Prof. Dr. rer. nat. Erwin Kr&amp#228;mer (auth.) - Dynamics of Rotors and Foundations-Springer-Verlag Berlin Heidelberg (1993).pdf

1、Erwin Kramer Dynamics of Rotors and Foundations With 304 Figures Springer-Verlag Berlin Heidelberg GmbH Prof.Dr.rer;nat.Erwin Krii.mer IsselstraJ3e 12 64297 Dannstadt-Eberstadt Gennany ISBN 978-3-662-02800-1 ISBN 978-3-662-02798-1(eBook)DOI 10.1007/978-3-662-02798-1 This work is subject to copyright

2、.AII rights are reserved,wether the whole or part of the material is concemed,specifically the rights oftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproduction on microfilm or in any other way,and storage in data banks.Duplication ofthis publication or parts thereofis permi

3、tted only under the provisions ofthe German Copyright Law of September 9,1965,in its current version,and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH.Violations are liable for prosecution under the German Copyright law.Springer-Verlag Berlin Heidelberg 1993

4、Originally published by Springer-Verlag Berlin Heidelberg New York in 1993 Softcover reprint ofthe hardcover Ist edition 1993 The use of general descriptive names,registered names,trademarks,etc.in this publication does not imply,even in the absence of a specific statement,that such names are exempt

5、 from the relevant protective laws and regulations and therefore frec for general use.Typesetting:Carnera-ready by author;6113020 543210 Printed on acid-frec paper Foreword My acquaintance with the Author began some 30 years ago while he was with Brown Boveri in Mannheim.Since then we have become cl

6、ose colleagues and it was a natural consequence to cooperate in writing a book on rotordynamics-he as an expert with a wealth of industrial experience and I as translator from German into English,with a background in industry and in university teaching and research into the vibration of rotating sys

7、tems.The outcome is a book with a traditionally German emphasis on a wide and detailed coverage of the dynamics of rotors and foundations.The bibliography is extensive and the author is not content to simply refer to this,but to give his own very lucid explanations of the phenomena involved.This is

8、backed up by detailed calculations and graphs which give the engineer a thorough appreciation of the different factors affecting the rotordynamic performance of machines.In addition,tools of the trade such as finite element modelling and stability analysis are covered in detail and the result is a b

9、ook which I am sure will be regarded as an essential volume on the book shelf of any student or engineer who has a need to consider machine vibration.Southampton,England Roy Holmes Preface In the last decades rotordynamics has developed into a wide area of speciality.Numerous investigations have app

10、eared in the literature and even for the spe-cialist it is difficult to appreciate the whole picture.A choice of the essential results and their correlation in as understandable a form as possible is therefore a prime requirement.It is hoped that this will be accomplished in this book through the kn

11、owledge and experience gained the author,over his working life.The book is written for anyone who is concerned with rotordynamics,whether by choice or necessity.It is recommended for lecturers and students and for the manufacturers and users of rotating machines and their founda-tions.On the one han

12、d the mechanics and mathematical derivations are dealt with in detail and,on the other,an attempt is made to simplify the under-standing of the results by presenting numerous figures and corresponding text for readers with little expert knowledge.The contents of this book are described in detail in

13、Chapt.1.They consist of the background literature,work in the specialist area of machine dynamics in the Technical University of Darmstadt and of the authors own personal experiences in industry,at university and as a specialist in the field.The cited literature has been chosen from personal knowled

14、ge and judgement and the readers indulgence is asked if the choice in some cases appears inadequate.The object of writing this book in English could only be realized because Professor R.Holmes,a well-known researcher in rotor dynamics,offered to translate the German manuscript.I would like to thank

15、Professor Holmes espe-cially for his unselfish readiness,for his critical appraisal and translation of the manuscript,as well as for many useful pieces of advice.Dr.Ing.H.D.Klement has also contributed extensively to the contents of this book.He conveyed to the author in many discussions his knowled

16、ge and experience on the subject of writing and using computer program MADYN,described in Chapt.25.For this and for the calculation of most of the examples,the author would like to thank Dr.Klement most warmly.Furthermore,thanks are due everyone who read parts of the manuscript and gave advice,espec

17、ially Dr.Ing.L.Eckert,Prof.H.Freund,Prof.J.Glienicke,Prof.H.J.Thomas and Dr.Ing.J.Schmied.Many questions and acknowledgements originate from the authors earlier employment at BBC,now ABB Zurich,and from discussions with experts of this company.The author wishes to thank former colleagues for their a

18、ssistance and ABB for information on some of the given examples and for authorization to publish the results.VIII Gratitude is expressed to Mrs.M.Mayer for the careful typing of the book,to Dipl.Ing.D.Glaser for drawing the figures and to Mrs.Dipl.Ing.E.Grunau for final reviewing of the manuscript.F

19、inally,the author would like to thank the representatives of Springer-Verlag for their pleasant and efficient cooperation.Darmstadt,Germany Erwin Kramer Table of Contents I Fundamentals 1 1 Introduction.3 2 The one Degree of Freedom System 7 2.1 Equation of Motion.7 2.2 Natural Vibration.8 2.3 Harmo

20、nic Excitation 11 2.4 Random Excitation.17 3 Shaft with Central Disc 19 3.1 Shaft with Rigid Bearings,Jeffcott Rotor.19 3.2 Startup,Run Down.24 3.3 Jeffcott Rotor with Flexible Bearings 29 3.4 Jeffcott Rotor with Bearing Damping 33 4 Shaft with Non Central Disc 37 4.1 Equations of Motion 37 4.2 Natu

