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1. Concepts of axial displacement and differential expansion: Axial displacement refers to the amount of displacement of the shaft, while differential expansion refers to the relative expansion of the shaft with respect to the cylinder. Generally, when axial displacement changes, its value remains relatively small. When the axial displacement is positive, the large-axis generator moves in that direction; if the expansion of the cylinder at this time is much less than that of the shaft, the expansion difference does not necessarily change in a positive direction ； If the unit parameters remain unchanged and the load is stable, the expansion difference and axial displacement do not change. During the startup and shutdown of the turbine, as well as when steam parameters change, the expansion difference will also change; consequently, the axial displacement must change due to variations in load. Changes in axial displacement during operation inevitably lead to changes in expansion difference. The differential expansion value, which is the difference between the rotor’s expansion and the cylinder’s expansion, is referred to as a positive differential expansion; when the cylinder’s expansion exceeds that of the rotor, this differential expansion value is called a negative differential expansion. Based on cylinder classification, it can be further divided into high difference, medium difference, low I difference, and low II difference. The expansion difference value is a very important operational parameter; if it exceeds the allowable limit, the thermal protection system will activate and shut down the main unit, thereby preventing collisions between the moving and stationary parts and avoiding equipment damage. During startup, a heating device is generally used to control the degree of expansion of the cylinder, while the rotor’s degree of expansion is primarily controlled by the inlet temperature and flow rate of steam in the turbine, as well as the temperature and flow rate of steam used for shaft sealing. During startup, the expansion difference generally moves in the positive direction. When a turbine is shut down, as the load and speed decrease, the rotor cools down faster than the cylinder; as a result, the expansion difference generally moves in a negative direction. This is particularly severe during shutdowns under sliding-parameter conditions. It is necessary to use steam heating devices to supply cooling steam to the cylinder’s interlayers and flanges in order to prevent the expansion difference protection from activating. In a steam turbine generator, there is a pressure drop in the steam pressure before and after the moving blades due to the work done by the steam in these blades, as well as steam leakage in the gaps of the diaphragm seals. This pressure drop generates an axial thrust on the turbine rotor in the direction of steam flow, thereby causing axial displacement. If the axial displacement exceeds the minimum clearance between the stationary and rotating parts of the turbine, it will cause the stationary and rotating components to collide and get damaged. An increase in axial displacement can raise the temperature of the thrust bearings, causing the white metal to burn out; moreover, the unit may experience severe vibrations. Therefore, an emergency shutdown is necessary; otherwise, serious consequences will ensue. Thermal expansion protection refers to the relative expansion difference between the turbine rotor and the steam. During the start-up and shutdown of the unit, since the rotor is relatively small compared to the cylinder, it has a low heat capacity, experiences rapid temperature changes, and expands quickly. If no measures are taken to control the rate of temperature rise, friction between the unit rotor and the cylinder will cause damage. Therefore, the differential expansion during operation must not exceed the allowable value. After the turbine rotor stops rotating, a negative expansion difference may worsen; therefore, shaft seal steam at a certain temperature should be maintained to avoid adverse consequences. 2. Causes of axial displacement and thermal expansion difference (factors affecting the thermal expansion difference of the unit). The main factors that cause the thermal expansion difference to increase toward positive values are summarized as follows: 1) Too short a warm-up time during startup, too rapid acceleration, or too rapid load increase. 2) The heating temperature of the cylinder interlayer and flange heating device is too low or the flow rate is too low, resulting in a weak heating effect. 3) The sliding performance of the slip pin system or bearing bedplate is poor; it tends to seize, preventing the cylinder from expanding. 4) Excessively high shaft seal steam temperature or excessive supply of steam to the shaft seal causes excessive elongation of the shaft journal. 5) During unit startup, parameters such as steam inlet pressure, temperature, and flow rate are too high. 6) The working and non-working surfaces of the thrust bearing experience increased stress and wear, resulting in increased axial displacement. 7) The insulation effect of the cylinder insulation layer is poor, or the insulation layer has come loose. During prohibited seasons, the room temperature in the turbine hall is too low, or there are drafts of cold air. 8) Cold steam (or cold water) is introduced into the interlayer of the double-cylinder structure. 9) An inaccurate zero point of the differential pressure indicator or worn contacts cause numerical deviations. 10) Multi-rotor units: the mutual influence caused by changes in the expansion difference between adjacent rotors. 11) Effects of vacuum changes (a decrease in vacuum leads to an increase in the steam flow rate entering the turbine). 12) Effect of speed variation (decrease in speed). 13) The impact of changes in the extraction volume at various levels: if the primary extraction is shut down, the effect on the pressure difference is significant. 