The first$-$stage turbine disk for a turbofan engine has a bore radius of $127$ mm $,$ a rim radius of $381$ mm $,$ and a thickness of $76$ mm $($assumed uniform from bore to rim$).$ Attached to the disk are $40$ turbine blades, each weighing $\backslash (4\mathrm{.}4$ N $\backslash )($including attaching hardware$).$ When the blades are mounted in the disk, the radius to the blade centroid is $410$ mm $.$ The maximum design rotor speed is $8000$ rpm $.$ Allow for a $\backslash (10\backslash \%\backslash )$ overspeed in the following analysis.

The disk material is Waspaloy, a high$-$temperature nickel$-$based alloy. It has density $\backslash (8138\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ elastic modulus of $184\mathrm{.}1$ GPa at a temperature of $\backslash (538^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ a corresponding tensile yield strength $980$ MPa $,$ and Poisson's ratio of $0\mathrm{.}3.$

Now consider the disk and a drive shaft together as single piece of material $($both have properties

of Waspaloy$).$ Suppose the interference fit is such that when the system reaches overspeed the press

fit interference pressure becomes zero. What is the radial stress at a radius of R$?$ The negative of

that would be the designed interference pressure pi$.$

$($vii$)$ For an interference pressure of pi$,$ what is the required radial interference $?$

$($viii$)$ Superimpose the the stresses due to rotation of the solid disk and due to internal pressure from

the interference pressure pi and the pressure caused by rotation of the turbine blades Part B In this part using an interference fit to mount the fan disk to the drive shaft is considered. You will want to refer to the Rotating Pressfit example from lecture.

$-($vi$)$ Now consider the disk and a drive shaft together as single piece of material $($both have properties of Waspaloy$).$ Suppose the interference fit is such that when the system reaches overspeed the press fit interference pressure becomes zero. What is the radial stress at a radius of R$?$ The negative of that would be the designed interference pressure pi$.$

$-($vii$)$ For an interference pressure of pi$,$ what is the required radial interference $\backslash (\backslash$delta $\backslash )?$

$-($viii$)$ Superimpose the the stresses due to rotation of the solid disk and due to internal pressure from the interference pressure pi and the pressure caused by rotation of the turbine blades.