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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The permanent magnetic linear contactless displacement (PLCD) sensor is a new type of displacement sensor operating on the magnetic inductive principle. It has many excellent properties and has already been used for many applications. In this article a Micro-PLCD sensor which can be used for microelectromechanical system (MEMS) measurements is designed and simulated with the CST EM STUDIO^{®} software, including building a virtual model, magnetostatic calculations, low frequency calculations, steady current calculations and thermal calculations. The influence of some important parameters such as air gap dimension, working frequency, coil current and eddy currents

The measurement of displacement or position is one of the most important and oldest tasks in sensor technology [_{1} and Φ_{2} of the same size but inversely orientated in the magnetic core. If a permanent magnet of adequate strength approaches the surface of the sensor, the corresponding section of the magnetic core will reach magnetic saturation, which results in a virtual separation of the magnetic core. Then magnetic fluxes Φ_{1} and Φ_{2} will be decoupled with each other. If the permanent magnet is located above the center of the magnetic core, Φ_{1} and Φ_{2} will cancel each other with regard to the measurement coil and output voltage is zero. Any non-central position of the permanent magnet will result in a non-zero output voltage which is linearly proportional to the position of the permanent magnet.

Based on the working principle of the PLCD sensor illustrated above, this Micro-PLCD sensor is simulated and studied using Finite Integration Technique (FIT) implemented by the CST EM STUDIO^{®} software [

The whole Micro-PLCD sensor model with the permanent magnet is shown in ^{®} for the convenience of changing model and parameter sweeping during low frequency calculation. In this model, all functional elements are completely sealed in insulator, which makes this Micro-PLCD sensor robust to harsh environments.

There are mainly two different kinds of materials in the sensor. The soft magnetic core is made of a non-linear soft magnetic material. All other components such as coils, insulator, substrate and permanent magnet use linear materials and their material properties are listed in ^{®} [^{®} is shown in ^{®} is 0.8 T; this is a very important parameter, mainly used to determine magnetic saturation regions.

Finally, all calculations in this article use electrical boundary condition, which means all simulation results below are based on the situation that the Micro-PLCD sensor works in a normal space around which it is all metal, just like it is embedded in a machine.

Two different kinds of electromagnetic sources exist in this model: the permanent magnet is a magnetostatic source and two excitation coils supplied by alternating current are low frequency sources. To couple these two different sources and following thermal calculation, four calculation steps are performed successively. The magnetostatic calculation is performed first to determine the position and dimension of the magnetic saturation regions in the core and feedback line. Based on the magnetostatic calculation results, three magnetic saturation region models are built and low frequency calculations are then performed to determine the relationship between the position of the permanent magnet and the output voltage. While their relationship is proved to be linear, a simplified partial sensor model is built to calculate the current distribution, which is also a thermal source of the following thermal calculation. Finally, the temperature field distribution while the sensor is working is determined.

In order to calculate the position and dimension of all magnetic saturation regions, nine tracking curves are defined in the soft magnetic core and another nine tracking curves are defined in one feedback line, as

After magnetostatic calculation is finished, magnetic flux density excited by the permanent magnet above the centre of the sensor along the nine tracking curves defined above in the soft magnetic core (curve 1 to curve 9) is shown in

The air gap between the permanent magnet and sensor surface _{m}_{m}_{m}

Flat tops of all resulting curves in

_{m}_{m}

To see this phenomenon more clearly, we choose two typical _{m}_{m}_{m}_{m}_{m}

Based on the results of the magnetostatic calculation, three cuboid-like magnetic saturation region models are built in the soft magnetic core and two feedback lines with their relative permeability almost equal to unity. At the same time, the permanent magnet is ignored and the non-linear material of the soft magnetic core is simplified to a linear material. All those modifications are aimed to replace the effect of magnetic saturation phenomenon that is caused by the permanent magnet and the soft magnetic material. The position of these magnetic saturation regions will be swept from one end of the sensor to the other end with the parameter sweep function of CST EM STUDIO^{®} instead of the movement of the permanent magnet. The magnetic saturation region models located in the middle of the sensor are shown in

After the modified model is ready, the monitor of CST EM STUDIO^{®} is set to record the voltage of the measurement coil. Finally, a low frequency calculation could be performed under the excitation of alternating excitation coil current. The relationship between the output voltage of the measurement coil and the position of magnetic saturation regions which corresponds to the position of the permanent magnet is shown in

_{m}

All calculation results finished until now show that output voltage will decrease with an increment of the air gap between the permanent magnet and sensor surface but with a decrement of excitation coil current. At the same time, the relationship between the output voltage and permanent magnet can remain linear.

Until now, all calculations performed before are based on a working frequency of

To obtain more information about the temperature field distribution of the whole sensor while the Micro-PLCD sensor is working, a thermal calculation is finally performed for reference. While the sensor is working, there are mainly two different kinds of currents in the sensor: coil currents and eddy currents. They are the main thermal source and make the temperature of the sensor increase. The eddy current field can be calculated based on the low frequency calculation results. In order to calculate the coil current field, a very detailed Micro-PLCD sensor model including all coil details must be used. Because the measurement coil has about 800 windings and the excitation coils have about 140 windings, a very large scale calculation model is needed for building a detail Micro-PLCD sensor model. In order to solve this problem, a simplified sensor is modelled as

Based on this simplified model, steady current calculation can be performed with the steady current solver of CST EM STUDIO^{®}. The steady current field of this partial sensor model is shown in

The eddy current field and the steady current field can be set as the thermal source and thermal calculations are then performed with the thermal solver of CST EM STUDIO^{®}. When the coil current is set to be the maximal value

Because the eddy current field of the sensor is very small, the highest temperature in

In this article, a Micro-PLCD sensor is designed and simulated in the CST EM STUDIO^{®} software, including magnetostatic calculation, low frequency calculation, steady current calculation and thermal calculation. All simulation results show the good performance of the designed Micro-PLCD sensor. In the near future, more parameters will be adjusted and optimized; more materials will be calculated to improve linearity and output voltage of the measurement coil. The influence of temperature, configuration of permanent magnet and sensor component, movement velocity of permanent magnet

We gratefully acknowledge the support from the ‘Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.

Design model of the Micro-PLCD sensor.

Feedback lines model.

Micro-PLCD sensor model.

B-H curve of MUMETALL^{®}.

Tracking curves in the soft magnetic core and feedback line.

Magnetic field distribution in the soft magnetic core.

Magnetic field distribution in the feedback line.

Magnetic flux density along tracking curve 2 with different _{m}

Magnetic flux density along tracking curve 11 with different _{m}

Magnetic field distribution of the whole sensor while _{m}

Magnetic field distribution of the whole sensor while _{m}

Magnetic saturation region models.

Low frequency calculation result.

Low frequency calculation results under different working conditions. _{m}_{m}

Low frequency calculation results under different working frequencies.

Simplified Micro-PLCD sensor model.

Steady current field of the partial sensor model.

Temperature field based on eddy current.

Temperature field based on coil current.

Material properties of the sensor.

^{3} | ||||||
---|---|---|---|---|---|---|

Coils | Copper | 1 | 5.8 · 10^{7} |
401 | 0.385 | 8,960 |

Substrate | Silicon | 11.9 | 1.56 · 10^{−3} |
148 | 0.703 | 2,329 |

Insulator | SU-8 | 3 | 1 · 10^{−10} |
0.25 | 1.3 | 1,200 |

Magnet | NdFeB | 1 | 7.14 · 10^{5} |
18 | 0.45 | 8,700 |

Core | MUMETALL^{®} |
1 | 1.82 · 10^{6} |
18 | 0.45 | 8,700 |