14) The bearing oil temperature is too high. 15) The effect of the Poisson effect during the coasting process after the unit is shut down. 16) The differential expansion indicator is inaccurate, or affected by frequency and voltage changes. The main reasons for an increase in the differential expansion to a negative value are: 1) a rapid drop in load or sudden load shedding. 2) A sudden drop in main steam temperature, or the inlet steam temperature during startup being lower than the metal temperature. 3) Water impact. 4) The bearing oil temperature is too low. 5) The shaft seal steam temperature is too low. 6) Changes in axial displacement. 7) Excessively high vacuum leads to a decrease in the temperature of the corresponding exhaust gas, which has an impact. 8) Upon startup, the rotational speed rises abruptly. Due to the axial dimension of the rotor decreasing under the effect of centrifugal force, this change is particularly noticeable at low speeds. 9) High-temperature steam flows into the double-cylinder interlayer; it may originate from the steam heating device, or from leaks in the steam inlet casing or the shaft seal. 10) The cylinder interlayer heating device has too high a temperature or a high flow rate, resulting in excessive heating. 11) The slip pin system or bearing plate becomes stuck, preventing the cylinder from retracting. 12) The differential expansion value indicator is inaccurate, or it is affected by frequency and voltage changes. Positive expansion difference – The main factors affecting it are: (1) a high rate of steam temperature increase or decrease; (2) the impact of rapid changes in negative pressure; (3) the influence of the temperature of the steam supplied to the shaft seals; (4) the effect of the condenser vacuum; (5) the impact of ambient temperature; (6) the effect of frictional blowing; (7) other factors such as the effect of heating devices for the cylinder flange bolts. When there is a high rate of steam temperature increase or decrease during startup, heating devices are generally used to control the amount of expansion of the cylinder, while the rotor’s expansion is primarily controlled by the temperature and flow rate of the steam entering the turbine, as well as the temperature and flow rate of the steam supplied to the shaft seals. During startup, the expansion difference generally moves in the positive direction. When a turbine is shut down, as the load and speed decrease, the rotor cools down faster than the cylinder; as a result, the expansion difference generally moves in a negative direction. This is particularly severe during shutdowns under sliding-parameter conditions. It is necessary to use steam heating devices to supply cooling steam to the cylinder’s interlayers and flanges in order to prevent the expansion difference protection from activating. After the turbine rotor stops rotating, a negative expansion difference may worsen; therefore, shaft seal steam at a certain temperature should be maintained to avoid adverse consequences. 2. Influence of the load change rate: When the load changes, the steam flow rates at various stages vary; especially within the low-load range, the steam temperatures at these stages change significantly. The faster the load increases, the quicker the temperature of the steam rises. As the rate of load reduction increases, the difference in temperature rise between the cylinder and the rotor also becomes greater. The rate of load increase is accelerating, and the positive expansion difference is increasing ； The load reduction rate accelerates, and the positive expansion difference decreases, eventually resulting in a negative expansion difference. Effect of the shaft seal supply air temperature: The shaft seal supply air heats the shaft seal section and the shaft seal body of the rotor. Since the shaft seal body is embedded at both ends of the cylinder, its expansion has little effect on the length of the cylinder shaft; however, the expansion of the rotor’s shaft seal section affects the length of the rotor, thereby increasing the positive thermal expansion difference. Since the shaft seal section accounts for a small proportion of the rotor length, its impact on the total expansion difference is minor; however, the local expansion difference at the shaft seal area is relatively large. If the shaft seal air supply temperature is too high, an excessive positive expansion difference occurs ； Conversely, the negative expansion difference is too large. It is generally specified that the shaft seal gas temperature should be slightly higher than the shaft seal metal temperature. 4. The effect of vacuum on low-pressure expansion differential: As the vacuum level decreases, the exhaust temperature rises, and the pressure at the exhaust port of the low-pressure cylinder increases. This reduces the pressure difference between the inside and outside of the cylinder, and both factors contribute to the expansion of the cylinder body, thereby reducing the low-pressure expansion differential. On the other hand, if the shaft seal air pressure remains unchanged, the amount of shaft seal air in the low-pressure cylinder’s shaft seal section decreases, resulting in reduced rotor heating and consequently a smaller low-pressure differential expansion. 5. Influence of ambient temperature: The low-pressure expansion difference is sensitive to ambient temperature. As the ambient temperature rises, the low-pressure expansion difference decreases; as the ambient temperature drops, the low-pressure expansion difference increases. The main reason is, on one hand, the decrease in ambient temperature, which intensifies the cooling of the low-pressure cylinder (the low-pressure cylinder has no thermal insulation) ； On the other hand, a decrease in the circulating water temperature leads to an increase in vacuum, a drop in exhaust temperature, and a decline in cylinder temperature. It was observed that under different loads, the pattern of change remains the same. Under the same load, the differential expansion between low pressure in winter and summer is 15%. 