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Frictional forces in fixed appliances
forces in fixed appliances . Tidy, FDS, D. Orth., PhD* Rundee, United Kingdom The aim of this investigation was to measure the frictional resistance to bodily tooth movement along a continuous arch wire. A fixed appliance was constructed in vitro to simulate tooth movement in a previously aligned arch. The effect of load, bracket width, slot size, arch wire size, and rnate~~a~ were studied. It was found that friction was proportional to applied load and inversely proportional to bracket width. Arch wire dimension and slot size had little effect. Nitinol and TMA (beta-titanium) arch wires produced frictional forces two and five times greater than those of stainless steel. (ANY J ORTHOD DENTOFAC ORTHOP 1989;96:249-54.)
ost fixed appliance techniques involve some degree of sliding between bracket and arch wire. Whenever sliding occurs, frictional resistance is encountered, but the magnitude and clinical significance of this frictional resistance is largely unknown. One approach to this problem is to adopt “frictionless” mechanics, which avoid tooth movement along the arch wire as far as possible. Another approach is to use sliding mechanics but to design the appliance to reduce friction as in the Begg technique. The widespread adoption of preadjusted bracket systems has increased interest in the use of sliding mechanics for the edgewise technique, in which friction may not be minimal. Therefore more information about the magnitude and clinical significance of frictional resistance is required. The classical laws of friction state that a frictional force is (1) proportional to the force normally acting on the contact, (2) independent of the area of contact, and (3) independent of the sliding velocity. For metals under normal conditions of use these laws are often reasonably accurate, although for other materials or for extreme conditions the laws break down.’ When a bracket is sliding along an arch wire, these laws imply that any friction arises from the force normally acting on the points of contact. Possible components of this force are (1) engagement of the arch wire in brackets that are out of alignment, (2) ligatures pressing the arch wire against the base of the slot, (3) active torque in rectangular wire, and (4) bodily tooth movement in which the tipping tendency is resisted by two-point contact between the bracket and arch wire.
From Dundee Dental Hospital. Supported by a research grant from the Tayside Health Board *Senior Registrar in Orthodontics, Dundee Dental Hospital. 811115136
The relative magnitudes of these components of the frictional force vary according to the clinical situation, and components that predominate in Ihe early stages of treatment may give way to others later. Clinical decisions at each stage, such as choice of arch wire and method of ligation, also influence the frictional force. Thinning of the arch wire is sometimes done in the buccal segments with the aim of reducing friction. Previous work on friction in fixed appliances has quantified some components of the frictional force. Friction caused by a bracket that is tilted out of alignment increases as the angle of tilt is increased. Friction also increases as the wire stiffness increases and for a given angle increases as the bracket width increases. 2-4 When nitinol wire replaces stainless steel wire in this type of experiment, friction is reduced.5 Ligation with elastomeric ligatures gives rise to frictional forces in the range of 50 gm to 175 gm. The friction caused by the elastomeric ligatures is increased slightly with the use of arch wires of greater dimensions, while nitinol gives more friction than stainless steel and TMA (beta-titanium) more than nitinol .6-8 The use of wire ligatures leads to frictional forces that are sensitive to the method used to apply the ligatures and may vary from zero to extremely high levels. Lubrication appears to play only a minor role. Tests done under dry conditions give the same results as tests in water, whereas the use of artificial saliva or glycerine has only produced reductions in friction of 37% or less.3,7-8 The purpose of this study was to obtain data on the friction caused by two-point contact during bodily movement of a tooth along the arch wire in a wellaligned arch, and, in particular, to investigate (1) the effect of load and bracket width, (2) the influence of slot and arch wire dimensions, and (3) the effect of arch wire material.
Tidy TO LOAD CELL
Archwire reaction
Friction
Single equivalent
Fig. 1. Forces acting on tooth/bracket system during translation.
