Belt Pulley. How get relative velocity?

Question

I'm trying to understand how belt pulley from Mathworks work. I have this simple sample:

In this case. I'm giving the velocity of a. And there is when appear my first question:

why the magnitude of velocity of b, is the same of a?

According to the theory of belt drive, the ratio between both velocities is this:

Va/Vb = 1 - (Ta - Tb)/EA

But the "Belt Pulley" description of Mathworks (http://es.mathworks.com/help/physmod/sdl/ref/beltpulley.html#zmw57dd0e1842), said that both will have the same magnitude but different direction.

Anyway, I could assume that they are not consider the elastic of the band, but I don't have any clue of how they get the angular velocity of the pulley to get then the relative velocity. At some point they need to know the elastic of the material for get the relative movement between the belt and the pulley.

Can anyone help me?

Answer 1

I think the answer to the first part of your question lies in the block assumptions:

Assumptions and Limitations

• The model does not account for compliance along the length of the belt.
• Both belt ends maintain adequate tension throughout the simulation.

To get the angular velocity of the pulley, use an Ideal Rotational Motion Sensor block. Connect the R port to the rotational free end of the pulley and the C port to a a Mechanical Rotational Reference block.

The motion between the belt and pulley is described by those equations (from the documentation page you mentioned in the question, where all the parameters are detailed):