Effect of archwire size and material on the resistance to sliding of self-ligating brackets with second-order angulation in the dry state.

When paired with a particular self-ligating bracket design, the material and the geometric characteristics of an archwire influence its resistance to sliding. Four designs of self-ligating brackets (1 with a slide, 3 with clips) were coupled with 5 types of archwires: 14-mil round austenitic nickel-titanium, 16 x 22-mil rectangular austenitic nickel-titanium, 19 x 25-mil rectangular austenitic nickel-titanium, 19 x 25-mil rectangular martensitic nickel-titanium, and 19 x 25-mil rectangular stainless steel. The resistance to sliding (RS) of each archwire-bracket couple was measured at second-order angles between -9 degrees and 9 degrees. Interbracket distances of 8 and 18 mm between the test bracket and the adjacent brackets mimicked closure of a premolar extraction. When clearance exists, the RS is negligible for self-ligating brackets with slides coupled to any size of wire as well as for those with clips when coupled to wires that do not contact the clip. Once the wire attains a certain size and contacts the clip, the RS depends on the archwire size, the bracket design, and the materials of the couple. When coupled with the 16 x 22-mil wire, the brackets with clips applied normal forces ranging from a low of 5.6 centi-Newtons (cN) (1 cN = 1 g) to a high of 230 cN. When clearance disappears, the RS increased proportionally with the second-order angle. The 19 x 25-mil stainless steel wires, which were the most stiff, increased at rates between 75 and 84 cN/degree; the 14-mil austenitic nickel-titanium wires, which were the least stiff, increased at rates from 2.6 to 5.4 cN/degree. The treatment objectives for a particular patient at a specific stage should determine the appropriate archwire-bracket combination.     

Assessment of second-order clearances between orthodontic archwires and bracket slots via the critical contact angle for binding

Twenty-six archwires and 24 brackets were selected from among the hundreds of products available that nominally have from 18 to 22 mil bracket slots and 14, 16, 17, 18, 19, and/or 21 mil archwire sizes. After the archwires and brackets were dimensioned, a minimization-maximization algorithm was applied to the measurements in order to establish the likely boundaries of the critical contact angle for binding (thetac) as defined by the presence and absence of second-order clearance. From among the myriad archwire-bracket permutations possible, 64 combinations were identified--20 using the bracket slot as the controlling dimension and 44 using the bracket width. Using a previously derived mathematical expression that relates the dimensions of each archwire-bracket couple to its calculated thetac, the corresponding sets of indices were plotted. The results show that the maximum value of the calculated thetac can never exceed about 5 degrees , or else sliding mechanics will always be hampered. Other outcomes were validated experimentally using 5 of the 64 archwire-bracket couples by measuring the resistance to sliding (RS) at 15 different contact angles (theta) ranging from theta=0 degrees to theta=12 degrees and by subsequently determining a measured thetac. These values agreed with the calculated thetac values. When the practitioner knows the thetac, treatment time might be reduced because the teeth do not need to be over-aligned prior to employing sliding mechanics (i.e., by not making thetathetac) These results underscore the importance of exact wire and bracket dimensions on packaging; otherwise, sliding mechanics can be compromised by miscalculating thetac.     

Frictional resistances of metal-lined ceramic brackets versus conventional stainless steel brackets and development of 3-D friction maps

The frictional resistances of 2 metal-lined ceramic brackets (Luxi and Clarity) were compared with 2 conventional stainless steel brackets (Mini-Taurus and Mini-Twin) in vitro. In method 1, we varied the second-order angulation from 0 degrees to 12 degrees while maintaining the normal or ligature force constant at 0.3 kg; in method 2, we varied the ligature force from 0.1 kg to 0.9 kg while maintaining the angulation at theta = 0 degrees or theta = 11 degrees. The hardware simulated a 3-bracket system in which the interbracket distances were always 18 mm. All couples were evaluated at 34 degrees C using the same size stainless steel archwire (19 x 26 mil) and ligature wire (10 mil). In the passive region, the static and kinetic frictional forces and coefficients of friction were key parameters; in the active region, the static and kinetic binding forces and coefficients of binding were critical parameters. From outcomes of methods 1 and 2, the 4 aforementioned parameters, and a knowledge of the critical contact angle for binding, 3-dimensional friction maps were constructed in the dry and wet states from which the frictional resistances could be determined at any ligature force or second-order angulation. Those 3-dimensional maps show that metal-lined ceramic brackets can function comparably to conventional stainless steel brackets and that 18-kt gold inserts appear superior to stainless steel inserts. As the morphologies of metal inserts are improved, these metal-lined ceramic brackets will provide not only good esthetics among ceramic brackets but also minimal friction among conventionally ligated brackets.     