MATERIALS AND METHOD
The forces acting on the surface of the tooth root were simulated by a single equivalent force acting at the center of resistance of the root.’ The couple produced by the two-point contact with the arch wire counters the moment of this force about the arch wire (Fig. 1). The measurements of friction between bracket and arch wire were done with the apparatus shown in Fig. 2. It consisted of a simulated fixed appliance with the arch wire in a vlertical position. Four edgewise brackets* were bonded to a rigid metal baseplate at 8 mm intervals with a 16 mm space for a movable bracket at the center. The arch wire was secured with wire ligatures. Both 0.018-inch slot and 0.022”inch slot brackets were set up in this way using in turn arch wires of 0.016 by 0.022 inch and 0.018 by 0.025 inch stainless steel, 0.016 by 0.022 inch nitinol,f’ and 0.016 by 0.022 inch TMA$ wires. The ligature on the movable bracket was at first fully tightened, then slackened to permit free sliding. The movable bracket was fitted with a 10 mm power arm from which weights could be hung to represent the single equivalent force acting at the center of resistance of the tooth root. The length of the power arm was *Dentaumm LSP; Hawley Russell and Baker, Potters Bar, United Kingdom. TUnitek Coqsoration, Monrovia, Calif. ~Onnco Corp., Glendora, Calif.
CROSSHEAD
!
MWNilNG
I
Fig. 2. Apparatus used to measure friction.
chosen to represent the distance from the slot to the center of resistance of a typical canine tooth, AH tests were conducted under dry conditions with an Instron” testing machine with the crosshead moving downward at a speed of 5 mm/min. The movable bracket was suspended from the load cell of the testing machine, while the baseplate moved downward with the crosshead on which it was mounted. In each test, the bracket was moved a distance of not less than 2.5 mm across the central space, and the load cell reading was recorded on chart paper. Weights suspended from the power arm provided loads of 50, 100, 150, or 200 gm. At low power arm loads, the reading remained almost constant through the test, whereas at high loads the reading rose *Instron Ltd., High Wycombe, Bucks, United Kisgdom.
Volume 96 Number 3
Frictional forces in jixed
800
appliances
800 Archwire: stainless steel , 0 1 8 ” x ,025”
Archwire: stainless steel .016” x .022”
S l o t s i z e : ,018”
S l o t s i z e : .018” 600 Friction (gm) 500
500
I/.’
50
100
/
/’ /
150
./
/
I
1.1 mm
Friction (gm) 400
.I’ ./ /.’
bracket widths
200
Single equivalent load (gm)
.3. R e l a t i o n s h i p b e t w e e n s i n g l e e q u i v a l e n t l o a d a n d f r i c t i o n .
slightly to a maximum when the bracket was near the center of the arch wire span. In such cases, the maximum reading was recorded. The load cell readings represented the clinical force of retraction that would be applied to the tooth, part of which would be lost in friction while the remainder was transmitted to the tooth root. The difference between the load cell reading and the load on the power arm thus represented the friction. For each combination of bracket and load, five readings were taken with each type of arch wire. At the start of each test, a trial run was performed with no load on the power arm to check that the wire ligature was not binding on the arch wire. In most cases, the friction caused by the ligature was less than 0.5 gm. When the force was greater than 2.0 gm, the bracket and ligature wire were discarded. To assess which factors exerted a significant influence on friction, the results were subjected to statistical assessment by analysis of variance. RESULTS Effect of load and bracket width The results for the two stainless steel arch wire sizes are shown in Figs. 3 and 4. Analyses of variance for these results show that the effects of load and bracket width on friction are both significant at the 0.1% level. The almost linear relationship in Figs. 3 and 4 indicates that friction is proportional to the applied load
bracket widths
./’ I
50
100
150
Single equivalent load (?im)
Fig. 4 . R e l a t i o n s h i p b e t w e e n s i n g l e e q u i v a l e n t l o a d a n d f r i c t i o n .
