Band Brake

Friction brake with a flexible belt wound on a rotating drum.

band brake

Description

The Band Brake unit is a friction brake with a flexible band that wraps around the periphery of a rotating drum to create a braking effect. Positive drive force causes the band to tighten around the rotating drum and brings the friction surfaces into contact. Viscous and contact friction between the surfaces of the drum and the flexible belt causes the rotating drum to slow down.

You can simulate the effects of heat flow and block temperature changes with the H port, an optional heat retention port.

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

Equations

The block uses a simple parameterization with simple brake geometry and friction parameters.

band brake 1

The braking torque as a function of the force of the external brake actuator, which tightens the belt, is:

where:

- braking torque;
- reaction force of the support in which the belt is fixed;
- force of the external braking drive;
- drum radius;
- viscous friction coefficient;
- coefficient of contact friction;
- girth angle.

The forces and satisfy the relationship:

Replacing the relationship in the brake torque formula eliminates the force so that:

To avoid discontinuities when the friction direction changes abruptly, when the relative velocity changes its sign, the model defines the resulting external braking force , as the following hyperbolic function:

Where:

- belt tension force input signal;
- angular velocity threshold.

Thermal model

You can model the effects of heat flow and temperature change by adding an optional thermal port. To use this port, select the Thermal Port checkbox.

Limitations and assumptions

The model does not account for the flow rate consumed by the actuator.

Ports

Input

# F — belt tension force
scalar

Details

An input physical signal associated with an external tension force applied to a belt.

Data types	`Float64`.
Complex numbers support	No

Conserving

# S — drum shaft
`rotational mechanics

Details

A non-directional port associated with the shaft of a rotating drum.

Program usage name

shaft_flange

# H — heat flux
`heat

Details

A non-directional port associated with heat flow.

The heat port allows modelling the heat flow between the unit and the connected network.

Dependencies

To use this port, select the Thermal Port check box.

Program usage name

thermal_port

Parameters

Geometry

# Drum radius — contact surface radius
m | cm | ft | in | km | mi | mm | um | yd

Details

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

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`150.0 mm`
Program usage name	`drum_radius`
Evaluatable	Yes

# Wrap angle — girth angle
deg | rad | rev | mrad

Details

The girth angle between the flexible belt and the rotating drum. The value must be greater than zero.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`270.0 deg`
Program usage name	`phi_wrap`
Evaluatable	Yes

Friction

# Viscous friction coefficient — viscous friction
N*m*s/rad | ft*lbf*s/rad

Details

Coefficient of viscous friction at the belt/drum contact surface. The value must be greater than or equal to zero.

Units	`Nms/rad` \| `ftlbfs/rad`
Default value	`0.01 Nms/rad`
Program usage name	`viscous_coefficient`
Evaluatable	Yes

# Thermal Port — thermal model

Details

Select this checkbox to use the model for heat flow and temperature changes.

Dependencies

If this option is checked, the H heat port and associated parameters will be displayed.

Default value	`false (switched off)`
Program usage name	`has_thermal_port`
Evaluatable	No

# Contact friction coefficient — Coulomb friction

Details

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

Dependencies

This parameter is available if the Thermal Port parameter is unchecked.

Default value	`0.3`
Program usage name	`friction_coefficient`
Evaluatable	Yes

Details

An array of temperatures used to construct a 1-D interpolation table of temperature and efficiency correspondence. The array values should be monotonically increasing.

Dependencies

To use this parameter, select the Thermal Port checkbox.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[280.0, 300.0, 320.0] K`
Program usage name	`temperature_vector`
Evaluatable	Yes

# Contact friction coefficient vector — Coulomb friction

Details

Coulomb friction coefficient on the belt-drum contact surface, given as a vector with the following constraints (conditions):

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 are monotonically increasing;
Each value must be greater than zero.

Dependencies

To use this parameter, select the check box for Thermal Port.

Default value	`[0.1, 0.05, 0.03]`
Program usage name	`friction_coefficient_vector`
Evaluatable	Yes

# Angular velocity threshold — rotational speed required for almost stationary contact friction
rpm | deg/s | rad/s

Details

The angular velocity at which the coefficient of contact friction almost reaches its stationary value. The value must be greater than zero.

Units	`rpm` \| `deg/s` \| `rad/s`
Default value	`0.01 rad/s`
Program usage name	`w_threshold`
Evaluatable	Yes

Thermal Port

# Thermal mass — temperature resistance
J/K | kJ/K

Details

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

Dependencies

To use this parameter, select the Thermal Port checkbox.

Units	`J/K` \| `kJ/K`
Default value	`50.0 kJ/K`
Program usage name	`thermal_mass`
Evaluatable	Yes

Initial Targets

Temperature

Priority - temperature priority
High (by default) | Low| None

Details

Temperature priority set as High, Low or None.

Value - temperature value
300 K (by default) | scalar

Details

Temperature value specified as a real scalar.

Data types

Float64.