Band Brake

Frictional brake with flexible band wrapped around rotating drum

Libraries:
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.

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

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

$T = (F_{T B} - F_{A}) \cdot r_{D} + μ_{v i s c} \cdot ω$

Where:

T is the braking torque.
F_TB is the tension force acting on the tense branch of the band.
F_A is the external brake actuation force.
r_D is the drum radius.
μ_visc is the viscous friction coefficient.
μ is the contact friction coefficient.
ϕ is the wrap angle.

Forces F_TB and F_A satisfy the relationship

$\frac{F_{T B}}{F_{A}} = e^{μ ϕ}$

Replacing the relationship in the braking torque formula eliminates force F_TB such that

$T = F_{A} (e^{μ ϕ} - 1) \cdot r_{D} + μ_{v i s c} \cdot ω$

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

$F_{A} = F_{i n} \cdot \tanh (\frac{4 ω}{ω_{t h r e s h o l d}})$

Where:

F_in is the force input signal.
ω_threshold is the angular velocity threshold.

Faults

To model a fault in the Band Brake block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

When you trigger a fault, the block applies the value of the Belt force when faulted parameter instead of the value at port F for the remainder of the simulation. When the value is 0, no braking occurs. When the value is relatively large, the brake is stuck.

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.

Limitations and Assumptions

The model does not account for actuator flow consumption.

Ports

Input

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F — Belt tensioning force
physical signal

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

Conserving

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S — Drum shaft rotation
rotational mechanical

Rotational conserving port associated with the rotating drum shaft.

H — Heat flow, in W
thermal

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

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Geometry

Drum radius — Contact surface radius
`150` `mm` (default) | positive scalar

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

Wrap angle — Contact angle
`270` `deg` (default) | positive scalar

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

Friction

Viscous friction coefficient — Viscous friction
`.01` `n*m/(rad/s)` (default) | nonegative scalar

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

Thermal port — Thermal model
`Omit` (default) | `Model`

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.

Temperature — Temperature
`[280, 300, 320]` `K` (default) | increasing vector

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.

Contact friction coefficient — Coulomb friction
`0.3` (default) | positive scalar

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.

Contact friction coefficient vector — Coulomb friction
`[.1, .05, .03]` (default) | increasing vector of positive values

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 threshold — Rotational velocity required for near steady-state contact friction
`0.01` `rad/s` (default) | positive scalar

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

Faults

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

Belt tension fault — Option to model a belt tension failure
`Add fault`

Whether to model a belt tension fault in the block. The fault replaces the value at port F with the value of the Belt tension when faulted parameter. To add a fault, click the Add fault hyperlink.

Belt tension when faulted — Faulted belt tension
`0` `N` (default) | positive scalar

Belt tension when a fault is triggered. When you trigger a fault, the block applies the value of the Belt tension when faulted parameter instead of the value at port F for the remainder of the simulation. When the value is 0, no braking occurs. When the value is relatively large, the brake is stuck.

Dependencies

To enable this parameter, enable faults for the block by clicking the Add fault hyperlink.

Thermal Port

Thermal mass — Resistance to temperature change
`50` `kJ/K` (default) | scalar

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

To enable this parameter, set Thermal Port to Model.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012b

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R2024a: Model faults with the Simscape faults interface

The Band Brake block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.

Band Brake

Description

Equations

Faults

Thermal Model

Limitations and Assumptions

Ports

Input

F — Belt tensioning force physical signal

Conserving

S — Drum shaft rotation rotational mechanical

H — Heat flow, in W thermal

Dependencies

Parameters

Geometry

Drum radius — Contact surface radius 150 mm (default) | positive scalar

Wrap angle — Contact angle 270 deg (default) | positive scalar

Friction

Viscous friction coefficient — Viscous friction .01 n*m/(rad/s) (default) | nonegative scalar

Thermal port — Thermal model Omit (default) | Model

Dependencies

Temperature — Temperature [280, 300, 320] K (default) | increasing vector

Dependencies

Contact friction coefficient — Coulomb friction 0.3 (default) | positive scalar

Dependencies

Contact friction coefficient vector — Coulomb friction [.1, .05, .03] (default) | increasing vector of positive values

Dependencies

Angular velocity threshold — Rotational velocity required for near steady-state contact friction 0.01 rad/s (default) | positive scalar

Faults

Belt tension fault — Option to model a belt tension failure Add fault

Belt tension when faulted — Faulted belt tension 0 N (default) | positive scalar

Dependencies

Thermal Port

Thermal mass — Resistance to temperature change 50 kJ/K (default) | scalar

Dependencies

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2024a: Model faults with the Simscape faults interface

See Also

Topics

F — Belt tensioning force
physical signal

S — Drum shaft rotation
rotational mechanical

H — Heat flow, in W
thermal

Drum radius — Contact surface radius
`150` `mm` (default) | positive scalar

Wrap angle — Contact angle
`270` `deg` (default) | positive scalar

Viscous friction coefficient — Viscous friction
`.01` `n*m/(rad/s)` (default) | nonegative scalar

Thermal port — Thermal model
`Omit` (default) | `Model`

Temperature — Temperature
`[280, 300, 320]` `K` (default) | increasing vector

Contact friction coefficient — Coulomb friction
`0.3` (default) | positive scalar

Contact friction coefficient vector — Coulomb friction
`[.1, .05, .03]` (default) | increasing vector of positive values

Angular velocity threshold — Rotational velocity required for near steady-state contact friction
`0.01` `rad/s` (default) | positive scalar

Belt tension fault — Option to model a belt tension failure
`Add fault`

Belt tension when faulted — Faulted belt tension
`0` `N` (default) | positive scalar

Thermal mass — Resistance to temperature change
`50` `kJ/K` (default) | scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.