Mesicopter Progress Report
February 2001


Summary

See the January report for the previous update. See also the Instructions for uploading images and be sure to include all of the referenced figures.

Aerodynamics

The most recent 3-D CFD calculation for the 2.5cm diameter rotor has been completed. The surface grids used in this calculation correctly model the as-built geometry. Analysis and post-processing of the data is ongoing, but initial results have provided significant insight into the discrepancies in required motor input power between experimental and estimated performance. The calculated thrust from the Overflow analysis at 48,000 RPM is 4.1g and agrees with the current analysis/design code within 4%, but the calculated torque at 48,000 RPM is approximately 17% greater than the analysis/design code prediction. The rotor was designed for the 5mm Smoovy motor operating at 10 V and 26% efficiency. A 17% increase in the rotor torque and the experimental input power of 3.025 W results in an experimental efficiency of 16.1%. The increase in rotor torque at a given RPM forces the motor onto an operating curve with a lower efficiency. A 10% reduction in motor efficiency for a 17% increase in output power is reasonable.

The two figures below depict the radial thrust and torque distributions on a single blade. The non-dimensionalization is based on the rotor radius and tip velocity. Results from the design/analysis code with and without the current viscous swirl correction are provided. The thrust prediction with swirl is significantly better than without, and matches the CFD result reasonably well over the inboard 90% of the blade. The opposite is seen in the torque distribution, with the viscous swirl solution consistently under-estimating the local torque. It is surprising how accurately standard blade-element/ momentum theory estimates torque under these conditions. The current swirl model assumes and average wake deficit velocity applied uniformly to each blade. Due to the large discrepancies in torque estimation, the model is being modified to account for the effects of downwash and vertical wake deficit variations.





The CFD results outboard of 90% span are distinctly different from the design/analysis predictions due to the effects of wake contraction, which are not incorporated in to the current design/analysis method. The two figures below depict vorticity contours in two planes directly behind and ahead of a single blade. Apparent from these two images is how rapidly the region of strong vorticity originating at the tip contracts inboard, causing significant differences in the induced velocities as compared to a simple cylindrical wake model.





Rotor Fabrication

As shown in the October report, the incidence distributions of the aluminum rotor from laser-scanned data were closer to the design values than those of epoxy rotors were. However, the data points were fluctuated with the maximum variations of around 2 degrees (except the tips) from the design values. We suspect the resolution of laser scanning is not sufficient, as the incidence variations get smaller. Therefore, we tried to gather incidence data of the aluminum rotor from the cross sections.

The basic idea is to embed the aluminum rotor in a transparent epoxy block and cut cross sections gradually. Each cross section was polished and observed under the optical microscope. Three major issues should be considered and planned before embedding the rotor: (1) how to ensure the cutting planes are perpendicular to the blades; (2) how to define the horizontal plane for incidence measurement; and (3) how to measure the radial locations correctly. To solve the first problem, a square pocket was machined in the center of the rotor hub, and the same size of square post was located at the center of the substrate. Fitting the rotor into the post of the substrate can ensure the blades are placed at 0, 90, 180, and 270 degrees. Polyurethane was cast and machined flatly to provide horizontal reference to solve the second issue. Moreover, the cast transparent epoxy block was cut into a square before detached from the substrate. The center of the block can be determined by measuring the distance between the two opposite sides. When cutting the cross sections, we only cut two adjacent sides and left the other two as reference. At every cross section, the width of the block was measured and could be converted to the radial location of the blade. After two adjacent sides were gradually cut down close to the hub, they were then performed as reference sides for the other two blades.

All photos taken from the optical microscope were analyzed in the CorelDRAW. Lines were drawn from the leading edge to the trailing edge and on the reference plane. By reading out the coordinates of the start and end points of lines, the angle between the chord and the reference plane can be calculated. The incidence distributions of four blades analyzed through this approach are shown in the following figure. The results are less noisy and less deviated than those from the laser scanning data. The maximum incidence deviation (except at tips) is less than 1 degree.



