Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four alloys Sunil Kapila, BDS, MS," Padmaraj V. Angolkar, BDS, MDS, b Manville G. Duncanson, Jr., DDS, PhD, ° and Ram S. Nanda, DDS, MS, PhD d San Francisco, Calif., and Oklahoma City, Okla. This investigation was designed to determine the effects of wire size and alloy on frictional force generated between bracket and wire during in vitro translatory displacement of bracket relative to wire. Stainless steel (SS), cobalt-chromium (Co-C0, nickel-titanium (NiTi), and 13-titanium (13-Ti) wires of several sizes were tested in narrow single (0.050-inch), medium twin (0.130-inch) and wide twin (0.180-inch) stainless steel brackets in both 0.018- and O.022-inch slots. The wires were ligated into the brackets with elastomeric ligatures. Bracket movement along the wire was implemented by means of a mechanical testing instrument, and frictional forces were measured by a compression cell and recorded on an X-Y recorder. 13-Ti and NiTi wires generated greater amounts of frictional forces than SS or Co-Cr wires did for most wire sizes. Increase in wire size generally resulted in increased bracket-wire friction. The wire size-alloy interaction on the magnitude of bracket-wire friction was statistically significant (p < 0.005). With most wire sizes and alloys, narrow single brackets were associated with lower amounts of friction than wider brackets were. The levels of frictional forces in 0.018-inch brackets ranged from 49 gm with 0.016-inch SS wires in narrow single brackets to 336 gm with 0.017 x 0.025-inch 13-Ti wires in wide twin brackets. Similarly for 0.022-inch brackets, frictional forces ranged from 40 gm with 0.018-inch SS wires in narrow single brackets to 222 gm with 0.019 x 0.025-inch NiTi wires in wide twin brackets. (AM J On-moo DENTOFAC ORTHOP 1990;98:117-26.)

C a n i n e retraction and space consolidation during orthodontic treatment with sliding mechanics involve a relative displacement of wire through bracket slots. During such mechanotherapy, biologic tissue response and tooth movement occur only when the applied forces adequately overcome the friction at the bracket-wire interface. High levels of bracket-wire friction may result in binding of the bracket accompanied by little or no tooth movement. Furthermore, binding of an anterior tooth under retraction may also lead to loss of anchorage. The most desirable and ideal situation, then, is one in which little or no friction exists between bracket and wire. Friction is a function of the relative roughness of two surfaces in contact, and it arises when there is relative motion or potential for it between the two surFrom the University of Oklahoma, College of Dentistry. 'Former Resident and Clinical Instructor, Department of Orthodontics, University of Oklahoma, College of Dentistry; presently Adjunct Assistant Professor and Doctoral Student at University of California, San Francisco. ~Visiting Assistant Professor, Department of Orthodontics, University of Oklahoma. CProfessorand Chairman, Department of Dental Materials, University of Oklahoma, College of Dentistry. dProfessor and Chairman, Department of Orthodontics and Division of Developmental Dentistry, University of Oklahoma, College of Dentistry. 811112478

faces./"2 When two surfaces in contact slide or tend to slide against each other, two components of total force arise. One of these is the frictional component, which is parallel in direction to the intended or actual sliding motion and opposes the motion (Fig. 1). The other component is perpendicular to or at right angles to one or both contacting surfaces and also to the frictional force component. The magnitude of the frictional force is proportional to the amount of normal force that pushes the two surfaces together. ,.3-5During orthodontic tooth movement such as canine retraction, the relationship of the bracket to the wire may vary considerably at different stages of treatment, as depicted in Fig. 1. Therefore, the magnitude and direction of the associated frictional and normal components of contact forces will also vary with time. Several variables have been found to affect the levels of friction between bracket and wire. These variables may be either mechanical or biologic. Mechanical variables include bracket material, 5.6 slot size, 2 bracket width 2"7and angulation, 2.8 wire shape, 2"6"9wire size, 2"6"8"9 and wire material, 2z,9"" as well as ligature material 2"6 and force of ligation. 2 Saliva, plaque, acquired pellicle, and corrosion have been implicated as some of the biologic factors that affect bracket-wire friction. 4'6"s 117

118

Am. J. Orthod. Dentofac. Orthop. August 1990

Kapila et al.

N

"~

~\\\\\\\\"~\\\\\\\\\',3

L go B

f

L go N C

D

N F

G

•® t: N:

Direction of bracket movement Frictional force component Normal force component

Fig. 1. Frictional and normal force components exerted by the arch wires on lower left canine bracket in three planes of space. For simplicity, ligatures and their associated force components are not illustrated. A to D, Facial view of bracket demonstrating the possible bracket-wire relationships and associated frictional and normal components of force during bodily tooth movement. E and F, Mesial aspect of bracket. (~) represents bracket movement perpendicular and into the page, and E) depicts frictional force component perpendicular to and out of the page. G, Occlusal view of bracket and wire.

