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Problem $1$

$(50$ marks$)$

Design problem: Design a heat$-$treated steel shaft to support a spur gear and an overhanging worm, as illustrated in the figure. The bearing at point $A$ is subjected to pure radial load, while the bearing at point B supports the worm thrust load for both directions of rotation. The figure includes the dimensions and loading conditions, with radial loads in the same plane.

Your task is to perform a complete design of the shaft, including:

A detailed sketch of the shaft with all dimensions clearly labeled $($using any CAD software$)$

$(10$ marks$)$

Selection of a suitable material and, if required, the recommended heat treatment process.

$(5$ marks$)$

An evaluation of the final design, addressing aspects such as strength, deflection, and service life.

Quality of design report.

$(30$ marks$)$

$(5$ marks$)$

The shaft operates at a speed of $310$ revolutions per minute $($rev$/$min$).$ All dimensions are provided in millimeters $($ mm $).$

Bonus $(10$ marks$)$: Any additional effort such as finite element analysis or prototype.