4.4 Model Control & Back-Effects in Bond Graphs

4.4.1 Back-Effects in Bond Graph Simulation

Simulations using Bond Graph have the advantage of representing the bi-directional exchange of power. This means that power flowing upstream due to changes in the response of downstream items are automatically reflected in the model and can be visualized in the Response Simulation graph.

For example, if the Wheel Resistance of an item increases or decreases, the back-effects on the previous item (Planetary Gearbox) can be simulated by generating its Response Simulation graph.

Figure 27 shows two overlaid Response Simulation graphs for the Planetary Gearbox angular velocity: the dark red graph shows the initial response when the Resistance value of the Wheel Resistance component is set to 1.5 (settling near 0.7, marked "FAILURE ACTIVATION" at x=50); the light red graph shows a second response when the Resistance value of the Wheel Resistance component is decreased to 0.01 (settling near 0.732, with more pronounced oscillation). The change in behavior shown between graphs indicates that a decrease in Wheel Resistance creates more oscillations in the angular velocity output of the upstream component.

4.4.2 Modeling Control Connections for Bond Graph Simulation

Control connections are used to provide control over a target item from a source item or Bond junction. The use of a control connection causes the target item response to no longer be a single constant value but a variable which can be viewed from the simulation response viewer.

To create a control connection in the system model:

• Select Create New Control Connection icon (labeled ↓K)
• Drag the control connection from a source item output flow to the input flow of a target item
• Choose Connection Type, Control Element and Amplitude in the Properties viewer

Figure 28 illustrates the Planetary Gearbox Front providing feedback to the Differential in the form of a control connection (labeled <K/D>), overlaid on the Driveline Subsystem block diagram (Transmission 1-IR → Driveshaft 0-C → Differential 1-IR → Half Shaft Front/Rear 0-C → Planetary Gearbox Front/Rear 1-IR → Wheel Resistance Front/Rear 0-R → Wheel Front/Rear 1-I → OUT).

Figure 29 shows the Properties viewer for a control connection "Mechanical - rotational -> Mechanical - rotational":

• Connection Type: options are K, K/D (selected), K/X
• Control Element: Resistance
• Amplitude: 1.00

The properties viewer shows three types of control connection: K, K/D & K/X. The equations and descriptions for each control connection type are found in MADE Help (not reproduced in this guide).

After selecting a connection type, the user can select whether the control element which represents the Bond Element in the target item shall be affected by the control connection. The Amplitude field captures the parameter value defining the ability of an item to store and release energy. The Equations tab shows the equations used to represent the control connection.

Figure 30 shows an example Equations tab entry for a K/D control connection named "Planetary Gearbox Front <K/D> Resistance":

28.Amplitude = 28.Amplitude
28.State = Integral(6.Flow)
28.Transfer Function = 28.Amplitude * 28.State

Control connections are represented as dashed energy Bonds in the Bond Graph editor (Figure 31 shows the Vehicle System Bond Graph with a dashed <K/D> control Bond running from the Half Shaft Front branch's Bond junction 6 to control element 28 at the Planetary Gearbox Front / Differential connection point).

5 Conclusion

This modeling guide for Bond Graph Simulation has outlined the recommended approaches to create and analyze a functional model for a Driveline Subsystem. This guide emphasizes how Bond Graph Simulation can be used to model the functional behavior of a complex system.

Bond Graph Simulation is a useful tool for modeling power transmission systems, especially when different physical or energy domains are involved. Bond Graph Simulations can be used to generate simulation response graphs and Failure Propagation Tables to qualitatively analyze and troubleshoot a system model.

Creating models and running simulations in MADE require an extensive understanding of physical and mathematical relationships in a system, as well as knowledge of hardware and familiarity with the modeling process. The graphical interface, flexibility in model representation, model reusability, and real-time hardware-in-the-loop simulation allows for an approachable modeling process in MADE.