CHAPTER

17 KEYS, PINS, COTTERS, AND JOINTS

S Y M B O L S 4,5,6

d dl 't2 't3 't4

C~mZ(Or dpm ) dnom D

F t, F tt

F~,F~

F~ F~ h

L lo, So rn

Mb M,

addendum for a flat root involute spline profile, m (in) area, m 2 (in 2) breadth of key, m (in) effective length of knuckle pin, m (in) dedendum for a flat root involute spline profile, m (in) diameter, m (in) major diameter of internal spline, m (in) minor diameter of internal spline, m (in) major diameter of external spline, m (in) minor diameter of external spline, m (in) core diameter of threaded portion of the taper rod, m (in) large diameter of taper pin, m (in) mean diameter of taper pin, m (in) nominal diameter of thread portion, m (in) diameter of shaft, m (in) pitch diameter, m (in) force, kN (lbf) force on the cotter joint, kN (lbf) pressure between hub and key, kN (lbf) force applied in the center of plane of a feather keyed shaft

which do not change the existing equilibrium but give a couple, kN (lbf)

two opposite forces applied on the center plane of a double feather keyed shaft which give two couples, but tending to rotate the hub clockwise, kN (lbf)

tangential force, kN (lbf) frictional force, kN (lbf) thickness of key, m (in) minimum height of contact in one tooth, m (in) length of key (also with suffixes), m (in) length of couple (also with suffixes), m (in) length of sleeve, m (in) length of spline, m (in) space width and tooth thickness of spline, m (in) module, mm, m (in) bending moment, N m (lbf in) twisting moment, N m (lbf in)

17.1

17.2 CHAPTER SEVENTEEN

P l

P2 Pd (or P) Q R

t

x m

z

O"

O 'b l

T

Oz

0 #

pressure, MPa (psi) tangential pressure per unit length, MPa (psi) maximum pressure where the shaft enters the hub, MPa (psi) pressure at the end of key, MPa (psi) diametral pitch external load, kN (lbf) resistance on the key and on the shaft to be overcome when the

hub is shifted lengthwise, kN (lbf) thickness of cotter, m (in) profile displacement, m (in)

number of teeth, number of splines stress tensile or compressive (also with suffixes), MPa (psi) nominal bearing stress at dangerous point, MPa (psi) shear stress, MPa (psi) angle of cotter slope, deg angle of friction, deg coefficient of friction (also with suffixes)

SUFFIXES ,.

b bearing c compressive d design m mean p pin s small end t tensile, tangential

Particular Formula

ROUND OR PIN KEYS

The large diameter of the pin key

STRENGTH OF KEYS

Rectangular fitted key (Fig. 17-1, Table 17-1)

Pressure between key and keyseat

FIGURE 17-1

d = 3.035v/-D to 3.45x/D

where d and D are in mm

d = 0.6x/D to 0 .7V~

where d and D are in in

d = 0.096x/D to 0.11 v ~

where d and D are in m

v--

SI (17-1a)

USCS (17-1b)

SI (17-1c)

t -

0~

Lo=2-25D =

..~.

t-

._

t- "0

t- t" ._

.._i

t~

"0

t~

t_

o._~

E

t-

m

m

m

t"-I t'~

c'4 ¢'4

t",4 t'q

c-4

t"-4

¢¢%

c-4 ¢

~

t"-,I t'~

t'4

t",l ~

-- w

%

~ ¢

~

t'-,i

~ t'-xl

tr'~ o

0

+ I

+ I

+~

÷

~

+~

÷

~

t.-4

it

t",

t"x ,..-

C /-

O

oc

¢,q

¢-4 "~

oc

tr~

C

c'4 C

C

C

C

C

C

C

c'4

r-,- c,,l

re) ..~

c',4

c'-,I c'4

t'--I 17.3

17.4 CHAPTER SEVENTEEN

Particular Formula

C r u s h i n g s t r e n g t h

The tangential pressure per unit length of the key at any intermediate distance L from the hub edge (Fig. 17-1, Table 17-2)

The torque transmitted by the key (Fig. 17-l)

The general expression for torque transmitted accord- ing to practical experience

For dimensions of tangential keys given here.

P = P l - L t a n a

Pl - -P2 Pl where tan a = L2 L0

M t = l p l D L 2 -- DL~ tan a

M t = ¼O'blhDL2 - l O'blbL2

where P2 = 0, when L 2 -- Lo = 2.25D;

tan a = - - Pl ffbl h

Lo 4.5D

Refer to Table 17-2.

