Step # 4 - Key Design |
W_{t}=2T/D_{shaft}
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
D_{shaft} is the shaft diameter at the location under consideration
Bearing Stress:
Shear Stress:
Where:
W_{t} is the tangential force
a is the side of the square key
l is the length of the key (to be solved)
S_{y} is the yield strength of the key material selected
S_{sy} 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
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:
y_{B} is the deflection in the y-direction at the pinion location
W_{t} 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 2^{nd} moment of area of the shaft at the location of the pinion = p d^{4}/64
l is the total distance between points A & C
Similarly, find the deflection (z_{B}) at B (pinion location), in the z-direction using W_{r} instead of W_{t}, and calculate the total deflection at the pinion using the following equation: