# Disc Brake

Frictional brake with pressure-applying cylinder and pads

• 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.

### 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.

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:

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

### 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 (Simscape).

#### 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.

### 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.

### 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.

### 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`.