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The dynamnic frictional resistance between orthodontic brackets and arch wires
The dynamic frictional resistance between orthodontic brackets and arch wires Michael Tselepis, BDSc (Mel b.), MDSc (Mel b.),· Peter Brockhurst, BTch (Mel b.), MSc (Melb.), PhD,b and Victor C. West, MDSc (Melb.), BSc (Melb.)C Brisbane, Queensland, and Melbourne, Australia Limited published research on friction deals mainly with conventional stainless steel brackets and arch wires. However, the clinician can choose from a range of modern materials in determining arch wire and bracket combinations. This study quantifies the dynamic frictional force of sliding between different modern orthodontic brackets and arch wires. From the multitude of factors involved in the frictional process, the following were selected for investigation: arch wire material, bracket material, bracket-to-arch wire angulation, and lubrication (artificial saliva). The frictional force involved in sliding a ligated arch wire through a bracket slot was measured with a universal materials testing machine. A four-way analysis of variance was used to assess the results. Of the four factors investigated, all were found to have a significant influence on friction. Polycarbonate brackets showed the highest friction and stainless steel brackets the lowest. Friction increased with bracket-to-arch wire angulation. Lubrication significantly reduced friction. A range of 0.9 to 6.8 N frictional force was recorded. The actual force values recorded were most useful for comparing the relative influence of the factors tested on friction, rather than as a quantitative assessment of friction in vivo. The forces observed suggest that friction may be a significant influence on the amount of applied force required to move a tooth in the mouth. Hence, arch wire and bracket selection may be an important consideration when posterior anchorage is critical. (AM J ORTHOD DENTOFAC ORTHOP 1994;106:131-8.)
Friction is the resistance to motion encountered when one solid body slides or tends to slide over another. It may be described as a force acting parallel to the direction of motion. 1 Friction is a factor in all forms of sliding mechanics, such as canine retraction into an extraction site, and in leveling and alignment where the wire must slide through the brackets and tubes present. Friction may exist in two forms: (1) Static friction, which is the resistance that prevents actual motion, and (2) dynamic (kinetic) friction, which exists during motion.2,3 Several techniques have been used to measure frictional resistance between arch wires and brackets, such as a dynamometer," a weighted basket' or bucket," a force gauge,":" and a universal testing machine."!" A review of the orthodontic literature revealed that friction between arch wires and brackets is multifactorial. In summarizing the results of the various authors,
'Orthodontist-In-Charge, Children's Dental Hospital, Brisbane, Australia. 'Senior Lecturer, Dental Faculty, University of Queensland. Australia. 'Head in the Department of Orthodontics University of Melbourne, Australia. Copyright © 1994 by the American Association of Orthodontists. 0889-5406/94/$3.00 + 0 8/1/43552
there was agreement that frictional resistance will increase (1 to 3) or vary (4,5) with the following: (1) wire size,* (2) angulation of wire to bracket,4.5,7,8 (3) ligature force,"!' (4) a change in wire shape,5.11,13.14,17 and, (5) a change in wire material.5.8.10.12.14,15-19 However, there are conflicting views on the influence of (1) bracket width,4,5.7.10.13.14.18 (2) lubrication.Y'":":" (3) surface roughness,5,6,10.12-17,20,21 and, (4) ligature design (stainless steel or elastic rings). 11.18,22 The specific objectives of this report were to investigate the influence on frictional resistance by (1) different arch wire and bracket materials, (2) bracketto-arch wire angulation, and (3) lubrication, in the form of artificial saliva. MATERIALS AND METHODS Thirty-two combinations were measured under both wet and dry conditions, as detailed in Table I. Each bracket was cemented to a 12.5 mm diameter stainless steel rod. Contaminants were removed by using an ultrasonic cleaner and 99.7% to 100% v/v ethanol. A period of 6 days elapsed before any readings were taken to allow the elastic ligature rings (Unitek AI) previously placed on the brackets to reach a stable level of force. This 'References 5, 7, 8,10,11,13,14,16-18
131
132
Tselepis, Brockhurst, and West
American Journal of Orthodontics and Dentofacial Orthopedics AURust 1994
Table I. Experimental sample Brackets I. Style: Lower anterior edgewise 2. Slot Width: 0.018 inch (0.46 mm) 3. Materials: Stainless steel (SS)' Polycarbonate (PC)b Porcelain (PO)' Sapphire (SA)' 4. Total sample size: 32 brackets (eight per type) equally subdivided into wet and dry test condition groups Wires I. Materials: Stainless steel (Hi-T) (SS)' Cobalt chromium (Blue Elgiloy) (CCl' Nickel titanium (Nitinol) (NT)' Beta titanium (TMA) (BT)' 2. Dimensions: 0.016 x 0.022 inches (0.41 x 0.56 mm) 3. Length: 7 inches (175 mm) 4. Total sample size: 32 archwires (eight per type) equally subdivided into wet and dry test condition groups "Unitek Corp., Monrovia, Calif. "American Orthodontics, Sheboygan, Wis. 'Tomy International, Tokyo, Japan. 'A-Company, Inc., San Diego, Calif. 'Rocky Mountain Orthodontics, Denver, Colo. 'Ormco Corp., Glendora, Calif.
Fig. 1. Test apparatus. Bracket and ligated arch wire in collet device located on universal testing machine platform.
