1st Edition

Computational Techniques of Rotor Dynamics with the Finite Element Method

By Arne Vollan, Louis Komzsik Copyright 2012
    296 Pages 210 B/W Illustrations
    by CRC Press

    296 Pages 210 B/W Illustrations
    by CRC Press

    For more than a century, we have had a firm grasp on rotor dynamics involving rigid bodies with regular shapes, such as cylinders and shafts. However, to achieve an equally solid understanding of the rotational behavior of flexible bodies—especially those with irregular shapes, such as propeller and turbine blades—we require more modern tools and methods.

    Computational Techniques of Rotor Dynamics with the Finite Element Method explores the application of practical finite element method (FEM)-based computational techniques and state-of-the-art engineering software. These are used to simulate behavior of rotational structures that enable the function of various types of machinery—from generators and wind turbines to airplane engines and propellers.

    The book’s first section focuses on the theoretical foundation of rotor dynamics, and the second concentrates on the engineering analysis of rotating structures. The authors explain techniques used in the modeling and computation of the forces involved in the rotational phenomenon. They then demonstrate how to interpret and apply the results to improve fidelity and performance.

    Coverage includes:

    • Use of FEM to achieve the most accurate computational simulation of all gyroscopic forces occurring in rotational structures
    • Details of highly efficient and accurate computational and numerical techniques for dynamic simulations
    • Interpretation of computational results, which is instrumental to developing stable rotating machinery
    • Practical application examples of rotational structures’ dynamic response to external and internal excitations
    • An FEM case study that illustrates the computational complexities associated with modeling and computation of forces of rotor dynamics
    • Assessment of propellers and turbines that are critical to the transportation and energy industries

    Useful to practicing engineers and graduate-level students alike, this self-contained volume also serves as an invaluable reference for researchers and instructors in this field.

    CRC Press Authors Speak

    Louis Komzsik introduces you to two books that share a common mathematical foundation, the finite element analysis technique. Watch the video.

    Part I: Theoretical Foundation of Rotor Dynamics

    Introduction to Rotational Physics

    Fixed Coordinate System

    Rotating Coordinate System

    Forces in the Rotating System

    Transformation between Coordinate Systems

    Kinetic Energy Due to Translational Displacement

    Kinetic Energy Due to Rotational Displacement

    Equation of Motion in Rotating Coordinate System

    Equation of Motion in the Fixed Coordinate System

    Coupled Solution Formulations

    Matrix Formulation of Lagrange’s Equations

    Coupling Nodal Translations to the Stationary Part

    Simultaneous Coupling of Translations and Rotations

    Full Coupling of the Stationary and Rotating Parts

    Time-Dependent Terms of Equations

    Finite Element Analysis of Rotating Structures

    Potential Energy of Structure

    Dissipative Forces

    Non-dissipative Forces

    Finite Element Equation Assembly

    Coupled Equilibrium Equation Assembly

    Analysis Equilibrium Equations

    Computational Solution Techniques

    Direct Time Domain Solution of the Equilibrium Equation

    Direct Frequency Domain Solution

    Direct Free Vibration Solution

    Modal Solution Technique

    Static Condensation

    Dynamic Reduction

    Numerical Solution Techniques

    The Lanczos Method

    Orthogonal Factorization

    The Block Lanczos Method

    Solution of Periodic Equations


    Part II: Engineering Analysis of Rotating Structures

    Resonances and Instabilities

    Analysis Type vs. Modeling Approach

    Resonances and Instabilities

    Critical Speed of Rotating Mass

    The Laval Rotor

    Influence of Damping

    Unsymmetric Effects of Bearing and Rotor

    A Rotating Tube

    Rotating Model with Flexible Arms

    The Ground Resonance

    Dynamic Response Analysis

    Frequency Response without Rotation

    Frequency Response with Rotation

    Transient Response without Rotation

    Transient Response with Rotation

    A Finite Element Case Study

    Turbine Wheel with Shaft and Blades

    Engineering Analysis

    Computational Statistics

    The Journal Bearing

    Active External Loads

    Analysis of Aircraft Propellers

    A Propeller Blade

    Quasi-steady Aerodynamics of Blade

    Unsteady Aerodynamics of Blade

    Propeller with Four Blades

    Analysis of Wind Turbines

    An Example Wind Turbine

    Modeling and Analysis of Wind Turbine Blade

    Wind Turbine with Three Blades

    Response Analysis of Wind Turbines

    Horizontal Axis Wind Turbines with Two Blades


    Arne Vollan studied aeronautical engineering at the Technical University of Trondheim (Norway) and Aachen (Germany), and holds the degree Diplom Ingenieur. He was employed by several aeronautical companies such as VFW-Fokker (now Airbus), Helicopter Technik Muenchen, Dornier, Nationaal Lucht- en Ruimtevaartlaboratorium, and Pilatus Aircraft as a dynamic and aeroelastic specialist. He was also a consultant and developed programs for the analysis of rotating structures like wind turbines and propellers. Since 2002 he has been working at AeroFEM GmbH in Switzerland on rotor dynamics and the aeroelasticity of aircraft and large wind turbines.

    Louis Komzsik is a graduate of the Technical University of Budapest with an engineering degree and the Eötvös University of Sciences in Budapest with a mathematics degree, and he holds a Doctorate from the Technical University of Budapest, Hungary. He was employed by the Hungarian Shipyards from 1972 to 1980 and worked at the McDonnell-Douglas Corporation in 1981 and 1982. He was the chief numerical analyst at the MacNeal-Schwendler (now MSC Software) Corporation for two decades. Since 2003 he has been the chief numerical analyst at Siemens PLM Software. For the past 30 years he has been the architect of the modern numerical methods of NASTRAN, the world’s leading finite element analysis tool in structural engineering.

    Aeronautical engineers Vollan and Komzsik have worked in many companies designing rotors that blow wind or that wind turns and have cooperated on several projects over the past quarter century. From that collaboration, they explain how to apply modern analysis tools such as finite elements to the rotational behavior of flexible bodies …
    —SciTech News, Vol. 66, September 2012