Best Practices for Modeling Pulley Networks

Like real-world pulleys, Simscape™ Driveline™ pulley blocks rely on belt tension and inertia for motion. To prevent initialization errors and to obtain the desired power transmission from your pulley system, apply these modeling methods.

Belt Direction

Pulley belt direction is not a geometric or physical constraint; it is purely a sign convention. For example, for a Belt Pulley block with Belt direction set to Ends move in opposite direction, the sign convention is such that a positive rotation in port S tends to give a negative translation for port A and a positive translation for port B. According to this convention, the angular velocity is the same for the two belt pulleys in the figure.

For a Belt Pulley block with Belt direction set to Ends move in same direction, the sign convention is such that a positive rotation in S tends to give a positive translation for port A and a positive translation for port B.

The Ends move in same direction option is applicable to most pulley systems. The Ends move in same direction option allows you to model a simplified representation of a complex block-and-tackle system with belt ends that move in the same direction.

Inertia

To facilitate motion, include inertia in the pulley system. You can include inertia in a pulley block by specifying a nonzero value for the Inertia parameter in the block configuration settings. Another way to include inertia is to add a downstream inertia block from the Simscape Driveline Inertias and Loads library or from the Simscape Rotational Elements library. Attribute some initial velocity to the inertia, as needed, to initiate motion in your pulley system.

Belt Tension

Maintain belt contact by including tensioners in your pulley system. Include no fewer than the number of pulley pairs less one. For example, if there are five pulley pairs, include at least four tensioners. You can build the tensioners using spring and damper blocks.

Power Window System Pulley Mechanism

The Simscape Driveline Power Window System example contains a pulley network that includes tensioners and inertia and follows recommended belt-direction practices.

To open the model, at the MATLAB^®command prompt, enter
```
sdl_power_window
```
The model contains the Mechanism subsystem, a masked subsystem that contains a pulley network. The DC Motor subsystem and a Worm Gear block work together to initiate motion in the pulley system. The system also contains an Inertia block.
To look inside the mask of the Mechanism subsystem, click the arrow in the lower-left corner of the block.

The arrows show how the four Belt Pulley blocks rotate in response to the rotation of the Cable Drum block. If the drum rotates in the opposite direction, the pulley directions reverse, and the Lift Plate is lowered. There are six pulley pairs:
- Cable Drum and Pulley 1
- Pulley 1 and Pulley 2
- Pulley 2 and Pulley 3
- Pulley 3 and Pulley 4
- Pulley 4 and Cable Drum
- Pulley 2 and Pulley 4
Therefore, it is recommended that the system includes at least five tensioners. The Lift Plate acts as a tensioner for the Pulley 2 and Pulley 4 pulley pair. The system contains four additional tensioners. Open one of the tensioner subsystems.

Each tensioner contains a spring and damper network that is parameterized with the spring and damping coefficients of the cable.
Run the simulation and plot the results by clicking the Plot motor torque link in the model canvas. When the Cable Drum has a negative velocity, the Lift Plate tends to go up, as does the window. When the Cable Drum has a positive velocity, both the Lift Plate and window tend to go down.
Open the Results Explorer by clicking the Explore simulation results link in the model canvas. On the Results Explorer toolbar, click the settings button and, for the Plot signals parameter, select Separate. Use Ctrl+click to open plots for:
- Mechanism > Cable Drum > A > v
- Pulley 1 > A > v
- Pulley 1 > B > v

As expected, the velocity of the drum belt end at port B matches the velocity of the Pulley 1 belt end at port B and is the opposite of the velocity of the Pulley 1 belt end at port A.

Documentation