a$02.$pdf $1].$ A flywheel is press fitted on to a tubular shaft. The shaft inner diameter is $25$ mm and

outer diameter $50$ mm $.$ The flywheel is a cylindrical disk with an inner diameter of $50$ mm $,$

an outer diameter of $300$ mm $,$ and the flywheel thickness is $35$ mm $.$ Both the shaft and

flywheel are made of aluminum alloy AA$2014$ of density, $=2800k\frac{g}{m^3}.$ Find the speed

at which the flywheel will start to slide if the coefficient of friction between the shaft and

flywheel is $0\mathrm{.}14$ and press$-$fit pressure is $30$ MPa $.$ The rotational acceleration $(=\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{t}})$ is

proportional to the angular speed $$ and its maximum value should be within $0\mathrm{.}2.[3$

marks$]$

Additional theory and Hints: This problem would require a calculation of initial torque

based on flywheel mass moment of Inertia $(J).J$ is given by $J=m_a\frac{d_o^2-d_i^2}{8}$ where $d_o$ and

$d_i$ are outer and inner diameters of the flywheel and $m_a$ is the mass of the flywheel. The

initial torque is given by $T=J=J$del$\frac{}{d}$elt where $$ is the angular acceleration and $$ is

the angular velocity. This torque value would be a function of unknown angular velocity,

and must be equal to the instantaneous torque value developed by friction at the flywheel

and shaft interface, also a function of angular velocity. Also, note that as the shaft rotates

with increasing angular velocity, the resulting interference $($or contact pressure$)$ decreases.

This instantaneous contact pressure value is the initial press fit pressure minus the

instantaneous radial stress evaluated at the flywheel and shaft interface where the

instantaneous radial stress should be a function of unknown angular velocity and other

known parameters.