## Best Practices for Modeling Pulley Networks

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

### Belt Direction

Belt direction is a pulley sign convention that is not constrained by physics or geometry. For a Belt Pulley block with Belt direction set to ```Ends move in opposite direction```, the velocities at port A and port B will have opposite signs that depend on the sign of the angular velocity, ω.

For a Belt Pulley block with Belt direction set to ```Ends move in same direction```, the velocities at port A and port B will have the same signs that depend on the sign of the angular velocity.

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 Rotational Elements library. Attribute some initial velocity to the inertia, as needed, to initiate motion in your pulley system.

You can also add mass to the tensioning device to aid with numerical initialization. If you are using the Rope block as a tensioning device, set Model mass to `On`.

### Belt Tension

Maintain belt contact by including Rope blocks in your pulley system. Include one fewer Rope blocks than the number of pulley pairs, at a minimum. For example, if there are five pulley pairs, include at least four Rope blocks. Use can confirm that the belts start and remain in tension by using the Simscape Results Explorer. Reversing the port connections may resolve this issue.

### Power Window System Pulley Mechanism

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

1. To open the model, at the MATLAB® command prompt, enter

`sdl_power_window`

The model contains the Mechanism subsystem, a masked pulley network subsystem. 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.

2. 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 lowers. 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

You need at least five Rope blocks to build this system. The Lift Plate acts as a tensioner for the Pulley 2 and Pulley 4 pulley pair. The system contains four additional Rope blocks. In the figure, you can see how these blocks are implemented in the system.

Each Rope block contains a spring and damper network separating the base port from the follower port.

3. 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 angular velocity, the Lift Plate raises the window. When the Cable Drum has a positive velocity, the Lift Plate lowers the window.

4. 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 +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 A 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.