(17-2)

(17-3)

(17-4)

S h e a r i n g s t r e n g t h

The torque transmitted by the key (Fig. 17-1)

The shear stress at the dangerous point (Fig. 17-1)

M t = 17-1 b D L 2 - 17.1 b L 2

where tan a = Pl = T l b Lo 2.25D

(17-5)

M t (17-6) "rl - L z b ( O . 5 D - 0.11L2)

T A P E R K E Y (F ig . 1 7 - 2 , T a b l e 1 7 - 3 )

The relation between the circumferential force Ft and the pressure F between the shaft and the hub

The pressure or compressive stress between the shaft and the hub

The torque

F

I-~ I " -I

FIGURE 17-2

Ft = # IF (17-7)

F = blp (17-8)

M , : ½ # , b l p D (17-9)

where ~1 ~--- coefficient of friction between the shaft and the hub

= 0.25

KEYS, PINS, COTTERS, A N D JOINTS 17.5

T A B L E 17-2

Dimensions (in mm) of tangential keys and keyways

aperl in 100

I!arallel assembled width b

A r h

/ -v,,. ax45 o

Enlarged view at A

Keyway Keyway Shaft Key Shaft diameter, D Height, h Width, b Radius, r chamfer, a diameter, D Height, h Width, b Radius, r

Key chamfer, a

100 10 30 2 3 460 46 138 4 5 110 11 30 2 3 480 48 144 5 6

120 12 36 2 3 500 50 150 5 6 130 13 39 2 3 520 52 156 5 6 140 14 42 2 3 540 54 162 5 6

150 15 45 2 3 560 56 168 5 6 160 16 48 2 3 580 58 174 5 6 170 17 51 2 3 600 60 180 6 7 180 18 54 2 3 620 62 186 6 7 190 19 57 2 3 640 64 192 6 7

200 20 60 2 3 660 66 198 6 7 210 21 63 2 3 680 68 204 6 7 220 22 66 2 4 700 70 210 6 7 230 23 69 3 4 720 72 216 6 7 240 24 72 3 4 740 74 222 6 7 250 25 75 3 4 760 76 228 6 7 260 26 78 3 4 780 78 234 6 7

270 27 81 3 4 800 80 240 6 7 280 28 84 3 4 820 82 246 6 7 290 29 87 3 4 840 84 252 6 7

300 30 90 3 4 860 86 258 6 7 320 32 95 3 4 880 88 264 8 9 340 34 102 3 4 900 90 270 8 9 360 36 108 3 4 920 92 276 8 9 380 38 114 4 5 940 94 282 8 9 400 40 129 4 5 960 96 288 8 9 420 42 126 4 5 980 98 294 8 9 440 44 132 4 5 1000 100 300 8 9

Notes: (1) The dimensions of the keys are based on the formula: width 0.3 shaft diameter, and thickness = 0.1 shaft diameter; (2) if it is not possible to fix the keys at 120 °, they may be fixed at 180°; (3) it is recommended that for an intermediate diameter of shaft, the key section shall be the same as that for the next larger size of the shaft in this table. Source: IS 2291, 1963.

T A B L E 17-3 Dimensions (in mm) of taper keys and keyways

Keyway in Hub

~ Basic taper 1 100 on this face

" I q

Key

' ' I_ ! t 1 b

~ ~ ~ K e yway in shaft

Assembly

r 1 x 45 ° rl

N Shaft Key

Up to and Width, b Above including (h9) Height, h

Chamfer or radius rl, min

Keyway width, b (DIO)

Keyway in shaft and hub

Depth in Tolerance Depth in Tolerance Radius, r2, shaft, t~ on tl hub, t 2 on t 2 max

6 8 2 2 0.16 2 8 10 3 3 3

10 12 4 4 4 12 17 5 5 5 17 22 6 6 0.25 6 22 30 8 7 8 30 38 10 8 10 38 44 12 8 12 44 50 14 9 0.40 14 50 58 16 10 16 58 65 18 11 18 65 75 20 12 20 75 85 22 14 0.60 22 85 95 25 14 25 95 110 28 18 28

110 130 32 10 32 130 150 36 25 36 150 170 40 22 1.00 40 170 200 45 25 45 200 230 50 28 50 230 260 56 32 56 260 290 63 32 1.60 63 290 330 70 36 70 330 380 80 40 80 380 440 90 45 2.50 90 440 500 100 50 100

1.2 +0.05 0.5 0.16 1.8 0.9 2.5 1.2 3.0 1.7 +0.1 0.25 3.5 2.1 4.0 +0.10 2.5 5.0 2.5 5.0 2.5 5.5 2.9 0.40 6.0 3.4 7.0 3.3 7.5 3.8 8.5 4.8 9.0 4.3 +0.2 0.60

10.0 5.3 11.0 6.2 12.0 7.2 13.0 +0.15 8.2 1.00 15.0 9.2 17.0 10.1 19.0 12.1 20.0 11.1 1.60 22.0 13.1 +0.3 25.0 14.1 28.0 16,1 2.50 31.0 18.1

Source: IS 2292, 1963.

17 .6

KEYS, PINS, COTTERS, AND JOINTS 17.7

Particular Formula

The necessary length of the key

The axial force necessary to drive the key home (Fig. 17-2)

The axial force is also given by the equation

1 = 2Mt #lbpD (1%10)

Fa = Fu + F/~ = 2#2F + F t a n f l (17-11)

where ~2 = 0.10, tan ~ -- 0.0104 if the taper is 1 in 100

Fa =0.21pbl (17-12)

FRICTION OF FEATHER KEYS (Fig. 17-3)

The circumferential force (Fig. 17-3)

The resistance to be overcome when a hub connected to a shaft by a feather, Fig. 17-3a and subjected to torque Mr, is moved along the shaft

The equation for resistance R, if # and #2 are equal

The equation for torque if two feather keys are used, Fig. 17-3b

The force F2 applied at key when two feather keys are used, Fig. 17-3b

The resistance to be overcome when the hub con- nected to the shaft by two feather keys Fig. 17-3b and subjected to torque Mt is moved along the shaft

For Gib-headed and Woodruff keys and keyways

m t Ft = ~ (17-13) a

R = #Ft + #2F' (17-14)

= (# + #2)Ft (17-15)

and F ' = F " = Ft = force assumed to be acting at the shaft axis without changing the equilibrium Fig. 17-3a

R = 2#Ft (17-16)

Mt = 2F2a (17-17)

Mt Ft F2 = ~-a +-~ - (17-18)

R R2 -- 2#F2 -- ~- (17-19)

Refer to Tables 17-4 and 17-5.

