Bachschmid / Pennacchi / Tanzi Cracked Rotors

A Survey on Static and Dynamic Behaviour Including Modelling and Diagnosis
1. Auflage 2010
ISBN: 978-3-642-01485-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 399 Seiten

Cracks can develop in rotating shafts and can propagate to relevant depths without affecting consistently the normal operating conditions of the shaft. In order to avoid catastrophic failures, accurate vibration analyses have to be performed for crack detection. The identification of the crack location and depth is possible by means of a model based diagnostic approach, provided that the model of the crack and the model of the cracked shaft dynamical behavior are accurate and reliable. This monograph shows the typical dynamical behavior of cracked shafts and presents tests for detecting cracks. The book describes how to model cracks, how to simulate the dynamical behavior of cracked shaft, and compares the corresponding numerical with experimental results. All effects of cracks on the vibrations of rotating shafts are analyzed, and some results of a numerical sensitivity analysis of the vibrations to the presence and severity of the crack are shown. Finally the book describes some crack identification procedures and shows some results in model based crack identification in position and depth. The book is useful for higher university courses in mechanical and energetic engineering, but also for skilled technical people employed in power generation industries.

Autoren/Hrsg.

Bachschmid, Nicoló

Pennacchi, Paolo

Tanzi, Ezio

Inhaltsverzeichnis

1;Foreword;5
2;Contents;7
3;Acronyms;12
4;Cracks in Rotating Shafts;14
4.1;Introduction;14
4.2;The Development of Transverse Cracks in Rotating Shafts;17
4.3;References;27
5;Typical Dynamic Behaviour of Cracked Shafts;29
5.1;Introduction;29
5.2;Analysis of the Vibrations at Rated Speed;29
5.3;Thermal Sensitivity of Cracked Rotors;34
5.3.1;Case A – Steam Turbine;34
5.3.2;Case B – Generator;36
5.4;Dynamic Behaviour during Speed Transients;38
5.4.1;Case A – Generator;39
5.4.2;Case B – Generator;43
5.4.3;Case C – Test Rig;45
5.4.4;Final Comments;47
5.5;References;47
6;Rotor Testing for Crack Detection;48
6.1;Dynamic and Static Tests for the Detection of Cracks in Rotors;48
6.1.1;Dynamic Tests;48
6.1.2;Static Tests;52
6.2;Non-destructive Testing for Power Generation Rotors;56
6.2.1;Basic Criteria for the Selection of Inspection Techniques;58
6.2.2;Methods Based on Visual Checks;60
6.2.3;Ultrasonic Inspections (UT);71
6.2.4;Reliability of NDT Inspections;89
6.2.5;NDT as a Fundamental Aspect of Damage Tolerance Design;95
6.3;References;98
7;Laboratory Tests on Cracked Shafts;102
7.1;Introduction;102
7.2;Laboratory Test about Breathing Mechanism on a Specimen;102
7.2.1;Description of the Experimental Apparatus;105
7.2.2;Experimental Results;107
7.3;Factory Test Results about Thermal Sensitivity on a Steam Turbine;111
7.3.1;Tests at Low Rotating Speed;112
7.3.2;Tests during Speed Transients;115
7.4;References;118
8;Crack Modelling;119
8.1;A Review about Crack Modelling;119
8.2;Fracture Mechanics Approach and Propagation of Cracks;121
8.2.1;Strain Energy Release Rate Approach;121
8.2.2;Finite Element Modelling of Cracked Elements;127
8.2.3;Fatigue Crack Propagation;136
8.3;Modelling the Breathing Behaviour and ts Thermal Sensitivity;141
8.3.1;The Breathing Crack Simplified Model;145
8.4;Modelling the Crack;154
8.4.1;Approach Based on Fracture Mechanics (SERR Approach);154
8.4.2;Approach Based on Energy Balance (EDF);160
8.4.3;Approach Based on “Equivalent Beam” (FLEX);163
8.4.4;The 3D Model;171
8.4.5;Comparison of Results Obtained with the Models;172
8.5;Basic Modelling of a Cracked Rotor;179
8.5.1;Equations of Motion and Linearization for a Horizontal Shaft with Breathing Crack;184
8.5.2;Stability;188
8.5.3;Vibration Forced by the Crack Influence;193
8.5.4;Crack and Unbalance Response;199
8.5.5;Deeper Cracks;200
8.5.6;Final Remarks;201
8.6;Modelling the Cracked Rotor Dynamical Behaviour;201
8.7;References;206
9;Results Obtained Using Simulations;209
9.1;Simulations Compared to Experimental Results;209
9.1.1;Results Obtained on EDF EURoPE Test-Rig;209
9.1.2;Results Obtained on PdM Test-Rig;211
9.1.3;Results Obtained on Real Machines;213
9.2;Sensitivity of Crack Induced Vibrations to Different Parameters;217
9.2.1;Sensitivity of Crack Excited Vibrations to Crack Depth and Position;217
9.2.2;Effect of Crack Shape;239
9.2.3;Effects of Shear Forces on Cracked Shaft Deflections and Vibrations;246
9.3;References;256
10;Some Special Effects Caused by Cracks;257
10.1;Effect of Transverse Cracks on Torsional and Axial Vibrations;257
10.1.1;Static Axial and Torsional Deflections due to Coupling with Bending and Torsional Loads;258
10.1.2;Shift of Natural Torsional Frequency;262
10.1.3;Excitation of Sideband Component in Torsional Vibrations of a Test-Rig Shaft;264
10.1.4;Axial Vibration Excitation of a Test-Rig Shaft;268
10.1.5;Torsional Excitation in a Vertical Axis Centrifugal Pump;269
10.1.6;Excitation of Torsional Vibrations in a 1300 MW Turbo Generator;275
10.2;Slant and Helical Cracks;283
10.2.1;Description of the Model;287
10.2.2;Breathing Mechanism;290
10.2.3;Deflections;291
10.2.4;Dynamic Tests;295
10.2.5;Final Remarks about Slant and Helical Cracks;296
10.3;Non-linear Behaviours in Cracked Rotors;296
10.3.1;Cracked Rotor Linear and Non-linear Modelling;298
10.3.2;Description of the Model and of the Method;299
10.3.3;Results Obtained with Shaft Loaded by Weight Only;302
10.3.4;Results Obtained with Shaft Loaded by Weight and Unbalance;302
10.3.5;Sub-harmonics;309
10.4;References;310
11;Crack Diagnosis in Rotating Shafts;312
11.1;Diagnosis;312
11.2;Qualitative Approach;312
11.2.1;Definition of the Fault Matrix;313
11.2.2;Inference;316
11.2.3;Knowledge Representation;320
11.2.4;Symptom Generation;320
11.2.5;Fault Description;328
11.2.6;Fault Matrix;333
11.2.7;Baseline;343
11.3;Results for the Qualitative Approach;346
11.4;Model Based Approach;349
11.4.1;Definition of Equivalent External Forces to Faults;350
11.4.2;Definition of Equivalent External Forces to Cracks;353
11.4.3;Crack Depth Identification;360
11.5;Results of Model Based Approach;366
11.5.1;Test-Rig of Politcnico di Milano;366
11.5.2;Test-Rig of Électricité de France;376
11.6;References;401
12;Index;404