Summary

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

Aerodynamics

An error in the grid geometry was discovered during post-processing of the 3-D CFD results for the four blade, 2.5cm diameter rotor. The airfoil camber-line used in the analysis has significantly more camber than the as-built section. A new grid with the correct geometry has been generated and another computation will be completed. This error does not explain the discrepancies in power required between the computational results and experiment. The results of the first analysis indicated separation near the leading edge on the lower surface of the blade. The reduction in camber in the second analysis will alleviate much of this problem. Aft separation on the upper surface should also be delayed. The reduction in camber in the second analysis should further reduce the power required, increasing the discrepancy with experiment.

All major components for the 150g vehicle have been fabricated allowing for a much more precise weight breakdown and performance estimate. The largest discrepancy between the initial estimate and the final vehicle is the weight of the rotors. The 19g value represents the first generation of 10" diameter rotors manufactured at Stanford. A redesign of the hub/mount region using a smaller amount of aluminum should bring the weight of the next set of rotors closer to the initial estimate. The initial power estimate was based on experimental data for the WES-Technik 10" rotor. The Stanford 10" rotors, designed for static thrust, require slightly more voltage for a given thrust, but at a significantly lower current. This reduction in power required is most easily translated into increased endurance rather than increased thrust, which requires an increase in operating voltage.

Rotor Fabrication

Verification of the Material Properties of Epoxy

In the structural analysis, we took the modulus of elasticity of the epoxy directly from the manufacturer's data. Since we did not shape the stock material but cast it ourselves according to the handling instructions, we needed to verify that the cast material had the same or similar properties as those specified. Therefore, we fabricated cantilever beams and performed bending tests. The cantilever beams have prismatic rectangular cross-section. The bending test applied loading at the end of the beam, and measured the forces and deflection at the same location. The tests were done by Testing Engineering, Inc., Oakland, CA using a 100 kip Instron universal testing machine. Specimens were secured to the bed of the test machine. Three sizes of beams in proportion were tested-(1) 2mm x 1mm x10mm, (2) 4mm x 2mm x 20mm, and (3) 8mm x 4mm x 40mm. The modulus of elasticity and the strength calculated from the measured forces and deflections were averaged and summarized in the following table. For comparison, the manufacturer's data are also listed.

	Beam (1)	Beam (2)	Beam (3)	Manufacturer's data
				Tensile	Flexural
E (N/m^2)	< 7.81E+08	7.63E+09	7.46E+09	5.63E+09	6.30E+09
Strength (psi)	8621.77	10547.21	8933.28	6166	10270

It was unclear why the modulus of elasticity of beam (1) is about one order of magnitude less than that of the manufacturer's data. The size effect should not be the reason, since beam (2) and beam (3), which are two times and four times the size of beam (1), did not have the same trend. The moduli of the larger beams ((2) and (3)) are consistent and higher than the manufacturer's. The strengths of the beam (2) and beam (3) are slightly higher than that of the beam (1), and all of them are within the reasonable range of manufacturer's data. We attribute the discrepancy of the moduli to a problem during casting and curing, or to some unidentified damage caused by shipping the beam in a smaller beam case.

Dynamics and Simulation

In last month's report, it was mentioned that further analysis of the model was required. To that end, an in depth study of the aerodynamic forces and torques acting on the rotor was developed. This derivation includes equations for the thrust and hub forces as well as the motor torque, and rolling and pitching torques. Consideration was also given to the effects of horizontal motion of the rotor on the inflow velocity. This was not included in the last model. A copy of the analysis is available as a PDF file from this link.

The improved aerodynamics were then incorporated with the existing two-dimensional and three-dimensional non-linear dynamic models. The dynamic models were also modified to represent the physical characteristics of the latest prototype that will utilize the ten inch two-bladed rotors. A cant angle of 15 degrees is still being used for the tilt of the rotor shafts. A sample simulation with an initial bank angle of .3 radians is plotted below.

Three-dimension simulation showing positions and orientations.

Three-dimension simulation showing velocities and angular rates.

Overhead view clearly shows slight coupling.

Once again, the coupling between the pitch and roll motions can be seen to occur gradually over time. But with the improved and corrected aerodynamic forces, the motion no longer damps out. The behavior exhibited in these plots is more representative of the actual observed behavior of the vehicle. With the greatly improved model, the vehicle design code will be revisted to perform a stability analysis to see what the affects are now of cant angle and center of gravity position. Finally, the control law design can be applied to the improved model to determine if rate feedback can stabilize the highly oscillatory motion.

Last update: 15-Feb-01 12:10:38 PM
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