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VERIFICATION OF OUTPUT PARAMETERS OF MAGNETOELASTIC SENSOR OF
PRESSURE FORCE
Hodulíková A., Ing., PhD., Technical University in Košice, assistant professor
Technical University of Košice, Letná 9, 042 00 Košice, Slovak Republic
Address: Park Komenského 3, 042 00 Košice, Slovak Republic
E-mail: [email protected]
In its first part the article described the utilization of elastomagnetic phenomena in magnetoelastic sensors of
pressure force (MES). In the second part the article is focused on verification of the output parameters (output voltage
and effective output voltage) of magnetoelastic sensor. The aim was to figure out, if the values of magnetic induction
obtained by MES model simulation in COSMOS/EMS environment and used for calculation of output parameters are
corresponding to the experimental results.
Key words: simulation, magnetoelastic sensor, model, finite element method, ferromagnetic material.
INTRODUCTION. In present days the sensors are
utilized more and more. In the field of measurement
they present the most important part of the
measurement chain. The overall accuracy of the
measurement is limited by them, therefore, there is a
higher requirement on their accuracy. They are used in
measurements of the big pressure force, rolling force,
measurement of the forces in bridge pylons, as a
protiection for mechanical overload or in the rough
weighing of the railway wagons [1].
PROBLEM STATEMENT. The advantage of the
EMS is their relatively high sensitivity and possibility
of utilization of the output quantity without the need of
signal amplification. When compared to other sensors,
they are more massive, however, their shape and
construction gives them better mechanical propertes,
resitance to overloading, air humidity, dust, shocks and
vibration. The disadvantage lies in higher energy
consumption and sensor´s error.
Magnetoelastic sensors of force are divided into two
groups - sensors of compressive and tensile force. The
sensors are of transformer type and have been designed
and assembled for the measurement of compressive
force from 1,2kN to 12MN. A lot of attention has been
given to the improvement of output parameters of the
sensors MES 120kN and 6MN. The verification of
output parameters and effective output voltage was
realised for magnetoelastic sensor of 120kN pressure
force (Fig.1).
F
Magnetoelastic sensors belong to the group of nonlinear
systems. They are operates on the Villari’s effect
principle, which is based on a change of feromagnetic
material permeability proportionally to acting
mechanical stress. The permeability increment Δμ
proportional to the mechanical stress σ can described
by relation [1]
Δμ 
2λ ms μ 2
.σ
2
Bsef
(1)
where λ ms is the middle value of magnetostriction
coefficient in fed state,
is permeability of

ferromagnetic material when the affecting force is zero,
Bsef is effective value of magnetic induction in fed
state, k M is the material coefficient. The equation (1)
is valid for case, when the direction of mechanical
tension and magnetic field intensity are parallel. From
the equation (1) we can see, that for magnetoelastic
sensors it is convenient to use the materials with high
permeability μ, high value of magnetostriction λs and
also low value of magnetic induction Bs .
Practical fabrication of magnetoelastic sensor of
pressure force 120 kN, which correspond to 100 MPa
pressure.
The input parameter of the sensor is the external
pressure force affecting the sensor and output parameter
is the effective value of voltage, which is induced in the
secondary winding of the sensor. For the voltage
expression we are utilizing the induction law. The
voltage will be induced in case when the whole
magnetic flux will be encircled by secondary wire. This
requirement is fulfilled in case when secondary winding
will be winded by the holes of the primary winding.
In case when the sensor is not affected by the external
pressure force, the induced voltage uv  t  can be
expressed as:
Figure 1 – Magnetoelastic force sensor 120kN
PREVIOUS
RESEARCHES
ANALYSIS.
uv  t    N 2


