The objective was to optimise the UH60-A rotor anhedral and sweep to reduce the pitch loads, stall on the retreating side and shock effects on the advancing side whilst maintaining or improving the thrust, torque and vibratory loads. The stall and shock effects are observed as large changes in the pitching moment. Therefore the objective can be captured with a function that includes the average and peak-to-peak pitching moments. The other parameters can be incorporated as constraints; as a margin of change in thrust, torque and vibratory moments. The vibratory mo- ment is calculated as the pitching moment less the mean and 1/rev oscillation.
The full and vibratory pitching moments for the blade from 0 to 360 degrees azimuth are shown in Figure 8.11 for varying sweep and anhedral. Adding more sweep decreases the peak-to-peak pitching moment. Adding anhedral does not have a large effect on the peak-to-peak moment but it changes the moment most around the front and advancing side of the disk. This change is larger with more sweep. The overall effect on the performance parameter is that it move the average pitching moment closer to zero pitching moment. Adding both, anhedral and sweep, increases the vibratory pitching moment and the effect of anhedral is more significant with more sweep.
Table 8.3 summarises the performance parameters to be used for the optimisation for a few
0 deg sweep, 20 deg sweep, 40 deg sweep,
varying anhedral varying anhedral varying anhedral
Total pitching moment
0 deg sweep, 20 deg sweep, 40 deg sweep,
varying anhedral varying anhedral varying anhedral
Vibratory pitching moment
Figure 8.11: Total and vibratory pitching moments for a single blade over a revolution of the rotor in forward flight. The original rotor has 20 degrees sweep and 0 degrees anhedral.
of the results to compare the effect of sweep and anhedral on these parameters. High anhedral tends to favour good average and peak-to-peak pitching moment, while more sweep favours good peak-to-peak but has worse average pitching moments. Both suffer higher amplitude vibratory pitching moment when increased.
Sweep (deg) Anhedral (deg) pitchavg ∆ pitch 40 0 -0.001462 0.002690 30 0 -0.001468 0.002713 20 0 -0.001412 0.002794 20 5 -0.001296 0.002783 20 10 -0.001223 0.002743 20 15 -0.001150 0.002706 Vibratory 40 0 0.000 0.001116 30 0 0.000 0.001032 20 0 0.000 0.001024 20 5 0.000 0.001012 20 10 0.000 0.001072 20 15 0.000 0.001153
Table 8.3: Summary of performance of design points using moments of a single blade.
8.5
Optimisation
The CT for all the designs were within about 4% of each other and since further trimming was not used, the thrust was neglected as long as it fitted within 5% of the original rotor’s perfor- mance. For CQ, the coefficients were within about 5% of each other. The torque constraint was relaxed to allow for diversity, as long as the anhedral and sweep values were constrained within the boundaries of the database. It was treated as a soft constraint, i.e. the points that violated this constraint of greater than 5% increase in torque were included in the next generation but were penalised first.
To capture the objectives, the average pitching moment (Cmpitch) and the overall peak-to-peak
pitching moment (∆Cmpitch) would make up the components of the objective and the vibratory pitching moment peak-to-peak (∆Cmvib-pitch) value would be added as a constraint to the torque coefficient.
The two components of the objective function were weighted equally. However, since on aver- age, the ratio of ∆Cmpitch to Cmpitch is 1.164:1, the weights that would weight them equally were
found to be: 1 n n ∑ i=0 ∆Cmpitch Cmpitch = 1.164 (8.18) ∆Cmpitch :Cmpitch = 0.47 : 0.53 (8.19) So the overall objective function was:
OF V = −0.47∆Cmpitch−0.53Cmpitch+ 1,if∆Cmvib−pitch≤5% and scaled CQ ≤1.0
otherwise,OF V = −0.47∆Cmpitch−0.53Cmpitch+ 1−0.5(∆Cmvib−pitch−1.05)−0.5(CQ−1.02)
All the performance values of the design points were scaled with a reference rotor, which was the original rotor in this case. These scaled values were used to train the ANN. The ANN predictions are shown in Figure 8.12 for each of the components of the objective function. The ANNs accuracy was also estimated relative to the change in the performance of the design obtained using the CFD data. The maximum error in the objective function obtained was found to be 0.85%.
The GA was then used to find the optimum design using 500 iterations over five generations. ∆Cmvib-pitch was constrained to be not more than 5% higher than that of the original blade and
CQ not more than 2%. The result are also shown in Figure 8.13(a). Table 8.4 shows some of the designs used to train the ANNs, as well as an additional data point that had a sweep 17 degrees and an anhedral of 11 degrees used to validate the ANN in scaled values. This point performed better than the baseline case and was not too far from the optimal region. The average, peak-to-peak moments, and torque coefficient are reduced and there was a 5% increase in vibratory peak-to- peak moment. The points selected by the GA also lay on the Pareto front as shown in Figure 8.13(b). Again, it can be seen that the objective function method confines the optima to a region of the design space as opposed to a spread of the best compromise between the design points. The aerodynamic benefit obtained from the optimisation is due to the change in distribution of the loads. This is shown in Figure 8.14. Generally, the anhedral off-loads the tip of the rotor for most of the cycle. This allows the sweep to be reduced which reduces the average pitching moment.
Sweep(deg) Anhedral(deg) Cmpitch ∆Cmpitch ∆Cmvib-pitch CQ OFV Remark
20.0 0.00 1.0000 1.0000 1.0000 1.000 0.000 original
20.0 15.00 0.7485 0.8145 1.1245 0.906 0.183 best in initial
population
17.1 11.00 0.7594 0.8239 1.0525 0.933 0.209 best new design
by GA
Table 8.4: Comparison of optimised and original UH60-A rotor blade in terms of pitching moment per- formance.
Figure 8.12: ANN prediction for pitching moments of a blade with varying sweep and anhedral. Values were scaled with original blade of 0 deg anhedral, 20 deg sweep. Black dots on the plot are data used for training the ANN. GA selections are shown as red dots.
(a) (b)
Figure 8.13: (a) Genetic algorithm results, (b) Comparison between Pareto front optimisation and objec- tive function selection.
Ψ = 70o
Ψ = 100o
Ψ = 150o
Ψ = 340o
Figure 8.14: Cp plots at different azimuth angles for the original (SW20AN0) and validation point