Solenoids are normally built by winding a coil of wire around a moveable soft iron core. When a current is passed through the coil, the core moves towards the centre of the solenoid. The current can be DC, AC, or a pulse-width modulated waveform that is partly DC and partly AC.

This page should help you if you are using bought-in solenoids in your robot, or if you are trying to design your own solenoid or electromagnetic actuator.

The permeability of free space,
μ_{0},
has a fixed value of 4πx
10^{-7}.

Now we have some terms to deal with, let’s examine a magnetic circuit.
This is a solid iron square ring with a cross sectional area of *A*
metres^{2}, and an average path length of *L*:

The coil has a resistance of R_{coil}, which is shown as a lumped
resistance, so the coil current for a DC supply, V, is I = V/R_{coil}.
The coil generates an mmf of *NI *ampere-turns, which drives a flux
Φ around the iron. Some simple equations can be written to describe this:

The mmf generated by the coil, is given by:

The reluctance of the iron is given by the equation:

where L is the average length of the path, and A is the cross sectional
area. Note that the symbol μ is used a simple term to cover both
μ_{0} and μ_{r}.

The flux generated is then:

and the flux density in the core is:

An equivalent electrical circuit can be drawn to represent this:

The inductance of the coil is given by the equation:

Now what happens if an air-gap is introduced:

The reluctance of the iron is still almost the same (it is nearly the same length and same csa), but there is an added reluctance in series, that of the airgap. The relative permeability of air is 1, so the reluctance of the airgap is

Now the electrical equivalent circuit looks like this:

DC is obviously the simplest to use. AC is generally only useful if you are using it from an AC supply derived from the mains. PWM is a lot harder to generate, but is the best to use.

The inductance of the coil is dependant on the reluctance of the magnetic
circuit. When an airgap is introduced, the total reluctance increases,
and so the inductance decreases. If the voltage source is AC, or PWM which
is a micture of AC and DC, then the inductance will also resist the flow
of current. The *impedance *(like resistance) of an inductor is given
by the equation:

where *f *is the frequency and *L *is the inductance. The
impedance of the whole circuit, including R is:

As the resistance, frequency, or inductance increases, the impedance increases, and the current will fall.

Let’s have a look at what a real solenoid looks like. This is a lengthwise cross section through a cylindrical solenoid:

The coil creates an MMF which drives flux (shown in red in the diagram) left through the plunger, then around the frame of the solenoid over to the right hand side, then through the airgap and back into the plunger. The reluctance of this path is mostly made up by the airgap.

When the plunger is out, as shown in the diagram, the reluctance is
quite high. When current is applied to the coil, the plunger moves to the
right, and the reluctance decreases. This is an example of what was said
before about forces in magnetic systems – they always act to *reduce
*the
reluctance, or *increase *the inductance. Eventually, the plunger
will collide with the frame on the right hand side, and the airgap will
be zero, and the reluctance will be at a minimum.

What happens to the inductance of the coil as the plunger moves. Remember the equation for the coil inductance:

With the plunger fully to the left, the airgap is quite wide, and so the reluctance is quite high, so the inductance is low. Remember from before that the impedance of the coil to the supply voltage is dependant on the inductance of the coil:

The current in the coil is simply the voltage divided by the impedance (Ohm’s law):

With the plunger fully out, the inductance is low, and so the current will be quite high. As the plunger moves in, the inductance increases, and the current falls. This high initial current is called the "inrush current" since it only last for a short time until the plunger is fully in. The inrush current is useful, because it allows a large current to start with which generates a large force to get the plunger going. Once the plunger has pulled in, less force is required to just hold it there, and conveniently, there is less force because the current is now lower.

This is why PWM drive is the best for solenoids. A solenoid designed for PWM drive will have quite a low coil resistance. If DC was applied to it, the coil would heat up and burn out. It is the inductance of the coil on a PWM signal that restricts the current to safe values. Of course this means that if for any reason the plunger gets stuck in the "out" position, where the inductance is low, the coil may burn-out.

Let’s have a look at an example force-stroke diagram for the BLP

There are four curves all superimposed on the same graph. Notice that the solenoids designed for shorter on-timesa in PWM mode have much larger forces due to the geater currents that they can carry.

