A novel method for estimating three-domain limit cycles in a 3D wing-aileron model with freeplay in aileron deflection

Abstract

Freeplay-induced limit-cycle oscillations (LCOs) have been a subject of concern for decades This paper proposes a novel method named the dual quasi-harmonic balance (DQHB) method for obtaining quick estimations on LCO behaviors. Two quasi-harmonic motions based on eigenvalues of the underlying and overlying linear systems are constructed so that a three-domain LCO can be interpreted as a dynamic balance between the two motions. Practicable formulations for LCO amplitudes and frequencies and hysteresis are proposed and applied to a 3D wing-aileron model with control-surface freeplay. Wind tunnel tests of flutter and LCOs were carried out with various degrees of freeplay. Numerical results show that the DQHB method produces the same air speeds of LCO onset (31.37 m/s) and critical instability (47.44 m/s) as the describing function (DF) method and time integrations do, which are also verified by test data. The DQHB method also predicts jump and hysteresis phenomena, which are confirmed by test data but not obtained by the DF method or time integrations. Notably the DQHB method can be implemented as fast and convenient as the DF method while provides more physical insights into the mechanism of freeplay-induced three-domain LCOs.