Investigation of an optimal magnetic attachment structure using
three-dimensional finite element method-An influence of different magnetic assembly and keeper structure on attractiveforceH .Nagai1, H .Kumano 1, R. Kanbara 1, A. Andou 1, K. Tuda 1, T. Iwata 1,Y .Nakamura 1, Y. Takada2 and Y .Tanaka1
1

Department of Removable Prosthodontics, School of Dentistry, Aichi-Gakuin University2

Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

Abstract
Magnetic attachments are designed to exert an attractive force at clinically useful levels. However, more
improvement is necessary considering strict clinical conditions. The present study analyzed andinvestigated magnetic attachments from the point of magnetic circuit using a three-dimensional finite
element method to enhance the performance of magnetic attachments.
An analysis model was constructed based on a dental magnetic attachment (GIGAUSS D 600, GC).
Round shaped non-magnetic body was embedded in the shield disk of a magnetic assembly and center of
the attractive surface of a keeper in the analysis model. Analysis was performed by changing the diameterof a non-magnetic material by 0.05 mm. Magnetic flux density distribution and attractive force wereevaluated by the analysis.
An increase in magnetic flux density on the attractive surface was confirmed by embedding a
non-magnetic body to a magnetic assembly and a keeper. However, magnetic flux density wasoversaturated when it exceeded a certain value. A similar tendency was confirmed in attractive force.

Introduction
Magnetic attachments have been continuing to improve. Various magnetic circuits have been designed sothat the minimal size of magnetic attachment can exert high attractive force.
A magnetic attachment consists of a magnet assembly and a keeper. A magnet in the magnetic assembly is
encapsulated by magnetic and non-magnetic bodies. Magnetic flux can penetrate a magnetic body, butcannot penetrate a non-magnetic body. Magnetic flux is the magnetic line of forces. It penetrates amagnetic body and forms the closed magnetic circuit that exerts attractive force when a magnetic assembly
and a keeper come into contact1）.
Attractive force is affected by attractive surface area of a magnetic assembly and a keeper, and magnetic
flux density. Since the size of a magnetic attachment should be minimal, it is impossible to increase theattractive surface area of a magnetic assembly and a keeper2）. Attractive force of a magnetic attachment canbe effectively increased by increasing magnetic flux density. A magnetic circuit changes by incorporating a
non-magnetic body in the inner structure of a magnetic assembly and a keeper, and this may increase amagnetic flux density. In other words, clinically-feasible magnetic assemblies and keepers can bedeveloped by introducing an optimal magnetic circuit. Finite element method is considered the mosteffective method to optimize the magnetic circuit as it can visualize the dynamic behavior of the magnetic
circuit inside a magnet, and simulation can be performed by changing the conditions.

Objective
A non-magnetic body was embedded in the center of a magnetic assembly shield disk and center of theattractive surface of a keeper. Three-dimensional finite element method was performed to analyze theinfluence of a difference in the magnetic circuit on the attractive force, and to optimize the magnetic circuit.

Materials and Methods
1. Analysis model
The size of a magnetic assembly was 1.8 mm in radius and 1.3 mm in height, and a magnet inside themagnetic assembly was a round shape, and was 1.3 mm in radius and 0.5 mm in height. The size of a ring
was 0.2 mm in width and 0.2 mm in height. A shield disk was 1.1 mm in radius and 0.2 mm in height. A
keeper was a round sharp, and was 1.8 mm in radius and 0.7 mm in height. Considering the model was
axial symmetry, 1/4 model was set as a basic model (Fig. 1).

Fig .1 Basic modelAnalysis range was 2 mm around a magnetic assembly and a keeper, and the analysis of the factor wasperformed. Marc mentat 2010 (Multi-Purpose Finite Element Pre and Post Processor, MSC) was used formodel construction, and μ-MF (electromagnetical field analysis system, μ-TEC) analysis software was used.
Element type was three-dimensional pentahedron and hexahedron elements. The element count was 53,802,
and nodal point count was 57,784.
The components of a magnet were Ne-Fe-B (Neodymium, ferrum, boron), and its magnetic properties werecalculated based on the thermal property of GIGAUSS D 600 and values provided by a manufacturer 3）. The

component of a yoke and a keeper was SUS447J1, and the B-H curve of the magnetic properties wascalculated by the approximation formula (Table 1).

