Part A $-$ Transmitted power

A solid circular rod is used to transmit power from a motor to a machine. The diameter of

the rod is D$=1\mathrm{.}5$in and the machine operates at $\backslash$omega $=130$rpm$.$ If the allowable shear

stress in the shaft is $11\mathrm{.}6$ ksi $,$ what is the maximum power transmissible to the machine?

Express your answer with appropriate units to three significant figures.

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Part B $-$ Minimum diameter

A solid circular shaft is required to transmit P$=43$kW from a motor to a machine. The

maximum allowable stress in the shaft is $\backslash$tau $\_($allow $)=80$MPa. If the machine runs at $\backslash$omega $=11$

ra$($d$)/($s$),$ what is the minimum diameter for the shaft?

Express your answer in cm to three significant figures.

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Learning Goal:

To determine the maximum possible power

transmission for a circular shaft and the minimum

diameter required to avoid exceeding shear stress

limits$.$

A rotating shaft can be used to transmit mechanical

power from one place to another. For example, a

shaft can be connected to a motor at one end and a

pulley at the other. The shaft can then transmit

power from the motor to the pulley. When the

machine is operating, the shaft will rotate at some

angular velocity $\backslash$omega and will be subject to a torque

T$.$ The power transmitted by the shaft is P$=$T$\backslash$omega $.$

The shaft's rotation can also be expressed as a

frequency, f$,$ which represents the number of

revolutions of the shaft per unit time. The frequency

and angular velocity are related by $\backslash$omega $=2\backslash$pi f$,$ so

the power can also be calculated using

P$=2\backslash$pi fT$.$

When designing a shaft, one consideration is limits

on shear stress. The torsion formula $\backslash$tau $\_($allow $)=($Tc$)/($J$)$

relates the allowable shear stress in a circular shaft

with outer radius c to the torque T$.$ The polar

moment of inertia is J$=(\backslash$pi $)/(2)$c$^(4)$N$*$m $1$W$=1$N$*($m$)/($s$)$ ft$*$lb ft$*$l$($b$)/($s$)1$hp$=550$ft$*$l$($b$)/($s$).$