A shaft with two counter$-$rotating spur gears will be designed. The gears transmit the torque from another gear, which is connected to them, to the shaft with a key. Gear $1$ has diameter and rotates with torque $\backslash (321,75\backslash$mathrm$\{$Nm$\}\backslash )$ T$.$ Gear $2$ has diameter d $2$ and rotates with torque $\backslash (321,75\backslash$mathrm$\{$Nm$\}\backslash )$ T$.$ The shaft is also supported by Bearing A and Bearing B at both ends. Within the parameters and constraints given in the table, calculate and determine the values of D$1,$ D$2,$ D$3,$ and D$4$ to satisfy the minimum safety factor given in the table, based on providing sufficient fatigue and static stress capacity for infinite life of the shaft.

Failure Criteria DE$-$Gerber Minimum Safety Factor $($n$)1,88$

Draw free$-$body diagram.

$\backslash (\backslash$therefore $\backslash )$ Calculate the tangential and radial components of the gear forces.

$3.$ Calculate and draw shear$/$moment diagram.

$1.$ Name the points on shaft. Determine the critical locations and explain why?

i$.$ Calculate the diameter for each section D$1,$ D$2,$ D$3$ and D$4,$ and make sure that they satisfy the minimum safety factor for that section. If the diameter not satisfies the minimum safety factor, try changing the material or increasing the diameter.

$).$ After specifying the shaft dimensions, calculate the volume of the shaft and make a weight analysis.