A schematic of a clutch$-$testing machine is shown. The steel shaft rotates at a constant speed. An axial load is applied to the shaft and is cycled from zero to $\backslash ($ P $\backslash ).$ The torque $\backslash ($ T $\backslash )$ induced by the clutch face onto the shaft is given by

$\backslash [$

$\backslash$mathrm$\{$T$\}=\backslash$frac$\{\backslash$mathrm$\{$fP$\}(\backslash$mathrm$\{$D$\}+\backslash$mathrm$\{$d$\})\}\{4\}$

$\backslash ]$

where $\backslash ($ D $\backslash )$ and $\backslash ($ d $\backslash )$ are defined in the figure and $\backslash ($ f $\backslash )$ is the coefficient of friction of the clutch face. The shaft is machined with $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$y$\}\}=120\backslash$mathrm$\{$kpsi$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$ut$\}\}=145\backslash$mathrm$\{$kpsi$\}\backslash ).$ The theoretical stress$-$concentration factors for the fillet are $3\mathrm{.}0$ and $1\mathrm{.}8$ for the axial and torsional loading, respectively. Assuming the load variation $\backslash ($ P $\backslash )$ is cycled between $4$ kips and $20$ kips and that it is rotating synchronous with the external load cycle, estimate the number of cycles to failure. Use the modified Goodman fatigue failure criteria. Consider $\backslash (\backslash$mathrm$\{$f$\}=0\mathrm{.}3\backslash ),$ with a factor of safety of $3.$

What is the factor of safety against fatigue? $($Round the final answer to three decimal places.$)$

The factor of safety against fatigue is