15. Analysis of Characteristics of Attractive Force of a Magnetic Attachment Using Finite Element Method

Kumano H., Nakamura Y., Masuda T., Imaoka S., Tanaka S., Ohno Y. and Tanaka Y

Removable Prosthodontics, School of Dentistry , Aichi-Gakuin University

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Introduction

A magnetic attachment is a new retainer for a removable denture using an attractive force of a permanent magnet. This device attained widespread clinical use since the first commercially available product was introduced in 1992. Two magnetic circuits of clinically used magnetic attachment assembly are cup and sandwich types (Fig 1). It is widely known that attractive force of a magnetic attachment is markedly affected by air gap between a magnetic assembly and a keeper. However, the functional behavior of a denture using a magnetic attachment still remains to be elucidated since the mechanism of a magnetic attachment is different from that of a conventional mechanical retainer. Although Nakamura2),3) from our department has already reported an analysis of a sandwich-type magnetic attachment, the mechanism of a cup type magnetic attachment remains largely unknown.

Objective

We performed an analysis of the mechanical properties of a cup type magnetic attachment as a denture retainer using the Finite Element Method, and compared with that of a sandwich type magnetic attachment to elucidate the mechanical behavior of a denture with magnetic attachments.

Analysis Method

1:Analysis model

GIGAUSS D 600 (GC) was used as a cup type analysis sample (Fig.2). This is the most frequently used magnetic attachment in clinical settings. The measurement of a sample was performed before modeling. The measurement provided by the maker and the actual measurement were checked to know the external shape of an attachment. As for the detailed internal shape, an attachment was embedded, sliced, and measured since the maker does not provide any information. Figure. 3 shows the measured size of a sample. The MENTAT (MSC. Software) was used to construct analysis model. Figure. 4 shows the analaysis model where a magnetic assembly and a keeper are in contact in maximum area. The element type was quadrilateral element. Element count was 10302, and nodal point was 10506. Element breakdown of the analysis area 10 mm in height and width was performed, and the result was set as an analysis object range.

2:Analysis condition

The magnet used in the present study was neodymium iron boron (Nd-Fe-B), and the magnetic stainless steel for the yoke and keeper were SUS447J1. The magnetic characteristic value was determined based on the thermal characteristic of GIGAUSS D600 obtained by Miyata4) in our department and maker's catalog. The original material of a yoke and keeper was SUSXM27. However, the value for SUS447J1 which is considered to have the similar magnetic characteristics as SUSXM27 was assigned since detailed information regarding its magnetic characteristics was not provided. The B-H curve was approximated from these values, and regarded as magnetic characteristics (Table 1). The GiD (CIMNE) was used for the input of the analysis condition. The MAGNA/FIM (CTC Solution) and GiD (CIMNE) were used for the analysis and the analysis result display, respectively. Nastran format was used for the file exchange between MENTAT and GiD.

3: Analysis items

There were 8 analysis items including 4 items of vertical displacement and 4 items of horizontal displacement (Fig. 5). The amount of displacement was set based on the Nakamura's 2),3)report regarding the analysis of a sandwich-type magnetic attachment. The analyses were performed on the magnetic flux density distribution and attractive force when the vertical and horizontal displacements were applied between a magnetic assembly and a keeper.

Results

1: Magnetic flux distribution

For the vertical displacement (Fig. 6), magnetic flux distribution density in a yoke decreased with an increase of displacement amount both in the sandwich and cup types. In the cup type, an increase in the leak magnetic field around the attraction face was confirmed with an increase of the displacement amount, but no leak magnetic field was found around the upper part of a magnetic assembly as was seen in the sandwich type. For the horizontal displacement (Fig. 7), the leak magnetic field was the smallest in 0.2 mm, followed by 0.70, 1.00, and 1.50 mm. This is because the right edge of a keeper has a contact with the lateral side of a yoke in the displacement amount of 0.2 mm, but not in the other displacement amount. An increase in the magnetic flux distribution density was observed in the left side of a yoke with an increase of horizontal displacement amount. A significant change was noted in the magnetic flux density in the horizontal displacement when unilateral yoke loses contact with a keeper.