The wide array of brackets, wires, and ligatures available now provides a multitude of combinations for use during various stages of orthodontic treatment. In the past most orthodontic tooth movement was done with stainless steel wires. Today, however, many clinicians prefer to use wires of alloys such as cobaltchromium (Co-Cr), nickel-titanium (NiTi), or 13titanium ([3-Ti) during different phases of treatment. Therefore, to deliver optimal forces for efficient and predictable tooth movement, it is necessary to have both an as sessment and a knowledge of the forces required to overcome friction when different wire sizes and alloys are used. This investigation was designed to determine the effects of wire size and alloy on the frictional forces generated between bracket and wire during in vitro translatory displacement of bracket relative to wire. MATERIALS AND METHODS

Stainless steel (SS) (Chrom Alloy, Ormco Corp., Glendora, Calif.), Co-Cr (blue Elgiloy, Rocky Mountain Orthodontics, Denver, Colo.), NiTi (Nitinol, Unitek Corp., Monrovia, Calif.), and 13-Ti (TMA, Ormco Corp.) wires of various cross-sectional sizes were tested in narrow single (NS), medium twin (MT), and wide twin (WT) edgewise canine brackets (Ormco Corp.). These brackets were 0.050, 0.130, and 0.180 inch wide, respectively. Only zero-torque/zero-angulation stainless steel brackets in both the 0.018- and 0.022inch slot sizes were used. The wire sizes tested in both the 0.018-inch brackets and the 0.022-inch brack-

ets included 0.016 inch, 0.016 x 0.016 inch, 0.016 x 0.022 inch, 0.017 × 0.017 inch, and 0.017 x 0.025 inch. In addition, 0.018-inch, 0.018 × 0.025-inch, and 0.019 × 0.025-inch wires were evaluated in 0.022-inch brackets. Some wire size-alloy combinations were not available and were excluded from the study. These included 0.016 x 0.016-inch SS and i3Ti wires, 0.017 × 0.017-inch Co-Cr and NiTi wires, and 0.018 x 0.025-inch 13-Ti wires. Bracket movement was implemented by an Instron universal testing machine (Instron Corp., Canton, Mass.). A force loading arm with provision for bracket attachment was fixed to the crosshead of the machine (Fig. 2, A). A ball beating, into which a plastic pedestal with attached bracket could be inserted, was mounted on the force-loading arm (Fig. 2, B). A frame for the wire was constructed to hold the wire under tension. The frame consisted of a lower immobile segment to hold the wire and a movable ann for introducing a measured level of tension into the wire. A calibrated spring (Accu Weigh, Metro Equipment, Inc., Sunnyvale, CaliL), was used to ensure that all wires were subjected to equal amounts of tension. The wire frame was placed on a compression cell (Instron Corp.) with a maximum range of 2000 gm. The compression cell, in turn, was connected to an X-Y recorder (Model 7005B, Hewlett Packard, Anaheim, Calif.). The recorder plotted in grams the magnitude of frictional forces generated as the bracket moved down along the wire.

Volume 98 Number 2

Evaluation of friction between stainless steel brackets and wires

forceloadingarm

[~"~

A

I

1

i ]

movablearmof wire frame

immobdepartol. wire trame

crosshead taOr~eloadlng [

__

H ' ~ " ,"--

ball beanngwith pedestalandbracket

119

plasbcpedestal w~thbracket ball beanng wire specimen

• c°mpressi°n cell

-

,

~

I-q,:

I

It 1 ~

i_Li_:_..?_,.I ])i

cahbratedspring ,,

I,_

I

[

frame to hold

ballbeanng

~7-I-~'-"wiresPec~men

II

~

'l X-Y recorder I:~

Fig. 2. A, Testing machine, bracket-wire assembly and force measuring equipment. B, Greater detail of the area enclosed by the dashed line in A.

Technique The brackets were bonded with composite to the plastic bracket pedestals. Straight 7 cm lengths of wire were then ligated into individual brackets by means of elastomeric ligatures (Power "O" modules, Ormco Corp.). Each plastic pedestal with its bracket and wire was inserted into the ball bearing mounted on the forceloading arm of the testing machine. The plastic pedestal was tightened into the ball bearing with a bolt. This arrangement allowed for a range of second-order relationships of bracket to wire with freedom for the bracket to tip to the limits permitted by the width and the slot size of the bracket relative to the occlusogingival dimensions of the wire. This experimental design also prevented excessive angulation of bracket relative to wire, which would simulate tipping movement of a tooth. The maximum bracket tip permitted by each bracket-wire combination used in this investigation was calculated and is presented in Table I. Since numerous wire sizes and alloys were tested for friction, a wide range of bending stiffnesses was present as an additional variable. To minimize the effect of this variable, the lower end of the wire was bolted into the wire frame and the upper end of the wire was hooked onto the calibrated spring. The movable arm of the wire frame was extended until the calibrated spring read 300 gm. This procedure ensured that all wires were

Table I. Second-order clearance permitted by

each bracket-wire combination derived mathematically with the use of occlusogingival wire dimension, bracket width, and bracket slot dimensions for calculations Bracket slot size Wire dimension (inch) 0.016