As the plunger approaches the end-stop (stroke approaching zero) the force is at its maximum. The equation that governs the force-stroke curve varies depending upon the physical construction of the solenoid. Most are based on an inverse square law however:

where *r* is the radius of the cylindrical plunger. This equation
would indicate that the force would be infinite when the stroke is 0mm.
This is obviously impossible, but this equation is only an approximation
and neglects the reluctance of the iron, and the fact that some of the
magnetic field will leak out into the air around the iron – "fringing effects".
It also assumes a perfect cylindrical solenoid – most are not built that
way.

In fact, often the force can be nearly independant of the stroke distance, andcan tend towards the much simpler equation:

where A is the cross sectional area of plunger and B is the flux denisty in the plunger.

These equations are only approximations. To find the actual force you
will need to refer to the solenoid daatsheet and examine the force-stroke
curves, or if it is a solenoid of your own manufacture, you can measure
the force at each position and plot your own curves.

Therefore, the plunger of the solenoid may have a chamfered look as
in the diagrams below. Generally, doing this increases the pulling force
at larger stroke lengths. When the stroke is 1mm or less, then a flat plunger
produces a higher force.

The following force-stroke graph shows the effects of the differing plunger end styles on the curve shape:

Latching solenoids integrate permanent magnets into the design which
hold the plunger in the zero stroke position, even when the coil current
is removed. To return the plunger to its extended position, a pulse of
coil current is applied *in the opposite direction* to push the plunger
away from its end-stop. This means that a latching solenoid driver must
be able to force current through the coil in either direction. This is
usually achieved using an H-bridge arrangement similar (although generally
lower power) to those used in
speed
controllers.

When the switch is closed, the current flowing down through the coil is limited by the resistance of the coil. Inductors do not like the current flowing through them to change quickly, and they will generate a voltage of their own to stop this happening. Therefore when the switch is opened, the inductor generates a voltage to make the current continue down through the coil. Because the switch is now opened, the current flows up through the diode, and back round into the inductor. The diode is called a "flywheel" diode.

PWM drivers for solenoids

L6213 single solenoid driver

L9822N Octal serial solenoid driver

**TI (Burr Brown)**

DRV102

TPIC2603

**Allegro**

UDN2962
Dual Solenoid/Motor Driver Pulse-Width Modulated

**Intersil (Harris)**

CA3282
Octal Low Side Power Driver with Serial Bus Control

The companies listed manufacture many more solenoid drivers, visit their
sites by clicking on the names and use their search facilities for the
keyword "solenoid".

- Use wire of a lower resistance – thicker wire.
- Split the wire into n sections and wire these in parallel.
- Use more than one coil.

It is best to solder the wires in parallel first, then wind them onto
the coil former, to make sure that they all wrap round in the same direction!

*force = spring constant × extension (stroke)*

By choosing the appropriate original length of spring and spring constant,
a suitable opposition force to that generated by the coil can be chosen.

A datasheet of suitable materials can be found here.

http://theory.uwinnipeg.ca/physics/mag/node1.html

http://www.gaussbusters.com/ppm93.html

http://www.acesinternational.org/Secrets%20&%20Tips%20Electronics3.htm

Magnetic design

http://www.dextermag.com/magnetic.htm

Non-technical – the solenoid as a magnet

http://www.arts.richmond.edu/~rubin/pedagogy/132/132notes/132notes_65.html

Effect of surrounding a coil with iron:

http://www.oz.net/~coilgun/theory/externaliron.htm

Solenoid manufacturers’ product index, links to datasheets:

BLP:
http://www.blpcomp.com/fmproductsidx.htm

Trombetta:
http://www.trombetta.com/defaultframeset.asp?ShowContent=solbasics

Mechetronics:
http://www.mechetronics.co.uk/

Emessem:
http://www.magnet-schultz.com/solenoid.htm

Relay technical links:

http://www.pandbrelays.com/application.stm

Books:

Linear
electric actuators & generators
I. Boldea and S.A. Nasar, Cambridge University Press, 1997