on the power arm. Because the total force used to retract a tooth is the sum of these two components, it follows that the friction remains a constant proportion of the total force for any given bracket and arch wire combination. In clinical terms, this implies that the friction rises in proportion to the applied force. The dependence of friction on bracket width is more clearly illustrated by Fig. 5, in which the data in Fig. 3 are replotted with the reciprocal of bracket width on the horizontal axis. A similar plot would result from the data in Fig. 4. The linear relationship con.firms that friction is inversely proportional to bracket width. Narrow brackets can therefore be expected to provide more friction in clinical use. Influence of slot and wire dimensions The influence of slot and wire dimensions on friction is illustrated in Fig. 6. Four different combinations of wire and slot are represented, and all results refer to the same bracket width (3.3 mm). Analysis of variance fails to detect a significant difference between the four sets of results, except at the highest load, at which significance at the 5% level is just achieved. Effect of arch wire material By contrast, the results in Fig. 7 show that choice of arch wire material produces marked differences in friction. Analysis of variance shows that the differences between arch wire materials are sign&cant at the 0.1%
2 Tidy
Friction Igm)
-1
0
I
,
0.1
0.2
I
I
I
,
0.3 0.4 0.5 0.7 Reciprocal bracket width (mm-’ )
I
I
I
0.8
0.9
1.0
Fig. 5. Friction vs. reciprocal bracket width.
Archwire:
Stainless
wire material, but is not significantly affected by the arch wire dimension. Therefore the proportion of force lost through friction can be expressed as a constant for each arch wire material. In clinical terms, this is a significant finding and is illustrated in Fig. 8. Important differences are seen between arch wire materials in the proportion of applied force lost on account of friction.
steel
Friction (gmi
DISCUSSION
Friction in sliding a bracket along an arch wire with the center of resistance at a distance from the arch wire can be predicted to a first approximation by simple mechanics. If it is assumed that the classical laws of friction are valid, then 2Fhh p=---.W
0
50
100
150
200
L o a d (gm)
Fig. 6. Effect of slot size on friction.
level. The nitinol wire gives approximately twice the friction of a stainless steel wire of the same dimension, whereas TMA wire gives frictional resistance some five times greater than that of stainless steel. These differences are clearly significant at a clinical level and indicate a possible disadvantage to the use of the newer resilient arch wires for sliding mechanics. As already shown, friction accounts for an almost constant proportion of the total applied force for a given bracket width. This proportion is dependent on the arch
where P is the frictional resistance, w the bracket width, A the coefficient of friction between bracket and arch wire, and F the equivalent force that acts at a distance h from the arch wire. (The coefficient of friction is approximately constant for any given pair of materials.) Friction should therefore be independent of arch wire stiffness, arch wire dimension or shape of arch wire cross section. The results obtained have confirmed the predicted dependence of friction on applied load and on bracket width. Equally, they have not shown a significant dependence on arch wire dimension under the conditions of these tests. The substantial differences in friction between stainless steel, nitinol, and TMA arch wires indicate differences in the coefficients of friction applicable for these materials sliding in contact with stainless steel. Friction caused by elastomeric ligatures’ also varies in a similar manner for these materials, which confirms the role of the coefficient of friction. Friction as a result of two-point contact remained
Frictional forces in
Volume 96 Number 3
jixed
appliances
800 Archwire size:
.016” x ,022”
Slot size:
.018”
80
Bracket width: 3.3 mm
TMA
70 600
O/ 0 60
500 Friction km) 400
Sbt size Nit.
300
200
100
0 0
50
100
Single equivalent load
150
200
Fig. 8. Percentage of force lost because of friction.
