Influence of inclination angle of attractive surface on the attractive force ofmagnetic attachment with optimal structural design.
H Kumano. 1, H Nagai.1, R Kanbara. 1, T Masuda.1, Y Nakamura.1, K Shoji.1,Y Takada.2,Y Tanaka3 andJ Takebe.1
1Department of Removable Prosthodontics, School of Dentistry, Aichi Gakuin University

2

Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

3

Aichi Gakuin University

Abstract
We analyzed and investigated the influence of the inclination angle of attractive surfaces on the attractiveforce in the magnetic attachment with the optimal structure design by using the three-dimensional finite
element method. Two types of analysis models were constructed: basic model and optimal model with
optimal structure design. In the analysis items, the attractive force when the magnetic assembly and thekeeper were in contact with each other, and the inclination and the detachment with the one end of thekeeper as a fulcrum were considered. There were 21 different inclination angles of the attractive surface
ranging from 0 to 20 in 1 degree increments. The keeper was observed with regards to an increase in theinclination angle of the attractive surface and the related decrease in the magnetic flux density inside themagnet assembly using both the basic model and the optimal models were. The attractive force in both thebasic model and the optimal model decreased in inverse proportion to the inclination angle of attractivesurface. The results of this analysis suggest that the magnetic attachment with the optimal structural design
is strongly influenced by the inclination angle of attractive surface.

Introduction
Recently magnetic attachments have continued to improve. Various magnetic circuits have been designed
so that a minimal size of magnetic attachment can exert a high attractive force. A magnetic attachment
consists of a magnet assembly and a keeper. A magnet in the magnetic assembly is encapsulated bymagnetic and non-magnetic materials. Magnetic flux can penetrate a magnetic body, but cannot penetratenon-magnetic material. Magnetic flux is the magnetic line of forces. It penetrates magnetic materials andforms the closed magnetic circuit that exerts attractive force when a magnetic assembly and a keeper comeinto contact.
Up to now, for the purpose of further improving the attractive force of magnetic attachment, thefollowing methods have been carried out: 1) Change of the magnetic circuit of magnetic attachment
structure, 2) Analysis on the attractive force, and 3) Using a three-dimensional finite element method1). As aresult of these methods, the central portion of the keeper and magnet set of non-magnetic material isapplied to the optimal structure, it was confirmed that there was an improvement in the attractive force ofmagnetic attachment2).

Objective
Three-dimensional finite element method was performed to analyze influence of attractive surface
inclination on the attractive force of magnetic attachment with optimal structural design.

Materials and Methods
1. Analysis model
The size of the magnetic assembly was 3.6 mm in diameter and 1.3 mm in height, and a magnet inside themagnetic assembly was a round shape, and was 2.6 mm in diameter and 0.5 mm in height. The size of thering was 0.2 mm in width and 0.2 mm in height. The disk yoke was 2.2 mm in diameter and 0.2 mm inheight. The keeper was round and sharp, and was 3.6 mm in diameter and 0.7 mm in height.
Considering the models were line-symmetry, half of the model is shown as the basic model (Fig. 1) andthe other half is shown as the optimal model (Fig.2). The optimal model structural design is the same as thebasic model but also has non-magnetic material inserted into the magnetic attachment.
Analysis range was 3.0 mm around a magnetic assembly and a keeper. 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. The element type was athree-dimensional pentahedron and hexahedron elements. The element count was 107,604, and nodal point
count was 112,468.

Fig.1 Basic model
2. Analysis condition

Fig.2 Optimal model
Table 1 Analysis conditions

The components of the magnet were
Ne-Fe-B (Neodymium, ferrum, boron),and its magnetic properties werecalculated based on the thermal propertyof GIGAUSS D 600 and values provided
by a manufacturer3）. The component ofthe disk yoke and the keeper wasmeasurement of magnetic properties of
SUSXM27, and the B-H curve of themagnetic properties was calculated by the approximation formula (Table 1)4).