was confinned in a pilot study using a control set-up consisting of a stainless steel bracket and stainless steel arch wire. The frictional force during 4 mm of arch wire travel was recorded for seven different ligature rings. The procedure was repeated using ligature rings that were prestretched over a bracket for 6 days. A collet apparatus was employed to rigidly hold the rods and, hence, fix the bracket-to-arch wire angulation to any chosen value as measured by a circular protractor attached to the collet. Each arch wire was pulled through a bracket slot by a pin vice suspended from a 50 N load cell through links of a metal chain. The varying amount of applied force (in newtons) required to move the arch wire a distance of 4 mm at a crosshead speed of 10 mm/min was recorded graphically by a universal testing machine (Shimadzu HAG-IOTA Autograph, Kyoto, Japan) (Fig. I) and mean force values were calculated. Ten trials for each bracket-to-arch wire angulation, over a total distance of 40 mm each, were performed. The arch wires and brackets were grouped and tested so that not one of the eight brackets in any group had more than one arch wire drawn through it. Similarly, no individual arch
wire was drawn through more than one bracket. This was to eliminate the influence of wear, as each bracket and arch wire were tested only once. By using the same protocol, a separate series of readings were taken for the arch wire and bracket set-up while lubricated by applying drops of artificial saliva (Salube, Orapharm Pty Ltd., Melbourne, Australia). RESULTS
Sixteen different types of devices (as a result of combining four types of brackets with four types of arch wires) were statistically analyzed. The frictional force was represented in newtons required to slide an arch wire along a bracket for a given distance. The term friction, when used in a quantitative sense, refers to the average dynamic frictional force associated with a specific movement. At each arch wire/bracket/condition/degree combination, 10 measurements were taken, resulting in 640 measurements in total. The results are presented in Table II. Analysis of variance
The statistical analysis used was a four-way analysis of variance. All variance ratios were greater than the critical values at a 95% confidence level. This meant that combinations of all four factors tested (arch wires,
AmericanJournal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West 133
Table II. Mean frictional force (newtons) and standard deviation (SD) for bracket!wire combinations (Based on 10 observations per entry) Bracket I wire angulation Dry condition
0° Bracket
SS
PO
SA
Wire
Mean
SS CC NT BT All SS CC NT BT All S5 CC NT
PC
BT All SS CC NT
All
BT All SS CC NT
BT All
I
Wet condition
if
10° (SD)
Mean
2.25 1.84 1.84 1.99 1.99
(0.22) (0.11) (0.11) (0.15) (0.23)
3.09 2.23 2.09 2.76 2.56
I
(SD)
Mean
2.69 3.06 2.30 2.85 2.72
(0.13) (0.06) (0.02) (0.05) (0.29)
(0.07) (0.03) (0.05) (0.04) (0.04)
3.89 2.86 2.59 3.51 3.21
3.07 2.36 2.95 2.85 2.81
(0.11) (0.08) (0.06) (0.06) (0.28)
3.25 2.71 2.69 3.27 2.98 2.91 2.30 2.39 2.73 2.58
I
10°
I
(SD)
(SD)
Mean
0.89 1.28 1.28 1.89 1.34
(0.04) (0.05) (0.03) (0.08) (0.36)
1.72 1.74 1.74 2.56 1.94
(0.02) (0.02) (0.03) (0.06) (0.36)
(0.07) (0.04) (0.04) (0.05) (0.52)
2.25 2.01 2.44 2.19 2.22
(0.03) (0.05) (0.05) (0.04) (0.16)
3.26 3.18 2.72 2.71 2.97
(0.06) (0.05) (0.03) (0.05) (0.26)
4.59 3.34 3.37 3.34 3.66
(0.05) (0.09) (0.07) (0.10) (0.55)
3.50 3.15 3.21 2.62 3.12
(0.14) (0.07) (0.14) (0.09) (0.35)
2.49 3.79 3.16 4.18 3.40
(0.06) (0.06) (0.05) (0.18) (0.66)
(0.18) (0.11) (0.06) (0.09) (0.30)
6.72 4.64 3.25 4.57 4.79
(0.29) (0.02) (0.06) (0.12) ( 1.26)
2.87 2.07 2.05 2.06 2.26
(0.06) (0.05) (0.05) (0.06) (0.36)
4.75 3.23 2.72 3.02 3.43
(0.05) (0.05) (0.11) (0.06) (0.80)
(0.42) (0.33) (0.45) (0.45) (0.48)
4.47 3.47 2.88 3.56 3.59
(1.49) (0.71) (0.46) (0.64) (1.07)
2.38 2.13 2.24 2.19 2.24
(0.98) (0.68) (0.71) (0.28) (0.71)
3.06 2.97 2.58 3.11 2.93
(1.13) (0.78) (0.53) (0.65) (0.82)
brackets, angulation, and lubrication) were significantly affecting friction. The analysis of variance also tested for interactions between the factors. To better appreciate the meaning of these interactions, the means of the bracket / arch wire combinations for each of the conditions and angulations were plotted in Figs. 2 and 3. As seen from the plots, different arch wires produce different amounts of friction with different brackets. If there were no interactions, then the relative frictional value of the arch wires would not change as the bracket type changes. Relative ranklngs of the bracket/arch wire combinations
From Table II the following trends were evident: (1) For the dry condition, the polycarbonate bracket! stainless steel arch wire combination produced the most friction at both angulations; (2) for the wet condition, the stainless steel bracket! stainless steel arch wire combination produced the least friction at both
angulations; (3) highest overall friction was for poly-. carbonate bracket! stainless steel arch wire (under dry conditions at 10°); and (4) the lowest overall friction was for stainless steel bracket! stainless steel arch wire (under wet conditions at 0°). These differences were highly significant. The range of mean frictional resistance was 0.89 to 6.72 N. Effect of angulation on friction
Ten degrees bracket! arch wire angulation gave highly significant greater values for friction than 0° for nearly all bracket! arch wire combinations under both wet and dry conditions. Effect of lubrication on friction
Zero degrees bracket/arch wire angulation. Lubrication in the form of artificial saliva gave highly significant lower frictional values than the dry condition for nearly all bracket! arch wire combinations. The greatest frictional reduction was 60.5% for the stainless
134
American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West
7.0 6.5 6.0
(jj
c 0
~ Ql
~
Ql
o
0 u. tii
5.5
0
.DRY
0
ADRY
10
0
5.0 4.5 4.0
C
Q
0 ~
3.5
o
3.0
'">.c
2.5
'E 0
2.0 1.5 1.0 0.5
Wire
Bracket
CC
NT
BT
SS
Stainless Steel
CC
NT
BT
Porcelain
SS
CC
NT
BT
SS
Sapphire
CC
NT
BT
SS
Polycarbonate
Bracket / Wire Combinations
Fig. 2. Average friction between arch wire/bracket combinations for dry condition at 0° and 10°.
steel bracket/stainless steel arch wire combination. The smallest reduction was 8.1% for the sapphire bracket/beta-titanium arch wire combination. Ten degrees bracket/ arch wire angulation. Lubrication gave highly significant lower values than the dry condition for nearly all bracket/ arch wire combinations. The greatest reduction in friction occurred for sapphire bracket/ stainless steel arch wire producing a 46% reduction in friction. The least reduction was for sapphire bracket/ nickel titanium arch wire producing a 6% reduction only. However, for some combinations lubrication increased the frictional resistance. The greatest frictional increase was by 20% for the sapphire bracket/beta titanium arch wire. Comparison ofindividual brackets. When there was an increase in friction, it involved only sapphire and porcelain brackets. The stainless steel brackets all showed a decrease in friction with lubrication, regardless of arch wire or angulation. The polycarbonte brackets either showed a decrease or no change.
