The picture shows gears C and D installed on a solid cylindr

The picture shows gears C and D installed on a solid cylindrical shaft supported by bearings A and B. The shaft is machined, has a diameter of 1.57 inches, made of AISI 1020 CD steel and rotates at 800 RPM transmitting 2500 in.lbf of steady torque between the two gears. Gear C is secured to the shaft with a key at point E. The end-mill key seat at that location has an “r/d” ratio equal to .02. The combined bending moment at the location where gear C is installed is 2178 in.lbf completely reversed. Temperature is 200F and reliability of 95% is required. Focusing on keyseat E only.

calculate: a) the safety factor for infinite life based on DE-Gerber

b) the safety factor against yielding in the first cycle.

M C 2178 bfin pletely reversed T@ C 2500 lbf in steady AISI 1020 CD End-mill keyseat (r/d a.02) A 1.57\" dia

Solution

The answer of following question is as follows

The factor of safety for the DE is 6.

The factor of safety for the yielding 1st cycle is 5