6. The effect of frictional blowing: During unit startup and at low load levels, the steam flow rate is low, while significant blowing friction losses occur in the high, medium, and low pressure stages (proportional to the cube of the rotational speed). The heat generated by these losses is absorbed by the steam, causing its temperature to rise. Since the impeller comes into direct contact with steam, the rotor temperature is higher than the cylinder temperature, resulting in a positive expansion differential. As the rotational speed increases, the heat generated by frictional blowdown losses in the rotor also increases accordingly. However, at this point, the increase in flow rate leads to a corresponding decrease in the number of stages contributing to such blowdown losses. Consequently, the amount of heat absorbed per kilogram of steam due to frictional blowdown losses initially rises with increasing rotational speed, thereby enlarging the positive expansion difference among the high-, medium-, and low-pressure cylinders; later, it decreases with further increases in rotational speed, resulting in a gradually diminishing effect on the expansion difference. 3. Hazards of axial displacement and expansion differential: 1. The Poisson effect affects the low-pressure expansion differential of the unit by about 10%; therefore, before starting up the unit, this differential should be maintained at over 10%. During shutdown, try to minimize the low-pressure expansion difference (it is best to keep it below 90%). When this difference exceeds 110%, an emergency shutdown is necessary; as the speed drops, the low-pressure expansion difference will go above 120%, and static and dynamic friction may occur at low speeds. 2. When the low-pressure expansion difference is too high in winter, attention should be paid to the pressure in the shaft seal air main; if this pressure is too high, it can be reduced appropriately, or the vacuum level can be lowered to decrease the low-pressure expansion difference. In winter, reduce the number of places where windows are opened; this is an effective measure to minimize low-pressure expansion differences during winter. 3. During startup in an extremely hot condition, it is preferable to use a high-temperature gas source for shaft seal ventilation; when auxiliary gas is used as the gas source, its temperature must be kept around 270°C. If the temperature is too low, it will cause the large shaft in the high-pressure shaft seal section to cool and contract rapidly, which may lead to friction between the moving and stationary parts in the earlier stages. 4. During cold start, when the shaft seal gas temperature is higher than that of the main shaft metal, the main shaft will heat up locally and expand, resulting in a large positive expansion difference. Therefore, it is necessary to select an air source that matches the temperature of the shaft seal metal in order to avoid delays in starting up. If the low-pressure expansion difference is excessive, it can be adjusted by reducing the vacuum; attempts should be made to initiate rotation and increase the speed as early as possible. During the unit startup phase, if the low-pressure positive expansion difference exceeds the limit, it can disrupt the vacuum and stop the shaft seal gas; the unit can be restarted once the expansion difference returns to normal. 5. Before cylinder reversal, the main steam temperature must be at least 50°C higher than the metal temperature of the high-pressure cylinder. The effect of axial displacement on the high-pressure differential expansion should be considered prior to cylinder reversal. During the startup and shutdown phases of the turbine, the expansion difference varies significantly; there are many influencing factors, and it is difficult to make adjustments. Therefore, operations must be carried out strictly in accordance with procedures. Appropriate turbine starting parameters and a suitable heating/pressurization curve should be selected based on the metal temperature of the cylinder. The proper heating rate must also be determined, while the acceleration rate and warm-up time need to be controlled. After loading, timely analysis and implementation of effective measures, depending on the specific circumstances, are necessary to effectively control the expansion difference. 4. Analysis and control of expansion difference changes during unit startup. During the startup and shutdown processes of a steam turbine, the heat exchange conditions between the rotor and the cylinder are different. Therefore, their expansion in the axial direction is also inconsistent, resulting in relative expansion. Relative expansion is also commonly referred to as differential expansion. The magnitude of the expansion difference indicates the changes in the axial clearances between the moving and stationary parts of the turbine. Monitoring expansion difference is an important task during the startup and shutdown of units. To prevent friction between the stationary and rotating components caused by changes in axial clearance, it is necessary not only to closely monitor the expansion difference, but also to have a thorough understanding of its impact on the operation of the steam turbine. When heated, the cylinder expands from the \"dead center\" in the direction of the machine head; therefore, the signal generator for measuring the expansion difference is generally installed at the \"dead center\" position of the cylinder relative to the foundation. The expansion differential transmitter is mounted on the front bearing housing. The startup of the unit is classified according to the metal temperature level of the turbine before startup into: cold start (metal temperature of 150–180 degrees) ； Warm start (180 degrees—350 degrees) ； Hot start (350 degrees—450 degrees) ； Hot-state startup (above 450 degrees). . Here is a brief analysis solely on the changes and control of the turbine expansion difference during common