Comparison of resistance to sliding between different self-ligating brackets with second-order angulation in the dry and saliva states.

Resistance to sliding was investigated for 3 self-ligating brackets having passive slides and 3 self-ligating brackets having active clips. Four of these products are currently marketed, and 2 are of historic interest. For all cases, an 0.018 x 0.025-in stainless steel archwire was drawn through each bracket at a rate of 10 mm/min over a distance of 2.5 mm. For each bracket, the resistances to sliding were measured at 14 second-order angulations, which ranged from -9 degrees to +9 degrees. Both the dry and the wet (human saliva) states were evaluated at 34 degrees C. From dimensional measurements, the critical contact angles for binding were determined for all products and ranged from 3 degrees to 5 degrees. Below each characteristic critical angle, brackets with passive slides exhibited negligible friction; brackets with active clips exhibited frictional forces as great as 50 cN (50 g). Above each critical angle, all brackets had elastic binding forces that increased at similar rates as angulation increased and were independent of bracket design. Generally speaking, at second-order angulations that exceeded the critical angle, brackets with active clips that had a low critical angle had more resistance to sliding than did brackets with active clips that had a higher critical angle. Brackets with passive slides that had a high critical angle exhibited the lowest resistance to sliding, but could do so at a cost of some loss of control. Nonetheless, self-ligating brackets represent a compromise between friction and control; ie, self-ligating brackets produce frictional forces that are more reproducible than do conventionally ligated stainless steel brackets but without the potential control problems associated with Begg-style brackets.     

Three-dimensional relationship between the critical contact angle and the torque angle.

The purpose of this study was to analyze the relationship between the critical contact angle and the torque angle in an orthodontic bracket and archwire assembly in 3 dimensions. Three-dimensional mathematical models were created with geometric bracket-archwire parameters that included 2 slot sizes, 3 bracket widths, and 3 to 4 wire sizes. From this, 3-dimensional mathematical equations (3DMEs) for the critical contact angle and the maximum torque that result in critical contact angles of 0 were derived and calculated. To evaluate the effects of archwire-bracket parameters on critical contact angles, analysis of variance (ANOVA) was performed at the significance level of P < or = .05. For all bracket-archwire combinations, the critical contact angle decreased as bracket width, torque angle, and wire size increased. Therefore, all bracket-archwire parameters except slot height had an effect on the critical contact angle. Results of the critical contact angle produced from our 3DMEs were the same as those produced by 3D computer-aided design (SolidWorks Corp, Concord, Mass), thus confirming the validity of our derived equations. In addition, the effect of a beveled edge was investigated in some archwires. Furthermore, torsional play angles were calculated and found to be similar to those in previous reports. The results of this study provide theoretic and experimental bases for clinical orthodontic practice and indicate that torque angles should be included in the evaluation of the critical contact angle.     

陶瓷托槽与金属弓丝第二序列成角状态下摩擦性能的研究

目的研究陶瓷托槽与金属弓丝在第二序列成角状态下的摩擦力,探讨影响托槽弓丝间摩擦力的因素。方法进行托槽外观形貌的测量与观察,计算托槽与弓丝第二序列成角下的临界角,并设计带可调节罗盘的载物台,用MTS Tytron250微力试验机体外测试三种陶瓷托槽（A、B、C）和一种金属托槽（D）与0.016英寸不锈钢圆丝（SS）在第二序列成角分别为0度、2度、5度、8度时的最大静摩擦力和滑动摩擦力。结果与0.016英寸SS的摩擦力总体表现出B托槽〉C托槽〉A托槽〉D托槽的趋势,在四种成角状态下的最大静摩擦力随角度加大而增大,总体表现为0度到2度的摩擦力增加没有显著性,增大夹角后摩擦力增加量不同托槽间有差异：A托槽与弓丝在2度到5度成角状态下的摩擦力增加没有显著性,而5度到8度的摩擦力有显著增加;B托槽在2度到5度摩擦力有显著增加,而5度到8度摩擦力增加不显著;虽然2度到5度摩擦力增大没有显著性,但8度与0度状态下相比,C托槽与弓丝间的摩擦力有显著增加;D托槽在2度、5度、8度时摩擦力间差异无显著性。结论选用带金属槽沟的陶瓷托槽,增加陶瓷托槽边缘的圆钝程度等能减缓牙齿移动中托槽-弓丝成角引起的滑动阻力增加;使用传统陶瓷托槽要注意充分排齐。     

