In this project, you will design a feasible solution for the shaft of a single$-$sided

grinder. The grinder uses a direct drive $($no gearhead$)$ motor to rotate a grinding

wheel at the required $2500$ RPM$.$ You can assume the motor rotor $($the rotating part

of the motor$)$ is already mechanically connected to the shaft and has a mass of $1$ kg

with a diameter and length of $20$ cm $.$ Your design should use a standard $10-$inch

diameter grinding wheel $(1\mathrm{.}5-$inch thick, $1-$inch arbor, mass $5$ kg $).$ See Figure $1$ for a

general sketch of the grinder configuration. Your design should fit on a standard

worktable with a dimensions of $30$ inches deep $x48$ inches wide.

General Assumptions:

Bearing friction is negligible.

The bearings supporting the shafts are accurately aligned.

The shaft remains linearly elastic.

The shaft is simply supported.

The ball bearings do not prevent angular deflection.

Ignore startup and focus on steady$-$state $($i$.$e$.$ spinning at desired speed of $2500$

RPM$)$

For your final proposed design, you should:

Parameterize the shaft dimensions, create a sketch of the cross$-$section of the

shaft along the axial dimension specifying the length of each section and its

diameter, and detail how the key elements are located, remain in the desired

location during use, and is able to transfer torque from the motor to the grinding

wheel.

To support your proposed design you should provide:

Moment diagram of the shaft bending with the given loads

Use critical speed analysis to support the design of your shaft.