Bearing Selection

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:

Where:

         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:

Where:

        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.

NOTE:

                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

KEY DESIGN

·        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.