01η
  • Date of Fabrication
    July 2001

  • Close up of the wing differential on 01η

    Description

    01η was constructed in August 2001 (the fourth attempt at building a 2 DOF differential using PZT actuators). The third attempt (which succeeded 00κ) was made to have a resonance of about 70 Hz, but turned out to have a resonance of only 35-40 Hz. This was not explainable by the previous dynamic model which assumed two seperate axes of flapping and rotation. A dynamic modeling of the differential based on a Lagrangian energy technique was undertaken which showed that the resonance depended on more than just the flapping and rotational inertia of the wing and identified an important cross-coupling inertia component of the wing. One important design change made at this time was that what was the "leading" spar in the original designs (the spar with the spherical joint at the end) now became the "lagging" spar. (See the figure above.)

    Another important advance in this generation was to use polyimide wings. This method enables the fabrication of very light, stiff wings with very accurate inertias which was found to be very critical for getting the right response. For the first time, we had a wing which has the same inertia as a calliphora wing.

    Salient Features

    1. The structure attained the resonant frequency it was designed for to a high degree of accuracy.
    2. The material used for flexures remained 6.25 um polyester. It was known that this will lead to a high differential stiffness which it turned out to have.
    3. The nominal frequency response of the structure was validated to a high degree of confidence by multiple measurements both with strain gage measurements as well as with capacitive sensing experiments.
    4. Inspite of the high coupling, τ showed a large rotation at high frequency (@100 Hz). The following movie shows the motion of the wing as seen under a strobe light when the structure was driven with 2 asymmetric triangular waves:

      Note
      1. The rotation is in the correct direction (i.e the wing has a positive angle of attack during its motion, or in other words, the leading spar acutally leads.)
      2. The rotation at the ends is quite high. We can easily see a 45 degree rotation if not more.
      3. The rotation is of the type "delayed at the top" and "timed at the bottom".

    Fabrication Parameters


    Actuator Parameters

    Two matched 16 x 3 PZT-5H actuators were used.

    Fourbar Parameters

    Differential Parameters

    Wing Parameters

    Predictions

    Measurements

    Comparisions