Electronics, Power

Further battery survey showed that the power requirements of current 15g mesicopter model couldn?t be met by any existing battery technology. The survey showed that NiCd, AgZn, Li-S, and Lithium inorganic chemistries have the highest power densities where NiCd has the lowest and Lithium Inorganic batteries the highest energy density. To build self powered hovering mesicopter a different motor has to be used. Following this conclusion performance of various small DC motors is being evaluated. These motors run on lower voltage (up to 4V) and don?t require any controllers compared to the brushless smoovy motors. But their efficiency is much lower (20% - 40%) than the efficiency of the smoovy motor (65%). Parallel with the motor testing batteries for the 3-4 V range are being evaluated. The promising chemistries are Lithium Sulfur (LiSO2), Lithium Thionyl Chloride (Li-SOCl2) and Lithium Ion. The major problem is to find batteries in the 5g range.

Dynamics and Simulation

Three dimensional feedback control has been successfully implemented into the improved dynamic dynamic model developed last month. Currently angular rate feedback is utilized along with integration of these rates to drive the them to zero. This essentially causes the the roll and pitch angles to also be driven to zero in the absence of any disturbances. The gains were chosen using LQR with a linearized two dimensional model. The pitch and roll dynamics are assumed to be decoupled for short time constants. Therefore, in implementing the feedback in three dimensions, the yaw rate feedback and pitch rate feedback were treated individually. The resulting behavior of the mesicopter with feedback is plotted below. Compare this behavior with the open loop dynamics shown last month. After an initial offset in the roll angle, both the roll and pitch angles are driven to zero in a well damped manner. Notice that there is only a slight amount of coupling between the two angles as seen in the time histories and the top view which is drawn to scale.



Three-dimension feedback simulation showing positions and orientations.



Three-dimension feedback simulation showing velocities and angular rates.



Overhead view (To Scale).

Work has also been done developing the flight control test bed. One model has already been built and tested briefly. In addition, a second test bed is currently under construction. Both models incorporate rate gyros which are incorporated in a feedback loop utilizing a PIC microcontroller. Shown below are photos of the completed vehicle as well as the second vehicle under construction. In parallel, another iteration of the vehicle hardware is being designed that will incorporate a miniature pressure sensor and magnetometers for measuring altitude and heading.



Photo of completed flight control test bed vehicle.



Photo of second vehicle under construction.



Photo of second vehicle under construction.

The work planned for the future includes completing the design of the next iteration of the flight control test bed, and completing the construction of these vehicles. With respect to the theoretical modeling, further work is planned to see if the rate measurements can be integrated forward in time with the equations of motion and last known vehicle state to determine the current state of the vehicle. Of course errors will accumulate in over time in the integration, even with perfect measurements, but the performance of such a system may be adequate for short periods of time.

Systems Integration Testbed

Control Issues

We have completed the 2 degree of freedom flight testbed described in the December 2000 progress report with no significant changes in the proposed design. In the past months we have focused on eradicating errors in the vision system, controller, and PWM module. Once the system was functional, we adjusted the gains of the controller to provide a moderately dampened response.

We provide plots presenting sample height and yaw trajectories of the vehicle in a single trial. The vehicle's controller was designed to track zero in both height and yaw. Initially, The vehicle's yaw and height positions were offset to non-zero values. When the feedback controller was enabled, the vehicle followed a trajectory to eliminate the position error. We recorded the response in the plots shown here.



Z Response



Yaw Response

The vertical response (z) has a small steady state error induced by inaccuracies in our model. Within our model, we omitted the effects of shaft friction affecting the response. We've made progress in improving this z response by applying oil to the shaft.

The yaw response is oscillatory. The oscillation is a combined effect of poor dampening, the existence of a dead band in the yaw calculation created by imprecise calibration, and lack of control effort, which is limited by a flaw in the PWM signal sent to the vehicle (at long lengths the controllers shutdown). These effects are repairable. Additionally, there are small adjustments that can be made to make our model more exact including the addition of nonlinear aerodynamic effects.

We are currently focusing on the design of the 6 degree of freedom testbed. We will remove the vehicle from the wire providing unrestricted motion. To track all 6 degrees of freedom, we will need two cameras. We are purchasing another camera, and in the meantime, designing software to synchronize information between multiple cameras. With both cameras we should be able to extract 6 degrees of information from the mesicopter localized to stable hover. This information can be input to a new controller/estimator which will be designed soon.

Systems, Applications, and Other Items

Last update: 20-Mar-01 12:30:33 AM
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