0.017

0.018

0.019

NS,

Bracket width

0.018 inch (degrees)

0.022 inch (degrees)

NS MT WT NS MT WT NS MT W NS MT WT

1.15 0.44 0.32 0.57 0.22 0.16 0 0 0 ----

3.43 1.32 0.95 2.86 1.10 0.80

2.29 0.88 0.64 1.72 0.66 0.48

Narrowsingle;MT, mediumtwin; WT, widetwin.

under equal amounts of tension and were relatively straight. The upper part of the wire was then bolted to the wire frame, and the calibrated spring was disconnected. The X-Y recorder was set to give a zero reading

120

Am. J. Orthod. Dentofac. Orthop. August 1990

Kapila et al.

t50 t50

C: Nickel - tflamum

A: Sta,nless steel 125

125 o

;'5

g ~ rs

}°

25

,

25

3O

~

~

,

T,rne lsec) i

romlum

D: fl - t=tanium 175

T,me (sec)

150

150

125

125

® u

_~ 75

~

75

-_-:,5o ft.

ft.

u

511

25

25

T=rne Isecl

TLme [sec)

Fig, 3. Representative graphs of frictional forces generated over time during tests with stainless steel (A), cobalt-chromium (B), nickel-titanium (C), and 13-titaniurn (D)wires.

at this point to compensate for the weight of the wire frame and the wire. This ensured that only the force that was transmitted by the loading arm to the bracket and through the bracket to the wire was recorded as the frictional force. The crosshead with its attached loading arm and bracket was activated, which caused the bracket to move down the wire at a rate of 0.20 inch per minute (5.1 mm/min) t'or a total of 2 minutes. The frictional forces generated by the bracket moving relative to the wire were registered by the compression cell and recorded on the X-Y recorder (Fig. 3). The mean of ten equally spaced readings of frictional forces over a distance representing 7 mm of movement of the bracket along the wire was determined from the X-Y plot. The assessment of mean frictional forces over this distance provided averages for bracket-wire friction over a distance equal to that of retraction of a canine into a premolar space/~nd incorporated values for various secondorder bracket-wire relationships. After each run, a n other bracket table with a new bracket-wire specimen was mounted on the apparatus, and the process was repeated. Ten specimens for each bracket-wire subsample were tested. In all, a total of 1290 wire specimens were subjected to these test procedures. Forty 0.018-inch brackets and sixty 0.022-inch brackets in each of the three bracket widths were circulated at random through the series of trials.

Data analysis

Means for the frictional forces generated by each bracket-wire subsample were determined. One-way analyses of variance and Duncan's multiple range test were used to determine the individual effects of wire alloy, wire size, and bracket width on bracket-wire friction. The Duncan's test detected statistical differences at the 95% confidence level. The interactive effect of wire size and alloy type on the magnitude of bracketwire friction was assessed by two-way analysis of variance. RESULTS

In all, 120 specimens each of SS, Co-Cr, NITi, and 13-Ti wires in four wire sizes were tested for friction in NS, MT, and WT 0.018-inch brackets. Similarly, 210 wire specimens each of SS, Co-Cr, and N i T i - - i n seven wire sizes--and 180 specimens of 13-Ti--in six wire sizes--were evaluated for frictional forces in NS, MT, and WT 0.022-inch brackets. The means of frictional forces produced by each bracket-wire combination and the statistical findings are reported in Tables II to V and summarized below. Effect of bracket width on bracket-wire friction

The effect of bracket width on the magnitude of frictional forces generated was statistically significant at the 0.001 level for both the 0.018-inch and the 0.022-

Volume98 Number 2

Evaluation of friction benveen stainless steel brackets and wires

121

Table I!. Mean frictional forces and statistical evaluation of the effect of wire alloy on bracket-wire friction for each wire size in 0.018-inch NS, MT, and WT brackets Narrow single Wire size (inch) 0.016

0.016 x 0.016 0.016 × 0.022

0.017 × 0.017 0.017 x 0.025

Alloy SS 13-Ti Co-Cr NiTi Co-Cr NiTi Co-Cr SS NiTi 13-Ti 13-Ti SS Co-Cr SS NiTi 13-Ti

Medium twin

Force I Duncan's (gm) ANOVA 49 50 53 I 11 64 109 71 139 143 170 93 96 97 103 107 172

A*** A A B A** B A*** B B B A (ns) A A*** A A B

Alloy Co-Cr SS NiTi 13-Ti Co-Cr NiTi Co-Cr SS NiTi 13-Ti SS 13-Ti Co-Cr SS NiTi 13-Ti

I Force (gm) 66 89 160 177 99 109 141 163 192 235 163 179 165 175 225 274

Wide twin Duncan's ANOVA

Alloy

(gin)

