Análise numérica tridimensional e experimental do comportamento mecânico de alças ortodônticas delta

Abstract

This study analyzed numerically and experimentally the mechanical characteristics of orthodontic springs with delta geometry with and without an upper loop. To our knowledge this kind of study of delta springs without an upper loop has not yet been described in the literature. The material used to make the springs was a titanium-molybdenum alloy commonly used in orthodontic applications. Numerical simulations were performed with finite element modeling (FEM) using three-dimensional elements and large-displacement analysis, unlike the analyses found in the literature to date for this type of spring, which are exclusively two-dimensional. The springs were simulated to reflect a real clinical situation with horizontal activation (in the x direction). In the experimental analysis to determine the reactive forces and moments, a platform with strain gauges mounted on a full Wheatstone bridge whose output voltages corresponded to the strain applied to the spring (the test specimen) was used. The voltage variations were read with the aid of a National Instruments data acquisition system, which, when used with the LabVIEW program, provides voltage values which are converted into forces and moments to calibrate the platform. Each value of force and reactive moment was recorded in a table, from zero activation to the maximum value, i.e., just before the yield strength of the material was reached. In addition to the reactive forces and moments, the moment-to-force ratios (M:F) were measured. According to the literature, these ratios define the type of tooth movement in a clinical case. The results show that the reactive forces along the x-axis in the springs without a loop were greater than in the springs with a loop. In contrast, the reactive intrusive/extrusive forces in the y-axis, which were very small and could be neglected in this study because they had little influence on the results, were similar for both types of spring. A curve showing the change in stress along the spring as a function of activation was plotted. This showed that springs without a loop had higher stresses for a given activation value and therefore a greater tendency to deform plastically. The predominant M:F ratio in this study was the Mz/Fx ratio, which is the moment-to-force ratio that produces most types of tooth movements described in the literature and is to date the only moment-to-force ratio described in the literature for the delta spring. The tooth movements in the xy-plane as a result of the Mz/Fx moment-to-force ratio produced by delta springs with and without a loop are root rotation, crown rotation and translation. Based on the values of My/Fx observed, it can be inferred that this type of spring does not produce any tooth movement in the xz-plane. Another factor that is not explored in the literature but that was considered here is the variation in the angle between the extremities of the spring and its impact on the final forces, moments and M:F ratio.