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Research Papers

Level Set-Based Topology Optimization of Hinge-Free Compliant Mechanisms Using a Two-Step Elastic Modeling Method

[+] Author and Article Information
Benliang Zhu

Guangdong Province Key Laboratory of Precision
Equipment and Manufacturing Technology,
South China University of Technology,
Guangzhou, Guangdong 510640, China
e-mail: lllang123@163.com

Xianmin Zhang

Professor
Guangdong Province Key Laboratory of Precision
Equipment and Manufacturing Technology,
South China University of Technology,
Guangzhou, Guangdong 510640, China
e-mail: zhangxm@scut.edu.cn

Sergej Fatikow

Division Microrobotics,
Department of Computing Science,
University of Oldenburg,
Uhlhornsweg 84, A1,
Oldenburg 26111, Germany
e-mail: sergej.fatikow@uni-oldenburg.de

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 6, 2013; final manuscript received November 11, 2013; published online January 10, 2014. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 136(3), 031007 (Jan 10, 2014) (10 pages) Paper No: MD-13-1110; doi: 10.1115/1.4026097 History: Received March 06, 2013; Revised November 11, 2013

This paper presents a two-step elastic modeling (TsEM) method for the topology optimization of compliant mechanisms aimed at eliminating de facto hinges. Based on the TsEM method, an alternative formulation is developed and incorporated with the level set method. An efficient algorithm is developed to solve the level set-based optimization problem for improving the computational efficiency. Two widely studied numerical examples are performed to demonstrate the validity of the proposed method. The proposed formulation can prevent hinges from occurring in the resulting mechanisms. Further, the proposed optimization algorithm can yield fewer design iterations and thus it can improve the overall computational efficiency.

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Figures

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Fig. 1

(a) De facto hinge in compliant mechanisms, and (b) revolute joint of the rigid body

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Fig. 2

The design domain of the topology optimization of compliant mechanisms

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Fig. 3

A hypothetic hinged-compliant mechanism: (a) with a spring attached to its output port and (b) with the spring removed

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Fig. 4

The boundary conditions for the second elastic analysis

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Fig. 5

The flow chart of the proposed algorithm

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Fig. 6

The design domain of the displacement inverter

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Fig. 7

The final designs of the displacement inverter obtained using the optimization model QN with different ω

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Fig. 8

The convergence history of GAΔ of the displacement inverter using QT (ω = 0) and QN (ω = 0.6)

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Fig. 9

A close look at the hinges in Fig. 7. The traditional approach QT produces de facto hinges where the two-step elastic modeling method QN with ω = 0.4 gives distributed hinges: (a) hinge region in Fig. 7(a); (b) hinge region in Fig. 7(c)

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Fig. 10

The final designs obtained using QN with different kout: (a) kout = 0.002, (b) kout = 0.0006, (c) kout = 0.0002, and (d) kout = 0.0002, ω = 0.994

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Fig. 11

The convergence histories of GA and GAΔ obtained using QN for the case of kout = 0.0006 (ω = 0.99)

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Fig. 12

The convergence histories of the topology optimization of the displacement inverter using QN (ω = 0.6): (a) the conventional level set method; and (b) the efficient level set method with iobj = 6

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Fig. 13

The design domain of the displacement redirector

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Fig. 14

The final topologies of the displacement redirector obtained using: (a) QT; and (b) QN

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Fig. 15

The convergence histories of the topology optimization of the displacement redirector using QT (a) and QN (b)

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Fig. 16

The final design of the displacement redirector with Volmax= 0.2 (a) and its deformed configuration (b)

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Fig. 17

The final topology of the displacement redirector obtained using the efficient level set method

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Fig. 18

The convergence history of the displacement redirector using the efficient level set method

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