Mathematical modelling malfunctions of marine diesel engine

The paper describes modelling methods of selected malfunctions in a four-stroke marine diesel engine. The model has been developed for purposes to assess methods of technical conditions selected elements of the engine structure. Modelling malfunctions allow to determine answers to energetic parameters of the faults. The paper is based on earlier publications, in which was carried out studies of the physical model of energetic processes in engine and additionally the mathematical model which was based on the developed physical model.


Introduction
The engines which are operated on the board of Polish Navy ships, most of them are supercharged, high speed, four-stroke engines.They are used as a main propulsion and an auxiliary engines both.The auxiliary engines drive electric generators acting together with dieselgenerator (ZSE).Most of them they are not equipped with indicator valves, especially auxiliary engines [1,2].This is the main reason for using the TBO hourly strategy relative to this engines.This method of operation presents several problems: • need to shut down an engine from service for maintenance.The combat readiness of the ship is low, • high operational costs resulting from a replacement of components that could be used in the further.This illustrates the Wöhler curve (Fig. 1).
Wöhler curve is a relationship between tension (periodically variable) and a number of load change cycles that could perform a part of machine until it will be destroyed due to fatigue.Wöhler curve is a statistical curve.An expected number of cycles must be under the curve.What is more, a problem is to estimate a load on an engine.As the result in most cases engine components are changed to fit for further use.These factors make necessary to look for alternative strategies according to exploitation marine engines.
Another operating strategy is the exploitation of a technical condition which is free of mentioned disadvantages [4,5].This strategy method involves periodic implementation of diagnostic tests.This allows to determine a technical condition of an engine (the diagnosis).What is more it could be expected changes of a technical condition in a future (prediction).It allows that a part of engine construction could be replaced in the pre-damage moment [6,7].
One Fluctuations are repeated periodically and the period of four-stroke cycle engines is: where: n -the rotational speed of engine's crankshaft [s -1 ], N cyl -the engine cylinders number.
Fluctuations are the result from gas forces and mass moments of inertia.The Period of fluctuation rotation speed (four-stroke engine) is: ( 2 ) It results from working cycle disruption, which is connected with engine's damage.

Modelling of marine diesel engine's working cycle
Teams of scientists work on the problem of modeling processes in diesel engines in many countries in the world [8][9][10].Most of the research is focused on a design of marine diesel engines and its environmental performance [11][12][13].Many commercial programs are usually designed for this purpose.In most cases these programs are based on the finite element FEM and BEM boundary element method.Using them for diagnostic tests is often problematic.This is due to the fact that malfunctions typically are modeled as a change in the geometry of an engine structure.This approach is associated with the commercial models of a need to modify respective mesh elements.It is a very labor and time-consuming process.The source code of commercial programs are unavailable and users have only executable file.User does not have information about calculation methods and what simplifying assumptions have been applied.Therefore, it has been decided to develop a mathematical model of the physical processes in the marine four-stroke diesel engines.For this reason the model must fulfill several conditions, the most important of which are: • versatility, must make possible of modeling all four stroke engines which are operated in Polish Navy, • must be able to quickly and easily modify the structure parameters of selected structural engine components (eg.enable of changing the fuel delivery to each cylinder independently), • performing rapid calculations for efficient and damaged engines both.
The algorithm of research methodology are shown on Fig. 2.
The object of the research is the ZSE -part of a ship's power plant.On a basis of a generating set the physical model of processes occurring in a marine engine is designed [15].Based on the physical model is developed mathematical model of these processes [16].

Modeling fault conditions marine diesel engines
Marine engines is degraded differently in various states of operations (standby, running).This is a result of chemical and physical processes such as erosion, corrosion, friction or semi-dry friction, clogging, fatigue.The consequence of the engine's structure degradation is a change of condition and could be gradual or sudden.The dose calculation of fuel is delivered during the engine cycle which is based on a value of the excess air ratio .By the fact that the parameter is easily measurable by exhaust gas analyzer this is the best way to determine the dose of calculation fuel.
The changing of the fuel chemical composition (in the model) is not a result of engine's technical condition.However, it is decided on the possibility of modifying this parameter.The calorific value is changed by the fuel composition, which shows the relation:  The model is highly sensitive to a technical failures.Simulation of damage by reducing the fuel dose in one of cylinders caused about 30% indicated power drop from a damaged cylinder.Remaining cylinders increased the load by about 6%.The total power indicated by engine cylinders practically did not change due to a simulated technical state.In simulation, the change of flow resistance in an exhaust duct caused about 8% decrease in excess air factor.In addition, an increase back pressure caused an increase about 6%.The indicated power was not changed for this damage.
Currently the mathematical model is being verified by comparing the results obtained during experimental research on Sulzer type 6AL20/24 and Leyland type 6SW400 engines.
of priorities of research in The Institute of Ships Construction and Operation (IBiEO) Polish Naval Academy (AMW) is development of technical condition of engines based on non-invasive methods.Mentioned methods are based on energetic parameters diesel's marine engines or electric generators.One of the ZSE's energetic parameters is interfacial voltage of synchronous generator which is driven by engine.Analysis of recorded waveform will determine fluctuations of crankshaft engine (shaft generator) angular velocity.Fluctuations of crankshaft engine angular velocity are the result of many factors.The main ones being: • order of cylinder work (torques generated by gas forces), • mass reciprocating and rotary movement, • working cycle disruption as a result of structural engine's elements damage.
The state of condition changes from technical efficiency to the state of unfitness.The model takes into account the ability to simulate changes in the technical condition of marine diesel engines.This is implemented by modifying the technical structure of engine.Modifications may concern elements comprising all or individual cylinder sections of engines.The modifications concern the structure of engine design (geometric dimensions) as well as the parameters of fuel and air supply.Modeled can be: • change of fuel dose for each cylinder's sections (modeling of damage to the engine fuel supply), • change fuel's chemical composition (for the whole engine), • change timing injection (for each cylinder), • change active cross-section area of intake and exhaust valves (for each cylinders), • change of a flow resistance in exhaust channel (for whole cylinders), • a leak in a piston-rings and cylinder (TPC) (for each of cylinders), • change active cross-section area of injector holes (for each of cylinders).