Introduction During the operation of large steam turbine generators, the vibration at the stator winding ends is mainly caused by two factors: the second-harmonic vibration force generated by the interaction between the winding current and the leakage magnetic field at the ends; and the elliptical vibration of the stator core. The amplitude of the stator end fixing elements under electromagnetic force is proportional to the square of the current. Therefore, in large-capacity steam turbine generators, the end windings will bear considerable excitation force. The irregular shape of the involute portion of the generator stator end winding means that it cannot be as securely fixed as the bars in the slots. Due to manufacturing processes and other issues, many pads only have point contact with the bars and cannot form a rigid structure. If resonance occurs at the winding ends under electromagnetic force excitation at twice the power frequency, the end binding structure and bar insulation are easily damaged. Practice shows that stator winding end vibration frequently causes phase-to-phase short circuits, water leakage, and strand breakage. These accidents are characterized by their suddenness and difficulty in simple repair, often resulting in extremely severe losses. Therefore, accurately measuring the vibration characteristics of the stator winding ends, predicting the vibration characteristics of the generator under actual operating conditions, and taking preventive measures as early as possible are particularly important. Modal analysis, a vibratory characteristic analysis method for the overall structure of generator winding ends, has become an effective approach developed in recent years. For end structures with elliptical mode shapes and vibration frequencies in the range of 94–115 Hz, necessary treatment can effectively prevent resonance and avoid stator winding insulation wear and loosening of the end binding structure. Standards such as JB/T 8990-1999 "Modal Test Analysis and Natural Frequency Measurement and Evaluation of Stator End Windings for Large Steam Turbine Generators," DL/T 735-2000 "Measurement and Evaluation of Dynamic Characteristics of Stator Winding Ends for Large Steam Turbine Generators," and the State Power Corporation's "Twenty-Five Key Requirements for Preventing Major Accidents in Power Production" all specify requirements for the vibration characteristic analysis of generator stator winding ends. A brief overview of modal analysis principles: Modal analysis is an effective means of analyzing the vibration characteristics of mechanical structures. It establishes a predictive model of the structure's response under known excitation conditions by analyzing the structure's dynamic characteristics, thereby predicting the structure's dynamic characteristics under actual operating conditions. The usual approach is to obtain the mechanical structure's response H(ω) under impact h(t) through experimental methods, construct the frequency response function matrix of the mechanical structure's dynamic characteristics, and then identify the structure's modal parameters: modal frequency, modal damping, and mode shape through curve fitting. According to the definition of the frequency response function, Hik = Fk/Xi, which physically represents the frequency response at point i caused by a unit force applied at point k. Based on the principle of linear superposition, the following form of the frequency response relationship for a multi-degree-of-freedom system can be obtained: Where {X}—frequency response; [H]—frequency response matrix; {F}—excitation force. [b]Based on vibration dynamics theory, the following is derived:[/b] Where {φr}—natural mode shape of the r-th mode; mr—mass of the r-th mode; kr—modal stiffness of the r-th mode; cr—modal damping of the r-th mode. From the above two equations, we can obtain the expression for the frequency response function matrix: Any column in the frequency response function matrix is: From the above brief analysis, it can be seen that any row or column in [H] contains all modal parameters, and the ratio of the frequency response function values ​​of the r-th mode in that row or column is the r-th mode shape. Therefore, if vibration is picked up at a fixed point i on the structure, and all test points are excited in turn, a row in [H] can be obtained. This row of frequency response functions contains all the information needed for modal analysis. Similarly, if vibration is picked up at a fixed point k on the structure, a column in [H] can be obtained. This column of frequency response functions also contains all the information needed for modal analysis. It is evident that to obtain all modal information, it is sufficient to measure only one row or column in the frequency response function matrix. This yields two methods for obtaining modal data: single-point fixed excitation, measuring the response sequentially at all measurement points (including the excitation point); and fixed-point measurement of the response, while exciting all measurement points in turn. The requirements for a modal data acquisition system: A measurement system generally includes an excitation device, a sensing system, an acquisition device, and modal analysis software. The sensor is an accelerometer, requiring a certain frequency response range (1–2000 Hz) and sensitivity (approximately 100 mV/g). The excitation device typically uses a hammer, with the impact force equivalent to a half-sine wave. The bandwidth of this wave is related to the pulse duration. For the frequency range of 0–200 Hz, a hammer with a soft rubber cap is usually used, ensuring an impact duration of approximately 1.5 ms. The acquisition device requires at least two synchronous acquisition channels, a sampling frequency above 10 kHz, and functions such as spectrum analysis and related calculations. The modal analysis software is used to combine modal test data, construct the frequency response matrix, perform curve fitting, and identify modal parameters. Requirements for modal data measurement points: When selecting the location, number, and direction of measurement points, the following should be considered: a. The ability