can anyone help me please show all work A class 50 gray cast

can anyone help me please, show all work

A class 50, gray cast iron flywheel of 20-in outside diameter and 1-in thickness is keyed to a shaft 1.75 in in diameter. The shaft is made from 1050 steel (normalized at 1, 650 degree F). Calculate the maximum speed at which the flywheel can be run with a safety factor of 2.

Solution

The approach to this is as follows:

The shaft is the limiting factor assuming the flywheel doesnt break apart.

You need to know the maxm shear stress due to the force by the flywheel. If there is no acceleration, the force on the shaft would come from the unbalance of the flywheel, there is no torque at zero angular accln.

Assume an unbalance for the c.m of the flwheel, find the centrifugal force pulling it outward and bending the shaft.

this force is m w² e whre e is the unbalance, w the rotn speed and m the mass of the flywheel.

There can be two stresses acting on the shaft now, bending stress and shear stress. Since there is free rotation, no shear stress. Only a bending stress due to unbalance of the wheel. You need to now assume a length for the shaft and get the moment from this.

The bending stress is then given by Mc/I = Bendingn moment/( inertia)* the rasius of the shaft. equate this tot he limiting stres for the material in question, I = pi r⁴/4.

Using Saftey factor reduce the limiting stress by 2

Stres/2 = 4M/(pi r^3) where M is the bending moment