Background
From as early as the mid-1800’s, magnetism has been a field of great scientific and practical
concern, with its roots spawning such developments as information storage in computers,
navigation, and motor-driven motion. In addition, magnetism has been harnessed into more
ancillary roles, such as position sensors, alarms, and valves. In all of these cases, magnetic fields
generate magentomotive forces which act upon other materials, causing these materials to
function in a useful way. For example, the earth’s magnetic field can create a magnetomotive
force on a compass needle, causing the needle to point towards the earth’s magnetic pole. This
magnetic pole is geographically very close to the North Pole, and thus can be used for
navigational purposes.
In this study, a very specific use of magnetics will be addressed. As mentioned, magnets can be
used to create accurate position sensors. The sensor would have an element sensitive to a
magnetic field, and in the presence of that field the sensor would process this and typically
output a signal to interpretted by another piece of equipment. This concept can be applied to the
application of liquid level sensing in automated equipment. A sensing element, in this case a
reed switch, will be placed at a predetermined level of interest in a container of liquid, while a
magnet would be placed in a float which resides in the liquid. When the liquid approaches the
level of interest, the magnet will close the switch, completing an electric circuit controlling other
pieces of equipment. For example, the closed circuit could turn off a pump or open a valve.
To begin, a brief look into the workings of a reed switch and magnetic fields is necessary.
Reed Switches
The reed switch was invented by Walter B. Elwood, an employee of Bell Telephone
Laboratories, in 1936. There were two patents published on the work involved with the
development of the reed switch – 2,187,115 and 2,264,746. The need for the reed switch was
based on the premise of having a relay unit contact device which is economical, reliable, and
easily replaceable1. A reed switch is comprised of two, sometimes three, cantilevered metal
contacts placed inside a sealed glass tube. Inside the sealed glass tube is an inert gas. Without
this inert gas, it would be necessary to plate the entire contact with a corrosion resistant material,
adding unnecessary cost.2 Modern reed switches are still plated, but only in the small contact
area, and its purpose was to ensure the contacts made an adequate electrical connection.
As mentioned previously, reed switches require a magnetic field to actuate it. The reeds of the
switch are made of an iron/nickel alloy susceptible to magnetic influence. Under a magnetic
field, the reeds are able to carry the magnetic field, as such a “north” and “south” pole is induced
on the reeds, with the north on one reed and the south on the other. From magnetic theory, a
magnetic circuit with an air gap in it allows for a tangible use of magnetic flux. Without an air
gap, magnetic flux within the reeds would be confined to only the reeds and therefore would not
be useful. The air gap creates a magnetic potential (analogous to a voltage drop in an electric
circuit), and the reeds will want to move to minimize that magnetic potential. If the magnetic
potential is strong enough, the reeds will close completely. Once the magnetic potential is not
there, the elastic properties of the reeds would return them to their original position.
Magnets
Knowing the basics of reed switches, it is also important to understand how magnets and their
magnetic fields work. The type of magnets that will be focused on here are permanent magnets.
If a magnetic field is associated with a ferromagnetic body in the absense of any external
excitation, the ferromagnetic body is said to be permanently magnetized. (STRAT 13) Magnetic
materials in general are materials in which the atoms do not have a third complete electron shell.
This means that there are free electrons that could be utilized to impart a magnetic moment on
the material. On an atomic level, these atoms will form localized groups of atoms with free
electons known as domains. Therefore, a material sample would have a myriad of magnetic
domains. In an unmagnetized material, these domains are oriented in a highly randomized
fashion, and in the magnetic realm are essentially useless. In order for a material with the
potential to be magnetic to actually become magnetized, these domains need to be orientated in
the same direction. However, there are various levels of magnetization which are dependant on
the degree of orientation of the domains. A material with a low percentage of oriented domains
will not make for a very strong magnet, while a magnet with as many domains oriented in one
direction as possible will make a much stronger magnet. These degrees of magnetization are
determined by intrinsic material properties, as well as method of magnetization
From the work of Maxwell, an electromagnetic field has four vectors associated with it, the E
and B vectors, and the D and H vectors. The E and D vectors are associated with strictly the
electric field, while the B and H vectors are associated with the magnetic field (STRAT, pg 1).
Since this study is devoted to the magnetic field, it is the magnetic intensity vector H and the
magnetic induction vector B that will be of the most intimate interest. The B and H vectors are
subject to Maxwell’s equations (XXXX) and (XXXXX) STRATTON, PAGE 2. These
equations define the behavior of the vectors within the magnetic field. To start, it should be
noted that the vector H is the what is ultimately responsible for the orientation of the magnetic
domains with in a material. Also, the B and H vectors are related by a material property known
as the permeability coefficient, m. The permeability of a material is its measure to carry the B
vector. Further, the relative permeability mr can be defined as the quantity m referenced to the
permeability of air, ma. The value for ma is 4p*10-7 henries per meter. Furthermore, typical
values for mr can range from less than one, known as diamagnetic, to greater than one, or
paramagnetic. As mentioned, the B and H vectors are related via B=mH.
It is useful to be able to plot the curves relating B and H into what is called a hysterisis curve.
