The purpose of this report is to determine the lateral and torsional dynamic characteristics of the complete system under synchronous conditions of excitation and response. A damped natural response study was made in order to investigate the combined effect of oil film stiffness and damping coefficients on system damping and stability characteristics at all damped natural resonance speeds. An unbalance response analysis is also performed to study the system sensitivity. This study was performed to investigate the lateral vibration characteristics of the subject system in order to avoid vibration problems that might interfere with the smooth and reliable operation of the system. Total system studies are important in that often the coupling effects of marrying driver and driven equipment result in resonant speeds that are not calculable when investigating the response of the separate components. Oil film stiffness and damping for all bearings must be properly considered in the system calculations along with the effective stiffness and damping of pedestal supports as required. The above effects are in the following calculation to ensure the proper calculation of resonant speeds.The following study concerns itself with the lateral analysis of gas turbine, load coupling, and 50 Hz/15.75Kva generator. This study reports the lateral natural frequencies and mode shapes calculated from the mass and stiffness distribution of the beam elements modeled using the DYROBES software. An unbalanced response analysis is also performed to study the system sensitivity. The significance of torsional vibration in high speed rotating machinery is well established. It is desirable to keep all torsional natural frequencies away from operating speed as well as twice the electrical frequency of the system. However, this is not always feasible and, therefore torsional criticals can be tolerated within these regions provided the response to excitation levels are low enough to keep the alternating shear stress within acceptable levels The following study concerns itself with the complete torsional analysis of gas turbine rotor including load coupling, gear box and 50Hz/15.75KVA generator rotor. This study reports the torsional natural frequencies, mode shapes and Campbell diagram by using transfer matrix method. The transient response shear stresses were also calculated for fault condition.
Table of Contents
1. INTRODUCTION
1.1 Gas Turbine
1.1.1 Theory of Operation
1.1.2 Rotor
1.2 Lateral and Torsional Analysis of Rotor
2. LITERATURE REVIEW
2.1 Lateral Vibration Analysis
2.2 Torsional Vibration Analysis
3. MATHEMATICAL BACK GROUND
3.1 Vibration
3.1.1 Single Degree Freedom Systems
3.1.2 Equation of motion for SDOF
3.1.3 Multi Degree of Freedom (MDOF) System
3.1.4 Vibration Model
3.1.5 Equations of Motion
3.1.6 Viscously Damped of Free Vibration
3.2 Rotor Dynamics
3.2.1 Definition of terms
3.2.2 Damped Unbalance Response Analysis
3.3 Finite Element Method in Rotor Dynamics
3.3.1 Division of Rotor into Discrete Systems
3.3.2 Gyroscopic Effects
3.3.3 Supports
3.3.4 Shear Deformation
3.3.5 Damped Natural Frequency/Stability
3.4 Imbalance Response of Rotor
3.5 Torsional Analysis (Method of Calculation)
3.5.1 Transfer Matrix Analysis
3.5.2 Generation of Campbell Diagrams
3.5.3 Electrical Fault Torque Calculations
4. RESULTS AND DISCUSSIONS
4.1 Lateral vibration analysis of Frame-GT Train
4.1.1 GT Rotor modeling
4.1.2 Damped Critical Analysis considering minimum stiffness
4.1.3 Unbalance Response Analysis
4.1.4 Logarthmic Decrement and Stability Analysis
4.2 Torsional Vibration Analysis of Rotor Train
4.2.1 Natural Frequency
4.2.2 Torsional Mode Shape
4.2.3 Campbell Diagram
4.2.4 Torque Magnification Factor
4.2.5 Alternating Shaft Stresses
5. Conclusions
Objectives and Research Focus
The primary goal of this report is to investigate the lateral and torsional dynamic characteristics of a complete gas turbine rotor system under synchronous excitation, aiming to determine natural frequencies, mode shapes, and system stability to ensure reliable operation and prevent premature failure.
- Lateral vibration characteristics and critical speed analysis
- Torsional analysis using the transfer matrix method
- Unbalance response analysis and system sensitivity
- Calculation of alternating shear stresses under electrical fault conditions
- Assessment of system stability and resonance avoidance
Excerpt from the Book
1.1 Gas Turbine
A gas turbine is an engine where fuel is continuously burnt with compressed air to produce a stream of hot, fast moving gas. This gas stream is used to power the compressor that supplies the air to the engine as well as providing excess energy that may be used to do other work. The engine consists of three main parts viz., compressor, combustor and turbine.