Table 1Analysis conditions

2. Analysis items
A non-magnetic body was embedded in the center of the shield disk of a magnetic assembly and center of
the attractive surface of a keeper. The radius of a non-magnetic body was changed by 0.05 mm incrementsfrom 0.05 mm to 0.5 mm in the center of a shield disk (10 patterns in total)(Fig. 2).

Fig.2

Analysis item of magnetic assembly

In the center of the attractive surface of a keeper, the radius of a magnetic body was changed by 0.05 mmincrements from 0.05 mm to 1.0 mm, and the depth was changed by 0.1 mm from 0.1 mm to 0.6 mm (120patterns in total)(Fig. 3).

Fig.3

Analysis item of keeper

These patterns were combined, and a total of 1,200 patterns were analyzed (Fig. 2). Analysis result wasevaluated as magnetic flux density and attractive force.

Fig.4

Total patterns

Results
1. Attractive force
Fig. 3 shows the influence of the radius of a non-magnetic body embedded in the keeper attractive surface
on the attractive force for the depth where the radius of a non-magnetic body in the center of a shield disk
was 0.15 mm. There was no influence of depth until the radius of a non-magnetic body in the attractive
surface of a keeper reached 0.5 mm. Attractive force was the highest at 0.5 mm in radius. When the radius
exceeded 0.55 mm, attractive force started to decrease and was affected by the depth.

Fig.5

Influence of the depth

Fig. 4 shows the influence of a change in radius of a non-magnetic body in the attractive surface of a keeper
on attractive force for the radius of a non-magnetic body in the center of a shield disk. Since there was alittle influence of the depth of a non-magnetic body until the radius of a non-magnetic body in the center ofa keeper attractive surface reached 0.5 mm where attractive force continued to increase (Fig. 3), the depthof a non-magnetic body was set at 0.1 mm. Attractive force increased with an increase of a radius of thenon-magnetic body in the center of a keeper attractive surface. The attractive force reached a maximum of598 gf when a radius of a non-magnetic body in the center of a shield disk was 0.15 mm and that in thecenter of an attractive surface of a keeper was 0.5 mm, but decreased thereafter with an increase of a radiusof a non-magnetic body on the attractive surface of a keeper. When attractive force of the basic model wasdefined as 100%, the attractive force was increased to approximately 110% at 0.15 mm radius of a
non-magnetic body in the center of a shield disk and 0.5 mm radius of a non-magnetic body in the center ofan attractive force of a keeper where attractive force reached the maximum.

Fig.6 Influence of shield disk and keeper2. Magnetic flux density distribution
Fig. 5 shows a typical magnetic flux density distribution of the analysis results. The radius of a
non-magnetic body in the center of an attractive surface of a keeper was changed when the radius of a
non-magnetic body in the center of a shield disk was 0.15 mm and the depth of a non-magnetic body in thecenter of an attractive surface of a keeper was 0.1 mm.
An increase in the magnetic density was confirmed in the magnetic assembly and attractive surface of akeeper. When the radius of a non-magnetic body in the center of an attractive surface of a keeper exceeded
0.75 mm, the magnetic flux density in the magnetic assembly and on the attractive surface of a keeper
became oversaturated, and a decrease in the magnetic flux density in the magnetic assembly and inside akeeper was observed.

Fig.7 Magnetic flux density distribution

Discussion
1．Efficiency of finite element method
It is difficult to measure and observe the detail of behavior of attractive and repelling force created by amagnet. This is because the magnetic field has a gradient in all directions, and, therefore, simple calculation
formula cannot be established. Although it is possible to measure magnetic force and magnetic field atspecific location, it is difficult to design the magnetic circuit from the measurements that exerts themaximum attractive force and verify optimal magnetic circuit that minimizes magnetic field leakage. Finite
element method is the only way to investigate the inner behavior of the magnetic circuit. Magnetic circuitcompartments were considered as micro-compartment to solve the simultaneous equation. Finite element
method allows visualization and simulation of the inner behavior of the magnetic circuit by adding various

