Sensors and Actuators A 106 (2003) 104–107
Demonstration of a new method for magnetic flux measurement
in the interior of a magnetic material
George Loisos
∗
, Anthony J. Moses
Wolfson Centre for Magnetics Technology, Cardiff University, P.O. Box 925, Cardiff CF24 0YF, UK
Abstract
A method is proposed for magnetic flux measurement in localised regions inside a magnetic material using a novel surface probe sensor.
The principle of operation is described and its potential use in steel products is experimentally verified.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Magnetic flux density measurements; Magnetic material characterisation
1. Introduction
The extreme non-linearity between B and H in a ferro-
magnetic material has prevented the exact calculation of the
internal eddy currents or flux density. Despite the good ap-
proximations by assuming linear B–H relationships it has
always been desirable to have a method or sensor, which
could give an indication of the actual flux density variation
inside a material. This would provide a better understanding
of eddy current distribution inside materials, which for ex-
ample is necessary for evaluating and attempting to reduce
losses in magnetic materials.
The proposed method is applicable to plates, strips and
laminations and also to any other shape of ferromagnetic ma-
terial but for convenience the theory and experiment refers
to a typical lamination of electrical steel.
The well-known search coil (Fig. 1a), the conventional
probe sensor [1] and the modified probe sensor (MPS)
(Fig. 1b) [2] are the three most common sensors for global
and more specifically localised flux density measurements
in laminations. However, these sensors only give an indica-
tion of the total flux in the material enclosed by the search
coils or the needle probe wirings whereas it is useful to
have a measure of the localised internal variation.
The modified probe sensor is more accurate than the con-
ventional probe sensor [2]. It can further be modified to
include diagonal positioning of the conductive probes (i.e.
PCB contact probes) (Fig. 1c) and it will be proved theoret-
ically and shown experimentally that it is possible to have
∗
Corresponding author.
E-mail addresses: loisosg1@cardiff.ac.uk (G. Loisos), mosesaj@cf.ac.uk
(A.J. Moses).
an induced voltage proportional to the flux density rate of
change in a triangular cross-sectional area such as shown in
Fig. 1c instead of the traditional orthogonal cross-sectional
areas.
2. Principle of modified probe sensor
A schematic diagram of a modified probe configuration
is shown in Fig. 2. The output voltage V
A
from the set of
probes at positions A and A
′
is given by
V
A
=-
∂
B
∂t
d
A
2
-
∂
B
air
∂t
d
A
air
+ V
AA
′ (1)
Similarly, the output voltage V
B
from the set of probes at
positions B and B
′
is given by
V
B
=-
∂
B
∂t
d
A
3
-
∂
B
air
∂t
d
A
3
-
∂
B
air
∂t
d
A
air
+ V
BB
′ (2)
where A
3
= A
1
+ A
2
; A
1
is the area enclosed by the path
ABB
′
A
′
, A
2
the area enclosed by OAA
′
O
′
and A
3
the area
enclosed by OBB
′
O
′
.
If we subtract Eq. (1) from (2) (|V
A
| < |V
B
|) the resulting
voltage e
output
is equivalent to a voltage induced in a one-turn
search coil enwrapping the cross-sectional area ABB
′
A
′
(that
is, area A
1
) plus an error due to air flux. This is given by,
e
output
= V
B
- V
A
=-
∂
B
∂t
d
A
1
-
∂
B
air
∂t
d
A
air
(3)
since it can be assumed that V
AA
′ = V
BB
′ .
0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0924-4247(03)00144-4