Research ArticleAPPLIED SCIENCES AND ENGINEERING

Topology optimization and 3D printing of multimaterial magnetic actuators and displays

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Science Advances  12 Jul 2019:
Vol. 5, no. 7, eaaw1160
DOI: 10.1126/sciadv.aaw1160
  • Fig. 1 Overview of the specification-driven 3D printing process.

    The structure of individual actuators (or the arrangement of multiple actuators) is optimized using a multiobjective topology optimization process. Note that, in general, the final optimized structure can be of any arbitrary shape as shown. The optimization uses the bulk physical properties of the individual materials and the functional objectives as inputs. The generated optimized voxel-based representation of the structure is used by the printer to fabricate the optimized structure using a drop-on-demand inkjet printing process. This allows high-dimensional designs to be automatically generated and fabricated with minimal human intervention. In this work, a rigid acrylate polymer (RIG), an elastic acrylate polymer (ELA), and a magnetic nanoparticle (Fe3O4)/polymer composite (MPC) are the main materials used. The contrast in the optical, mechanical, and magnetic properties is used to simultaneously optimize the visual appearance and the actuating forces while generating the voxel-level design.

  • Fig. 2 Material property library.

    (A) The transmission through the MPC shown as a function of the wavelength for films of varying thickness, measured using a spectrophotometer. (B) The transmission through the clear rigid material shown as a function of wavelength for multiple film thicknesses. (C) Magnetization versus applied magnetic field for the MPC measured at room temperature. Magnetic nanoparticles make up ∼12% of the overall weight of the MPC. Typical mechanical stress-strain curves for the ELA, MPC, and the rigid polymer (RIG) are shown in (D) to (F), respectively. Elastic moduli of the polymers at linear strains, averaged from three samples each, vary significantly—ELA (528 kPa), MPC (507 MPa), and RIG (1290 MPa). (G) The schematic shows the fundamental hinge-based design with panel length lp and thickness tp. In this design, the panel is sectioned into two equal portions of RIG and MPC. The panel is attached to rigid boundaries on two sides with ELA torsional hinges of length lh, width wh, and thickness th. On the application of a magnetic field, the magnetic portion of the panel generates a torque. This is used as the fundamental block in the manually designed samples. (H) Image of a 2 × 2 array of panels each with two axes of rotation. The dark brown regions of the image show the MPC material, and the translucent portions show the rigid materials. The elastic torsional hinges are nearly identical to the rigid polymer in appearance. On the application of a magnetic field, each panel exhibits a unique combination of two-axis angular rotations. The top view of the flat as-printed sample is shown on the left. (Photo credit: S.S. and D.S.K., MIT.)

  • Fig. 3 Actuator characteristics—Forces, displacements, and actuation bandwidth.

    (A) To characterize the actuator performance, we used the fundamental design (Fig. 2G) with a small change. Here, only a fraction of the panel thickness, tp, is filled with MPC, denoted by λ. The following results were obtained with a rectangular panel of size lp1 × lp2 = 8 mm × 9 mm, thickness tp = 1 mm, λ = 0.15, and hinges with dimensions Wh = 0.5 mm, lh = 1 mm, and th = 0.25 mm. (B) Measured blocking forces of four identical devices shown as a function of the distance from the 2 by 2 by 0. 5 magnet along with corresponding simulation results (see magnet, measurement setup, and simulation details in Materials and Methods). (C) Measured angular deflections of three identical devices as a function of distance from the magnet. (D) Optically tracked angular displacements as a function of time for actuation at frequencies from 0.01 to 10 Hz. (E) Angular displacement amplitudes as a function of frequency for three devices. (F) The apparent large-amplitude bandwidth depends on the setup of the magnetic field since the force experienced by the actuator itself varies with the displacement. This is highlighted in this plot with two cases—in one case, the force experienced by the actuator increases monotonically with angular displacement (⋆), and in the other case, there is a stable angular displacement when the panel aligns with the direction of maximum gradient (⋆⋆). See fig. S5 for corresponding time curves and details of the setup.

  • Fig. 4 Applications of 3D-printed multimaterial soft magnetic actuators.

    (A) Five-material actuated display. Each panel consists of the design shown in Fig. 2G, on top of which four vertical walls of a white rigid polymer are printed. The side walls are patterned based on the image to be displayed. Here, the letters “M”, “I”, and “T” are chosen to be patterned on the side wall. An applied magnetic field generates a torque on the panel, allowing different sides of the walls to be visible from a fixed viewing angle. (B) A six-element array of mirrors is mounted next to an electromagnet powered by a current source (0 to 7.5 A). The torque experienced by each individual panel is controlled by the position of the MPC regions. Different images are rastered on a screen by shining a laser line across the mirror array. Here, the panels are designed to raster the MIT logo. See fig. S7 for a schematic of the setup. (C) The two sets of images show the still photographs of the screen and a snapshot of the mirror array with the electromagnet turned off and on (7.5 A). Dynamic actuation using a linear current ramp is shown in movie S1. (D) To demonstrate the use of the magnetic actuator arrays in liquid interfaces, we design water lilies that are positioned on water interfaces. The petal patterns are printed using three layers of the magnetic ink, and torsional hinges are made from the elastic polymer. Left: The top view of the as-printed part is shown where the solid dark regions are the actuating regions made with MPC. Right: When placed on the air-water (with 0.2% FC4430, σ = 20.9 mN/m) interface, the leaves are held flat because of the interfacial tension of water. While it can be deformed by an applied field, as shown, some panels return to their flat position easily when the water is disturbed. (E) When tested in conditions with lower interfacial tension σ12 = 3.7 ± 0.78 mN/m (interface of silicone oil and water with 0.2% FC4430), the array can be actuated back and forth reliably (movie S2). The schematic shows the restoring nature of the interfacial tension. (F) Experimental results of actuation at the silicone oil-water interface. (G) An array of 16 identical actuators with serrated edges is shown with and without an applied magnetic field (design in fig. S9). (Photo credit: S.S. and D.S.K., MIT.)

