Stresses induced in the flywheel (PSG-7.120)

A flywheel, as shown in fig. consists of a rim at which the major portion of the mass or weight of the flywheel is concentrated, a boss or hub for fixing the flywheel on to the shaft and a number of arms for supporting the rim on the hub.

The following types of stresses are induced in the rim of a flywheel:

1. Tensile stress due to centrifugal force, $\sigma_{t}=\frac{\gamma v^{2}}{g}=\frac{\mathrm{pv}^{2}}{10^{6}} M P a$

2. Tensile bending stress caused by the restraint of the arms, $\sigma_{b}=\frac{\pi^{2} v^{2} D \rho}{n^{2} \mathrm{h}}$

3. The shrinkage stresses due to the unequal rate of cooling of casting. These stresses may be very high but there is no easy method of determining. This stress is taken care of by a factor of safety.

It has been shown by G. Lanza that the arms of a flywheel stretch about $3/4^{th}$ of the amount necessary for free expansion. Therefore, the total stress in the rim is

$$\boldsymbol{\sigma}_{\mathrm{total}}=\frac{3}{4} \boldsymbol{\sigma}_{t}+\frac{\mathbf{1}}{4} \boldsymbol{\sigma}_{\boldsymbol{b}}$$