Influence of archwire and bracket dimensions on sliding mechanics: derivations and determinations of the critical contact angles for binding.

There is every indication that classical friction controls sliding mechanics below some critical contact angle, theta c. Once that angle is exceeded, however, binding and notching phenomena increasingly restrict sliding mechanics. Using geometric archwire and bracket parameters, the theta c is calculated as the boundary between classical frictional behaviour and binding-related phenomena. What these equations predict is independent of practitioner or technique. From these derivations two dimensionless numbers are also identified as the bracket and the engagement index. The first shows how the width of a bracket compares to its Slot; the second indicates how completely the wire fills the Slot. When nominal wire and bracket dimensions are calculated for both standard Slots, the maximum theta c theoretically equals 3.7 degrees. Thus, knowledge of the archwire or bracket alone is insufficient; knowledge of the archwire-bracket combination is necessary for theta c to be calculated. Once calculated, sliding mechanics should be initiated only after the contact angle, theta, approaches the characteristic value of theta c for the particular archwire-bracket combination of choice--that is, when theta approximately theta c.     

Ongoing innovations in biomechanics and materials for the new millennium

Material innovations are reviewed within the context of ongoing biomechanical developments that relate the critical contact angle of second-order angulation (theta c) to the overall resistance to sliding (RS). As a science in its embryonic stage of development, RS is partitioned into classical friction (FR), elastic binding (BI), and physical notching (NO). Both FR and BI are defined in terms of normal forces (N) and kinetic coefficients (mu k). The angulation at which NO occurs (theta z) is introduced as a second boundary condition to theta c. Given this scientific backdrop, material modifications are sought that reduce RS. Approaches include minimizing mu k or N within the context of FR and theta < theta c, as, for example, by surface modifications of arch wires and brackets or by engineering novel ligation materials. Stabilizing theta at theta approximately equal theta c should provide more efficient and effective sliding mechanics by developing innovative materials (eg, composites) in which stiffness (EI) varies without changing wire or bracket dimensions. Between the boundaries of theta c and theta z (ie, theta c < theta < theta z), BI may be reduced by decreasing EI or increasing interbracket distance (IBD), independent of whether a conventional or composite material is used.     

A comparative study of frictional resistances between orthodontic bracket and arch wire

Practitioners are aware of the presence of friction in those orthodontic appliances where relative motion between bracket system and arch wire occurs in ordinary deactivation processes. Numerous comments on friction have appeared in the published dental/orthodontic literature, but little controlled research into the problem has been reported. The objective of this investigation was to evaluate and compare frictional forces generated in an experimental stimulation of the canine-retraction procedure on a continuous arch wire. Six independent variables were chosen for study: arch wire size and shape, bracket width and style, second-order angulation between bracket and passive arch wire, arch wire material, ligature force and type of ligation, and interbracket distances. Frictional resistance was found to be nonlinearly dependent upon bracket/arch wire angulation. With small and generally nonbinding angulations, bracket width and ligature force were the dominant influences on level of friction. As angulations were increased, producing binding between wire and bracket, this variable itself became the controlling parameter. Wire shape and arch wire stiffness in bending, a function of three of the variables studied, apparently exerted substantial influence on frictional-force magnitude at relatively high angulations. The reduced data, together with structural computations, were employed to deduce a minimum frictional-resistance combination of edgewise appliance components.     

