Attractive Force of the Magnetic Attachment Using
Three-Dimensional Finite Element Method-An Influence of Magnetic CircuitH. Kumano, Y. Nakamura, H. Nagai, R. Kanbara, T. Masuda, K. Hayashi, Y. Takada1, Y. Ohno,
Y. Tanaka
Department of Removable Prosthodontics, School of Dentistry, Aichi-Gakuin University
1
Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

Introduction
The functional retention of dental magnetic attachments is based upon the simple physics of magnetic
attractive force. Permanent magnets used as early dental magnetic attachments were first introduced inearly 1950’s, and were applied in different mechanical applications and clinical uses. Magnet implantation
to the jaws1), and an opposing use of magnetic repulsion2) are two main examples. Various magnetic
attachments designs of significant design have since been developed. As stainless steel micro laser welding
technology became available in the 1990’s, corrosion resistance was improved by the protective stainlesssteel encasement covering. These newer encased magnets provided improved corrosion resistance andimproved magnetic attachment retention and clinical durability. As newer magnetic materials have beendeveloped, the advantages of size reduction, stronger attractive retentive force, and improved clinical utility
and use have substantially improved the range of useful applications compared to earlier versions
previously available.
While certain types of esthetically hidden precision attachments are considered rigid and inflexible,
magnetic attachments are considered more capable of stress release due to an inherent ability to minimize
and reduce unfavorable horizontal mechanical force transfer. Reduced horizontal force transfer for
prosthetic retentive elements has been considered advantageous in preventing abutment overload andunwanted breakdown. A smaller attachment size is also of greater benefit for esthetic adaptability andconstrained space applications. 3-5).
Different designs of keeper and magnetic assembly have been developed to reduce attachment size andprovide optimum attractive force for useful retention. Different designs have been shown to vary inmagnetic circuit and retention strength. An ideal design will have an optimal magnetic circuit, providing
for the development of a magnetic attachment assembly of high retentive value for clinical application
while maintaining a minimal profile requirement.
Finite element analysis has been considered an effective means of magnetic circuit evaluation for theevaluation of design parameters. The finite element method permits qualitative visualization the physicaldynamics of the magnets tested while also rendering quantitative values useful for comparative evaluationof different designs and conditions. Objective
Repeated load was applied on a keeper of the implant to investigate loosening at the junction between akeeper and abutment during function.

Materials and Methods
1. Analysis model
A proprietary dental magnet design was selected as an analysis sample for component configuration
testing (GIGAUSS D600, GC.) The dimensional shape and size of the test sample dental magnet weremeasured prior to modeling procedures. Comparative measurements of the outer surface structures of theattachment were obtained for comparison of manufacturer specifications and actual values obtained.
The inner structure of the magnetic attachment was evaluated by embedment sectioning and evaluation.
The magnetic assembly was embedded with embedding agent (SCANDIQUICK, SCANDIA) andsectioned using an automatic precision cutter (Isomet, BUELER). The resulting sections were evaluatedand measured using a surface shape measurement apparatus (VF-7510, KEYENCE).
The analysis model was constructed based on the measurements obtained. The size of a magnetic
assembly was 3.6 mm in diameter and 1.3 mm in height, and the inner magnetic assembly was determinedto be a round-shape with 2.2 mm diameter and 0.5 mm height dimensions. The size of the shield ring was0.2 mm in width and its height was 0.2 mm. (Fig. 1).

The shield disc components of the magnetic assembly were fabricated using a non-magnetic material as
the analysis object. The diameter of a non-magnetic material was incrementally thickened by 0.1 mm to 2.0
mm maximum thickness for each of the 21 modeling test samples prepared (Fig. 2).

Each model was fabricated as a one fourth size model. The model were designed to be axiallysymmetric. The defined scope of FEM analysis range was set as 2 mm around a keeper and magneticassembly.
The models were constructed using a general purpose finite element pre-/post-processor (Femap USG)
and an electromagnetic field analysis system (μ-MF analysis software). The shaping elements were definedby three-dimensional pentahedron and hexahedron elements. The element count was 53,802, and the nodal
points number was 57,784 (Fig. 3).

2. Analysis conditions
The magnetic property was determined based on previously obtained the thermal property data for theGIGAUSS D600 magnetic attachment6) and the manufacture’s reported thermal property data values.
Although the material of a yoke and keeper was SUSXM27, the magnetic property details are undisclosed.
An extrapolated value was thus selected. The extrapolated value used SUS447J1 material values, and wasutilized to approximate the B-H curve. The approximated curve was used for the finite element magnetic
material property values. (Table 1) Analysis results were then obtained for magnetic flex density
distribution and attractive force.

