ORIGINAL ARTICLES
A comparative study of frictional forces between orthodontic brackets and arch wires James R. Bednar, DDS, MS,* Gary W. Gruendeman, DDS,* and James L. Sandrik, PhD** Chicago, Ill. An in vitro study of simulated canine retraction was undertaken to evaluate the difference in frictional resistance between stainless steel arch wires and steel and ceramic brackets with elastomerie, steel, and self-ligation. Each bracket slot was 0.018 x 0.025 inch. The arch wires used were 0.014-inch, 0.016-inch, 0.018-inch, 0.016 x 0.016-inch, and 0.016 x 0.22-inch stainless steel. A testing apparatus was designed to attempt to simulate the clinical situation in which teeth tip slightly while they slide along the arch wire. Under these testing conditions, the self-ligating steel bracket did not demonstrate less friction than the elastic or steel-ligated stainless steel brackets. For most wire sizes, elastomer-ligated ceramic brackets demonstrated the greatest friction when compared with other bracket/ligation technique combinations. The clinical significance of this study becomes apparent when stainless steel brackets are used on the posterior teeth and ceramic brackets are used on the anterior teeth. If sliding mechanics are used, the anterior teeth may be more resistant to movement than the posterior teeth because of the greater friction of the ceramic brackets. This could result in more posterior anchorage loss than would be expected if only one type of bracket were used. (AM J ORTHOD DENTOFACORTHOP 1991 ;100:513-22.)
O n e of the most common methods of translating a tooth orthodontically is by the use of sliding mechanics. In this technique, mesiodistal tooth movement is accomplished by guiding a tooth along a continuous arch wire with the use of an orthodontic bracket. A disadvantage of this technique is that friction is generated between the bracket and the arch wire, which tends to resist the movement of the bracket and tooth in the desired direction. Friction is defined as a force that retards or resists the relative motion of two objects in contact, and its direction is tangential to the common boundary of the two surfaces in contact. 1In physics, the frictional force between any two sliding surfaces is directly proportional to the force with which the surfaces are pressed together--F~r = u x F. The value of u (the coefficient of friction) depends on the materials that are sliding and is only very slightly affected by other factors, such as speed or contact areas between the surfaces. 2 In orthodontic sliding mechanics, friction is determined by the type of arch wire, the type of bracket, and the method of ligation. The force pressing the wire and the bracket surfaces together (F) is determined by
From the Loyola University School of Dentistry. *Assistant Professor, Department of Orthodontics. **Professor and Chairman, Department of Dental Materials. 8/1/26074
the angulation between the arch wire and the bracket slot, the size of the arch wire, and the method of ]igation. An investigation of the frictional forces in orthodontic tooth movement was conducted by Andreasen and Quevedo) They performed in vitro tests to quantify the frictional force generated by moving an edgewise bracket along a fixed arch wire. The angulation between the bracket slot and the arch wire was varied, as was the dimension of the arch wires. They found that the larger the arch wire, and the greater the angulation between arch wire and bracket, the greater the friction. Their test showed that there was little difference in friction between dry samples and those tested with saliva as a lubricant. Among other variables, the effect of bracket width and bracket-to-arch wire angulation was studied by Frank and Nikolai. 4 At a given fixed bracket-to-arch wire angulation, wider brackets produced more friction than narrow bracketsl As angulations were increased, binding between the wire and the bracket occurred, and this variable itself became the controlling parameter. They noted that clinically, tooth movement takes place as a series of short steps rather than a smooth continuous motion. Initially, static friction between the arch wire and the bracket must be overcome to initiate tooth movement. While the tooth is moving, kinetic friction occurs as the crown of the tooth tips in the direction of
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am. J. Orthod. Dentofiw. Orthop. December 1991
GAC Allure 500 394
400
Steel Ligation Elastomeric Ligation
388
364
300
200 100
0
i
t.O14
i
0.0!6
0.618
WIRE SIZE
' x 0.016 0.016
0.016 X 0.022
Fig, 2. Relationship between wire size and friction for steel- and elastomeric-ligated GAC ceramic brackets.
Fig. 1. Friction-testing apparatus. applied force. Gradually, because the crown invariably moves before the root does, a couple arises between the wire and the bracket; this eventually stops crown movement and acts to upright the root. After further periodontal remodeling along the root surface, the cycle continues. The center of resistance of a tooth is not located along the same plane as that of the bracket, where force is applied to the tooth. Because o f this, tooth movement is a complicated process that involves tipping of the crown, resulting in the occurrence of some angulation between the bracket slot and the arch wire. Tidy 5 sought to simulate this situation with an apparatus in which a power arm was attached to the bracket and various weights were suspended from this attachment. This, in effect, mimicked the Crown tipping that occurs during clinical tooth movement. Tidy found that nitinol and TMA (beta-titanium) produced frictional fomes two and five times greater than stainless steel. Under his testing conditions, friction was inversely proportional to bracket width; arch wire and slot dimension had relatively little effect, Garner, Allai, and Moore ~ also compared the fric-
tional forces during simulated canine retraction using different wire types. They, too, found significantly larger frictional force with beta-titanium and nitinol when compared with stainless steel. They postulated that the differences in surface smoothness of the various wires may account for the differences in friction, Differences in ligation techniques and their effects on friction was studied by Berger. ~ For his tests, the brackets were locked in place, so that the bracket slot was parallel to the arch wire. He found that self-ligated brackets produced less friction than elastomeric or steeltie ligated brackets. Friction between the arch wire and the bracket has been shown to be an important factor in orthodontic tooth movement. Surface roughness of the arch wire has been shown to play a significant role in contributing to the amount of friction, as does bracket design and ligation technique. At present, orthodontic brackets are fabricated from several types of materials with varying degrees of roughness. This study was designed to investigate the effect of bracket material and ligation technique on the amount of frictional force generated during simulated tooth movement. MATERIALS AND METHODS A testing apparatus was constructed to simulate the clinical situation in which the center of resistance of a tooth is not on the same plane as that of the bracket, thereby resulting in some tipping of the bracket slot relative to the arch wire. This device consisted of a stainless steel framework with a freely rotating plastic disk on which each bracket was mounted. Attached to this disk was a 12 mm stainless steel power arm from which a 100 gm weight was suspende d (Fig.
Volume 100
Comparative study of fi'ictional forces
Ntmzber 6
OREC Speed Bracket
ORMCO Mini Diamond Twin 5OO
Steel Ligation Elastomeric Ligation
500
r-I E3
Spring Clip Ligation
[]
400
400
~
30O
300
200
200
100
100-
27"/
~-/,
0
515
i
0.014
0.0'16
i
i
i
0.018 0.016 x W I R E SIZE 0.016
0.014
0.016 x 0.022
Fig. 3. Relationship between wire size and friction for steel- and elastomericdigated Ormco steel brackets.
