The 23rd International Conference on Magnetic Applications in Dentistry (Feb. 26 to Mar 15, 2024)
http://jsmad.jp/international/23/

A feature of the retentive force of combination of two magnetic assemblies:
a cup-yoke type magnetic attachment
M. Takahashi1, H. Yamaguchi1,2, K. Numazaki1,3 Y. Takada1
1

Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry, JAPANDivision of Advanced Prosthetic Dentistry, Tohoku University Graduate School of Dentistry, JAPAN
3
Division of Orthodontics and Dentofacial Orthopedics, Tohoku University Graduate School ofDentistry, JAPAN2Introduction
Dental magnetic attachments are one of the retainers used for removable partial or complete dentures. They
can be easily used with implants and are often used for implant overdentures such as 2-IOD and 4-IOD1-3).
They have been covered by the Japanese medical insurance system since 2021, making it easier to design
dentures with superior esthetics compared to dentures using only clasps4,5). Therefore, it is expected to
become more and more popular in Japan. All dental magnetic attachments made in Japan are used in
combination with a magnetic assembly and a keeper. The magnetic assembly is implanted in the denture, andthe keeper is attached to the abutment tooth or implant. In the magnetic assembly, rare earth magnets arecovered with magnetic and non-magnetic stainless steel to form a closed magnetic circuit6). Therefore, it has
the advantages of great retentive force even in a small size and low leakage magnetic field. On the other hand,dental magnetic attachments manufactured outside of Japan include products that use open-circuit magnets,
which are simply rare earth magnets with inferior corrosion resistance coated with stainless steel or titanium7).
Open-circuit magnets have a simpler structure than magnetic assemblies and are easier to manufacture.
However, open-circuit magnets have high magnetic field leakage and low retentive force for their size. To
compensate for the weak retentive force, it is used not only in magnet-keeper combination, but also in
combine two magnets. In summary, dental magnetic attachments are currently used in three different
combinations: a magnetic assembly and a keeper, a magnet and a keeper, and a magnet and a magnet.
In a previous report8), we focused on a previously unused combination of magnetic assemblies withmagnetic assemblies. The combination of magnets with each other exhibits a grater retentive force than thecombination of a magnet and a keeper. Therefore, it is expected that the combination of magnetic assemblies
with each other also has a greater retentive force than the combination of a magnetic assembly and a keeper.
The aim of previous study8) was to explore possibility of combining two sandwich-type magnetic assemblies
and investigate the retentive force characteristics. As a result, it was found that the retentive force was greater
when the magnetic assemblies were combined with each other than with a keeper, and that the decrease in
the retentive force was moderate after the mating faces separated.
Dental magnetic attachments are believed to protect abutment teeth from lateral forces because they do
not exert strong retentive force against lateral forces that are harmful to the abutment teeth6,9). Therefore, ina previous study10), we investigated the mechanical behavior of magnetic attachments against lateral forcesby measuring the resistance and attractive force during lateral displacement between the magnetic assembly
and the keeper, or between the magnet and the keeper. The results showed that the resistance force ofmagnetic attachments of commonly used sizes was about 1 N, indicating that they are more root-friendlyabutments for abutment teeth than circumferential clasps or O-ring attachments. It was also found that theresistance force against the lateral force to displace the magnetic assembly from the keeper is related not only
to the frictional force but also to the magnetic attraction force. In the combination of the magnet and thekeeper, we found that when the magnet is displaced significantly, it moves itself in the direction where thecenter of the magnet and the keeper coincide. We named the force that tries to restore this position the"restoring force". In the study on the retentive force when sandwich-type magnetic assemblies are combinedwith each other, we did not measure the resistance force against lateral forces, but we confirmed aphenomenon that suggests the existence of a restoring force8).
There are two types of magnetic assemblies for dental magnetic attachments: cup-yoke type and sandwich
type11). Since interesting results were obtained by the combination of sandwich-type magnetic structures, weare also interested in the behavior of cup-yoke type magnetic structures with each other. However, unlike thesandwich type, it is difficult to combine cup-yoke type magnetic structures because the poles of the contacting
parts of the mating faces are the same and therefore repel each other due to repulsion. If the magnetization
direction of one of the magnetic assemblies is reversed, the cup-yoke type can be combined (Figure 1).