(gm)
Fig. 7. Effect of arch wire material on friction. Nit., Nitinol; S.S., stainless steei.
a relatively constant proportion of the applied load as the load increased, with no “locking” tendency at higher loads. Such friction is therefore unlikely to completely prevent tooth movement, although the movement may be retarded. “Locking” is nevertheless liable to arise when an arch wire is engaged in a malaligned bracket, for example, on a distally tilted canine, and may persist until the tooth becomes more upright. These results are in marked contrast to those previously obtained for friction with brackets tilted out of alignment .2-5 Those results had shown that friction for stainless steel wires was substantially increased with the use of heavier arch wires or wider brackets, whereas the use of nitinol arch wires reduced friction. The discrepancies between investigations reflect differences in the clinical situations being simulated. With brackets out of alignment, arch wire stiffness strongly influences forces normal to the points of contact and hence friction. In a well-aligned arch, forces that result from arch wire deflection are not important and friction is largely independent of arch wire stiffness. The apparent importance of arch wire clearance in previous work with tilted brackets therefore reflects the greater stiffness of arch wires that fill the slot. The clearance between arch wire and slot is not of itself important in controlling friction. However, kinks or deposits along a closely fitting arch
wire are more likely to lead to binding in the slot and clearance is therefore of some secondary importance. The component of friction caused by active torque may also be greater for a closely fitting wire because of its greater torsional stiffness and the reduced play between wire and slot. To reduce friction clinically, some practitioners prefer the use of round wire, or they reduce rectangular wire in the buccal segments to a more rounded cross section. Round wires, of course, eliminate friction caused by active torque. Round wires generally produce less friction than rectangular wire when engaged in brackets out of alignment because of their greater flexibility. Friction as a result of two-point contact is largely independent of wire stiffness or cross section and so is likely to be little affected by the choice of round or rectangular wire. It is therefore concluded that after insertion of the arch wire, friction with round wire may be initially less than with rectangular wire. However, as the brackets align and any torque becomes passive, the difference will become small. In this respect, the common practice of leaving a rectangular wire in position for a month before sliding forces are begun is to be recommended. CONCLUSIONS
Friction as a result of two-point contact between arch wire and bracket has been shown to vary as follows: 1. The friction is greatest for narrow brackets. For
Am. .I. Or&xi. Deniofac. Onhop, Sepzcmber 1989
example to produce a 100 gm force on a tooth with an 0.016 by 0.022 inch stainless steel arch wire in an 0.01%inch slot requires the application of a force of 295 gm to a 1.1 mm bracket, whereas such a force requires only 176 gm, 168 gm, and 155 gm, respectively, for bracket widths of 2.9 mm, 3.3 mm, and 4.2 mm. The frictional force is in fact inversely proportional to the bracket width. 2. Arch wire and slot dimensions have relatively little influence on friction. To produce a 100 gm force on a tooth with 3.3 mm wide 0.01%inch slot brackets and an 0.018 by 0.025 inch stainless steel arch wire requires a force of 188 gm. Reducing the arch wire to 0.016 by 0.022 reduces the force to 168 gm, whereas increasing the slot size to 0.022 inch only reduces the force to 181 gm. 3. Nitinol and TMA arch wires give rise to significantly greater friction than do stainless steel arch wires. To achieve a force of 100 gm on the tooth with 3.3 mm brackets and 0.016 by 0.022 inch arch wires in an 0.01%inch slot requires 381 gm for TMA and 251 gm for nitinol, but only 168 gm for stainless steel. 4. Friction may therefore be minimized by the use of wide brackets and stainless steel arch wires in preference to nitinol or TMA arch wires. I am grateful to Professor R. Yemm and Dr. C. Lloyd for the use of materials testing facilities, and to Mrs. J. Davies for statistical analysis.