0.0'16 0J.018 W I R E SIZE
--.
t
0.016x 0.016
0.016 x 0.022
Fig. 4. Relationship between wire size and friction for selfligated Orec steel brackets.
T a b l e I. Bracket characteristics
Company
Slot dimension
Bracket width
Torque (degree)
Tip (degree)
Composition
GAC Allure*
0.46 × 0.64 mm 0,018 × 0.025 inch
3.56 mm 0.140 inch
- 2
10
Polyerystalline ceramic, machined slot
Ormco Mini-Diamond**
0,46 X 0.64 mm 0.018 × 0,025 inch
3.56 mm 0.140 inch
0
10
Machined metal, machined slot, tunable deburred
Orec SPEED***
0.46 x 0.64 mm 0.018 × 0.025 inch
2.29 mm 0.090 inch
-2
9
Machined metal, turned slot
*GAC Allure, GAC International, Inc., Central Islip, N.Y. **Ormco Mini-Diamond, Ormco Corp., Glendora, Calif. ***Orec SPEED, Orec Corp., San Clemente, Calif.
1). Two pins were placed I0 rmn superior and inferior to the disk to aid in guiding the arch wire. Each bracket was bonded (Phase II bracket adhesive, Reliance Orthodontic Products, Inc,, Itasca, Ill.) to the disk in such a way that the center of the bracket corresponded with the center of the disk and that the bracket slot was perpendicular to the power arm. All testing was done under dry conditions with an Instron Universal machine (Instron Corporation, Canton, Mass.). Each wire was suspended from the 10-pound (4.54 kg) load cell with a heavy brass swivel. The wire was drawn up through the testing apparatus with the crosshead moving at 0.5 inch/min (12,7 mm/rnin). Three different 0.018-inch-slot maxillary right canine orthodontic brackets were tested (Table I). An effort was made to obtain brackets of identical dimensions and prescription. Unfortunately, ceramic brackets were unavailable in the same width as the Orec self-ligating brackets. The bracketmounting protocol helped to minimize any slight differences
in prescriptions. Sampling was done without replacement from a finite population. All arch wires used were made of Tru-Chrome stainless steel orthodontic wire (Rocky Mountain Orthodontics, Denver, Colo.), their dimensions were 0.014 inch (0.36 mm), 0.016 inch (0.41 ram), 0.018 inch (0.46 ram), 0.016 x 0.016 inch (0.41 x 0.41 ram), and 0.016 x 0.022 inch (0.41 x 0.56 ram). The elastomeric-ligated brackets were ligated with Power "O" modules (Ormco Corporation, Glendora, Calif.). The steel-tied brackets were ligated with 0.010-inch (0.25 ram) steel ligatures. Each ligature was initially tightened, then slightly slackened to allow the arch wire to slide freely. The self-ligated brackets were ligated with the integral spring clips. For the elastomeric-ligated brackets, three sample brackets of each bracket type (Mini-Diamond or Allure) were used with each wire size. Each sample bracket was tested three times in succession with each size wire. For the self-ligated
516 Bednar, G r u e n d e m a n , a n d S a n d r i k
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J.
Orthod. Dentofac. Orthop. December 1991
T a b l e II. S u m m a r y statistics for the frictional force generated with each b r a c k e t / l i g a t i o n technique/wire size combination Applied force (gin) Steel-tie ligation
Elastomeric ligation
Minimum
Maximum
Average
SD mean average friction
210,92 114.91
343.97 154.22
277.45 1134.57
27.99 14.76
314.11 192.02
475.14 227.80
394.62 209.91
41.13 33.85
220.75 116.42
327.34 145.15
274.04 130.79
39.74 7.29
316.00 250.99
460.02 280.22
388.01 265.60
62.17 41.42
148.I7 164,81
182.19 192.02
165.18 178.41
13.41 7,29
313.73 234.86
415.04 269.13
364.39 252.00
58.97 32.47
179,17 185.97
238.14 258.55
208.65 222.26
31.30 15.88
282,74 245.44
365.14 279.71
323.94 262.58
54.45 24.94
142.13 155.73
237.38 216.21
189.75 185.97
12.23 9.07
282,36 266.11
354.94 297.86
318.65 281.98
42,27 29.90
Mean
Minimum
Mean "I Maximum I Average
SD Mean average friction
Bracket Wire size (0,36 mm/O.014 inch)
GAC Ormco Orec
Wire size (0.41 mmlO.Old inch)
GAC Ormco Orec Wire size (0.46 mm/O,OJ8 inch)
GAC Ormco Orec Wire size (0.41 x 0.41 mralO.016 × 0.016 inch)
GAC Ormco Orec Wire size (0.41 X 0.56 mm/O.016 X 0,022 inch)
GAC Onnco Oree
SPEED bracket, three sample brackets were used with each wire size, and each bracket was tested three times with each size wire. For the steel-tied ceramic brackets, two sample brackets were tested with each size wire. For the steel-tied metal bracket only one bracket was used, it was tested three times with each wire size. The Instron testing machine was zeroed and calibrated before each bracket type/arch wire/ligation technique series was run. At the initiation of each test run, 0.15 inch (3,8 mm) of wire was drawn through the testing apparatus to take out all the slack. Then 0.25 inch (6.35 mm) of wire was pulled through the bracket. The high and low friction values over this duration were recorded.
