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

Abstract

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.

On the Integrity of Large-Scale Direct-Drive Wind Turbine Electrical Generator Structures: An Integrated Design Methodology for Optimisation, Considering Thermal Loads and Novel Techniques

“…Maxwell stress arises as a consequence of the attraction between the magnetism produced by the stator and the permanent magnets mounted on the rotor and is the largest of the operating loads. The local magnetic stress experienced by the rotor under different deflection modes, through its circumference, can be estimated using Equation (3) [16], below.…”

“…Likewise, there exists a number of different rotor-supporting topologies, such as the simple single-sided disk-supported rotor outlined in the IEA-15 MW-RWT's supporting documentation [8] or the variations of spoked, conical, and other supports detailed in [17] and displayed in Figure 3. Rotor structure deformation can occur in a number of ways, and therefore, closure of the airgap and structural failure can occur, as demonstrated in Figure 4, where the deformation of the outer rotor under different mode shapes are shown, with the undeformed shape in black and the deformed shape in grey -arising from the electromagnetic forces represented by arrows where, as stated in [16], (a) is Mode 0: radial expansion of the outer rotor into the airgap,…”

“…Torque (τ f ), rotational velocity (ω), and the in-plane component of gravity (g) were all unchanged from Mode 0, however, under Mode 1 loading, Maxwell's stress (σ PM ) was applied sinusoidally between a minimum of 433.4 kPa and a maximum of 461.7 kPa, as calculated following Equation (4) [16]:…”