Modeling and Identification of Friction Torque in Harmonic Drive Systems

Harmonic drive systems are favored due to their compact design, lightweight, and affordability. However, their transmission accuracy, stability, and efficiency can be impeded by the friction torque present within them. More specifically, the periodic friction torque, triggered by the teeth engagement of the circular spline and flex spline, may provoke resonance in the harmonic drive system, causing unsteady speed fluctuations and jumps. To enhance transmission performance, experts have scrutinized the modeling and identification issues related to friction torque in these systems. Despite this, current studies focused on modeling friction torque, particularly those analyzing periodic friction torque arising from spline engagement, remain insufficient. Currently employed identification methods for friction torque model parameters, such as limit cycles, are nonlinear. These methods are computationally complex and demand substantial computing power. This study introduced a friction torque model in harmonic drive systems, with a particular emphasis on the model of periodic friction torque resulting from the teeth engagement of circular spline and flex spline. A linear parameter identification method, utilizing the Moore - Penrose pseudoinverse, was suggested. Experimental data were analyzed using fast Fourier methods to corroborate the friction torque model in harmonic drive systems. The accuracy of the identification method was assessed by comparing the identified friction torque with the actual one. This study broadens the understanding of friction torque in harmonic drive systems, especially the periodic friction torque component. The proposed identification method is simple to calculate and easy to implement, thereby enhancing the efficiency of identifying friction torque parameters in engineering applications.