REFERENCES 1. Rabinowicz E. Friction and wear of materials. 1st rd. New York: John Wiley, 1965:56-7. 2 . Nicholls J. Frictional forces in fixed orthodontic appliances. Dent Prac 1968;18:362-6. 3 . Andreasen GF, Quevado FR. Evaluation of frictional forces in the ,022” x .028” edgewise bracket in vitro. J Biomech 1970; 3:151-60. 4 . Frank CA, Nikolai RJ. A comparative study of frictional resistances between orthodontic bracket and arch wire. AM J QRTHOD 1980;78:593-609. 5 . Peterson L, Spencer R, Andreasen G. A comparison of friction resistance for nitinol and stainless steel wire in edgewise brackets. Quintessence Int 1982;5:563-71. 6 . Echols PM. Elastic ligatures: binding forces and anchorage taxation. AM J ORTHOD 197.5;67:219-20, I. Gamer LD, Allai WW, Moore BK. A comparison of frictional forces during simulated canine retraction of a continuous edgewise arch wire. AM J ORTHOD DENTOFAC ORTHOP 1986;90: 199-203. 8 . Baker KL, Nieberg LG, Weimer AD, Karma M. Frictional changes in force values caused by saliva substitution. AM J ORTHOD
DENTOFAC ORTHOP 1987;91:316-20.
9 . Burstone CJ, Pryputniewicz RJ. Holographic determination of centers of rotation produced by orthodontic forces. AM J ORTHOD 1980;77:396-405, Reprint requests 10:
Dr. D. C. Tidy University of Dundee Department of Orthodontics and Child Dental Health Dental School Park Place Dundee DDl 4HN, United Kingdom.
ost fixed appliance techniques involve some degree of sliding between bracket and arch wire. Whenever sliding occurs, frictional resistance is encountered, but the magnitude and clinical significance of this frictional resistance is largely unknown. One approach to this problem is to adopt “frictionless” mechanics, which avoid tooth movement along the arch wire as far as possible. Another approach is to use sliding mechanics but to design the appliance to reduce friction as in the Begg technique. The widespread adoption of preadjusted bracket systems has increased interest in the use of sliding mechanics for the edgewise technique, in which friction may not be minimal. Therefore more information about the magnitude and clinical significance of frictional resistance is required. The classical laws of friction state that a frictional force is (1) proportional to the force normally acting on the contact, (2) independent of the area of contact, and (3) independent of the sliding velocity. For metals under normal conditions of use these laws are often reasonably accurate, although for other materials or for extreme conditions the laws break down.’ When a bracket is sliding along an arch wire, these laws imply that any friction arises from the force normally acting on the points of contact. Possible components of this force are (1) engagement of the arch wire in brackets that are out of alignment, (2) ligatures pressing the arch wire against the base of the slot, (3) active torque in rectangular wire, and (4) bodily tooth movement in which the tipping tendency is resisted by two-point contact between the bracket and arch wire.
From Dundee Dental Hospital. Supported by a research grant from the Tayside Health Board *Senior Registrar in Orthodontics, Dundee Dental Hospital. 811115136
The relative magnitudes of these components of the frictional force vary according to the clinical situation, and components that predominate in Ihe early stages of treatment may give way to others later. Clinical decisions at each stage, such as choice of arch wire and method of ligation, also influence the frictional force. Thinning of the arch wire is sometimes done in the buccal segments with the aim of reducing friction. Previous work on friction in fixed appliances has quantified some components of the frictional force. Friction caused by a bracket that is tilted out of alignment increases as the angle of tilt is increased. Friction also increases as the wire stiffness increases and for a given angle increases as the bracket width increases. 2-4 When nitinol wire replaces stainless steel wire in this type of experiment, friction is reduced.5 Ligation with elastomeric ligatures gives rise to frictional forces in the range of 50 gm to 175 gm. The friction caused by the elastomeric ligatures is increased slightly with the use of arch wires of greater dimensions, while nitinol gives more friction than stainless steel and TMA (beta-titanium) more than nitinol .6-8 The use of wire ligatures leads to frictional forces that are sensitive to the method used to apply the ligatures and may vary from zero to extremely high levels. Lubrication appears to play only a minor role. Tests done under dry conditions give the same results as tests in water, whereas the use of artificial saliva or glycerine has only produced reductions in friction of 37% or less.3,7-8 The purpose of this study was to obtain data on the friction caused by two-point contact during bodily movement of a tooth along the arch wire in a wellaligned arch, and, in particular, to investigate (1) the effect of load and bracket width, (2) the influence of slot and arch wire dimensions, and (3) the effect of arch wire material.