Duncan's ANOVA

A*** A B B A (ns) A A*** A B B C A (ns) A A*** A B C

SS Co-Cr NiTi 13-Ti Co-Cr NiTi NiTi Co-Cr SS 13-Ti SS 13-Ti Co-Cr NiTi SS 13-Ti

107 144 182 202 154 217 192 202 228 299 154 238 232 247 251 336

A*** B C C A** B A*** A A B A*** B A*** A A B

ns,

Not significant. **p < 0.01; ***p < 0.001. Results of Duncan's test are represented by letters A, B, and C. Means of frictional forces accompanied by dissimilar letters in each cell indicate significant differences at less than a 0.05 level of significance. The asterisks indicate the level of significance for ANOVA.

inch brackets. In the 0.018-inch slot size, MT brackets were associated with about one and one half times as much friction as NS brackets, and WT brackets produced almost twice as much friction as NS brackets. Medium twin and WT 0.022-inch brackets demonstrated no statistical difference in levels of friction. However, these brackets were associated with more friction than NS 0.022-inch brackets were. The larger frictional forces with wider brackets may be attributed to the higher forces of ligation that result from the greater stretching of elastic ligatures on wider brackets. Effect of wire alloy on bracket-wire friction

Statistical analyses on the effects of wire alloy the magnitude of bracket-wire friction for the three bracket widths in both 0.018- and 0.022-inch slot sizes are outlined in Tables II and III and are described below. Narrow single O.O18-inch brackets. Nickel-titanium and 13-Ti wires generated larger frictional forces than either Co-Cr or SS wires. Exceptions to this rule included wires that measured 0.016 x 0.022-inch, for which SS wires produced levels of friction similar to those produced by NiTi and [3-Ti wires and 0.016-inch wires for which 13-Ti wires generated frictional forces similar in magnitude to those produced by SS and Co-Cr wires.

For 0.017 × 0.017-inch wires, 13-Ti produce d levels of friction similar to those produced by SS wires. Medium twin O.018-inch brackets. Medium twin 0.018-inch brackets demonstrated a more definite relationship between alloy and magnitude of frictional forces than NS 0.018-inch brackets did. 13-titanium wires produced the highest levels of friction, followed by NiTi wires, of all wire sizes. The frictional forces produced by Co-Cr and SS wires were statistically similar and less than those generated by NiTi and IBrTi wires. Exceptions to this rule were 0.016 × 0.016-inch Co-Cr and NiTi wires as well as 0.017 X 0.017-inch SS and [3-Ti wires; each pair demonstrated similar magnitudes of friction. Wide twin O.018-inch brackets. [3-Ti wires demonstrated higher levels of friction than the other alloys did in almost all wire sizes. For wires measuring 0.016inch and 0.016 × 0.016-inch, NiTi was associated with higher friction than SS or Co-Crwires were. Stainless steel, Co-Cr, and NiTi wires produced similar frictional forces in sizes 0.016 × 0.022-inch and 0.017 × 0.025-inch. Round 0.016-inch SS wires generated less friction than Co-Cr wires of the same size did. Narrow single O.022-blch brackets. All four alloys produced statistically similar magnitudes of frictional

122

Am. J. Orthod. Dentofac. Orthop. August 7990

Kapila et al.

Table III. Mean frictional forces and statistical evaluation of the effect of wire alloy on bracket-wire friction for each wire size in 0.022-inch NS, MT, and W T brackets

Narrow shlgle Wire size finch) 0.016

0.016 x 0.016 0.016 × 0.022

0.017 × 0.017 0.017 × 0.025

0.018

0.018 × 0.025

0.019 × 0.025

Alloy SS 13-Ti NiTi Co-Cr Co-Cr NiTi SS [3-Ti Co-Cr NiTi "[3-Ti SS NiTi [3-Ti Co-Cr SS SS Co-Cr 13-Ti NiTi SS Co-Cr NiTi SS Co-Cr 13-Ti NiTi

Medium nvhl

Force (gm)

Duncan's ANOVA

75 81 83 97 79 83 120 127 130

A (ns) A A A A (ns) A A (ns) A A

135

A

83 99 114 131 136 150 40 68 83 109 149 153 170

A (ns) A A (ns) A A A A*** B B C A (ns) A A

Wide twin

Alloy

Force (gin) 94 100 118 127 101 120 130 147 153 166 99 136 115 176 178 215 85 101 113 162 139 I50 194 155 156 192

CB C A* B A** B BC C A** B A*** B B C A*** AB B C A** A B A*** A B

193

B

! 28

A*

13! 133

A A

Co-Cr SS 13-Ti NiTi NiTi Co-Cr SS Co-Cr NiTi ]3-Ti SS 13-Ti SS Co-Cr NiTi [3-Ti SS Co-Cr [3-Ti NiTi NiTi SS Co-Cr 13-Ti NiTi Co-Cr

179

B

SS

Duncan's ANOVA A** A B

Alloy Co-Cr SS 13-Ti NiTi Co-Cr NiTi Co-Cr SS 13-Ti NiTi SS 13-Ti Co-Cr NiTi SS 13-Ti Co-Cr SS [3-Ti NiTi Co-Cr SS NiTi Co-Cr SS ]3-Ti NiTi