3. Analysis items
From the condition where the magnet
assembly and the keeper were in contact witheach other in the optimal model, the attractive
force when inclined and detached from one
end of the keeper as a fulcrum was analyzed.
There were 21 different inclination angles of
the attractive surface ranging from 0 to 20 in
1 degree increments. In addition, the same
analysis item was used in the basic modelFig. 3 Analysis items(Fig. 3).
Analysis result was evaluated as magnetic flux density vs. attractive force.

Results
1. Magnetic flux density distribution
Representative magnetic flux density distribution (Fig. 4, 5).

Fig. 4 Magnetic flux density distribution(Basic Model)

Fig. 5 Magnetic flux density distribution(Optimal Model)

In both the basic model and optimal models, concurrent with an increase in the inclination angle of theattractive surface, a decrease in the magnetic flux density inside the magnet assembly, the keeper, and the in
the magnetic flux density in the disk yoke on the right side of the magnet assembly was observed. Inaddition, an increase of magnetic field leakage at the top of the keeper of attractive surface was observedwith the increase of the inclination angle of the attractive surface in both the basic model and the optimalmodel. Inclination angles of 0,1, and 5 degrees of the attractive surface when comparing the basic andoptimal model showed an increase of the magnetic flux density at the shield disk of the magnet assembly
was observed in the optimal model. However, at 7 and 10 degrees, this increase in magnetic flux density
was not observed.

2. Attractive force
A graph of the analysis of theattractive force results is shown(Fig. 6). Attractive force in both thebasic and optimal models
decreased in inverse proportion to
the inclination angle of attractivesurface. The inclination angles ofattractive surface up to 5 degrees
was more optimal in the model
than in the basic model, it was thus
Fig.6 Attractive force

confirmed that the attractive force is large.

When the inclination angle of attractive surface was 6 degrees or more, it was confirmed that the attractive
force was almost the same for both the basic and optimal models.
The reduction rate of the attractive force in the inclination angle of attractive surface of 6 degrees was
about 44% in the basic model and about 58% in the optimal.

Discussion
1．Efficiency of finite element method
It is difficult to measure and observe the details of the behavior of attractive and repelling forces createdby a magnet. This is because the magnetic field has a gradient in all directions, and, therefore, a simple
calculation formula cannot be established. The 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 for optimal magnetic circuits using the finite element method.
2．Efficiency of analysis model
Magnets have a magnetic field distribution in space defined as a “leaky magnetic field.” In other words, it
has a magnetic field around the magnetic attachment. Therefore, the accuracy of the analysis results will beincreased if the analysis range of the magnetic structure of the magnetic attachment and the circumferenceof the keeper are analyzed. In this study, we confirmed the range of magnetic field leakage, and analyzed
the elements of the magnet assembly and the keeper around 3mm in the construction model. In the finalanalysis, the accuracy of the analysis in this model is high.
3．The relationship between the attractive force 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}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 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 magnetic flux density than

by a decrease in the attractive surface area, resulting in an increase in the attractive force.
However, from the results of this analysis, the reduction rate of the attractive force was larger in theoptimal model than in the basic model. The reason is that the optimal model sets the non-magnetic material
in the center of the magnet assembly and keeper, so as to increase as much as possible the magnetic flux
density. Therefore, in the optimal model, since the attractive surface of the keeper is inclined and detached,
the magnetic flux density distribution inside the magnetic assembly and the keeper are strongly influenced,
so that the reduction rate of the attractive force becomes larger than the basic model considered.

Conclusion
The results of this analysis using the three-dimensional finite element method for determining the effect of
the inclination angle of attractive Surface on the magnetic flux density distribution and the attractive force
in the magnet attachment which gave optimal structural design obtained the following conclusions:
1. The influence on the magnetic flux density distribution by the inclination angle of attractive surface waslarger in the optimal model than in the basic model.
2. The reduction rate of the attractive force by the inclination angle of the attractive surface was larger inthe optimal model than in the basic model.
3. The results of this analysis suggested that the magnetic attachment with the optimal structural design isstrongly influenced by the inclination angle of attractive surface.

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