Model and experimental analysis of a rotor rig dynamics with time-varying characteristics

This work is motivated by the rapid developments of a broad range of electrically powered vertical take-off and landing vehicles which frequently feature two-bladed thrust generating rotor propulsion units. The interaction between a two-bladed rotor and the surrounding structure causes an emergence of the complex dynamics specific to the systems with the time-varying characteristics. This paper introduces a new rotor-structure test rig aimed to support the focused analyses of such systems. The test rig is realized as an idealised configuration consisting of a flexible slender cantilevered beam-like support structure which accommodates a single brushless electrical motor and a two-bladed propeller at its free end. Whilst retaining relative simplicity and scalability, this system allows analysis of complex flexible structure-propeller coupled phenomena, some of which are evidenced in this study. To form a compact and fully defined low-order model suitable for the computationally efficient in-vacuo analysis presented here, a Lagrange-based energy formulation is used to derive the equations of motion. The frequency and time domain techniques, including the complex modal analysis of the linear timeperiodic systems, frequency response function and Udwadia-Kalaba method, are used to describe and explain the observed dynamics. The predicted dynamic changes, their impact on the modal interactions and the validity of the finite-sized time-invariant approximating system are successfully demonstrated through correlation with the experiment in the frequency range which encompasses the first four modal families and the rotor speed range spanning up to the first observed experimental instability. Specifically, the study confirms the occurrence of the modal veering and lock-in phenomena, modal splits as well as the strong dominance of the 0th order frequency modulation clusters in the structural response. The results presented in this work show that the proposed experimental platform represents a useful minimal dynamic system with the behavioral characteristics of high significance for the design of novel electrically powered and propeller-driven aircrafts.