20-mm diameter
solid round shaft
b
Kay Faz
C
Pump
Housing
Z
y
X
200-mm diameter
gear
Fax
Figure 1.0
180-mm
Figure 1.0 shows a portion of a mechanical system at uniform load and constant speed of 600
rev/min. The system has a 200 mm diameter helical spur gear that is mounted on the overhung
end of a shaft, 180 mm from the nearest bearing. The AISI 4340 HR shaft is supported by bearings
mounted in the pump housing. The loads acting on the gear are $F_{ax} = 1400$ N, $F_{ay} = 2000$ N, and
$F_{az} = 1200$ N. Experienced engineers suggest that the safety factor of the shaft is 2.0. Use
Distortion Energy Theory.
1.1 Sketch the free body diagrams for the gear and the shaft using isometric
projection. Label the diagrams properly and provide the values for all the action-
and-reaction loads.
1.2 Draw the shear force, the bending moment and torsion diagram for the shaft. Label
the diagrams properly and provide the values at key points.
1.3 Draw the element stress at the critical point of the shaft and compute the stresses
developed. Indicate clearly the direction of the stresses.
1.4 Will the shaft survives under these static loadings? Prove it.
1.5 You have drawn the shear force diagram in part 1.2, but what are your justifications
for not including the transverse shear stress in your calculations in part 1.3?
1
