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1
Keys, Pins, & Splines
Section XI
2
Keys? Common Types of Keys Design of Square & Flat Keys
Pins? Stresses Causing Pin Joint Failure Tapered Pins
Splined Connections? Torque Capacity of a Splined Connection
Talking Points
3
Keys are basically wedge-like steel fasteners that are positioned in a gear, sprocket, pulley, or coupling and then secured to a shaft for the transmission of power.
Keys?
Keys prevent relative motion between a shaft and the connected member through which torque is being transmitted.
Even though gears, pulleys, etc., are assembled with an interference fit, it is desirable to use a key designed to transmit the full torque.
4
Common Types of Keys
Notes:- The width of the square and the flat key is usually one
fourth the diameter of the shaft. - These keys may be either straight or tapered
approximately 0.6 degree, as in Gib-head key.
5
Design of Square & Flat Keys
It is based on the shear and compressive stresses induced in the key as a result of the torque being transmitted.
The force F' acts as a resisting couple to prevent the key from tending to roll in the fitted keyway.
The exact location of the force F is not known and it is conveniently assumed that it acts tangent to the surface of the shaft. This force produces both shear and compressive stresses in the key. Resistance to the shaft torque T may be approximated by:rFM t where, r = the radius of the
shaft
Mt
The shearing stress ( ) in the key is:
The compressive stress ( ) in the key is:
sh
rLb
M
rLb
rF
Lb
F t
sh
where, L = the key length
c
rL2t
M
rL2t
rF
L2t
F t
c
The shaft torque that the key can sustain from the standpoint of shear is:
The shaft torque that the key can sustain from the standpoint of compression is:
rLbM shsht
rL2tM cct
6
Pins are used in knuckle joints which connect two rods or bars loaded in either tension or compression.
Pins?
7
Stresses Causing Pin Joint Failure
An excessive load F may cause the joint to fail due to any of the following induced stresses: 1) Tensile stress in the rod:
2) Tensile stress in the net area of the eye, (see Fig. b):
3) Shear stress in the eye due to tear out, (see Fig. c):
4) Tensile stress in the net area of the fork:
5) Shear stress in the fork due to tear out:
2D
4F
t
(a)
(b)
(c)
bdd
F
o t
bdd
F
o sh approximately
2add
F
o t
2add
F
o sh approximately
8
Stresses Causing Pin Joint Failure – Cont.
6) Compressive stress in the eye due to bearing pressure of the pin:
7) Compressive stress in the fork due to bearing pressure of the pin:
8) Shear stress in the pin:
9) Bending stress in the pin, based on the assumption that the pin is supported and loaded as shown in Figure (d): (The maximum
bending moment Mb occurs at the center of the pin)
bd
F
c
d2a
F
c
2πd
2F
A
Fsh
2
d c ,
64
dI ,
8
bFM
4
b
3b
b πd
b4F
I
cM
9
Stresses Causing Pin Joint Failure – Cont.
10) Compressive stress in the pin due to the eye:
11) Compressive stress in the pin due to the fork:bd
F
c
d2a
F
c
10
Tapered pins are used to key hubs to shafts.
The diameter of the large end of the pin is usually about one-fourth the diameter of the shaft.
The capacity of this type of pin key is determined by the two shear areas of the pin.
Tapered Pins
11
Splined connections are used to permit relative axial motion between the shaft and hub of the connected member.
The splines are keys made integral with the shaft and usually consists of four, six, or ten in number.
Splined Connections?
12
Torque Capacity of a Splined Connection
The torque capacity of a splined connection is:
where,
mrApM t
m radius,mean r
m hub, oflength L
m splines, ofdepth the twice D d
m diameter,shaft D
splines ofnumber Ld D2
1
m splines, of area load totalA
MPa 7.0 splines, on the pressure epermissibl p
m
2
The splines are usually made with straight sides or cut with an involutes profile. When there is relative axial motion in the splined connection, the side pressure on the splines should be limited to about 7.0 MPa.
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