, R1993

As with DIN 5480 there are also di erent versions possible.

Here are the formulas for the calculation of di erent diameters. Term

Symbol

Flat root, side t

Flat root Maj Dia t

Fillet root side t

Stub pitch

Ps

2.P

2.P

2.P

Pitch diameter

Dp

N/P

N/P

N/P

Base diameter

Db

D.cosφD

D.cosφD

D.cosφD

Circular pitch

p

p/P

p/P

p/P

Space width

sv

p/2.P

p/2.P

p/2.P

Major diameter int

Dri

Major diameter ext

Do

Minor diameter int

Di

Minor diameter 2,5/5DP – 12/24DP

Dre

Minor diameter 16/32DP and ner Minor diameter 10/20DP and ner Form diameter int

DFi

Form diameter ext

DFe

Form clearance

cF

E 22-151 NF

E 22-141 NF

0,001.D

0,001.D

0,001.D

Following

are the tables with the available hobs and cutters. NF – E22-151

Module

Z

Type

Ld. max

Øprimitive

1,5 1,5 1,217 2

18 22 28 16

Tail Tail – Tail

65 45 – 105

27 33 – 32

Zmin

AP

NBN 270 / NF – E22-141 /NF – E22-143

Module

Z

Type

Ld. max

Øprimitive

Zmin

AP

0,5

–

hob

0,8

–

hob right

–

39,5

–

27°26’

1,25

–

hob right

–

–

–

20°

1,25

12

tail

65

15

20

1,25

20

tail

50

25

30

1,25

60

–

–

75

–

1,667

–

hob right

–

50

–

1,667

8

tail

75

13,336

16

1,667

18

tail

60

30

27

2,5

–

hob right

–

–

–

2,5

10

tail

80

25

18

2,5

10

tail

90

25

18

3,75

–

hob right

–

–

–

3,75

5

tail

65

18,75

12

3,75

20

–

–

75

29

3,75

9

tail

77

33,75

17

5

–

hob right

–

87,71

5

6

tail

135

30

13

5

6

tail

70

30

13

5

10

tail

135

50

18

5

10

tail

120

50

18

5

15

–

–

75

24

7,5

–

hob right

–

–

–

7,5

5

tail

150

37,5

12

10

–

hob right

–

–

–

10

6

tail

250

60

13

20°

20°

20°

20°

20°

20°

20°

DIN 5480 / 5482

Modulus

Z

type

Ld. max

Øprimitief

Zmin

AP

1,25

–

hob right

–

–

–

30°

1,6

–

hob right

–

–

–

30°

1,6

6

Tail

65

9,6

13

1,9

0

hob right

–

48,8

–

1,75

10

Tail

55

17,5

18

1,75

10

Tail

60

17,5

18

2

10

Tail

98

20

18

2

–

hob right

–

78

–

1,9

1

Tail

70

20

18

1,9

11

Tail

45

20,9

19

30°

2

12

Tail

130

24

20

30°

2

15

Tail

75

30

24

2,1

20

Tail

85

42

29

2,1

0

hob right

–

53,4

0

30°

2,25

0

hob right

–

59,3

0

30°

2,25

18

Tail

95

40,2

27

2,5

–

hob right

–

80,86

0

30°

2,5

–

hob right

–

–

–

30°

2,5

12

Tail

80

30

20

3

0

hob right

–

71

0

3

15

Tail

125

45

24

3

25

Tail

0

75

35

3

12

Tail

75

36

20

3

12

Tail

150

36

20

30°

4

–

hob right

–

59,9

0

30°

4

9

Tail

120

36

17

4

25

–

0

100

35

4

14

Tail

0

56

22

5

–

hob right

0

70,85

–

30°

5

–

hob right

0

–

–

30°

5

10

Tail

100

50

18

5

12

Tail

75

60

20

5

20

–

–

100

29

6

0

hob right

–

103,4

0

6

9

Tail

120

54

17

8

6

Tail

140

48

13

8

–

hob right

–

110,4

–

30°

Zmin

AP

30°

30°

30°

30°

ANSI B92.1 – 1970, R1993

Modulus

Z

type

Ld. max

Øprimitief

32/64

–

hob right

–

60,212

32/64

12

Tail

40

9,52

30° 20

30°

32/64

90

–

–

71,44

–

30°

24/48

–

hob right

–

59,914

–

30°

24/48

10

Tail

60

10,58

18

30°

24/48

72

–

–

76,2

–

30°

20/40

–

hob right

–

60,116

–

30°

20/40

–

hob right

–

0

–

30°

20/40

9

Tail

45

11,43

17

30°

20/40

9

Tail

60

11,43

17

30°

16/32

–

hob right

–

61,4

–

30°

16/32

–

hob right

–

59

–

30°

16/32

–

hob right

–

60,216

–

30°

16/32

6

Tail

–

13

30°

16/32

9

Tail

80

14,28

17

30°

16/32

9

Tail

60

14,28

17

30°

16/32

9

Tail

80

14,28

17

30°

16/32

9

Tail

75

14,28

17

30°

16/32

15

Tail

90

17

30°

16/32

20

Tail

120

3,7

29

30°

12/24

–

hob right

–

62,2

0

30°

12/24

6

Tail

45

12,9

13

30°

12/24

9

Tail

80

19,05

17

30°

12/24

14

Tail

120

26,63

10/20

–

hob right

–

66,83

10/20

10

Tail

100

10/20

6

Tail

50

15,24

13

30°

10/20

9

Tail

108

22,86

17

30°

10/20

9

Tail

90

22,86

17

30°

8/16

–

hob right

–

69,23

0

30°

8/16

0

hob right

–

72,24

–

30°

8/16

10

Tail

120

31,75

18

30°

8/16

5

Tail

85

15,87

12

30°

8/16

10

Tail

105

31,75

18

30°

8/16

24

–

–

76,2

34

30°

8/16

7

Tail

95

22,22

14

30°

7/14

0

hob right

–

63,5

–

30°

6/12

0

hob right

–

71,43

–

30°

6/12

18

–

–

27

30°

6/12

8

Tail

120

33,86

16

30°

6/12

5

Tail

–

21,167

11

30°

6,5/13

6

Tail

60

23,45

13

30°

5/10

–

hob right

–

70,36

–

30°

5/10

5

Tail

75

25,4

12

30°

5/10

7

Tail

140

35,56

14

30°

30° –

30° 30°

5/10

20

–

–

101,6

29

30°

5/10

15

–

–

76,2

24

30°

4/8

–

hob right

–

0

–

30°

4/8

6

Tail

150

38,1

13

30°

4/8

16

–

–

101,6

25

30°

2,5/5

–

hob right

–

101,65

–

30°

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