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# Band Brake

Frictional brake with flexible band wrapped around rotating drum

## Library

Brakes & Detents/Rotational

## Description

The 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 drum and the flexible band surfaces cause the rotating drum to decelerate. 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. The model employs a simple parameterization with readily accessible brake geometry and friction parameters.

The following formula provides the braking torque as a function of the external brake actuation force that tightens the belt.

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

In the formula, the parameters have the following meaning:

ParameterDescription
TBraking torque
FTBForce acting on the tense branch of the band
FAExternal brake actuation force
μviscViscous friction coefficient
μContact friction coefficient
ϕWrap 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:

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

To avoid discontinuity at zero relative velocity, the model defines the actuation force FS as a hyperbolic function:

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

In the previous formula, the parameters represent the following quantities:

ParameterDescription
FinForce input signal
ωthresholdAngular velocity threshold

Connection F is a physical signal port that represents the external tensioning force applied on the belt. Connection S is a conserving rotational port that represents the rotating drum shaft.

## Assumptions and Limitations

• The model does not account for actuator flow consumption

## Dialog Box and Parameters

### Geometry

Radius of the drum contact surface. The parameter must be greater than zero. The default value is 150 mm.

Wrap angle

Contact angle between the flexible belt and the rotating drum. The parameter must be greater than zero. The default value is 130 mm.

### Friction

Viscous friction coefficient

Value of the viscous friction coefficient at the belt-drum contact surface. The parameter must be greater than or equal to zero. The default value is .01 N*m/(rad/s).

Contact friction coefficient

Value of the Coulomb friction coefficient at the belt-drum contact surface. The parameter must be greater than zero. The default value is 0.3.

Angular velocity threshold

Angular velocity at which the friction coefficient at the belt-drum contact surface practically reaches its steady-state value. The parameter must be greater than zero. The default value is 0.01 rad/s.

## Ports

PortDescription

F

Physical signal port that represents the belt tensioning force

S

Conserving rotational port that represents the rotating drum shaft