2. Attractive force

For the vertical displacement (Fig. 8), the attractive force significantly decreased with an increase of the displacement amount. The attractive force in displacement amount of 0.03 mm was 370 g in the cup type, and 500 g in the sandwich type. The reduction rate in the attractive force was 30% in the cup type, and 20% in the sandwich type. In displacement amount of 0.15 mm, the attractive force decreased by 80% in the cup type, and 63% in the sandwich type. For the horizontal displacement (Fig. 9), a decrease in the attractive force was milder compared to the vertical displacement. In displacement amount of 0.2 mm, the attractive force decreased by 10% in the cup type, and by 5% in the sandwich type. The attractive force in the displacement amount of 1.0 mm was 190 g in the cup type, and 290 g in the sandwich type. The reduction rate in the attractive force was 64% in the cup type, and 53% in the sandwich type. The decreasing trend in the attractive force during the vertical and horizontal displacements of a magnetic attachment was similar between the cup and sandwich types.

Discussions

Little is known about the detail in the dynamics of the attractive and repulsion forces created by a magnet. Although magnetic force and magnetic field can be calculated using a device, it is difficult to design a magnet with maximum magnetic force based on the results, and to verify the optimization of the minimal leak magnetic field. Finite Element Method is the most effective and only way to visualize the dynamics and run a simulation by changing conditions. The two dimensional analysis in the present study reproduced the internal shape precisely, and simulate a change in the magnetic force and magnetic field by a subtle displacement. In the cup type magnetic attachment that we focused in the present study, an increase in the leak magnetic field was more evident compared with a sandwich type when a magnetic assembly displaced horizontally against a keeper, and the contact area between a yoke and keeper of a magnetic assembly decreased. A magnetic attachment protects an abutment by reducing the lateral force. However, the structure that minimizes the leak magnetic field needs to be validated. The value for SUS447J1 which is considered to have the similar magnetic characteristics as SUSXM27 was assigned since detailed information regarding SUS447J1 was not provided.

The B-H curve was approximated, and regarded as magnetic characteristics of a magnetic attachment. The challenges for the future include the accurate measurement of values, and finding a material with better magnetic characteristics. Nakamura in our department reported that the difference in the magnetic reduction trend was found between the two and three dimensional models with an increase of air gap. Further study is needed to verify the maximum degree of air gap when valid two dimensional analysis results can be obtained considering the complexity of three dimensional model construction, time efficiency, and performance of a computer.

Conclusions

We performed an analysis of the mechanical properties of a cup type magnetic attachment as a denture retainer using the Finite Element Method, and compared with that of a sandwich type magnetic attachment to elucidate the mechanical behavior of a denture with magnetic attachments. The following results were drawn:

1. In the cup type magnetic attachment, the attractive force decreased significantly when a magnetic assembly and a keeper separate vertically and horizontally, and create a magnetic space.

2. The results reaffirmed the difference in the magnetic flux density distribution around a magnetic assembly and a keeper in different magnetic circuit.

Reference

1． Tanaka，Y.：Dental Magnetic Attachment，Q＆A，Ishiyaku Publishers，Inc（Tokyo），1995

2． Nakamura，Y．：Stress analysis of overlay denture and a magnetic attachment using finite element method. J Jpn Prosthodont Soc, 42:234-245,1998

3． Nakamura，Y．Tanaka，Y．Ishida，T．and et al：Dynamic Analysis of a Magnetic Attachment using Finite Element Method -Comparison of the two dimensional analysis with the three dimensional one-.J J Mag Dent.8:57-62,1999

4． Miyata，T．Niimi，J．Ando，A．and et al: Influence of heating of a magnetic attachment on the attractive force. J J Mag Dent.17:44-50,2008

Discussion Board