Ligature testing-pilot study
The effect on frictional force when using different elastic ligature rings was shown to be statistically insignificant by the low coefficients of variation obtained (4.8% to 8.6%) for new rings (Table III). Ligature rings prestretched for 6 days exhibited highly significant lower frictional values by comparison to new rings, and lower coefficients of variation (Table IV). DISCUSSION Comparison of results
A characteristic of the current orthodontic literature on friction is the significant number of variables involved in the experimental techniques used. These may include: (1) arch wires and brackets from different manufacturers, with inherent differences in surface finish, hardness, and stiffness, (2) sliding velocity, (3) ligation mode, (4) the use of flats instead of brackets," and (5) whether a bracket is in a rigid mount or one that allows movement in one or more planes. 14 Hence, differences
American Journal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West
135
7 0 0.5 6.0 (/l
c 0
55
~ Q) ~ Q)
o
0 11. (ij
0
WET
0°
c:
WET
10°
50 4 5 40
C
.Q
t5
~
.~
3.5
<::
30
E
ell
c >-
2 5
0
2.0 1.5 1.0 05
:A
Wire Bracket
CC
NT
8T
SS
Stainless Steel
~
CC
NT
8T
Porcelain
SS
CC
NT
8T
SS
Sapptur e
CC
NT
8T
SS
polycarbonate
Bracket / Wire Combinations Fig. 3. Average friction between arch wire/bracket combinations for wet condition at 0° and 10°.
in experimental results for any given arch wire and bracket couple should not be surprising. Stainless steel bracket
There was no significant difference in friction betweenthe stainless steel bracket and different arch wire combinations under dry conditions at 0°. This supports Peterson et al., 8 but differs with other investigators5,6.12,14-1?,19 who found nickel-titanium arch wire to show very high frictional resistance with such a bracket. The explanation may be in fact that nickel titanium arch wires from different manufacturers show differences in recorded friction, as well as surface roughness, as shown by Prososki et al." They found no significant correlation between surface roughness and friction for the various nickel titanium wires tested. At 10° bracket! arch wire angulation the arch wires could be ranked in increasing order of friction as: nickel-titanium followed by stainless steel or beta-titanium, followed by cobalt-chromium. These results supported those of Frank and Nikolai" and Peterson et al. 8
Hence, frictional values may vary for a given bracket-arch wire combination as a tooth moves along an arch wire in a tipping and uprighting fashion. Clinically, tooth movement occurs not in a continuous manner, but rather as a cycle of short steps. To simulate this, some investigators have mounted the bracket so as to allow free movement (Kapila et al., 14 Bednar et aI,23). However, the validity of this to the actual clinical situation is yet to be proven. lubrication
The function of a lubricant is to reduce the strength and number of bridges formed between the asperities of sliding surfaces. 24 It is generally perceived that saliva acts as a lubricant. Frictional resistance was found to decrease under wet conditions (artificial saliva). This supported the findings of Baker et al. 9 It was at variance with Andreasen and Quevedo? who found no significant difference, while others.t-":" have found an increase in friction with artificial saliva. Pratten et al., 6 suggested that at high loads (undefined), saliva may be forced out from
136
American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West
Table III. Effect of new ligatures on bracket/ arch wire friction (newtons) (5 ligatures per sample) Ligature sample I 2 3 4 5 6 7
Meanforce 3.38 4.26 5.08 4.02 3.70 3.63 3.39
(0.13) (0.37) (0.18) (0.31) (0.23) (0.26) (0.21)
95% confidence interval
Coefficient variation
(3.12, 3.64) (3.51,5.02) (4.70, 5.46) (3.38, 4.66) (3.31,4.09) (3.20, 4.06) (3.04, 3.74)
4.8% 8.6% 3.6% 7.7% 6.2% 7.2% 6.2%
Table IV. Effect of relaxed ligatures on bracket/arch wire friction (newtons) (5 ligatures per sample) Ligature sample I 2 3 4 5 6 7
Meanforce 2.02 1.87 2.10 2.37 1.62 1.99 0.72
(0.13) (0.12) (0.12) (0.17) (0.11) (0.08) (0.02)
the contacts between the bracket and the arch wire, resulting in an increase in friction. Hence, saliva may act as a lubricant only at low loads as determined by ligature force. However, according to the engineering literature, it is impossible to force out completely even an oil film from between two plane surfaces, no matter how heavy the load." The different findings may be related to the formulations of different artificial saliva solutions, as well as the technique of applying the saliva to the bracket/arch wire assembly, which is often not specified in the publications. That is, it may be expected that using a bath of saliva would provide continuous lubrication as opposed to simply applying the saliva as drops. Kusy et al. 26 was the first to employ a peristaltic pump to inject fresh human saliva onto a bracket-arch wire assembly. As was the case for studies that used artificial saliva, Kusy et al. 26 reported mixed results, in that human saliva could both reduce and increase friction depending on the particular bracket-arch wire combination. Bracket/arch wire angUlation
As bracket/ arch wire angulation increased, so did frictional resistance. Similar results were found by Frank and Nikolai,", Andreasen and Quevedo," and Peterson et al. 8 An angulation of 10° allows comparison
95% confidence interval
Coefficient variation
(1.80, 2.25) (1.66, 2.09) (1.56, 2.66) (2.14,2.61) (1.10,2.13) (1.53, 2.45) (0.49, 0.96)
6.4% 8.5% 18.6% 7.2% 15.4% 4.0% 15.3%
to previous published reports. Clinically, however, bracket-arch wire angulation is determined by such variables as wire cross-section, wire material, and magnitude of applied force to the tooth. Stainless steel arch wire
At 0°, under dry conditions, and with stainless steel arch wire, brackets were ranked in order of increasing friction as stainless steel, followed by polycarbonate, sapphire, or porcelain. This supported the work of Riley et al., 11 Berger," Angolkar et aI., 17 and Popli et al. 19 These rankings may represent variation in surface roughness of the bracket slot surfaces, which has yet to be fully investigated. Porcelain bracket
In general, porcelain brackets demonstrated greater friction than stainless steel brackets. According to Kusy" this is due not to their surface roughness but rather to their chemical structure. This may explain why both sapphire and ceramic brackets showed increased friction under lubrication. Popli et al. 19 found that with nickel-titanium (Nitinol) arch wire, porcelain brackets generate more friction than stainless steel brackets. This was not supported by the present study that found no difference
American Journal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West
between these brackets for nickel-titanium arch wire. Kusy and Whitley" state that bracket material does not significantly influence the coefficient of friction. What to measure, static, or kinetic friction?
