SEED Guides ShaftHub Connections
Worked ExampleNotation
| d | Shaft diameter | mm |
| F | Interface force | N |
| h | Key height | mm |
| kf | Sress concentration factor | - |
| L | Key length | mm |
| pi | circumference/diameter | - |
| s | Stress(direct) | N/mm2 |
| T | Torque | Nm |
| t | Stress(shear) | N/mm2 |
| w | Key width | mm |
Solution The shaft diameter is calculated first. This depends on the material chosen which, in the first instance, should be 07OM20 (to BS 970) with a minimum shear strength of 12OMPa. A factor of safety needs to be built into the calculation and 3 is used since there are no particular problems with dynamic loading and step inputs. It has been assumed that the shaft is short and will not twist significantly. Using equation 6 in the Guide for shaft strength and rigidity, MPT 6.1
t = 16T/pi(d)3 and rearranging gives:-
d= (40 *pi* l06/(16 * l00))(1/3). (* denotes multiplication)
d = 23.4mm
At this point it is necessary to decide on the type of connection to use. Because regular hub replacement is required pinning, press and shrink fits can be rejected and, since the torque to be transmitted is relatively high, using a grub screw is discounted. Clamping generally involves using an integral hub and fixing, and splines are used to allow axial motion between the shaft and hub or to transmit very high torques. Both are rejected at this stage. This leaves two potential connections, keys and taper bushes. The calculation that follows is based on the use of a key but involves an increase in shaft size due to the cutting of the keyway. The cost implications of this would in practice be compared with using (say) a 25mm diameter shaft and a taper bush.
In the standards, relations between shaft diameter and key section are fixed. For a shaft diameter between 22 and 30mm a key with rectangular cross section 8mm wide by 7mm deep is recommended. Note that this accounts for the stress raising factor discussed earlier. From the table in the standards the centre line depth of the keyway in the shaft is 4mm (3.3mm in the hub). The recognised method for establishing the diameter of the shaft is to increase the calculated value by half the depth of the key. Hence, the required shaft diameter is: -
d = 23.4 + 4/2 = 25.4mm
At this stage it is important to regard the diameter calculated as the minimum and to consider using a standard shaft diameter coupled with standard bores in which the components to be mounted on the shaft are available. For example, bearings are generally available with 25, 30, and 35mm inside diameters so a 30mm diameter shaft is selected.
The required length of the key needs calculating and hence the material for the key must be selected. It is usual practice to use a slightly weaker material for the key than for the shaft and hub, so that any damage will occur in the relatively inexpensive key, and to ensure that, in the case of overload, the key will shear and prevent damage to the major components. A material for the key is selected with a working shear strength of 3OMPa and working crushing stress of 6OMPa.
F = 2T /d = 100 ( 2/ 30) 10-3
F = 6.66 * 103 N
For shear = w F/L
30 * 106 = 6.66 * 103/L * 8 * 10-3
L = 0.0278m = 27.8mm
For crushing stress = F/L * 0.5 * h
60 * 106 = 6.66 x 103/L * 3.5 * 10-3
L = 0.0317m = 31.7mm
The larger of the two lengths must be chosen and since 31.7mm is between 1 and 2 times the shaft diameter it is acceptable. The calculated length of 31.7mm represents the minimum length and a longer length could be chosen to suit the functioning of the connection.