I Force (gin) 82 95 IlO 149 107 150 102 150 178 193 104 184 147 151 166 212 80 110 136 199 143 158 174 122 191 199 222

Duacan's ANOVA A*** A A B

A* B m**:g B

BC C A*** B

A** A A B

A*** B

C D A (ns) A A A*** B B B

Interpretationsof the statistical tests may be found in the footnote tO Table It. ns, Not significant *p < 0.05; **p < 0.0l; ***p < 0.00l.

forces for wires measuring 0.016-inch, 0.016 × 0.016-inch, 0.016 × 0.022-inch, 0.017 × 0.017inch, 0.017 × 0.025-inch, and 0.018 × 0.025-inch. Within the 0.018-inch round wires, SS demonstrated levels of friction lower than those of Co-Cr or IB-Ti wires, which in turn were less than those of NiTi wires. Stainless steel, Co-Cr, or 13-Ti wires that measured 0.019 × 0.025-inch produced statistically similar levels of ifiction that were lower than those produced by NiTi wires of the same size. Medium twh~ O.022-inch bs:ackets. Medium twin 0.022-inch brackets generally produced higher frictional forces with [3-Ti and NiTi wires than with CoCr and SS wires in most wire sizes. This pattern was reversed, however, for 0.019 × 0.025-inch wires in which [3-Ti and NiTi wires demonstrated lower frictional forces than Co-Cr and SS wires. Nickel-titanium

wires also generated lower friction than Co-Cr or SS alloys for wires measuring 0.016 × 0 . 0 1 6 - i n c h and 0.018 × 0.025-inch. Wide twh~ O.022-hzch brackets. NiTi wires 0.016inch in diameter produce d more friction than Co-Cr, SS, or 13-Ti wires of the same size. Similarly, in 0.017 × 0.025-inch wires, [3-Ti geneI"ated greater levels Of friction than the other three alloys. Cobaltchromium, SS, and NiTi wires that measured 0.018 × 0.025-inch demonstrated 'statistically similar levels of friction. Stainless steel, [3-Ti, and NiTi wires that measured 0.019 × 0.025-inch produced similar magnitudes of frictional forces that were greater than those associated with Co-Cr wires of the same size. In all other wire sizes, Co-Cr wires produced the lowest levels of friction, followed by SS,' [3-Ti, and NiTi wires in order of increasing frictional forces.

Volume98 Number2

Evaluation of friction between stainless steel brackets and wires

123

Table IV. Mean frictional forces and statistical evaluation of the effect of wire size on bracket-wire friction for each wire alloy on 0.018-inch NS, MT, and WT brackets

Medium twin

Narrow single Wire alloy SS

Co-Cr

NiTi

13-Ti

Wire size (inch) 0.016 0.017 0.017 0.016 0.016 0.016 0.016 0.017 0.017 0.016 0.016 0.016 0.016 0.017 0.016 0.017

× 0.017 × 0.025 × 0.022 x x x x x

0.016 0.022 0.025 0.025 0.016

x 0.022 x 0.017 x 0.022 x 0.025

I Force I Duncan's ANOVA (gin) 49 96 103 139 53 64 71 97 107 109 lll 143 50 93 170 172

A*** B B C A* A A B B A (ns) A A A A*** B C C

Wire size (inch) 0.016 0.016 0.017 0.017 0.016 0.016 0.016 0.017 0.016 0.016 0.016 0.017 0.016 0.017 0.016 0.017

× 0.022 X 0.017 × 0.025 x × × X

0.016 0.022 0.025 0.016

x 0.022 × 0.025 X 0.017 × 0.022 x 0.025

Wide twin

I F°rce ] Duncan's ANOVA (gm) 89 163 163 175 66 99 141 165 109 160 192 225 177 179 235 274

A*** B B B A*** B C D A*** B C D A*** A B B

Wire size (inch) 0.016 0.017 0.016 0.017 0.016 0.016 0.016 0.017 0.016 0.016 0.016 0.017 0.016 0.017 0.016 0.017

× 0.017 x 0.022 × 0.025 x 0.016 x 0.022 x 0.025 x 0.022 x 0.016 x 0.025 × 0.017 × 0.022 x 0.025

Duncan's IF°rce (gm) I ANOVA 107 154 228 251 144 154 202 232 182 192 217 247 202 238 299 336

A,g* B C C A** A B B A* AB CB C

A*** A B B

Interpretations of the statistical tests may be found in the footnote to Table II. ns, Not significant *p < 0.05; **p < 0.001; ***p < 0.0001.