The compressor usually sits at the front of the engine. There are two main types of compressor, the centrifugal compressor and the axial compressor. The compressor will draw in air and compress it before it is fed into the combustion chamber. In both types the compressor rotates and it is driven by a shaft that passes through the middle of the engine and is attached to the turbine.
The combustor is where fuel is added to the compressed air and burnt to produce high velocity exhaust gas. Down the middle of the combustor runs the flame tube. The flame tube has a series of holes in it to allow in the compressed air. It is inside the flame tube that fuel is injected and burnt. There will be one or more igniters that project into the flame tube to start the mixture burning. Air and fuel are continually being added into the combustor once the engine is running. Combustion will continue without the use of the igniters once the engine has been started. The combustor and flame tube must be very carefully designed to allow combustion to take place efficiently and reliably. This is especially difficult given the large amount of fast moving air being supplied by the compressor. The holes in the flame tube must be carefully sized and positioned. Smaller holes around where the fuel is added provide the correct mixture to burn. This is called the primary zone. Holes further down the flame tube allow in extra air to complete the combustion. This is the secondary zone. A final set of hole just before the entry to the turbine allow the remainder of the air to mix with the hot gases to cool them before they hit the turbine. This final zone is known as the dilution zone. The exhaust gas is fed from the end of the flame tube into the turbine.
Summary of Chapters
1. INTRODUCTION: Provides an overview of gas turbine components and defines the importance of analyzing rotor dynamics for operational reliability.
2. LITERATURE REVIEW: Summarizes previous research regarding lateral and torsional vibration analysis in rotating machinery, citing various methodologies and studies.
3. MATHEMATICAL BACK GROUND: Details the theoretical foundations of vibration, including single and multi-degree of freedom systems, rotor dynamics, and finite element modeling.
4. RESULTS AND DISCUSSIONS: Presents the specific analysis of the GT train, including modal analysis, unbalance responses, and torsional stresses under electrical fault conditions.
5. Conclusions: Evaluates the system's safety and confirms that the identified resonance frequencies and stress levels are within acceptable design limits.
Keywords
Gas Turbine, Rotor Dynamics, Lateral Vibration, Torsional Vibration, Campbell Diagram, Unbalance Response, Finite Element Method, Transfer Matrix Method, Critical Speed, Resonance, Damping, Shear Stress, Synchronous Generator, Modal Analysis, Mechanical Reliability
Frequently Asked Questions
What is the primary purpose of this vibration analysis report?
The report aims to determine the lateral and torsional dynamic characteristics of a complete gas turbine system to ensure it operates reliably without encountering problematic resonances or fatigue failure.
Which key components of the gas turbine system are analyzed?
The study focuses on the gas turbine rotor, load coupling, and the 50 Hz/15.75KVA generator as an integrated train.
What is the primary goal regarding critical speeds?
The primary goal is to ensure that critical speeds are adequately separated from the unit’s operating speed range to avoid resonant excitation.
Which scientific methods are employed for this analysis?
The analysis utilizes Finite Element Method (FEM) for lateral vibration and the Transfer Matrix Method for torsional analysis, supported by DYROBES software.
What does the main body of the work cover?
It covers the mathematical background of vibration, the methodology for rotordynamic modeling, specific results from lateral and torsional analyses, and stability assessments.
Which terms characterize this research?
Key terms include rotor dynamics, lateral and torsional vibration, Campbell diagrams, unbalance response, and transient shear stress calculations.
What role does the Campbell diagram play in this analysis?
The Campbell diagram is used to plot natural frequencies against rotational speeds to identify potential interference points or critical speeds within the operating range.
How is the turbine rotor modeled for the analysis?
The rotor is treated as a continuous system divided into 50 distinct sections, incorporating mass, stiffness, and inertia properties to accurately simulate its dynamic behavior.
What conclusions were drawn regarding the electrical fault conditions?
The analysis concluded that the transient torques and alternating shear stresses induced by sudden short circuits are well within the allowable limits for the shaft materials.
Why is bearing damping crucial for this rotor system?
Bearing damping is essential to control vibration amplitudes at critical speeds, thereby preventing excessive structural stresses and enabling safe supercritical operation.
- Citation du texte
- Asst.Professor Srinivasa Rao Dokku (Auteur), 2016, Vibration Analysis of Gas Turbine Rotors, Munich, GRIN Verlag, https://www.grin.com/document/441946
