The developing of polar ships is an important support of the polar strategic target in China, while the multi-working conditions of ships sailing in polar ice regions complicate the strength design of the propulsion machinery system - the heart of a vessel. The design principle and the corresponding rules and specifications for the strength of the propulsion shafting of DNV are introduced to ensure the reliability and safety of the ships sailing in polar regions. Regarding the impact of the ice load excitation on the propulsion system and the shafting components, DNV recommends a digital solution considering the excitation of the diesel engine cylinder and the phase angle of the ice load excitation based on its experience. In the current study, the Nauticus Machinery software developed by DNV is used to calculate the torsional vibration of a PC4 polar ship in time and frequency domain. The shafting dimension is then evaluated by using the Palmgren-Miner linear damage rule, and the results of the time-domain analysis are compared with those of the frequency-domain analysis. An iteration procedure has been provided for the design and optimization of the shafting dimension aiming at the strength design of the propulsion shafting for polar ships.