Abstract: The stability of the turbine rotor is a crucial guarantee for the safe and stable operation of the turbine-generator unit in power plants. Changes in the oil film thickness of the sliding bearing can significantly affect the stability of the turbine rotor. This paper analyzes the causes of vibration in the turbine rotor induced by changes in oil film thickness and delves into the underlying mechanism.

Keywords: sliding bearing; oil film thickness; turbine rotor; Stability

I. The function of the sliding bearing in a steam turbine

In the turbine rotor-bearing-foundation system, bearings play a crucial role in the dynamic characteristic matching of the system. Serving as a bridge between the shaft and the foundation, well-designed bearings can provide significant damping and absorb vibrations from the shaft. Conversely, poorly designed bearings, due to their inherent cross-stiffness and damping characteristics, can introduce negative damping to the system, becoming the root cause of oil film instability. Therefore, to achieve good dynamic characteristics, the rationality of the bearing structure and its parameters is key. Turbine bearings are affected by various factors during operation, and their geometric positions can vary due to differences in bearing structures and their locations within the unit. Bearing displacement occurs under thermal conditions, with cylinder bearings experiencing much more severe displacement than floor bearings. However, if the sliding of floor bearings is not smooth, it can hinder cylinder expansion and cause the bearing seat to tilt. The low-pressure cylinder of domestically produced large turbine generator sets experiences severe "runout" during thermal conditions, sometimes exceeding 1mm. This leads to bearing displacement in the low-pressure cylinder. The difference in bearing displacement redistributes the load on the rotor-support system across the bearings, thereby changing the critical speed at which each bearing becomes unstable. It also alters the overall damping level of the rotor-support system and the stability range of the shafting. Bearing displacement can also cause a bearing to become dislodged, significantly changing the critical speed of the shafting. In large turbine rotor-support systems, the types of bearings vary. Some bearings are sensitive to load changes, resulting in significant changes in stability when the load varies; others are less sensitive to load changes, with little change in stability. After the load redistribution across the bearings on the shafting, some bearings may experience reduced stability, while others may experience increased stability. When the unit vibrates, it is necessary to specifically analyze the working conditions of each bearing. Changes in the alignment state of the turbine rotor during thermal conditions can generate unbalanced excitation forces on the shafting and redistribute the static load values among the bearings, potentially leading to changes in critical speed or oil film oscillation, which affects the stability of the turbine.

II. Relationship between oil film thickness and stability of sliding bearings

1. The influence of oil film thickness on damping coefficient

In structural mechanics, the damping coefficient is used to measure the ability of a vibrating structure to dissipate energy. In typical turbine structures, the actual damping characteristics are complex and difficult to determine using established damping theories, which also poses challenges for calculating the damping coefficient. To address this issue, many empirical and semi-empirical formulas for calculating the damping coefficient have been developed based on engineering experience. In the calculation of the damping coefficient for turbine sliding bearings, a semi-empirical formula provided in the "Mechanical Vibration Handbook" is commonly used

In the above formula, represents the viscosity coefficient of the turbine lubricating oil, L denotes the width of the bearing pad, D1 and D2 respectively represent the inner diameter of the bearing pad and the journal diameter, and denotes the average thickness of the oil film. As can be seen from Formula 1, the damping coefficient of the oil film is inversely proportional to the thickness of the oil film, and the thickness of the oil film depends on the size of the gap between the journal and the bearing pad. The smaller the gap, the thinner the oil film. Since the values of all parameters in the formula are easily determined, the damping coefficient of the turbine sliding bearing can be calculated once the thickness of the oil film is calculated.

2. The influence of oil film stress on oil film stability

Since the tangential force on the journal shaft does positive work, while the damping force does negative work, the stability of the oil film largely depends on the algebraic sum of these two works. The force conditions during journal whirl are shown in Figure 1, and the whirl direction is indicated by Ω. The product of the tangential force on the oil film and the whirl circumference of the journal shaft represents the work done by the tangential force on the oil film on the journal shaft. The whirl work refers to the difference between the work done by the tangential force on the oil film and the work done by the damping force. The stability of the oil film can be judged based on the magnitude of the whirl work W. When the whirl work is positive, it indicates that the input energy from the lubricating oil system to the journal shaft is greater than the energy absorbed due to damping. This will cause the axis trajectory to diverge, and in severe cases, may lead to oil film instability. When the whirl work is negative, it indicates that the input energy from the lubricating oil system to the journal shaft is less than the energy absorbed due to damping, resulting in a convergent axis trajectory and preventing the occurrence of whirl. When the whirl work is zero, it indicates that the input energy and absorbed energy of the lubricating oil system are balanced, and the oil film is in a critical state. As the thickness of the oil film increases, the radius of journal whirl increases accordingly, which increases the work done by the tangential force. At the same time, as can be seen from formula (1), an increase in oil film thickness decreases the damping coefficient, which in turn reduces the work done by the damping force. Therefore, the whirl work significantly increases, intensifying the whirl phenomenon. Conversely, when the oil film is relatively thin, the opposite situation occurs, weakening the whirl phenomenon and facilitating the maintenance of oil film stability.

3. Example of the relationship between oil film thickness variation and turbine rotor stability

In the previous section, we analyzed the impact of changes in oil film thickness on oil film stability from a theoretical perspective, and the stability of the turbine rotor depends on the stability of the oil film. Therefore, changes in oil film thickness directly affect the stability of the turbine rotor. A power plant in China conducted a statistical analysis of oil film thickness and turbine shaft vibration before and after the turbine overhaul, and obtained some data as shown in the table below.

From Table 1, it can be seen that before the overhaul, the relatively large thickness of the oil film caused severe shaft vibration in the steam turbine, and the shaft center trajectory exhibited a diverging pattern. After the overhaul, the reduced thickness of the oil film significantly decreased the shaft's vibration amplitude, with the fluctuation value of the shaft center being only 2μm, achieving stable operation of the steam turbine. Due to significant differences in the design and operating parameters of various steam turbines, the relationship between changes in oil film thickness and shaft vibration is not exactly the same for different turbines. However, this example demonstrates that an increase in oil film thickness is one of the important factors causing shaft vibration in steam turbines.

III. Measures to enhance the stability of oil film thickness

Given the impact of increased oil film thickness on the stability of turbine rotors, measures must be taken to maintain the stability of oil film thickness and prevent its increase during turbine operation. Based on the author's many years of work experience, the following measures can be taken:

(1) Reduce the viscosity of lubricating oil. Since the viscosity of lubricating oil is directly proportional to the cohesive force between oil molecules, the higher the viscosity, the greater the number of oil molecules that are carried by the rotating shaft neck, leading to an increase in the thickness of the oil film and a decrease in its stability. Therefore, power plants can choose a type of turbine lubricating oil with lower viscosity; in addition, increasing the inlet oil temperature of the bearing bush is also one of the effective measures to reduce the viscosity of lubricating oil.

(2) Increase the width of the upper bearing tile's tungsten layer to facilitate the formation of an oil film and enhance the stability of the bearing tile.

(3) Use bearing pads with good stability. This can form convergent oil wedges between each pad, which is beneficial for eliminating self-excited oscillations of the oil film.

(4) Fully balance the unbalance of the same phase. Balancing the unbalance between the same phases can greatly reduce the resonance excitation capability at the critical speed, thereby reducing the amplitude of oil film oscillation.

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