The dilemma was to decide which form of friction was relevant to the clinical orthodontic situation. There is a constant alternating between static and dynamic friction as a tooth intermittently slides and binds along the arch wire during orthodontic movement. It was decided to measure frictional resistance by programming the universal testing machine to calculate the average of all the peaks recorded over 4 mm of arch wiresliding, with the exception ofthe first peak. Hence, kinetic friction was measured rather than static friction, because of the variable nature of the frictional process. Similar approaches to the problem were made by other authors9-14.17.20 who all measured kinetic friction. Othershave measured static friction only, by measuring the weight of lead shot" or water in a container" required to initiate sliding, or by using a force gauge.":" Kusy and Whitley" determined both static and kinetic coefficients of friction.
2.
3.
4.
5.
6.
7.
Clinical significance
The clinical significance of friction is its role in lessening the force actually received by a tooth from an active component such as a spring, loop, or elastic. Hence, greater applied force is needed to move a tooth with a bracket-arch wire combination demonstrating high magnitudes of friction (e.g., polycarbonate bracket) compared with one with a low frictional value (e.g., stainless steel bracket). This has clinical implications in cases demonstrating critical posterior anchorage, such as those requiring reduction of a large overjet. In such malocclusions, one would be wise to use a bracket and arch wire combination that minimizes friction so as to conserve the available anchorage. A limitation of the study was the difficulty in extrapolating the values for friction determined in vitro to an in vivo situation. This was due to the difficulty of reproducing oral conditions such as muscular and occlusal forces, and tooth movement through bone, which may affect the binding of the arch wire to the bracket. Hence, the relative rankings of the arch wires and brackets were considered to be more meaningful than actual force values recorded for a given experimental set-up. CONCLUSIONS
1. Combinations of all four factors tested (arch wire, brackets, angulation, and lubrication) were
8.
137
statistically significant in the frictional process. Interactions between the factors were also significant. In general, polycarbonate brackets showed the highest values for friction and stainless steel brackets showed the lowest values. Specifically, the combination with the highest frictional resistance was a polycarbonate bracket with a stainless steel arch wire (wet conditions at 10°). The lowest frictional resistance was for a stainless steel bracket with a stainless steel arch wire (wet conditions at 0°). Bracket-to-arch wire angulation was shown to have a significant effect under both wet and dry conditions. In general, frictional resistance increased with angulation, but exceptions did exist. Lubrication significantly reduced the frictional resistance (up to 60.5%) for both 0° and 10° bracket-to-arch wire angulation. Exceptions were found. The difference between the least (0.9 N) and the greatest frictional force (6.8 N) recorded was significant. Elastic ligature rings, especially when prestretched or allowed to relax, were not a significant source of bias toward the frictional forces recorded.
REFERENCES 1. Halling J. Principles of tribology. New York: Macmillan, 1975. 2. Bowden FP, Tabor D. Friction. An introduction to tribology. Garden City, New York: Anchor Press/Doubleday, 1973. 3. Rabinowicz E. Friction and wear of materials. New York: J Wiley, 1965. 4. Nicolls J. Frictional forces in fixed orthodontic appliance. Dent Practit 1968;18:362-6. 5. Frank CA, Nikolai RJ. A comparitive study of frictional resistances between orthodontic bracket and archwire. AMJ ORTHOD 1980;78:593-609. 6. Pratten DH, Popli K, Germane N, Gunsolley JC. Frictional resistance of ceramic and stainless steel orthodontic brackets. AM J ORTHOD DENTOFAC ORTHOP 1990;98:398-403. 7. Andreasen GF, Quevedo FR. Evaluation of friction forces in the 0.022*0.028 edgewise bracket in-vitro. J Biomechanics 1970;3:151-60. 8. Peterson L, Spencer R, Andreasen G. A comparison of friction resistance for nitinol and stainless steel wire in edgewise brackets. Quintessence Int 1982;5:1-9. 9. Baker KL, Nieberg LG, Weimer LD, Hanna M. Frictional changes in force values caused by saliva substitution. AM J ORTHOD DENTOFAC ORTHOP 1987;91:316-20. 10. Garner LD, Allai WW, Moore BK. A comparison of frictional forces during simulated canine retraction of a continuous edge-
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American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West wise arch wire. AM 1 ORTHOD DENTOFAC ORTHOP 1986;90:199203. Riley 1L, Garrett SG, Moon PC. Frictional forces of ligated metal and edgewise brackets. 1 Dent Res 1979;58:A21, IADR Abstract, 98. Stannard1G, Gau 1M, Hanna MA. Comparitive friction of orthodontic wires under dry and wet conditions. AM 1 ORTHOD 1986;89:485-91. Berger 1L, The influence of the SPEED bracket's self-ligating design on force levels in tooth movement: a comparitive in vitro study. AM 1 ORTHOD DENTOFAC ORTHOP 1990;97:219-28. Kapila S, Angolkar PV, Duncanson MG, Nanda RS. Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four different alloys. AM 1 ORTHOD DENToFAc ORTHOP 1990;98:117-26. Kusy RP, Whitley 1Q. Coefficients of friction for archwires in stainless steel and polycrystalline alumina bracket slots. I. The dry state. AM 1 ORTHOD DENTOFAC ORTHOP 1990;98:300-12. Drescher D, Bourauel C, Schumacher H. Frictional forces between bracket and arch wire. AM 1 ORTHOD DENTOFAC ORTHOP 1989;96:397-404. Angolkar PV, Kapila S, Duncanson MG, Nanda RS. Evaluation of friction between ceramic brackets and orthodontic wires of four alloys. AM 1 ORTHOD DENTOFAC ORTHOP 1990;98:499-506. Echols PM. Elastic ligatures: binding forces and anchorage taxation. AM 1 ORTHOD 1975;67:219-20. Popli K, Pratten D, Germane N, Gunsolley 1. Frictional resistance of ceramic and stainless steel orthodontic brackets. Special Issue Mar. 15-19.1 Dent Res 1989;68:275.
