MECHANICAL CHARACTERISTICS OF SPECTACLES
H. Kaneko*, S. Kakunai*, M. Morita** and J. Nishimura***
* University of Hyogo, Graduate School of Engineering,
Mechanical and System Engineering, Himeji, Hyogo, Japan
** Formerly: University of Hyogo, Himeji, Hyogo, Japan
*** Paris Miki Inc, Okayama, Japan
* 2167 Shosha, Himeji, Hyogo, 671-2201, Japan
[email protected]
ABSTRACT
For a person to wear spectacles comfortably, the frame should be designed by thoroughly considering the mechanical
characteristics. In general, however, priority is given to fashion, and the mechanical characteristics are hardly analyzed. In this
study, we investigated the deformation behaviors of three types of spectacle frames on the market: a titanium frame of the
full-rim type that retains the whole rim of each lens, a gum metal frame that is a new material, and a titanium frame of the
rimless type that retains each lens with two screws. Then we created CAD models of these frames and compared the
mechanical behaviors of these spectacles by finite element analysis.
Introduction
For a person to feel comfortable wearing spectacles, it is preferable to keep lenses at the appropriate face position [1 - 5]. To
realize this comfortable wearing, the spectacle form should be fit to the face. For a good fit, the frame should be designed by
considering the mechanical characteristics at the design and manufacturing stages of spectacles. In the actual design and
manufacture of spectacle frames, priority is given to design requirements; in contrast, the mechanical characteristics are hardly
discussed. This is because many kinds of spectacles are marketed from many manufacturers every year and their complicated
decorations, forms, and materials have made adequate drafting and CAD difficult. However, the recent and remarkable
advances of techniques for 3D profile measurement and mechanical analysis have made high-accuracy measurement and
analysis comparatively easy [6 - 9].
Spectacle frames should be strong enough to retain lenses safely and also lightweight and flexible so that the wearer
experiences no discomfort even after wearing them for prolonged periods. It is also important that the frame be made of a
material that is easy to process. Most metal frames used to be made of conventional titanium alloys. These days, however, the
β-type titanium alloy called gum metal has also been put to use. Gum metal has a low Young's modulus and high strength, and
it is easy to deform elastically. Because of its flexibility, the alloy is expected to fit the head more closely.
In this study, we evaluated the mechanical characteristics of spectacle frames on the market by optical 3D profile measurement
and finite element analysis. An experiment was conducted to compare and investigate the following frame types: a titanium
frame that retains each lens by the rim, a gum metal frame, and a rimless spectacle frame that retains each lens with two
securing screws. First, the mechanical deformation behaviors of the spectacles were obtained by optical 3D measurement.
Then, a CAD model of each spectacle frame was created and analyzed by FEM to compare the deformation behavior with the
experimental result. By analyzing the stress and strain of each lens or temple, the influences of the lens retaining by spectacle
frame and spectacle wearing or fitting were discussed. This consequently clarified the differences of deformation behavior due
to the material.
Deformation Behaviors of Spectacles by the Optical Profile Measurement Method
Experimental Device and Measuring Sample
Figure 1 shows spectacles of a full-rim frame made of titanium material. These spectacles are widely marketed. Each lens is
retained by the rim, and the right and left rims are bridged to form the front. The temple is attached to an end piece through a
hinge. When wearing spectacles, the tips at the ends of temples rest on the ears and the pad on the nose root secures the
spectacles on the face. If the spectacles fit the face well, the right and left temples grip the head with appropriate pressure and
the cells disperse along the ear forms. Titanium is the most popular for spectacles because it is lightweight and not harmful to
Lens
Temple
Bridge
Rim
Tip
Hinge
y
x
z
End piece
Figure 1. Spectacle frame made of titanium
humans. A gum metal frame has a one digit (2.5%) greater elastic deformation performance. Cold working does not cause work
hardening and the yield strength is great [10 – 12]. This material is mainly used for the temples of spectacle frames. In this
experiment, the bridge at the front center of spectacles was secured with resin and a load was applied where the opened temple
made visible contact with the head (i.e., at the tip about 107 mm from the end piece). Then the deformation behaviors of the
front and temples were obtained by 3D form measurement using a laser beam.
