The ability of a loop to generate a certain moment/force ratio (M/F ratio) can achieve the desired tooth movement in orthodontics. The present study aimed to investigate the effects of elastic modulus, cross-sectional dimensions, loop configuration geometry dimensions, and activation force on the generated M/F ratio of vertical, L- and T-loops. A total of 120 three-dimensional loop models were constructed with the Solidworks 2017 software and used for simulating loop activation with the Abaqus 6.14 software. Six vertical loop variations, 9 L-loop variations, and 9 T-loop variations were evaluated. In each group, only one parameter was variable [loop height, ring radius, leg length, leg step distance, legs distance, upper length, different archwire materials (elastic modulus), cross-sectional dimension, and activation force]. The simulation results of the displacement and von Mises stress of each loop were investigated. The maximum displacement in the height direction was recorded to calculate the M/F ratio. The quantitative change trends in the generated M/F ratio of the loops with respect to various variables were established. Increasing the loop height can increase the M/F ratio of the loop. This increasing trend is, especially, much more significant in T-loops compared with vertical loops and L-loops. In vertical loops, increasing the ring radius is much more effective than increasing the loop height to increase the M/F ratio of the loop. Compared with SS, TMA archwire loops can generate a higher M/F ratio due to its lower elastic modulus. Loops with a small cross-sectional area and high activation force can generate a high M/F ratio. The introduction of a leg step to loops does not increase the M/F ratio of loops.

中文翻译：

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弓丝参数和激活力对垂直，L形和T形环的M / F比率的有限元分析。

环产生一定力矩/力比（M / F比）的能力可以实现牙齿矫正中所需的牙齿运动。本研究旨在研究弹性模量，横截面尺寸，回路构型几何尺寸和激活力对垂直，L型和T型回路的M / F比的影响。使用Solidworks 2017软件构建了总共120个三维回路模型，并使用Abaqus 6.14软件模拟了回路激活。评估了六个垂直回路变化，9个L回路变化和9个T回路变化。在每组中，只有一个参数是可变的[环的高度，环的半径，腿的长度，腿的步距，腿的距离，上部的长度，不同的弓丝材料（弹性模量），横截面尺寸和激活力]。研究了每个环的位移和冯·米塞斯应力的仿真结果。记录高度方向上的最大位移以计算M / F比。建立了相对于各种变量的回路的M / F比的定量变化趋势。增加回路高度可以增加回路的M / F比。与垂直回路和L回路相比，这种增加的趋势在T回路中尤其重要。在垂直回路中，增加环半径比增加回路高度来增加回路的M / F比有效得多。与SS相比，TMA弓丝环由于其较低的弹性模量而可产生较高的M / F比。具有较小横截面积和高激活力的环会产生较高的M / F比。