20. Kusy RP, Whitley 1D. Effects of sliding velocity on frictional coefficients of archwires. Special Issue Mar. 15-19. 1 Dent Res 1989;68:275. 21. Prososki RR, Bagby MD, Erickson K. Static frictional force and surface roughness of nickel-titanium arch wires. AM 1 ORTHOD DENTOFAC ORTHOP 1991;100;341-8. 22. Thurow RC. Edgewise orthodontics. 3rd ed. St Louis: CV Mosby, 1972. 23. Bednar 1R, Gruendeman GW, Sandrik 1L. A comparitive study of frictional forces between orthodontic brackets and arch wires. AM 1 ORTHOD DENTOFAC ORTHOP 1991;100:513-22. 24. West AC. Friction and boundary lubrication. Lubrication Engineering 1953;9:211-7. 25. Finch GI. The sliding surface. 34th Guthrie lecture. Proc Phys Soc 1950;B63:465-83. 26. Kusy RP, Whitley 1Q, Prewitt M1. Comparison of the frictional coefficients for selected archwire-bracket slot combinations in the dry and wet states. Angle Orthod 1991;61:293-302. 27. Kusy RP. Commentary: ceramic brackets. Angle Orthod 1991;61:291-2. Reprint requests to:
Michael Tselepis Brisbane Children's Dental Hospital 134 St. Pauls Tee, Spring Hill Queensland, Australia 4000
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Friction is the resistance to motion encountered when one solid body slides or tends to slide over another. It may be described as a force acting parallel to the direction of motion. 1 Friction is a factor in all forms of sliding mechanics, such as canine retraction into an extraction site, and in leveling and alignment where the wire must slide through the brackets and tubes present. Friction may exist in two forms: (1) Static friction, which is the resistance that prevents actual motion, and (2) dynamic (kinetic) friction, which exists during motion.2,3 Several techniques have been used to measure frictional resistance between arch wires and brackets, such as a dynamometer," a weighted basket' or bucket," a force gauge,":" and a universal testing machine."!" A review of the orthodontic literature revealed that friction between arch wires and brackets is multifactorial. In summarizing the results of the various authors,
'Orthodontist-In-Charge, Children's Dental Hospital, Brisbane, Australia. 'Senior Lecturer, Dental Faculty, University of Queensland. Australia. 'Head in the Department of Orthodontics University of Melbourne, Australia. Copyright © 1994 by the American Association of Orthodontists. 0889-5406/94/$3.00 + 0 8/1/43552
there was agreement that frictional resistance will increase (1 to 3) or vary (4,5) with the following: (1) wire size,* (2) angulation of wire to bracket,4.5,7,8 (3) ligature force,"!' (4) a change in wire shape,5.11,13.14,17 and, (5) a change in wire material.5.8.10.12.14,15-19 However, there are conflicting views on the influence of (1) bracket width,4,5.7.10.13.14.18 (2) lubrication.Y'":":" (3) surface roughness,5,6,10.12-17,20,21 and, (4) ligature design (stainless steel or elastic rings). 11.18,22 The specific objectives of this report were to investigate the influence on frictional resistance by (1) different arch wire and bracket materials, (2) bracketto-arch wire angulation, and (3) lubrication, in the form of artificial saliva. MATERIALS AND METHODS Thirty-two combinations were measured under both wet and dry conditions, as detailed in Table I. Each bracket was cemented to a 12.5 mm diameter stainless steel rod. Contaminants were removed by using an ultrasonic cleaner and 99.7% to 100% v/v ethanol. A period of 6 days elapsed before any readings were taken to allow the elastic ligature rings (Unitek AI) previously placed on the brackets to reach a stable level of force. This 'References 5, 7, 8,10,11,13,14,16-18
131
132
Tselepis, Brockhurst, and West
American Journal of Orthodontics and Dentofacial Orthopedics AURust 1994
Table I. Experimental sample Brackets I. Style: Lower anterior edgewise 2. Slot Width: 0.018 inch (0.46 mm) 3. Materials: Stainless steel (SS)' Polycarbonate (PC)b Porcelain (PO)' Sapphire (SA)' 4. Total sample size: 32 brackets (eight per type) equally subdivided into wet and dry test condition groups Wires I. Materials: Stainless steel (Hi-T) (SS)' Cobalt chromium (Blue Elgiloy) (CCl' Nickel titanium (Nitinol) (NT)' Beta titanium (TMA) (BT)' 2. Dimensions: 0.016 x 0.022 inches (0.41 x 0.56 mm) 3. Length: 7 inches (175 mm) 4. Total sample size: 32 archwires (eight per type) equally subdivided into wet and dry test condition groups "Unitek Corp., Monrovia, Calif. "American Orthodontics, Sheboygan, Wis. 'Tomy International, Tokyo, Japan. 'A-Company, Inc., San Diego, Calif. 'Rocky Mountain Orthodontics, Denver, Colo. 'Ormco Corp., Glendora, Calif.
Fig. 1. Test apparatus. Bracket and ligated arch wire in collet device located on universal testing machine platform.
was confinned in a pilot study using a control set-up consisting of a stainless steel bracket and stainless steel arch wire. The frictional force during 4 mm of arch wire travel was recorded for seven different ligature rings. The procedure was repeated using ligature rings that were prestretched over a bracket for 6 days. A collet apparatus was employed to rigidly hold the rods and, hence, fix the bracket-to-arch wire angulation to any chosen value as measured by a circular protractor attached to the collet. Each arch wire was pulled through a bracket slot by a pin vice suspended from a 50 N load cell through links of a metal chain. The varying amount of applied force (in newtons) required to move the arch wire a distance of 4 mm at a crosshead speed of 10 mm/min was recorded graphically by a universal testing machine (Shimadzu HAG-IOTA Autograph, Kyoto, Japan) (Fig. I) and mean force values were calculated. Ten trials for each bracket-to-arch wire angulation, over a total distance of 40 mm each, were performed. The arch wires and brackets were grouped and tested so that not one of the eight brackets in any group had more than one arch wire drawn through it. Similarly, no individual arch
wire was drawn through more than one bracket. This was to eliminate the influence of wear, as each bracket and arch wire were tested only once. By using the same protocol, a separate series of readings were taken for the arch wire and bracket set-up while lubricated by applying drops of artificial saliva (Salube, Orapharm Pty Ltd., Melbourne, Australia). RESULTS
Sixteen different types of devices (as a result of combining four types of brackets with four types of arch wires) were statistically analyzed. The frictional force was represented in newtons required to slide an arch wire along a bracket for a given distance. The term friction, when used in a quantitative sense, refers to the average dynamic frictional force associated with a specific movement. At each arch wire/bracket/condition/degree combination, 10 measurements were taken, resulting in 640 measurements in total. The results are presented in Table II. Analysis of variance
