16 th IMEKO TC4 Symposium Exploring New Frontiers of Instrumentation and Methods for Electrical and Electronic Measurements Sept. 22-24, 2008, Florence, Italy Conversion from geometrical to electrical model of LVDT Cleonilson Protásio de Souza 1 , Michel Bruno Wanderley 2 1 Federal Center of Technological Education of Maranhão-Brazil (CEFET-MA) Av. Getúlio Vargas, 04 Monte Castelo – São Luís-MA, Brazil, 65030-000, protasio@cefet-ma.br 2 Research Grant supported by Research Support Foundation of Maranhão-Brazil (FAPEMA), Av.Beira-Mar, 342, Centro – São Luís-MA, Brazil, 65010-070, mbwander@gmail.com Abstract - The Linear Variable Differential Transformer (LVDT) is an inductive sensor which is used to measure linear displacement and finds uses in modern machine-tool, robotics, avionics, and computerized manufacturing. Its basic structure consists of a primary coil and two secondary coils like an electrical transformer. However, LVDT has a movable magnetic core that when the primary coil is excited with an AC voltage source, induced secondary voltages vary with the displacement of the core. In general, this accurate and reliable displacement-to-electrical sensor can be modeled in two forms: geometrical-parameter-based model and electrical-parameter-based model. Both are very used. However, research results based in geometrical-based model may become useless when only parameters from electrical one are known. In this paper, it is shown a way of conversion from geometrical- to electrical-based model in order to allow the interaction from one to other. I. Introduction The Linear Variable Transformer Differential (LVDT) is used to measure linear displacement or position. LVDT can be used in several applications as: automobiles’ suspension [1], seismic shocks measurement [2], orthodontia [3], femoral prosthesis in medicine [4], deformations in concrete frames in civil engineering [5], position system of robotic arms [6], besides other physical measurements. The basic structure of LVDT consists of a primary coil and two secondary coils like an electrical transformer. However, LVDT has a movable magnetic core that when is dislocated it varies the mutual inductances among secondary coils and the primary coil. In operation, it is applied an AC voltage, ܧ ௜ in the primary coil, as is shown in Figure 1. The secondary coils are connected in series with opposing phase, so when the magnetic core is exactly at the physical center between them, then the output voltage, ܧ ௢ , is zero, as the net output is the difference between the two secondary voltages, ܧ ௢ ൌ ܧ ௢ଵ െ ܧ ௢ଶ . If the core is moved from the center, it is obtained an output voltage that is proportional to the core displacement, because there is a misbalance of magnetic flux intensities among the primary coil and the secondary coils and one secondary coil receives more flux than the other. This misbalance produces non-zero output voltage proportional to the core displacement [7]. On the other hand, mathematical models are very important tools for engineering and for previous developments. For LVDT, the determination of a model and the estimation of its parameters is an important way to develop new applications using this sensor. Also, when it is commercialized there is a dependence of the manufacturer with regard to the calibration and the precision of the sensor. Figure 1. LVDT: (a) Internal Schematic. (b) Internal Model.