On Blade Arrangement for Multi-Blade Rotors

Abstract

This paper concerns the blades of multi-bladed water-pumping windmills when they have variable mass and centre of mass. The paper explores blade arrangement strategies that will minimize the eccentricity of the rotor centre of mass and hence any rotor-induced vibration. The number of blades in the rotor is assumed to equal the number made in each production batch, in contrast to the case where a batch of up to 22 blades was optimally matched to produce two- and three-bladed rotors, Hitz & Wood [1]. Using the measured mass and centre of mass of 24 blades for the rotor of a 26 ft Kijito windmill described by Harries [3], three strategies are considered. Random matching of the blades is shown to become increasingly effective as blade number increases. Pairing the blades by ordering in the product of mass and centre of mass, d, followed by random selection of pairs also produces rotors with low eccentricities. The numerical experiments show that the best strategy involving random selection is to pair by ordering, swapping the blades of every second pair, and then randomly arrange the resulting pairs. Finally, a heuristic based on blade pairing is shown to give eccentricities which are high compared to the minimum value determined exactly for 12 blades or less, but apparently low enough to be useful.