A flexible rotor balancing method

Abstract

This invention discloses a flexible rotor balancing method, belonging to the field of aerospace electromechanical technology. The method includes: performing finite element analysis based on the structural parameters of the flexible rotor to determine the critical speed and target location for bending deformation; determining multiple balancing speeds and corresponding balancing surfaces based on the critical speed, target location, and initial imbalance concentration location of the flexible rotor; and performing multi-stage balancing processing on the flexible rotor based on the multiple balancing speeds and corresponding balancing surfaces to eliminate the imbalance. This method reduces the risk of acceleration through staged pre-balancing, avoiding severe vibrations caused by large initial imbalances; avoids trial weight conflicts and reduces material damage by using inner and outer ring counterweight holes in groups; balances safety and efficiency, has good repeatability, and can achieve stable operation of aerospace flexible rotors with large initial imbalances at all speeds.

Description

Technical Field

[0001] This invention belongs to the field of aviation electromechanical technology, and specifically relates to a flexible rotor balancing method. Background Technology

[0002] In aero-engines and related electromechanical systems, flexible rotors often operate at speeds higher than the first or second critical speeds, making their dynamic characteristics extremely sensitive to imbalance. Unbalanced vibration is one of the key factors affecting the overall safety and reliability of the aircraft. Traditional high-speed dynamic balancing methods typically apply trial weights and corrections directly near the operating speed or critical speed. However, for multi-salient pole structures such as switched reluctance rotors, which are made by bonding and pressing magnetic steel sheets, the manufacturing process inherently results in a large initial imbalance. If these imbalances are directly introduced to high speed, they can easily cause severe vibrations, even damaging the supports and the rotor body, posing a serious safety risk.

[0003] Furthermore, existing balancing schemes often lack step-by-step strategies for reducing such large initial imbalances, and do not fully consider the process of first performing coarse balancing at low speeds and then gradually increasing the speed for fine correction. This results in low balancing efficiency, poor repeatability, and difficulty in meeting stringent vibration limits. Therefore, there is an urgent need to propose a systematic, phased balancing method that, while ensuring safety, effectively eliminates large initial imbalances and flexible mode imbalances, enabling stable rotor operation across the entire speed range. Summary of the Invention

[0004] One object of the present invention is to provide a flexible rotor balancing method that can solve the above-mentioned technical problems in the prior art.

[0005] According to a first aspect of the present invention, a flexible rotor balancing method is provided, comprising:

[0006] Finite element analysis is performed based on the structural parameters of the flexible rotor to determine the critical speed and target location where the flexible rotor undergoes bending deformation.

[0007] Based on the critical speed, target location, and initial imbalance concentration location of the flexible rotor, determine multiple equilibrium speeds of the flexible rotor and the equilibrium surface corresponding to each equilibrium speed.

[0008] The flexible rotor is subjected to multi-stage balancing treatment based on multiple balancing speeds and the balancing surface corresponding to each balancing speed, in order to eliminate the imbalance of the flexible rotor.

[0009] Optionally, the flexible rotor includes a switched reluctance rotor, which is a multi-salient pole structure formed by bonding and pressing magnetic steel sheets, with the target part being the switched reluctance rotor.

[0010] Optionally, the balancing speed includes a first balancing speed and a second balancing speed, and the balancing surface includes a first balancing surface and a second balancing surface;

[0011] Based on multiple balancing speeds and the balancing surface corresponding to each balancing speed, a multi-stage balancing process is performed on the flexible rotor, including:

[0012] Based on the first equilibrium speed and the first equilibrium surface, a first low-speed dynamic balance is performed on the flexible rotor to eliminate large initial imbalance.

[0013] After the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balance speed and the second balance surface to eliminate rigid imbalance.

[0014] At the end of the second low-speed dynamic balancing, determine whether the flexible rotor meets the preset balance conditions.

[0015] High-speed dynamic balancing is performed on the flexible rotor when the preset balance conditions are not met.