Tidy TO LOAD CELL
Archwire reaction
Friction
Single equivalent
Fig. 1. Forces acting on tooth/bracket system during translation.
MATERIALS AND METHOD
The forces acting on the surface of the tooth root were simulated by a single equivalent force acting at the center of resistance of the root.’ The couple produced by the two-point contact with the arch wire counters the moment of this force about the arch wire (Fig. 1). The measurements of friction between bracket and arch wire were done with the apparatus shown in Fig. 2. It consisted of a simulated fixed appliance with the arch wire in a vlertical position. Four edgewise brackets* were bonded to a rigid metal baseplate at 8 mm intervals with a 16 mm space for a movable bracket at the center. The arch wire was secured with wire ligatures. Both 0.018-inch slot and 0.022”inch slot brackets were set up in this way using in turn arch wires of 0.016 by 0.022 inch and 0.018 by 0.025 inch stainless steel, 0.016 by 0.022 inch nitinol,f’ and 0.016 by 0.022 inch TMA$ wires. The ligature on the movable bracket was at first fully tightened, then slackened to permit free sliding. The movable bracket was fitted with a 10 mm power arm from which weights could be hung to represent the single equivalent force acting at the center of resistance of the tooth root. The length of the power arm was *Dentaumm LSP; Hawley Russell and Baker, Potters Bar, United Kingdom. TUnitek Coqsoration, Monrovia, Calif. ~Onnco Corp., Glendora, Calif.
CROSSHEAD
!
MWNilNG
I
Fig. 2. Apparatus used to measure friction.
chosen to represent the distance from the slot to the center of resistance of a typical canine tooth, AH tests were conducted under dry conditions with an Instron” testing machine with the crosshead moving downward at a speed of 5 mm/min. The movable bracket was suspended from the load cell of the testing machine, while the baseplate moved downward with the crosshead on which it was mounted. In each test, the bracket was moved a distance of not less than 2.5 mm across the central space, and the load cell reading was recorded on chart paper. Weights suspended from the power arm provided loads of 50, 100, 150, or 200 gm. At low power arm loads, the reading remained almost constant through the test, whereas at high loads the reading rose *Instron Ltd., High Wycombe, Bucks, United Kisgdom.
Volume 96 Number 3
Frictional forces in jixed
800
appliances
800 Archwire: stainless steel , 0 1 8 ” x ,025”
Archwire: stainless steel .016” x .022”
S l o t s i z e : ,018”
S l o t s i z e : .018” 600 Friction (gm) 500
500
I/.’
50
100
/
/’ /
150
./
/
I
1.1 mm
Friction (gm) 400
.I’ ./ /.’
bracket widths
200
Single equivalent load (gm)
.3. R e l a t i o n s h i p b e t w e e n s i n g l e e q u i v a l e n t l o a d a n d f r i c t i o n .
slightly to a maximum when the bracket was near the center of the arch wire span. In such cases, the maximum reading was recorded. The load cell readings represented the clinical force of retraction that would be applied to the tooth, part of which would be lost in friction while the remainder was transmitted to the tooth root. The difference between the load cell reading and the load on the power arm thus represented the friction. For each combination of bracket and load, five readings were taken with each type of arch wire. At the start of each test, a trial run was performed with no load on the power arm to check that the wire ligature was not binding on the arch wire. In most cases, the friction caused by the ligature was less than 0.5 gm. When the force was greater than 2.0 gm, the bracket and ligature wire were discarded. To assess which factors exerted a significant influence on friction, the results were subjected to statistical assessment by analysis of variance. RESULTS Effect of load and bracket width The results for the two stainless steel arch wire sizes are shown in Figs. 3 and 4. Analyses of variance for these results show that the effects of load and bracket width on friction are both significant at the 0.1% level. The almost linear relationship in Figs. 3 and 4 indicates that friction is proportional to the applied load
bracket widths
./’ I
50
100
150
Single equivalent load (?im)
Fig. 4 . R e l a t i o n s h i p b e t w e e n s i n g l e e q u i v a l e n t l o a d a n d f r i c t i o n .