!

F2 a

(a) ' (b)

FIGURE 17-3 Feather key.

E

'-'~

m

~ ~

c

,.,-~

0

F-

o...~ r~

.,..,

X

o ,,i,i,

'° .,,,i

x

,if

i _=I

~I

x ~

~ I

. l..c

~ L

~

~

==

i

i

1,1

u

o

1.1

u oii=

,i

~i~ -~

o_. i

ii

°if

°~

+

+

+

÷ }

+

+

+

+

,=-~ ~

,-~ ,.--~ C',I C',I C'.I C',I c

~

c~

• ,~

e-

o

0

• |

I~

om

"~ ~

~xSx.~///F

. ,/.//,, ~

r~

d g

,gg

..=

ol

Z

o~

0~

o~

-- ¢'!.

" ¢'!.

+ +

+ +

"e,i "¢

q~

cq~

~/~

6~

6r-:~

r-:~q

r-:~K

"o<

"~

/

"¢q " ¢q t'-,i M

d tr:, ¢H

tr:, ~ ~

~ r-: tH

,,6 t--: d ~

d d

t--: d M

,"-~ ,--"~ --~

,--'~

,---~ ,--* ,---~

¢'q ,.-~

¢'-1 ¢'q

¢',1 ¢'-1

t'q

¢r~ eq

ee~

~-

+ +

~,~

o

o

~ ~

t'q

¢'-1 eq

~

t'-. r--

t~

¢--1 ¢-,I

¢-q ~

~ ~

~ o

o

oo

o

o

oo

o

o

oo

..

..

..

.

~~

N

~

~

O

o2

o2

rz. ee~

X

eq

o2 N

o2

o2

e~

X

t"4

~k0 .~

o2

o2

+ i 17

.9

17.10 CHAPTER SEVENTEEN

Particular Formula

S P L I N E S

Parallel-sided or straight-sided spline T h e t o r q u e w h i c h an i n t eg ra l mu l t i sp l i n e sha f t c a n

t r a n s m i t (T ab l e s 17-6 to 17-12)

M t - - ½ P h l i ( D - h ) (17-20)

T A B L E 17-6 P r o p o r t i o n s of S A E standard para l le l side spl ines

Types of spline fittings Symbols Proportions

Bearing pressure, p

Fit MPa kpsi

I D m

!

~,~ " D m

w = 0.241D

4A, h = 0.075D 4B, h = 0.125D

w = 0.250D 6A, h = 0.050D

6B, h = 0.075D 6C, h = 0.100D

w = 0.156D 10A, h = 0.045D 10B, h -- 0.070D

10C, h = 0.095D

w = 0.098D 16A, h = 0.045D 16B, h = 0.070D 16C, h -- 0.095D

20.6 13.7

20.6 13.7 6.9

20.6 13.7

6.9

20.6 13.7 6.9

3.00 2.00

3.00 2.00 1.00

3.00 2.00 1.00

3.00 2.00

1.00

KEYS, PINS, C O T T E R S , A N D J O I N T S 17.11

T A B L E 17-7

Proportions of involute spline profile (American Standard)

Internal Spline .{ • External Spline

Side of Major d iameter ~ / p / / ~ , ~ fillet radius I tooth Major diameter

p chamfer dimen. Major diameter fillet height

Minor diameter chamfer height

Major diam t e te r / ~ ~ _ _ _ . Minor diameter " ~ " M~nor Piitc! Minor chamfer angle

diameter diameter mIF ~ /ete diameter TIF

diameter

Major diameter chamfer height

Minor diameter fillet radius

Minor diameter fillet height

Spline characteristics Symbols P = ½ through lZ

Proportions

P = ~ through 48

Z Pitch diameter D D = zm = - P

Circular pitch p p = (TriP)

~-m 7r Too t h thickness t t - - - - 2 2P

Diametra l pitch P P = (Trip)

A d d e n d u m a a = 0.5m 0.500 P

D e d e n d u m (internal) b 1 b 1 = 0.90m 0.900 P

D e d e n d u m b b - 0.5m = 0.500 P

D e d e n d u m (external) bl bl - 0.9m = 0 . 9 0 0 / P

Ma jo r diameter (internal) Doi Doi = (z + 1.8)m

= (z + 1 .8 ) /P

Mino r diameter (external) Dme Dme = ( z - 1.8)m

- ( z - 1 .8 ) /P

D = zm = z i P

p : (~/P)

t = (Trm/2) = (Tr/2P)

p - (~/p)

a - 0.5m = 0 . 5 0 0 / P

b~ = 0.9m = 0 .900 /P

b = 0.5m = 0 . 5 0 0 / P

bl = 1 . 0 m - 1 .000/P

Doi = (z Jr- 1.8)m = (z + 1 .8 ) /P

Dine -- ( z - 2.0)m = ( z - 2 . 0 ) / P

Source: Courtesy H. L. Horton, ed., Machinery's Handbook, 15th ed., The Industrial Press, New York, 1957.