The statistical analysis used was a four-way analysis of variance. All variance ratios were greater than the critical values at a 95% confidence level. This meant that combinations of all four factors tested (arch wires,
AmericanJournal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West 133
Table II. Mean frictional force (newtons) and standard deviation (SD) for bracket!wire combinations (Based on 10 observations per entry) Bracket I wire angulation Dry condition
0° Bracket
SS
PO
SA
Wire
Mean
SS CC NT BT All SS CC NT BT All S5 CC NT
PC
BT All SS CC NT
All
BT All SS CC NT
BT All
I
Wet condition
if
10° (SD)
Mean
2.25 1.84 1.84 1.99 1.99
(0.22) (0.11) (0.11) (0.15) (0.23)
3.09 2.23 2.09 2.76 2.56
I
(SD)
Mean
2.69 3.06 2.30 2.85 2.72
(0.13) (0.06) (0.02) (0.05) (0.29)
(0.07) (0.03) (0.05) (0.04) (0.04)
3.89 2.86 2.59 3.51 3.21
3.07 2.36 2.95 2.85 2.81
(0.11) (0.08) (0.06) (0.06) (0.28)
3.25 2.71 2.69 3.27 2.98 2.91 2.30 2.39 2.73 2.58
I
10°
I
(SD)
(SD)
Mean
0.89 1.28 1.28 1.89 1.34
(0.04) (0.05) (0.03) (0.08) (0.36)
1.72 1.74 1.74 2.56 1.94
(0.02) (0.02) (0.03) (0.06) (0.36)
(0.07) (0.04) (0.04) (0.05) (0.52)
2.25 2.01 2.44 2.19 2.22
(0.03) (0.05) (0.05) (0.04) (0.16)
3.26 3.18 2.72 2.71 2.97
(0.06) (0.05) (0.03) (0.05) (0.26)
4.59 3.34 3.37 3.34 3.66
(0.05) (0.09) (0.07) (0.10) (0.55)
3.50 3.15 3.21 2.62 3.12
(0.14) (0.07) (0.14) (0.09) (0.35)
2.49 3.79 3.16 4.18 3.40
(0.06) (0.06) (0.05) (0.18) (0.66)
(0.18) (0.11) (0.06) (0.09) (0.30)
6.72 4.64 3.25 4.57 4.79
(0.29) (0.02) (0.06) (0.12) ( 1.26)
2.87 2.07 2.05 2.06 2.26
(0.06) (0.05) (0.05) (0.06) (0.36)
4.75 3.23 2.72 3.02 3.43
(0.05) (0.05) (0.11) (0.06) (0.80)
(0.42) (0.33) (0.45) (0.45) (0.48)
4.47 3.47 2.88 3.56 3.59
(1.49) (0.71) (0.46) (0.64) (1.07)
2.38 2.13 2.24 2.19 2.24
(0.98) (0.68) (0.71) (0.28) (0.71)
3.06 2.97 2.58 3.11 2.93
(1.13) (0.78) (0.53) (0.65) (0.82)
brackets, angulation, and lubrication) were significantly affecting friction. The analysis of variance also tested for interactions between the factors. To better appreciate the meaning of these interactions, the means of the bracket / arch wire combinations for each of the conditions and angulations were plotted in Figs. 2 and 3. As seen from the plots, different arch wires produce different amounts of friction with different brackets. If there were no interactions, then the relative frictional value of the arch wires would not change as the bracket type changes. Relative ranklngs of the bracket/arch wire combinations
From Table II the following trends were evident: (1) For the dry condition, the polycarbonate bracket! stainless steel arch wire combination produced the most friction at both angulations; (2) for the wet condition, the stainless steel bracket! stainless steel arch wire combination produced the least friction at both
angulations; (3) highest overall friction was for poly-. carbonate bracket! stainless steel arch wire (under dry conditions at 10°); and (4) the lowest overall friction was for stainless steel bracket! stainless steel arch wire (under wet conditions at 0°). These differences were highly significant. The range of mean frictional resistance was 0.89 to 6.72 N. Effect of angulation on friction
Ten degrees bracket! arch wire angulation gave highly significant greater values for friction than 0° for nearly all bracket! arch wire combinations under both wet and dry conditions. Effect of lubrication on friction
Zero degrees bracket/arch wire angulation. Lubrication in the form of artificial saliva gave highly significant lower frictional values than the dry condition for nearly all bracket! arch wire combinations. The greatest frictional reduction was 60.5% for the stainless
134
American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West
7.0 6.5 6.0
(jj
c 0
~ Ql
~
Ql
o
0 u. tii
5.5
0
.DRY
0
ADRY
10
0
5.0 4.5 4.0
C
Q
0 ~
3.5
o
3.0
'">.c
2.5
'E 0
2.0 1.5 1.0 0.5
Wire
Bracket
CC
NT
BT
SS
Stainless Steel
CC
NT
BT
Porcelain
SS
CC
NT
BT
SS
Sapphire
CC
NT
BT
SS
Polycarbonate
Bracket / Wire Combinations
Fig. 2. Average friction between arch wire/bracket combinations for dry condition at 0° and 10°.
steel bracket/stainless steel arch wire combination. The smallest reduction was 8.1% for the sapphire bracket/beta-titanium arch wire combination. Ten degrees bracket/ arch wire angulation. Lubrication gave highly significant lower values than the dry condition for nearly all bracket/ arch wire combinations. The greatest reduction in friction occurred for sapphire bracket/ stainless steel arch wire producing a 46% reduction in friction. The least reduction was for sapphire bracket/ nickel titanium arch wire producing a 6% reduction only. However, for some combinations lubrication increased the frictional resistance. The greatest frictional increase was by 20% for the sapphire bracket/beta titanium arch wire. Comparison ofindividual brackets. When there was an increase in friction, it involved only sapphire and porcelain brackets. The stainless steel brackets all showed a decrease in friction with lubrication, regardless of arch wire or angulation. The polycarbonte brackets either showed a decrease or no change.
Ligature testing-pilot study
The effect on frictional force when using different elastic ligature rings was shown to be statistically insignificant by the low coefficients of variation obtained (4.8% to 8.6%) for new rings (Table III). Ligature rings prestretched for 6 days exhibited highly significant lower frictional values by comparison to new rings, and lower coefficients of variation (Table IV). DISCUSSION Comparison of results
A characteristic of the current orthodontic literature on friction is the significant number of variables involved in the experimental techniques used. These may include: (1) arch wires and brackets from different manufacturers, with inherent differences in surface finish, hardness, and stiffness, (2) sliding velocity, (3) ligation mode, (4) the use of flats instead of brackets," and (5) whether a bracket is in a rigid mount or one that allows movement in one or more planes. 14 Hence, differences
American Journal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West
135
7 0 0.5 6.0 (/l
c 0
55
~ Q) ~ Q)
o
0 11. (ij
0
WET
0°
c:
WET
10°
50 4 5 40
C
.Q
t5
~
.~
3.5
<::
30
E
ell
c >-
2 5
0
2.0 1.5 1.0 05
:A
Wire Bracket
CC
NT
8T
SS
Stainless Steel
~
CC
NT
8T
Porcelain
SS
CC
NT
8T
SS
Sapptur e
CC
NT
8T
SS
polycarbonate
Bracket / Wire Combinations Fig. 3. Average friction between arch wire/bracket combinations for wet condition at 0° and 10°.
