For shaft mounting good quality spur gears, the deflection at the gear mesh should not exceed 0.005 in. (0.125 mm).
The slope at ball bearings should be limited to 1̊
We will use the principle of super position to calculate deflection of the shaft at gear 3 (Q) and slope at the left hand bearing (P).
Consider shaft as a simply supported beam with load at any point (for 0≤x≤a)
Deflection is given by:
Calculate total deflection in Y-direction at the gear location,
Total deflection in Z-direction is equal to as there is no force in Z-direction at pulley,
Calculate resultant deflection,
Slope is given by:
Total slope in y-direction,
Total slope in z-direction at bearing A,