(Solved): A shaft is required for the chain drive illustrated in the figure below. The power transmitted is ...

A shaft is required for the chain drive illustrated in the figure below. The power transmitted is \( 10 \mathrm{~kW} \) at \( 120 \mathrm{rpm} \). The masses of the sprockets are 5 and \( 20 \mathrm{~kg} \), with respective diameters of 260 and \( 460 \mathrm{~mm} \). The material selected for the shaft is quenched and drawn 817M40 with \( \sigma_{u t s}=850 \mathrm{MPa} \) and \( \sigma_{\mathrm{y}}=700 \mathrm{MPa} \). The torque is transmitted between the shaft and sprockets by means of keys in profiled keyways. Determine the minimum diameter for the shaft based on the ASME equation for the design of transmission shafting if the desired reliability is 90 per cent. Use an initial estimate for the shaft diameter of \( 55 \mathrm{~mm} \).