Three-dimensional analysis of an orthodontic delta spring

Abstract

Introduction: The purpose of this study was to analyze the force system, moment-force ratios (M/F) and von Mises stresses in an orthodontic delta spring using a 3D finite element model. The M/F ratio produced by an orthodontic spring is related to the different types of tooth movement that are likely to occur in the sagittal and occlusal planes. Methods: Analyses were performed using a 3D finite element model, and a data acquisition system was used to validate the numerical results. Results: Reactive forces between 0.0 and 2.0 N were observed along the x-axis, while null values were observed along the y-and z-axes. The maximum activation that ensured geometric stability and mechanical stresses below the elastic limit of the material was 10.0 mm. Conclusions: The results indicate that a delta spring can provide (i) uncontrolled tipping for activation of less than 1.0 mm; (ii) controlled counterclockwise tipping for activation between 1.0 and 4.5 mm; (iii) translation for activation between 4.5 and 5.0 mm; and (iv) controlled clockwise tipping in the sagittal plane for activation between 5.0 and 10.0 mm. No tooth movement was observed in the occlusal plane for the M/F ratios observed.