conditions. It is considered time-efficient and cost-effective to search optimal magnetic circuit using a finite
element method.
2．Accurate of the analysis result of the present study
The magnetic field analysis was performed in the present study. Since there is a magnetic field distribution
in the space, it is prerequisite that the paths of integration in the space around the analysis model and theinterface between a magnetic assembly and a keeper are subdivided. Exploratory analysis was performed tocalculate the value with the least effect. Therefore, the analysis result of the present study is consideredhighly accurate4）.
3．The relationship between the attractive surface area and magnetic flux density
The attractive force of a magnet can be expressed as F = (1/2μ0)・S・B2{μ0: space permeability, S:attractivesurface area, B: magnetic flux density}5）. The attractive force of a magnetic attachment is affected more bymagnetic flux density than attractive surface area. Therefore, attractive force can be increased efficiently byincreasing the magnetic flux density. The magnetic circuit changes by replacing part of a keeper of amagnetic attachment with a non-magnetic body, resulting in an increase in the magnetic flux density on theattractive surface. The attractive force was affected more by an increase in the magnetic flux density than adecrease in the attractive surface area, resulting in an increase in the attractive force. However, there is alimit of magnetic flux density in the magnetic body called “saturated magnetic flux density”. When themagnetic body reaches that point, an increase in the magnetic flux density stops even with the continuous
increase of the size of a non-magnetic body. As a result, the attractive force decreases due to an influence of
the attractive surface area. The relationship between the attractive surface area and magnetic flux density isextremely important for the optimization of the magnetic circuit.
4．Inference of the depth
In the present study, a non-magnetic body was embedded in the center of a shield disk and attractive
surface of a keeper. The magnetic circuit of a magnetic assembly and inside a keeper was changed bychanging the radius of a non-magnetic body, resulting in an increase in the magnetic flux density
distribution on the attractive surface. The attractive force is affected more by the magnetic flux density thana decrease in the attractive surface area, resulting in an increase in the attractive force. The attractive force
reached its maximum at 0.15 mm radius of a non-magnetic body in the center of a shield disk and 0.5 mm
radius of a non-magnetic body in the center of an attractive surface of a keeper. When the magnetic flux
density on the attractive surface became oversaturated, attractive force decreased due to a decrease in themagnetic flux density and attractive surface area. When the radius of a non-magnetic body in the center of ashield disk is constant, the attractive force continued to increase until the radius of a non-magnetic body isincreased to 0.5 mm. The attractive force is affected by an increase of the magnetic flux density on theattractive surface, and is rarely affected by the depth of a non-magnetic body. However, when the radius ofa non-magnetic body in the center of an attractive surface of a keeper exceeds 0.5 mm, the magnetic flux
density on the attractive surface becomes oversaturated. The magnetic flux that could not penetrate theattractive surface flows into the non-magnetic body. The magnetic flux is hard to penetrate a non-magneticbody, but a small amount of magnetic flux can flow. The deeper the non-magnetic body gets, the moredifficult the magnetic flux can penetrate the non-magnetic body. It is considered that a decrease in theattractive force is caused by the depth of a non-magnetic body.
Further analyses are necessary to optimize the magnetic circuit.

Conclusion
The influence of a non-magnetic body in the center of a shield disk and attractive surface of a keeper wasanalyzed and investigated using a three-dimensional finite element method, and the following results wereobtained:
1．In the present analysis model, the optimal inner structure of a magnetic attachment was 0.15 mm radiusof the non-magnetic body in the center of a shield disk and 0.5 mm radius of the non-magnetic body inthe center of an attractive surface of a keeper.
2．The attractive force increased until the optimal inner structure value was reached, and decreased
thereafter with an increase of the radius.
3．The influence of the depth of a non-magnetic body in the center of an attractive surface of a keeper wassmall until the radius reached the value where the maximum attractive force was achieved.
4．When the radius of a non-magnetic body in the center of a shield disk and attractive surface of a keeper
exceeded the value where the maximum attractive force was achieved, the magnetic flux density on theattractive surface became oversaturated.

References
1．Y.Kinouchi:Fundamental physical properties of magnetic attachment,sika Journal,17-26,1993
2．O.Okuno:Structure and characteristics of magnetic attachments,Tohoku Univ.Dent.J,13:1-10,1994
3．T.Miyata,J.Niimi,A.Ando and et al:Infuence of heating of a magnetic attachment on the attractiveforce,JJ mag Dent,17:44-50,2008
4．Y.Tegawa,Y.Kimouchi:Infuruences on attractive force in different clinical uses of a cup yoke magnetic
attachments:JJ mag Dent,5:31-38,1996
5．Y.Nakamura:Stress Analysis of an Overlay Denture and a Mgnetic Attachment using Finite Element
Method:Nihon Hotetsu Shika Gakkai Zasshi,42(2),234-245,1998