RESULTS A l l data were g r o u p e d according to bracket type (stainless steel or ceramic) and ligation technique (elas-
tomeric, steel, or self-ligating). T h e summary statistics for each bracket type/ligation technique (GAC ceramic bracket/steel-tie ligation, GAC ceramic bracket/elastomeric ligation, Ormco steel bracket/steel-tie ligation, Ormco steel bracket/elastomeric ligation, and Orec steel bracket/self-ligation) showing the mean minimum friction value, the mean m a x i m u m friction value, and the mean average friction value are shown in Table II. Analysis o f variance for the results show that the effect of w i r e size is significant at the 0.05 level. The effects of bracket type/ligation technique and the interaction between wire size and bracket type/ligation technique are both significant at the 0.001 level. For every bracket t y p e / l i g a t i o n technique, the friction was plotted for each wire size. This is illustrated in Figs. 2, 3, and 4. T h e s t e e l - t i e - l i g a t e d ceramic
Comparative study of frictional forces 517
Volume100 Number 6
Applied force (gm) Spring-clip ligation Mean Maximum
Average
SDMean average friction
166.82
219.24
193.03
38.41
231.33
306.43
268,88
52.90
248.47
306.43
277.45
34.45
244.94
299.37
272.16
21,21
323.56
399.16
361.36
6.03
Minimum
l
brackets and the steel-tie-ligated steel brackets demonstrated less friction than the elastomeric-ligated ceramic and steel brackets at every arch wire size. All bracket type/ligation technique data were then grouped and analyzed for each specific wire size. Analysis of variance for these results shows that for each wire size the effects of bracket type/ligation technique were significant at the 0.001 level. The mean friction value at each wire size for all five bracket type/ligation techniques were analyzed. The results are illustrated in Fig. 5. Statistical analysis of the friction value of each bracket type / ligation technique for each wire size was done to further evaluate the differences in friction between these groups for each wire size. For the 0.014-inch wire size, the steel-ligated
Ormco steel bracket exhibited less statistically significant friction than the other bracket type/ligation technique groups. The elastomeric-ligated GAC ceramic bracket demonstrated greater statistically significant friction than the other types. For the 0,016-inch wire size, the results were similar to the 0.014-inch wire in that the steel-ligated Ormco steel bracket exhibited less statistically significant friction than the other bracket type/ligation technique groups. The elastomeric-ligated GAC ceramic brackets demonstrated the greatest statistically significant friction. For the 0.018-inch wire size, the steel-ligated Ormco steel brackets and the steel-ligated GAC ceramic brackets exhibited statistically similar friction values. For the 0.016 x 0.016-inch wire size, the range of
518
Bednar, Gruendeman, and Sandrik
Mean
Atn. J. Orthod. Dento~w. Orthop. December 1991
Friction Force x Wire Size
1.00
()RE(" SPEED Sell' i . i g a t i n g
.90 (;A(' AI,LURE Elastic Tied
.80 .70
/ ORMCO Mini Dianlond Elastic Tied
.60
¢ .so @
',= .40 '~, .30 ~J
"" '2"" , "N. . , $~,.-"
""'1
(;AC ALLURE
l.ightly Steell'ied
Ot-,ma=,,O," ORMCO Mini Diamond I.ighlly Steel Tied .... ,.,,,
.20
:~ .1o 0.014
0.016
0.018
0.0162
0.016 x 0.022
W i r e Size
Fig. 5. Relationship between wire size and friction for all bracket type/ligation techniques.
friction values for all bracket type/ligation technique groups was smaller than for wire of any other size. Still, the elastomeric-ligated GAC ceramic bracket demonstrated the greatest friction. For the 0.016 X 0.022-inch wire size, the selfligated Orec steel bracket exhibited the greatest statistically significant friction values. The steel-ligated GAC ceramic and steel-ligated Ormco steel brackets demonstrated the least statistically significant friction. The mean friction values for the elastomeric-ligated Ormco steel bracket and the elastomeric-ligated GAC ceramic bracket, combining all wire sizes, were 258.55 gm and 358.34 gm, respectively. The mean friction value for the self-ligated Orec steel bracket, combining all wire sizes, was 290.30 gin.
DISCUSSION As with any in vitro study, this investigation does not replicate what actually occurs intraorally during tooth movement. This study provides a means by which to compare different brackets under similar testing conditions. Some principles and conclusions can be drawn from the results, but one must be careful about applying this information to clinical situations. After initial leveling and aligning, the arch wire is parallel to the bracket slot. As a tooth is translated with sliding mechanics, the crown moves before the root apex does. This results in some tooth tipping and angulation occurring between the bracket and the arch
wire. This angulation, in turn, significantly contributes to the overall friction between arch wire and bracket. Eventually, this friction or binding becomes so great that crown movement stops; the couple created by the bracket/wire interaction works to upright the root. This study sought to simulate the clinical situation in which some tooth tipping occurs during translation along an arch wire, since the center of resistance is located on the root and not at the level of the bracket. Where these results differ from previous studies on friction, this might be explained by differences in testing techiques. Some investigators lock the bracket in a fixed angulation relative to the arch wire; in this study a freely moveable bracket with a load off-center was used. From Fig. 3, for the Ormco steel bracket, two basic principles can be observed. The larger the arch wire, the greater the friction; the ligation technique can significantly influence friction. For every wire size, steelligated steel brackets had less friction than elastomericligated steel brackets. Steel tying is subjective and can be variable. In this experiment, the brackets were deliberately lightly steel-tied. It is possible that when brackets are tightly tied, as with Coon or Steiner tying pliers, the friction may be increased. For the GAC ceramic bracket (Fig.' 2), the friction values were different than for the steel bracket. Like the steel bracket, lightly steel-tied GAC ceramic brackets had less friction than elastomeric-ligated ceramic brackets for each wire size. Unlike the steel brackets,
voh,,e loo
Comparative study of.frictional forces
519
Number 6
Fig. 6. Scanning electron micrograph of the Ormco steel bracket arch wire slot surface (original magnification x 1500).
Fig. 7. Scanning electron micrograph of the Orec steel bracket arch wire slot surface (original magnification x 1500).
greater friction was produced with lighter wires than with heavier ones. From the mean' friction value tbr elastomeric-ligated steel brackets compared with elastomeric-ligated ceramic brackets, and from Fig. 5 it can be seen that elastomeric-ligated steel brackets have much less friction than elastomeric-ligated ceramic brackets. The greater fi:iction of ceramic brackets and their greater friction with lighter wires is most likely related to the surface roughness of the ceramic bracket arch wire slot. Figs. 6, 7, and 8 present scanning electron
micrographs of the Ormco steel bracket arch wire slot surface, the Orec steel bracket arch wire slot surface, and the GAC ceramic bracket arch wire slot surface. The ceramic surface demonstrates significantly greater surface roughness than the stainless steel surface does. This greater roughness likely increases friction. For lighter, more resilient arch wires (0.014 inch) a greater angulati0n was observed between the bracket and the arch wire than for heavier, stiffer arch wires (0.016 x 0.022 inch). In both circumstances, the moments created by the arch wire-bracket couple were
520
Bednar, Gruendeman, and Sandrik
Am. J. Orthod. Dent@w, Orthop. December 1991
Fig. 8. Scanning electron micrograph of the GAC ceramic bracket arch wire slot surface (original magnification x 700, x 1500).
