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 self-sustained 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. 1. Introduction The term "whirling" was introduced into mechanical engineering by W. J. M. Rankine in 1869. The main aim of whirling vibration calculations of rotating machinery was, and is now, to determine the critical speeds of the shaft. Any whirling vibration resonance caused by a residual out-of-balance moment in a fast-rotating turbine might result in a catastrophic failure. The theory of whirling vibration was also applied to marine propulsion shafting. Nowadays, all classification societies require a propulsion shafting whirling vibration calculation, also called in some class rules as bending or lateral vibration calculations. The classification societies make reference to whirling vibration calculations, requiring the calculation of critical speeds. In reference to forced whirling vibration, the classification societies only say that this calculation may be required. The classification societies have clear requirements for shaft modeling and acceptance criteria in the case of torsional vibration calculations. However, in the case of whirling vibrations, the criteria are not as specific as the torsional vibration calculations.