Coupled Clutches

By coupling clutches together, a variable structure drivetrain can be achieved. With different clutches engaged at different times, torque is supplied to different parts of the system. In the notebook accompanying the model, the system is analyzed using built-in templates. These simplify many of the model analytics tasks that can be performed on SystemModeler models in Mathematica.

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The Model

The model consists of a series of coupled inertia components separated by clutches between them. When a clutch is engaged, friction will be present between two adjacent inertia components, causing them to transfer momentum to each other. The first and the last inertia components are damped by rotational dampers, and a constant torque is applied to the first inertia. From left to right, the first two clutches are timed so that they disengage after 15 seconds and engage after 5 seconds, respectively. The third clutch can be controlled by user input. On the top level, that user input is also connected to a timer, engaging the clutch after 10 seconds.
The inertias are separated by clutches that can be engaged or disengaged to vary the structure of the drivetrain.

Simulation

By simulating the model, the angular velocities of the inertias over time can be studied. The effect of engaging the different clutches can be seen in the plot below.
After 5 seconds, the second clutch from the left is engaged, followed by the third after 10 seconds. After 15 seconds, the first clutch is disengaged.

Analysis

Several simulation and model analytics templates exist in SystemModeler that can quickly set up different procedures. Some of the simpler ones include changing parameters and initial values and sweeping different parameter values. More advanced templates include real-time simulation templates. An input, such as the force applied on the last clutch in the model above, can be changed in real time using one of the templates.
Real-time simulation of the system. The slider below the plot allows the force on the last clutch to be controlled in real time.

Real-Time Simulation

Quickly set up real-time simulations of your system!

By applying a sinusoidal function to the last clutch, a pattern emerges that can be studied using Fourier analysis. A template is built in that guides you through the steps necessary to create a Fourier analysis of the system response.
Fourier analysis applied on the acceleration signal of the last inertia when the final clutch is applied using a sinusoidal force.