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

Review of performance optimization techniques applied to wind turbines

In this paper we outline a general method that can be used to model spindle assembly, which consists of spindle shaft, angular contact ball bearings and housing. The spindle shaft and housing are modeled as Timoshenko's beam by including the centrifugal force and gyroscopic effects. The bearing is modeled as a standard nonlinear finite element based on Jones' bearing model that includes the centrifugal force and gyroscopic effects from the rolling elements of bearings. By applying cutting forces to the spindle for a given preload, the stiffness of the bearings, contact forces on bearing balls, natural frequencies, time history response, and frequency response functions of the spindle assembly can be evaluated. In the paper we provide details of the mathematical model supported by experimental results obtained from an instrumented test spindle.

A General Method for the Modeling of Spindle-Bearing Systems

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.

/pdf/active-balancing-and-vibration-control-of-rotating-machinery-3edr2htqn3.pdf

Active Balancing and Vibration Control of Rotating Machinery: A Survey

High speed machining (HSM) is a promising technology for drastically increasing productivity and reducing production costs. Development of high-speed spindle technology is strategically critical to the implementation of HSM. Compared to conventional spindles, motorized spindles are equipped with built-in motors for better power transmission and balancing to achieve high-speed operation. However, the built-in motor introduces a great amount of heat into the spindle system as well as additional mass to the spindle shaft, thus complicating its thermo-mechanical-dynamic behaviors. This paper presents an integrated model with experimental validation and sensitivity analysis for studying various thermo-mechanical-dynamic spindle behaviors at high speeds. Specifically, the following effects are investigated: the bearing preload effects on bearing stiffness, and subsequently on overall spindle dynamics; high-speed rotational effects, including centrifugal forces and gyroscopic moments on the spindle shaft and, subsequently, on overall spindle dynamics; and the spindle dynamics on the cutting point receptance. The proposed integrated model is a useful tool for differentiating quantitatively different effects on the spindle behaviors. The results show that a motorized spindle softens at high speeds mainly due to the centrifugal effect on the spindle shaft.

An integrated thermo-mechanical-dynamic model to characterize motorized machine tool spindles during very high speed rotation

A Finite Rotating Shaft Element Using Timoshenko Beam Theory

Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis

This study investigates the effect of constant axial torque on the dynamics of rotorbearing systems using a finite element model. The finite element equation of motion is formulated using the variational approach and the inclusion of axial torques gives rise to an incremental torsional stiffness matrix. This matrix is circulatory since the system is non-conservative. The finite element model is used to determine the static buckling torques and the critical speeds of a uniform shaft for short and long bearings.

H. D. Nelson

Papers

A Finite Rotating Shaft Element Using Timoshenko Beam Theory

Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis

The Dynamics of Rotor-Bearing Systems With Axial Torque—A Finite Element Approach

Iterative Determination of Squeeze Film Damper Eccentricity for Flexible Rotor Systems