Resistance force of magnetic attachments against external lateraldisplacement
M. Takahashi1, G. Togawa1, K. Numazaki2, M. Kanyi3 and Y. Takada1
Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry, JAPANDivision of orthodontics and dentofacial orthopedics, Tohoku University Graduate School ofDentistry, JAPAN3Moi Teaching and Referral Hospital, KENYA
12Introduction
Support, retention, and bracing or resistances against lateral forces are the three fundamental aspects
required for stability of dentures during function1). Elements of a denture such as abutments, proximal plate,connectors, occlusal rests, clasps, reciprocators and base plate, contribute towards stability solely or incombination. Dental magnetic attachments are devices incorporated into the abutments to offer retention
and support with minimal bracing (horizontal stability) 2). These characteristics are absent in other abutment
devices. The use of magnetic attachments eliminates most of the rotational and lateral forces which aredetrimental to the longevity of a tooth’s root3). Use of magnetic attachments also allows for a decrease inabutment teeth loading forces which is an advantage, but a compromise in terms of denture functionality.
However, it is possible to actively increase force generated by bracing components using magneticattachments of improved root cap shape or using MT crown2).
Dental magnetic attachments are associated with weak bracing force because only frictional force of themating face provides resistance to external forces acting in the horizontal direction. The magnets attractive
force is not directly involved2). Generally, when force is exerted on an object placed on a horizontal surface
in an attempt to slide it laterally, static friction provides a counter force. Static friction force shows thegreatest magnitude just before the object starts to move. It is termed as the maximum static friction.
Maximum static friction Fs is proportional to the normal force N acting perpendicularly through the object
to the contact surface. The proportionality constant μs at that point is called the coefficient of static friction,
whose relationship is represented by the following equation (1).
Fs=μsN(1)When the force applied to move the object becomes greater than Fs, the object starts to slide, and kineticfriction begins to act on the object instead of static friction. Kinetic friction is a smaller force thanmaximum static friction. It has been proven experimentally that kinetic friction Fk is proportional to normal
force N. The proportionality constant μk is called coefficient of kinetic friction, and the following equation(2) describes the relationship.
Fk =μkN(2)

The values represented by μs and μk are constants which are determined by properties of the contact surface,such as surface roughness, surface energy. The contact surface area and velocity of the moving object haveno direct influence on the constants. The normal force N in most scenarios is the force of gravity acting on
the object. Magnetic attachments possess a very small gravity due to their minute mass. Therefore, it is theattractive force of a magnet that predominantly acts as the normal force N. The bracing force of a magnetic
attachment which is its resistance to forces that try to shift the magnetic assembly laterally from its keeper,is majorly dependent on the attractive force. Out of the few studies that investigated the friction force ofmagnetic attachments, only one study reported a magnetic attachment with a friction force of 70~90 g. It isa well-known that dental magnetic attachments are gentle on the roots of the abutment teeth, but themechanism needs to be understood well by studying resistance force and its behavior against forces thatcause lateral displacement.

Objective
The purpose of this study was to demonstrate the resistance forces of a magnetic attachment against
lateral displacement. The resistance and attractive forces of magnetic assembly and magnet against its
keeper during lateral displacement were examined.

Materials and Methods
Dental magnetic attachment and magnet
A dental magnetic attachment, Physio Magnet 5213 (magnetic assembly: 5.2 mm in diameter and 1.3
mm in height, with keeper: 5.2 mm in diameter and 0.8 mm in height, Morita) was used in this study. The
set is subsequently referred to as magnetic attachment. A magnet, cylindrical neodymium magnet(Nd-Fe-B: 5.0 mm in diameter and 1.5 mm in height, Trusco) was used. The cylindrical neodymium
magnet was combined with the Physio Magnet keeper. The set is hereinafter referred to as magnet. In orderto have the magnet and keeper in a position whereby their centers match, the magnets diameter must be
smaller than the keepers4). Therefore, the magnet selected for use in this study had a slightly smaller
diameter than the keeper's.
Experimental device
The retentive force measuring device used in this study matches the basic description in ISO
13017:20205). It was connected to a digital force gauge (ZPS, Imada). The device was installed in auniversal testing machine (AGS-5kNG, Shimadzu) which controlled the crosshead speed.
Measurement of resistance force of a magnetic attachment or magnet and keeper against
external forces that cause lateral displacement
As shown in the Figure 1, aluminum jigs were fixed with their long axis in a vertical plane. One jig wasfixed to the lower table of the measuring device whereas the other was fixed onto the upper table. A
magnetic assembly and magnet combined with keeper were fixed onto the jigs using cyanoacrylateadhesive with the long axis in a vertical plane as shown in Fig 1. The magnetic assembly or magnet waspulled upwards so that the mating faces slide against each other at the crosshead speed of 1mm/min, andthe resistance force measured by the force gauge. Recording of measurements was done at a sampling rateof 1 kHz until the magnetic assembly or magnet completely separated from the keeper. After themeasurement, the time values were converted to distance to generate a displacement distance-resistancecurve.

