# Reluctance Force Actuator

Magnetomotive device based on reluctance force

## Library

Magnetic Elements

## Description

The Reluctance Force Actuator block models a generic magnetomotive device based on reluctance force.

The block is based on the following equations:

$$F=-0.5\cdot {\Phi}^{2}\cdot \frac{d\Re}{dx}$$

$$\Re (x)=\frac{x}{{\mu}_{0}\cdot {\mu}_{r}\cdot A}$$

$$u=dx$$

where

F | Reluctance force |

Φ | Flux in the magnetic circuit |

$$\Re $$ | Reluctance |

x | Thickness or length of the air gap |

μ_{0} | Permeability constant |

μ_{r} | Relative permeability of the material |

A | Cross-sectional area of the section being modeled |

u | Velocity |

Connections N and S are magnetic conserving ports, and connections C and R are mechanical translational conserving ports. The magnetic force produced by the actuator acts to close the gap, therefore the resulting force is negative when it acts from C to R.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use
the **Initial Targets** section in the block dialog box or Property
Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model.
Using system scaling based on nominal values increases the simulation robustness. Nominal
values can come from different sources, one of which is the **Nominal
Values** section in the block dialog box or Property Inspector. For more
information, see Modify Nominal Values for a Block Variable.

## Basic Assumptions and Limitations

The current excitation in the system is constant.

Only axial reluctance is modeled.

## Parameters

**Initial air gap**Thickness or length of air gap at the beginning of simulation. The default value is

`2`

mm.**Minimum air gap**Minimal value of air gap, with the reluctance force acting to close the air gap. The parameter value has to be greater than 0. The default value is

`1e-4`

mm.**Cross-sectional area**Area of the section being modeled. The default value is

`0.01`

m^2.**Relative permeability of material**Relative permeability of the section material. The default value is

`1`

.**Contact stiffness**Stiffness that models the hard stop at the minimum air gap position. The default value is

`10e6`

N/m.**Contact damping**Damping that models the hard stop at the minimum air gap position. The default value is 500 N/(m/s).

## Ports

The block has the following ports:

`N`

Magnetic conserving port associated with the block North terminal.

`S`

Magnetic conserving port associated with the block South terminal.

`R`

Mechanical translational conserving port associated with the rod.

`C`

Mechanical translational conserving port associated with the case.

## Extended Capabilities

## Version History

**Introduced in R2010a**