KEY & SPLINES DESIGN
Prof. Dr. Mohamed Omar Mousa El-Minia University
Prod. & Mech. Design Dept.
Prof. Dr. Mohamed Omar Mousa February 2006
1. TYPES OF KEYS
- Key is a piece of mild steel inserted between two mechanical elements (usually shaft and hub) to connect them together and transmit power from one of them to the other.
- The power should be transmitted without any loss.
-It is inserted parallel to the axis of the shaft in a groove or slot which called “keyway”.
Design10- shaft example of a gear animation
L
Hub-Key-Shaft Connection PRINCIPLE OF WORK
Keyway Key W
h Key
Hub
Key
Prof. Dr. Mohamed Omar Mousa February 2006
- Sunk keys.
- Saddle keys.
- Tangent keys.
- Round keys.
- Splines.
- Keys can be classified into the following main groups:
2. SUNK KEYS
The sunk keys are provided half in the keyway of
the shaft and the other half in the keyway of the
hub. The sunk keys have the following types:
2.1 RECTANGULAR SUNK KEY W
t L
W = Width of key
t = Thickness of key.
4
W d W
3 t 2
Where: “d” is the diameter of the shaft.
If the sunk key is tapered, therefore, the tapered top side has an inclination of 1:100.
1:100
Prof. Dr. Mohamed Omar Mousa February 2006
2.2 SQUARE SUNK KEY
The main difference between rectangular and square sunk keys is that the width (W) of the square key is equal to its thickness (t).
i.e.; W = t
2.3 PARALLEL SUNK KEY
The parallel sunk key can be either rectangular or
square cross sectional sunk keys with a uniform
width and thickness i.e. the parallel sunk key is a
taper-less top side sunk key with a square or
rectangular cross section. The parallel sunk keys
are important for connecting the movable pulley,
gear or hubs with there carrying shafts.
2.4 GIB-HEAD KEY
It is a rectangular sunk key with a head at one end known as gib-head. This type has the advantage that it is more easily to removal than the other above mentioned types.
TAPER 1:100
Gib-head sunk key.
Hub
Shaft
1.75 t t
45
0Prof. Dr. Mohamed Omar Mousa February 2006
The usual proportions of the Gib-head key are:
TAPER 1:100
Hub
Shaft
1.75 t t
45
04 W d
W
6 W d
3
t 2
2.5 FEATHER KEY
It is a key, which is attached to one member of the pair and allows the other to be movable along it. The feather key can be screwed to the shaft as in figure.
Feather key.
Screw Hub
Movement Direction
The proportions of the feather key are the same as that of the parallel rectangular or parallel gib-head keys.
The following table shows the standard dimensions of parallel, tapered and gib-head keys.
Prof. Dr. Mohamed Omar Mousa February 2006
Design14- Keyway cutting in a pully
Key cross sec.
Shaft diameter up to (mm)
Key cross sec.
Shaft diameter up
to (mm) W(mm) t (mm) W (mm) t (mm)
14 25
85 2
2 6
16 28
95 3
3 8
18 32
110 4
10 4
20 36
130 5
5 12
22 40
150 6
6 17
25 45
170 7
8 22
28 50
200 8
30 10
32 56
230 8
38 1 2
32 63
260 9
14 44
36 70
290 10
1 6 50
40 80
330 1 1
1 8 58
45 90
380 12
65 20
50 100
440 14
22 75
Table 1: Key dimensions according to IS 2292 and 2293-1963.
2.6 WOODRUFF KEY
-It is a piece from a cylindrical disc having segmental cross section.
-It is an easily adjustable key.
Woodruff key.
Prof. Dr. Mohamed Omar Mousa February 2006
Design15- Keyway cutting A Woodruff
-The woodruff key is capable of tilting in a recess milled out in the shaft by a cutter having the same curvature as the disc form which the key is made (form milling cutter).
-This type is usually used in machine tool and
automobile constructions.
ADVANTAGES WOODRUFF KEY
1 2 3 4
1- Easy in assembly and disassembly
2- Its extra depth in the shaft prevents any tendency to turn over in its keyway.
Prof. Dr. Mohamed Omar Mousa February 2006
3. SADDLE KEYS
Saddle key.
12 d 3
t W
4. ROUND AND DOWEL PINS
- The round keys and dowel pins are circular elements and fit into holes drilled partly in two contact parts.
Dowel pins.
Prof. Dr. Mohamed Omar Mousa February 2006
- Tapered pins are held in place by friction between pin and reamed tapered holes.
- Round keys are usually considered to be most appropriate for low power drives.
Dowel and Taper pins
5. SPLINES
-Spline shafts are shafts with integrated number of keys (more than 2 keys), which fit in the keyways, which are broached in the hub.
D = 1.25 d b = 0.25 D
D d
b
- Usually, the shaft has 4, 6, 10 or 16 splines.
Prof. Dr. Mohamed Omar Mousa February 2006
-Splined shafts are stronger than the shafts with one key. Therefore, the spline shafts are used when the power to be transmitted is large in proportional to the size of the shaft as in automobile transmission and sliding gear transmission.
-Also, axial movements of hubs with respect to
shaft can be achieved by spline shafts.
IMPORTANT NOTICES
1- Number of keys can be:
1 – 2/180 0 – 4 or more.
Prof. Dr. Mohamed Omar Mousa February 2006
2- Width and height of key are assumed as a
function of shaft diameter where the key length
is determined from strength equations.
D = 1.25 d b = 0.25 D
D d
b
d
D
b
6. TORQUE TRANSMISSION BY KEYS According to stress
analysis, keys can be classified into four main groups. These included:
M
tF
F b
h/2 h
Rectangular sides keys.
