Shaft key types,function and stress calculation

A key is a piece of mild steel inserted between the shaft and hub to connect these together in order to prevent relative motion between them.

It is always inserted parallel to the axis of the shaft. Keys aroused as temporary fastenings and are subjected to consider-able crushing and shearing stresses.

Types of Keys:
(a) Shunk keys,
(b) Saddle keys,
(c) Tangent keys,
(d) Round keys, and
(e) Splines. 

The Function of Keys
There are two main functions of keys when they are used to lock the transmission shaft.
The primary function is to restrict relative rotational motion and axial movement between the shaft and the machine element.
Some special types of keys are also available, such as feather and splines, keys that allow axial movement between them.
The second function of the key is to transfer torque from the rotating shaft to the rotary element of the machine. The same key works to transmit torque in both directions; from shaft to the machine element, or from machine element to the shaft.

The shear and compressive stresses in a key are calculated using the following equations:
Shear Failure of Keys
Shear stress is the cause of this type of key failure. Actually, during rotation the shaft and the machine element, say hub, each element exerts equal and opposite force on the key. These opposite forces introduce shear stress along the radius of the shaft. The key is then starts deforming and after some time it fails.

The ultimate stress depends on the material strength of the key and angular velocity of the rotation. You can calculate the shear force applied on the key using the formula given below.

F = π ω l
T = Fr
Where,
F= the shear stress acting on the key,
L= effective length of the key,
ω= angular velocity of the shaft,
r= radius of the shaft, and 

T= maximum torque transferred by the key.

Crushing Failure of Key
Crushing of a key is the reason of this type of key failure. During rotation the shaft and the hub impose compressive force on the key. This compressive force causes its deformation. The key is then permanently deformed under this force and finally crushing occurs. This compressive force can be calculated using the parameters of the shaft and the key. The formula for the calculation is given below.

The shear and compressive stresses in a key are calculated using the following equations:

Shear stress, Ss = 2T/DWL

Where,
Ss = Shear stress in Psi
T = Shaft torque in pound-inch
D = Shaft diameter in inch
W = width of key in inch
L = effective length of key in inch

Compressive stress, Sc = 2T/DhL

Where,
Sc = Shear stress in Psi
T = Shaft torque in pound-inch
D = Shaft diameter in inch
h = height the key in the shaft that bears against the key way in inch
L = effective length of key in inch