T A B L E 17-8

Straight sided splines (all dimensions in mm)

B

Splined shaft and hub profile

. . , , , , . - g x 4 5 °

f e

Splined shaft Splined hub

Minor Nominal size No. of diameter, i × d x D splines, i d

Major diameter, Width, dl ,a e,a g, k, r, D B min max f a max mix max

Centering on

6 × 23 × 26 6 23 26

6 × 26 × 30 6 26 30

6 × 28 x 32 6 28 32

8 x 32 x 36 8 32 36

8 x 36 x 40 8 36 40

8 x 42 x 46 8 42 46

8 × 46 x 50 8 46 50

8 x 52 × 58 8 52 58

8 x 56 × 62 8 56 62

8 x 62 x 68 8 62 68

10 x 72 x 78 10 72 78

10 x 82 x 88 10 82 88

10 x 92 x 98 10 92 98

10 x 102 x 108 10 102 108

l O x 112x 120 10 112 120

6 x 11 x 14 6 11 14

6 x 13 × 16 6 13 16

6 x 16 x 20 6 16 20

6 x 18 x 22 6 18 22

6 x 21 x 25 6 21 25

6 x 23 x 28 6 23 28

6 × 26 x 32 6 26 32

6 x 28 x 34 6 28 34

8 x 32 x 38 8 32 38

8 x 36 x 42 8 36 42

8 × 42 x 48 8 42 48

8 x 46 x 54 8 46 54

8 x 52 x 60 8 52 60

8 x 56 × 65 8 56 65

8 x 62 x 72 8 62 72

10 x 72 × 82 10 72 82

10 x 82 × 92 10 82 92

10 × 92 × 102 10 92 102

10× 102× 112 10 102 112

10 × 112 × 125 10 112 125

Light-Duty Series

6 22.1 1.25 3.54 0.3 0.3 0.2

6 24.6 1.84 3.85 0.3 0.3 0.2

7 26.7 1.77 4.03 0.3 0.3 0.2

6 30.4 1.89 2.71 0.4 0.4 0.3

7 34.5 1.78 3.46 0.4 0.4 0.3 q

8 40.4 1.68 5.03 0.4 0.4 0.3

9 44.6 1.61 5.75 0.4 0.4 0.3

10 49.7 2.72 4.89 0.5 0.5 0.5

10 53.6 2.76 6.38 0.5 0.5 0.5

12 59.8 2.48 7.31 0.5 0.5 0.5

12 69.6 2.54 5.45 0.5 0.5 0.5

12 79.3 2.67 8.62 0.5 0.5 0.5

14 89.4 2.36 10.08 0.5 0.5 0.5

16 99.9 2.23 11.49 0.5 0.5 0.5

18 108.8 3.23 10.72 0.5 0.5 0.5

Medium-Duty Series

3 9.9 1.55 0.3 0.3 0.2

3.5 12.0 1.50 0.32 0.3 0.3 0.2

4 14.5 2.10 0.16 0.3 0.3 0.2

5 16.7 1.95 0.45 0.3 0.3 0.2

5 19.5 1.98 1.95 0.3 0.3 0.2

6 21.3 2.30 1.34 0.3 0.3 0.2

6 23.4 2.94 1.65 0.4 0.4 0.3

7 25.9 2.94 1.70 0.4 0.4 0.3

6 29.4 3.30 0.15 0.4 0.4 0.3

7 33.5 3.01 1.02 0.4 0.4 0.3

8 39.5 2.91 2.54 0.4 0.4 0.3

9 42.7 4.10 0.86 0.5 0.5 0.3

10 48.7 4.00 2.44 0.5 0.5 0.5

10 52.2 4.74 2.50 0.5 0.5 0.5

12 57.8 5.00 2.40 0.5 0.5 0.5

12 67.4 5.43 2.70 0.5 0.5 0.5

12 77.1 5.40 3.00 0.5 0.5 0.5

14 87.3 5.20 4.50 0.5 0.5 0.5

16 97.7 4.90 6.30 0.5 0.5 0.5

18 106.3 6.40 4.40 0.5 0.5 0.5

Inside

diameter a

Inside

diameter or flanks b

Inside

diameter a

Inside

diameter or flanks b

a These values are based on the generating process. Source: IS 2327, 1963.

b Inside centering is not always possible with generating processes.