Effects of third-order torque on frictional force of self-ligating brackets

Objective:To investigate the effects of third-order torque on frictional properties of self-ligating brackets (SLBs).Materials and Methods:Three SLBs (two passive and one active) and three archwires (0.016 × 0.022-inch nickel-titanium, and 0.017 × 0.025-inch and 0.019 × 0.025-inch stainless steel) were used. Static friction was measured by drawing archwires though bracket slots with four torque levels (0°, 10°, 20°, 30°), using a mechanical testing machine (n  =  10). A conventional stainless-steel bracket was used for comparison. Results were subjected to Kruskal-Wallis and Mann-Whitney U-tests. Contact between the bracket and wire was studied using a scanning electron microscope.Results:In most bracket-wire combinations, increasing the torque produced a significant increase in static friction. Most SLB-wire combinations at all torques produced less friction than that from the conventional bracket. Active-type SLB-wire combinations showed higher friction than that from passive-type SLB-wire combinations in most conditions. When increasing the torque, more contact between the wall of a bracket slot and the edge of a wire was observed for all bracket types.Conclusions:Increasing torque when using SLBs causes an increase in friction, since contact between the bracket slot wall and the wire edge becomes greater; the design of brackets influences static friction.     

Torque Expression in Stainless Steel Orthodontic Brackets: A Systematic Review

Objective:To evaluate the quantitative effects on torque expression of varying the slot size of stainless steel orthodontic brackets and the dimension of stainless steel wire, and to analyze the limitations of the experimental methods used.Materials and Methods:In vitro studies measuring torque expression in conventional and self-ligating stainless steel brackets with a torque-measuring device, with the use of straight stainless steel orthodontic wire without second-order mechanics and without loops, coils, or auxiliary wires, were sought through a systematic review process.Results:Eleven articles were selected. Direct comparison of different studies was limited by differences in the measuring devices used and in the parameters measured. On the basis of the selected studies, in a 0.018 inch stainless steel bracket slot, the engagement angle ranges from 31 degrees with a 0.016 × 0.016 inch stainless steel archwire to 4.6 degrees with a 0.018 × 0.025 inch stainless steel archwire. In a 0.022 inch stainless steel bracket slot, the engagement angle ranges from 18 degrees with a 0.018 × 0.025 inch stainless steel archwire to 6 degrees with a 0.021 × 0.025 inch stainless steel archwire. Active stainless steel self-ligating brackets demonstrate an engagement angle of approximately 7.5 degrees, whereas passive stainless steel self-ligating brackets show an engagement angle of approximately 14 degrees with 0.019 × 0.025 inch stainless steel wire in a 0.022 inch slot.Conclusions:The engagement angle depends on archwire dimension and edge shape, as well as on bracket slot dimension, and is variable and larger than published theoretical values. Clinically effective torque can be achieved in a 0.022 inch bracket slot with archwire torsion of 15 to 31 degrees for active self-ligating brackets and of 23 to 35 degrees for passive self-ligating brackets with a 0.019 × 0.025 inch stainless steel wire.     

An ex vivo laboratory study to determine the static frictional resistance of a variable ligation orthodontic bracket system

OBJECTIVE: To determine the effects of static frictional resistance on varying the ligation technique in a Delta Force bracket system (Ortho Organizers Ltd, Hampton, UK) and using increasing degrees of bracket/archwire angulation to simulate binding. DESIGN: An ex vivo laboratory investigation using the Instron Universal Testing Machine (Instron Ltd, High Wycombe, UK) to generate sliding forces on an archwire through the Delta Force bracket. The system was lubricated with Saliva Orthana artificial saliva (Nycomed Ltd, Buckinghamshire, UK). SETTING: Biomaterials Laboratory, Eastman Dental Institute, London, UK. MATERIALS AND METHOD: Ninety Delta Force brackets were tested against 0.018-inch stainless steel wire. Three modes of ligation were tested with three different angulations: 0, 5 and 10 degrees to simulate increasing levels of binding. RESULTS: The average static frictional resistance went from 0.20 N, at 0 degrees angulation and minimum ligation, to 2.37 N with 10 degrees angulation and maximum ligation. Results revealed that the ligation pattern was found to be highly statistically significant (P<0.001) in influencing frictional force. The binding angle showed a trend of increasing frictional force with increasing bracket/archwire angulation. Repeatability testing showed no evidence of bias (P=0.171). CONCLUSIONS: These results suggest that the Delta Force variable ligation system does in fact enable friction to be varied, which may have implications in clinical application.     