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The 23rd International Conference on Magnetic Applications in Dentistry (Feb. 26 to Mar 15, 2024)
http://jsmad.jp/international/23/

NS

NS

Fig. 1 Combination of cup-yoke type of magnetic assemblies

Objective
In this study, we prepared a magnetic assembly with the magnetization direction reversed, and investigated
the retentive force and the characteristics of lateral displacement when two cup-yoke type magnetic
assemblies are combined.

Materials and Methods
1. Dental magnetic attachment
A magnetic assembly of a cup-yoke type dental magnetic attachment (Physio Magnet 5213, Morita, Tokyo,Japan) was prepared. A magnetic assembly with the magnetization direction reversed from that of thecommercial product was prepared by special order from the manufacturer, and combinations of magnet
structures were used in the experiments.
2. Retentive force measurement
According to ISO 13017:202011), a digital force gauge (ZPS, Imada, Aichi, Japan) was connected to aretentive force measuring device, and the crosshead speed was set to 2 mm/min, and the retentive force(attractive force) of the combine two magnetic assemblies was measured while recording the retentive force
curve. The retentive force was measured when the mating surfaces were in contact with each other at theexact position and when they were displaced horizontally from the exact contact position. The retentive force
was measured for each 100 µm displacement of one magnetic assembly in the horizontal direction. The
measurement was repeated until the magnetic assembly was displaced from the other magnetic assembly.
3. Measurement of the resistance force against the external force of displacement
As in previous study10), an aluminum jig was attached to the upper and lower tables to create verticalsurfaces facing each other in the retentive force measuring device, and the magnetic assemblies were fixed
to the jig with cyanoacrylate adhesive. The magnetic assembly was pulled in the direction in which the mating
surface slides at a crosshead speed of 1 mm/min, and the resistance force at that time was measured with aforce gauge. The force was recorded at a sampling rate of 1 kHz until the magnetic assembly was removed
from the other magnetic assembly. After the measurement, the time was converted to distance and a distance-resistance curve was generated.

Results
1. Retentive force
The retentive force of the combination of magnetic assemblies was 12.16 N. The retentive force of thecombination of magnetic assembly and a keeper was 10.64 N10). The retentive force of the pair of magnetic
assemblies was 1.14 times greater than that of magnetic assembly combined with keeper. A typical retentiveforce curve is shown in Figure 2. The results of the magnetic assembly and keeper combinations are also
shown together. The position at the instant when the mating surfaces are separated is set to 0 mm. In bothcases, the retentive force decreased as the distance between the mating surfaces increased. The retentive force
between the magnetic assemblies decreased more moderate than magnetic assembly and keeper combinations
after the surfaces separated.

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The 23rd International Conference on Magnetic Applications in Dentistry (Feb. 26 to Mar 15, 2024)
http://jsmad.jp/international/23/Force (N)15.0
two magneticassemblies
magnetic assemblyand keeper

10.0

5.0

0.0-1

0123Distance (mm)4Fig. 2 Retentive force curve

14.0

3.5

12.0

3.0

Resistance force (N)Attractive force (N)

2. Horizontal displacement and change in magnetic attractive force
The relationship between horizontal displacement and attractive force is shown in Figure 3. The attractiveforce decreased as the horizontal displacement increased, but the decrease in attractive force was not constant,and multiple inflections were observed.

10.0
8.0
6.0

4.0
2.0
0.0

0.0

1.0 2.0 3.0 4.0 5.0 6.0
Horizontal displacement (mm)Fig. 3 Retentive force against displacement

2.5
2.0
1.5

1.0
0.5
0.0

0.0

1.0

2.0 3.0 4.0 5.0
Displacement (mm)6.0

Fig. 4 The displacement -resistance force curve

3. Resistance force to external forces that cause displacement
The distance -resistance force curve between two magnetic assemblies is shown in Figure 4. The horizontal
axis represents the distance that the centers of the two magnetic assemblies were displaced along the mating
surface from the state where their centers were coincident, and the vertical axis represents the resistance force
at that position. The resistance force just before the magnetic assembly moved, i.e. the maximum staticfriction force, was 2.81 N. When the magnetic assembly started to move, the resistance force dropped to 2.45
N for a moment. After that, the resistance force increased to 3.03 N at a movement distance of about 0.55mm, and further decreased with an increase in the movement distance, changing the inclination several times.
The resistance force became zero when the travel distance exceeded 5.3 mm.