1 7 . 1 2

KEYS, PINS, COTTERS, AND JOINTS 17.13

T A B L E 17-9 Tolerances for straight-sided splines (all dimensions in mm)

Assembly of splined hub and shaft

/

Width of hub B

Soft or hardened

Tolerance on

Minor Major diameter of diameter of hub, d hub, D

Soft or Soft or hardened hardened

Splined hub

Splined shaft

For centering on inner diameter or flanks

For centering on inner diameter

For centering on flanks

Shaft sliding or fixed D9

Shaft sliding inside hub h8

Shaft fixed in hub p6 Shaft sliding inside hub h8 Shaft fixed in hub u6

F10 H7 H l l

e8 f7 a 11

h6 e8 k6

j6 a l l a l l a l l

Particular Formula

Involute-sided spline

A M E R I C A N S T A N D A R D (Table 17-7) The adden- dum a and dedendum b for a fiat root, Table 17-7

The area resisting shear, Table 17-7

The minimum height of contact on one tooth

The corresponding area of contact of all z teeth

The torque capacity of teeth in shear

The torque capacity of the spline in bearing with O'b = 2Cr ac

1 a = b = m = -

P

7rDL A~_= 2

0.8 0.8D h = 0.8m . . . .

P z

A = (0"8D) z L = O ' 8 D L ~ z

M t = ( T r D L ) D z -~- ~-d -- 0.7854DZL~-d

Mtb : 0.8D2 LO-dc

(17-21)

(17-22)

(17-23)

(17-24)

(17-25)

(17-26)

17.14 CHAPTER SEVENTEEN

T A B L E 17-10

Straight-sided splines for machine tools (all dimensions in mm)

B

External spline profile Internal spline profile

B B

D

External spline profile Internal spline profile

Type B Type M Internal spline (External splines)

(a) Straight sided splines - 4 splines

4 Splines

Nominal size, Minor Major i a × d x D diameter, d diameter, D Width, B

4 x 11 x 15 11 15 3

4 x 13 x 17 13 17 4

4 x 16 x 20 16 20 6

4 x 18 x 22 18 22 6

4 x 21 x 25 21 25 8

4 x 24 x 28 24 28 8

4 x 28 x 32 28 32 10

4 x 32 x 38 32 38 10

4 x 36 x 42 36 42 12

4 x 42 x 48 42 48 12

4 x 46 x 52 46 52 14

4 x 52 x 60 52 60 14

4 x 5 8 x 6 5 58 65 16

4 x 62 x 70 62 70 16

4 x 6 8 x 7 8 68 78 16

i = number of splines Source: IS 2610, 1964.

Type A Type B Type M Internal spline (External splines)

(b) Straight sided splines - 6 splines

6 Splines

Nominal size, Minor Major i a x d x D diameter, d diameter, D Width, B

6 x 21 x 25 21 25 5

6 x 23 x 28 23 28 6

6 x 26 x 32 26 32 6

6 x 28 x 34 28 34 7

6 x 32 x 38 32 38 8

6 x 36 x 42 36 42 8

6 x 42 x 48 42 48 10

6 x 4 6 x 5 2 46 52 12

6 x 52 x 60 52 60 14

6 x 58 x 65 58 65 14

6 x 62 x 70 62 70 16

6 x 68 x 78 68 78 16

6 x 72 x 82 72 82 16

6 x 78 x 90 78 90 16

6 x 82 x 95 82 95 16

6 x 88 x 100 88 100 16

6 x 9 2 x 105 92 105 20

6 x 9 8 x 110 98 110 20

6 x 1 0 5 x 120 105 120 20

6 x 115 x 130 115 130 20

6 x 130 x 145 130 145 24

T A B L E 17-11 Undercuts, chamfers, and radii for straight-sided splines a (all dimensions in mm)

External splines

Type A Type B Type M Designation, i x d x D B all, min g, max f , min h rl, max m n r 2

Internal splines Projected tip width

k, max r3, max of hub

4 × 11 x 15 3 9.6 0.2 1.50 5.0 0.10 2.82 1.70 0.3

4 x 13 x 17 4 11.8 0.2 2.37 5.5 0.10 3.76 1.70 0.3

4 x 16 × 20 6 15.0 0.3 2.87 6.7 0.15 5.64 1.70 0.3

4 x 18 × 22 6 16.9 0.3 4.35 7.7 0.15 5.64 1.70 0.3

4 x 21 × 25 8 20.1 0.3 5.00 8.9 0.15 7.52 1.70 0.6

4 x 24 × 28 8 23.0 0.3 7.30 10.4 0.15 7.52 1.70 0.6

4 × 28 × 32 10 26.8 0.5 7.39 12.1 0.25 9.40 1.63 0.6

4 x 32 × 38 10 30.3 0.5 9.56 14.2 0.25 9.40 2.55 0.6

4 x 36 x 42 12 34.5 0.5 11.03 15.9 0.25 11.28 2.55 0.6

4 x 42 x 48 12 40.2 0.5 15.41 19.0 0.25 11.28 2.55 1.0

4 x 46 x 52 14 44.4 0.5 16.79 20.7 0.25 13.16 2.55 1.0

4 × 52 × 60 14 49.5 0.5 21.63 23.7 0.25 13.16 3.40 1.0

4 x 56 x 65 16 56.2 0.5 23.26 26.4 0.25 15.04 2.98 1.0

4 × 62 x 70 16 59.5 0.5 23.61 28.3 0.25 15.04 3.40 1.0

4 x 68 x 78 16 64.4 0.5 27.57 31.2 0.25 15.04 4.25 1.0

0.2 0.15 0.5

0.2 0.15 0.5

0.3 0.25 0.7

0.3 0.25 0.7

0.3 0.25 0.7

0.3 0.25 0.7

0.5 0.40 1.0

0.5 0.40 1.0

0.5 0.40 1.0 O.5 0.4O 1.0

0.5 0.40 1.3

0.5 0.40 1.3

0.5 0.40 1.6

0.5 0.40 1.6

0.5 0.40 1.6

a Four splines; see Fig. 17-4a. Source: IS 2610, 1964

T A B L E 17-12 Undercuts, chamfers, and radii for straight-sided splines a (all dimensions in mm)