两种不同弹力结扎对滑动摩擦力大小影响的体外实验研究

目的通过体外实验研究MBT金属托槽应用两种不同的弹力结扎时滑动摩擦力的大小。方法选择3M公司的上颌第二双尖牙MBTmini金属托槽和0．46×0．64mm（0．018×0．025英寸）不锈钢弓丝,分别采用意大利Leone公司生产的Slide^TM结扎圈和美国TP公司生产的传统弹力圈结扎,应用自行设计开发的摩擦力测试仪,弓丝沿托槽低速滑动,并在滑动中保持特定的托槽——弓丝成角,共计12个角度。测量每一种弓丝、不同角度下的滑动摩擦力大小。结果在被动状态下两种结扎方式的滑动摩擦力均基本保持不变,Slide^TM结扎的摩擦力非常小,几乎可以忽略不计;在主动状态下,摩擦力随角度增加而增大,slide^TM结扎产生的滑动摩擦力仍明显小于传统弹力结扎。结论应用LeoneSlide^TM结扎圈,可以显著减小矫治器的滑动摩擦力。     

A comparison of self-ligating and conventional orthodontic bracket systems.

Abstract

This ex-vivo study compared the static frictional resistance of three self-ligating brackets with a conventional steel-ligated Ultratrimm bracket. The effects of archwire size (0.020, 0.019 x 0.025 and 0.021 x 0.025-inch), bracket/archwire angulation (0, 5 and 10 degrees) and the presence of unstimulated human saliva were investigated. The study demonstrated that both increases in wire size and bracket/archwire angulation resulted in increased static frictional resistance for all bracket types tested, with the presence of saliva having an inconsistent effect. Mobil-Lock Variable-Slot had the least friction for all wires for 0 degree angulation. However, with the introduction of angulation, the values were comparable to those of the other brackets. Activa brackets had the second lowest frictional resistance, although high values were found with 0.019 x 0.025-inch wires. SPEED brackets demonstrated low forces with round wires, although with rectangular wires or in the presence of angulation, friction was greatly increased. Ultratrimm brackets produced large individual variation, confirming the difficulty in standardizing ligation force, although under certain conditions, significantly larger frictional forces were observed. In conclusion, self-ligating brackets showed reduced frictional resistance in comparison to steel ligated brackets only under certain conditions.     

Measurements of the torque moment in various archwire-bracket-ligation combinations

The torque moment generated by third-order bends is important for tooth movement. The purpose of this study was to measure the torque moment that can be delivered by various archwire and bracket combinations at the targeted tooth. Stainless steel (SS) upper brackets with 0.018 and 0.022 inch slots, two sizes of nickel-titanium (Ni-Ti) alloy wires, and three sizes of SS wires for each bracket were used. The wire was ligated with elastics or wire. The torque moment delivered by the various archwire-bracket-ligation combinations was measured using a torque gauge. Statistical analysis was undertaken using analysis of variance (multiple comparison tests and post hoc using Tukey's honestly significant difference test. The torque moment increased as the degree of torque and wire size increased. There was no significant difference in torque moment between the SS and Ni-Ti wires at lower or higher than 40 degrees torque. The torque moment with wire ligation was significantly larger than that with elastic ligation with 0.016 × 0.022 and 0.017 × 0.025 inch Ni-Ti wires in the 0.018 inch slot brackets and the 0.017 × 0.025 and 0.019 × 0.025 inch SS and Ni-Ti wires in the 0.022 inch slot brackets. However, there was no significant difference in torque moment between either ligation method when using the full slot size wires.     

