Psychoacoustic optimization of the spacing of propellers, helicopter rotors and axial fans

The paper deals with the minimization of the subjective annoyance (i.e., of the quality of the received sound rather than of its acoustic power) due to tonal noise generated by subsonic, low-solidity, axial-flow rotors. The employed method is based on the uneven spacing of the blades, is typically applied to open or nearly open rotors and is based on acoustic interference. Thus, linear propagation of the acoustic waves is a prerequisite for its application. An optimization problem is formulated whose objective function is derived from a psychoacoustic metric, the decision variables are the blades angular positions, the SPL spectrum generated by a single blade is a parameter, and the constraints are the rotor balancing and the minimum angular distance between adjacent blades. A further intuitive criterion, based on lowering the highest peaks has also been considered. The solution of the problem is critical due to the presence of a very large number of minima in the objective function, which prevents from employing the most common optimization algorithms. Thus, a method based on the simulated annealing has been modified and adapted to the present problem. The application to a number of test cases and the analysis of the results show that the method is effective in finding the optimal solution and is computationally affordable.