Mutual
Inductance
(The
Basis for Eddy Current Inspection)
The magnetic flux through a circuit can be related to the current
in that circuit and the currents in other nearby circuits, assuming
that there are no nearby permanent magnets. Consider the following
two circuits.
The magnetic field produced by circuit 1 will intersect the wire
in circuit 2 and create current flow. The induced current flow
in circuit 2 will have its own magnetic field which will interact
with the magnetic field of circuit 1. At some point P, the magnetic
field consists of a part due to i_{1}
and a part due to i_{2}.
These fields are proportional to the currents producing them.
The coils in the circuits are labeled L1
and L2 and this term represents the self inductance
of each of the coils. The values of L1
and L2 depend on the geometrical arrangement
of the circuit (i.e. number of turns in the coil) and the conductivity
of the material. The constant M, called the mutual
inductance of the two circuits, is dependent
on the geometrical arrangement of both circuits. In particular,
if the circuits are far apart, the magnetic flux through circuit
2 due to the current i_{1} will
be small and the mutual inductance will be small. L_{2}
and M are constants.
We can write the flux, _{B}
through circuit 2 as the sum of two parts.
_{B2}
= L_{2}i_{2}
+ i_{1}M
An equation similar to the one above can be written
for the flux through circuit 1.
_{B1}
= L_{1}i_{1}
+ i_{2}M
Though it is certainly not obvious, it can be shown
that the mutual inductance is the same for both circuits. Therefore,
it can be written as follows:
M_{1,2}
= M_{2,1}
How is mutual induction
used in eddy current inspection?
In
eddy current inspection, the eddy currents are generated in the
test material due to mutual induction. The test probe is basically
a coil of wire through which alternating current is passed. Therefore,
when the probe is connected to an eddyscope instrument, it is
basically represented by circuit 1 above. The second circuit
can be any piece of conductive material.
When alternating current is
passed through the coil, a magnetic field is generated in and
around the coil. When the probe is brought in close proximity
to a conductive material, such as aluminum, the probe's changing
magnetic field generates current flow in the material. The induced
current flows in closed loops in planes perpendicular to the magnetic
flux. They are named eddy
currents because they are thought to resemble the eddy
currents that can be seen swirling in streams.
The
eddy currents produce their own magnetic fields that interact
with the primary magnetic field of the coil. By measuring changes
in the resistance and inductive reactance of the coil, information
can be gathered about the test material. This information includes
the electrical conductivity and magnetic permeability of the material,
the amount of material cutting through the coils magnetic field,
and the condition of the material (i.e. whether it contains cracks
or other defects.) The distance that the coil is from the conductive
material is called liftoff, and this distance affects the
mutualinductance of the circuits. Liftoff can be used to make
measurements of the thickness of nonconductive coatings, such as
paint, that hold the probe a certain distance from the surface
of the conductive material.
It should be noted that if
a sample is ferromagnetic,
the magnetic flux is concentrated and strengthened despite opposing
eddy current effects. The increase inductive reactance due to
the magnetic
permeability of ferromagnetic materials makes it easy
to distinguish these materials from nonferromagnetic materials.
In the applet below, the probe and the sample are
shown in crosssection. The boxes represent the crosssectional
area of a group of turns in the coil. The liftoff distance and
the drive current of the probe can be varied to see the effects
of the shared magnetic field. The liftoff value can be set to
0.1 or less and the current value can be varied from 0.01 to 1.0.
The strength of the magnetic field is shown by the darkness of
the lines.
