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.