0 / 0 1 4 Incll Wire
tl.l)l~'~ \ 0.022 I n , : h W i r e
Fig. g. Contact surface area between arch wire and bracket.
identical, 1200 gm-mm. At greater wire-to-slot angulations, the 0.014-inch wire was pressed tightly against the ceramic slot, not just at the mesial and distal edges of the slot (as was the case for the 0.016 x 0.022-inch
wire) but along the interior of the slot as well (Fig. 9). This greatly increased area of arch wire pressing against the rough ceramic surface may account for the greater friction observed with lighter arch wires. With regard to the effect of wire size, the selfligating Orec steel brackets behaved similar to metal brackets. The greater the wire size, the greater the friction. The friction produced by the 0.016 × 0.022-inch wire in the self-ligating Orec steel bracket was greater than for any other bracket type/ligation technique (Fig. 5). This is probably due to the design of the bracket and the way the self-ligating spring clip engages the arch wire. The spring clip actually presses into the slot itself to engage the arch wire (Fig. 10). This same spring reduces the amount of space in the slot available for the wire. During trial runs, a full-size 0,0118 x 0.025-inch arch wire could not be engaged in
Comparative study of fi'ictional forces 521
Voh.,e I00 Nmnber 6
Fig. 10. Orec self-ligating bracket, reduction of available slot dimension due to spring clip.
the 0.018-inch slot Orec steel bracket. In fact, the manufacturer recommends that a beveled edgewise arch wire be used with the appliance to optimize arch wireto-bracket engagement. Frorn the mean friction values for the self-ligated Orec steel bracket and the elastomeric-ligated Ormco steel bracket, it would appear that under the testing conditions used the self-ligated steel bracket exhibited similar or greater friction than the elastomeric-ligated steel bracket. However, it is impossible from the data to determine whether the self-ligation characteristic inherently has more or less friction than the conventional ligation techniques. The Orec steel brackets were narrower than the twin brackets with which they were compared. They were not available in the same mesial-distal dimension that the twin brackets were. Under the testing conditions used, in which brackets are made to tip relative to the arch wire, it has been shown that narrower brackets have greater friction than wider brackets. 6 Many different aspects of bracket design contribute to and influence friction. It may be that the self-ligating characteristic of the Orec steel bracket inherently decreases friction, but once the tooth tips during translation, the narrower bracket width tends to increase fi'iction in spite of the self-ligating clip design. This would account for the difference between the study by Berger, 7 which found greatly decreased friction with the self-ligating Orec bracket, and this investigation, which did not find this decreased friction, In his investigation, the bracket was locked in place so that the slot was parallel to the arch wire. Under these circumstances, the influence of bracket width did not come into play. Under the testing conditions of this study,
the narrower Orec bracket width contributes to greater friction than one might otherwise suspect. The finding that lightly steel-ligated brackets have much Iess friction than elastomeric-ligated brackets may be of limited use to most practitioners. Many cIinicians use elastomeric power chains to translate teeth. The chains are attached to bracket tie wings, which in effect results in the teeth being ligated with high-friction elastomeric-type ties, regardless of whether the teeth are atso lightly steel-ligated. One way to minimize friction with a twin bracket would be to lightly steel-tie the wire to the bracket and attach any elastomeric chains to a power arm or hook on the bracket rather than to the tie wings. The clinical significance of this study may be manifested where steel brackets are used on the posterior teeth and ceramic brackets are used on the anterior teeth. Typically, the posterior teeth are used as anchorage to retract the anterior teeth. If sliding mechanics were used, the differences in friction between steel and ceramic brackets could result in the posterior teeth moving more readily than the anterior teeth, the consequence of which would be more anchorage loss than would otherwise be expected. This would be especially true when light arch wires are used. Light arch wires tend to exenuate the differences in friction between steel and ceramic brackets. It might be better for sliding mechanics to use heavier arch wires in which the friction of both ceramic and steel brackets is more similar (Fig. 5). CONCLUSIONS 1. The type of" bracket material and ligation technique significantly influenced friction.
522
Bednar, Gruendeman, and Sandrik
2. Lightly steel-tied brackets had less friction than elastomeric-ligated brackets. 3. For Ormco steel brackets, friction increased with increased wire size. For GAC ceramic brackets, friction decreased with increased wire size. In general, ceramic brackets produced more friction than steel brackets. 4. U n d e r the testing conditions used, i n which the bracket tipped relative to the arch wire, selfligated Orec steel brackets did not demonstrate less friction than either steel-tie or elastomericligated Ormco steel brackets.
Am. J. Orthod. Dentofac. Orthop. December 1991
3. Andreasen GF, Quevedo FR. Evaluation of frictional forces in the .022" x .028" edgewise bracket in vitro. J Biomed 1970; 3:151-60. 4. FrankCA, NikolaRJ. A comparativestndyof frictionalresistance between orthodontic bracket and arch wire, AM J ORTHODD~r~TOFACORTHOP1980;78:593-609. 5. Tidy DC. Frictional forces in fixed appliances. AM J ORTHOD DENTOFACOR'rHOP1989;96:249-54. 6. Garner LD, Allai WW, Moore BK. A comparison of frictional forces during simulatedcanineretractionof a continuousedgewise arch wire. AM J ORTHODDENTOFACORTHOP1986;90:199-203. 7. Berger JL. The influence of the SPEED bracket's self-ligating design on force levels in tooth movement: a comparative in vitro study, AM J ORTHODD~NTOFACORTHOP1990;97:219-28. Reprint requests to:
REFERENCES 1. Drescher D, Bouravel C, Schumach HA. Frictional forces between bracket and arch wire. AM J ORTHODDENTOFAOORTHOP 1989;96:397-404. 2. GamowC. Physics:foundationsand frontiers. 3rded. NewJersey: Prentice-Hall, 1976:25.
