How can I implement the magic formula by Pacejka in Simscape Multibody between a wheel modeled as a disk and the ground modeled as a prismatic piece?

How can I implement the magic formula by Pacejka in Simscape Multibody between a wheel modeled as a disk and the ground modeled as a prismatic piece?

How can I ensure the contact between the disk and the plane, that is, between the wheel and the ground, and where and how to implement the magic formula? I have no idea, I'm really stuck.

[Lorenzo]

Hello Mathlouthi,

Are you aware of the Magic Formula Tire Force and Torque? It is part of the Simscape Multibody library and it seems to me that it implements exactly what you need.

Best,

Lorenzo

[Mathlouthi Malek]

Hi Lorenzo,

I have my model of a rolling wheel without slipping, and I want to implement it into my model,

[Mathlouthi Malek]

Here's another simple model that I want to implement using the Pacejka magic formula.

Answer 1

[Steve Miller]

You can look at File Exchange submission Spatial Contact Force Examples Simscape Multibody to see an example of how to add a custom force law model to a Simscape Mutlibody model. You can use the Spatial Contact Force block to obtain quantities at the point of contact, such as positions and velocities, use those quantities to calculate the forces and torques according to the Magic Formula, and then apply those calculated forces to the block.

This is likely to be quite challenging. An example of the full implementation is shown on the File Exchange here: MFeval

We provide in our libraries a Magic Formula Tire Force and Torque block that does this for you, and it handles both longitudinal and lateral dynamics. For purely longitudinal studies, you could use the tire blocks in Simscape Driveline, such as Tire (Magic Formula)

--Steve