Finite Element Analysis Of An Electromagnetic Linear Displacement Transducer - Felicia Gheorghe, Virgiliu Fireteanu

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

FINITE ELEMENT ANALYSIS OF AN ELECTROMAGNETIC LINEAR DISPLACEMENT TRANSDUCER Felicia Gheorghe, Virgiliu Fireţeanu POLITEHNICA University of Bucharest, EPM_NM Laboratory 313 Splaiul Independentei, 060042 Bucharest, Romania http://www.amotion.pub.ro/~epm/ Abstract – This paper deals with is the study of a linear displacement transducer based on finite element analysis. The electromagnetic configuration of the transducer consists in a sensor head and a mobile pattern guide in two variants – an eddy current solid conductor guide, respectively a magnetic pattern guide. The linear displacement – output voltage dependences are evaluated, the influence of the supply frequency and magnetic permeability is studied and the structure of the magnetic field and of the current density are analyzed in order to obtain pertinent information for optimal design of such a magnetic transducer.

Introduction It is usually necessary to measure displacements in modern industrial processes and devices. One of the simple and commonly used methods consists in a displacement sensor based on the inductive concepts [1]. This method overcomes major problem of the some displacement sensors, for example of optical sensors, where the existence of any obstacle between the detection objects decreases the accuracy. Other types of displacement sensors [2, 3] are sensitive to the environmental influences such as oil, dirt and water. The linear displacement transducer studied in this paper uses a meander coils [4] sensor and a pattern guide of solid conductor type, respectively of magnetic core type.

Electromagnetic configuration and the Finite element 3D model The operation of an electromagnetic transducer for the measurement the linear displacement with respect a reference position is based on the dependence of the electromagnetic field structure on the relative position between the mobile and fixed parts of the transducer. The transducer studied in this paper, Fig. 1, consist in a field coil, a.c. current supplied, an output/measurement coil connected to a voltmeter and a pattern guide able to change the electromagnetic coupling between the field and the output coil. The pattern guide of the transducer can be an electro-conducting plate, in which the time dependent magnetic field created by the field coil generates eddy currents. This case corresponds to an eddy current transducer with pattern guide of solid conductor type. Output coil

Sensor

Field coil Pattern guide

Displacement Fig. 1. Linear displacement transducer principle

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

A second transducer variant contains a magnetic non-conducting pattern guide, respectively a pattern guide of magnetic core type. The magnetic coupling between the output coil and the coil generating the magnetic field is characterized by the mutual inductance M. If the current in the field coil is independent on the relative position sensor – guide, the output voltage Uo is proportional with M. This mutual inductance depends on the sensor displacement with respect a reference position; consequently the value of output voltage is dependent on displacement that is the input transducer quantity. The main parameters of the sensor - pattern guide electromagnetic coupling are: - the geometry and the number of turns of the sensor coils; - the geometry and the electromagnetic properties of the pattern guide; - the relative position sensor – pattern guide, defined by displacement parameter. The 3D computation domain of the electromagnetic field, Fig. 2, includes: (a) the sensor head that contains the field and the output coils of meander type, resistivity 2e-8 Ωm; (b) the pattern guide, which can be a conducting plate or a non-conducting magnetic core; (b) the Air and Infinity regions, Fig. 2, non-magnetic and non-conducting regions, the last representing the model of an infinitely extended computation domain. Infinity Air

Sensor head

Pattern guide

sensor head and pattern guide - zoom with mesh Fig. 2. Regions of the computation domain, sensor geometry (1)

The circuit model of the transducer includes two coil components of solid conductor type corresponding to the field and output coils, a supply voltage source of 5 mV, independent on the frequency value and a resistor of 1 MΩ connected to the output coil terminals for output voltage measurement. The chart of current density in the field coil is presented in the Fig. 3.

a) geometry (2) Fig. 3. Current density chart in the field coil

b) geometry (3)

