Prob $1.$

Determine the required key geometry$($length$,$ width, and height$)$ for a gear to be mounted on a shaft with a $2\mathrm{.}00$ in diameter. The gear transmits $\backslash (21000\backslash$mathrm$\{$lb$\}-\backslash$mathrm$\{$in$\}\backslash )$ of torque and has a hub length of $4\mathrm{.}00$ in $.$

Prob $2.$

Determine the required key geometry$($length$,$ width, and height$)$ for a gear carrying $21000$ lb $-$in of torque if it is mounted on a $3\mathrm{.}60-$in$-$diameter shaft. The hub length of the gear is $4\mathrm{.}00$ in $.$

Use SAE $1018$ steel for the keys if a satisfactory design can be achieved. If not, use a higher strength material from Table $11-4.$ Unless otherwise stated, assume that the key material is weakest when compared with the shaft material or the mating elements.

TABLE $11-4$ Examples of Materials Used for Keys

Tensile strength

s$\_($u$)$ Yield strength s$\_($y$)$ designation $($ksi$)($MPa$)($ksi$)($MPa$)$ Carbon steels $($SAE$)1018644415437210357249639\mathrm{.}527210459162777531109514096583572$ Alloy steels $($SAE$)414010270390621863010069095655$ Stainless steels $($SAE$)3039062135241304855863524131685586352414167551740276$ Aluminum $6061181241283$

Source: Adapted from Internet site $20.$

Note: Strength properties typical, not guaranteed.

TABLE $11-1$ Key Size vs$.$ Shaft Diameter

U$.$S$.$ inch sizes

Nominal shaft diameter Key dimensions to$-$including $($in$)$ Width, W $($in$)$ Height, H $($in$)0\mathrm{.}31250\mathrm{.}43750\mathrm{.}093750\mathrm{.}093750\mathrm{.}43750\mathrm{.}56250\mathrm{.}12500\mathrm{.}12500\mathrm{.}56250\mathrm{.}8750\mathrm{.}18750\mathrm{.}18750\mathrm{.}8751\mathrm{.}2500\mathrm{.}25000\mathrm{.}25001\mathrm{.}2501\mathrm{.}3750\mathrm{.}31250\mathrm{.}31251\mathrm{.}3751\mathrm{.}750\mathrm{.}3750\mathrm{.}3751\mathrm{.}752\mathrm{.}250\mathrm{.}5000\mathrm{.}5002\mathrm{.}252\mathrm{.}750\mathrm{.}6250\mathrm{.}6252\mathrm{.}753\mathrm{.}250\mathrm{.}7500\mathrm{.}7503\mathrm{.}253\mathrm{.}750\mathrm{.}8750\mathrm{.}8753\mathrm{.}754\mathrm{.}501\mathrm{.}001\mathrm{.}004\mathrm{.}505\mathrm{.}501\mathrm{.}251\mathrm{.}255\mathrm{.}506\mathrm{.}501\mathrm{.}501\mathrm{.}506\mathrm{.}507\mathrm{.}501\mathrm{.}751\mathrm{.}507\mathrm{.}509\mathrm{.}002\mathrm{.}001\mathrm{.}509\mathrm{.}0011\mathrm{.}002\mathrm{.}501\mathrm{.}7511\mathrm{.}0013\mathrm{.}003\mathrm{.}002\mathrm{.}0013\mathrm{.}0015\mathrm{.}003\mathrm{.}502\mathrm{.}5015\mathrm{.}0018\mathrm{.}004\mathrm{.}003\mathrm{.}0018\mathrm{.}0022\mathrm{.}005\mathrm{.}003\mathrm{.}5022\mathrm{.}0026\mathrm{.}006\mathrm{.}004\mathrm{.}0026\mathrm{.}0030\mathrm{.}007\mathrm{.}005\mathrm{.}00$

SI metric sizes

Nominal shaft diameter Key dimensions Over $($mm$)$ to$-$including $($mm$)$ Width, W $($mm$)$ Height, H$($mm$)6822810331012441217551722662230873038108384412844501495058161058651811657520127585221485952514951102816110130321813015036201501704022170200452520023050282302605632260290633229033070363303808040380440904544050010050$

Note: Key sizes above the horizontal line are square; others are rectangular.

$*$ Please solve both quotients $*$