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Basic knowledge of LVDT linear variable differential transformer

Author: Date:2012-2-8 17:19:24

The linear variable differential transformer is a magnetic position transducer. Its use is very widespread due to its features of being a contactless sensor, with virtually infinite resolution and high accuracy. Resolution and accuracy are mainly determined by the conditioning electronics and can be improved by means of ratiometric reading. Its use is, therefore, quite common in harsh environments such as nuclear plants and particle accelerators.

The LVDT sensor is basically a transformer with one primary winding, in the center of the cylindrical structure, and two secondary windings, one of each side of the primary, wound on a cylindrical support (Figure 1). A ferromagnetic core can move along the axis, and the flux linkage between the primary and secondary windings changes accordingly to its position. In particular, when the core is completely on one side of the structure, one secondary voltage is maximum whereas the other one is minimum. When the core is in the middle, the two voltages are equal. The position of the core can be extracted by a differential reading of the secondary signals. The frequency used for the feeding signal is often in the range of a few kHz . Usually, the core is made up of Ni-Fe alloy, a material which exhibits high magnetic permeability and commonly used for these applications.

Figure 1: Typical LVDT layout and working principle (longitudinal section).

Although the LVDT reading accuracy can be guaranteed even in critical and noisy installations, this sensor has shown to be sensitive to external slowly varying magnetic fields. This is the case, for example, of installations next to devices with significant leakage or generated fields, such as motors or high current cables. The influence of such devices can lead to a position reading error which can be of the order of magnitude of hundreds of micrometers. It is, therefore, evident that this kind of error can represent a serious issue in applications where nominal accuracy of a few microns is required. To the authors’ knowledge, this problem is barely addressed in a few LVDT data sheets and completely overlooked by the vast majority of the producers; even when a warning is present, no quantitative indications on the induced errors on the position reading, nor about possible countermeasures, are present. In the scientific literature, this problem has been firstly introduced and discussed by , although no quantitative validated models are available. In this paper, a finite element (FE) model of linear variable differential transformer for the magnetic interference study is presented, in order to conceive a tool to (i) study and quantify the interference effects, (ii) aid the conception and the development of an analytical model of the phenomenon, and (iii) design possible countermeasures for existing LVDTs or completely immune structures.

FEM-aided analysis allows a deeper investigation regarding local variables and physical magnitudes, such as local values of magnetic flux density or magnetic field , practically very difficult or too expensive to measure directly.

The results coming from the FE analysis are then validated on a customized LVDT prototype, whose structure closely reflects the one of the finite elements model itself. A complete set of measurements has been performed on the manufactured prototype, in standard working conditions and in presence of an external interfering magnetic field, in order to verify the agreement with the model. Since the LVDT can be supplied by either voltage or current excitation , the measurements have been performed in both cases, in order to point out possible differences and eventually compare the interference effects in different supply cases.

In Section 2, the finite element model and the simulation outline are presented. The simulation results are discussed in Section 3. In Section 4, the measurements setup and the experimental results are presented and the comparison with the simulations is then discussed.

2. LVDT Finite Element Model and Simulation Procedure

An FEM model for the simulation of the LVDT sensor has been developed using the simulation software FLUX. This simulator is particularly suited for the finite element analysis of electromagnetic problems involving 2D and 3D geometries .

The purpose of such an FEM analysis is to conceive a model of linear variable differential transformer which can be used as a tool for analysis and design of LVDT exposed to external magnetic fields. The availability of such a model would allow an immediate feedback in the analytical study of the physical phenomenon of the external magnetic fields influence on LVDT reading, as well as in the design process of an LVDT-like structure with immunity to external magnetic fields.

Being in principle the external field not known in many applications (neither in terms of amplitude, nor in terms of time evolution), a recalibration of the device in presence of interfering field, which could be an effective solution for purely DC fields, cannot be of help in this case. Furthermore, the external field may not be always present. Indeed, in presence of a slowly varying external field (i.e., the frequency content of such a field being in the ultralow frequency range whereas the internal LVDT magnetic field harmonics are in the range of few kHz), at each reading the LVDT will experience an error which is a function of the value of the interfering field (which is nearly constant). Therefore, at each reading, the effect on the position can be seen as due to a DC external field. However, the existence of an intrinsic time variation of such a field, for what has been said, invalidates the possibility to recalibrate the device.

2.1. 2D Modeling

The LVDT geometry presents cylindrical symmetry. On the other hand, an interfering magnetic field impinging the LVDT structure can be in principle arbitrarily oriented. However, an arbitrarily oriented magnetic field can be seen as the superposition of longitudinal (parallel to the LVDT axis) and transversal (perpendicular to the axis) components. Given that such sensor is more sensitive to longitudinal magnetic fields, this case is here considered. Thus, the simulation geometry has to include the sensor itself and an external longitudinal magnetic field source. Actually, the impinging magnetic field (the magnetic field generated by the external source when the LVDT is not present) can be uniform or nonuniform along the LVDT axis. For a first-step model, the interfering magnetic field has been chosen to be uniformly distributed along the axis and on the cross-section. For this reason, the interfering magnetic field will exhibit a rotational symmetry too. Thus, the magnetic field source can be a solenoid. In this way, the whole structure has complete cylindrical symmetry and the simulation geometry can be built in two dimensions.

The simulated LVDT model slightly differs from the simple structure presented in Section 1 and displayed in Figure 1. In the actual model, the primary coil is indeed wound on the entire length of the winding support whereas the secondary coils are wound over the primary, one of each side of the structure (Figure 2). In this way, the leakage inductances of the transformer are significantly reduced. The model presents insulator washers and layers, treated as nonmagnetic regions.

Figure 2: 2D longitudinal scheme of the LVDT sensor FEM model (not in scale).

The structure is enclosed in a ferromagnetic cylindrical case with two end caps. The ferromagnetic case, together with the end caps, has two main functions: it closes the LVDT magnetic circuit and acts like a first shielding against external magnetic fields. The core is a cylinder whose length is equal to the secondary coils length.

Given the cylindrical symmetry, the simulation geometry takes into account only half of the longitudinal section of the sensor (Figure 3). Actually, the complete 3D geometry is obtained by rotating the simulation geometry around the symmetry axis by 360 degrees (Figure 3). However, even though the finite element analysis can be performed totally in the 2D environment, the results are provided anyway for the whole volume of the device, resulting in a significant reduction of computational time.

Figure 3: 2D simulation geometry and 3D reconstruction. In the infinite box, a geometrical transformation is performed in order to simulate the infinite space.

The structure has a high aspect ratio, thus a fine mesh has been chosen in order to discretize the thicknesses whereas the mesh along the length of the sensor can be coarser. By doing so, the mesh has been optimized using triangular elements on all the geometry. The meshing and the solving parameters for the geometry are reported in Table 1. The presence of a small amount of poor elements (i.e., nearly flat triangular elements), disposed axially, is not a concern; indeed in such a structure, the variation of the fields in a single region is supposed to be more rapid in the transversal direction, rather than in the longitudinal one. This assumption applies also to the regions of the structure between the coils and the external case, in which the poor elements are present. In addition, in the regions corresponding to the magnetic media, the mesh density has been adapted to the penetration depth. Being in principle the magnetic permeability a function of the magnetic field, the penetration depth has been calculated in the worst case (i.e., maximum permeability) and the meshing density arranged so as to have at least two meshing elements inside the skin depth area.