Question

A shaft with a shoulder fillet radius, r = 2 mm is loaded in a completely reversed stress such that M = 7.8 Nm and T = 4.1 Nm at the critical point. For the shaft, Sut = 1.4 GPa and a fully corrected endurance limit of Se =9.3 MPa is assumed. Given that d = 40 mm and D = 60 mm, determine the minimum acceptable diameter of the shaft using the DE-Goodman criterion.

Answer 1

The DE-Goodman criterion is used to determine the minimum acceptable diameter of a shaft based on stress and fatigue properties. This criterion compares the equivalent alternating stress to the endurance limit of the material.

Step-by-step explanation:

The DE-Goodman criterion is used to determine the minimum acceptable diameter of a shaft based on the stress and fatigue properties of the material. The criterion states that the equivalent alternating and static stresses must be less than the endurance limit of the material. In this case, the equivalent alternating stress is calculated as:

Sa = (M / Z) + (T / rho)

where M is the bending moment, T is the torque, Z is the section modulus, and rho is the radius of the shaft. The section modulus is calculated as:

Z = (pi / 32) * ((D^4 - d^4) / D)

where D is the outer diameter of the shaft and d is the inner diameter.

Using the given values, we can calculate the section modulus and the equivalent alternating stress. Then, we can compare the alternating stress to the endurance limit to find the minimum acceptable diameter of the shaft.