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Mechanical Design of Metal Dome for Industrial Application

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In this paper, the mechanical design of metal domes is studied using finite element analysis. The snap-through behavior of a practical button design that uses a metal dome is found. In addition, the individual click ratio and maximum force for a variety of metal domes are determined. This paper provides guidance on button design for industrial engineers.
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Mechanical Design of Metal Dome for Industrial Application
To cite this article: Thomas Jin-Chee Liu et al 2018 IOP Conf. Ser.: Mater. Sci. Eng. 311 012020
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ICSMM 2017 IOP Publishing
IOP Conf. Series: Materials Science and Engineering 311 (2018) 012020 doi:10.1088/1757-899X/311/1/012020
Mechanical Design of Metal Dome for Industrial Application
Thomas Jin-Chee Liu, Li-Wei Chen and Nai-Pin Lin
Department of Mechanical Engineering, Ming Chi University of Technology,
Taishan, New Taipei City, Taiwan
E-mail: jinchee@mail.mcut.edu.tw
Abstract. In this paper, the mechanical design of metal domes is studied using finite element
analysis. The snap-through behavior of a practical button design that uses a metal dome is
found. In addition, the individual click ratio and maximum force for a variety of metal domes
are determined. This paper provides guidance on button design for industrial engineers.
1. Introduction
The metal dome shown in Fig. 1 is a type of thin shell structure, which is known as a spherical cap in
solid mechanics. This element is usually applied in the button design of electronic products such as
cameras, mobile phones, or audio players. Due to the snap-through/buckling deformation typical of a
metal dome, one can feel the jumping or clicking motion when pressing the button.
Using either an analytical or a numerical method, the snap-through deformation of a spherical cap or
arch shell has been extensively studied [1-7], while their applications were discussed by Tomitsuka et
al. [5]. However, the practical application and discussion of a metal dome for button design was
presented in very few references.
In this paper, non-linear finite element analysis will be applied for a metal dome used in a button
design. The snap-through deformation and click ratio will be obtained for some practical design cases.
Design guidelines will be proposed on the basis of the results of this research.
Figure 1. Metal dome.
2. Problem definition and finite element model
The geometry of the metal dome to be analyzed is shown in Fig. 2. It is composed of a curved cap and
flat ring. The dome is a thin-shell structure and made of high-strength stainless steel (JIS SUS 301 EH).
Its main dimensions are R, Q, H, and t. The indenter with radius r experiences a downward force and
displacement that cause it to press into the metal dome. In Table 1, the material constants of JIS SUS
301 EH are listed, while the elasto-plastic stressstrain curve is shown in Fig. 3. Due to its relative
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ICSMM 2017 IOP Publishing
IOP Conf. Series: Materials Science and Engineering 311 (2018) 012020 doi:10.1088/1757-899X/311/1/012020
rigidity, the indenter is assumed to be a rigid body. The metal dome is constrained on L2 and subjected
to the load from the indenter.
Figure 2. Geometry of metal dome.
Figure 3. Elasto-plastic stress-strain curve of stainless steel (JIS SUS 301 EH).
Figure 4. Finite element model.
Table 1. Material properties of stainless steel (JIS SUS 301 EH).
Material
Youngs modulus E (GPa)
Poissons ratio

JIS SUS 301 EH
Stainless steel
186
0.30
ANSYS software is employed for the non-linear finite element analysis. The contact condition
between the dome and indenter is considered as well as the large displacement and elasto-plastic
stressstrain curve. For the finite element simulation in ANSYS, the element types used are as follows:
SHELL93, TARGE170, and CONTA174.
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ICSMM 2017 IOP Publishing
IOP Conf. Series: Materials Science and Engineering 311 (2018) 012020 doi:10.1088/1757-899X/311/1/012020
A typical finite element model is shown in Fig. 4. The indenter has a prescribed displacement along
the y-direction, which can be downward or upward to control its motion.
3. Design rules
The snap-through behavior (path a-b-c) of the metal dome is shown in Fig. 5. In this figure, F and v
represent the applied force and indentation displacement, respectively. Along the snap-through path a-
b-c, one can feel a click or jump motion when the dome or button is pressed.
The click ratio Rc is defined as follows:
Rc= (F1F2) / F1 *100% (1)
Rc is an important parameter for the metal dome or button. A larger Rc value represents a more obvious
jump motion when the button or dome is pressed. Referring to past studies [5], the click ratios are
designed within a range of 30% to 60% to achieve a satisfying feeling for the user when the button is
pressed. Past studies [5,8] also proposed that the range of maximum force F1 should be designed to be
from 1 N to 5 N for mobile communication products.
Figure 5. Snap-through behavior.
(a) (b) (c)
Figure 6. (a) F-v relation, (b) Rc variation, (c) F1 variation. (effects of t)
4. Numerical results
First, the effects of the thickness on the click ratio (Rc) and maximum force (F1) are discussed. The
dimensions R = 1 mm, Q = 0.2 mm, H = 0.1 mm, i1 = 0.2 mm, and r = 0.3 mm are kept constant. In
Fig. 6, the Fv relation, Rc variation, and F1 variation for different thicknesses are obtained from the
finite element analysis.
