Question

ection 3-6. A shaft driven by an electrical motor is used to rotate an impeller. The conn between the shaft and the impeller involves a keyway and a fillet, as shown in the figure. Assume that the total force needed to rotate the impeller is 5 (11.1 kips) and the shear strength of the cylindrical fillet is 400 MPa (58.0 ksi), Will a fillet with a diameter of 10 mm (0.4 in.) be sufficient to prevent shear yielding? If a safety factor of 4.0 is used to guard against yielding, is the size of the fillet still sufficient? Finally, what else must we consider in order to prevent failure of the fillet, shaft, and impeller? If you were allowed to modify the design, what would you do? ,000 N Fillet Shaft Connector for the impeller

Answer 1

Let's first find the shear stress, ($\tau$):

$\tau = \frac{Force}{Area}$

$\tau = \frac{Force needed to rotate the impeller}{Area under shear}$

$\tau = \frac{5000N}{\pi r^{2}}$

$\tau = \frac{5000N}{\pi (5*10^{-3})^{2}}$ (Given Diameter of fillet= 10mm i.e. radius in meters =5x10^-3

$\tau = 63.66MPa$

Hence, as the obtained shear stress is less than the shear strength which is 400MPa, Hence the fillet will not go under shear yielding.

Now,

Given factor of safety is 4,

i.e $4\tau = 4*63.66= 254.64MPa$ (Given shear strength of the cylindrical fillet = 400MPa)

As shear strength of the fillet is more than 254.64MPa, Hence at the factor of safety 4, the fillet is still strong enough to prevent shear yielding.

Now,

As we know that sharp edges and corners are the sites for highest stress development during fatigue loading. Moreover, in our case, the design does not consider this fatigue loading condition. Hence it would be better to go for rounded corners to prevent fatigue failure of the fillet, impeller, and shaft under fatigue loading.