in experimental results for any given arch wire and bracket couple should not be surprising. Stainless steel bracket
There was no significant difference in friction betweenthe stainless steel bracket and different arch wire combinations under dry conditions at 0°. This supports Peterson et al., 8 but differs with other investigators5,6.12,14-1?,19 who found nickel-titanium arch wire to show very high frictional resistance with such a bracket. The explanation may be in fact that nickel titanium arch wires from different manufacturers show differences in recorded friction, as well as surface roughness, as shown by Prososki et al." They found no significant correlation between surface roughness and friction for the various nickel titanium wires tested. At 10° bracket! arch wire angulation the arch wires could be ranked in increasing order of friction as: nickel-titanium followed by stainless steel or beta-titanium, followed by cobalt-chromium. These results supported those of Frank and Nikolai" and Peterson et al. 8
Hence, frictional values may vary for a given bracket-arch wire combination as a tooth moves along an arch wire in a tipping and uprighting fashion. Clinically, tooth movement occurs not in a continuous manner, but rather as a cycle of short steps. To simulate this, some investigators have mounted the bracket so as to allow free movement (Kapila et al., 14 Bednar et aI,23). However, the validity of this to the actual clinical situation is yet to be proven. lubrication
The function of a lubricant is to reduce the strength and number of bridges formed between the asperities of sliding surfaces. 24 It is generally perceived that saliva acts as a lubricant. Frictional resistance was found to decrease under wet conditions (artificial saliva). This supported the findings of Baker et al. 9 It was at variance with Andreasen and Quevedo? who found no significant difference, while others.t-":" have found an increase in friction with artificial saliva. Pratten et al., 6 suggested that at high loads (undefined), saliva may be forced out from
136
American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West
Table III. Effect of new ligatures on bracket/ arch wire friction (newtons) (5 ligatures per sample) Ligature sample I 2 3 4 5 6 7
Meanforce 3.38 4.26 5.08 4.02 3.70 3.63 3.39
(0.13) (0.37) (0.18) (0.31) (0.23) (0.26) (0.21)
95% confidence interval
Coefficient variation
(3.12, 3.64) (3.51,5.02) (4.70, 5.46) (3.38, 4.66) (3.31,4.09) (3.20, 4.06) (3.04, 3.74)
4.8% 8.6% 3.6% 7.7% 6.2% 7.2% 6.2%
Table IV. Effect of relaxed ligatures on bracket/arch wire friction (newtons) (5 ligatures per sample) Ligature sample I 2 3 4 5 6 7
Meanforce 2.02 1.87 2.10 2.37 1.62 1.99 0.72
(0.13) (0.12) (0.12) (0.17) (0.11) (0.08) (0.02)
the contacts between the bracket and the arch wire, resulting in an increase in friction. Hence, saliva may act as a lubricant only at low loads as determined by ligature force. However, according to the engineering literature, it is impossible to force out completely even an oil film from between two plane surfaces, no matter how heavy the load." The different findings may be related to the formulations of different artificial saliva solutions, as well as the technique of applying the saliva to the bracket/arch wire assembly, which is often not specified in the publications. That is, it may be expected that using a bath of saliva would provide continuous lubrication as opposed to simply applying the saliva as drops. Kusy et al. 26 was the first to employ a peristaltic pump to inject fresh human saliva onto a bracket-arch wire assembly. As was the case for studies that used artificial saliva, Kusy et al. 26 reported mixed results, in that human saliva could both reduce and increase friction depending on the particular bracket-arch wire combination. Bracket/arch wire angUlation
As bracket/ arch wire angulation increased, so did frictional resistance. Similar results were found by Frank and Nikolai,", Andreasen and Quevedo," and Peterson et al. 8 An angulation of 10° allows comparison
95% confidence interval
Coefficient variation
(1.80, 2.25) (1.66, 2.09) (1.56, 2.66) (2.14,2.61) (1.10,2.13) (1.53, 2.45) (0.49, 0.96)
6.4% 8.5% 18.6% 7.2% 15.4% 4.0% 15.3%
to previous published reports. Clinically, however, bracket-arch wire angulation is determined by such variables as wire cross-section, wire material, and magnitude of applied force to the tooth. Stainless steel arch wire
At 0°, under dry conditions, and with stainless steel arch wire, brackets were ranked in order of increasing friction as stainless steel, followed by polycarbonate, sapphire, or porcelain. This supported the work of Riley et al., 11 Berger," Angolkar et aI., 17 and Popli et al. 19 These rankings may represent variation in surface roughness of the bracket slot surfaces, which has yet to be fully investigated. Porcelain bracket
In general, porcelain brackets demonstrated greater friction than stainless steel brackets. According to Kusy" this is due not to their surface roughness but rather to their chemical structure. This may explain why both sapphire and ceramic brackets showed increased friction under lubrication. Popli et al. 19 found that with nickel-titanium (Nitinol) arch wire, porcelain brackets generate more friction than stainless steel brackets. This was not supported by the present study that found no difference
American Journal of Orthodontics and Dentofacial Orthopedics Volume 106, No.2
Tselepis, Brockhurst, and West
between these brackets for nickel-titanium arch wire. Kusy and Whitley" state that bracket material does not significantly influence the coefficient of friction. What to measure, static, or kinetic friction?
The dilemma was to decide which form of friction was relevant to the clinical orthodontic situation. There is a constant alternating between static and dynamic friction as a tooth intermittently slides and binds along the arch wire during orthodontic movement. It was decided to measure frictional resistance by programming the universal testing machine to calculate the average of all the peaks recorded over 4 mm of arch wiresliding, with the exception ofthe first peak. Hence, kinetic friction was measured rather than static friction, because of the variable nature of the frictional process. Similar approaches to the problem were made by other authors9-14.17.20 who all measured kinetic friction. Othershave measured static friction only, by measuring the weight of lead shot" or water in a container" required to initiate sliding, or by using a force gauge.":" Kusy and Whitley" determined both static and kinetic coefficients of friction.
2.
3.
4.
5.
6.
7.
