Part I $[60\backslash \%]-$ Create an Excel Spreadsheet, Python$/$MATLAB Script, a Jupyter Notebook Code, OR any other Open$-$source Software $($OSS$)$ of your choice to solve the following problem:

A $\backslash (\backslash$left$(12+2(\backslash$mathbf$\{$y$\})\backslash$right$.\backslash )-$tooth $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle spur pinion rotates at $\backslash ((2000-10(\backslash$mathbf$\{$z$\}))\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash )$ and transmits $6$ hp to a $60-$tooth disk gear. The diametral pitch is $16$ teeth $\backslash (/\backslash$mathrm$\{$in$\}\backslash ),$ the face width is $3$ in $,$ and the quality standard is No$.\backslash ((3+\backslash$mathbf$\{$x$\})\backslash ).$ The gears are straddle$-$mounted with bearings immediately adjacent. The pinion is a grade $1$ steel with a hardness of $\backslash ((200+\backslash$mathbf$\{$z$\})\backslash )$ Brinell tooth surface and through$-$hardened core. The gear is steel, through$-$hardened, and grade $1$ material, with a Brinell hardness of $200,$ tooth surface, and core. The loading is smooth because of the motor and load. Assume a pinion life of $\backslash (10^\{8\}\backslash )$ cycles and a reliability of $0\mathrm{.}999.$ The tooth profile is uncrowned. This is a commercial enclosed gear unit.

$($a$)$ Find the factor of safety of the pinion against failure due to bending.

$($b$)$ Find the factor of safety of the pinion against failure due to wear $($contact$)$

$($c$)$ By examining the factors of safety, determine the critical failure mode for the pinion.

In your spreadsheet$/$program$,$ do not use $\backslash (\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\}\backslash )$ and z as the input parameters. Instead, use the actual term as the input parameter. For example, the spreadsheet$/$program should require the user to input $\backslash ($ N $\backslash )$ as the number of teeth for the pinion instead of y in $\backslash ((12+2*\backslash$mathrm$\{$y$\})\backslash ).$

Part II $[20\backslash \%]-$ Now, show the results of your spreadsheet$/$program$,$ with $\backslash (\backslash$mathbf$\{$x$\}\backslash )$ as the second last digit of your student number, $\backslash (\backslash$mathbf$\{$y$\}\backslash )$ as the last digit, and $\backslash (\backslash$mathbf$\{$z$\}\backslash )$ as the combined last two digits. For example, if your student number is $445223245$ then $\backslash (\backslash$mathbf$\{$x$\}=\backslash$mathbf$\{4,$ ~$\}\backslash$mathbf$\{$y$\}=\backslash$mathbf$\{5\}\backslash ),$ and $\backslash (\backslash$mathbf$\{$z$\}=\backslash$mathbf$\{45\}\backslash ).$ Therefore, the pinion teeth value will be $\backslash (12+2*\backslash$mathbf$\{5\}=22\backslash ),$ the pinion rotational speed will be $\backslash (2000-10^\{*45\}=1550\backslash$mathrm$\{$rpm$\}\backslash ),$ the quality standard will be $\backslash (3+4=7\backslash ),$ and the hardness of the pinion will be $\backslash (200+\backslash$mathbf$\{45\}=245\backslash )$ Brinell.

Part III $[20\backslash \%]-$ Upload a short video explanation $(8-10$ minutes$),$ which can be uploaded as a URL link or a file on eClass. In the video, you should run through the spreadsheet$/$program of Part I $($above$)$ and its output in Part $2($above$).$ Your explanation should outline the approach and the outcomes, including showing the output of your student number$-$based variables. Be sure to show your face and state your name and student number at the start of the video. Also, ensure your screen is being shared, and your program is visible during your recording. Zoom is a great platform on which to record your video.