As H is increased, B also increases. Because m is not always linear for the entire range of the
curve, the curve itself has linear and curved portions. There is a limit where increasing H no
longer increases B, otherwise known as the saturation limit. However, when H is decreased, the
curve of B does not retrace the path of curve corresponding to the initial increase in H, instead
choosing to decrease at a different rate than the rate of change on increasing H. However, once
H is again increased, the curve returns to its original starting point, thereby forming a closed
hysterisis loop. The shape of this hysterisis curve is useful to determining the appropriate usage
conditions for any given magnetic system. In the case of a material that has a predetermined
magnetization in addition to an applied H, there is an added term that must be added to the
equation. The magnetization M in permanent magnets is independent of the applied fields, and
therefore the equation relating B to H changes to B=m(H+m).
When it comes to permanent magnets, B and H can be specified as a magnetic material property.
(NEEDS MORE DEVELOPMENT AND DOCUMENTATION)
Application Notes
The genesis for this project is to attempt to determine the position of a magnet relative to a reed
switch at the moment where the magnet closes the reed switch. In the case we wish to document,
the switch is kept in a fixed position while the magnet swings towards and away from the switch
on an arc. A diagram of this situation is shown in FIGURE XXXX. Here, the magnet is
embedded in a plastic float, while the switch is embedded in a plastic housing. The float is
attached to a pivot point which gives the float its ability to move on an arc. This assembly is
designed to detect the liquid level in an enclosed container. As the liquid level is increasing, the
float will move up and closer to the switch. As the float moves closer to the switch, the magnetic
field will actuate the switch and close it. For the purposes of accuracy, it is therefore extremely
useful to know and to be able to closely predict where the magnet needs to be for the switch to
close and open.
Prior methods of determining proper design of this particular magnet/switch system involved
extensive empirical testing of both the proposed magnet and the proposed switch. Using a gauss
meter and probe, the flux density of a magnet was determined along a line parallel to the
magnet’s axis. The location of the measurements was selected judiciously to accurately recreate
the intended design. Likewise, the switches themselves were also tested for their sensitivity to a
magnetic field. Once an appropriate magnet and switch combination were found, further testing
had to be done to determine where the magnets need to be placed.
The biggest obstacle to simplifying this process was the lack of magnetic field visualization. It is
very easy to determine the necessary field needed to actuate a reed switch, however, determining
the location of a particular magnetic field strength is not a simple empirical task. Use of finite
element model (FEM) to visualize the magnetic field and to determine the strength at any given
point greatly reduces the amount of time necessary to either design a new system or to find faults
in a given system. With an FEM, the designer need only know the sensitivity of the reed switch
in use.
Testing the reed switch for its sensitivity to a magnetic field is a very straightforward task. A
switch can be placed inside a coil wound with a known number of turns of wire. This coil is
connected to ammeter and a power supply. A ohmmeter can be placed across the switch. With
zero current in the coil, the ohmmeter should read infinite resistance, i.e. the switch is open.
While the switch is inside the coil, the current into the coil is increased from zero until the
ohmmeter shows a finite resistance close to zero, indicating the switch has closed. The value of
current at the time of closure of the switch is recorded and multiplied by the number of wire
turns in the coil.
However, it should be noted that the magnet field strength at any point is in units of gauss (G)
while the units of reed switch sensitivity, analgious to magnetomotive force, are in units of
ampere-turns (AT). There is no direct conversion between gauss and ampere-turns, therefore
one additional data gathering is needed. Using a gauss meter and probe, the probe was placed
inside the coil without current flowing in the coil. The current in the coil is increased, thereby
increasing the magnetic strength in the coil. For a particular current reading, a gauss
measurement is taken and plotted on a graph, ampere-turns on the absicca and gauss on the
ordinate. This relationship is linear, thereby a correlation between gauss and ampere-turns can
easily be established empirically for a given test coil. Thus the reed switch can be associated
with the stength of the magnetic field of the magnet.
With the necessary data gathered from the switch, the analysis of the magnetic field with an
FEM can begin. Using COMSOL, an axisymmetric magnetostatic analysis was used. The
magnet used for this analysis is an Alnico 5 magnet, 0.128” in diameter, 0.400” long. The
material properties of the magnet XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX The
mesh settings for the model are XXXXXXXXXXXXXXXXXXXXXX.
(use this part to talk about model formation and settings and how you got all your pretty graphs)
To verify the validity of the model, it is necessary to map a section of the magnetic field of an
actual Alnico 5 magnet with the dimensions specified. To do this, a precise XY measurement
station was used with a magnet mounted to it. The gauss probe was mounted in a fixed location,
thereby allowing the magnet and the field to move relative to the probe. A picture of the setup
for this test can be found in XXXXXXXXXX. Here, the magnet is left in the float for easier
mounting purposes. The float was placed into a holder which was in turn secured to the top of
the XY measuement station. The probe was located on the radial axis of the magnet
approximately XXXX” from the surface of the magnet and moved along the length of the
magnet.
Readings of the gauss measurement were taken from XX past either end of the magnet
at intervals of YY. This data was then plotted with position on the abscissa and gauss on the
ordinate. In the COMSOL model, a cross-sectional plot was generated to match the same
measuring path as the empirical test and then plotted on the same plot as the empirical data. This
plot is shown in XXXXXX.