Spectral Characterization of Nonlinear Load Torque Effects in Linear Tooth Belt-Driven Systems

Accurate modeling of mechatronic motion systems requires accounting for nonlinear load torque effects arising from mechanical and electromagnetic interactions. This paper presents a non-invasive methodology to characterize such effects through spatial frequency analysis of electromagnetic motor torque signals collected during constant velocity experiments. Using the Nonuniform Fast Fourier Transform (NUFFT), the torque signal is analyzed in the spatial domain without requiring uniform positional sampling. The load torque is decomposed according to a proposed formulation into dominant periodic features and a nonlinear friction profile, enabling interpretable, position-dependent insights into system behavior. The approach is demonstrated on a linear tooth belt-driven system, revealing periodic components related to 1) belt-to-pulley tooth engagement, 2) motor cogging torque, and 3) additional motor-induced oscillations. These features are consistently identified across a range of velocities, without requiring additional sensors or excitation signals. The resulting decomposition enhances understanding of individual torque contributions and supports model-based control, digital twin implementation, condition monitoring, and compensation strategies in mechatronic systems.