Design of high speed cylindrical NMR sample spinners

Abstract

Simple approximate solutions to compressible fluid flow problems are used to arrive at useful design equations for high‐speed spinning on cylindrical air bearings for NMR studies of solids. The optimum radial clearance is shown to depend on the 1/3 power of the rotor diameter, and is 0.027 mm for a 12‐mm rotor, with a surface speed of one half the speed of sound, c. The required air bearing hole diameter is about 0.3 mm with a square root dependence on the rotor diameter. A few general comments are made concerning turbine design, and a simple combination impulse‐reaction type is described which offers some improvement in drive efficiency. Drive air flow is shown to depend approximately on the square root of the rotor volume for a surface speed 0.5 c. Relevant data for a number of high strength materials including hard ceramics are tabulated, and limiting speeds are calculated. The design equations are verified for 8 and 12 mm rotors made from Al₂O₃ with wall thicknesses equal to 6% of the diameter.