Bursting Oscillations and Chaos Analysis of Precision Harmonic Drive

Abstract

Abstract. A nonlinear torsional vibration model of precision harmonic drives is developed, incorporating stiffness degradation, static transmission errors, piece-wise backlash, and periodic torque excitation. Dynamic responses are quantified through angular domain solutions of the dimensionless governing equations using the Runge−Kutta method. The research identifies two types of bursting oscillations caused by stiffness and backlash, and reveals their triggering mechanisms. Furthermore, the effects of factors such as the damping coefficient, excitation torque, and speed on the chaotic characteristics are analyzed using bifurcation diagrams, time histories, phase trajectories, and Poincaré maps. The results indicate that with prolonged service time, interface damage-induced stiffness degradation or enlargement of backlash may simultaneously induce bursting oscillations and chaotic motion. Furthermore, the amplitude of the torque fluctuation component critically governs the emergence of bursting oscillations, with these phenomena occurring when Ab′ ≥ To′. The dynamic behavior of harmonic drives exhibits strong dependence on operating conditions, with numerical simulations demonstrating that progressive increases in speed and load torque induce transitions toward increasingly unstable chaotic regimes. Increasing damping can suppress this transition. These findings elucidate the mechanisms underlying undesirable nonlinear oscillations in the system, while establishing theoretical foundations for control strategies in precision harmonic drive applications.