Torque Transmission between Square Wire and Bracket as a Function of Measurement,Form and Hardness Parameters

The aim of the study was to investigate the influence of cross section, edge geometry and structural hardness on torque transmission between square wire and bracket. For this purpose, 5 different brands of stainless steel square wire in 3 dimensions (0.016" x 0.016", 0.016" x 0.022" and 0.017" x 0.025") were inserted into edgewise brackets with a slot size of 0.018" and loaded with different torques (1 and 3 Ncm). The slot and wire geometries were analyzed by computer on ground specimens before and after loading. In addition, the Vickers hardness and micro-hardness of the unstressed and stressed metal surfaces were determined. While the slot size was very accurately maintained, the wire dimensions deviated downwards by an average of 10%. Torque transmission led to notching and bending-up phenomena on the bracket slot flanks. A torque loading of 3 Ncm increased the torque play of 0.016" x 0.022" wires by 3.6 degrees, and of 0.017" x 0.025" wires by 3.7 degrees. In the case of 0.016" x 0.016" wires, an effective torque transmission was no longer possible. The average Vickers hardness of the wires was 533 kp/mm2, and that of the brackets 145 kp/mm2. The micro-hardness in the deformation area of stressed internal slot walls increased with increasing load transmission from 204 to 338 kp/mm2. As a result of excessively small wire dimensions and plastic deformation of the brackets, a relatively large torque play occurs. Deformation and notching in the area of the internal slot walls are inconsistent with demands for recycling brackets. A standardization of bracket wire systems stating the actual torque play would be desirable.     

Friction of conventional and silica-insert ceramic brackets in various bracket-wire combinations

OBJECTIVE: To compare the level of friction resistance (FR) of conventional and silica-insert ceramic brackets using various bracket-wire combinations and angulations. MATERIALS AND METHODS: Four types of ceramic brackets were examined: (1) polycrystalline alumina bracket (PCA-C), (2) polycrystalline alumina bracket with a stainless steel (SS) slot (PCA-M), (3) polycrystalline alumina bracket with a silica layer (PCA-S), and (4) monocrystalline sapphire bracket (MCS). A conventional SS bracket was used as the control. The static and kinetic FR in four bracket-wire angulations (0 degrees, 5 degrees, 10 degrees, and 15 degrees) was examined using SS and beta-titanium (beta-Ti) orthodontic wires, 0.019 x 0.025 inches in size, under elastic ligature in the dry state. RESULTS: The FR generated by the PCA-S bracket was significantly lower than that generated with the other ceramic brackets, and was similar to that of the SS bracket. The PCA-S bracket showed the lowest FR with both the SS and the beta-Ti wires at zero bracket angulation. The FR to sliding increased rapidly and nonlinearly when the bracket wire angulation was >5 degrees. The PCS-S bracket showed the lowest FR from 5 degrees to 15 degrees of angulation. The MCS bracket demonstrated the highest increase in FR from 0 degrees to 15 degrees of angulation, showing the highest FR at 15 degrees of angulation. CONCLUSION: PCA-S showed minimal FR among the ceramic brackets, and was comparable to the conventional SS bracket. The silica layer and rounded edges of the ceramic slot lowered FR considerably.     

An ex vivo laboratory study to determine the static frictional resistance of a variable ligation orthodontic bracket system

Abstract

Objective: To determine the effects of static frictional resistance on varying the ligation technique in a Delta Force bracket system (Ortho Organizers Ltd, Hampton, UK) and using increasing degrees of bracket/archwire angulation to simulate binding.

Design: An ex vivo laboratory investigation using the Instron Universal Testing Machine (Instron Ltd, High Wycombe, UK) to generate sliding forces on an archwire through the Delta Force bracket. The system was lubricated with Saliva Orthana artificial saliva (Nycomed Ltd, Buckinghamshire, UK).

Setting: Biomaterials Laboratory, Eastman Dental Institute, London, UK.

Materials and method: Ninety Delta Force brackets were tested against 0.018-inch stainless steel wire. Three modes of ligation were tested with three different angulations: 0, 5 and 10° to simulate increasing levels of binding.

Results: The average static frictional resistance went from 0.20 N, at 0° angulation and minimum ligation, to 2.37 N with 10° angulation and maximum ligation. Results revealed that the ligation pattern was found to be highly statistically significant (P<0.001) in influencing frictional force. The binding angle showed a trend of increasing frictional force with increasing bracket/archwire angulation. Repeatability testing showed no evidence of bias (P=0.171).

Conclusions: These results suggest that the Delta Force variable ligation system does in fact enable friction to be varied, which may have implications in clinical application.