on the power arm. Because the total force used to retract a tooth is the sum of these two components, it follows that the friction remains a constant proportion of the total force for any given bracket and arch wire combination. In clinical terms, this implies that the friction rises in proportion to the applied force. The dependence of friction on bracket width is more clearly illustrated by Fig. 5, in which the data in Fig. 3 are replotted with the reciprocal of bracket width on the horizontal axis. A similar plot would result from the data in Fig. 4. The linear relationship con.firms that friction is inversely proportional to bracket width. Narrow brackets can therefore be expected to provide more friction in clinical use. Influence of slot and wire dimensions The influence of slot and wire dimensions on friction is illustrated in Fig. 6. Four different combinations of wire and slot are represented, and all results refer to the same bracket width (3.3 mm). Analysis of variance fails to detect a significant difference between the four sets of results, except at the highest load, at which significance at the 5% level is just achieved. Effect of arch wire material By contrast, the results in Fig. 7 show that choice of arch wire material produces marked differences in friction. Analysis of variance shows that the differences between arch wire materials are sign&cant at the 0.1%
2 Tidy
Friction Igm)
-1
0
I
,
0.1
0.2
I
I
I
,
0.3 0.4 0.5 0.7 Reciprocal bracket width (mm-’ )
I
I
I
0.8
0.9
1.0
Fig. 5. Friction vs. reciprocal bracket width.
Archwire:
Stainless
wire material, but is not significantly affected by the arch wire dimension. Therefore the proportion of force lost through friction can be expressed as a constant for each arch wire material. In clinical terms, this is a significant finding and is illustrated in Fig. 8. Important differences are seen between arch wire materials in the proportion of applied force lost on account of friction.
steel
Friction (gmi
DISCUSSION
Friction in sliding a bracket along an arch wire with the center of resistance at a distance from the arch wire can be predicted to a first approximation by simple mechanics. If it is assumed that the classical laws of friction are valid, then 2Fhh p=---.W
0
50
100
150
200
L o a d (gm)
Fig. 6. Effect of slot size on friction.
level. The nitinol wire gives approximately twice the friction of a stainless steel wire of the same dimension, whereas TMA wire gives frictional resistance some five times greater than that of stainless steel. These differences are clearly significant at a clinical level and indicate a possible disadvantage to the use of the newer resilient arch wires for sliding mechanics. As already shown, friction accounts for an almost constant proportion of the total applied force for a given bracket width. This proportion is dependent on the arch
where P is the frictional resistance, w the bracket width, A the coefficient of friction between bracket and arch wire, and F the equivalent force that acts at a distance h from the arch wire. (The coefficient of friction is approximately constant for any given pair of materials.) Friction should therefore be independent of arch wire stiffness, arch wire dimension or shape of arch wire cross section. The results obtained have confirmed the predicted dependence of friction on applied load and on bracket width. Equally, they have not shown a significant dependence on arch wire dimension under the conditions of these tests. The substantial differences in friction between stainless steel, nitinol, and TMA arch wires indicate differences in the coefficients of friction applicable for these materials sliding in contact with stainless steel. Friction caused by elastomeric ligatures’ also varies in a similar manner for these materials, which confirms the role of the coefficient of friction. Friction as a result of two-point contact remained
Frictional forces in
Volume 96 Number 3
jixed
appliances
800 Archwire size:
.016” x ,022”
Slot size:
.018”
80
Bracket width: 3.3 mm
TMA
70 600
O/ 0 60
500 Friction km) 400
Sbt size Nit.
300
200
100
0 0
50
100
Single equivalent load
150
200
Fig. 8. Percentage of force lost because of friction.