Dr. James Bednar Department of Orthodontics Loyola UniversitySchool of Dentistry 2160 South First Ave. Maywood, iL 60153
AAO MEETING CALENDAR
1992--St. Louis, Mo., May 9 to 131 St. Louis Convention Center 1993--Toronto, Canada, May 15 to 19, Metropolitan Toronto Convention Center 1994--Orlando, Fla,, May I to 4, Orange County Convention and Civic Center 1995--San Francisco, Calif,, May 7 to 10, Moscone Convention Center
(International Orthodontic Congress) 1996--Denver, Colo., May 12 to 16, Colorado Convention Center 1997--Philadelphia, Pa., May 3 to 7, Philadelphia Convention Center 1998--Dallas, Texas, May 16 to 20, DalLas Convention Center 1999--San Diego, Calif., May 15 to 19, San Diego Convention Center
A comparative study of frictional forces between orthodontic brackets and arch wires James R. Bednar, DDS, MS,* Gary W. Gruendeman, DDS,* and James L. Sandrik, PhD** Chicago, Ill. An in vitro study of simulated canine retraction was undertaken to evaluate the difference in frictional resistance between stainless steel arch wires and steel and ceramic brackets with elastomerie, steel, and self-ligation. Each bracket slot was 0.018 x 0.025 inch. The arch wires used were 0.014-inch, 0.016-inch, 0.018-inch, 0.016 x 0.016-inch, and 0.016 x 0.22-inch stainless steel. A testing apparatus was designed to attempt to simulate the clinical situation in which teeth tip slightly while they slide along the arch wire. Under these testing conditions, the self-ligating steel bracket did not demonstrate less friction than the elastic or steel-ligated stainless steel brackets. For most wire sizes, elastomer-ligated ceramic brackets demonstrated the greatest friction when compared with other bracket/ligation technique combinations. The clinical significance of this study becomes apparent when stainless steel brackets are used on the posterior teeth and ceramic brackets are used on the anterior teeth. If sliding mechanics are used, the anterior teeth may be more resistant to movement than the posterior teeth because of the greater friction of the ceramic brackets. This could result in more posterior anchorage loss than would be expected if only one type of bracket were used. (AM J ORTHOD DENTOFACORTHOP 1991 ;100:513-22.)
O n e of the most common methods of translating a tooth orthodontically is by the use of sliding mechanics. In this technique, mesiodistal tooth movement is accomplished by guiding a tooth along a continuous arch wire with the use of an orthodontic bracket. A disadvantage of this technique is that friction is generated between the bracket and the arch wire, which tends to resist the movement of the bracket and tooth in the desired direction. Friction is defined as a force that retards or resists the relative motion of two objects in contact, and its direction is tangential to the common boundary of the two surfaces in contact. 1In physics, the frictional force between any two sliding surfaces is directly proportional to the force with which the surfaces are pressed together--F~r = u x F. The value of u (the coefficient of friction) depends on the materials that are sliding and is only very slightly affected by other factors, such as speed or contact areas between the surfaces. 2 In orthodontic sliding mechanics, friction is determined by the type of arch wire, the type of bracket, and the method of ligation. The force pressing the wire and the bracket surfaces together (F) is determined by
From the Loyola University School of Dentistry. *Assistant Professor, Department of Orthodontics. **Professor and Chairman, Department of Dental Materials. 8/1/26074
the angulation between the arch wire and the bracket slot, the size of the arch wire, and the method of ]igation. An investigation of the frictional forces in orthodontic tooth movement was conducted by Andreasen and Quevedo) They performed in vitro tests to quantify the frictional force generated by moving an edgewise bracket along a fixed arch wire. The angulation between the bracket slot and the arch wire was varied, as was the dimension of the arch wires. They found that the larger the arch wire, and the greater the angulation between arch wire and bracket, the greater the friction. Their test showed that there was little difference in friction between dry samples and those tested with saliva as a lubricant. Among other variables, the effect of bracket width and bracket-to-arch wire angulation was studied by Frank and Nikolai. 4 At a given fixed bracket-to-arch wire angulation, wider brackets produced more friction than narrow bracketsl As angulations were increased, binding between the wire and the bracket occurred, and this variable itself became the controlling parameter. They noted that clinically, tooth movement takes place as a series of short steps rather than a smooth continuous motion. Initially, static friction between the arch wire and the bracket must be overcome to initiate tooth movement. While the tooth is moving, kinetic friction occurs as the crown of the tooth tips in the direction of
513
514
Bednar, G r u e n d e m a n , a n d S a n d r i k
am. J. Orthod. Dentofiw. Orthop. December 1991
GAC Allure 500 394
400
Steel Ligation Elastomeric Ligation
388
364
300
200 100
0
i
t.O14
i
0.0!6
0.618
WIRE SIZE
' x 0.016 0.016
0.016 X 0.022
Fig, 2. Relationship between wire size and friction for steel- and elastomeric-ligated GAC ceramic brackets.
Fig. 1. Friction-testing apparatus. applied force. Gradually, because the crown invariably moves before the root does, a couple arises between the wire and the bracket; this eventually stops crown movement and acts to upright the root. After further periodontal remodeling along the root surface, the cycle continues. The center of resistance of a tooth is not located along the same plane as that of the bracket, where force is applied to the tooth. Because o f this, tooth movement is a complicated process that involves tipping of the crown, resulting in the occurrence of some angulation between the bracket slot and the arch wire. Tidy 5 sought to simulate this situation with an apparatus in which a power arm was attached to the bracket and various weights were suspended from this attachment. This, in effect, mimicked the Crown tipping that occurs during clinical tooth movement. Tidy found that nitinol and TMA (beta-titanium) produced frictional fomes two and five times greater than stainless steel. Under his testing conditions, friction was inversely proportional to bracket width; arch wire and slot dimension had relatively little effect, Garner, Allai, and Moore ~ also compared the fric-
tional forces during simulated canine retraction using different wire types. They, too, found significantly larger frictional force with beta-titanium and nitinol when compared with stainless steel. They postulated that the differences in surface smoothness of the various wires may account for the differences in friction, Differences in ligation techniques and their effects on friction was studied by Berger. ~ For his tests, the brackets were locked in place, so that the bracket slot was parallel to the arch wire. He found that self-ligated brackets produced less friction than elastomeric or steeltie ligated brackets. Friction between the arch wire and the bracket has been shown to be an important factor in orthodontic tooth movement. Surface roughness of the arch wire has been shown to play a significant role in contributing to the amount of friction, as does bracket design and ligation technique. At present, orthodontic brackets are fabricated from several types of materials with varying degrees of roughness. This study was designed to investigate the effect of bracket material and ligation technique on the amount of frictional force generated during simulated tooth movement. MATERIALS AND METHODS A testing apparatus was constructed to simulate the clinical situation in which the center of resistance of a tooth is not on the same plane as that of the bracket, thereby resulting in some tipping of the bracket slot relative to the arch wire. This device consisted of a stainless steel framework with a freely rotating plastic disk on which each bracket was mounted. Attached to this disk was a 12 mm stainless steel power arm from which a 100 gm weight was suspende d (Fig.
