Belt Drive

Power transmission system with taut belt connecting two pulleys

Library:
Simscape / Driveline / Couplings & Drives

Description

The Belt Drive block represents a pair of pulleys connected with a flexible ideal, flat, or V-shaped belt. The ideal belt does not slip relative to the pulley surfaces.

The model accounts for friction between the flexible belt and the pulley periphery. If the friction force is not sufficient to drive the load, the model allows slip. The relationship between the tensions in the tight and loose branches conforms to the Euler equation. The model accounts for centrifugal loading in the flexible belt, pulley inertia, and bearing friction.

The Belt Drive block is a structural component based on the Simscape™ Driveline™ Belt Pulley block and Simscape Translational Spring and Translational Damper blocks. The Translational Spring and Translational Damper blocks model the compliance of the belt. For the equations governing the contact dynamics between the belt and the pulley, see the Belt Pulley block. The figure shows the block diagram for the Belt Drive block.

Equations

The diagrams show the open and crossed belt drive configurations. In the open belt configuration, both pulleys tend to rotate in the same direction and the larger pulley has a larger belt wrap angle. In the crossed belt configuration, the pulleys tend to rotate in opposite directions and have the same wrap angle.

Belt Drive Diagrams

In the open configuration, the wrap angle of the belt around each pulley is given by the expressions:

$\begin{array}{l} θ_{A} = π + 2 * \sin^{- 1} \frac{R_{A} - R_{B}}{C}, \\ θ_{B} = π - 2 * \sin^{- 1} \frac{R_{A} - R_{B}}{C} \end{array}$

where:

θ_A is the wrap angle of pulley A.
θ_B is the wrap angle of pulley B.
R_A is the effective radius of pulley A.
R_B is the effective radius of pulley B.
C is the distance between the centers of pulleys A and B.

The diagram shows the open-configuration wrap angles and parameters.

In the crossed configuration, the two wrap angles are equal and the wrap angle of the belt around each pulley is

$θ_{A} = θ_{B} = π + 2 * \sin^{- 1} \frac{R_{A} + R_{B}}{C}$

The diagram shows the closed-configuration wrap angles and parameters.

Assumptions and Limitations

The pulleys do not translate.
The friction coefficient and friction velocity threshold between the belt and each of the pulleys is the same.

Ports

Conserving

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`A` — Pulley shaft A angular velocity
mechanical rotational

Rotational conserving port associated with the shaft of pulley A.

`B` — Pulley shaft B angular velocity
mechanical rotational

Rotational conserving port associated with the shaft of pulley B.

Parameters

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Belt

`Drive type` — Belt drive configuration
`Open belt` (default) | `Crossed belt`

Belt drive configuration. For more information, see Belt Drive Diagrams.

`Belt type` — Belt model
`Ideal - No slip` (default) | `Flat belt` | `V-belt`

Belt model:

Ideal - No slip — Model an ideal belt, which does not slip relative to the pulley.
Flat belt — Model a belt with a rectangular cross-section.
V-belt— Model a belt with a V-shaped cross-section.

Dependencies

This parameter affects the visibility of related belt parameters and the Contact settings.

`Compliance` — Compliance model
`No compliance - Suitable for HIL simulation` (default) | `Specify stiffness and damping`

Compliance model.

No compliance - Suitable for HIL simulation — Model a noncompliant belt, which does not yield elastically when subjected to a force. To prioritize performance, select this model.
Specify stiffness and damping — Model a compliant belt, which does yield elastically when subjected to a force. To prioritize fidelity, select this model.

Dependencies

This parameter is visible only if Belt type is set to Ideal - No slip. This parameter affects the visibility of related belt parameters.

`V-belt sheave angle` — Sheave angle
`30` `deg` (default) | nonneagative scalar

Sheave angle of the V-belt.

Dependencies

This parameter is visible only when Belt type is set to V-belt.

`Number of V-belts` — Number of belts
`1` (default) | positive scalar integer

Number of V-belts.

Noninteger values are rounded to the nearest integer. Increasing the number of belts increases the friction force, effective mass per unit length, and maximum allowable tension.

Dependencies

This parameter is visible only when Belt type is set to V-belt.

`Centrifugal force` — Centrifugal force model
`Do not model centrifugal force - Suitable for HIL simulation` (default) | `Model centrifugal force`

Centrifugal force model. If included, centrifugal force saturates to approximately 90 percent of the value of the force on each belt end.

Dependencies

This parameter is visible only if Belt type is set to Flat belt or V-belt. If this parameter is set to Model centrifugal force, the Belt mass per unit length parameter is exposed.

`Belt mass per unit length` — Mass per unit length
`0.6` `kg/m` (default) | scalar

Centrifugal force contribution in terms of linear density expressed as mass per unit length.

Dependencies

Selecting Model centrifugal force for the Centrifugal force parameter exposes this parameter.