Fig. 1Set up of the sample mounted on device to measure resistance forces

Measurement of attractive force during lateral displacement
The measuring device, magnetic attachment and magnet were set up in accordance with the test methodof ISO 130175), and retentive force (attractive force) was measured at crosshead speed of 2 mm/min. The
measurements started when the magnetic assembly or magnet had its center aligned to that of the keeper.
Attractive force measurements were done at intervals of 100 µm horizontal displacement of keeper. The
experiment was run until the magnetic assembly or magnet completely separated from its keeper.

Results
1. Resistance force of magnetic attachment or magnet and keeper against external forcesthat cause lateral displacement along the mating face
The displacement -resistance force curve of the magnetic attachment is shown in Figure 2. The
horizontal axis shows the distance of horizontal shift (displacement) by the magnetic assembly away fromthe keeper whereas the vertical axis shows the resistance force measured. The resistance force just before
the magnetic assembly started to move (maximum static friction force) was 1.78N. Once the assembly
started to move, the force dropped drastically to 1.34 N. Afterwards, the resistance force increased as thedistance approached 0.25 mm, then decreased with increasing distance. The curve had several inflection
points. Beyond 5.2 mm, the resistance dropped to zero.

2.0Resistance (N)

1.5

1.0

0.5

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

displacement distance (mm)Fig. 2 The displacement distance-resistance force curve of the Physio magnetic attachment
The displacement distance-resistance force curve of the neodymium magnet -keeper is shown in Figure 3.
The resistance force just before the initial movement of the magnet (maximum static friction force) was
0.39 N. Afterwards, the force dropped to 0.37 N then showed a transient rise and fall at 0.54 mm. Beyond
that, the force increased monotonically with the increase in distance. As the distance exceeded 4.5 mm, theresistance force decreased to reach zero at 6.4 mm. The decline in resistance force to zero from 5.1 mm
distance point, showed a smooth convex shape.

Resistance (N)

1.0

0.5

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

displacement distance (mm)Fig. 3The displacement distance-resistance curve of neodymium magnet-keeper2. Horizontal displacement and magnetic attractive force
The relationship between horizontal displacement and the attractive force of magnetic attachment andneodymium magnet are shown in Figure 4 and Figure 5 respectively. In both cases, the attractive forces
decreased with increasing displacement and showed multiple inflections.

12.0

Attractive force (N)

10.0
8.0
6.0
4.0
2.0
0.0

0.0

1.0

2.0
3.0
4.0
Horizontal displacement (mm)

5.0

6.0

Fig. 4The attractive force against horizontal displacement in magnetic attachment

3.5

Attractive force (N)

3.0
2.5
2.0
1.5
1.0
0.5
0.0

0.0

1.0

2.0
3.0
4.0
Horizontal displacement (mm)

5.0

6.0

Fig. 5 The attractive force against horizontal displacement of neodymium magnet and keeper

Discussion
1. Resistance force of magnetic attachment against external forces that cause lateraldisplacement along the mating faceIn this study, the mating face of the magnetic attachment was fixed onto the measuring device with thelong axis parallel to the vertical plane so that only the attractive force of the magnet affects the normalforce which in turn relates to friction force. The maximum static friction was determined from theresistance displacement curve. Normal force N is the attractive force at zero displacement. The coefficientof static friction was calculated using equation (1). The kinetic friction which is active soon after themagnetic assembly or magnet starts to move, was derived from the resistance displacement curve. The
coefficient of kinetic friction was calculated using equation (2). The calculated coefficients of static friction
and of kinetic friction for the magnetic attachment 5213 were equal to 0.17 and 0.13 respectively. The
values reinforced a well-known concept of, coefficient of static friction being greater that of kinetic friction.
Ishihata et al. in a previous study3) reported that the frictional force of a magnetic attachment was about 1/3
its attractive force. The coefficient of friction in that study was about 0.33. The large difference between thetwo studies is that the material of the magnetic attachments used was different. The magnetic attachment in
Ishihata et al.'s study was made of stainless steel and experimental magnetic alloy E6), while the magnetic
attachment used in this study was made of magnetic stainless steel. The coefficient of friction exhibited bya pair of contacting surfaces is highly dependent on the different material deformation characteristics andthe surface roughness.
Friction force is proportional to the normal force but independent of the contact surface area (Amontons'law). Therefore, kinetic friction force was calculated at different positions of displacement using Equation(2), after acquisition of coefficient of kinetic friction and data on attractive forces at different positions. Theresults are shown in Figure 6 alongside the resistance force. If kinetic friction is the only force that resists
the external forces responsible for lateral displacement of magnetic attachments, then the two sets of values
would be identical and the two curves superimposed onto each other. However, in this case, the resistanceforce was larger than the kinetic friction force calculated. This implies that the resistance force measured
includes laterally attraction force related to the magnetic attachments. The magnetic assembly creates amagnetic circuit on the mating face when in contact with the keeper which generates a strong attractiveforce. Even when the magnetic assembly has been displaced until it is no longer in contact with the keeper,a small attraction force towards the keeper persists. The small attraction force attempts to restore themagnetic assembly back in contact with the keeper. Therefore, the measured resistance force is the sum of
kinetic friction force acting along the mating face and the attraction force due to the magnetic fields.

