The LVDT displacement sensor consists of a primary coil and two secondary coils which are wound side by side on a common winding body as shown in Fig. 1.








 Fig. 1: Schematic of a Linear Voltage Differential Transformer (Principle)


In the central drilling of the winding body there is a soft magnetic material which can move freely. Advantageously, the two secondary coils are wound in opposite directions to obtain a positive or negative secondary output voltage depending on the displacement of the soft iron core. In this way the direction of movement is clearly established.

LVDTs are the preferred way of building linear displacement sensors for harsh industrial environments, and hence good simulation models are needed that can also reflect all sorts of environmental issues. Peer Technologies has developed precise LVDT simulation models as part of the pro-INNO digiLVDT research project which have led to substantial new insight. Taking these simulation models forward has fostered an entire new class of LVDTs with improved accuracy and size-to-displacement ratios approaching one.

ANSYS 14 allows the definition and calculation of all essential fields that are common practice in electrical engineering. The basic division is made into electric current fields, electrostatic fields, magnetostatic fields, quasi-stationary electromagnetic fields and finally wave fields. In the course of the harmonic analysis, the LVDT simulation can be referred to the calculation of quasi-stationary electromagnetic fields. Finite elements describing fields of this type must have the degree of freedom of magnetic vector potential A (Ansys ax, ay, az) and have the material property of permeability (in Ansys murx, mury, murz) as well as the material property of conductivity (in Ansys electrical resistivity rsvx, rsvy, rsvz). The magnetic flux density is achieved via B (in Ansys bx, by, bz). This is basically what the structural elements PLANE13, PLANE53, SOLID97 and SOLID117 are available for.

Fig. 2 shows a half-symmetry display of an LVDT’s entire field domain, including the external circuit, after the automatic discretization of the individual elements has been performed.



Fig. 2: Display of half-symmetry field domain after automatic discretization



On the top left side the voltage signal generator is shown, consisting of the sinusoidal voltage source V0 with coupling capacitor C0. The coupling element N0 connects the output of the discrete voltage source to the primary coil in the field domain on the right (see Fig. 3). The lower part shows the external wiring of the secondary coils. For each of the two secondary coils S1 and S2 a coupling element N0 is used, which transmits the signals from the field domain into the discrete circuit. To form the complex differential output voltage the measuring resistor R0 is used. All discrete circuit elements are modeled with the ANSYS structural element CIRCU124. In the right half of Fig. 2 we see the LVDT embedded in its semi-circular air environment. The materials are color-coded (see Fig. 3).


Element-PlotFig. 3: Sample LVDT half-symmetry finite element representation with color coding of the material assignment. Red = soft iron core, light blue = stainless steel inner tube, dark blue = primary (inner) and secondary coils (outside), purple = upper and lower end disks, housing, turquoise = ambient air


The sensor characteristic U (s) will provide a first impression of the sensor quality as depicted in Fig. 4, which shows the amplitude of the complex sensor output voltage U as a function of the path coordinate s. Excel spreadsheets will provide the sensor complex output voltage magnitude and phase for numeric post processing. Obviously, there is lots of room to improve the linearity of the sensor characteristic U (s) in this case. ANSYS Goal Driven Optimization (GDO) is a way to achieve optimization by driving the appropriate LVDT design parameters automatically. It is also important to note that a multi-domain physics simulator, like ANSYS 14, is able to reflect all sources of signal deterioration individually and relate them to the appropriate components or physical issues, respectively. E.g. thermal compensation of the sensor characteristic can be improved by an order of magnitude by selecting material properties accordingly.


U-sFig. 4: Sensor characteristic U (s). Amplitude of the sensor output voltage U as a function of the path coordinate s



Of course, ANSYS will provide far more insight into the physics of sensor operation by asking for details of the associated magnetic fields. Figures 5 through 9 suggest just a short illustration of what might be available.


 Fig. 5: Magnetic Flux Lines associated with sample LVDT assembly



H-densityFig. 6: Magnetic Field HSUM [A/m] associated with sample LVDT assembly



FluxdensityFig. 7: Magnetic Flux Density BSUM [T] associated with sample LVDT assembly



H-vectorFig. 8: Magnetic Field Vector H [A/m] associated with sample LVDT assembly




Fig. 9: Magnetic Induction Vector B [T] associated with sample LVDT assembly