IBMMAE – 3- Machine Elements
1
Fatigue resistance of a transmission shaft
Figure 1 : Transmission shaft, dimensions in (mm), forces in (N)
One considers the transmission shaft represented in figure 1. It is made of steel with the following characteristics σE=700 MPa, σr=800 MPa. The objective is to determine the shaft diameter d.
IBMMAE – 3- Machine Elements
2 a. Determine the reaction force at points A (Ay,Az) and B(By, Bz) , the axial components are assumed to be
nil (Ax, Bx), round your result to the N,
b. Plot the cohesion forces/moments diagrams, conclude on the critical section location. Check that in this section the cohesion wrench reads : FR/L={0, 8000, 0} N and MR/L (A) ={400, 0,1280} N.m.
c. Static resistance, in the critical section,
i. Express as a function of the diameter d, the bending, torsion and shear stresses for a point on the shaft surface,
ii. By neglecting the shear stress due to the internal shear force, determine the minimum shaft diameter with a safety factor 2.
d. Fatigue resistance, in the critical section, for any point M of the shaft surface,
i. Determine the mean and amplitude stresses σa, σm, τa, τm and deduceσa_equi, σm_equi
ii. By neglecting the shear stress due to the internal shear force, determine the minimum shaft diameter with a fatigue safety factor 2, (Use Goodmann diagram, the endurance limit can be estimated from the ultimate stress),
