Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Topology optimization of contact-aided compliant mechanisms for tracing multi-kink paths

Prabhat Kumar, Roger A Sauer, Anupam Saxena

Abstract

This paper presents a topology optimization approach to design 2D contact-aided compliant mechanisms (CCMs) that can trace the desired output paths with more than one kink while experiencing self and/or external contacts. Such CCMs can be used as mechanical compliant switches. Hexagonal elements are used to parameterize the design domain. Negative circular masks are employed to remove material beneath them and generate rigid contact surfaces. Each mask is assigned five design variables. The first three decide the location and radius of the mask, whereas the last two determine the presence of the contact surface and its radius. To ensure continuity in contacting surfaces' normal, we employ a boundary smoothing scheme. The augmented Lagrange multiplier method is employed to incorporate self and mutual contact. An objective is formulated using the Fourier shape descriptors with the permitted resource constraint. The hill-climber optimization technique is utilized to update the design variables. An in-house code is developed for the entire process. To demonstrate the method's efficacy, a CCM is optimized with a two-kink path. The desired and obtained paths are compared.

Topology optimization of contact-aided compliant mechanisms for tracing multi-kink paths

Abstract

This paper presents a topology optimization approach to design 2D contact-aided compliant mechanisms (CCMs) that can trace the desired output paths with more than one kink while experiencing self and/or external contacts. Such CCMs can be used as mechanical compliant switches. Hexagonal elements are used to parameterize the design domain. Negative circular masks are employed to remove material beneath them and generate rigid contact surfaces. Each mask is assigned five design variables. The first three decide the location and radius of the mask, whereas the last two determine the presence of the contact surface and its radius. To ensure continuity in contacting surfaces' normal, we employ a boundary smoothing scheme. The augmented Lagrange multiplier method is employed to incorporate self and mutual contact. An objective is formulated using the Fourier shape descriptors with the permitted resource constraint. The hill-climber optimization technique is utilized to update the design variables. An in-house code is developed for the entire process. To demonstrate the method's efficacy, a CCM is optimized with a two-kink path. The desired and obtained paths are compared.

Paper Structure

This paper contains 9 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem formulation
  4. Boundary smoothing scheme
  5. Contact finite element analysis formulation
  6. Objective function and optimization formulation
  7. Search algorithm: Hill Climber
  8. Results and discussions
  9. Concluding remarks

Figures (2)

  • Figure 1: Design domain and the optimized result are shown in (a) and (b). Fixed corners, input location for actuation, and out location with two-kink path are indicated in (a). The optimized design depicts the negative masks' final positions, shapes, and sizes in (b). The optimally generated five rigid surfaces are also depicted using solid black circles.
  • Figure 2: Optimized design in gray and deformed profiles in red at different force steps. The desired path and actual trace path are shown in black and blue. The final locations and sizes of the negative circular masks are shown. One can notice that though the optimizer suggests five rigid contact surfaces, the mechanism uses only one of them to perform the task, i.e., only this contact surface is active, while the remaining are inactive; thus, they should be excluded during fabrication.