Continuity of R and RS for Systems with/without Thermal Ports

Continuity of R and RS for Systems with/without Thermal Ports

We will now study some application examples of pure bond graph models with thermal effects. Only isolated systems are analyzed. In each system the power variables are highlighted, and the power balance is established. The expression of and if they exist, is also given.

The power sensors which are included in the sketch indicate the positive direction of the power at the system ports. Their locations (inside or outside the studied system) do not affect the results since the power sensor only computes the power value at a given point.

N	Sketch	Power variables in the studied system	Power balance and variables expressions
1
2
3
4
5
6			with percpowithe percentage of total power losses of geari transmitted to thermal port Plostithe total power losses of geari

In this section we will focus on examples based on the Electrical Basics library (EB_lib) to check the consistency between a Bond-Graph model and a non Bond-Graph model. In the following table, example 1 is the reference. It is a Bond-Graph model. Examples 2, 3 and 4 are similar to example 1 but are non Bond-Graph models since they include thermal components.

Bar charts and plots

Example N	1: reference	2: thermal port	3: capacity	4: capacity + flux
Sketch
Power variables
Power bar chart	1: reference	2: thermal port
3: capacity	4: capacity + flux
Power plot	1: reference	2: thermal port
3: capacity	4: capacity + flux
Energy bar chart	1: reference	2: thermal port
3: capacity	4: capacity + flux
Energy plot	1: reference	2: thermal port
3: capacity	4: capacity + flux

In the next section a Transmission (TR_lib) model will be studied. In the first model (example 5) the parameters of the two gears will be defined so that all the dissipated energy goes to the thermal ports. In the second case (example 6) each gear will transmit half of the dissipated energy through the thermal port and the remaining half will be transmitted to the outside. In the third case (example 7), all the dissipated energy will be transmitted to the outside. It is worth mentioning that due to the parameters which were chosen, the C and I variables will be equal to 0.

In most submodels (see the previous EB examples), if a component dissipates power and includes a thermal port, this component includes an RS variable and no R variable. This is due to the fact that all the dissipated power is transferred through the heat port. However, in particular submodels such as the two submodels used in the examples of this section (TRTHGT01B and TRTHGT01C), one part of the heat is transmitted to the environment and the other part is retained inside the submodel.

According to the power and energy framework, the total dissipated power is equal to the dissipated power kept inside the system (RS) plus the power given to the environment (R). The following examples will show the continuity between R and RS variables. For this example:

Example N	5: all the dissipated power is transmitted through the thermal port	6: 50% of the dissipated power is transmitted through the thermal port	7: 0 % of the dissipated power is transmitted through the thermal port
Sketch
Power variables
Power bar chart	5: all the dissipated power is transmitted through the thermal port
6: 50% of the dissipated power is transmitted through the thermal port
7: 0 % of the dissipated power is transmitted through the thermal port
Power plot	5: all the dissipated power is transmitted through the thermal port
6: 50% of the dissipated power is transmitted through the thermal port
7: 0 % of the dissipated power is transmitted through the thermal port
Energy bar chart	5: all the dissipated power is transmitted through the thermal port
6: 50% of the dissipated power is transmitted through the thermal port
7: 0 % of the dissipated power is transmitted through the thermal port
Energy plot	5: all the dissipated power is transmitted through the thermal port
6: 50% of the dissipated power is transmitted through the thermal port
7: 0 % of the dissipated power is transmitted through the thermal port
value for each gear	5: all the dissipated power is transmitted through the thermal port
6: 50% of the dissipated power is transmitted through the thermal port
7: 0 % of the dissipated power is transmitted through the thermal port