  B  t  dS  ,
t  s

(2)
uvF  t    N 2

 F
  B  t  dS  ,
t  s

(3)
where BF  t  is the magnetic inductance in sensor´s
core when external pressure affects the sensor in time t.
The magnetic field in sensor´s core is activated by
harmonic current i1  t   I m1 sin t  A , where Im1 is
the maximal value of the current i1  t  ,  = 2 f is the
angle frequency of time changes of feeding current
which passes through the primary winding of the
sensor. Magnetic induction and output voltage then
have the timely harmonic course.
The question is, which value of the time changing
course should be measured. The results of the practical
measurements point to the value of effective value of
output voltage.
In order to express the effective value of output voltage
it will be convenient to to come out from the simplified
assumption, that the course of sensor´s magentic
induction is also harmonic and for effective value of
voltage U vef a U vef voltage uv (t) is:
1T 2
1T


 uv dt 
  N 2   B  t  dS   dt
T0
T 0
t  S

2
U vef 
(4)
U vef 
1T 2
 uv dt 
T0
1T 

F
   B  t   B  t   dS  dt
T 0  S t

affected by external pressure force as well as the case
when the sensor is affected by external pressure force.
For the needs of magnetostatic analysis, the
magnetization curve had to be measured. This curve
was for ferromagnetic material (transformator sheet)
from which the sensor´s core lamellas are
manufactured. The values measurement for these curves
was realised by Epstein´s device for frequencies f =
200 and 400 Hz. From the measured and calculated
values the graphical representation had been made µ = f
(B ), shown on (Fig. 2).
magnetic permeability [H/m] 10E-03
where
N2 is the amount of the threads of secondary
winding, B  t  is magnetic induction in the sensor´s
core without the external pressure force in time t, dS is
the surface element, S is the surface of the cross section
of sensor´s core.
In case, when the external pressure force affects the
sensor, the induced voltage uvF  t  can be expressed as:
4
f = 200Hz
3
2
f = 400Hz
1
0
0
0,2
0,4
0,6
0,8
1
magnetic flux density B [T]
Figure 2 – The dependence of the permeability on the
magnetic flux density μ = f  B 
From the results it can be seen, that with increasing
pressure force the value of magnetic inductance is
rapidly decreasing, the magnetic field gets deformed
resulting in change in core´s magnetic properties which
result in the change of magnetic permeability.
The graphs on Fig. 3 and Fig. 4 show not only the
abovementiond conclusions, but it can be seen, that the
value of magnetic inductance decreases also with
increased value of frequency.
2
 N2
(5)
The output signal of sensor is the effective value of
voltage measured by voltmeter.
From the equations (4) and (5) we can see, that for the
effective value of output signal and output effective
signal we need to know the value of magnetic
induction, which we can obtain by solving the magnetic
field of the magnetoelastic sensor.
The output signal of the sensor is directly proportional
to the change of permeability and the deformation of
magnetic field.
The task was solved as a magnetostatic problem for
chosen value of current I1max = 1A in nonlinear
environment for the case, when the sensor is not
Figure 3 - The dependencies of magnetic flux density,
in the dependence on pressure force applied to the
sensor, F = 0, 80, 100, 120 kN, f = 400Hz
Fi
gure 7 - Dependency of output voltage value from
affecting force for f = 200Hz
Figure 4 - The dependencies of magnetic flux density,
in the dependence on pressure force applied to the
sensor, F = 0, 80, 100, 120 kN, f = 200Hz
The effective values of output voltage and effective
signal of sensor proportional to affecting force were
calculated by equations (4) and (5) and compared to the
experimental values. The comparison of the calculated
and measured values is shown in graphical way on
following figures. (Fig. 5, Fig. 6, Fig. 7 and Figr. 8) .
Figure 8 - Dependency of output effective voltage
value from affecting force for f = 200Hz
Figure 5- Dependency of output voltage value from
affecting force for f = 400Hz
CONCLUSION.
In the article, the relation between the input and output
parameter of the elastomagnetic sensor of 120kN had
been verified. By the comparison of calculated and
experimental values, the results diferences had been
obtained. These differences are caused by the utilization
of simplified assumption, that the magnetic induction
dourse is harmonic and permeability in sensor´s core is
constant. In reality however, the permeability is
dependent on magnetic induction. Therefre, the sensor´s
field had to be solved as a nonstationary magnetic field.
ACKNOWLEDGMENT. The paper has been prepared by
the support of Slovak grant projects VEGA No.
020069/15.
REFERENCES
1. Hodulíková A. Computer simulation model of
EMS of force to the PhD Thesis, Košice, 2012.
2. Mayer,D Ulrych,B, Škopek,M. Solution of
electromagnetic fields using modern software products,
Journal EE, vol 7, no1, 2 , 2001.
Figure 6 Dependency of output effective voltage
value from affecting force for f = 400Hz