External splines

Type A Type B Type M Designation, i x d × D B dl, min g, max f , min h rl, max m n r 2

Internal splines Projected tip width

k, max r3, max of hub

6 x 21 x 25 5 19.50 0.3 1.95 9.7 0.15 4.70 1.70 0.6

6 x 23 x 28 6 21.30 0.3 1.34 11.0 0.15 5.64 2.13 0.6

6 x 26 × 32 6 23.40 0.4 1.65 11.8 0.15 5.64 2.55 0.6

6 x 28 × 34 7 25.90 0.4 1.70 12.9 0.25 6.58 2.55 0.6

6 x 32 x 38 8 29.90 0.5 2.83 14.8 0.25 7.52 2.55 0.6 6 x 36 x 42 8 33.70 0.5 4.95 16.5 0.25 7.52 2.55 0.6

6 × 42 × 48 10 39.94 0.5 6.02 19.3 0.25 9.40 2.55 1.0

6 x 46 x 52 12 44.16 0.5 5.81 21.1 0.25 11.28 2.55 1.0

6 × 52 × 60 14 49.50 0.5 5.89 23.9 0.25 13.16 3.40 1.0

6 × 58 x 65 14 55.74 0.5 8.29 26.7 0.25 13.16 3.98 1.0 6 x 62 x 70 16 59.50 0.5 8.03 28.6 0.25 15.04 3.40 1.0

6 x 68 x 78 16 64.40 0.5 9.73 31.4 0.25 15.04 4.25 1.0

6 x 72 x 82 16 68.30 0.5 12.67 33.4 0.25 15.04 4.25 1.6

6 x 78 x 90 16 73.00 0.5 13.07 36.2 0.25 15.04 5.10 1.6

6 z 82 × 95 16 79.60 0.5 13.96 38.0 0.25 15.04 5.53 1.6

6 x 88 × 100 16 82.90 0.5 17.84 41.3 0.25 15.04 5.10 1.6

6 x 92 x 105 20 87.10 0.6 18.96 43.1 0.30 18.80 5.53 1.6

6 x 98 x 110 20 93.40 0.6 19.22 46.4 0.30 18.80 5.10 2.0

6 x 105 x 120 20 98.80 0.6 19.25 49.2 0.30 18.80 6.38 2.0

6 z 115 x 130 20 108.4 0.6 24.75 54.2 0.30 18.80 6.38 2.5

6 x 130 x 145 24 123.9 0.6 29.20 61.8 0.30 22.56 6.38 2.5

a Six splines see Fig. 17-4b.

0.3 0.2 0.7

0.3 0.2 0.7

0.4 0.3 1.0

0.4 0.3 1.0

0.5 0.4 1.0

0.5 0.4 1.0

0.5 0.4 1.0

0.5 0.4 1.3

0.5 0.4 1.3

0.5 0.4 1.6 0.5 0.4 1.6

0.5 0.4 1.6

0.5 0.4 2.0

0.5 0.4 2.0

0.5 0.4 2.0

0.5 0.4 2.0 0.6 0.5 2.0

0.6 0.5 2.0

0.6 0.5 2.4

0.6 0.5 2.4

0.6 0.5 2.4

1 7 . 1 5

17.16 CHAPTER SEVENTEEN

Particular Formula

The theoretical torque capacity of straight-sided spline with sliding according to SAE

Equating the strength of the spline teeth in shear to the shear strength of shaft, the length of spline for a hollow shaft

The length of spline for a solid shaft

The effective length of spline for a hollow shaft used in practice according to the SAE

For diametrical pitches used in involute splines (SAE and ANSI)

TABLE 17-13 Diametral pitches a used in involute splines (SAE and ANSI)

6.895 x 106i (D + d ) h z SI ( 1 7 - 2 6 a ) M t \ 4 /

where

i = number of splines D, d = diameter as shown in Table 17-7, m

d = inside diameter of spline, m D = pitch diameter of spline, m L -- length of spline contact, m h = minimum height of contact in one tooth of

spline, m Mt i n N m

Mt = lOOoi(D + d ) USCS (17-26b)

where M t in lb in; d, D, L, and h in in 4 4 D 3 e ( 1 - D i / D m e )

L = 4D 2

where

Di = internal diameter of a hollow shaft, m (in) Dme - -minor diameter (external), m (in)

D3e L =

4D 2

4 4 D3me(1 - D i ~Dine)

L e = D2

(17-26c)

(17-26d)

(17-26e)

For solid shaft D i -- O.

Refer to Table 17-13.

