The notation above tells us that the direction of which positive power flows, is from A to B. Input and output of system A is flow and effort, respectively. For system B, effort is input while flow is output.
The simultaneously representation of physical and computational structure is a unique and very powerful property of the bond graph which other representations like the linear graph or the block diagram do not have.
3. PROPULSION SYSTEM
Figure 1 shows a schematic drawing of an example propulsion system containing a clutch so the propeller can be disconnected from the main engine.
The most common type of clutch used in ship propulsion systems is what is known as frictional plate clutch, employing one or more plates as the operating members. When the mating frictional surfaces, attached to the driving member are brought into contact with those attached to the driven member, frictional forces are created because of the normal pressure between the elements. These frictional forces allow torque to be transmitted from one member to the other and enable a load on the driven shaft to be accelerated up to the speed of the driving member. The mating surface is brought in contact by hydraulic or pneumatic actuation, which admits oil or air to a cylinder.
In performing the clutching operation, large transient loads may occur in the shafting system. If these transient loads exceed the limits for which the system is designed, failures or breakdowns may occur. It is therefore, of interest to be able to provide an explicit evaluation of the performance at the design stage in order to ensure that the system will behave as intended and that the transient loading will be at a satisfactory level. This means that the system must be designed based on a dynamic transient analysis. In order to perform such an analysis, computer simulation on a system model is the only answer.
The system in question is not large in scale, but rather complicated to model in that it involves a clutch which changes the system structure during operation, and it contains gears which means dependent system elements. It will be shown in the following that the bond graph method is an effective answer to these problems.
Fig. 1. Example propulsion system.
4. NUMERICAL MODEL
The creation of a mathematical model of a system is central to the concept of computer simulation. It is important to note that the abstraction level of the bond graph language is essentially different from that of the mathematical representation. This allows us to keep a clear distinction between the physical level and the computational level, In what follows the system illustrated in Figure 1, is modelled using the bond graph methodology in that we will first construct the graph and from it derive the state equations in an algorithmic manner.
The main components except the clutch are the same ones that marine engineers are used to when performing steady-state torsional vibration analysis. In our model the engine, generator, gear wheels and propeller are modelled as lumped inertias. System stiffness is concentrated to the two flexible couplings and propeller shaft.
Before starting the modelling exercise, it is important to define the objectives of the study where the model is to be used. The model presented here is to be used for the study of transient loading in the system due to closing of the clutch. The bond graph model of the example system is shown in Figure 2.