[0016] Optionally, the first balancing speed is 10% of the critical speed, the second balancing speed is 30% of the critical speed, the first balancing surface is the left counterweight plate and the right counterweight plate, and the second balancing surface is the turbine plate and the coupling plate.

[0017] Optionally, a first low-speed dynamic balancing of the flexible rotor is performed based on a first equilibrium speed and a first equilibrium surface, including:

[0018] The left and right counterweights are installed at both ends of the switched reluctance rotor using a hot-fitting process.

[0019] In the initial state, the flexible rotor is started to the first equilibrium speed, the first vibration parameter at the measuring surface of the shaft is detected, and then the rotor is stopped.

[0020] Add the first test weight to the outer ring counterweight hole of the left counterweight plate, start the flexible rotor to the first equilibrium speed, detect the second vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0021] Remove the first test weight, add the second test weight to the outer ring counterweight hole of the right counterweight plate, start the flexible rotor to the first equilibrium speed, detect the third vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0022] After removing the second test weight, the first influence coefficient and the first correction mass are calculated using the influence coefficient method based on the first vibration parameter, the second vibration parameter, and the third vibration parameter.

[0023] Based on the first correction mass, balance weights are added to the left and right counterweight plates respectively. The flexible rotor is started to the first balance speed, the fourth vibration parameter at the measuring surface of the rotating shaft is detected, and then the rotor is stopped.

[0024] The first residual unbalance is calculated using the influence coefficient method based on the first influence coefficient and the fourth vibration parameter.

[0025] If the first remaining imbalance meets the preset first balance accuracy requirement, the first low-speed dynamic balancing ends.

[0026] If the first remaining imbalance does not meet the first balance accuracy requirement, the material is ground off at the corresponding edge positions of the left and right counterweight plates according to the first remaining imbalance until the first balance accuracy requirement is met.

[0027] Optionally, after the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balancing speed and the second balancing surface, including:

[0028] After the first low-speed dynamic balancing is completed, start the flexible rotor to the second balancing speed, detect the fifth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0029] Add a third test weight to the outer ring counterweight hole of the turbine disk, start the flexible rotor to the second equilibrium speed, detect the sixth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0030] Remove the third test weight, add the fourth test weight to the outer ring counterweight hole of the coupling disc, start the flexible rotor to the second equilibrium speed, detect the seventh vibration parameter at the shaft measuring surface, and then stop the machine.

[0031] Remove the fourth test weight, and calculate the second influence coefficient and the second correction mass using the influence coefficient method based on the fifth, sixth, and seventh vibration parameters. Add balancing weights to the turbine disk and coupling disk respectively based on the second correction mass, start the flexible rotor to the second equilibrium speed, detect the eighth vibration parameter at the shaft measuring surface, and then stop the machine.

[0032] The second residual unbalance is calculated using the influence coefficient method based on the second influence coefficient and the eighth vibration parameter.

[0033] If the second remaining imbalance meets the preset second balance accuracy requirement, the second low-speed dynamic balancing ends.

[0034] If the second remaining imbalance does not meet the second balance accuracy requirement, the material is ground off at the corresponding edge positions of the turbine disk and coupling disk according to the second remaining imbalance until the second balance accuracy requirement is met.

[0035] Optionally, the preset balance conditions include a first balance condition and a second balance condition;

[0036] High-speed dynamic balancing of flexible rotors includes:

[0037] If the flexible rotor does not meet the first balance condition, the third balance speed is determined according to the critical speed. Based on the third balance speed and the first balance surface, the flexible rotor is subjected to the first high-speed dynamic balance to eliminate the unbalance of the flexible vibration mode.

[0038] If the flexible rotor satisfies the first balance condition, determine whether the flexible rotor satisfies the second balance condition.

[0039] If the flexible rotor does not meet the second balance condition, a second high-speed dynamic balance is performed on the flexible rotor based on the operating speed of the flexible rotor and the second balance surface to eliminate the residual imbalance at the operating speed.