cold start and hot start operations: During the cold start of the turbine, the changes in the expansion difference and the control measures for it can be roughly divided into the following stages: 1. The stage of vacuum extraction using steam supplied to the steam seal. From vacuum extraction using steam from the steam seal until just before the rotor is started up, the expansion difference value increases continuously in the positive direction. Because during the heating or cooling process, the temperature of the rotor rises or falls faster than that of the cylinder, and accordingly its rate of expansion or contraction is also faster than that of the cylinder. When we supply steam to the steam seal using a voltage equalizing box, the steam seal sleeve expands outward on both sides as it heats up, but this has little effect on the expansion of the entire cylinder. The rotor spindle section corresponding to the steam seal expands when heated. The effect of steam sealing heating on the rotor elongation is determined by the steam supply temperature; however, the heating time also has an influence. Therefore, during cold start-up, the pressure in the voltage equalization tank should not be too high; it should generally remain below 0.1 MPa, while the temperature should be around 250 degrees Celsius. Once the evacuation system is activated and vacuum pumping begins, if the differential expansion rate changes too rapidly in the positive direction, it is possible to reduce the pressure in the equalization tank or appropriately increase the vacuum level in the condenser; increasing the vacuum level helps to reduce the time that steam remains in the steam seal. Generally speaking, during a cold start, the temperature and pressure of the steam supplied to the steam seal should be lower, and the vacuum level should increase more rapidly, so as to meet the conditions for starting up as soon as possible while ensuring safety. 2. Warm-up and acceleration phase. From surge to constant speed, the expansion difference generally continues to rise. At this stage, the steam flow rate is low, and the steam primarily does work within the control stage. Only after warming up at a moderate speed and then increasing the speed does the expansion difference show a tendency to decrease. This is mainly because as the rotational speed increases, the centrifugal force rises, and so does the axial component of force, which causes the rotor to become thicker and shorter. At the same time, the cylinder temperature gradually rises, and the expansion rate of the cylinder also increases, which relatively delays the expansion amount of the rotor. During startup, both the pressure and temperature of the steam should be kept relatively low, but a certain degree of superheat must be maintained, and the startup rate should be slow. During the startup process, close attention must be paid to changes in cylinder temperature. If the expansion difference is too high at this point, it is necessary to stabilize the rotational speed or reduce the vacuum level, thereby allowing steam to remain in the cylinder for a longer time and ensuring proper warming up of the machine. Sometimes, during the warm-up and acceleration process, improper adjustment of the steam trap on the cylinder body can also affect the expansion difference; therefore, care should be taken to control the steam trap on the cylinder body when starting up the machine. To prevent distortion in the data from the expansion difference gauge, we should also closely monitor changes in the thermal expansion and axial displacement of the unit, and use the comparison between these values to further assess any changes in the expansion difference. At the same time, closely monitor the vibration of the unit, which is particularly important when crossing the critical speed. 3. Constant speed and parallel load operation phases. Due to the short time from acceleration to steady speed, the steam temperature and flow rate remain almost unchanged, so the impact on the expansion difference becomes apparent only after reaching steady speed. After reaching a constant speed, the increase in differential expansion is significant and lasts for a long time, especially after the generator is connected to the grid. During the low-load warm-up phase, the steam heats the rotor and cylinders quite intensely. After connection to the grid, as the control steam valve is opened wider, the temperature of the control stage rises relatively quickly; the opening speed of the control steam valve has a significant impact on the expansion difference. In other words, in order to prevent too rapid changes in the expansion difference, it is necessary to warm up the system for a period of time at low load levels after it is connected to the grid; the specific duration of this low-load warming-up is determined by the temperatures of the upper and lower walls of the cylinders, the temperature of the regulation stages, and the trend of changes in the expansion difference. Loading can only be increased gradually once the differential expansion value shows a downward trend and drops by 10% compared to the value at grid connection; once the differential expansion starts to rise again and reaches the value at grid connection, the rate of loading increase should be appropriately reduced or even stopped to continue with the warming-up process. This continues until the unit load reaches its rated value. Generally speaking, the main factors affecting the expansion difference of the turbine unit include the following: the length of the warm-up time, changes in the condenser vacuum, the temperature and duration of the steam supply to the shaft seals, the rate of temperature increase and decrease of the main steam, and the impact of load changes. In simple terms, cold-starting a unit involves: adjusting the vacuum level, ensuring a stable supply of steam, increasing the speed gradually, and warming up the machine slowly. Low load, don’t rush; wait until the cylinder temperature rises before increasing it.