Study on nonlinear torsional vibration of permanent magnet direct-driven system with uncertainties

There are complicated sources of uncertainty in electromechanical systems, and only by comprehensively considering the uncertainties from electromagnetic parameters, mechanical structures, and loads can the vibration response of the system be better forecasted. A high-power electromechanical device directly powered by a permanent magnet synchronous motor is taken as the object of research, and a nonlinear dynamic electromechanical coupling model of the system is established. In the case of the primary parameter resonance, the multi-scale technique is then used to determine the first-order approximation solution and numerical methods are employed to investigate the stability. Under uncertain parameter conditions, the vibration response of a permanent magnet direct-drive system is further predicted using the multi-scale method and the Chebyshev interval method in combination. Meanwhile, the scanning method is employed to obtain the reference values to evaluate the performance of the proposed approach. Numerous numerical examples demonstrate that the primary resonance response is more susceptible to variations in the magnetic remanence of the permanent magnet material, current amplitude, internal power angle, and torsional stiffness. In addition, under the influence of multi-source parameter uncertainties, the peak and area of the primary resonance are highly variable, which greatly reduces the operation stability of the electromechanical system. These results can provide a theoretical reference for vibration response prediction and anti-resonance design of permanent magnet direct-drive systems with multi-source uncertainties.