Vibrations of Power Plant Machines (eBook)

Preface 6
Contents 8
1 Basics of Vibrations 11
1.1 Kinematic of Vibrations 12
1.1.1 Periodic and Harmonic Vibration Signals in the Time Domain 13
1.1.2 Vibrations in the Time and Frequency Domain (Fourier Analysis) 15
1.1.3 Relations Between Deflections, Velocities and Accelerations 19
1.2 Vibrations of a Single Degree of Freedom (SDOF) System 21
1.2.1 Effect of Damping on Free Vibration 25
1.2.2 Effect of Damping on Forced Vibration 28
1.3 Vibrations of a Simple Rotating Shaft—The Laval Rotor 30
1.4 Rotors in Practice 33
2 Instrumentation and Measurement 39
2.1 Measuring and Analyzing Instruments 39
2.1.1 Velocity Transducers 41
2.1.2 Eddy Current Measuring Chain (Proximity Transducers) 43
2.1.3 Acceleration Sensors (Accelerometer) 44
2.2 Measuring Positions and Units 45
2.3 Visualization of Vibration Data 48
2.3.1 Time Trend 50
2.3.2 The Bode Plot 50
2.3.3 The Polar Plot 51
2.3.4 The Shaft Centerline Plot 52
2.3.5 The Orbit/Time-Base Plot 53
2.3.6 The Waterfall Spectrum Plots 54
3 Fault Analysis: Vibration Causes and Case Studies 56
3.1 Mass Unbalance 57
3.1.1 Rigid Rotors 57
3.1.2 Flexible Rotors 58
3.2 Thermal Unbalance 59
3.2.1 Example of a 120 MW Gas Turbine 59
3.2.2 Example of a 250 MW Gas Turbine 61
3.2.3 450 MW Combined Cycle Plant, Compromise Balancing 61
3.2.4 Instant Vibration Increase (Step Change) 69
3.3 Non-homogenous Rotor Material 72
3.4 80 MW Gas Turbine Starting Behavior 79
3.5 Magnetic Unbalance of a 20 MW Hydroplant in Switzerland 84
3.6 Instable (Non-repeatable) Unbalance 87
3.7 Structural Resonance Problems 92
3.7.1 200 MW Steam Turbine, the Netherlands 92
3.7.2 1300 MW Generator Test Run 101
3.7.3 700 MW Turbo-Set in a Power Plant in Scotland 108
3.8 Axial Vibrations 114
3.8.1 300 MW Turbo-Set in Switzerland 114
3.8.2 Combined Cycle Plant in Saudi Arabia 118
3.8.3 150 MW Steam Turbine at the Philippines 128
3.9 Structural Resonance Problems 133
3.9.1 Vertical Machines 133
3.9.2 Mechanical Looseness 134
3.10 Alignment Faults—Coupling Errors 135
3.10.1 100 MW Gas Turbine in Brazil 136
3.10.2 750 MW Generator in Former Yugoslavia 139
3.10.3 150 MW Generator in Spain 141
3.11 Rubbing 144
3.11.1 80 MW Steam Turbine 144
3.11.2 150 MW Steam Turbine 146
3.11.3 Spiral Vibrations—Rotating Vectors 147
3.11.4 750 MW Steam Turbine Generator 154
3.11.5 150 MW Generator Rotor in the Spin Pit 161
3.11.6 400 MW Single-Shaft Combined Cycle Plant in Chile 167
3.11.7 300 MW Steam Turbine Generator in China 173
3.11.8 General Conclusions of Vector Rotation—Spiral Vibrations 174
3.12 Development of 2X (Twice Rotation Frequency) Vibrations 175
3.12.1 Sag Excitation 175
3.12.2 Magnetic 2X Vibrations 179
3.13 Rotor Cracks 185
3.13.1 Considerations Regarding Lateral Cracks 185
3.13.2 4?×?930 MW Steam Turbine Plant, Lateral Crack 187
3.13.3 MW Steam Turbine, Lateral Crack 197
3.13.4 MW Combined Cycle Plant, Ring-Shaped Cracks 206
3.14 Bearing Instabilities: Oil Whip, Medium Flow Instabilities 211
3.14.1 Feed Water Pump, Oil Whip 217
3.14.2 50 MW, 60 Hz, Combined Cycle Plant, Friction Whirl 220
3.14.3 80 MW Air-Cooled Generator of a Gas Turbine 222
3.14.4 Small Steam Turbine, Rotor 760 kg, 12,000 rpm 225
3.14.5 Medium Flow Instability 230
3.14.6 135 MW Steam Turbine 231
3.14.7 Instable Compressor Air Flow, Rotating Stall 234
4 Jobsite Balancing 238
5 Vibration Limits 253
6 Some Hints to Identify Vibration Problems 257
References 258