Results
1. Magnetic flux density distribution
Fig. 4 shows the magnetic flux density distribution of the analysis results. The magnetic flux density
distribution of the magnetic assembly and the attractive surface of a keeper demonstrate increase as thediameter of a non-magnetic material increases. However, as the diameter of non-magnetic material became
greater than 0.6 mm, the areas of the oversaturated magnetic flux density field were observed within theshield disk. As the diameter of a non-magnetic material increased further, the interior areas of the shielddisk became completely oversaturated with the magnetic flux density and the overall magnetic flux
distribution within the magnetic assembly decreased.

2. Attractive force
Fig. 5, records the attractive force analysis results. Attractive force moderately increased to 540 g until
the diameter of a non-magnetic material became 0.5 mm, and decreased with further increasing diameter.
When the attractive force of a non-magnetic material with 0.0 mm diameter was considered as 100%,
attractive force peaked to 103% at 0.5 mm in diameter, decreased to 100% at 0.7 mm in diameter, and 86%
at 1.2 m in diameter.

Discussion
Although direct measurement of a magnetic force and field is possible, it is extremely difficult to design amagnet that exerts the maximum magnetic force based on the measurement results, without verifying anoptimization for minimum magnetic field leakage. The present study performed a magnetic field analysis
using the 3D Finite Element Method.
As magnetic field distribution occurs in space, the space around the analysis model and integration pathon the interface between a magnet assembly and keeper should be properly contained and subdivided.
Preliminary analysis was performed and calculated optimal shield thickness values with minimal negative
influence, suggesting high analysis accuracy of the present study.
Although the specific magnetic properties of a magnetic stainless steel and magnet are important analysis
conditions, little is known about these individual properties. To solve the problem, the value of SUS447J1,

which is considered to have the close approximation magnetic properties based on formulation content as
SUSXM27, was substituted to approximate the B-H curve for the study analysis. Accurate measurement ofthese values, and a continued search for better magnetic property materials are true challenges for thefuture.
The attractive force of a magnet is defined as F = (1/2 μ0)·S·B2{μ0: space permeability, S: attractive
surface area, B: magnetic flux density}. This formula shows that attractive force is proportional to themagnetic flux density and attractive magnetic surface. Magnetic flux density is a magnetic flux flow perunit area, and shows the magnetic strength. Magnetic flux density increases with an increase of external
magnetic field. The ratio between the magnetic flux density and magnetic field is called magnetic
permeability, and higher magnetic flux density can be obtained in higher magnetic permeability even in aweak magnetic field. Since an external magnetic field was not applied in the present study, the magnetic
permeability is constant. Therefore, attractive force of a magnet increases with an increase of magnetic flux
density. Moreover, the magnetic flux density reaches a limit when magnetic field is added to magnetic
material. This is called saturated magnetic flux density, and as magnetic flux density becomes oversaturated,
it decreases as it exceeds this inversion point.
In the present study, the magnetic flux density within a magnetic assembly was significantly altered bychanging the diametric thickness of a non-magnetic shield material. Magnetic flux density within themagnetic assembly became saturated when the diameter of a non-magnetic material exceeded a 0.5 mm
threshold. Attractive force is therefore shown to be influenced by a magnetic flux density increase rather
than by a simple decrease of magnetic attractive surface area. Exceeding the threshold diameter of a
non-magnetic material resulted decreased magnetic flux density and decreased attractive surface area,lowering the resulting attractive force. Further analysis is required to obtain information and optimized
magnetic attachments.

Conclusion
A non-magnetic material was designed at the center of a shield disk of a magnetic assembly of a dental
magnetic attachment. The influence of magnetic circuit was analyzed and evaluated using athree-dimensional finite element method, and the following results were obtained.
1. Attractive force increased until the diameter of a non-magnetic material in the shield disk became 0.5mm. A peak attractive force was approximately 540 gf at 0.5 mm diameter. When the attractive force ofa non-magnetic material with 0.0 mm diameter was considered as 100%, a peak attractive force was103%.
2. Attractive force started decreasing when the diameter of a non-magnetic material in the shield disk
exceeded 0.5 mm. Attractive force decreased to 86% when the diameter of a non-magnetic material
was 1.2 mm.

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