Marine Propulsion Shafting: A Study of Whirling Vibrations

Whirling vibration is an important part of the calculations of the design of a marine shaft. In fact, all classification societies require a propulsion shafting whirling vibration calculation giving the range of critical speeds, i.e., free whirling vibration calculation. However, whirling vibration is a source of fatigue failure of the bracket and aft stern tube bearings, destruction of high-speed shafts with universal joints, noise, and hull vibrations. There are numerous uncertainties in the calculation of whirling vibration, namely, in the shafting system modeling and in the determination of excitement and damping forces. Moreover, whirling vibration calculation mathematics is much more complex than torsional or axial calculations. The marine propulsion shaft can be studied as a selfsustained vibration system, which can be modeled using the Van der Pol equation. In this document, a new way to solve the Van der pol equation is presented. The proposed method, based on a variational approach without local minima extra to the solution, converges for whatever initial point and parameter in the Van der Pol equation.