CCD camera
Object
Load
Laser
Cylindrical lens
Galvano mirror
Figure 2. Schematic diagram of 3D measurement system
Figure 2 is a schematic diagram of the laser 3D profile measurement method used for measuring the deformation behaviors of
the spectacle frames. The principle of measurement is based on triangulation by the light sectioning method, which uses a laser
beam for scanning. An oscillated laser beam is converted into a slit beam by a cylindrical lens and irradiated to an object
through a galvano mirror. In the experiment on staged objects using this device, the measuring accuracy was ±0.008 mm.
Displacement Distributions of Temple and Lens
Displacement of tip (mm)
6
Gum m etal
T itanium
5
4
3
2
1
0
0
40
80
120
160
200
Load (mN)
Figure 3. Relationship between load and displacement
Figure 3 shows the relationship between the tip displacement and load for full-rim spectacle frames made of titanium and gum
metal. Both frames were deformed in proportion with the load, and the gum metal frame showed about 1.8 times greater
displacement than the titanium frame. When measuring the deformation behaviors of the spectacle frames, the experimental
load was applied by assuming the force of gripping the head when the spectacles are actually worn. In this experiment, we
measured the opening of titanium-frame spectacles between temples when worn and when not worn. To obtain this
displacement, a 160-mN load was applied.
Displacement (mm)
6
5
Gum metal (full rim)
Titanium (rimless)
Titanium (full rim)
4
3
2
Apparent
loading point
1
0
0
20
40
60
80
100
120
Distance from the end piece (mm)
Figure 4. Comparison of temple displacements when a 160-mN load is applied
Displacement (mm)
0.5
Titanium (rimless)
Gum metal (full rim)
Titanium (full rim)
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
Distance from the end of reference line on the lens (mm)
Figure 5. Front displacement when load is applied on the temple
Figure 4 compares the temple displacements of various frames. The vertical broken line in the figure indicates the loading point.
At the temple distance of about 50 mm from the end piece, the temple displacement gradients of all the frames begin to show
different distributions. This is probably because the temples are locally thinned near the point. The rimless frame has a
displacement about 1.5 times greater than that for the titanium frame. Figure 5 shows the front lens displacement of each frame
in the out-of plane direction. Each front shows a displacement distribution resembling a gentle secondary curve. The
displacement distribution is almost equal between the two full-rim types. The rimless type of small retention strength shows the
greatest lens retention strength of about 1.4 times greater than that for the full-rim type. The rimless type allows free working of
the lens form. Therefore, this type is lightweight and fashionable but may not be strong enough. Regarding the titanium and gum
metal frames, the temple displacement is different but the front displacement is almost the same.
Mechanical Analysis of Spectacles by Finite Element Method
Creation of FEM Analysis Model
Since there were no detailed drawings of the forms of spectacle frames, analysis models were created by optical 3D form
measurement and CAD. Since spectacles have a complicated structure, a CAD model of each spectacle element was created
first. Then these models were integrated into a surface model of a general spectacle frame to fabricate a detailed solid model of
spectacles. Figure 6 shows a CAD model of a titanium frame divided into elements for finite element analysis. The analysis
Tip
Bridge
Rim
Temple
Hinge
y
x
z
End piece
Figure 6. Titanium full-rim model for FEM analysis
model of 10 tetrahedral components consisting of about 50,000 contact and about 31,000 elements was fabricated by using the
analysis software ANSYS. Since spectacle frames are made of various materials, it is difficult to identify the property values. In
this experiment, the lens (CR-39: diethylene glycol diarycarbonate) and tip (CAP: cellulose acetate propionate) material
characteristics were obtained from reference data. For analysis, the bridge of the spectacle frame was completely constrained
and a horizontal load was applied in the temple opening direction on the tip.
