Radiation Research and Management Center
Tokyo Institute of Technology
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Stacked-type Electrostatic Actuator

1. Operating Principle and Structure

1-1 Basic Model -- A Parallel Plate Electrode --
  The basic structure of a stacked-type electrostatic actuator is a parallel plate electrode. The generative force F under applied voltage V is expressed below :


Here, d , S and ε represent the gap length between the facing electrodes, the area of an electrode and the dielectric constant of the electrode gap, respectively.
A stacked-type electrostatic actuator utilizes electrostatic force between the facing electrodes as a generative force. Its force is inversely proportional to the square of the gap length d Therefore, the shorter the gap length becomes, the larger the force we can get.

Fig.1 : the parallel plate electrode

1-2 The Model of Our Actuator with Two Insulators
  Try and imagine that two electrodes which are insulated with insulative film to prevent short-circuiting and discharge are applied voltage in insulating fluid. The insulative film and the insulating fluid can be regarded as insulating layers. The symbols, t and d symbolize each thickness of the insulating layer, ε1 and ε2 symbolize each relative permittivity. In this case, the generative force F is expressed in the following equation :

Here, S is the area of an electrode and ε0 is the dielectric constant of vacuum. The above equation contains the polarizing effect of the insulating fluid.

Fig.2 : the parallel plate electrode with solid and fluid insulators

1-3 Structure of a Stacked-type Electrostatic Actuator
  A stacked-type electrostatic actuator which is constructed by alternately folding two ribbon electrodes has paper spring and stacked parallel plate structure. A ribbon electrode is a thin and long electrode insulated with polymer like polyethylene terephthalate (PET).

Fig.3 : the ribbon electrode

Fig.4 : the method of fabrication

2. Structure Improvement to Realize Ideal Motion

2-1 Ideal Spring Property
  A stacked-type electrostatic actuator has its own spring property caused by paper spring structure. If the spring constant is too large, the contractive force becomes small because the elastic force acting in a direction opposite to contractive force becomes large. If the spring constant is too small, the actuator can't contract because the electrode changes its shape and the gap length between electrodes expands beyond necessity by a load. Therefore, ideal spring property is that the spring constant is 0 in the working region and infinity in the overload region.
To get an ideal spring property, the electrode part needs to have resistance to bending. To realize that, we are experimentally producing actuators like the following structures.
  • The structure thickened electrode part
  • The structure triangulated electrode part

2-2 The Structure Thickened Electrode Part
  The thickening electrode part makes itself rigid keeping the hinge part soft. This structure can produce in two following ways: one of the methods is thickening the electrode part by sticking insulative chips like PET on the ribbon electrodes, the other method is reducing the thickness of the hinge part by using etching. Fig.5 and 6 are pictures of 2mm-square actuator produced by Mr.Okuda, our co-researcher (Suzuka National College of Technology).

Fig.5 : the cross-section surface of the ribbon electrode   Fig.6 : the made-up 2mm-square actuator

Fig.7 : the displacement-elastic force graph of an actuator thickened electrode part

2-3 The Structure Triangulated Electrode Part
  Distortion of electrode part is large if the actuator has quadrangular electrodes because the number of sides which are shared with an opposite electrode is only two of four (two adjacent sides). On the other hand, electrode distortion of triangular actuator which has a triangular electrode part can decrease since the number of shared sides is two of three.
A triangular actuator can be produced by alternately folding. The angle between ribbon electrodes is set 120° this time.

Fig.8 : a triangular actuator (left),
a quadrangular actuator (right)
  Fig.9 : fabrication method of a triangular actuator

3. Miniaturization

  As already discussed in chapter 1-1, shortening gap length is effective to get larger force. We are making generative force per unit area larger by miniaturization which can shorten gap length.
Today, we have succeeded in driving of 0.3mm size actuator and increasing generative force per unit area. In addition, 0.1mm width of ribbon electrodes has already been produced.

4. Parallelization

  Generative force is able to be larger by using parallelization even though only one miniaturized actuator has weak generative force.
Parallelization enables us to use stacked-type electrostatic actuators on the macroscale.

Fig.10 : parallelization

5. Current Approach

5-1 Micro Fabrication
  We are fabricating microscopic ribbon electrodes to get larger generated force per unit area of actuator. Photolithography and laser ablation are used as micro fabrication methods.
>> more detail click here

5-2 Development of Folding Machine
  We are developing automatic ribbon folding machines for mass production of microscopic actuators.
>> more detail click here

5-3 Toward the Practical Use -- Electrostatic Engine --
  under construction ...


Exhibition Micromachine/MEMS 2011
  We exhibited our actuator at Micromachine/MEMS 2011. You can see the posters here.

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