Step # 4 - Key Design
1. Select the material of the key from any grade of HR or preferably CD steel (material selected must have a yield strength lesser than the material of the shaft)
2. Select square keys for both key locations from table (8-15), interpolate the data for shaft sizes greater than 3¼". Note the key data (a), the side of the square key
3. Calculate the tangential forces acting at the key location using the torque value at the location and the shaft diameter
4. Wt=2T/Dshaft

Where:

Wt is the value of tangential force to be calculated at the key location

T is the torque value at the location under consideration

Dshaft is the shaft diameter at the location under consideration

5. Calculate the length required for the key by solving Shear and Bearing stress equations for the key

Bearing Stress:

Shear Stress:

Where:

Wt is the tangential force

a is the side of the square key

l is the length of the key (to be solved)

Sy is the yield strength of the key material selected

Ssy is the shear yield strength of the key material

n is the safety factor

The final value of the length (l) of the key will be the larger of the two values calculated for each location. Generally, key sizes must fall within the following range by length:

Step # 5 - Rigidity Analysis

1. Perform a rigidity analysis at the pinion location for the input shaft using the following procedure:
2. The deflection at location B (pinion location), in the y-direction can be found using the following equation:

Note: If a=b, first simplify the equation before solving by using a=b=l/2

where:

yB is the deflection in the y-direction at the pinion location

Wt is the tangential force acting on the pinion

a is the distance between points A & B

b is the distance between points B & C

E is the Young's Modulus of Elasticity for the material of the shaft (Carbon Steel)

I is the 2nd moment of area of the shaft at the location of the pinion = p d4/64

l is the total distance between points A & C

Similarly, find the deflection (zB) at B (pinion location), in the z-direction using Wr instead of Wt, and calculate the total deflection at the pinion using the following equation:

3. Repeat the entire procedure shown above to find the total deflection at the gear location on the output shaft