Optimal structural design evaluation
three-dimensional finite element methodofmagnetic

attachmentsusing

H Nagai.1, H Kumano. 1, R Kanbara. 1,T Itakura.1, K Hayashi.1,A Ando.1,T Masuda.1,Y Nakamura.1,Y Takada.2,Y Tanaka1 and J Takebe.1
1Department of Removable Prosthodontics, School of Dentistry, Aichi-Gakuin University

2

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,improvement of the attractive force is necessary, in order to deal with complexed clinical conditions. The
present study analyzed and investigated magnetic attachments from the point of a magnetic circuit using athree-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 non-magnetic material was embedded in 1) the disk yoke only , 2) the keeper only and 3) both thedisk yoke and keeper in the analysis model. Magnetic flux density distribution and attractive force wereanalyzed by changing the diameter of non-magnetic material by 0.05 mm.
An increase in magnetic flux density on the attractive surface was confirmed by embedding non-magnetic
material to the magnetic assembly and the keeper. However, magnetic flux density was oversaturated when
it exceeded a certain value. A similar tendency was observed 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 materials. Magnetic flux can penetrate a magnetic body, butcannot penetrate non-magnetic material. Magnetic flux is the magnetic line of forces. It penetrates magnetic
materials and forms the closed magnetic circuit that exerts attractive force when a magnetic assembly and akeeper 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
non-magnetic material in the inner structure of a magnetic assembly and a keeper, and this may increase amagnetic 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 mosteffective 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
Three-dimensional finite element method was performed to analyze the influence of differences in themagnetic circuit on the attractive force, and to optimize the magnetic circuit by changing the internal
structure of magnetic attachment.

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 disk yoke was 1.1 mm in radius and 0.2 mm in height. Akeeper 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).
Analysis range was 2.0 mm around a magnetic assembly and a keepe. Marc mentat 2010 (Multi-Purpose
Finite Element Pre and Post Processor, MSC) was used for model construction, and μ-MF
(electromagnetical field analysis system, μ-TEC) analysis software was used. Element type wasthree-dimensional pentahedron and hexahedron elements. The element count was 53,802, and nodal point
count was 57,784.
The components of a magnet were Nd-Fe-B (Neodymium, Ferrum, Boron), and its magnetic properties
were calculated based on the thermal property of GIGAUSS D 600 and values provided by amanufacturer3）. The component of a yoke and a keeper was measurement of magnetic properties ofSUSXM27, and the B-H curve of the magnetic properties was calculated by the approximation formula(Table 1).

Table 1 Analysis conditions

Fig. 1 Basic model
2. Analysis items(1) The disk yoke only
Non-magnetic material was embedded in the center of the disk yoke of a magnetic assembly and center of
the attractive surface of a keeper. The radius of non-magnetic material was changed by 0.05 mm incrementsfrom 0.05 mm to 1.0 mm in the center of a disk yoke (20 patterns in total)(Fig. 2).

(2) The keeper only
In the center of the attractive surface of a keeper, the radius of non-magnetic material was changed by
0.05 mm increments from 0.05 mm to 1.0 mm, and the depth was changed by 0.1 mm from 0.1 mm to 0.6mm (120 patterns in total)(Fig. 3).

Fig. 2 Analysis item

Fig. 3

Analysis item

Fig. 4

Analysis item

(3) Both the disk yoke and keeper
Part of (1) and (2) were respectively combined, anda total of 1,200 patterns were analyzed (Fig. 4).
Analysis result was evaluated as magnetic flux
density and attractive force.

Results
Attractive force and Magnetic flux density distribution(1) The disk yoke only
A graph of the attraction force of the analysis result is shown (Fig. 5). Gradual increase in the attractive
force was observed. The attractive force reached the maximum of 560 gf when a radius of non-magnetic
material in the center of a disk yoke was 0.3 mm, but decreased thereafter with an increase of a radius of
non-magnetic material.
Representative magnetic flux density distribution (Fig. 6). An increase in the magnetic density wasconfirmed in the magnetic assembly and attractive surface of a keeper. When the radius of non-magnetic
material in the center of a disk yoke exceeded 0.3 mm, the magnetic flux density in the magnetic assemblyand on the attractive surface of a keeper became oversaturated, and a decrease in the magnetic flux density
in the magnetic assembly and inside a keeper was observed.