Volume 100
Comparative study of fi'ictional forces
Ntmzber 6
OREC Speed Bracket
ORMCO Mini Diamond Twin 5OO
Steel Ligation Elastomeric Ligation
500
r-I E3
Spring Clip Ligation
[]
400
400
~
30O
300
200
200
100
100-
27"/
~-/,
0
515
i
0.014
0.0'16
i
i
i
0.018 0.016 x W I R E SIZE 0.016
0.014
0.016 x 0.022
Fig. 3. Relationship between wire size and friction for steel- and elastomericdigated Ormco steel brackets.
0.0'16 0J.018 W I R E SIZE
--.
t
0.016x 0.016
0.016 x 0.022
Fig. 4. Relationship between wire size and friction for selfligated Orec steel brackets.
T a b l e I. Bracket characteristics
Company
Slot dimension
Bracket width
Torque (degree)
Tip (degree)
Composition
GAC Allure*
0.46 × 0.64 mm 0,018 × 0.025 inch
3.56 mm 0.140 inch
- 2
10
Polyerystalline ceramic, machined slot
Ormco Mini-Diamond**
0,46 X 0.64 mm 0.018 × 0,025 inch
3.56 mm 0.140 inch
0
10
Machined metal, machined slot, tunable deburred
Orec SPEED***
0.46 x 0.64 mm 0.018 × 0.025 inch
2.29 mm 0.090 inch
-2
9
Machined metal, turned slot
*GAC Allure, GAC International, Inc., Central Islip, N.Y. **Ormco Mini-Diamond, Ormco Corp., Glendora, Calif. ***Orec SPEED, Orec Corp., San Clemente, Calif.
1). Two pins were placed I0 rmn superior and inferior to the disk to aid in guiding the arch wire. Each bracket was bonded (Phase II bracket adhesive, Reliance Orthodontic Products, Inc,, Itasca, Ill.) to the disk in such a way that the center of the bracket corresponded with the center of the disk and that the bracket slot was perpendicular to the power arm. All testing was done under dry conditions with an Instron Universal machine (Instron Corporation, Canton, Mass.). Each wire was suspended from the 10-pound (4.54 kg) load cell with a heavy brass swivel. The wire was drawn up through the testing apparatus with the crosshead moving at 0.5 inch/min (12,7 mm/rnin). Three different 0.018-inch-slot maxillary right canine orthodontic brackets were tested (Table I). An effort was made to obtain brackets of identical dimensions and prescription. Unfortunately, ceramic brackets were unavailable in the same width as the Orec self-ligating brackets. The bracketmounting protocol helped to minimize any slight differences
in prescriptions. Sampling was done without replacement from a finite population. All arch wires used were made of Tru-Chrome stainless steel orthodontic wire (Rocky Mountain Orthodontics, Denver, Colo.), their dimensions were 0.014 inch (0.36 mm), 0.016 inch (0.41 ram), 0.018 inch (0.46 ram), 0.016 x 0.016 inch (0.41 x 0.41 ram), and 0.016 x 0.022 inch (0.41 x 0.56 ram). The elastomeric-ligated brackets were ligated with Power "O" modules (Ormco Corporation, Glendora, Calif.). The steel-tied brackets were ligated with 0.010-inch (0.25 ram) steel ligatures. Each ligature was initially tightened, then slightly slackened to allow the arch wire to slide freely. The self-ligated brackets were ligated with the integral spring clips. For the elastomeric-ligated brackets, three sample brackets of each bracket type (Mini-Diamond or Allure) were used with each wire size. Each sample bracket was tested three times in succession with each size wire. For the self-ligated
516 Bednar, G r u e n d e m a n , a n d S a n d r i k
Am.
J.
Orthod. Dentofac. Orthop. December 1991
T a b l e II. S u m m a r y statistics for the frictional force generated with each b r a c k e t / l i g a t i o n technique/wire size combination Applied force (gin) Steel-tie ligation
Elastomeric ligation
Minimum
Maximum
Average
SD mean average friction
210,92 114.91
343.97 154.22
277.45 1134.57
27.99 14.76
314.11 192.02
475.14 227.80
394.62 209.91
41.13 33.85
220.75 116.42
327.34 145.15
274.04 130.79
39.74 7.29
316.00 250.99
460.02 280.22
388.01 265.60
62.17 41.42
148.I7 164,81
182.19 192.02
165.18 178.41
13.41 7,29
313.73 234.86
415.04 269.13
364.39 252.00
58.97 32.47
179,17 185.97
238.14 258.55
208.65 222.26
31.30 15.88
282,74 245.44
365.14 279.71
323.94 262.58
54.45 24.94
142.13 155.73
237.38 216.21
189.75 185.97
12.23 9.07
282,36 266.11
354.94 297.86
318.65 281.98
42,27 29.90
Mean
Minimum
Mean "I Maximum I Average
SD Mean average friction
Bracket Wire size (0,36 mm/O.014 inch)
GAC Ormco Orec
Wire size (0.41 mmlO.Old inch)
GAC Ormco Orec Wire size (0.46 mm/O,OJ8 inch)
GAC Ormco Orec Wire size (0.41 x 0.41 mralO.016 × 0.016 inch)
GAC Ormco Orec Wire size (0.41 X 0.56 mm/O.016 X 0,022 inch)
GAC Onnco Oree
SPEED bracket, three sample brackets were used with each wire size, and each bracket was tested three times with each size wire. For the steel-tied ceramic brackets, two sample brackets were tested with each size wire. For the steel-tied metal bracket only one bracket was used, it was tested three times with each wire size. The Instron testing machine was zeroed and calibrated before each bracket type/arch wire/ligation technique series was run. At the initiation of each test run, 0.15 inch (3,8 mm) of wire was drawn through the testing apparatus to take out all the slack. Then 0.25 inch (6.35 mm) of wire was pulled through the bracket. The high and low friction values over this duration were recorded.