2.5 3 4 5 6 8 10 5 6 8 10 12 16 20

12 16 20 24 32 40 48 24 32 40 48 64 80 96

a Diametral pitches are designated as fractions; the numera tor of these fractions is the diametral pitch, P.

INDIAN STANDARD (Figs. 17-4 and 17-5, Tables 17-14 and 17-15)

The value of profile displacement (Fig. 17-4) xm = ½ (dl - m z - 1.1m)

The value xm varies from -0.05m to +0.45m

(17-27)

KEYS, PINS, COTTERS, AND JOINTS 17.17

Particular Formula

The number of teeth

The minor diameter of the internal spline (Fig. 17-4a)

The major diameter of the external spline (Fig. 17-4a)

The minor diameter of the external spline (Fig. 17-4a)

1 z = - - ( d l - 2 x m - 1.1m)

m

d2 = m z + 2 x m - 0 . 9 m = d l - 2m

d3 = m z + 2 x m + 0.9m = d l - 0.2m

d4 - m x + 2 x m - 1. l m = dl - 2.2m

(17-28)

(17-29)

(17-30)

(17-31)

. f x m = o a ~ , , _ _ / / / / / / v Y - . g 6. o

f ~ / / / / / f / ' / / / / / / / / / • ' INTERNAL SPLINE ~ I " ~ t DATUM LINE~ m l 0-55m 0.45 T

0-45m "'~-Tm - O~5m

d2 '°"emi [" Ll'o='o--'16' m oTJ,

FIGURE 17-4(a) Reference profile of an involute-sided spline. (Source: IS 3665, 1966.)

Internal

Major dia. ~ ~- Base circle

-'4 External r

~ ,~ a ' ~ . ~ chamfered

D

FIGURE 17-4(b) Nomenclature of the involute spline profile.

I 0 ; / " ~ .

o .

FOR EVEN • ~ , ~ - / / / / , v - I / " 7 " " / 4 , ¢ I NUMBER

• Mi I ~ S 0.~ MoOF TEETH) (FOR ODD( FOR EVEN (FOR ODD~ NUMBER NUMBER NUMBER"

OF T~ETH) OF l~EETH) OF TEETH)t

Internal spline External spline

FIGURE 17-5 Measurement between pins and measurement over pins of an involute-sided spline. (Source: IS 3665, 1966.)

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17.19

17.20 CHAPTER SEVENTEEN

Particular Formula

The value of tooth thickness and space width of spline lo = So = m ~ + 2 x m tan a (17-32)

P I N S

Taper pins

The diameter at small end (Figs. 17-6 and 17-7, Tables 17-16 and 17-17)

dps = dp, - 0.0208• (17-33)

The mean diameter of pin dm = 0.20D to 0.25D (17-34)

t dpm ~ . x ~ . . . .

. ,_

FIGURE 17-6 Tapered pin. FIGURE 17-7 Sleeve and tapered pin joint for hollow shafts.

Sleeve and taper pin joint (Fig. 17-7)

AXIAL LOAD The axial stress induced in the hollow shaft (Fig. 17-7) due to tensile force F

The bearing stress in the pin due to bearing against the shaft an account of force F

The bearing stress in the pin due to bearing against the sleeve

The shear stress in pin

The shearing stress due to double shear at the end of hollow shaft

The shear stress due to double shear at the sleeve end

F (17-35) o"

~(a~ - d ~ ) - 2 ( a 2 - d , ) d m 4

F a,. = 2(d2 - d l )din 17-36)

F ac =2'--ta3 - d 2 ) d m (17-35)

2F ~- = 7rd2 (17-38)

F ~ = 2(d2 - dl)12 (17-39)

F ~- = 2(d3 - d2)ll (17-40)

= =

_

o

LO

I |

J A

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'

A

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17.21

17.22 CHAPTER SEVENTEEN

Particular Formula

The axial stress in the sleeve

TORQUE The shear due to twisting moment applied

For the design of hollow shaft subjected to torsion

(7" -- 7r (d 2 _ d2 ) _ 2(d3 - dz)dm 4

m t

7r 2 dmd2

Refer to Chapter 14.

(17-41)

(17-42)

Taper joint and nut

The tensile stress in the threaded portion of the rod (Fig. 17-8) without taking into consideration stress concentration

[1 m

1 I ~ I ~ l

FIGURE 17-8 Tapered joint and nut.

The bearing resistance offered by the collar

The diameter of the taper d2

Provide a taper of 1 in 50 for the length ( l - ll)

F O't =71" 2

~ a c

F

4

d2 > dnom

(17-43)

(17-44)

(17-45)

Knuckle joint

The tensile stress in the rod (Fig. 17-9)

The tensile stress in the net area of the eye

Stress in the eye due to tear of

4F at - 7rd2

F

~' = (d4 - d2)b

F

~" =b(d4 -d2 )

(17-46)

(17-47)

(17-48)

KEYS, PINS, COTTERS, AND JOINTS 17.23

Particular Formula

-g d '

(a)

FIGURE 17-9 Knuckle joint for round rods.