Effect of wire s i z e o n b r a c k e t - w i r e friction

The effects of wire size on bracket-wire friction were considered separately for each alloy type. Findings of the statistical analyses, including mean frictional forces, are reported in Tables IV and V and are summarized in the following paragraphs. Narrow single O.O18-inch brackets. Stainless steel, Co-Cr, and [3-Ti wires demonstrated increased bracketwire friction with increase in wire size. In contrast, an increase in size of NiTi wires did not have a significant effect on the amount of friction between bracket and wire. Medium twin O.O18-inch brackets. A well-defined increase in friction with increase in wire size was evident with Co-Cr and NiTi wires. In contrast, all rectangular SS wires had statistically similar levels of friction which were greater than those with 0.016-inch round SS wires. [3-Ti wires measuring 0.016-inch and 0.017 × 0.017-inch produced similar amounts of friction that were less than those generated by 0.016 × 0.022-inch and 0.017 × 0.025-inch wires. Wide twin O.O18-inch brackets. The effect of increase in wire size on frictional forces was not as well defined in WT brackets as in NS and NIT brackets. Statistically similar levels of friction were observed be-

tween 0.016 x 0.022-inch and 0.017 × 0.025-inch wires made of SS, Co-Cr, or [3-Ti. Within each of these alloy subsamples the frictional forces produced by 0.016 × 0.022-inch and 0.017 × 0.025inch wires were, however, statistically greater than those generated by 0.016-inch, 0.016 × 0.016-inch, and 0.017 × 0.017-inch wires. NiTi wires, 0.016-inch round and 0.016 × 0.022-inch, produced similar levels of friction but less friction than 0.016 × 0.016inch and 0.017 × 0.025-inch NiTi wires. Narrow single O.022-inch brackets. A trend toward increasing bracket-wire friction with increasing wire size was evident in NS 0.022-inch brackets. An exception to this was the lower levels of friction associated with 0.018-inch SS wires in comparison with 0.016inch SS wires. Statistically similar magnitudes of friction were observed among 0.016-inch, 0.016 × 0.016-inch, and 0.018-inch wires in both Co-Cr and NiTi alloys. Nonsignificant differences in frictional forces were also demonstrated by [3-Ti wires which measured 0.016-inch, 0.017 × 0.017-inch, and 0.018inch. Medium twin O.022-bwh brackets. Increases in frictional forces with increasing wire size were noted in both SS and Co-Cr wires. Wires measuring 0.016 inch, 0.018 inch, and 0.017 × 0.017 inch, made of either

124

Am. J. Orthod.Dentofac.Orthop. August 1990

Kapila et al.

Table V. Mean frictional forces and statistical evaluation of the effect of wire size on bracket-wire friction

for each wire alloy in 0.022-inch NS, MT, and WT brackets

Narrow single Wire alloy SS

Co-Cr

NiTi

13-Ti

Wiresize IForcelDuncan's (inch) (gin) ANOVA 0.018 0.016 0.017 0.016 0.019 0.018 0.017 0.018 0.016 0.016 0.016 0.019 0.017 0.018 0.016 0.016 0.018 0.017 0.016 0.018 0.019 0.016 0.017 0.018 0.016 0.017 0.019

x × × × x

0.017 0.022 0.025 0.025 0.025

x 0.016 x x x x x

× x x x

0.022 0.025 0.025 0.025 0.016

0.025 0.022 0.025 0.025

× 0.017 x 0.022 × 0.025 x 0.025

40 75 99 120 128 149 150 68 79 97 130 131 136 153 83 83 109 114 135 170 179 81 83 83 127 131 133

Wide twin

Medium twin

A*** B BC D C D E E E A*** A A B C B C B C C A*** A A B B B C C A** A A B B B

Wiresize (inch) 0.018 0.017 0.016 0.017 0.016 0.018 0.019 0.016 0.018 0.016 0.016 0.017 0.019 0.018 0.016 0.016 0.018 0.016 0.019 0.018 0.017 0.018 0.016 0.017 0.019 0.016 0.017

x 0.017 x x × x

0.025 0.022 0.025 0.025

× x x x x x

0.016 0.022 0.025 0.025 0.025 0.016

x 0.025 × 0.022 × 0.025 x 0.025

× x × ×

0.017 0.025 0.022 0.025

ForcelDuncan's (gm) ANOVA 85 99 I00 115 130 150 193 94 101 120 147 176 192 194 101 127 139 153 156 162 178 113 ll8 136 155 166 215

A*** A B A B C B C D D E A*** A B B C D D D A*** B BC D C D C D E E A*** A A B C B C D

Wiresize IForcel Duncan's (inch) (gm) ANOVA 0.016 0.017 0.018 0.016 0.018 0.017 0.019 0.018 0.016 0.016 0.016 0.019 0.018 0.017 0.016 0.016 0.017 0.018 0.016 0.018 0.019 0.016 0.018 0.016 0.017 0.019 0.017

x 0.017 x x x x

0.022 0.025 0.025 0.025

× x x x x

0.016 0.025 0.025 0.025

× × x ×

0.016 0.025 0.025 0.022

0.022

x 0.025

× x × ×

0.022 0.017 0.025 0.025

95 104 110 150 158 166 191 80 82 102 107 122 143 147 149 150 151 174 193 199 222 110 136 178 184 199 212

A*** A A B C B C C C A*** A A B A B C B C C A*** A A A B C B C B C A*** A B B BC C

Interpretations of the statistical tests may be found in the footnote to Table II. **p < 0.001; ***p < 0.0001.