The color bands in figures (b) and (c) denote the design ranges according to past research [5,8]. Only
the cases of t = 0.0325 mm and t = 0.035 mm meet the design requirements. For the cases of t
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ICSMM 2017 IOP Publishing
IOP Conf. Series: Materials Science and Engineering 311 (2018) 012020 doi:10.1088/1757-899X/311/1/012020
0.0225 mm, the snap-through behavior is lost and the click ratio cannot be defined. In summary, the
click ratio decreases when the thickness increases.
(a) (b) (c)
Figure 7. (a) F-v relation, (b) Rc variation, (c) F1 variation. (effects of H)
Figure 8. Special case.
(a) (b) (c)
Figure 9. (a) F-v relation, (b) Rc variation, (c) F1 variation. (effects of W)
The effects of H are also discussed. The dimensions R = 1 mm, Q = 0.2 mm, t = 0.03 mm, i1 = 0.2 mm,
and r = 0.3 mm are kept constant; the results are shown in Fig. 7. Only the cases of H = 0.02 mm and
H = 0.03 mm meet the design requirements. In figures (b) and (c), we see that the case of H = 0.02 mm
gives the peak value.
A special case for a metal dome with four holes is shown in Fig. 8. The dimensions R = 1.95 mm, Q =
0.3 mm, H = 0.2 mm, t = 0.05 mm, i1 = 0.2 mm, and r = 0.3 mm are kept constant. The dimension W is
a variable.
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ICSMM 2017 IOP Publishing
IOP Conf. Series: Materials Science and Engineering 311 (2018) 012020 doi:10.1088/1757-899X/311/1/012020
The results of these cases are shown in Fig. 9; they nearly meet the design requirements. Similar Fv
curves are plotted as for the previous case. We can see that the click ratios vary slightly with different
W values. However, F1 consistently increases as the width increases.
In addition, Fig. 10 shows the stress and deformation of the metal dome with W = 0.7 mm.
(a) (b)
Figure 10. Contour of von Mises stress under (a) maximum indentation and (b) unloading condition.
(units of stress: Pa)
5. Conclusion
The finite element results provide information and a methodology for metal dome and/or button design.
The ideal snap-through behavior, click ratio, and maximum force of various metal domes were
obtained. The mechanical behavior of the dome was shown to be affected by the geometric condition.
By controlling the shape, the metal dome can meet the design requirements. In particular, the
disappearance of the snap-through behavior for some domes must be avoided. In summary, the JIS
SUS 301 EH stainless steel is a good choice for metal dome design.
6. References
[1] Brush D O and Almroth B O 1975 Buckling of Bars, Plates, and Shells (New York: McGraw-
Hill)
[2] Wempner G and Talaslidis D 2003 Mechanics of Solids and Shells: Theories and
Approximations (New York: CRC Press)
[3] Mescall J F 1965 ASME J. Appl. Mech. 32 936
[4] Bathe K J and Ozdemir H 1976 Comput. Struct. 6 81
[5] Tomitsuka T, Ajimura S, Kawahira T and Noguchi Y 2003 Fujikura Tech. Rev. 104 42 (in
Japanese)
[6] Sankar A, El-Borgi S, Ben Zineb T and Ganapathi M 2016 Composites Part B: Engineering 99
472
[7] Soltanieh G, Kabir M Z and Shariyat M 2017 Composite Structures 180 581
[8] Ma R H 2011 Human Factor Engineering (Beijing: Peking University Press) (in Chinese)
ResearchGate has not been able to resolve any citations for this publication.
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As the theories and methods have evolved over the years, the mechanics of solid bodies has become unduly fragmented. Most books focus on specific aspects, such as the theories of elasticity or plasticity, the theories of shells, or the mechanics of materials. While a narrow focus serves immediate purposes, much is achieved by establishing the common foundations and providing a unified perspective of the discipline as a whole. Mechanics of Solids and Shells accomplishes these objectives. By emphasizing the underlying assumptions and the approximations that lead to the mathematical formulations, it offers a practical, unified presentation of the foundations of the mechanics of solids, the behavior of deformable bodies and thin shells, and the properties of finite elements. The initial chapters present the fundamental kinematics, dynamics, energetics, and behavior of materials that build the foundation for all of the subsequent developments. These are presented in full generality without the usual restrictions on the deformation. The general principles of work and energy form the basis for the consistent theories of shells and the approximations by finite elements. The final chapter views the latter as a means of approximation and builds a bridge between the mechanics of the continuum and the discrete assembly. Expressly written for engineers, Mechanics of Solids and Shells forms a reliable source for the tools of analysis and approximation. Its constructive presentation clearly reveals the origins, assumptions, and limitations of the methods described and provides a firm, practical basis for the use of those methods.
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  • J Mescall
Mescall J F 1965 ASME J. Appl. Mech. 32 936
  • K J Bathe
  • H Ozdemir
Bathe K J and Ozdemir H 1976 Comput. Struct. 6 81
  • T Tomitsuka
  • S Ajimura
  • T Kawahira
  • Y Noguchi
Tomitsuka T, Ajimura S, Kawahira T and Noguchi Y 2003 Fujikura Tech. Rev. 104 42 (in Japanese)
  • R Ma
Ma R H 2011 Human Factor Engineering (Beijing: Peking University Press) (in Chinese)