# 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.

• FTB is the force acting on the tense branch of the band.

• FA is the external brake actuation force.

• rD is the drum radius.

• μvisc is the viscous friction coefficient.

• μ is the contact friction coefficient.

• ϕ is the wrap angle.

Forces FTB and FA satisfy the relationship

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

Replacing the relationship in the braking torque formula eliminates force FTB 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, FS, as a hyperbolic function

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

Where:

• Fin is the force input signal.

• ωthreshold is the angular velocity threshold.

### Faults

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

expand all

Physical signal inport associated with the external tensioning force that is applied to the belt.

Physical signal port for an external fault trigger. Triggering occurs when the value is greater than 0.5. There is no unit associated with the trigger value.

#### Dependencies

This port is visible when Enable faults is set to `On` and Enable external fault trigger is set to `On`.

### Conserving

expand all

Rotational conserving port associated with the rotating drum shaft.

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only when, in the Friction settings, the Thermal Port parameter is set to `Model`.

Exposing this port makes related settings visible.

## Parameters

expand all

### Geometry

Radius of the drum contact surface. The parameter must be greater than zero.

Contact angle between the flexible belt and the rotating drum. The parameter must be greater than zero.

### Friction

Viscous friction coefficient at the belt-drum contact surface. The parameter must be greater than or equal to zero.

Model for heat flow and temperature change:

• `Omit` — Neglect thermal dynamics.

• `Model` — Include thermal dynamics.

#### Dependencies

When this parameter is set to `Model`, the thermal port and related parameters and variables are visible.

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase left to right.

#### Dependencies

This parameter is only visible when the Thermal Port parameter is set to `Model`.

Coulomb friction coefficient at the belt-drum contact surface. The value must be greater than zero.

#### Dependencies

This parameter is only visible when the Thermal Port parameter is set to `Omit`.

Coulomb friction coefficient at the belt-drum contact surface, such that:

• The number of elements in the vector must be the same as the number of elements in the specified vector for the Temperature parameter

• The values increase left to right.

• Each value must be greater than zero.

#### Dependencies

This parameter is only visible when the Thermal Port parameter is set to `Model`.

Angular velocity at which the contact friction coefficient practically reaches its steady-state value. The value must be greater than zero.

### Faults

Enable externally or temporally triggered faults. When faulting occurs, the brake belt force normally received at port F will be set to the value specified in the Belt force when faulted parameter.

Set faulted belt force. When faulting occurs, the brake belt force normally received at port F will be set to the value specified in the Belt force when faulted parameter. A value of `0` implies that braking does not occur. A relatively large value implies that the brake is stuck.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables port T. A physical signal at port T that is greater than `0.5` triggers faulting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables fault triggering at a specified time. When the Simulation time for fault event is reached, the brake belt force normally received at port F will be set to the value specified in the Belt force when faulted parameter.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

When the Simulation time for fault event is reached, the brake belt force normally received at port F will be set to the value specified in the Belt force when faulted parameter.

#### Dependencies

To enable this parameter, set Enable faults to `On` and Enable temporal fault trigger to `On`.

Reporting preference for the fault condition. When reporting is set to `Warning` or `Error`, a message is displayed in the Simulink Diagnostic Viewer. When `Error` is selected, the simulation will stop if faulting occurs.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

### Thermal Port

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

#### Dependencies

This parameter is only visible when, in the Friction settings, the Thermal Port parameter is set to `Model`.

## Version History

Introduced in R2012b