SS or p-Ti, produced statistically similar levels of bracket-wire friction. NiTi wires measuring, 0.016inch square, were associated with less friction than all other sizes of NiTi wires. Similarly, for both NiTi and 13-Ti alloys, 0.019 x 0.025-inch wires generated lower frictional forces than 0.017 x 0.025-inch wires. Wide twin O.022-inch brackets. Although an increase in wire size was generally associated with an increase in bracket-wire friction, the differences were not statistically significant for several wire sizes in each alloy category. Thus statistically similar values of frictional forces were produced between SS wires that measured 0.016-inch, 0.017 x 0.017-inch, and 0.018inch; Co-Cr wires that measured 0.018-inch, 0.016inch, 0.016 x 0.022-inch, and 0.016 x 0.016-inch; NiTi wires that measured 0.016-inch, 0.016 × 0.016inch, 0.017 x 0.025-inch, and 0.018 x 0.025-inch;

and p-Ti wires that measured 0.016-inch and 0.018inch. Interaction between wire size and alloy

The interaction between wire size and alloy on bracket-wire friction was significant within both bracket slots and in all bracket width subsamples at less than a 0.005 level of significance. This implies that selection of an appropriate wire during phases of treatment that involve tooth movement along a wire would necessitate consideration of both the wire size and the alloy. DISCUSSION

Evaluation of individual graphs obtained for all bracket-wire specimens revealed an initially rapid increase in the recorded force as the applied force at-

Volum~ 98 Number 2

Evaluation of friction between stainless steel brackets and wires 125

tempted to overcome the static friction before movement of the bracket commenced (Fig. 3). Once bracket movement had been initiated, subsequent displacement of the bracket relative to the wire required smaller forces. However, during the entire length of each run, undulations in the magnitude of forces required to overcome friction were noted. These force variations generally occurred within a narrow range of values and probably resulted from the second-order movement of the bracket relative to the wire permitted by the experimental design. Similarly, in vivo factors such as occlusion, mastication, wire resilience, and tooth movement may alter the second-order bracket-wire relationship as the bracket moves in relation to the wire. 2 This freedom of second-order orientation of the brackets to the wire alters the frictional and normal components of force with time (Fig. 1, A-D) so that the forces required to cause movement of the bracket will vary at different bracket-wire angulations. The individual bracket-wire friction graphs also demonstrated greater magnitude and more frequent variation in frictional forces per unit distance of bracket travel with NiTi and 13-Ti wires than with SS or Co-Cr wires (Fig. 3). This, together with the higher mean frictional forces observed with NiTi and 13-Ti wires, may indicate surface roughness of these alloys that is greater than that of SS or Co-Cr wires with relation to stainless steel brackets. This concept is supported by the electron microscopic and laser spectroscopic findings on the surface texture of wires by Gamer et al. II and Kusy et al., 12 respectively. Kusy et al. 12 noted that SS wires had the smoothest surface followedby CoCr, 13-Ti, and NiTi wires in order of increasing surface roughness. In addition to their relatively high surface roughness, 13-Ti wires may form microwelds with stainless steel brackets in dry conditions,* thereby further increasing the frictional forces. In the present investigation the levels of frictional forces observed in 0.018-inch brackets ranged from 49 gm with 0.016-inch SS wires in NS brackets to 336 gm with 0.017 × 0.025-inch 13-Ti wires in WT brackets (Tables II and IV). Similarly, for 0.022-inch brackets, frictional forces ranged from 40 gm with 0.018-inch SS wires in NS brackets to 222 gm with 0.019 × 0.025-inch NiTi wires in WT brackets (Tables III and V). Several bracket-wire combinations generated low levels of frictional forces. These included a number of wire sizes of all four alloys in both the 0.018-inch and 0.022-inch NS brackets. Within MT brackets, *KusyRP. Personalcommunication,1988.

