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Library of Congress Cataloging‐in‐Publication Data
Names: Breńkacz, Łukasz, author.
Title: Bearing dynamic coefficients in rotordynamics : computation methods and practical applications / Łukasz Breńkacz.
Description: First edition. | Hoboken, NJ : Wiley, 2021. | Includes bibliographical references and index.
Identifiers: LCCN 2020053700 (print) | LCCN 2020053701 (ebook) | ISBN 9781119759263 (hardback) | ISBN 9781119759249 (adobe pdf) | ISBN 9781119759171 (epub) | ISBN 9781119759287 (obook)
Subjects: LCSH: Rotors–Dynamics. | Bearings (Machinery)
Classification: LCC TJ1058 .B74 2022 (print) | LCC TJ1058 (ebook) | DDC 621.8/2–dc23
LC record available at https://lccn.loc.gov/2020053700 LC ebook record available at https://lccn.loc.gov/2020053701
Cover Design: Wiley
Cover Image: © photosoup/iStock/Getty Images
to my wife Dagmara, my daughter Agata, and my son Wojciech
List of Tables
| Table 3.1 | Successive eigenfrequencies and the corresponding damping values calculated for the laboratory test rig. |
| Table 5.1 | Parameters of the numerical model. |
| Table 5.2 | Stiffness coefficients. |
| Table 5.3 | Damping coefficients. |
| Table 5.4 | Mass coefficients. |
| Table 7.1 | Summary of the real and calculated stiffness, damping and mass coefficients for the two bearings for the reference case; representation of the relative calculations error. |
| Table 7.2 | Summary of the real and calculated stiffness, damping, and mass coefficients for the two bearings for a case with displaced force; results “with correction” take into account the uneven distribution of excitation force in the calculation procedure. |
| Table 7.3 | Summary of the real and calculated stiffness, damping and mass coefficients for the two bearings for a case with an excitation at an angle of α = 15°. |
| Table 7.4 | Summary of the real and calculated stiffness, damping and mass coefficients of two bearings for an asymmetrical rotor. |
| Table 8.1 | Stiffness, damping and mass coefficients of the rotor–bearing system for the entire speed range. |
| Table 8.2 | Standard deviation of stiffness, damping and mass coefficients of the rotor – bearing system for the entire speed range. |
| Table 9.1 | Parameters of the numerical model in the KINWIR program. |
| Table 9.2 | Stiffness and damping coefficients obtained from linear calculations in the KINWIR. |
| Table 9.3 | Minimum and maximum values of stiffness coefficients (N/m) calculated in the NLDW program. |
| Table 9.4 | Minimum and maximum values of damping coefficients (N·s/m) calculated in the NLDW program. |
| Table 10.1 | Comparison of the calculated stiffness and damping coefficients for the three methods used for a speed of 3000 rpm. |
Preface
This monograph concerns the experimental and numerical methods of determination of dynamic coefficients of hydrodynamic radial bearings. Bearings are one of the basic elements influencing the dynamics of rotor machinery. The main parameters with which the operation of bearings can be described (and thus the operation of the entire rotating system) are their stiffness and damping coefficients.
This book includes a chapter about practical applications of bearing dynamic coefficients. It is shown how changes of bearing dynamic coefficients affect the dynamic performance of rotating machinery. Some examples are included with all the necessary data to allow rotordynamics analysis to be conducted and the dynamic coefficients of journal bearings to be calculated so that the readers can replicate the results presented in this book and compare them with their own results. This book presents in detail an experimental method of determining dynamic coefficients of bearings. An additional objective is to describe numerical methods of determining dynamic coefficients of hydrodynamic bearings (linear and non‐linear). The range of applicability of various calculation methods was determined based on measurements made for a rotating machine equipped with hydrodynamic bearings with clearly non‐linear operating characteristics.
Experimental research was carried out with the use of the impulse method, on the basis of which dynamic parameters of hydrodynamic bearings were determined. The applied method with a linear calculation algorithm allows the determination of stiffness and damping coefficients and the determination of mass coefficients in one algorithm. The stiffness and damping coefficients cannot be determined directly, thus indirect calculation methods are used. The mass of the rotor is a directly measurable parameter. Indirectly calculated mass coefficients can be compared with the known mass of the rotor. On this basis, it is possible to make preliminary estimations of the correctness of the results obtained.
As part of the study, the sensitivity analysis of the aforementioned experimental method was carried out with the use of a model created in Samcef Rotors software. The influence of unbalance, displacement of measuring sensors, and various variants of driving force were analyzed. Based on experimental research, dynamic coefficients of hydrodynamic bearings in a wide range of rotational speeds, taking into account resonance speeds and higher speeds, were determined. They were verified using Abaqus software.
Numerical
