# Disc Brake

Frictional brake with pressure-applying cylinder and pads with faulting

• Library:
• 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.

You can also enable faulting. When faulting occurs, the brake will exert a user-specified pressure. Faults can occur at a specified time or due to an external trigger at port T.

### 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 $\Omega \ne 0$,

`$T=\frac{{\mu }_{k}P\pi {D}_{b}{}^{2}{R}_{m}N}{4}.$`

However when $\Omega =0,$ 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 $\Omega =0,$ is

`$T=\frac{{\mu }_{s}P\pi {D}_{b}{}^{2}{R}_{m}N}{4}.$`

In both cases, $Rm=\frac{Ro+Ri}{2}$.

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.

• μs is the disc pad-rotor coefficient of static friction.

• μk is the disc pad-rotor coefficient of kinetic friction.

• Db is the brake actuator bore diameter.

• Rm is the mean radius of brake pad force application on brake rotor.

• Ro is the outer radius of brake pad.

• Ri 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, kv, to a nonzero value. The torque on the wheel in a wet brake system is:

`${T}_{wet}=T+{k}_{v}\Omega .$`

### Faulty Behavior

When faults are enabled, a brake pressure 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 pressure is replaced by the Brake pressure 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 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

### 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`.

## Ports

### Input

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Physical signal port associated with cylinder pressure.

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

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Rotational mechanical conserving port associated with the 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 parameters and variables visible.

## Parameters

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### Geometry

Diameter of the piston.

Number of friction pads.

### Friction

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.

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`.

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`.

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 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 speed at which friction switches from static to kinetic.

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

Enable externally or temporally triggered faults. When faulting occurs, the brake pressure normally received at port P will be set to the value specified in the Brake pressure when faulted parameter.

Set faulted brake pressure. When faulting occurs, the brake pressure normally received at port P will be set to the value specified in the Brake pressure 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 pressure normally received at port P will be set to the value specified in the Brake pressure when faulted parameter.

#### Dependencies

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

When the Simulation time for fault event is reached, the brake pressure normally received at port P will be set to the value specified in the Brake pressure 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`.