Transient Response Analysis of Marine propulsion shafting systems by computer simulation

Abstract

The dynamic behaviour of marine propulsion shafting systems is transient in nature and can be described under either steady state or transient operating conditions; the former being a special case of the latter. The differential equations describing the dynamic behaviour of systems take into account the non-linearities associated with engine and propeller operation over the speed range. However, it is normal practice to linearise such non-linearities about the steady operating conditions in the frequency domain calculation to enable the formulation of the problem. This means that a frequency domain calculation is unable to predict the response time of the system in traversing the speed range of the system in response to changes in the engine governor setting or variations in the propeller pitch settings. Therefore, a time domain computer simulation program for the analysis of the torsional dynamic behaviour of marine propulsion shafting systems under transient operating conditions has been developed. A modular approach is used for the simulation, where the shafting system is considered to comprise a collection of component models, each with its own set of dynamic characteristics. A fixed step, fourth-order Runge-Kutta integration technique is used for time marching. The correctness of the program has been demonstrated by comparing preliminary torsional vibration results obtained from frequency domain vibration analysis and time domain simulation of the system under steady operating conditions. Under such conditions the frequency domain analysis and time domain simulation produce the same results. The initial conditions of shaft speeds and torques specified in the time domain simulation define the starting operating condition of a system and the simulation automatically converges to the steady operating condition, whereas the frequency domain analysis implicitly assumes steady state operation at the given conditions. The time domain simulation therefore presents a more realistic representation of the system's dynamic energy balance by taking into account the mean speed of the system and its velocity perturbations due to torsional vibration instead of "assuming" a steady system speed as in the frequency domain analysis thus eliminating erroneous matching of the operation of shafting system components and the associated non-linearities. The full capabilities of the time domain program are then demonstrated by the simulation of a marine propulsion shafting system example under transient operating conditions. The time domain simulation is a comprehensive method for analysing the torsional vibration dynamic characteristics of marine propulsion shafting systems under transient operating conditions. However, frequency domain analysis is computationally much more efficient in determining the torsional vibration response under steady operating conditions.