Fig. 4. Sensor head – eddy current pattern guide geometries

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

Eddy current pattern guide transducer A transducer with eddy current pattern guide for linear displacement measurement reflects the relative position of the sensor head with respect the guide as a result of magnetic field generated by the currents induced in the electro-conductive plate of the guide. The intensity of eddy currents in the pattern guide changes when the position of the sensor head modifies and this modification is reflected in the value of the output voltage. The eddy current pattern guide is copper made, resistivity 2e-8 Ωm. Three geometries of the sensor head – pattern guide assembly are considered: (1) adjacent field and output coils, both on the same part of the pattern guide plate, Fig. 2, (2) superposed identical coils on the same part of the pattern guide plate, Fig. 4 a) and (3) identical field and output coils, symmetrically placed with respect the pattern guide plate, Fig. 4 b). The charts of eddy current in the pattern guide plate for the three geometries, Fig. 5, correspond to the frequency 5 kHz and the value 40 mm of the displacement parameter. The smallest value of maximum of current density, 0.71 A/mm2, is obtained with the geometry number (2); for the geometries number (1) and (3) this maxim of the induced current density is 1.28 A/mm2, repectively 1.26 A/mm2.

Fig. 5. Charts of the eddy currents density in the pattern guide plate

2,5

0,006

2,0

0,005 sensibility [mV/mm]

output voltage [mV]

The curves output voltage versus sensor head displacement with respect zero reference position, Fig. 6, show the decrease of the voltage output when the displacement value increases. These dependences are non-linear, the maximum of the sensibility, Fig. 7, corresponding to the value 30 mm of the input transducer parameter – displacement.

1,5 1,0 geometry (1)

0,5

geometry (2)

0,004 0,003 0,002

geometry (1) geometry (2)

0,001

geometry (3)

0,0

geometry (3)

0 0

10

20

30

40

50

60

70

80

displacement [mm]

Fig. 6. Output voltage – displacement curves of eddy current transducer

0

10

20 30 40 50 displacement [mm]

60

Fig. 7. Eddy current transducer sensibility

70

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

Values of the supply frequency higher than 5 kHz increase the value of the output 2,5 voltage and the transducer sensibility, Fig. 8. For the analysis of frequency influence, the 2,0 geometry (3) was used. Since the increase of 1,5 the output voltage diminishes over 100 kHz, the range 10 … 100 kHz of the supply 1,0 frequency can be considered as optimum in the design of the studied eddy current 0,5 transducers for linear displacement 0,0 measurements. 0 10 20 30 40 50 60 70 80 The option for values to the upper limit of displacement [mm] supply frequency range, respectively around Fig. 8. Influence of frequency supply 100 kHz, is also underlie by the comparison for eddy current transducer of numerical results related to the Joule power Pfc in the field coil and Ppg in the pattern guide, Table 1. The lower values of these powers correspond to the upper limit of the frequency. 3,0

output voltage [mV]

f f f f f

= 5 kHz = 10 kHz = 20 kHz = 50 kHz = 100 kHz

Table 1. The Joule power in the field coil and the pattern guide

Frequency [kHz] Current [A] Pfc [mW] Ppg [mW]

5 0.085 10.807 0.458

10 0.064 6.270 0.491

20 0.041 2.561 0.267

50 0.018 0.571 0.082

100 0.009 0.174 0.033

Magnetic core type pattern guide transducer This section studies another variant of the linear displacement transducer, in which the pattern guide is a magnetic and non-conductive region. In this case, the pattern guide, operating as a magnetic core, can be laminations, or soft magnetic ferrites, or magneto-dielectric materials made. The pattern guide presence ensures the increase of the magnetic coupling between the two sensor-head coils. The reference values for the relative magnetic permeability of pattern guide plate is 150 and for the frequency 2 kHz. In order to define the optimal design of this transducer variant, four geometries of the sensor head – pattern guide are considered: (1) adjacent field and output coils, both on the same part of the pattern guide plate, Fig. 3, (2) superposed identical coils on the same part of the pattern guide plate, Fig. 9 a), (3) adjacent field and output coils between two identical pattern guide plates, Fig. 9 b), and (4) superposed identical coils between two identical pattern guide plates, Fig. 9 c).

a)

b) Fig. 9. Sensor head – magnetic pattern guide geometries

c)

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

The maximum values of the magnetic flux density in the pattern guide plates, Fig. 10, are in a range starting from 7 mT for the geometry (2) and 13 mT for the geometry (3).