0.016-inch SS and Co-Cr wires, 0.016 x 0.016-inch Co-Cr and NiTi wires in 0.018-inch brackets, as well as 0.016-inch and 0.018-inch Co-Cr and SS wires, 0.016 × 0.016-inch NiTi wires, and 0.017 × 0.017-inch SS wires in 0.022-inch brackets generated relatively small amounts of friction. Similarly, in WT brackets, 0.016-inch SS wires in 0.018-inch brackets, and 0.016-inch, 0.016 x 0.016-inch, 0.016 × 0.022-inch, and 0.018-inch Co-Cr wires, as well as 0.016-inch and 0.017 × 0.017-inch SS wires produced low frictional forces. All these bracket-wire combinations generated less than 110 gm of frictional force. In general an increase in wire size was associated with increased bracket-wire friction. This finding is in concordance with the findings of Frank and Nikolai, 2 Riley et al., 6 and others. 8"9 Previous findings on the effects of bracket width on bracket-wire friction have been inconsistent. Although Frank and Nikolai 2 have reported an increase in friction with increased bracket width, other investigators 8"9have noted an insignificant effect of bracket width on bracket-wire friction. In the present study wider brackets were generally associated with greater levels of frictional forces than narrow brackets were. This finding may be attributed to the use of elastic modules for ligation. Such an arrangement would cause a greater stretching and larger normal forces of the ligature with wider brackets than with narrow brackets and thus, a resultant increase in bracket-wire friction with wide brackets. Several theories about the relationship between orthodontic forces and tooth movement have been previously proposed. 13-17A critical review of these theories has been done by Quinn and Yoshikawa, 17 who conclude that the rate of tooth movement increases with increase in force up to a point, after which increased forces do not result in an appreciable increase in tooth movement. This theory emphasizes that tooth movement occurs most efficiently at an optimal range of forces. When sliding mechanics are used, a proportion of the applied force is dissipated as friction and much of the remainder is transferred to supporting structures of the tooth to mediate tooth movement. This implies that in order to achieve efficient tooth movement in the presence of bracket-wire friction, the total force applied to the tooth will be determined by the optimal force necessary to move the tooth as well as by the magnitude of bracket-wire friction. Since different magnitudes of friction are generated by various bracket-wire combinations, the amount of force reWe express our gratitude to Mr. John Welch for con-

126

Am. J. Orthod. Dentofac. Orthop. August 1990

Kapila et al.

q u i r e d to o v e r c o m e f r i c t i o n will d e p e n d o n t h e b r a c k e t wire combination used. structing the experimental apparatus, to Ms. Elaine Brown for doing the statistical analyses, to Ms. Rebecca Robinson for preparing the manuscript, and to the suppliers for donating the materials. Our appreciation is also extended to Dr. Bob Boyd, Dr. Gary Reichhold, and Dr. Ken Yoshikawa for reviewing the article.

9.

10. I I.

REFERENCES 1. Serway RA. Physics: For Scientists and Engineers. Philadelphia: Saunders College Publishing, 1982:82. 2. Frank CA, Nikolai RJ. A comparative study of frictional resistances between orthodontic bracket and arch wire. AM J OR~OD 1980;78:593-609. 3. Tipler PA. Physics. New York: Worth Publishers, Inc., 1978: 156. 4. Baker KL, Nieberg LG, Weimer AD, Hanna M. Frictional changes in force values caused by saliva substitution. AM J ORI-~OD DENTOFACORI"HOP 1987;91:316-20. 5. Stannard JG, Gau JM, Hanna M. Comparative friction of orthodontic wires under dry and wet conditions. AM J ORTHOD 1986;89:485-91. 6. Riley JL, Garrett SG, Moon PC. Frictional forces of ligated plastic and metal edgewise brackets. J Dent Res 1979;58:A21. 7. Feeney F, Morton J, Burstone C. The effect of bracket width on bracket-wire friction. J Dent Res 1988;67:A1969. 8. Andreasen GF, Quevedo FR. Evaluation of frictional forces in

12.

13. 14. 15. 16.

17.

the 0.022 x 0.028 edgewise bracket in vitro. J Biomech 1970;3:151-60. Peterson L, Spencer R, Andreasen G. A comparison of friction resistance for nitinol and stainless steel wire in edgewise brackets. Quintessence Int 1982;13:563-71. Greenberg AR, Kusy RP. A survey of specialty coatings for orthodontic wires. J Dent Res 1979;58:A21. Garner LD, AIIai WW, Moore BK. A comparison of frictional forces during simulated canine retraction of a continuous edgewise arch wire. AM J ORTHODDENTOFACORTHOP 1986;90:199203. Kusy RP, Whitley JQ, Mayhew MJ, Buckthal JE. Surface roughness of orthodontic archwires via laser spectroscopy. Angle Orthod 1988;58:33-45. Schwartz AM. Tissue changes incident to orthodontic tooth movement. Is'r J ORTHOD 1932;18:331-52. Storey E, Smith R. Force in orthodontics and its relation to tooth movement. Aust Dent J 1952;56:11-8. Reitain K. Some factors determining the evaluation of forces in orthodontics. AM J ORTHOD 1957;43:32-45. Boester CH, Johnston LE. A clinical investigation of the concepts of differential and optimal force in canine retraction. Angle Orthod 1974;44:113-9. Quinn RB, Yoshikawa DK. A reassessment of force magnitude in orthodontics. AM J ORTHOD 1985;88:252-60.

Reprint requests to: Dr. Sunil Kapila HSW 604, University of California San Francisco, CA 94143-0512.

AAO MEETING CALENDAR

1991--Seattle, Wash., May 12 to 15, Seattle Convention Center 1992--St. Louis, Mo., May 10 to 13, St. Louis Convention Center 1993mToronto, Canada, May 16 to 19, Metropolitan Toronto Convention Center 1994--Orlando, Fla., May 1 to 4, Orange County Convention and Civic Center 1995--San Francisco, Calif., May 7 to 10, Moscone Convention Center 1996-- Denver, Colo., May 12-15, Colorado Convention Center