The rapid increase in operating speeds of mechanisms and machines during the last few decades has posed mechanical and technical engineers aseries of new problems. One of these is that of the investigation of the dynamics of flexible rotors operating at speeds greater than the first- and higher-order critical speeds. In con temporary machine design we must cope with various machines and assemblies containing shafts which operate under such conditions: turbogenerators. gas and steam turbines. spinning shafts. high-capacity pumps, and a multitude of special-purpose machines. One of the problems in the dynamics of flexible rotors-the passage through the resonance state-has re cently been almost completely solved in the work of Yu. A. Mitropol'skii. F. M. Dirnentberg, V. O. Kononenko. A. P. Fillippov. and others. Much less attention has been devoted to two other interrelated problems in the dynamics of high-speed rotors: the loss of stability in regime-combining forced vibrations due to imbalance in the supercritical region, along with self-induced or self-exc1ted vibrations. These problems are rapidly becoming more important as self-induced vibrations occurring at speeds beyond the critical speed are being met with more and more often in practice [1-3]. One of the main causes for the loss of stability of a rotor in the supercritical region. as was first estab lished by Kimball in [4] and Newkirk in [5] during the ninteen-twenties, is the force due to interna1 friction.
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Verlagsort
Verlagsgruppe
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46 s/w Abbildungen
46 illus.
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ISBN-13
978-1-4684-9075-6 (9781468490756)
DOI
10.1007/978-1-4684-9075-6
Schweitzer Klassifikation
I. Linear Transverse Vibrations of Rotors with Concentrated Mass Distribution.- § 1. Critical Speeds of Rotors. The Differential Equations and Boundary Conditions.- § 2. Determination of Critical Velocities by the Initial-Parameters Method.- § 3. Forced Vibrations in Rotors Caused by Imbalance. Characteristic Frequencies of Transverse Vibrations of Rotors.- § 4. Examples. Bending Vibrations of High-Speed Spindles.- § 5. Generalized Conditions for the Orthogonality of the Characteristic Functions of Nonrotating Shafts with Distributed and Concentrated Loads.- II. The Nonlinear Differential Equations for Flexural Vibrations of Unbalanced Rotors.- § 1. The Differential Equations for the Motion of a Rotor in the Absence of Gyroscopic Moments.- § 2. The Differential Equations of Motion of a Rotor with Operating Speed Between the First- and Second-Order Critical Speeds.- § 3. Properties of the Nonlinear Differential Equations for the Flexural Vibrations of a Rotor with no Mass Gyroscopic Action.- III. Almost-Periodic Solutions of Quasi-Linear Systems and Their Stability Under Conditions of Multiple Resonance.- § 1. The Case of Perfect Resonance.- § 2. The Case When the Resonance Relations Are Approximately Satisfied.- § 3. The Case of Nonresonance.- IV. A Qualitative Analysis of the Nonlinear Oscillations of Rotors. Mixed and Self-Induced Oscillation.- A. The Nonlinear Oscillations of Rotors Operating at Speeds Between the First- and Second-Order Critical Speeds.- B. Self-Induced Oscillations Beyond the Second Critical Speed.- V. Self-Induced Oscillations of Rotors with Gyroscopic Moments Present in the System (Simplest Case).- § 1. The Differential Equations of Motion of a Cantilever-Supported Disc. The Reduction of a Quasi-Linear, Gyroscopic System to StandardForm.- § 2. The Standard Solutions of the Nonlinear Equations of Motion for a Disc at the End of a Shaft for the Nonresonance Case.- § 3. A Numerical Method for the Investigation of the Stability of Gyroscopic Systems (Linear Problem).- VI. An Experimental Investigation of Self-Induced Oscillation of Rotors. The Self-Induced Oscillations of High-Speed Spindles.- § 1. A Description of High-Speed Spindles of the V 25 and V 28 Families.- § 2. The Bench for the Experimental Investigation of Spindle Vibrations.- § 3. Self-Induced Oscillations of Spindles Without Damping. The Effect of Elastic Coupling on Self-Induced Vibrations.- § 4. The Damping of Spindle Self-Induced Oscillations. Bushings with Cylindrical and Spherical Sleeves. Dampers with Damping Sleeves. Rubber Dampers. The Experiments of M. I. Chaevskii.- § 5. The Effect of Shocks on the Self-Excitation of Rotor Vibrations.- Appendix. The Stability of Periodic Solutions of Quasi-Linear Systems with Nonsimple Elementary Divisors.- Literature Cited.