to clearly display the deformation characteristics of all modes within the test frequency band and the differences in deformation between modes after the mechanical structure has deformed. b. Ensure that the structural points of interest are included in the selected measurement points, and the number of measurement points should not be less than half the number of stator slots. A common practice is to take three circles on the conical section of the stator winding ends on both sides of the excitation winding, as shown in Figure 1, and uniformly select the upper layer of the generator end bars as test points on these circles. The choice between single-point excitation and multi-point excitation methods depends on the ease of implementation. Determining the Modal Analysis Results: Modal analysis of the stator winding ends can yield the inherent vibration characteristics (natural frequency, damping, mode shape) of the ends. To correctly evaluate the generator's end vibration characteristics, it is also necessary to consider the influence of factors such as whether the winding is circulated with water, the water temperature, insulation aging, and the end lead structure on the modal parameters. a. Influence of Bar Temperature on End Modes: During generator operation, the temperature of the core and bars is higher than the ambient temperature and changes with load. Heating the insulation, binding ropes, and various conformal materials of the bars leads to a decrease in the overall stiffness of the ends, resulting in a downward trend in modal frequency and an increase in damping. a. The increase in damping reduces the actual vibration amplitude, and the modal frequency decreases by approximately 5–10 Hz. b. The effect of internal cooling water on end modes: Introducing internal cooling water into the winding increases the equivalent mass of the end structure, which also causes a decrease in modal frequency, with an effect of approximately 1–3 Hz. c. The effect of insulation aging on end modes: After many years of operation, the insulation of the generator rods, binding ropes, and fasteners in the slots will experience wear and aging due to vibration, resulting in a decrease in the tightness of the connections between various components. The mechanical strength and elasticity will also decrease year by year, leading to a decrease in modal stiffness and damping. Therefore, the end modal frequency tends to decrease with the age of the generator, but the vibration amplitude tends to increase. Checking these changes during major overhauls is essential. d. The effect of leads on end modes: The six leads of the generator stator winding are on the excitation side, while the steam-side winding is structurally symmetrical. Due to the presence of the leads, the fixing structure on the excitation side is more complex than that on the steam side. The transition leads are generally fixed in a semi-circle to the back of the insulation support, which implicitly strengthens the overall end fixing support. Severe vibration and wear at the stator winding ends, or accidents caused by wear, mostly occur on the steam side, which is determined by the inherent vibration characteristics of both sides. To evaluate the vibration characteristics of the generator stator winding ends, the modal frequencies, mode shapes, and damping obtained from tests should be considered, along with all these factors, to predict the vibration response of the generator ends during actual operation. Example of modal analysis application: Three mode shapes were obtained from the steam side of a 300 MW steam turbine generator, with the modes selected at the points of maximum and minimum amplitude. Figure 2 shows the elliptical mode shape at 93.2 Hz, Figure 3 shows the irregular multi-lobed mode shape at 105 Hz, and Figure 4 shows the three-lobed mode shape at 116 Hz. The mode shape diagrams show that, according to relevant test procedures, there is no elliptical vibration within the range of 94–115 Hz; only the irregular multi-lobed mode shape falls within this range. Therefore, under the action of elliptical frequency-doubled excitation force, none of the three vibration modes will form high-intensity resonance at the generator end, and will not cause serious damage to the generator end. Inspection of the generator stator end also confirms this conclusion, finding no insulation wear or loose binding ropes. Preventive measures for generator end vibration: After obtaining the vibration characteristics of the generator stator winding end through modal analysis and other means, corresponding measures must be taken based on the test results. Since the generator's end structure is basically fixed after the design is finalized, it cannot be easily changed on-site, and its internal electrical and mechanical characteristics are relatively complex, making it difficult to treat it like a simple mechanical structure by changing the modal frequency. Generators with obvious insulation wear, loose binding ropes, or pressure plates at the end should be given high priority. During major overhauls, the binding and fixing structures must be re-bound and reinforced to improve vibration damping, reduce vibration amplitude, and decrease vibration intensity. For cases where the end structure does indeed have an elliptical vibration mode of around 100 Hz, and although treatment has been carried out, the modal parameters still do not show significant changes, in addition to strengthening monitoring during operation, it is recommended to install an online monitoring device for generator stator winding end vibration to achieve early fault alarm. Currently, online vibration monitoring devices are widely used in large-capacity generator units abroad, such as those manufactured by companies like GE, Westinghouse, ABB, and Siemens (600 MW and above). They are also used in large-capacity hydro generators in China, but rarely in domestically produced large-capacity steam turbine generators. It is recommended that all generator manufacturers and operators pay sufficient attention to generator end-point vibration and take measures to prevent serious phase-to-phase and phase-to-ground short-circuit accidents.