(gm)
Fig. 7. Effect of arch wire material on friction. Nit., Nitinol; S.S., stainless steei.
a relatively constant proportion of the applied load as the load increased, with no “locking” tendency at higher loads. Such friction is therefore unlikely to completely prevent tooth movement, although the movement may be retarded. “Locking” is nevertheless liable to arise when an arch wire is engaged in a malaligned bracket, for example, on a distally tilted canine, and may persist until the tooth becomes more upright. These results are in marked contrast to those previously obtained for friction with brackets tilted out of alignment .2-5 Those results had shown that friction for stainless steel wires was substantially increased with the use of heavier arch wires or wider brackets, whereas the use of nitinol arch wires reduced friction. The discrepancies between investigations reflect differences in the clinical situations being simulated. With brackets out of alignment, arch wire stiffness strongly influences forces normal to the points of contact and hence friction. In a well-aligned arch, forces that result from arch wire deflection are not important and friction is largely independent of arch wire stiffness. The apparent importance of arch wire clearance in previous work with tilted brackets therefore reflects the greater stiffness of arch wires that fill the slot. The clearance between arch wire and slot is not of itself important in controlling friction. However, kinks or deposits along a closely fitting arch
wire are more likely to lead to binding in the slot and clearance is therefore of some secondary importance. The component of friction caused by active torque may also be greater for a closely fitting wire because of its greater torsional stiffness and the reduced play between wire and slot. To reduce friction clinically, some practitioners prefer the use of round wire, or they reduce rectangular wire in the buccal segments to a more rounded cross section. Round wires, of course, eliminate friction caused by active torque. Round wires generally produce less friction than rectangular wire when engaged in brackets out of alignment because of their greater flexibility. Friction as a result of two-point contact is largely independent of wire stiffness or cross section and so is likely to be little affected by the choice of round or rectangular wire. It is therefore concluded that after insertion of the arch wire, friction with round wire may be initially less than with rectangular wire. However, as the brackets align and any torque becomes passive, the difference will become small. In this respect, the common practice of leaving a rectangular wire in position for a month before sliding forces are begun is to be recommended. CONCLUSIONS
Friction as a result of two-point contact between arch wire and bracket has been shown to vary as follows: 1. The friction is greatest for narrow brackets. For
Am. .I. Or&xi. Deniofac. Onhop, Sepzcmber 1989
example to produce a 100 gm force on a tooth with an 0.016 by 0.022 inch stainless steel arch wire in an 0.01%inch slot requires the application of a force of 295 gm to a 1.1 mm bracket, whereas such a force requires only 176 gm, 168 gm, and 155 gm, respectively, for bracket widths of 2.9 mm, 3.3 mm, and 4.2 mm. The frictional force is in fact inversely proportional to the bracket width. 2. Arch wire and slot dimensions have relatively little influence on friction. To produce a 100 gm force on a tooth with 3.3 mm wide 0.01%inch slot brackets and an 0.018 by 0.025 inch stainless steel arch wire requires a force of 188 gm. Reducing the arch wire to 0.016 by 0.022 reduces the force to 168 gm, whereas increasing the slot size to 0.022 inch only reduces the force to 181 gm. 3. Nitinol and TMA arch wires give rise to significantly greater friction than do stainless steel arch wires. To achieve a force of 100 gm on the tooth with 3.3 mm brackets and 0.016 by 0.022 inch arch wires in an 0.01%inch slot requires 381 gm for TMA and 251 gm for nitinol, but only 168 gm for stainless steel. 4. Friction may therefore be minimized by the use of wide brackets and stainless steel arch wires in preference to nitinol or TMA arch wires. I am grateful to Professor R. Yemm and Dr. C. Lloyd for the use of materials testing facilities, and to Mrs. J. Davies for statistical analysis.
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Dr. D. C. Tidy University of Dundee Department of Orthodontics and Child Dental Health Dental School Park Place Dundee DDl 4HN, United Kingdom.