# Loaded-Contact Rotational Friction

Loaded-contact friction between two rotating surfaces

**Library:**Simscape / Driveline / Brakes & Detents / Rotational

## Description

The Loaded-Contact Rotational Friction block simulates friction between two rotating surfaces loaded with a normal force.

The block is implemented as a structural component based on the Fundamental Friction Clutch block. From the locked state, the two surfaces unlock if the transmitted torque exceeds the static friction, as defined by the static coefficient of friction and current normal force. For details on how the locking and unlocking are modeled, see the Fundamental Friction Clutch block reference page.

Torque is transmitted for normal forces larger than the **Threshold
force** parameter.

You can also enable faulting. When faulting occurs, the surfaces will remain
locked or will be unable to transmit power. Faults can occur at a specified
time or due to an external trigger at port **T**.

### Equations

The block simulates friction between two rotating surfaces loaded with a normal force. When the two rotating surfaces are not locked, the transmitted torque is determined with the following equations:

$$\tau =N\xb7\mu \xb7{r}_{\text{eff}}\xb7\text{sign}(\omega )\text{}+{\tau}_{\text{visc}},$$

$${r}_{\text{eff}}=\frac{2}{3}\cdot \frac{{r}_{o}^{3}-{r}_{i}^{3}}{{r}_{o}^{2}-{r}_{i}^{2}},$$

$${\tau}_{visc}={\mu}_{\text{visc}}\xb7\text{}\omega ,$$

where:

*τ*is the transmitted torque.*N*is the normal force.*μ*is the friction coefficient.*r*is the effective radius._{eff}*r*is the surface outside radius._{o}*r*is the surface inside radius._{i}*ω*is the relative angular velocity.*τ*is the viscous drag torque._{visc}*μ*is the viscous drag torque coefficient._{visc}

### Velocity-Dependent Model

You can model the effects of rotational velocity change by selecting a
velocity-dependent model. To choose a velocity-dependent model, in
the **Friction** settings, set the
**Friction model** parameter to
```
Velocity-dependent kinetic friction
coefficient
```

. For information about a friction
model that depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.

For the velocity-dependent model these related parameters become
visible in the **Friction** settings:

**Relative velocity vector****Kinetic friction coefficient vector****Friction coefficient interpolation method****Friction coefficient extrapolation method**

### Thermal Model

You can model the effects of heat flow and temperature change by
selecting a temperature-dependent model. To choose a
temperature-dependent model, in the **Friction**
settings, set the **Friction model** parameter to
```
Temperature-dependent friction
coefficients
```

. For information about a friction
model that depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.

For the temperature-dependent model, thermal port
**H** and these settings are visible:

In the

**Friction**settings:**Temperature vector****Static friction coefficient vector****Kinetic friction coefficient vector****Friction coefficient interpolation method****Friction coefficient extrapolation method**

In the

**Thermal Port**settings:**Thermal mass****Initial Temperature**

### Thermal, Velocity-Dependent Model

You can model the effects of rotational velocity change and heat flow
by selecting a velocity-dependent and temperature-dependent model.
To choose a model that depends on both velocity and temperature, in
the **Friction** settings, set the
**Friction model** parameter to
```
Temperature and velocity-dependent friction
coefficients
```

.

For the velocity-dependent and temperature-dependent model, thermal
port **H** and these related settings and
parameters become visible:

In the

**Friction**settings:**Relative velocity vector****Temperature vector****Static friction coefficient vector****Kinetic friction coefficient matrix****Friction coefficient interpolation method****Friction coefficient extrapolation method**

In the

**Thermal Port**settings:**Thermal mass****Initial Temperature**

### Faults

You can enable faulty behavior in response to:

Simulation time — Faulting occurs at a specified time.

Simulation behavior — Faulting occurs in response to an external trigger. This exposes port

**T**.

You can choose either or both of these settings for block faulting. If
faulting is triggered, the clutch responds according to the
**Behavior when faulted** setting for the
remainder of the simulation. The fault options are:

`Cannot transmit power`

`Cannot unlock`

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.

## Limitations and Assumptions

The model does not account for inertia. Add inertia terms externally to the

**B**and**F**ports as required.The model computes the torque assuming a uniform distribution of the normal force.

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2011a**