21、ral Vibrations.41 4.3 Unbalance Vibrations.52 4.4 Harmonic Excitation in one Direction.56 4.5 Shaft with Flexible Bearings 59 5 The Short and the Long Rotor 65 5.1 Unbalance Moment.66 5.2 Natural Frequencies.68 5.3 Unbalance Vibrations.71 6 Oil-Film Bearings.77 6.1 Hydrodynamic Bearing Theory 77 6.2

22、 Short Bearing Theory.83 6.3 Static and Dynamic Properties 89 7 Rotors with Oil-film Bearings 97 7.1 Equations of Motion.97 X Table of Contents 7.2 Stability.7.2.1 Rigid Rotor.7.2.2 The Jeffcott Rotor 7.3 Unbalance Vibrations.7.4 Summary 8 Vertical Rotors 8.1 Tilt-pad Bearings.8.2 Vibrations.9 Rolli

23、ng-element Bearings 9.1 Deformation of the Rolling-element 9.2 Stiffness of Rolling-element Bearings 9.3 Lateral Stiffness,Critical Speeds.9.4 Consequences of Element Rotation.9.5 Damping of Rolling-element Bearings.10 Shaft Seals.10.1 Restoring Force.10.2 Jeffcott Rotor with Seals 10.3 Smooth Seals

24、.10.4 Labyrinth Seals.10.5 Floating Ring Seals.11 Steam Whirl.11.1 The Steam Whirl Force.11.2 Jeffcott Rotor with Steam Whirl.12 Internal Damping.12.1 Jeffcott Rotor with Internal Viscous Damping 12.2 Damping due to the Shaft Material.12.3 Damping from Assembly Components.12.4 Conclusion and an Exam

25、ple 13 Non-circular Shafts.13.1 Non-circular Jeffcott Rotor 13.2 Supplementary Comments.II Rotors with Several Bearings 14 Computer Model.15 Influence Coefficients 99 99 104 108 113 115 115 123 129 130 132 135 138 140 143 144 146 152 156 157 161 161 164 169 169 174 177 184 191 192 199 201 205 207 Ta

26、ble of Contents XI 16 Equation of Motion 211 16.1 Statics.211 16.2 Dynamics.217 16.2.1 lligid Masses 217 16.2.2 Beam Element.221 16.2.3 Flexible Couplings 224 16.2.4 Bearing Supports.227 16.2.5 Shaft Seals,Steam Whirl.228 16.3 Reduction in the Number of Coordinates 228 16.4 Discussion of the Equatio

27、n of Motion 230 17 Results.233 17.1 General Discussion of Natural Vibrations.233 17.2 Rotors with two Bearings.236 17.3 Rotors with Several Bearings.247 18 Static Bearing Loads.255 III Rotor-foundation Coupling 19 Foundation.19.1 Calculations.19.1.1 Ground Dynamics.19.1.2 lligid Foundation Block 19.

28、1.3 Flexible Foundation.19.2 Results.19.2.1 lligid Foundation.19.2.2 Frame Foundation 19.2.3 Table Foundation.19.2.4 Spring Foundation 19.2.5 Reinforced Concrete and Steel.20 Rotor and Foundation 20.1 Calculations.20.2 Results.20.2.1 Small Machine Sets with Frame Foundations 20.2.2 Large Turbine Set

29、s 20.2.3 Conclusion.IV Further Features 21 Rough Calculations.21.1 Natural Frequencies and Critical Speeds 257 261 262 262 266 269 277 277 283 283 287 287 293 294 296 298 305 311 315 317 317 XII Table of Contents 21.2 Resonance Amplitudes 22 Bending Stresses in Rotors 23 Cracked Rotors.23.1 Vibratio

30、ns of a Rotor with a Transverse Crack.23.1.1 Jeffcott Rotor.23.1.2 General Rotor.23.1.3 Results.23.2 Case Studies.23.3 Summary.24 Solution of the Equation of Motion 24.1 Homogeneous Equation,Natural Frequencies.24.2 Harmonic Excitation.24.3 General Excitation.24.4 Modal Method of Calculation 24.4.1

31、Symmetric Matrices.24.4.2 Harmonic Excitation.24.4.3 Reduced Modal Calculation 24.4.4 Transfer Function.24.4.5 Unsymmetric Matrices 24.5 Rayleigh Quotient.25 Program MADYN.25.1 Review.25.2 Building the Model 25.3 Eigenvalue Algorithm.References Index.322 325 329 329 329 334 335 342 345 349 349 353 3

32、53 353 354 356 358 360 360 362 365 365 367 368 371 381 Part I Fundamentals 1 Introduction Rotors of machines have,while in operation,a great deal of rotational energy,and a small amount of vibrational energy.The purpose of rotordynamics as a subject is to ascertain how this latter can be kept as sma

33、ll as possible.Its significance can be underlined by the following example.The rotational energy of a rotor turning with angular velocity n is the same as the kinetic energy of a non-rotating rotor with translational motion of velocity v=nip where ip is its radius of gyration.For example,for a rotor with radius of gyration 200 mm and 3000 rpm,the velocity v is 63 m/s or 226 km/h.The typical veloci