Clinical significance
The clinical significance of friction is its role in lessening the force actually received by a tooth from an active component such as a spring, loop, or elastic. Hence, greater applied force is needed to move a tooth with a bracket-arch wire combination demonstrating high magnitudes of friction (e.g., polycarbonate bracket) compared with one with a low frictional value (e.g., stainless steel bracket). This has clinical implications in cases demonstrating critical posterior anchorage, such as those requiring reduction of a large overjet. In such malocclusions, one would be wise to use a bracket and arch wire combination that minimizes friction so as to conserve the available anchorage. A limitation of the study was the difficulty in extrapolating the values for friction determined in vitro to an in vivo situation. This was due to the difficulty of reproducing oral conditions such as muscular and occlusal forces, and tooth movement through bone, which may affect the binding of the arch wire to the bracket. Hence, the relative rankings of the arch wires and brackets were considered to be more meaningful than actual force values recorded for a given experimental set-up. CONCLUSIONS
1. Combinations of all four factors tested (arch wire, brackets, angulation, and lubrication) were
8.
137
statistically significant in the frictional process. Interactions between the factors were also significant. In general, polycarbonate brackets showed the highest values for friction and stainless steel brackets showed the lowest values. Specifically, the combination with the highest frictional resistance was a polycarbonate bracket with a stainless steel arch wire (wet conditions at 10°). The lowest frictional resistance was for a stainless steel bracket with a stainless steel arch wire (wet conditions at 0°). Bracket-to-arch wire angulation was shown to have a significant effect under both wet and dry conditions. In general, frictional resistance increased with angulation, but exceptions did exist. Lubrication significantly reduced the frictional resistance (up to 60.5%) for both 0° and 10° bracket-to-arch wire angulation. Exceptions were found. The difference between the least (0.9 N) and the greatest frictional force (6.8 N) recorded was significant. Elastic ligature rings, especially when prestretched or allowed to relax, were not a significant source of bias toward the frictional forces recorded.
REFERENCES 1. Halling J. Principles of tribology. New York: Macmillan, 1975. 2. Bowden FP, Tabor D. Friction. An introduction to tribology. Garden City, New York: Anchor Press/Doubleday, 1973. 3. Rabinowicz E. Friction and wear of materials. New York: J Wiley, 1965. 4. Nicolls J. Frictional forces in fixed orthodontic appliance. Dent Practit 1968;18:362-6. 5. Frank CA, Nikolai RJ. A comparitive study of frictional resistances between orthodontic bracket and archwire. AMJ ORTHOD 1980;78:593-609. 6. Pratten DH, Popli K, Germane N, Gunsolley JC. Frictional resistance of ceramic and stainless steel orthodontic brackets. AM J ORTHOD DENTOFAC ORTHOP 1990;98:398-403. 7. Andreasen GF, Quevedo FR. Evaluation of friction forces in the 0.022*0.028 edgewise bracket in-vitro. J Biomechanics 1970;3:151-60. 8. Peterson L, Spencer R, Andreasen G. A comparison of friction resistance for nitinol and stainless steel wire in edgewise brackets. Quintessence Int 1982;5:1-9. 9. Baker KL, Nieberg LG, Weimer LD, Hanna M. Frictional changes in force values caused by saliva substitution. AM J ORTHOD DENTOFAC ORTHOP 1987;91:316-20. 10. Garner LD, Allai WW, Moore BK. A comparison of frictional forces during simulated canine retraction of a continuous edge-
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11.
12.
13.
14.
15.
16.
17.
18. 19.
American Journal of Orthodontics and Dentofacial Orthopedics August 1994
Tselepis, Brockhurst, and West wise arch wire. AM 1 ORTHOD DENTOFAC ORTHOP 1986;90:199203. Riley 1L, Garrett SG, Moon PC. Frictional forces of ligated metal and edgewise brackets. 1 Dent Res 1979;58:A21, IADR Abstract, 98. Stannard1G, Gau 1M, Hanna MA. Comparitive friction of orthodontic wires under dry and wet conditions. AM 1 ORTHOD 1986;89:485-91. Berger 1L, The influence of the SPEED bracket's self-ligating design on force levels in tooth movement: a comparitive in vitro study. AM 1 ORTHOD DENTOFAC ORTHOP 1990;97:219-28. Kapila S, Angolkar PV, Duncanson MG, Nanda RS. Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four different alloys. AM 1 ORTHOD DENToFAc ORTHOP 1990;98:117-26. Kusy RP, Whitley 1Q. Coefficients of friction for archwires in stainless steel and polycrystalline alumina bracket slots. I. The dry state. AM 1 ORTHOD DENTOFAC ORTHOP 1990;98:300-12. Drescher D, Bourauel C, Schumacher H. Frictional forces between bracket and arch wire. AM 1 ORTHOD DENTOFAC ORTHOP 1989;96:397-404. Angolkar PV, Kapila S, Duncanson MG, Nanda RS. Evaluation of friction between ceramic brackets and orthodontic wires of four alloys. AM 1 ORTHOD DENTOFAC ORTHOP 1990;98:499-506. Echols PM. Elastic ligatures: binding forces and anchorage taxation. AM 1 ORTHOD 1975;67:219-20. Popli K, Pratten D, Germane N, Gunsolley 1. Frictional resistance of ceramic and stainless steel orthodontic brackets. Special Issue Mar. 15-19.1 Dent Res 1989;68:275.
20. Kusy RP, Whitley 1D. Effects of sliding velocity on frictional coefficients of archwires. Special Issue Mar. 15-19. 1 Dent Res 1989;68:275. 21. Prososki RR, Bagby MD, Erickson K. Static frictional force and surface roughness of nickel-titanium arch wires. AM 1 ORTHOD DENTOFAC ORTHOP 1991;100;341-8. 22. Thurow RC. Edgewise orthodontics. 3rd ed. St Louis: CV Mosby, 1972. 23. Bednar 1R, Gruendeman GW, Sandrik 1L. A comparitive study of frictional forces between orthodontic brackets and arch wires. AM 1 ORTHOD DENTOFAC ORTHOP 1991;100:513-22. 24. West AC. Friction and boundary lubrication. Lubrication Engineering 1953;9:211-7. 25. Finch GI. The sliding surface. 34th Guthrie lecture. Proc Phys Soc 1950;B63:465-83. 26. Kusy RP, Whitley 1Q, Prewitt M1. Comparison of the frictional coefficients for selected archwire-bracket slot combinations in the dry and wet states. Angle Orthod 1991;61:293-302. 27. Kusy RP. Commentary: ceramic brackets. Angle Orthod 1991;61:291-2. Reprint requests to:
Michael Tselepis Brisbane Children's Dental Hospital 134 St. Pauls Tee, Spring Hill Queensland, Australia 4000
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