A Stiffness Approach for Coupling Structural and Magnetic Models for the Sustainable Design, Optimisation and Real-Time Structural Integrity Assessment of Radial Flux Permanent Magnet Generators for Direct-Drive Wind Turbines

The mass of a direct-drive generator is often defined by the requirements for structural stiffness to meet the magnetic stiffness between the rotor and stator surfaces. This paper analyses this magnetic stiffness and estimates the structural stiffness of direct-drive generators for different modes of deflection. The magnetic stiffness modelling is based on an analytical model of the airgap closing forces. The final models are verified using finite element analysis and developed for both permanent magnet and wound rotor generators. It shows that wound rotor machines have higher stiffness requirements than permanent magnet machines. The structural stiffness of the generator rotor and stator is evaluated for different modes by applying spatially varying forces and finding the associated deflections. Structural stiffnesses for the rotor, stator and bearing are then combined. Finally, the magnetic and structural stiffnesses are combined and a stiffness margin can be found. This method is applied to a relatively stiff and a relatively compliant set of generator structures in a case study. The analytical model presented in this paper is useful for structural optimisation purposes or as part of an online structural health monitoring system as it could assess the integrity of the machines in real time.