  • Fig. 5 Panel appearance computation.

    (A) The appearance of the panel as viewed from above is computed by shooting vertical rays through the panel. By computing the total distances traversed by each ray through each material, the ray-traced images can be obtained. Here, three layers each filled with RIG and MPC are shown. Multiple images can be volumetrically encoded in space based on the desired viewing angles. This can be seen in different ray-traced images obtained from a single structure with varying tilting angles. While not explicitly shown here, the volumetric positions of the MPC cells also define the torque in response to a magnetic field. Note that only three layers are shown in the schematic for simplicity; in practice, more than 100 layers are typically used. (B) A vertical column of MPC voxels (top) is widened in practice due to droplet spreading (middle) or slight misalignment in the positions of the drops in consecutive layers (bottom).

  • Fig. 6 Panel optimization for both optical and mechanical properties.

    Given a pair of target grayscale images. Left: ‘Self portrait with Grey Felt Hat’, van Gogh. Image from public domain. Right: from (63). Image used with permission. (A) Corresponding to desired top views of the panel array at two different tilting angles (here, 0° and 30°), our topology optimization framework optimizes the distribution of the RIG and MPC in the panels such that they tilt to the desired angles and their appearances match the target images. (B) Optimized panel appearances as computed by our ray-tracer. (C) Photographs of the 3D-printed topology-optimized sample showing the gradual transition from the “Van Gogh” portrait to the “Scream” image with increasing tilt angle (additional results in fig. S11 and movie S4).

  • Fig. 7 Characteristics of the topology-optimized actuator and long-term tests.

    (A) The blocking force produced by the Van Gogh actuator (Fig. 6) was measured and simulated as a function of distance to the magnet. To ensure that the actuator was consistently actuated on the same side each time, the actuating magnet was offset toward one-half in all simulations and experimental characterization. The measurement setup is shown in fig. S12. In addition, note that all simulations are performed without any fitting parameters. (B) Measured and simulated angular displacement of the topology-optimized Van Gogh actuator as a function of the normal distance between the actuator and the magnet (setup in fig. S12). (C) To test the long-term performance of the large actuator and the reliability of the hinges, we cycled a scaled version of the basic design (Fig. 3A) with dimensions identical to the Van Gogh actuator for 1000 cycles (see movie S3).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaaw1160/DC1

    Fig. S1. Material characteristics.

    Fig. S2. Experimental verification of tilting angles.

    Fig. S3. Two-axis tilting panels.

    Fig. S4. Dynamic mechanical analysis of the elastic material family used in the soft torsional hinges.

    Fig. S5. Large-amplitude bandwidth measurements.

    Fig. S6. Actuator long-term cycling.

    Fig. S7. Experimental setup for dynamic actuation.

    Fig. S8. 3D-printed water lily design.

    Fig. S9. Spike actuator arrays design.

    Fig. S10. Dot gain images.

    Fig. S11. Topology optimization—Optical and mechanical properties.

    Fig. S12. Measurement setup for characterizing the Van Gogh actuator.

    Fig. S13. Modeling of the external magnetic field.

    Movie S1. Video showing the dynamic actuation of the reflective panel array used to raster the MIT logo.

    Movie S2. The printed water lily is placed at fluid interfaces and actuated using a permanent magnet.

    Movie S3. Actuation of panel actuators at different frequencies for bandwidth measurements and long-term actuation (1000 cycles).

    Movie S4. Topology optimization of actuators.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Material characteristics.
    • Fig. S2. Experimental verification of tilting angles.
    • Fig. S3. Two-axis tilting panels.
    • Fig. S4. Dynamic mechanical analysis of the elastic material family used in the soft torsional hinges.
    • Fig. S5. Large-amplitude bandwidth measurements.
    • Fig. S6. Actuator long-term cycling.
    • Fig. S7. Experimental setup for dynamic actuation.
    • Fig. S8. 3D-printed water lily design.
    • Fig. S9. Spike actuator arrays design.
    • Fig. S10. Dot gain images.
    • Fig. S11. Topology optimization—Optical and mechanical properties.
    • Fig. S12. Measurement setup for characterizing the Van Gogh actuator.
    • Fig. S13. Modeling of the external magnetic field.
    • Legends for movies S1 to S4

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Video showing the dynamic actuation of the reflective panel array used to raster the MIT logo.
    • Movie S2 (.mp4 format). The printed water lily is placed at fluid interfaces and actuated using a permanent magnet.
    • Movie S3 (.mp4 format). Actuation of panel actuators at different frequencies for bandwidth measurements and long-term actuation (1000 cycles).
    • Movie S4 (.mp4 format). Topology optimization of actuators.

    Files in this Data Supplement:

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