RESUMO
Eddy current displacement sensors (ECDSs) are widely used for the noncontact position measurement of small displacements (lift-offs). Challenges arise with larger displacements as the sensitivity of the ECDSs decreases. This leads to a more pronounced impact of temperature variations on the inductance and, consequently, an increased position error. Design solutions often rely on multiple coils, suitable coil carrier materials, and compensation measures to address the challenges. This study presents a single-coil ECDS for large displacement ranges in environments with high temperatures and temperature variations. The analysis is based on a sensor model derived from an equivalent circuit model (ECM). We propose design measures for both the sensing coil and the target, focusing on material selection to handle the impact of temperature variations. A key part of improving performance under varying temperatures includes model-based temperature compensation for the inductance of the sensing coil. We introduce a method to calibrate the sensor for large displacements, using a modified coupling coefficient based on field simulation data. Our analysis shows that this single-coil ECDS design maintains a position error of less than 0.2% full-scale for a temperature variation of 100 K for the sensing coil and 110 K for the target.
RESUMO
Introduction: Numerical modeling of the intervertebral disc (IVD) is challenging due to its complex and heterogeneous structure, requiring careful selection of constitutive models and material properties. A critical aspect of such modeling is the representation of annulus fibers, which significantly impact IVD biomechanics. This study presents a comparative analysis of different methods for fiber reinforcement in the annulus fibrosus of a finite element (FE) model of the human IVD. Methods: We utilized a reconstructed L4-L5 IVD geometry to compare three fiber modeling approaches: the anisotropic Holzapfel-Gasser-Ogden (HGO) model (HGO fiber model) and two sets of structural rebar elements with linear-elastic (linear rebar model) and hyperelastic (nonlinear rebar model) material definitions, respectively. Prior to calibration, we conducted a sensitivity analysis to identify the most important model parameters to be calibrated and improve the efficiency of the calibration. Calibration was performed using a genetic algorithm and in vitro range of motion (RoM) data from a published study with eight specimens tested under four loading scenarios. For validation, intradiscal pressure (IDP) measurements from the same study were used, along with additional RoM data from a separate publication involving five specimens subjected to four different loading conditions. Results: The sensitivity analysis revealed that most parameters, except for the Poisson ratio of the annulus fibers and C01 from the nucleus, significantly affected the RoM and IDP outcomes. Upon calibration, the HGO fiber model demonstrated the highest accuracy (R2 = 0.95), followed by the linear (R2 = 0.89) and nonlinear rebar models (R2 = 0.87). During the validation phase, the HGO fiber model maintained its high accuracy (RoM R2 = 0.85; IDP R2 = 0.87), while the linear and nonlinear rebar models had lower validation scores (RoM R2 = 0.71 and 0.69; IDP R2 = 0.86 and 0.8, respectively). Discussion: The results of the study demonstrate a successful calibration process that established good agreement with experimental data. Based on our findings, the HGO fiber model appears to be a more suitable option for accurate IVD FE modeling considering its higher fidelity in simulation results and computational efficiency.