Disc Brake

Frictional brake with pressure-applying cylinder and pads

Libraries:
Simscape / Driveline / Brakes & Detents / Rotational

Description

The Disc Brake block represents a brake arranged as a cylinder applying pressure to one or more pads that can contact the shaft rotor. Pressure from the cylinder causes the pads to exert friction torque on the shaft. The friction torque resists shaft rotation.

Disc Brake Model

This figure shows the side and front views of a disc brake.

A disc brake converts brake cylinder pressure from the brake cylinder into force. The disc brake applies the force at the brake pad mean radius.

The equation that the block uses to calculate brake torque, depends on the wheel speed, Ω, such that when $Ω \neq 0$ ,

$T = \frac{μ_{k} P π D_{b}^{2} R_{m} N}{4} .$

However when $Ω = 0,$ the torque applied by the brake is equal to the torque that is applied externally for wheel rotation. The maximum value of the torque that the brake can apply when $Ω = 0,$ is

$T = \frac{μ_{s} P π D_{b}^{2} R_{m} N}{4} .$

In both cases, $R m = \frac{R o + R i}{2}$ .

Where:

T is the brake torque.
P is the applied brake pressure.
Ω is the wheel speed.
N is the number of brake pads in disc brake assembly.
μ_s is the disc pad-rotor coefficient of static friction.
μ_k is the disc pad-rotor coefficient of kinetic friction.
D_b is the brake actuator bore diameter.
R_m is the mean radius of brake pad force application on brake rotor.
R_o is the outer radius of brake pad.
R_i is the inner radius of brake pad.

The block default models a dry brake. You can model fluid friction in a wet brake by setting the Viscous friction coefficient, k_v, to a nonzero value. The torque on the wheel in a wet brake system is:

$T_{w e t} = T + k_{v} Ω .$

Faults

To model a fault in the Disc 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 Brake pressure when faulted parameter instead of the value at port P 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. Exposing the port also exposes or changes the default value for these related settings, parameters, and variables:

Friction > Temperature
Friction > Static friction coefficient vector
Friction > Coulomb friction coefficient vector
Thermal Port > Thermal mass
Variables > Temperature

Ports

Input

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P — Cylinder pressure
physical signal

Physical signal port associated with cylinder pressure, in bars.

Conserving

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S — Shaft
rotational mechanical

Rotational mechanical conserving port associated with the shaft.

H — Heat
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 parameters and variables visible.

Parameters

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Geometry

Mean pad radius — Pad radius
`150` `mm` (default) | positive scalar

Mean radius of the friction pads.

Cylinder bore — Bore diameter
`10` `mm` (default) | positive scalar

Diameter of the piston.

Number of brake pads — Pad quantity
`2` (default) | positive scalar integer

Number of friction pads.

Friction

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 parameter 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.

Static friction coefficient — Static friction
`0.9` (default) | scalar

Coefficient of static friction. The value that you specify for this parameter must be greater than the value that you specify for the Coulomb friction coefficient parameter.

Dependencies

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

Static friction coefficient vector — Static friction
`[.9, .8, .7]` | vector

Coefficient of static friction, 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 must be greater than the corresponding value that you specify for the Coulomb friction coefficient vector parameter.

Dependencies

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

Coulomb friction coefficient — Contact friction
`0.7` (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.

Coulomb friction coefficient vector — Contact friction
`[.8, .7, .6]` (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.

Breakaway friction velocity — Friction threshold
`0.1` `rad/s` (default) | scalar

Angular speed at which friction switches from static to kinetic.

Viscous friction coefficient — Viscous friction
`0` `N*m/(rad/s)` (default) | nonnegative scalar

For a wet brake, the viscous friction represents the energy loss to the cooling/lubricating fluid between the clutch plates. To model a wet brake, specify a nonzero value for the coefficient of viscous friction. The default value represents a dry brake.

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.

Brake pressure fault — Option to model brake pressure fault
`Add fault`

Whether to model a fault in the block. To add a fault, click the Add fault hyperlink.

Brake pressure when faulted — Set faulted brake pressure
`0` `bar` (default) | positive scalar

Belt force when a fault is triggered. When you trigger a fault, the block applies the value of the Brake pressure when faulted parameter instead of the value at port P 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

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

Extended Capabilities

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

Version History

Introduced in R2017b

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R2024a: Model faults with the Simscape faults interface

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

Disc Brake

Description

Disc Brake Model

Faults

Thermal Model

Ports

Input

P — Cylinder pressure physical signal

Conserving

S — Shaft rotational mechanical

H — Heat thermal

Dependencies

Parameters

Geometry

Mean pad radius — Pad radius 150 mm (default) | positive scalar

Cylinder bore — Bore diameter 10 mm (default) | positive scalar

Number of brake pads — Pad quantity 2 (default) | positive scalar integer

Friction

Thermal port — Thermal model Omit (default) | Model

Dependencies

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

Dependencies

Static friction coefficient — Static friction 0.9 (default) | scalar

Dependencies

Static friction coefficient vector — Static friction [.9, .8, .7] | vector

Dependencies

Coulomb friction coefficient — Contact friction 0.7 (default) | positive scalar

Dependencies

Coulomb friction coefficient vector — Contact friction [.8, .7, .6] (default) | increasing vector of positive values

Dependencies

Breakaway friction velocity — Friction threshold 0.1 rad/s (default) | scalar

Viscous friction coefficient — Viscous friction 0 N*m/(rad/s) (default) | nonnegative scalar

Faults

Brake pressure fault — Option to model brake pressure fault Add fault

Brake pressure when faulted — Set faulted brake pressure 0 bar (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

P — Cylinder pressure
physical signal

S — Shaft
rotational mechanical

H — Heat
thermal

Mean pad radius — Pad radius
`150` `mm` (default) | positive scalar

Cylinder bore — Bore diameter
`10` `mm` (default) | positive scalar

Number of brake pads — Pad quantity
`2` (default) | positive scalar integer

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

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

Static friction coefficient — Static friction
`0.9` (default) | scalar

Static friction coefficient vector — Static friction
`[.9, .8, .7]` | vector

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

Coulomb friction coefficient vector — Contact friction
`[.8, .7, .6]` (default) | increasing vector of positive values

Breakaway friction velocity — Friction threshold
`0.1` `rad/s` (default) | scalar

Viscous friction coefficient — Viscous friction
`0` `N*m/(rad/s)` (default) | nonnegative scalar

Brake pressure fault — Option to model brake pressure fault
`Add fault`

Brake pressure when faulted — Set faulted brake pressure
`0` `bar` (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™.