Multi-Scale Modeling of Aerostatic Spindles Based on Shape Error Harmonic Analysis and Static Characteristic Evaluation

Rotor machining errors strongly influence the air-film pressure distribution of aerostatic spindles and fundamentally limit performance enhancement. However, existing studies rarely provide a comprehensive statistical characterization based on measured manufacturing errors. To address this gap, a multi-scale modeling framework based on harmonic analysis of form errors is developed. Measured surface topography data from a batch of rotors are decomposed to establish a harmonic statistical model, which is then incorporated into a modified Reynolds equation together with macro-scale and micro-scale error components. The static performance of the aerostatic spindle is subsequently analyzed. Results show that low-order harmonics (1st–5th) dominate cylindricity errors, with amplitudes following a log-normal distribution. The statistical bounds are described by 3σ envelopes. When the eccentricity ε exceeds 0.3, barrel-shaped errors reduce the load capacity by more than 15%, whereas waist-drum-shaped errors exhibit a self-stabilizing tendency under small deviations. Performance degradation can be partially mitigated by adjusting the supply pressure and orifice diameter. This study addresses the research gap in understanding the impact of measured manufacturing errors on aerostatic spindle performance and provides a quantitative basis for tolerance allocation and performance optimization.