8
Gum metal (analysis)
Gum metal (experiment)
Titanium (experiment)
Titanium (analysis)
Displacement (mm)
7
6
5
4
3
2
1
0
0
20
40
60
80
100
120
140
Distance from the end piece (mm)
Figure 7. Comparison of temple displacements
Experimental and Analytical Results of Spectacle Deformation Behaviors
Figure 7 compares the measurement and FEM analytical results of the temple displacement of full-rim spectacles when a
160-mN load was applied 107 mm from the end piece. The experimental and analytical results are almost similar. The
displacement gradient of the temple changes at about 40 to 50 mm from the end piece. Across this area, the difference of the
Displacement (mm)
0.5
Gum metal (analysis)
Titanium (analysis)
Gum metal (experiment)
Titanium (experiment)
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
Distance from the bridge (mm)
Figure 8. Comparison of front displacements
displacement distribution between the gum metal and titanium are notable.
Under similar experimental conditions, Figure 8 compares the measurement and FEM analytical results of displacement
distribution from the lens bridge to the end piece. The experimental results are slightly greater than the analytical results, but the
titanium and gum metal almost similar. Judging from these results, the influence of temple material on lens displacement seems
small, whether it is titanium or gum metal. The displacement gradient is gentle near the bridge but becomes greater as it
becomes closer to the end piece.
(A)
(B)
(D)
(C)
Equivalent strain (x10-3)
0.7
0.6
0.5
Titanium
Gum metal
Titanium model with gum metal temple
0.4
0.3
0.2
0.1
0.0
(A) Rim and
bridge joint
(B) Rim and
temple joint
(C) End piece
(D) Temple
Figure 9. Comparison of equivalent strain
43.6 (19.8）
15.6 (14.0)
13.3 (25.7)
(Titanium full-rim model)
3.1 (8.0) MPa
Figure 10. Maximum principal stresses of titanium (gum metal) frame
Temple Stress and Strain Analysis
In this experiment, we compared the mechanical characteristics of spectacles with titanium and gum metal temples that are on
the market. Since the detailed form differs between the frames, however, we investigated the advantage of using gum metal by
changing the temple material of the titanium frame spectacles to gum metal. Figure 9 compares the equivalent strain at each
frame section for a full-rim titanium frame, a full-rim gum metal frame, and a titanium frame model with gum metal temple. The
gum metal frame shows greater strain at (D) than the titanium frame because the tip deflected the temple greatly. This influence
remains until the end piece (C) and the rim joint (B). At the rim and bridge joint (A), the titanium frame shows a slightly greater
value. The titanium frame produces almost the same strain at the temple (D), the rim and temple joint (B) and the rim and bridge
joint (A). Compared with the gum metal frame, the frame of the titanium frame model with gum metal temple produces almost
half the strain at the temple (D). The strain at the rim and bridge joint (A) become small. Figure 10 shows the titanium frame with
the maximum principle stresses on the titanium and gum metal frames. From these results, we can estimate that gum metal
frames on the market suppress influences on the rim and bridge joints by their flexible temples (great strains) and well-designed
rims connected to end pieces.
Lens Retention System and Lens Strain
Figure 11 compares the distribution of X-direction strain on the lens surface between full-rim frame spectacles and rimless
frame spectacles. The full-rim type produces great strain near the bridge and end piece joint and the rimless type produced
great compressive and tensile strain locally around the screws. If great external force is suddenly given, the spectacles may
break at this region. At the lens center located in the viewing direction, the rimless type produces about 8 times greater strain
Compressive
Compressive
Tensile
Bridge
Bridge
Compressive
0 (x10-3)
-0.6
(a) Full rim
-12
0
5 (x10-3)
(b) Rimless
Figure 11. Distribution of X-direction strain on the lens surface
than the full-rim type. Since the strain gradients of both types are small, their influences on vision seem small. To ease the
strains around the screws of the rimless type, it seems useful to design the end piece structure so that the load on the temple
will not be transmitted to the lens easily and to use gum metal and other materials.
Conclusion
In this study, we reached the following conclusion:
1) The displacement gradient of the temple changes greatly at about 40 to 50 mm from the end piece.
2) By considering the forms of the end piece and other frame sections, the flexibility of gum metal can be used effectively.
3) The full-rim type produces great strain around the bridge and end piece joint and the rimless type produces great strain at the
lens securing sections. Irrespective of the type, however, the strain gradient at the lens center is small.
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