2.0
Kinetic friction force
Resistance force

Force (N)

1.5

1.00.50.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Horizontal displacement (mm)Fig. 6 Kinetic friction force and resistance force corresponding to different positions of horizontal
displacement of magnetic attachment
The difference between the resistance force and the kinetic friction force was calculated to obtain theattraction force of the magnetic attachments in each position. Using the coefficient of static friction andattractive force values at each position, the maximum static friction force exerted at each position of lateraldisplacement was obtained using formula (1). The results are shown in the Figure 7. As demonstrated on
this figure, the attraction force that attempts to restore the magnetic assembly into congruence with thekeeper is generally smaller than the maximum static friction force. Therefore, the attraction force does not
automatically get an already displaced magnetic attachment back to its original position with keeper ormove further.

2.0
Magnetic attraction force
Maximum static friction force

Force (N)

1.5

1.0

0.5

0.0

0.0

1.0

2.0
3.0
4.0
5.0
6.0
Horizontal displacement (mm)Fig. 7 Magnetic attraction force and maximum static friction force at each displaced position of magneticattachment

2. Resistance force of neodymium magnet against forces that cause lateral displacement
along the mating face
The coefficients of static and kinetic friction while using neodymium magnet were determined in asimilar manner to that of magnetic attachment. The attained coefficients of static and kinetic friction were0.12 and 0.11. Coefficient of static friction was larger than that of kinetic friction. Kinetic friction force ateach position of lateral displacement was calculated in a manner similar to that of magnetic attachment.
The data of kinetic force along with the resistance force are represented in a graph shown as in figure 8.
Similar to the case of magnetic attachment, the resistance force was larger than the kinetic friction. This isbecause the attraction force between magnet and keeper even in their displaced condition is incorporated
into the measured resistance force. The measured resistance force is the sum of the kinetic friction force atthe mating face and the attraction force due to the magnetic force. Since neodymium magnets arecharacterized by open magnetic circuit, the magnetic fields from the bottom side (opposite to mating face)of the magnet and the exposed surface of the keeper generate an attraction force. This attraction force pulls
the magnet back towards the fixed keeper. Contrary to the case of the magnetic attachment in which theresistance force quickly dropped to zero when the magnetic assembly completely separated from the keeper,
the attraction force in this case persisted even after the separation point (distance of 5.1 mm). The abovefinding is a feature of open magnetic circuit, whose magnetic force after separation is inversely
proportional to the square of the distance (inverse square law) causing the magnetic force to decrease
slowly in a convex shape. On the other hand, the Physio magnetic attachment used in this study has aclosed magnetic circuit in which the two poles close to each other undergo little magnetic flux leaks
causing quick decay of magnetic force.

1.0
Kinetic friction force

Force (N)Resistance force

0.5

0.0

0.0

1.0

2.0
3.0
4.0
5.0
Horizontal displacement (mm)6.0

7.0Fig. 8Kinetic friction force and resistance force corresponding to positions of lateral displacement of theneodymium magnet
The neodymium magnet’s laterally attraction force and the maximum static friction force at each positionof lateral displacement were determined in the same method as the magnetic attachment. The results areshown in the Figure 9. Unlike the magnetic attachment scenario, the magnets attraction force exceeded themaximum static friction force when the magnet was displaced significantly by more than 2.5 mm. The
resultant force can restore the magnet to coincide with its keeper. The restoring force generated in themagnet combination used in this study was small, but it may be possible to increase it through use ofcertain selective combination of magnets. Although magnetic attachments are gentle on the tooth root, they
act as weak bracing components. Clinical application of the restoring forces, would simplify alignment of
the keeper to magnetic assembly. It may also be possible to develop a new magnetic attachment withenhanced bracing function using the information on the phenomenon of restoring forces.

1.0
Magnetic attraction forceForce (N)Maximum static friction force

0.5

0.0

0.0

1.0

2.0
3.0
4.0
5.0
6.0
Horizontal displacement (mm)Fig. 9 Magnetic attraction force and maximum static friction at each position of the neodymium magnet

Conclusion
The maximum friction force of the Physio Magnet 5213 recorded was 1.78 N. It was clearly
demonstrated that besides frictional force, magnetic attraction force also influences the overall resistanceforce that stops displacement and restores a magnetic assembly to its keeper.

Acknowledgments
The authors greatly acknowledge KEDC Co., Ltd. for providing the Physio Magnet 5213.

References
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