Discussion
1. Retentive force
Use of a second magnetic assembly instead of keeper raised the retentive force by 1.14 times. This was thesame as in the case of the sandwich type dental magnetic attachments8). The reason for this may be that thedistance between the magnetic poles was shorter when the magnetic assemblies were combined with eachother (b) than when the magnetic assembly was combined with the keeper (a), as shown in Figure 5. Anotherreason is that the volume of the magnets has doubled, and the energy of the magnets has increased. However,since the magnetic flux density of the yoke of the magnetic assembly has almost reached the saturation flux
density, the retentive force is not doubled even if the energy is doubled. We found that although magnetic
assemblies with closed magnetic circuit are characterized by their small size and great retentive force, theretentive force can be further increased by combining magnetic assemblies with each other. In addition, thedecrease in retentive force after the mating surfaces separated was moderate for magnetic assemblies
compared to magnetic assembly and keeper. As shown in Figure 6, the magnetic assembly is characterized
by a small leakage magnetic field, and the retentive force quickly decreases to zero when the mating surface[Web Presentation] PS4-4-3

The 23rd International Conference on Magnetic Applications in Dentistry (Feb. 26 to Mar 15, 2024)
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leaves the keeper. On the other hand, with magnetic assemblies, it is thought that the drop is moderate because
the different poles of the magnetic assemblies attract each other even when they are separated from eachother. Therefore, it can be evaluated that magnetic assemblies are more resistant to air gaps because they canattract each other farther away from each other (attractive force) even when they are separated. Accordingly,
when magnetic assemblies are paired with each other, a stronger retentive force can be obtained in a smaller
space, and they are also found to be more resistant to air gaps.

(a)(b)
Fig. 5 Schematic diagram of magnetic flux
flow in the magnetic attachments (a)combination of magnetic assembly andkeeper, (b) a pair of magnetic assemblies(a)(b)
Fig. 6 Images of magnetic flux flow after separationof mating faces. (a) magnetic assembly and keeper
combination, (b) pair of magnetic assemblies

2. Resistance force during lateral movement
In a similar past study10), the coefficients of static and dynamic friction between the magnetic assembly
and the keeper of a Physio Magnet 5213 were 0.17 and 0.13, respectively. The material used for the magnetic
assembly and the keeper of this magnetic attachment is the same magnetic stainless steel. Therefore, it canbe concluded that the coefficient of friction between the magnetic assemblies is the same as that between themagnetic assembly and the keeper. The frictional force is proportional to the normal force but independentof the contact surface area (Amonton's law). In this study, the attractive force of a magnetic assembly acts asthe normal force. We therefore calculated the dynamic frictional force at each position where the magnetic
assembly moved laterally, based on the data of the attractive force between the magnetic assemblies and thecoefficient of dynamic friction. The results are shown in Figure 7 alongside the resistance force. The resistiveforce was larger than the dynamic frictional force calculated. This fact means that, as in the previous studies10),
the attraction force in the direction parallel to the mating surface due to the magnetic force between magnetic
assemblies is included in the resistance force.
The difference between the resistance force and the dynamic friction force was calculated to obtain thelaterally attraction force due to the magnetic force at each position. The maximum static friction force at eachposition moved sideways was calculated from the attractive force data and the static friction coefficient. Theresults are shown in Figure 8. As this figure shows, when the magnetic assembly is displaced by more than
0.5 mm, the attraction force due to the magnetic force exceeds the maximum static frictional force, and thus
becomes a restoring force, restoring the magnetic assembly to the position where the center coincides withthe center. Since the frictional force when the magnetic assembly is moving is the dynamic frictional force,it theoretically returns to the 0.3 mm position. Consequently, a large restoring force can be obtained whenmagnetic assemblies are paired with each other.
2.5

