# Band Brake

Frictional brake with flexible band wrapped around rotating drum with triggered faults

**Library:**Simscape / Driveline / Brakes & Detents / Rotational

## Description

The Band Brake block represents a frictional brake with a flexible band that wraps around the periphery of a rotating drum to produce a braking action. A positive actuating force causes the band to tighten around the rotating drum and it places the friction surfaces in contact. Viscous and contact friction between the surfaces of the drum and the flexible band causes the rotating drum to decelerate.

You can model the effects of heat flow and temperature change for the block by using
port **H**, an optional thermal conserving port.

You can also enable faulting. When faulting occurs, the belt will exert a
user-specified force. Faults can occur at a specified time or due to an external trigger
at port **T**.

Band brakes provide high braking torque at the cost of reduced braking precision in applications that include winch drums, chainsaws, go-karts, and mini-bikes.

### Equations

The model employs a simple parameterization with readily accessible brake geometry and friction parameters.

The braking torque as a function of the external brake actuation force that tightens the belt is

$$T=\left({F}_{TB}-{F}_{A}\right)\cdot {r}_{D}+{\mu}_{visc}\cdot \omega $$

Where:

*T*is the braking torque.*F*is the force acting on the tense branch of the band._{TB}*F*is the external brake actuation force._{A}*r*is the drum radius._{D}*μ*is the viscous friction coefficient._{visc}*μ*is the contact friction coefficient.*ϕ*is the wrap angle.

Forces *F _{TB}* and

*F*satisfy the relationship

_{A}$$\frac{{F}_{TB}}{{F}_{A}}={e}^{\mu \varphi}$$

Replacing the relationship in the braking torque formula eliminates force
*F _{TB}* such that

$$T={F}_{A}\left({e}^{\mu \varphi}-1\right)\cdot {r}_{D}+{\mu}_{visc}\cdot \omega $$

To avoid discontinuity at zero relative velocity, the model defines the actuation
force, *F _{S}*, as a hyperbolic function

$${F}_{A}={F}_{in}\cdot \mathrm{tanh}\left(\frac{4\omega}{{\omega}_{threshold}}\right)$$

Where:

*F*is the force input signal._{in}*ω*is the angular velocity threshold._{threshold}

### Faulty Behavior

When faults are enabled, a belt force is applied in response to one or both of these triggers:

Simulation time — Faulting occurs at a specified time.

Simulation behavior — Faulting occurs in response to an external trigger. This exposes port

**T**.

If a fault trigger occurs, the input force is replaced by the **Belt force
when faulted** value for the remainder of the simulation. A value of
`0`

implies that no braking will occur. A relatively large
value implies that the brake is stuck.

You can set the block to issue a fault report as a warning or error message in
the Simulink Diagnostic Viewer with the **Reporting when fault
occurs** parameter.

### Thermal Model

You can model the effects of heat flow and temperature change by exposing the
optional thermal port. To expose the port, in the **Friction**
settings, set the **Thermal Port** parameter to
`Model`

. Exposing the thermal port also exposes these
related settings:

**Friction**>**Temperature****Friction**>**Contact friction coefficient vector****Thermal Port**>**Thermal mass****Variables**>**Temperature**

### Variables

Use the **Variables** settings to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

**Dependencies**

Variable settings are visible only when, in the **Friction** settings, the
**Thermal port** parameter is set to
`Model`

.

## Limitations and Assumptions

The model does not account for actuator flow consumption.

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2012b**