RESULTS A l l data were g r o u p e d according to bracket type (stainless steel or ceramic) and ligation technique (elas-
tomeric, steel, or self-ligating). T h e summary statistics for each bracket type/ligation technique (GAC ceramic bracket/steel-tie ligation, GAC ceramic bracket/elastomeric ligation, Ormco steel bracket/steel-tie ligation, Ormco steel bracket/elastomeric ligation, and Orec steel bracket/self-ligation) showing the mean minimum friction value, the mean m a x i m u m friction value, and the mean average friction value are shown in Table II. Analysis o f variance for the results show that the effect of w i r e size is significant at the 0.05 level. The effects of bracket type/ligation technique and the interaction between wire size and bracket type/ligation technique are both significant at the 0.001 level. For every bracket t y p e / l i g a t i o n technique, the friction was plotted for each wire size. This is illustrated in Figs. 2, 3, and 4. T h e s t e e l - t i e - l i g a t e d ceramic
Comparative study of frictional forces 517
Volume100 Number 6
Applied force (gm) Spring-clip ligation Mean Maximum
Average
SDMean average friction
166.82
219.24
193.03
38.41
231.33
306.43
268,88
52.90
248.47
306.43
277.45
34.45
244.94
299.37
272.16
21,21
323.56
399.16
361.36
6.03
Minimum
l
brackets and the steel-tie-ligated steel brackets demonstrated less friction than the elastomeric-ligated ceramic and steel brackets at every arch wire size. All bracket type/ligation technique data were then grouped and analyzed for each specific wire size. Analysis of variance for these results shows that for each wire size the effects of bracket type/ligation technique were significant at the 0.001 level. The mean friction value at each wire size for all five bracket type/ligation techniques were analyzed. The results are illustrated in Fig. 5. Statistical analysis of the friction value of each bracket type / ligation technique for each wire size was done to further evaluate the differences in friction between these groups for each wire size. For the 0.014-inch wire size, the steel-ligated
Ormco steel bracket exhibited less statistically significant friction than the other bracket type/ligation technique groups. The elastomeric-ligated GAC ceramic bracket demonstrated greater statistically significant friction than the other types. For the 0,016-inch wire size, the results were similar to the 0.014-inch wire in that the steel-ligated Ormco steel bracket exhibited less statistically significant friction than the other bracket type/ligation technique groups. The elastomeric-ligated GAC ceramic brackets demonstrated the greatest statistically significant friction. For the 0.018-inch wire size, the steel-ligated Ormco steel brackets and the steel-ligated GAC ceramic brackets exhibited statistically similar friction values. For the 0.016 x 0.016-inch wire size, the range of
518
Bednar, Gruendeman, and Sandrik
Mean
Atn. J. Orthod. Dento~w. Orthop. December 1991
Friction Force x Wire Size
1.00
()RE(" SPEED Sell' i . i g a t i n g
.90 (;A(' AI,LURE Elastic Tied
.80 .70
/ ORMCO Mini Dianlond Elastic Tied
.60
¢ .so @
',= .40 '~, .30 ~J
"" '2"" , "N. . , $~,.-"
""'1
(;AC ALLURE
l.ightly Steell'ied
Ot-,ma=,,O," ORMCO Mini Diamond I.ighlly Steel Tied .... ,.,,,
.20
:~ .1o 0.014
0.016
0.018
0.0162
0.016 x 0.022
W i r e Size
Fig. 5. Relationship between wire size and friction for all bracket type/ligation techniques.
friction values for all bracket type/ligation technique groups was smaller than for wire of any other size. Still, the elastomeric-ligated GAC ceramic bracket demonstrated the greatest friction. For the 0.016 X 0.022-inch wire size, the selfligated Orec steel bracket exhibited the greatest statistically significant friction values. The steel-ligated GAC ceramic and steel-ligated Ormco steel brackets demonstrated the least statistically significant friction. The mean friction values for the elastomeric-ligated Ormco steel bracket and the elastomeric-ligated GAC ceramic bracket, combining all wire sizes, were 258.55 gm and 358.34 gm, respectively. The mean friction value for the self-ligated Orec steel bracket, combining all wire sizes, was 290.30 gin.
DISCUSSION As with any in vitro study, this investigation does not replicate what actually occurs intraorally during tooth movement. This study provides a means by which to compare different brackets under similar testing conditions. Some principles and conclusions can be drawn from the results, but one must be careful about applying this information to clinical situations. After initial leveling and aligning, the arch wire is parallel to the bracket slot. As a tooth is translated with sliding mechanics, the crown moves before the root apex does. This results in some tooth tipping and angulation occurring between the bracket and the arch
wire. This angulation, in turn, significantly contributes to the overall friction between arch wire and bracket. Eventually, this friction or binding becomes so great that crown movement stops; the couple created by the bracket/wire interaction works to upright the root. This study sought to simulate the clinical situation in which some tooth tipping occurs during translation along an arch wire, since the center of resistance is located on the root and not at the level of the bracket. Where these results differ from previous studies on friction, this might be explained by differences in testing techiques. Some investigators lock the bracket in a fixed angulation relative to the arch wire; in this study a freely moveable bracket with a load off-center was used. From Fig. 3, for the Ormco steel bracket, two basic principles can be observed. The larger the arch wire, the greater the friction; the ligation technique can significantly influence friction. For every wire size, steelligated steel brackets had less friction than elastomericligated steel brackets. Steel tying is subjective and can be variable. In this experiment, the brackets were deliberately lightly steel-tied. It is possible that when brackets are tightly tied, as with Coon or Steiner tying pliers, the friction may be increased. For the GAC ceramic bracket (Fig.' 2), the friction values were different than for the steel bracket. Like the steel bracket, lightly steel-tied GAC ceramic brackets had less friction than elastomeric-ligated ceramic brackets for each wire size. Unlike the steel brackets,
voh,,e loo
Comparative study of.frictional forces
519
Number 6
Fig. 6. Scanning electron micrograph of the Ormco steel bracket arch wire slot surface (original magnification x 1500).
Fig. 7. Scanning electron micrograph of the Orec steel bracket arch wire slot surface (original magnification x 1500).
greater friction was produced with lighter wires than with heavier ones. From the mean' friction value tbr elastomeric-ligated steel brackets compared with elastomeric-ligated ceramic brackets, and from Fig. 5 it can be seen that elastomeric-ligated steel brackets have much less friction than elastomeric-ligated ceramic brackets. The greater fi:iction of ceramic brackets and their greater friction with lighter wires is most likely related to the surface roughness of the ceramic bracket arch wire slot. Figs. 6, 7, and 8 present scanning electron
micrographs of the Ormco steel bracket arch wire slot surface, the Orec steel bracket arch wire slot surface, and the GAC ceramic bracket arch wire slot surface. The ceramic surface demonstrates significantly greater surface roughness than the stainless steel surface does. This greater roughness likely increases friction. For lighter, more resilient arch wires (0.014 inch) a greater angulati0n was observed between the bracket and the arch wire than for heavier, stiffer arch wires (0.016 x 0.022 inch). In both circumstances, the moments created by the arch wire-bracket couple were
520
Bednar, Gruendeman, and Sandrik
Am. J. Orthod. Dent@w, Orthop. December 1991
Fig. 8. Scanning electron micrograph of the GAC ceramic bracket arch wire slot surface (original magnification x 700, x 1500).
