Department of Mechanical and Electrical Engineering, Hainan University, Present address: #58 People Avenue, Meilan District, Haikou City, Hainan Province, China.
BMC Oral Health. 2020 Mar 13;20(1):70. doi: 10.1186/s12903-020-1059-z.
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.
环的产生一定的力矩/力比值（M/F 比值）的能力可以在正畸中实现期望的牙齿移动。本研究旨在探讨弹性模量、横截面尺寸、环结构几何尺寸和激活力对垂直、L 和 T 环产生的 M/F 比值的影响。
使用 Solidworks 2017 软件构建了总共 120 个三维环模型，并使用 Abaqus 6.14 软件模拟环激活。评估了 6 种垂直环变体、9 种 L 环变体和 9 种 T 环变体。在每组中，只有一个参数是变量[环高、环半径、腿长、腿阶距、腿距、上长、不同弓丝材料（弹性模量）、横截面尺寸和激活力]。
研究了每个环的位移和 von Mises 应力的模拟结果。记录最大高度方向的位移以计算 M/F 比值。建立了环的生成 M/F 比值随各种变量的定量变化趋势。
增加环高可以增加环的 M/F 比值。这种增加趋势在 T 环中比在垂直环和 L 环中更为显著。在垂直环中，增加环半径比增加环高更有效地增加环的 M/F 比值。与 SS 相比，TMA 弓丝环由于其较低的弹性模量可以产生更高的 M/F 比值。具有小横截面积和高激活力的环可以产生高 M/F 比值。在环中引入腿阶距不会增加环的 M/F 比值。
