This study proposes a dynamic model of a deep-groove ball bearing with six degrees of freedom. The model includes descriptions of non-linear Hertzian contact deformation and elastohydrodynamic (EHD) fluid film. The geometry, material properties and diametral clearance of the bearing are given as the input to the proposed model. The bearing force and torque components are calculated from the relative displacements and velocities between bearing rings. Distributed defects, such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. The proposed ball bearing model could be used in the general multi-body or rotor dynamics computer code as an interference element between the rotor and the housing. The numerical results obtained from the model are compared with those found in the literature in Part 2 of this paper.

The model of the ball bearing proposed in Part 1 is implemented and analysed using a commercial multi-body system software application (MSC. ADAMS). The effect of the diametral clearance of the bearing on the natural frequencies and vibration response of the rotor-bearing system is studied. The diametral clearance is found to have a significant effect on the level of vibration as well as on the natural frequencies. Low-order waviness, also known as out-of-roundness, is found to generate vibration at frequencies of the waviness order multiplied by the rotation speed. On the other hand, the waviness orders close to the number of balls in the bearing (z± 1 and z) are found to generate vibrations at the ball passage inner ring and ball passage outer ring frequencies. Various excitations produce sum and difference frequencies. Localized defects in the inner and outer ring are found to generate vibrations at bearing defect frequencies. The simulation results are in line with the analytical and experimental results available in the literature.

Mechanical interactions between a wind turbine and a direct-driven permanent-magnet synchronous generator (PMSG) are studied, and a model to analyze the system behavior is suggested. The proposed model can be applied to analyze the mechanical vibrations of direct-driven wind turbine installations both in steady state and in dynamic cases. The cogging torque and torque ripple of the PMSG are used as excitation sources in the mechanical model. Four different permanent-magnet rotor constructions are analyzed. It is shown that the maximum allowable value of the cogging torque of the direct-driven permanent-magnet wind generator in this case is 1.5%-2% of the rated torque even when the corresponding resonance frequency does not occur in the operational speed range of the wind turbine. Furthermore, it was noticed that the resonance caused by the excitation torque should occur at the lowest possible speed.