0 / 0 1 4 Incll Wire
tl.l)l~'~ \ 0.022 I n , : h W i r e
Fig. g. Contact surface area between arch wire and bracket.
identical, 1200 gm-mm. At greater wire-to-slot angulations, the 0.014-inch wire was pressed tightly against the ceramic slot, not just at the mesial and distal edges of the slot (as was the case for the 0.016 x 0.022-inch
wire) but along the interior of the slot as well (Fig. 9). This greatly increased area of arch wire pressing against the rough ceramic surface may account for the greater friction observed with lighter arch wires. With regard to the effect of wire size, the selfligating Orec steel brackets behaved similar to metal brackets. The greater the wire size, the greater the friction. The friction produced by the 0.016 × 0.022-inch wire in the self-ligating Orec steel bracket was greater than for any other bracket type/ligation technique (Fig. 5). This is probably due to the design of the bracket and the way the self-ligating spring clip engages the arch wire. The spring clip actually presses into the slot itself to engage the arch wire (Fig. 10). This same spring reduces the amount of space in the slot available for the wire. During trial runs, a full-size 0,0118 x 0.025-inch arch wire could not be engaged in
Comparative study of fi'ictional forces 521
Voh.,e I00 Nmnber 6
Fig. 10. Orec self-ligating bracket, reduction of available slot dimension due to spring clip.
the 0.018-inch slot Orec steel bracket. In fact, the manufacturer recommends that a beveled edgewise arch wire be used with the appliance to optimize arch wireto-bracket engagement. Frorn the mean friction values for the self-ligated Orec steel bracket and the elastomeric-ligated Ormco steel bracket, it would appear that under the testing conditions used the self-ligated steel bracket exhibited similar or greater friction than the elastomeric-ligated steel bracket. However, it is impossible from the data to determine whether the self-ligation characteristic inherently has more or less friction than the conventional ligation techniques. The Orec steel brackets were narrower than the twin brackets with which they were compared. They were not available in the same mesial-distal dimension that the twin brackets were. Under the testing conditions used, in which brackets are made to tip relative to the arch wire, it has been shown that narrower brackets have greater friction than wider brackets. 6 Many different aspects of bracket design contribute to and influence friction. It may be that the self-ligating characteristic of the Orec steel bracket inherently decreases friction, but once the tooth tips during translation, the narrower bracket width tends to increase fi'iction in spite of the self-ligating clip design. This would account for the difference between the study by Berger, 7 which found greatly decreased friction with the self-ligating Orec bracket, and this investigation, which did not find this decreased friction, In his investigation, the bracket was locked in place so that the slot was parallel to the arch wire. Under these circumstances, the influence of bracket width did not come into play. Under the testing conditions of this study,
the narrower Orec bracket width contributes to greater friction than one might otherwise suspect. The finding that lightly steel-ligated brackets have much Iess friction than elastomeric-ligated brackets may be of limited use to most practitioners. Many cIinicians use elastomeric power chains to translate teeth. The chains are attached to bracket tie wings, which in effect results in the teeth being ligated with high-friction elastomeric-type ties, regardless of whether the teeth are atso lightly steel-ligated. One way to minimize friction with a twin bracket would be to lightly steel-tie the wire to the bracket and attach any elastomeric chains to a power arm or hook on the bracket rather than to the tie wings. The clinical significance of this study may be manifested where steel brackets are used on the posterior teeth and ceramic brackets are used on the anterior teeth. Typically, the posterior teeth are used as anchorage to retract the anterior teeth. If sliding mechanics were used, the differences in friction between steel and ceramic brackets could result in the posterior teeth moving more readily than the anterior teeth, the consequence of which would be more anchorage loss than would otherwise be expected. This would be especially true when light arch wires are used. Light arch wires tend to exenuate the differences in friction between steel and ceramic brackets. It might be better for sliding mechanics to use heavier arch wires in which the friction of both ceramic and steel brackets is more similar (Fig. 5). CONCLUSIONS 1. The type of" bracket material and ligation technique significantly influenced friction.
522
Bednar, Gruendeman, and Sandrik
2. Lightly steel-tied brackets had less friction than elastomeric-ligated brackets. 3. For Ormco steel brackets, friction increased with increased wire size. For GAC ceramic brackets, friction decreased with increased wire size. In general, ceramic brackets produced more friction than steel brackets. 4. U n d e r the testing conditions used, i n which the bracket tipped relative to the arch wire, selfligated Orec steel brackets did not demonstrate less friction than either steel-tie or elastomericligated Ormco steel brackets.
Am. J. Orthod. Dentofac. Orthop. December 1991
3. Andreasen GF, Quevedo FR. Evaluation of frictional forces in the .022" x .028" edgewise bracket in vitro. J Biomed 1970; 3:151-60. 4. FrankCA, NikolaRJ. A comparativestndyof frictionalresistance between orthodontic bracket and arch wire, AM J ORTHODD~r~TOFACORTHOP1980;78:593-609. 5. Tidy DC. Frictional forces in fixed appliances. AM J ORTHOD DENTOFACOR'rHOP1989;96:249-54. 6. Garner LD, Allai WW, Moore BK. A comparison of frictional forces during simulatedcanineretractionof a continuousedgewise arch wire. AM J ORTHODDENTOFACORTHOP1986;90:199-203. 7. Berger JL. The influence of the SPEED bracket's self-ligating design on force levels in tooth movement: a comparative in vitro study, AM J ORTHODD~NTOFACORTHOP1990;97:219-28. Reprint requests to:
REFERENCES 1. Drescher D, Bouravel C, Schumach HA. Frictional forces between bracket and arch wire. AM J ORTHODDENTOFAOORTHOP 1989;96:397-404. 2. GamowC. Physics:foundationsand frontiers. 3rded. NewJersey: Prentice-Hall, 1976:25.
Dr. James Bednar Department of Orthodontics Loyola UniversitySchool of Dentistry 2160 South First Ave. Maywood, iL 60153
AAO MEETING CALENDAR
1992--St. Louis, Mo., May 9 to 131 St. Louis Convention Center 1993--Toronto, Canada, May 15 to 19, Metropolitan Toronto Convention Center 1994--Orlando, Fla,, May I to 4, Orange County Convention and Civic Center 1995--San Francisco, Calif,, May 7 to 10, Moscone Convention Center
(International Orthodontic Congress) 1996--Denver, Colo., May 12 to 16, Colorado Convention Center 1997--Philadelphia, Pa., May 3 to 7, Philadelphia Convention Center 1998--Dallas, Texas, May 16 to 20, DalLas Convention Center 1999--San Diego, Calif., May 15 to 19, San Diego Convention Center
