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Your team have been contacted to design a speed multiplier helical gearbox with an input speed of $100$ rpm and an output speed of $5000$ rpm$.$ Your task is to design this speed multiplier helical gearbox which should include housing, ball bearings, helical gears, shafts with mechanical keys to meet the specifications. The gearbox will be driven by a $20$ hp engine. The following are defined for the gearbox

Power and torque requirements. Power considerations should be

addressed, as this will determine the overall sizing needs for

the entire system. Any necessary speed or torque ratio from input

to output must be determined before addressing gear$/$pulley

sizing.

Gear specification. Necessary gear ratios and torque transmission

issues can now be addressed with selection of appropriate gears.

Determine the number of teeth, geometry of the gear, etc.

Shaft layout. The general layout of the shaft, including axial

location of gears and bearings must now be specified. Decisions

on how to transmit the torque from the gears to the shaft need to

be made $($keys$,$ splines, etc.$),$ as well as how to hold gears and

bearings in place $($retaining rings, press fits, nuts, etc.$).$

Force analysis. Once the gear$/$pulley diameters are known, and the

axial locations of the gears and bearings are known, the free$-$

body, shear force, and bending moment diagrams for the shafts can

be produced. Forces at the bearings can be determined.