Numerical modeling and design decisions for aerostatic bearings with relatively large nozzle sizes in Magic-Angle Spinning (MAS) systems

Numerical stability analysis for aerostatic bearings was performed to obtain optimized design parameters for small submillimeter to millimeter range diameter cylindrical rotors. Such rotors are used in nuclear magnetic resonance (NMR) application to rotate sample around an axis inclined by magic angle (54.74o) relative to the magnetic field direction at rotational frequencies of about 100 kHz (magic-angle spinning, MAS). The governing Reynolds equation for the fluid film between rotor and bearing was modified for small size aerostatic bearings with relatively large nozzle diameters. The modified Reynolds equation was solved using a finite-volume method to obtain pressure and film thickness around the rotor. This led to the solution of the maximum stable inertial force as a function of rotational frequency and design parameters. The comparison with aerostatic bearings with infinitesimal nozzle sizes was obtained for supported rotor weight and critical vibrational frequency of the rotor. The stable inertial force was found to correspond to a specific nozzle diameter and a specific rotor–bearing clearance. Numerical investigation also shows an enhancement of stable inertial force with decreasing nozzle number or increasing molecular mass of the impinging gas for a specific range of nozzle parameters. Experimental observations further confirmed the role of nozzle diameter, nozzle number and molecular weight of the gas in enhancing the rotor spinning frequency. Further, design decisions were made based on such analysis and were tested for varying rotor size and bearing properties. Using design optimization based on numerical simulation, the maximum frequency of rotation for a home-built 0.4mm MAS rotor could be enhanced from 25 kHz up to 110 kHz, still below the extrapolation from large rotors.