# 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 any case, $Rm=\frac{Ro+Ri}{2}$.

In the equations:

• 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.

### Thermal Model

You can model the effects of heat flow and temperature change by selecting a thermal block variant. Selecting a thermal variant:

• Exposes port H, a conserving port in the thermal domain.

• Enables the Thermal mass parameter, which allows you to specify the ability of the component to resist changes in temperature.

• Enables the Temperature variable, which allows you 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).

To select a thermal variant, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port.

## 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.

The thermal conserving port is optional and is hidden by default. To expose the port, select a variant that includes a thermal port.

#### Dependencies

Selecting a thermal variant enables thermal parameters.

## Parameters

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#### Geometry

Diameter of the piston.

#### Friction

Independent vector for determining static and kinetic frictions. The values in the vector, in K, must increase from left to right.

#### Dependencies

Selecting a thermal block variant for the Block choice parameter enables this parameter.

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

If you select a thermal block variant for the Block choice parameter, specify this parameter using a vector. The vector must contain the same number of elements as the temperature vector. Each value must be greater than the value of the corresponding element in the kinetic friction coefficient vector.

Coefficient of kinetic friction. The value that you specify for this parameter must be greater than `0`.

#### Dependencies

If you select a thermal block variant for the Block choice parameter, specify this parameter as a vector. The vector must contain the same number of elements as the temperature vector.

Angular speed at which friction switches from static to kinetic.

Coefficient of viscous friction.

#### 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

Selecting a thermal block variant for the Block choice parameter enables this parameter.