The picture shows gears C and D installed on a solid cylindrical shaft supported

Question

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 seat E only, calculate: a) the safety factor for infinite life based on DE-Gerber, b) the safety factor against yielding in the first cycle.

Explanation / Answer

S- N curve

Some materials , such as steel , show an endurance limit stress below which the fatigue life is essentialy infinte . other materials may not show such behaviour but an effective endurance limit may be specified at some large number of cycles.

s- n teting is done under alternating loading and stress

gerber = sigma a / sigma e + (sigma m / sigma f ) 2 =1

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