F = M t / R
R 1. Rectangular fitted key
in which the torque is transmitted by means of compressive and shear stresses as shown in Figure.
Prof. Dr. Mohamed Omar Mousa February 2006
2. Tangential keys, in which the torque is transmitted by means of compressive stress alone as shown in Figure.
Tangential keys.
M
tF
h R
F = M t / R
3. Tapered keys, in which the torque is transmitted by means of friction induced by compressive stress as in Figure.
Transmission of torque due to frictional forces generated by taper sides keys.
Transmission of torque due to frictional forces generated by taper sides keys.
M
tF R
p
Prof. Dr. Mohamed Omar Mousa February 2006
4. Tapered keys fitted on the sides and round keys, in which torque is transmitted by the simultaneous action of compressive and shear stresses and friction as shown in Figure.
M
tF R
F’
R’
M
tF R
F’
R’
7. FORCES ACTING ON SUNK KEYS
L
L
W t
t
W F
F F’
F’
F’ << F
F’ neglected
Prof. Dr. Mohamed Omar Mousa February 2006
Therefore, when key transmitted torque between shaft and hub, the following forces appear:
B. Forces “F” that generate due to the transmitted torque.
F = Torque /radius
F
F F’
F’
A. Force “ F’ ” due to the fit of the key in its keyway (Compressive - difficult to determine in magnitude - small).
These forces produced shearing and compressive
(crushing) stresses in the key.
8. STRENGTH OF SUNK KEY
During the design of sunk key, the following assumptions should be taken into consideration:
1. The forces due to fit (F’) are small and negligible.
2. The forces are uniform distributed along the length of the key.
Prof. Dr. Mohamed Omar Mousa February 2006
Let us consider the following;
T : Torque transmitted by the system.
F : Tangential force acting on the key at the circumference of the shaft.
D :Diameter of the shaft.
L : Length of the key.
W : Width of the key.
t : Thickness of the key.
: Shear stress for the material of the key.
: Compressive stress of the material of the key.
Now, considering shear of the key:
The tangential shearing force acting on the circumference of the shaft can be computed as follows:
F = Area resisting shearing x shear stress F = (L.w)
i.e.; Torque transmitted = T
2 F d T
2 LW d
T
Prof. Dr. Mohamed Omar Mousa February 2006
t
W F
F F’
F’
Considering, c rushing of key, the tangential crushing force acting on the circumference of the shaft can be determined as follows:
F = Crushing area x crushing stress
2 L t F
2 d 2
L t 2
F d
T
t
W F
F F’
F’
Then, the key can be equally strong in both of shear and crushing, if :
Crushing stress = Shear stress
2 d 2
L t 2
W d
L
It is important to notice that the permissible crushing stress for the usual key material is at least twice the permissible shear stress.
i.e., = 2 Therefore,
W = t
Prof. Dr. Mohamed Omar Mousa February 2006
i.e. the square key is equally strong in shearing and crushing.
To calculate the length of the key to transmit full power of the shaft, the shearing strength of the shaft is equal to the torsion shear strength of the shaft.
The shear strength of the key is:
2 W d
L
T --- (Equ. I)
And, the torsion shear strength of the shaft is:
d 3
16 ' T
--- (Equ. II)
Prof. Dr. Mohamed Omar Mousa February 2006
where,
: The shear strength of the key.
’ : The shear strength of the shaft material.
Equ. I = Equ. II , Therefore
W d '
L 8 2 --- Equ. III Take: W = d/4, then;
'
. 57 d 1
L --- Equ. IV
Equation (IV) can be used to determine the key length.
For special cases when the material of the shaft and key is similar,
'
W 8 L d
& 2
And, if w = d/4 then,
d 571
. 1 2 d
L
Prof. Dr. Mohamed Omar Mousa February 2006
9. SOLVED PROBLEM
A 20 h.p., 960 revolution per min. motor has a mild steel shaft of 40 mm diameter and extension being 75mm.
The permissible shear and crushing stresses for the mild steel key are 560 kp/cm and 1120 kp/cm . Design the keyway in the motor shaft extension. Check the shear strength of the key against the normal strength of the shaft.
Solution Given:
P = 20 h . p. N = 960 r.p.m.
D = 40 mm L = 75 mm
all = 560 kp/cm 2 all = 1120 kp/cm2
cm .
kp 1492
m . kp 92
. 960 14
x 2
4500 x
T 20
1.Design of keyway
2 W d
L
T
Prof. Dr. Mohamed Omar Mousa February 2006
As the width of the keyway is too small, then,
“W” should be 0.25 d i.e.
W = d/4 = 4/4 = 1 cm = 10 mm
Checking the shear strength of the key against the normal strength of the shaft
Checking the shear strength of the key against the
normal strength of the shaft
2 . 1
4 x
1 x 5 . 7 x 8
d LW 8
3 3
d
316 '
2 LW d shaft
the of strength Normal
key the of strength Shear
Notice: The value of “ ” is twice “ ”.
Prof. Dr. Mohamed Omar Mousa February 2006
10. EFFECT OF KEYWAYS
Cutting of keyways in the shafts tends to reduce the load carrying capacity of the shaft due to the occurrence of the stress concentration. Therefore, a shaft strength factor is determined from experimental results which can be expressed as follows;
d 1 1 h d 1
2 W 0 1
e . .
“e” is the ratio of the strength of the shaft with keyway to the strength of the same shaft without keyway.
where:
e : Shaft strength factor.
W : Width of keyway.
d : Shaft diameter.
h : Depth of keyway.
However, it is usually assumed that the strength of the
keyed shaft is 75% that of the solid shaft without
keyway, which is higher than the value obtained by the
above relation.
Prof. Dr. Mohamed Omar Mousa February 2006
