Desarrollo de un modelo matemático utilizando interpolación de Lagrange para el comportamiento dinámico de sensores de presión LVDT.

Abstract

The main objective was to implement an adequate system of acquisition and interpretation of signal data from a pressure sensor Linear Variable Differential Transformer (LDVT) that is located inside of a test chamber for materials of Civil Engineering at Universidad Nacional de Chimborazo to be independent of the data interpretation equipment, due to its inefficient mobility toward the field trials outside the laboratories. To determine the mathematical model about dynamic behavior of the sensor voltage vs deformation, takes data from a laboratory test that are plotted and sought through interpolation and experimentation the curve that most equals this behavior. It mentions the six most outstanding results, and the curve used is Ln (x) = - 0.016714859437751x + 0.000012 with a maximum error of 1.39%. On the other hand, it verifies the results when measuring standard plates of 1mm, but obtains a value of -10.7049mm with an error of 970.49% which does not have to do with the calculated one; taking into account that the model based on the data of the equipment is not correct and therefore is working wrongly. The LVDT sensor is again modeled with the standardized plates, then the curve y = 15.3214x-8.1080 showed the smallest error of 0.84% and verify the results with the other plates. Finally, it demonstrates that it satisfies the hypothesis by comparing our system with analog meters. The values of the analog and the new system respectively are a variation of results or Accuracy = 3.09% and 0.141%, Data dispersion = 0.01mm and 0.0005mm, test Time = 34.33min and 2.141min. It concludes that our system is more efficient than an analogue and allows verifying the hypothesis of knowing the dynamic behavior of the LVDT sensor to replace the material testing equipment at the laboratory of Civil Engineering.