3.5
3.02.0

Dynamic friction force

2.5Force (N)Force (N)Dynamic friction force

Resistance force

2.0
1.5
1.0

Maximum static friction force
Magnetic attraction force

1.5
1.0

0.5

0.5
0.0
0.0

2.0
4.0
6.0
Horizontal displacement (mm)Fig. 7 Dynamic friction force and resistance force
corresponding to different positions of horizontal
displacement of magnetic attachment

0.0
0.0

2.0
4.0
6.0
Horizontal displacement (mm)Fig. 8 Magnetic attraction force and maximum
static and dynamic friction forces at eachdisplaced position of magnetic attachment[Web Presentation] PS4-4-4

The 23rd International Conference on Magnetic Applications in Dentistry (Feb. 26 to Mar 15, 2024)
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3. Advantages in clinical application
Since dental magnetic attachments do not provide adequate retentive force if they are misaligned,alignment of the magnetic assembly when embedded in the denture is important, but the technique is difficult
and requires a certain amount of sense and experience. However, when magnetic assemblies are used together,restoring forces guide both magnetic assemblies to the correct position (a position with no misalignment of
the axes of both), so that anyone can easily and correctly align them without depending on their skills. Whenfunctioning, the retentive force is stronger than when combined with a keeper of the same size. Also, when
the patient wears the denture, the restoring force guides the denture to the correct position. Since the weightof a complete denture is between 20 and 40 g and the frictional force is hardly increased, the restoring force
is sufficient to move the denture. This is a great advantage for patients who have difficulty in taking adaptive
action and for caregivers working in nursing homes.

Conclusion
The retentive force was greater when the magnetic assemblies were combined with each other than withthe keeper, and the decrease in retentive force after the mating surfaces separated was moderate. The
resistance force against lateral movement was greater than the dynamic friction force, and the difference, thelaterally magnetic attraction force, exceeded the maximum static friction force. Therefore, it was found thatcombining cup-yoke type magnetic assemblies with each other facilitates alignment and provides restoring
force.

Acknowledgments
The authors greatly acknowledge KEDC Co., Ltd. for providing magnetic assemblis (Physio Magnet 5213)
with the magnetization direction reversed.

References
1. P. Ceruti, SR. Bryant, JH. Lee, MI. MacEntee: Magnet-retained implant-supported overdentures: review
and 1-year clinical report, J Can Dent Assoc, 76, a52, 2010.
2. M. Cune, F. van Kampen, A. van der Bilt, F. Bosman: Patient satisfaction and preference with magnet,
bar-clip, and ball-socket retained mandibular implant overdentures: a cross-over clinical trial, Int J
Prosthodont, 18(2), 99-105, 2005.
3. JS. Ellis, G. Burawi, A. Walls, JM. Thomason: Patient satisfaction with two designs of implant supported
removable overdentures; ball attachment and magnets, Clin Oral Implants Res, 20(11), 1293-1298, 2009.
4. C. Ohkubo: Appropriate procedures and viewpoints for magnetic attachments, J J Mag Dent, 31(1), 1-6,2022.
5. A. Kikuchi: Magnet denture – from DMA study group to application of health insurance, J J Mag Dent,32(1), 9-13, 2023.
6. Y. Tanaka, New dental magnetic attachment, pp 2-90, Ishiyaku Publishers, Inc, Tokyo, 2016.
7. Y. Takada, M. Takahashi, Y. Kinouchi, Y. Nakamura, Y. Tanaka, H. Sato, A. Izumida and T. Tenkumo:
Materials and internal structures of foreign-made dental magnetic attachments, J J Mag Dent, 22(1), 96102, 2013.
8. M. Takahashi, G. Togawa, M. Kanyi, K. Ishikawa Y. Takada: Retentive force of combined sandwich-typemagnetic assemblies, J J Mag Dent, 32(2), 18-22, 2023.
9. N. Ishihata, H. Mizutani and M. Ai: Application of ferromagnetic alloy for prosthodontics Part 5.
Application of magnetic attachment for prosthetically hopeless teeth, J JpnProsthodont Soc, 31(6), 14451453, 1987.
10. M. Takahashi, G. Togawa, K. Numazaki, M. Kanyi and Y. Takada: Resistance force of magneticattachments against external lateral displacement, J J Mag Dent, 31(2), 4-12, 2022.
11. ISO 13017:2020. Dentistry—Magnetic attachments.

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