Stability of a Rotor Partially Filled With a Viscous Incompressible Fluid

Abstract

A hollow circular cylinder rotating with constant angular velocity and partially filled with a viscous incompressible fluid has been analyzed for stability. The analysis can be extended to apply to many different rotor geometries. The results of this analysis predict that over a range of operating speeds, the system is unstable. The extent of this unstable region is determined by the system parameters. The interplay between viscosity of the fluid and damping on the rotor is especially important in determining stability boundaries. A parametric study is presented for a rotor modeled as a cup in the middle of a symmetrically supported massless shaft. The rotor is subject to a linear spring and a linear damper. Rotor unbalance, gravity, and axial effects are considered negligible.

On the dynamics of the fluid balancer

“…The acceleration vector f € X r € Y r g T is given by (e.g. Hendricks and Morton, 1979;Chandrasekhar, 1961, p. 82)…”

An analytical investigation on the dynamic stability of a rotor filled with liquid

“…In the early study, the liquid of rotor chamber was assumed to be ideal and rotor body was rigid. For this reason, the dynamic stability was investigated for rotor filled with viscous liquid by Hendricks, Daich and Bar, Saito and Holm-Christensen [6][7][8][9]. Furthermore, rigid body angular displacement was introduced by Hendricks and Lichtenberg, the research on rotor filled with liquid was extended to three dimensions [10,11].…”

Dynamic characteristics of liquid motion in partially filled tanks of spinning spacecraft

“…For large Reynolds numbers, Re>0(lQ 5 ), the boundary-layer approximation is appropriate. For INTELSAT VI parameters, the Reynolds number is greater than 10 6 . During the INTEL-SAT VI study, 12 all of the analytical models discussed here were compared and the conclusion reached was that the boundary-layer model gives the most accurate prediction of liquid dynamic characteristics.…”

“…Using the procedure proposed by Hendricks and Morton, 6 the unknown parameters are expanded in the power of Re~l /2 as follows:…”

“…Viscous effects are considered only for a boundary layer near the wetted surface. Hendricks and Morton 6 analyzed the stability of a rotor partially filled with a viscous incompressible fluid. Stergiopoulous and Aldridge 7 studied inertial waves in a partially filled cylindrical cavity during spin up.…”