# Loaded-Contact Rotational Friction

Loaded-contact friction between two rotating surfaces

**Libraries:**

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.

### 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.

### 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.

### 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
```

.

### Faults

To model a fault in the Loaded-Contact Rotational Friction block, in the
**Faults** section, click the **Add fault** hyperlink next
to the fault that you want to model. When the Add Fault window opens, you can to specify the
fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

When you trigger a fault, 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`

### 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

**N** — Normal force

physical signal

Physical signal port associated with the normal force. This signal is positive or zero. A signal of less than zero is interpreted as zero.

### Conserving

**B** — Base

mechanical rotational

Rotational conserving port associated with the driving (base) surface.

**F** — Follower

mechanical rotational

Rotational conserving port associated with the driven (follower) surface.

**H** — Heat flow

thermal

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only when, in the
**Friction** settings, the
**Friction model** parameter is
set to ```
Temperature-dependent friction
coefficients
```

or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction model and Friction Parameter Dependencies.

## Parameters

### Geometry

**Geometry model** — Parameterization method

```
Define effective
radius
```

(default) | ```
Define annular
region
```

Parameterization method for the loaded-contact friction model:

`Define effective radius`

— Provide a value for the friction effective radius.`Define annular region`

— Define the friction effective radius in terms of the inside and outside diameters of the friction surface. If you select this option, the panel changes from its default.

#### Dependencies

The value of this parameter affects the
visibility of other parameters in the
**Geometry** settings.

**Effective torque radius** — Effective friction surface radius

`130`

`mm`

(default) | positive scalar

Effective radius
*r*_{eff}.
The value must be greater than zero.

#### Dependencies

This parameter is visible only if the
**Geometry model** parameter is
set to ```
Define effective
radius
```

.

**Friction surface outside diameter** — Friction surface outer diameter

`150`

`mm`

(default) | positive scalar

Outside diameter, 2 *
*r _{o}*, of
the friction surfaces. Must be greater than
zero.

#### Dependencies

This parameter is visible only if the
**Geometry model** parameter is
set to ```
Define annular
region
```

.

**Friction surface inside diameter** — Friction surface inner diameter

`100`

`mm`

(default) | positive scalar less than outer
diameter

Inside diameter, 2 *
*r _{i}*, of
the friction surfaces. Must be greater than zero,
but less than the friction surface outside
diameter.

#### Dependencies

This parameter is visible only if the
**Geometry model** parameter is
set to ```
Define annular
region
```

.

### Friction

The table shows how the visibility of some ports, parameters, and settings depends on the option that you choose for other parameters.

**Friction Parameter Dependencies**

Friction | ||||||
---|---|---|---|---|---|---|

Friction model | ||||||

```
Fixed kinetic
friction coefficient
``` | ```
Velocity-dependent
kinetic friction coefficient
``` | ```
Temperature-dependent friction
coefficients
``` | ```
Temperature and velocity-dependent
friction coefficients
``` | |||

Exposes: Conserving port **H**Thermal parameters in the **Friction**settings**Thermal Port**settings
| Exposes: Conserving port **H**Thermal parameters in the **Friction**settings**Thermal Port**settings
| |||||

- | - | Temperature vector | Temperature vector | |||

- | Relative velocity
vector | - | Relative velocity
vector | |||

Static friction
coefficient | Static friction
coefficient | Static friction coefficient
vector | Static friction coefficient
vector | |||

Kinetic friction
coefficient | Kinetic friction coefficient
vector | Kinetic friction coefficient
vector | Kinetic friction coefficient
matrix | |||

- | Friction coefficient interpolation
method | Friction coefficient interpolation
method | Friction coefficient interpolation
method | |||

- | Friction coefficient extrapolation
method | Friction coefficient extrapolation
method | Friction coefficient extrapolation
method | |||

Velocity
tolerance | Velocity tolerance | Velocity tolerance | Velocity tolerance | |||

Threshold
force | Threshold force | Threshold force | Threshold force | |||

Viscous drag torque
coefficient | Viscous drag torque
coefficient | Viscous drag torque
coefficient | Viscous drag torque
coefficient |

**Friction model** — Friction model

```
Fixed kinetic
friction coefficient
```

(default) | ```
Velocity-dependent kinetic
friction coefficient
```

| ```
Temperature-dependent friction
coefficients
```

| ```
Temperature and
velocity-dependent friction
coefficients
```

Parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the friction model that you select for the block. The options are:

`Fixed kinetic friction coefficient`

— Provide a fixed value for the kinetic friction coefficient.`Velocity-dependent kinetic friction coefficient`

— Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between discs.`Temperature-dependent friction coefficients`

— Define the kinetic friction coefficient by table lookup based on the temperature.`Temperature and velocity-dependent friction coefficients`

— Define the kinetic friction coefficient by table lookup based on the temperature and the relative angular velocity between discs.

#### Dependencies

The friction model setting affects the visibility of other parameters, settings, and ports. For more information, see Friction Parameter Dependencies.

**Relative velocity vector** — Relative velocity

```
[0, 100,
1000]
```

`rad/s`

(default) | vector

Input values for the relative velocity as a vector. The values in the vector must increase from left to right. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Velocity-dependent kinetic
friction coefficient
```

or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Temperature vector** — Temperature

```
[280, 300,
320]
```

`K`

(default) | increasing vector

Input values for the temperature as a vector. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension. The values in the vector must increase from left to right.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Temperature-dependent friction
coefficients
```

or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Static friction coefficient** — Static friction coefficient

`0.35`

(default) | scalar

Static or peak value of the friction coefficient. The static friction coefficient must be greater than the kinetic friction coefficient.

