Type of coupling

The type of coupling defines the mathematical relation between two physical models.

Weak coupling

Proper dynamics of each model are very different from each other. Model reduction of one model is achievable from the point of view of the other model, either by static characterization or by replacing outputs by scheduled values.

• Cascaded systems There is no coupling at all; output of one model is the input of another, with no feedback loop. Example: a model of hydraulic brake circuit is strictly cascaded with a longitudinal model of vehicle dynamics.

• Model reduction The original model is reduced before interfacing with another model. The resulting system couples one model with a reduced one, without altering the whole dynamics. Static coupling: this is a way to reduce a model, by characterizing it statically, and building an equivalent map model which is used directly in another model. Example: static characterization of an internal combustion engine model to be used in a global vehicle performance and fuel consumption simulation.

• Relaxed coupling Dynamics of interfaced models are mildly decoupled, such that it is possible to cascade model on a short horizon, i.e. perform simulation of first model, provide the outputs of first model to second model inputs, perform simulation of second model, provide outputs of second model to first model inputs, and repeat cycle. Example: a thermal model of heat diffusion in a disk clutch can be coupled by relaxation with a mechanical model of the clutch system. Dissipated heat computed by mechanical model over a cycle is the source term of the thermal model. Temperature field on the disk alters the friction coefficient, which is a parametric input of mechanical model.

Strong coupling

The dynamics of interfaced models have the same order of magnitude, and thus are impossible to decouple. The most important dynamics of the whole system lie in the coupling: one model cannot be reduced without altering the global dynamics of the whole system.

Example: injector nozzle model coupling a mechanical model of needle with a hydrodynamics model of fuel flow through the nozzle. Squeezing effect for small lift values forbids decoupling.