Rigidity Analysis

1. Perform a rigidity analysis at the pinion location for the input shaft using the following procedure:

The deflection at the pinion, 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 (B)

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 d⁴/64

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: