Question

A notched circular shaft shown is subjected to fully reversed bending. D=12.7mm, d=10.16 mm, and r=0.5mm. The steel material has the following mechanical and fatigue properties: yield strength (σ0)=1000 MPa, ultimate strength (σu)=1200 MPa, the fatigue strength coefficient (σf’)=1600 MPa, the fatigue strength exponent (b)=-0.1, and the fatigue limit (σe)=400 MPa.

5. (20 pts) A notched circular shaft shown is subjected to fully reversed bending. D-12.7mm, d-10.16 mm, and r-0.5mm. The steel material has the following mechanical and fatigue properties: yield strength (σ)-1000 MPa, ultimate strength (o )-1200 MPa, the fatigue strength coefficient (σί)-1600 MPa, the fatigue strength exponent b)--01, and the fatigue limit (o)-400 MPa a) (10 pts) Determine the fatigue (S-N) curve for the given notched circular shaft under fully reversed bending (computer generated graph is required). b) (10 pts) What is the bending moment amplitude if the desired fatigue life of the notched shaft is 60,000 cycles (considering a safety factor of one)?

Answer 1

Given data: Yield strength, σ,-1000 MPa Ultimate strength, σ-1200MPa Fatigue strength coefficient, o,-1600 MPa Fatigue strength exponent, b Fatigue limit. ơ-400 MPa --0.1 (a)l Consider the expression between stress and number of cycles -1600Ni Take log of both sides. log S log 1600-0.1xlog N log S 3.2041-0.1xlog N Plot the S-N curve for the component

2.95 2.9 2.85 2.8 냥 2.75 2.7 2.65 2.6 2.55 4 6 logN Consider the stress amplitude corresponding to 60,000 cycles

ơ,-1600 x( 60000) 532.48 MPa Calculate the maximum and minimum actual bending stress as the loading is fully reversed Ơmax-532.48 MPa Ơmin-532.48 MPa Calculate the maximum theoretical bending stress Here, k, is the stress concentration factor Calculate the value of the stress concentration factor for given shaft. D 12.7 d 10.16 k, 2.35 r 0.5 d 10.16 and-0.04921 Substitute the values in above equation. 532.48 );- 2.35 -226.58 MPa

Calculate the value of amplitude of bending moment 32M id 226.58-32xM Tx10.16 M 23329.35 N-mm -23.329 N-m Hence, the value of amplitude of bending moment is 23.239 N-m