# Actuator with Diode

Actuators with MagNetThis actuator example demonstrates the power of a fully integrated MagNet's Transient 3D with motion solver which simultaneously solves the circuit equations, the field equations on the finite element mesh, and the equations of motion. All three sets of equations include some sort of non-linearity. For the circuit the non-linear element is the diode. The finite element solver must deal with non-linear magnetic materials, and the motion solver handles the instantaneous reversal of velocity, which occurs when the plunger bounces off a bumper.

### METHODS and RESULTS

## MESH VIEW

The mesh of the actuator is shown as the right figure, which takes advantage of symmetry to reduce the problem to one-quarter of its full size. When the plunger moves, the region of air immediately adjacent to it is remeshed. Since this is a small, well defined volume, the remesh is quick, and the solution time is still dominated by the conjugate gradient and Newton iterations used to solve the sparse matrix equation. Thus remeshing is preferable to other methods which increase the number of degrees of freedom and hence the size of the matrix, and the number of iterations required to solve it.

A detailed view of the model and the mesh can be seen on the right.

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## CIRCUIT SIMULATION

The actuator is connected to a simple circuit which applies a voltage pulse to the coil. With the switch closed the diode is reverse biased and the voltage applied across the coil terminals causes the coil current to increase. After the switch opens, any current in the coil is forced to find an alternate conduction path, which is provided by the diode.

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## VOLTAGE ACROSS the ACTUATOR COIL

This graph shows the voltage across the terminals of the actuator coil. The 55 V pulse (13.75 V in this graph since this is only a quarter model) lasts only 2 ms, at which time the switch opens, forcing the current in the coil to re-route through the diode. From this point on the coil sees only the diode forward voltage drop, until the current drops below the threshold at 55 ms.

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## CURRENT in the ACTUATOR COIL

The current in the coil of the actuator is shown here. The effect of motion on the magnetic circuit is clearly seen when the plunger bounces off the lower bumper at 13 ms.

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## PLUNGER POSITION

The plunger undergoes rapid acceleration once the current nears its peak, such that it is still moving quite rapidly when it hits the lower bumper. After rebounding the spring pulls it back as the current decays, so it bounces against the upper stop. It would keep bouncing indefinitely if it weren't for the viscous friction which damps out the oscillations.

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## MAGNETIC FORCE on the PLUNGER

The magnetic force on the plunger is calculated by MagNet using a tuneable Maxwell stress method, which gives accurate forces. The force reaches its first (negative) peak when the current peaks, but has a second peak when the plunger reaches the lower bumper, due to the small air gap at that point.

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