[0040] Optionally, the third equilibrium speed is determined based on the critical speed, including:

[0041] After the second low-speed dynamic balancing is completed, the flexible rotor is started. During the speed-up process of the flexible rotor, the ninth vibration parameter at the measuring surface of the shaft is detected until the ninth vibration parameter reaches the first vibration limit value or the speed of the flexible rotor exceeds the critical speed, then the rotor is stopped.

[0042] If the ninth vibration parameter reaches the first vibration limit value before the speed of the flexible rotor reaches the critical speed, record the target speed corresponding to the first time the ninth vibration parameter reaches the first vibration limit value, and determine the third equilibrium speed as 90% of the target speed;

[0043] If the rotational speed of the flexible rotor exceeds the critical speed, the ninth vibration parameter does not exceed the first vibration limit, and the difference between the maximum value of the ninth vibration parameter and the first vibration limit is less than the vibration threshold, the third equilibrium speed is determined to be 95% of the critical speed.

[0044] Optionally, a first high-speed dynamic balancing of the flexible rotor is performed based on the third balancing speed and the first balancing surface, including:

[0045] Add the fifth test weight to the inner ring counterweight hole of the left counterweight plate, start the flexible rotor to the third equilibrium speed, detect the tenth vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0046] Remove the fifth test weight, add the sixth test weight to the inner ring counterweight hole of the right counterweight plate, start the flexible rotor to the third equilibrium speed, detect the eleventh vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0047] The sixth test weight is removed. The third correction mass is calculated using the influence coefficient method based on the first original vibration parameter, the tenth vibration parameter and the eleventh vibration parameter. The first original vibration parameter is the vibration parameter when the flexible rotor is started to reach the third equilibrium speed after the second low-speed dynamic balancing state is completed.

[0048] Based on the third correction mass, balance weights are added to the left and right counterweights respectively. The flexible rotor is started to pass through the critical speed, and the twelfth vibration parameter at the measuring surface of the rotating shaft is detected.

[0049] Whether the first balance condition is met is determined based on the twelfth vibration parameter during the speed-up process of the flexible rotor. The first balance condition is that the twelfth vibration parameter is lower than the first vibration limit value.

[0050] If the first balance condition is not met, repeat the first high-speed dynamic balancing steps described above until the first balance condition is met.

[0051] Optionally, a second high-speed dynamic balancing of the flexible rotor is performed based on the operating speed of the flexible rotor and the second balancing surface, including:

[0052] Add the seventh test weight to the inner ring counterweight hole of the turbine disk, start the flexible rotor to the working speed, detect the thirteenth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0053] Remove the seventh test weight, add the eighth test weight to the inner ring counterweight hole of the coupling disc, start the flexible rotor to the working speed, detect the fourteenth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0054] The eighth test weight was removed, and the fourth correction mass was calculated using the influence coefficient method based on the second original vibration parameter, the thirteenth vibration parameter, and the fourteenth vibration parameter. The second original vibration parameter was the vibration parameter at the shaft measurement surface detected when the flexible rotor reached the working speed after the first high-speed dynamic balancing was completed.

[0055] Based on the fourth correction mass, balance weights are added to the turbine disk and coupling disk respectively. The flexible rotor is started to the operating speed, and the fifteenth vibration parameter is detected.

[0056] The second balance condition is determined based on the fifteenth vibration parameter, wherein the second balance condition is that the fifteenth vibration parameter at the flexible rotor operating speed is less than the second vibration limit value.

[0057] If the second equilibrium condition is not met, repeat the above second high-speed dynamic balancing steps until the second equilibrium condition is met.

[0058] If the second balance condition is met, the entire balancing process for the flexible rotor is complete.

[0059] The beneficial effects of this invention are as follows: This invention reduces the risk of acceleration by pre-balancing in stages, avoiding severe vibration caused by large initial imbalance; it avoids trial weight conflicts and reduces material damage by using the inner and outer ring counterweight holes in groups; it balances safety and efficiency, has good repeatability, and can achieve stable operation of aerospace flexible rotors with large initial imbalance at full speed. Attached Figure Description

[0060] Figure 1 This is a flowchart of a flexible rotor balancing method according to an embodiment of the present invention.

