Rotational accuracy of an aerostatic motorized spindle under gas–magnetic field coupling

Assembly eccentricities of the stator and rotor disturb the motor air-gap distribution and induce unbalanced magnetic pull (UMP), which subsequently affects the rotational accuracy of aerostatic motorized spindles. To clarify the underlying mechanism, this study establishes a gas–magnetic coupled dynamic model incorporating motor eccentricity. This model employs VBS scripts to realize bidirectional co-simulation between the finite-difference gas-bearing model in MATLAB and the finite-element electromagnetic-field model in ANSYS Maxwell. The developed framework enables real-time feedback of UMP into the rotor dynamic equations. The results indicate that the dominant effect of stator eccentricity is a shift of the whirl center, with a regular 11-lobed waviness superimposed on the shaft-center orbit. By contrast, rotor eccentricity produces a substantially more pronounced enlargement of the whirl radius than stator eccentricity, indicating an amplitude-amplification-dominated response similar to that induced by an additional unbalance mass. Mixed eccentricity simultaneously causes both whirl-center offset and whirl-radius enlargement, while producing more complex local petal-like waviness in the shaft-center orbit, thereby exerting the strongest adverse effect on spindle rotational accuracy. Frequency-domain analysis indicates that the eccentric orbit is formed by the combined action of the fundamental-frequency response and higher-order harmonics, suggesting that its local response contains richer higher-order disturbance components. Experimental results confirm that the synchronous radial error increases with increasing stator and rotor eccentricities. The experimental trends are in good agreement with the corresponding simulation results. The study reveals the distinct mechanisms of UMP under different eccentricity forms and provides a theoretical basis for assembly-error control and high-precision operation of aerostatic motorized spindles.