#### Dependencies

this parameter is visible only when the
**Friction model** parameter is
set to ```
Fixed kinetic friction
coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

. For more information,
see Friction Parameter Dependencies.

**Static friction coefficient vector** — Static friction coefficient

```
[.4, .38,
.36]
```

(default) | vector

Static, or peak, values of the friction coefficient as a vector. The vector must have 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.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Temperature-dependent friction
coefficients
```

or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Kinetic friction coefficient** — Kinetic friction coefficient

`0.3`

(default) | positve scalar

The kinetic, or Coulomb, friction coefficient. The coefficient must be greater than zero.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Fixed kinetic friction
coefficient
```

. For more information,
see Friction Parameter Dependencies.

**Kinetic friction coefficient vector** — Kinetic friction coefficient

```
[.3, .22,
.19]
```

(default) | `[.3, .28, .25]`

| vector

Output values for kinetic friction coefficient as a vector. All values must be greater than zero.

If the **Friction model**
parameter is set to

`Velocity-dependent kinetic friction coefficient`

— The vector must have same number of elements as relative velocity vector.`Temperature-dependent friction coefficients`

— The vector must have the same number of elements as the temperature vector.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Velocity-dependent kinetic
friction coefficient
```

or
```
Temperature-dependent friction
coefficients
```

. For more information,
see Friction Parameter Dependencies.

**Kinetic friction coefficient matrix** — Kinetic friction coefficient

```
[.34, .32, .3; .3,
.28, .25; .25, .2, .15]
```

(default) | matrix

Output values for kinetic friction coefficient as a matrix. All the values must be greater than zero. The size of the matrix must equal the size of the matrix that is the result of the temperature vector × the kinetic friction coefficient relative velocity vector.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Friction coefficient interpolation method** — Extrapolation method

`Linear`

(default) | `Smooth`

Interpolation method for approximating the output value when the input value is between two consecutive grid points:

`Linear`

— Select this option to get the best performance.`Smooth`

— Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Velocity-dependent kinetic
friction coefficient
```

,
```
Temperature-dependent friction
coefficients
```

, or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Friction coefficient extrapolation method** — Interpolation method

`Linear`

(default) | `Nearest`

| `Error`

Extrapolation method for determining the output value when the input value is outside the range specified in the argument list:

`Linear`

— Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.`Nearest`

— Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.`Error`

— Select this option to avoid going into the extrapolation mode when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is only visible when you set
the **Friction model** parameter
to ```
Velocity-dependent kinetic
friction coefficient
```

,
```
Temperature-dependent friction
coefficients
```

, or
```
Temperature and velocity-dependent
friction coefficients
```

. For more
information, see Friction Parameter Dependencies.

**Velocity tolerance** — Relative velocity locking threshold

`0.001`

`rad/s`

(default) | scalar

Relative velocity below which the two surfaces
can lock. The surfaces lock if the torque across
the **B** and
**F** rotational ports is less
than the product of the effective radius, the
static friction coefficient, and the applied
normal force.

**Threshold force** — Normal contact force threshold

`1`

`N`

(default) | scalar

The normal force applied to the physical
signal port **N** is applied to
the contact only if the amount of force exceeds
the value of the **Threshold
force** parameter. Forces below the
**Threshold force** are not
applied, so there is no transmitted frictional
torque.

### Viscous Losses

**Viscous drag torque coefficient** — Viscous drag torque

`0`

`N*m/(rad/s)`

(default) | nonnegative scalar

Viscous drag coefficient,
*μ _{visc}*,
for computing the drag torque. The coefficient
depends on the type of operating fluid, fluid
temperature, and the maximum distance between the
surfaces.

### Initial Conditions

**Initial state** — Initial clutch state

`Unlocked`

(default) | `Locked`

State of the internal Fundamental Friction Clutch block state at the start of simulation.

`Locked`

— Rotational ports**B**and**F**are initially locked together.`Unlocked`

— Rotational ports**B**and**F**are initially sliding relative to each other.

### 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.

**Friction fault** — Option to model friction fault

`Add fault`

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

**Behavior when faulted** — Response to fault trigger

```
Cannot transmit
power
```

(default) | ```
Cannot
unlock
```

Behavior when a fault is triggered. You can select the faulting between the surfaces as either:

`Cannot transmit power`

`Cannot unlock`

#### Dependencies

To enable this parameter, enable faults for
the block by clicking the **Add
fault** hyperlink.

### Thermal Port

**Thermal Port** settings are visible only when, in
the ** Friction** settings, the **Friction
model ** parameter is set to
```
Temperature-dependent friction
coefficients
```

or ```
Temperature and
velocity-dependent friction
coefficients
```

.

**Thermal mass** — Thermal mass

`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

To enable this parameter, set
**Friction model ** to
```
Temperature-dependent friction
coefficients
```

or
```
Temperature and velocity-dependent
friction coefficients
```

.

**Initial temperature** — Initial temperature

`300`

`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

To enable this parameter, set
**Friction model ** to
```
Temperature-dependent friction
coefficients
```

or
```
Temperature and velocity-dependent
friction coefficients
```

.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced in R2011a**

### R2024a: Model faults with the Simscape faults interface

The Loaded-Contact Rotational Friction block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.

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