Fig. 10. Charts of the magnetic flux density in the pattern guide plates

The dependences output voltage - displacement, Fig. 11, for the reference frequency 2 kHz show the increase of the transducer output when its input that is the displacement increases. The transducer with pattern guide of magnetic core type is also a non-linear transducer, Fig. 12, with the maximum of sensibility to the lover limit of the displacement measurement range. The geometry number (4), Fig. 9 c), offers the best sensibility for this transducer type. 0.018

2.8 geometry (1) geometry (2) geometry (3) geometry (4)

2.0

geometry (1) geometry (2) geometry (3) geometry (4)

0.015 sensibility [mV/mm]

output voltage [mV]

2.4

1.6 1.2 0.8

0.012 0.009 0.006 0.003

0.4

0

0.0 0

10

20

30 40 50 60 displacement [mm]

70

80

Fig. 11. Output voltage – displacement curves of magnetic pattern guide transducer

0

10

20 30 40 50 displacement [mm]

60

70

Fig. 12. Magnetic pattern guide transducer sensibility

For the analysis of frequency influence on the transducer output parameters, Fig. 13, the geometry (4) was used. Values of the supply frequency higher than 2 kHz increase the value of the output voltage, and transducer sensibility. Since the increase of the output voltage diminishes over 20 kHz, the range 5 … 20 kHz of the supply frequency can be considered as optimum in the design of the studied magnetic core type pattern guide transducer.

ISEF 2009 - XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Arras, France, September 10-12, 2009

In order to study the influence of the magnetic properties of the pattern guide three values of the relative magnetic permeability were considered for the geometry number (4), respectively µr = 10 for a magneto-dielectric material, µr = 150 for ferrite and µr = 2000 for magnetic steel laminations. The curves in figure 14 show the increase of the transducer output voltage and sensibility when the magnetic permeability of the pattern guide increases. Consequently, taking into account the interest for high values of both output voltage and transducer sensibility, the best solution for the magnetic pattern guide linear displacement transducer is the geometry with superposed identical coils between two identical pattern guide plates, Fig. 9 c), 20 kHz for frequency supply and laminations made pattern guide. 3 f = 1 kHz f = 2 kHz f = 5 kHz f = 20 kHz f = 50 kHz

6

µr = 10 µr = 150

2.5

µr = 2000

output voltage [mV]

output voltage [mV]

8

4

2

2 1.5 1 0.5 0

0 0

10

20

30

40

50

60

70

80

0

10

20

30

40

50

60

70

80

displacement [mm]

displacement [mm]

Fig. 13. Influence of frequency supply for the magnetic pattern guide transducer

Fig. 14. Influence of magnetic permeability of the pattern guide material

Conclusions The results of finite element analyses of different geometric and electromagnetic configurations offer important information for optimal design of the linear displacement transducer. The study of the influence of the frequency on the output voltage and on the transducer sensibility and of the influence of the magnetic permeability orients the choice for the field coil supply and for the material of the magnetic pattern guide magnetic. References [1] J. Brauer, Magnetic actuators and sensors, John Wiley & Sons, New Jersey, 2007. [2] M. Jagiella, S. Fericean, R. Droxler, A. Dorneich, New magneto-inductive sensing principle and its implementation in sensors for industrial applications, in: Proceedings of IEEE Sensors, Vienna, Austria, October 24–27, 2004, pp. 1020– 1023. [3] S. Zurek, T. Meydan, A. J. Moses, Analysis of twisting of search coil leads as a method reducing the influence of stray fields on accuracy of magnetic measurements, Sensors and Actuators A 142 , 2008, pp. 569– 573. [4] M. Nohisam, A. Norrimahb, R.Wagirana, R.M. Sideka, N. Mariuna, H.Wakiwakac, Consideration of theoretical equation for output voltage of linear displacement sensor using meander coil and pattern guide, Sensors and Actuators A 147, 2008, pp 470-473.