[0061] Figure 2 This is a flowchart of a flexible rotor balancing method according to another embodiment of the present invention. Detailed Implementation

[0062] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0063] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0064] Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0065] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0066] In the specification of this invention, the terms "first" and "second" may explicitly or implicitly include one or more of the same feature. In the description of this invention, unless otherwise stated, "multiple" means two or more. Furthermore, in the specification, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0067] This embodiment introduces a flexible rotor balancing method, such as... Figure 1 As shown, steps 1100-1300 are included.

[0068] Step 1100: Perform finite element analysis based on the structural parameters of the flexible rotor to determine the critical speed at which the flexible rotor undergoes bending deformation and the target location.

[0069] Specifically, the flexible rotor has a switched reluctance rotor, which is a multi-salient pole structure made by bonding and pressing magnetic steel sheets, and the target part is the switched reluctance rotor.

[0070] To accurately obtain the dynamic characteristics of the rotor system, a simplified solid model was first established in 3D modeling software based on the actual rotor structural drawings. Non-critical features such as local chamfers, oil holes, and threads that do not affect mass distribution and support stiffness were reasonably omitted. The simplified model was then imported into a finite element analysis platform for rotor modal calculations, obtaining the flexible critical speed and its corresponding mode shape. The modal analysis results show that when the rotor reaches this critical speed, it will exhibit significant first-order bending deformation. The peak bending position is concentrated in the switched reluctance rotor section in the middle of the rotor, indicating that this section is the most sensitive part to unbalanced excitation in the flexible state and is also the area that needs to be focused on in subsequent high-speed balancing.

[0071] Step 1200: Based on the critical speed, target location, and initial imbalance concentration location of the flexible rotor, determine multiple equilibrium speeds of the flexible rotor and the equilibrium surface corresponding to each equilibrium speed.

[0072] Based on the above modal calculation results, and combined with the initial imbalance concentration locations determined by the structural characteristics and manufacturing processes of each component, the selection of the balancing surface and the setting of the balancing speed for each balancing stage are comprehensively determined. Because the switched reluctance rotor is formed using a magnetic sheet bonding and pressing process and has a four-salient pole structure, it carries a large initial imbalance amplitude and high concentration, making direct high-speed balancing extremely risky. Therefore, a low-speed pre-balancing stage must be set before high-speed balancing. For example... Figure 2 As shown, the entire balancing process includes a low-speed pre-balancing stage and a high-speed fine balancing stage.

[0073] The balancing speed includes a first balancing speed and a second balancing speed, and the balancing surface includes a first balancing surface and a second balancing surface. The first balancing speed is 10% of the critical speed, and the second balancing speed is 30% of the critical speed. The first balancing surface consists of the left and right counterweight discs, and the second balancing surface consists of the turbine disc and the coupling disc.

[0074] Step 1300: Based on multiple balancing speeds and the balancing surface corresponding to each balancing speed, perform multi-stage balancing processing on the flexible rotor to eliminate the imbalance of the flexible rotor.

[0075] Specifically, step 1300 includes steps 1310-1340.

[0076] Step 1310: Perform a first low-speed dynamic balance on the flexible rotor based on the first equilibrium speed and the first equilibrium surface to eliminate large initial imbalance.

[0077] Step 1320: After the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balancing speed and the second balancing surface to eliminate rigid imbalance.

[0078] Step 1330: At the end of the second low-speed dynamic balancing, determine whether the preset balance conditions are met.

[0079] Step 1340: Perform high-speed dynamic balancing on the flexible rotor if the preset balance conditions are not met.

[0080] Low-speed balancing is implemented in two steps: First, using the left and right counterweight discs installed at both ends of the switched reluctance rotor as balancing surfaces, double-plane balancing is performed at 10% of the critical speed to specifically eliminate its large initial imbalance; second, using the turbine disc and coupling disc as balancing surfaces, balancing is performed again at 30% of the critical speed to further eliminate the rigid imbalance remaining after the entire machine is assembled. After completing the above low-speed pre-balancing, based on the vibration monitoring data during the actual rotor speed-up process, decisions are made on whether and how to implement high-speed dynamic balancing near the critical speed and at the operating speed.

