The tool RD-04 computes the dynamic coefficients of liquid annular seal using Black's model.
In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.
Liquid Annular Seal (Black Model)
The input in the toolbox is
After clicking "Run", the results will be shown as follows in another page.
Kxx=Kyy= 6912209.40233639 N/m
Kxy=-Kyx= 6872962.45169094 N/m
Cxx=Cyy= 109386.59478716 N-s/m
Cxy=-Cyx= 9354.76593832 N-s/m
Mxx=Myy= 74.44286203 N*s^2/m
Black model of liquid annular seals is developed based on Lomakin's theory. Due to the Bernoulli effect during the leakage process, radial forces are generated to support the rotation shaft in pumps.
For small whirl motion around a centered position, the linearized forces acting on the rotor are
Kxx=Kyy: Direct Stiffness
Kxy=Kyx: Cross-coupled Stiffness
Cxx=Cyy: Direct Damping Coefficient
Cxy=Cyx: Cross-coupled Damping Coefficient
Mxx=Myy: Mass Inertial
1. D. Childs, Turbomachinery Rotordynamics: Phenomena, Modeling, & Analysis, 1993, John Wiley & Sons Inc, New York.
2. W.J. Chen and E.J. Gunter, Introduction to Dynamics of Rotor-Bearing Systems, 2007, Trafford Publishing.