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 vonMises stresses in an orthodontic delta spring using a 3D fi nite 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 fi nite 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.

Von Mises stresses on Mushroom-loop archwires for incisor retraction: a numerical study

“…Besides spring geometry, properties as low load deflection rates, adequate spring gradient (spring rate) and working range should be considered in closing loops. [13][14][15][16][17][18][19][20][21] Also, torque control and gable bends are important second-order bends to avoid incisors to move lingually during retraction and posterior anchorage loss, respectively. Retraction closing loops should have a low load/deflection rate and work in an elastic, range to prevent plastic deformation.…”

“…It was found high tension levels at the top of the loop (1201-1352 N/mm 2 ). Another paper 15 verified the behavior of DRS to know the von Mises stresses comparing prototypes with and without helicoids inserted on the top of the springs. The authors concluded that the insertion of helicoids decreases the deflection rates according to early studies.…”

“…Studies concerning the von Mises tensions show that the higher tensions normally occurs at horizontal legs near the attachments (brackets or molar tubes) and in the superior part of the loops due to energy concentration. 13 , 15 , 16 ML archwires are a modified version originated from T-loops developed by Nanda 23 aiming to obtain more flexibility during the controlled retraction or translation of the four incisors, after the canine retraction (two-step procedure). 7 For an ideal tooth movement of the anterior teeth, the translation movement should have a M:F ratio of approximately 10:1.…”