_L F

t T ~-b-~ (b)

B =

Tensile stress in the net area of the fork ends

Stress in the fork ends due to tear of

Compressive stress in the eye due to bearing pressure of the pin

Compressive stress in the fork due to the bearing pressure of the pin

Shear stress in the knuckle pin

The maximum bending moment, Fig. 17-9 (panel b)

The maximum bending stress in the pin, based on the assumption that the pin is supported and loaded as shown in Fig. 17-9b and that the maximum bending moment Mb occurs at the center of the pin

The maximum bending moment on the pin based on the assumption that the pin supported and loaded as shown in Fig. 17-10b, which occurs at the center of the pin

The maximum bending stress in the pin based on the assumption that the pin is supported and loaded shown in Fig. 17-10b

F O'i = 2a(d4 - d2)

F O'tr = 2a( d4 - d2 )

F O'e "-- d2b

F ac = 2~/2a

2F , '/- - - - m

Fb g b = ~ 8

4Fb O ' b 7 1 . d 3

F ( b a ) (approx.)

4(3b + 4a)F O - b - - 37rd 3

(17-49)

(17-50)

(17-51)

(17-52)

(17-53)

(17-54)

(17-55)

(17-56)

(17-57)

17.24 CHAPTER SEVENTEEN

Particular Formula

COTTER

The initial force set up by the wedge action

The force at the point of contact between cotter and the member perpendicular to the force F

The thickness of cotter

The width of the cotter

F = 1.25Q

H = F t an(a + 0)

t = 0 . 4 D

b = 4t = 1.6D

(1%58)

(1%59)

(17-60)

(1%61)

Cotter joint

The axial stress in the rods (Fig. 17-10)

Axial stress across the slot of the rod

Tensile stress across the slot of the socket

The strength of the cotter in shear

Shear stress, due to the double shear, at the rod end

Shear stress induced at the socket end

The bearing stress in collar

Crushing strength of the cotter or rod

O" =

(7 =

O" -~-

4F

7rd 2

4F

7rd~ - 4dl t

4F

~-(~ - d~) - 4t(d3 - d, )

F = 2brr

F

2adl

F T ~ -

2 c ( d 4 - d l )

4F

~" :~(d~ -d, ~)

F = dl tG,

(17-62)

(17-63)

(17-64)

(17-65)

(17-66)

(17-67)

(17-68)

(17-69)

. . . .

(a)

FIGURE 17-10 Cotter joint for round rods.

L

KEYS, PINS, COTTERS, AND JOINTS 17.25

Particular Formula

Crushing stress induced in the socket or cotter

The equation for the crushing resistance of the collar

Shear stress induced in the collar

Shear stress induced in the socket

The maximum bending stress induced in the cotter assuming that the bearing load on the collar in the rod end is uniformly distributed while the socket end is uniformly varying over the length as shown in Fig. 17-10b

F

°c = (d4 - dl)t

F = 7r(d2 - d12)

4

F T ~

7rdl e

F T =

7rd] h

F(d, + 2d4) a b = 4tb 2

(17-70)

o% (17-71)

(1%72)

(17-73)

(17-74)

Gib and cotter joint (Fig. 17-11) The width b of both the Gib and Cotter is the same as far as a cotter is used by itself for the same purpose (Fig. 17-11). The design procedure is the same as done in cotter joint Fig. 17-10.

- T

L_)

FIGURE 17-11 Gib and cotter joint for round rods.

~ --a I ~ ~:7~i

t .. m ,\ , \ ,\ , \ , \ , \ , \ , \ , \ ~ ~i ~ ~ i v!/!/~., t

t " FIGURE 17-12 Coupler or turn buckle.

Threaded joint

COUPLER OR TURN BUCKLE Strength of the rods based on core diameter de, (Fig. 17-12)

The resistance of screwed portion of the coupler at each end against shearing

From practical considerations the length a is given by

The strength of the outside diameter of the coupler at the nut portion

7r F = ~ d2o-t

F~= ~ a d T

a = d to 1.25d for steel nuts

a = 1.5d to 2d for cast iron

7r ( d 2 _ d2)crt F = - ~

(17-75)

(17-76)

(17-77a)

(17-77b)

(17-78)

17.26 CHAPTER SEVENTEEN

Particular Formula

The outside diameter of the turn buckle or coupler at the middle is given by the equation

The total length of the coupler

71" F = -~ (d~ - dZ)at (17-79)

l = 6d (17-80)

REFERENCES

1. Maleev, V. L., and J. B. Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954.

2. Shigley, J. E., and L. D. Mitchell, Mechanical Engineering Design, McGraw-Hill Book Company, New York, 1983.

3. Faires, V. M., Design of Machine Elements, The Macmillan Company, New York, 1965. 4. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Cooperative

Society, Bangalore, India, 1962. 5. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I (SI and Customary Metric

Units), Suma Publishers, Bangalore, India, 1986. 6. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI and Customary Metric Units), Suma Publishers,

Bangalore, India, 1986. 7. Juvinall, R. C., Fundamentals of Machine Component Design, John Wiley and Sons, New York, 1983. 8. Deutschman, A. D., W. J. Michels, and C. E. Wilson, Machine Design--Theory and Practice, Macmillan

Publishing Company, New York, 1975. 9. Bureau of Indian Standards.

10. SAE Handbook, 1981.