Decide whether to use deep groove ball bearing or angular contact bearing.
Calculate resultant reactions at bearing A
Depending on the type of application, select bearing life (no. of hours) from Table 11-4 and Load-Application factor from Table 11-5.
Assume a reliability of 0.9
Assume a rating life of one million revolutions as the base value.
Using following equation from the text book, calculate the rated force for each bearing:
is the Catalog Load Rating
is the Design Load
is the Design Life in Hours
is the Design Speed (given in rpm)
is the Rated Life = 106 rev.
R is the Reliability
a for ball bearing = 3
For the values of , use the values of the resultant reaction calculated for locations A ,
To calculate C, use the following equation:
A.F. is the Load-application Factor.
Select Bearings for the bearing locations A on the shaft using Table 11-2. Use the value of C, calculated above to select the bearing and note down all bearing data.
Convert to rev. before solving the equation
The bearing shoulder diameter should be greater than the diameter calculated from fatigue analysis and take bearing shoulder diameter as
· When the diameter of a gear is more than double that of the shaft diameter, it is usually keyed to the shaft.
· Keys are generally made of cold-drawn low carbon steel.
· Select suitable CD steel from (Table E-20) of Appendix.
· Compare yield strength of the shaft with the yield strength of the key material and use weakest of the two in calculations,
· With diameter calculated, select square keys for gear 3 from (Table 8-20).
Now we need to calculate length of the key.
Keys generally have two types of failures:
(1) Shear Failure: Keys of the shaft and hub exert equal and opposite forces of value F, these forces attempt to shear the key at the radius of the shaft.
Shear area =
Shear force , where T = torque
Using distortion –energy theory
Yield strength in shear,
, where n = factor of safety
(2) Bearing or Crushing Failure: Keys can suffer permanent compressive deformation where it contacts the keyways in the shaft and hub.
· Since one-half of the key is in the hub and one-half is in the shaft, as measured at the side of the keyway, the bearing area in each is .
· The line of action of the force between the hub and the key would be a little above, and force between the shaft and the key would be a little below from the force acting at the surface of the shaft.
· Because of inherent inaccuracies in the analysis and the small difference involved, the moment arm of the force is taken as .
Where is the yield strength in compression.
· Use larger of the length obtained from two types of failure.
· Generally key lengths fall within the following ranges:
· If key length is less than , then take key length equal to .
· If the required key length is greater than , consider using two keys, apart.