Rotordynamics of Gas-Lubricated Journal Bearing Systems, 1999 Mechanical Engineering Series

A discussion of models for the behaviour of gas bearings, particularly of the aspects affecting the stability of the system. The text begins with a discussion of the mathematical models, identifying the stiffness and damping coefficients, and describing the behaviour of the models in unstable regions. It then turns to apply these results to bearings: static characteristics and stability of various rotor systems and an extensive discussion of air rings.

I Theory.- 1. Mathematical Model of a Gas Journal Bearing.- 1.1. Reynolds Equation.- 1.2. Numerical Solution of the Reynolds Equation.- 1.3. Equations of Mass Flow through Feeding System.- 1.4. “Orbit” Model of Gas Bearing.- 2. Identification of Stiffness and Damping Coefficients.- 2.1. Free Vibrations.- 2.2. Step-Jump.- 2.3. Harmonic Forcing.- 2.4. Harmonic Motion of the Shaft.- 2.4.1. Accuracy of the Method.- 2.4.2. Estimation of the Coefficients for any ? andV— Interpolation.- 3. Mathematical Model of Rotor-Gas Bearing System.- 3.1. Equations of Motion — Symmetrical System.- 3.2. Reduced System.- 3.3. Method of Calculation of Eigenvalues.- 3.4. Equations of Motion — Unsymmetrical System.- II Applications.- 4. Gas Bearings.- 4.1. Static Characteristics of Gas Bearings.- 4.2. Stiffness and Damping Coefficients of Gas Bearings.- 4.2.1. Self-Acting Bearings.- 4.2.2. Bearings with the Direct Feeding System.- 4.2.3. Bearings with the Chamber Feeding System.- 4.2.4. Conclusions.- 5. Stability of Rotor — Gas Bearing System.- 5.1. Stability of Rotor with Unmovable Bushes.- 5.2. Stability of Rotor with Elastically Mounted Bushes — Symmetrical (Reduced) System.- 5.2.1. How to Design the Rotor Support.- 5.3. Stability of Unsymmetrical Rotor with Elastically Mounted Bushes.- 5.3.1. Stability of the Homogeneous Shaft Supported in Two Bearings.- 5.3.2. Stability of the Rotor with Concentrated Mass of the Shaft.- 5.3.3. Stability of the Unsymmetrical Rotor with the Unsymmetrical Support of the Bushes.- 5.3.4. An Influence of the Mass of the Bushes on the Size of Always-Stable Loops.- 6. Air Rings.- 6.1. Air Rings with the Direct Feeding System.- 6.2. Air Rings with the Chamber Feeding System.- 6.2.1. Air Hammer.- 6.2.2. Stiffness and Damping Coefficients of Air Rings.- 7. Stability of the Rotor — Bearing — Air Rings System (Applications)..- 7.1. Application 1.- 7.2. Application 2.- 7.3. Application 3.- 7.4. Application 4.- References.- Notation.