A new dynamic model of hysteresis in harmonic drives

• Published in: IEEE transactions on industrial electronics (1982) Vol. 50; no. 6; pp. 1165 - 1171
• Main Authors: Dhaouadi, R., Ghorbel, F.H., Gandhi, P.S.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Differential equations; Dynamic models; Dynamical systems; Dynamics; Friction; Gears; Harmonics; Hysteresis; Instruments; Kinematics; Mathematical model; Mathematical models; Nonlinear dynamics; Nonlinearity; Space technology; Studies; Torque
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2003.819661

In this paper, we propose a new dynamic model to describe the hysteresis phenomenon in harmonic drives. The experimental observation of the dynamic torque-displacement relationship for a harmonic drive shows a hysteresis characteristic indicating the simultaneous presence of energy storage and energy dissipation mechanisms. To completely characterize these mechanisms and yet have a simple representation for control, we develop a new hysteresis model using the heredity concept of dynamic systems. This model represents the hysteresis phenomenon by a combination of a nonlinear stiffness component and a nonlinear damping component leading to a mathematically well-posed nonlinear differential equation. The parameters of the model are identified using optimization techniques. We present some important mathematical properties of the model that give insight into model behavior and thus establish a mathematical basis for control. Numerical simulations in comparison with experimental data using our Harmonic Drive Test Apparatus verify the accuracy of the proposed model to represent the complex hysteresis dynamics of harmonic drives.