F
Fig. 5

Attraction force

Fig. 6

Magnetic flux density distribution

(2) The keeper only
A graph of the attraction force of the analysis result is shown (Fig. 7). Gradual increase in the attractive
force was observed. The attractive force reached the maximum of 582 gf when a radius of non-magnetic
material in the center of a keeper was 0.6 mm, but decreased thereafter with an increase of a radius of
non-magnetic material. There was a little influence of the depth of non-magnetic material until the radius of
non-magnetic material in the center of a keeper attractive
surface reached 0.6 mm where attractive force continued toincrease.
Representative magnetic flux density distribution (Fig. 8).
An increase in the magnetic density was confirmed in themagnetic assembly and attractive surface of a keeper. Whenthe radius of non-magnetic material in the center of anFig. 7

attractive surface of a keeper exceeded 0.6 mm, theAttraction force

magnetic flux density in the magnetic assembly and on theattractive surface of a keeper became oversaturated, and adecrease in the magnetic flux density in the magnetic
assembly and inside a keeper was observed.
(3) Both the disk yoke and keeper
A graph of the attraction force of the analysis result isshown (Fig. 9). This is the influence of the radius ofnon-magnetic material embedded in the keeper attractive

Fig. 8Magnetic flux density distribution

surface on the attractive force for the depth where theradius of non-magnetic material in the center of a disk yoke
was 0.15 mm. There was no influence of depth until theradius of non-magnetic material in the attractive surface ofa 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 thedepth.

Fig. 9 Attraction force (Influence of the depth)

A graph of the attraction force of the analysis result isshown (Fig. 10). This is the influence of a change in radiusof non-magnetic material in the attractive surface of akeeper on attractive force in the center of a disk yoke. Since
there was a little influence of the depth of non-magnetic
material until the radius of non-magnetic material in thecenter of a keeper attractive surface reached 0.5 mm where
attractive force continued to increase (Fig. 9), the depth of
non-magnetic material was set at 0.1 mm. Attractive force

Fig. 10

Attraction force(Influence of disk yoke and keeper)increased with an increase of a radius of non-magnetic
material in the center of a keeper attractive surface. The
attractive force reached the maximum of 598 gf when aradius of non-magnetic material was 0.15 mm and that of akeeper was 0.5 mm, but decreased thereafter with anincrease of a radius of non-magnetic material on theattractive surface of a keeper.
Representative magnetic flux density distribution (Fig.

Fig. 11

Magnetic flux density distribution

11). This is the radius of non-magnetic material in thecenter of an attractive surface of a keeper was changed
when the radius of non-magnetic material in the center ofa disk yoke was 0.15 mm and the depth of non-magnetic
material in the center 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 a keeper.

Fig. 12 Optimal structural design model

When the radius of non-magnetic material in the center ofan attractive surface of a keeper exceeded 0.75 mm, the magnetic flux density in the magnetic assemblyand on the attractive surface of a keeper became oversaturated, and a decrease in the magnetic flux density
in the magnetic assembly and inside a keeper was observed.
From the analysis result so far, when attractive force of the basic model was defined as 100%, theattractive force was increased to approximately 110% at 0.15 mm radius of non-magnetic material in thecenter of a disk yoke, 0.5 mm radius of non-magnetic material in the center of an attractive force of akeeper and 0.1 mm the depth of non-magnetic material in a keeper where attractive force reached themaximum (Fig. 12).

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. Finite element method allows visualization and simulation of the inner
behavior of the magnetic circuit by adding various conditions. It is considered time-efficient andcost-effective to search optimal magnetic circuit using a finite element method.
2．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:attractive
surface area, B: magnetic flux density}4）. The attractive force of a magnetic attachment is affected more bymagnetic flux density than attractive surface area5）. Therefore, attractive force can be increased efficiently
by increasing the magnetic flux density. The magnetic circuit changes by replacing part of a keeper of amagnetic attachment with non-magnetic material, resulting in an increase in the magnetic flux density on
the attractive surface. The attractive force was affected more by an increase in the magnetic flux density
than a decrease in the attractive surface area, resulting in an increase in the attractive force. However, there
is a limit 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 non-magnetic material. As a result, the attractive force decreases due to an influenceof the attractive surface area. The relationship between the attractive surface area and magnetic flux density
is extremely important for the optimization of the magnetic circuit.
3．Inference of the depth
The attractive force is affected by an increase of the magnetic flux density on the attractive surface, and israrely affected by the depth of non-magnetic material. However, when the radius of non-magnetic material
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 the attractive surface flows into
non-magnetic material. The magnetic flux is hard to penetrate non-magnetic material, but a small amountof magnetic flux can flow. The deeper non-magnetic material gets, the more difficult the magnetic flux canpenetrate non-magnetic material. It is considered that a decrease in the attractive force is caused by thedepth of non-magnetic material.

Conclusion
Optimal structural design evaluation of magnetic attachments was analyzed and investigated using athree-dimensional finite element method, and the following results were obtained:
1. An increase in the attractive force was confirmed by setting non-magnetic material inside the magneticattachment and changing the magnetic circuit.
2. It was confirmed that the increase in the attractive force was greater when the non-magnetic material was
set at the center of an attractive surface of a keeper than the center of a disk yoke of the magnetic assembly.
3. The influence of the depth of non-magnetic material in the center of an attractive surface of a keeper wassmall compared to the size of the radius.

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