A Stiffness Approach for Coupling Structural and Magnetic Models for the Design and Optimization of Radial Flux PM Generators for Sustainable 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 carried out 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 are 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. For the airgap not to close, this combined stiffness must be greater than 0. This method is applied to a relatively stiff and a relatively compliant set of generator structures in a case study in order to find the optimum and more sustainable configuration.