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]n the field of gas liquefaction and low temperature refrigeration, small high-speed expansion turbines ar e often employed as the so urce of refrigeration. In the smaller sizes of machin es however , the life and speed of comren tional bearings are limi ted, and co n· sequently a lower limit is set to t he practical size of such machines. This limitation may be aU6\'iated by t he use of gas-lubricated bearings to suppor t the shaft. The bearings may be lubricated wi th process gas, thus eliminating the risk of con tamination with oil. Since t here is no solid friction, there should be no wear and co nsequently t he life of the bearings should be of indefini te duration. In the operation of a gas-lubricated bearing, the surface of the shaf t must never touch the surface of the bearing, since at the high-surface speeds usually employed, such co ntact may resul t in seizure and the consequ en t destruction of the bearing, Under normal operating conditions t he shaft should be supported by forces due to pressure in the gas film between the shaft and the bearing and these forces must be such that the shaft is maintained in a position of stable equilibrium. In certain types of gas-lubricated bearings, a form of instability known as whirl is sometimes obser ved , particularly at high speeds of operation. If the speed of the shaft is increased above a critical valu e, the cen ter of the shaft orbits about the center of the bearing at a speed approximately one-half the speed of the shaftcommonly known as half-speed whirl. Whirl may be stable or un stable: Stable whirl is characterized by the cen ter of th e shaf t moving in a closed orbit about its former po ition of equilibrium. This is illustrated in figure 1. Unstable whirl (fig. 2) is characterized by the center of the shaft mo\ring along a spiral orb it of increasing amplitude. '1'he exten t of the increase in amplitude is, of course, limited to the exten t of the radial clearance between the shaft and the bearing. The bearing described below has been specially des igned to ensure stability even at the highest speeds of operation wi th heliu m gas as the presslU'izing medium. The theory of this bearing was presen ted at t he First In tern ittional Symposium on Gas Lubricated Bearings [Sixsmith, 1959bJ. In the present paper , t he theory has bee n extended and applied to t he design of the bearings of a helium-expansion t urbine [Binniogham, Sixsmith, Wilson , 1962J. The

The theory of a stable high-speed externally pressurized gas-lubricated bearing