Methods of Feasible Directions. By G. Zoutendijk. Pp. 126. 30s. 1960. (D. van Nostrand Co. London)

This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.

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Dynamics of rotating machines

Vibration suppression of rotating machinery is an important engineering problem. In this paper, a review of the research work performed in real-time active balanc- ing and active vibration control for rotating machinery, as well as the research work on dynamic modeling and analy- sis techniques of rotor systems, is presented. The basic methodology and a brief assessment of major difficulties and future research needs are also provided.

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Active Balancing and Vibration Control of Rotating Machinery: A Survey

Survey of nonlinear vibration of gear transmission systems

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

Theoretical analysis of lateral response due to torsional excitation of geared rotors

Dynamic analysis of gear-rotor system with viscoelastic supports under residual shaft bow effect

An efficient optimal algorithm is developed to minimize, individually or simultaneously, the total weight of the shaft and the transmitted forces at the bearings. These factors play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross-sectional area of the shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multi-objective optimization algorithm can greatly reduce both the weight of the shaft and the forces at the bearings with critical speed constraints.

Multi-objective Optimization of Rotor-Bearing System With Critical Speed Constraints

The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems; however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of the method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

Generalized polynomial expansion method for the dynamic analysis of rotor-bearing systems

The vibration and active control of a flexible rotor system with magnetic bearings are investigated using Hybrid Method (HM) and H{sup {infinity}} control theory with consideration of gyroscopic effect. The hybrid method, which combines the merits of the finite element method (FEM) and generalized polynomial expansion method (GPEM) is employed to model the flexible rotor system with small order of plant. The mixed sensitivity problem of H{sup {infinity}} control theory is applied to design the control of system vibration with spillover phenomena for the reduced order plant. The H{sub 2} control design is also employed for comparison with the H{sup {infinity}} design. The experimental simulation is used to illustrate the effects of control design. It is shown that the H{sup {infinity}} controller design can be very effective to suppress spillover phenomena. In addition, the H{sup {infinity}} control design has robustness to the variation of the model parameters. The application of the hybrid method (HM) together with H{sup {infinity}} control design is highly recommended for vibration control of flexible rotor systems with magnetic bearings.

Ting Nung Shiau

Papers

Theoretical analysis of lateral response due to torsional excitation of geared rotors

Dynamic analysis of gear-rotor system with viscoelastic supports under residual shaft bow effect

Multi-objective Optimization of Rotor-Bearing System With Critical Speed Constraints

Generalized polynomial expansion method for the dynamic analysis of rotor-bearing systems

Vibration and Control of a Flexible Rotor in Magnetic Bearings Using Hybrid Method and H∞ Control Theory