Relative Rotor Phasing for Multicopter Vibratory Load Minimization

This study focuses on vibration reduction for quadcopters and octocopters with elastic, 2-bladed, synchronized-RPM,
variable-pitch rotors through the use of relative rotor phasing. The study defines phase modes such as a pitch phase
mode with relative phasing between the front and aft rotors, a roll phase mode with relative phasing between the left
and right rotors, and a differential phase mode with relative phasing between the clockwise and counterclockwise
spinning rotors for both the quadcopter and the octocopter, as well as additional higher harmonic phase modes for
the octocopter. Parametric studies on individual phase modes indicate that for the quadcopter in forward flight the
pitch and roll phase modes can almost entirely eliminate the 2/rev vibratory forces (at the aircraft level), but the
2/rev vibratory moments cannot be minimized at the same time. By simultaneously using multiple phase modes a
Pareto-front can be generated and a solution selected based on the relative emphasis on force or moment vibration
reduction. For the octocopter it was observed that individual higher harmonic modes (specifically the 2c or 2s modes)
could almost entirely eliminate both the 2/rev vibratory forces and moments, simultaneously. Compared to vibration
levels in forward flight that might, on average, be expected if the rotors were randomly phased, reductions of 62% and
96% in a composite vibration index (equally weighting 2/rev vibratory forces and moments) were calculated for the
quadcopter and octocopter, respectively, with appropriate rotor phasing.