[0081] The balancing components include a counterweight plate (mainly to solve the problem of not being able to add test weights or remove material counterweights at high speeds due to the original unbalanced surface); and counterweight blocks (for adding test weights / counterweights).

[0082] To address the issue of adding counterweights to the left / right end balance surfaces of a switched reluctance rotor, and to avoid damaging the original structure of the switched reluctance rotor during material removal, a counterweight disc is fabricated to fit the left / right end surfaces of the switched reluctance rotor. The structural features of the counterweight disc are as follows:

[0083] The counterweight plate is made of TC4 material, which reduces the added weight to the original rotor;

[0084] The outer diameter of the left and right counterweight discs is the same as the maximum radial dimension of the salient pole of the switched reluctance rotor;

[0085] The inner diameter of the left / right counterweight discs matches the outer diameter of the bosses at the bottom of the left / right end faces of the switched reluctance rotor, and the design tolerance is negative.

[0086] The thickness of the left / right counterweight discs needs to be determined by comprehensively considering the structural space, stiffness requirements, and impact on the rotor's critical speed. After analysis, it was finally determined to be 6mm, which minimizes the impact on the rotor's dynamic characteristics while ensuring structural strength and installation reliability.

[0087] Both the left and right counterweight discs are designed with two rings of counterweight holes distributed circumferentially. The counterweight holes are threaded holes. The purpose of this design is to use the outer ring counterweight holes to balance the initial imbalance of the rotor, and to use the inner ring counterweight holes to balance the residual imbalance after the initial imbalance is eliminated at higher speeds.

[0088] The counterweight is a threaded rod structure, and its outer diameter matches the outer diameter of the counterweight hole. Different counterweight designs can be achieved by changing the processing material and its length.

[0089] Two rings of counterweight holes are machined on the back of the turbine disk and coupling disk hub, which are distributed circumferentially. The counterweight holes are threaded holes. Similarly, the outer ring counterweight holes are used to balance the rotor's flexible imbalance near the critical speed, and the inner ring counterweight holes are used to balance the rotor's final residual imbalance at the operating speed.

[0090] In this embodiment, the first low-speed dynamic balancing of the flexible rotor is performed based on the first equilibrium speed and the first equilibrium surface, including:

[0091] The left and right counterweights are installed at both ends of the switched reluctance rotor using a hot-fitting process.

[0092] In the initial state, the flexible rotor is started to the first equilibrium speed, the first vibration parameter at the measuring surface of the shaft is detected, and then the rotor is stopped.

[0093] Add the first test weight to the outer ring counterweight hole of the left counterweight plate, start the flexible rotor to the first equilibrium speed, detect the second vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0094] Remove the first test weight, add the second test weight to the outer ring counterweight hole of the right counterweight plate, start the flexible rotor to the first equilibrium speed, detect the third vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0095] Remove the second test weight, calculate the first influence coefficient and the first correction mass using the influence coefficient method based on the first vibration parameter, the second vibration parameter and the third vibration parameter, add balancing weights to the left and right counterweight plates respectively based on the first correction mass, start the flexible rotor to the first balance speed, detect the fourth vibration parameter at the measuring surface of the rotating shaft, and then stop the machine;

[0096] The first residual unbalance is calculated using the influence coefficient method based on the first influence coefficient and the fourth vibration parameter.

[0097] If the first remaining imbalance meets the preset first balance accuracy requirement, the first low-speed dynamic balancing ends.

[0098] If the first remaining imbalance does not meet the first balance accuracy requirement, the material is ground off at the corresponding edge positions of the left and right counterweight plates according to the first remaining imbalance until the first balance accuracy requirement is met.

[0099] Since the initial large imbalance is concentrated in the switched reluctance rotor, its amplitude is extremely large. To ensure absolute safety, an extremely low speed needs to be selected, which must be much lower than the critical speed (to avoid interference from flexible deformation) and sufficient to generate measurable centrifugal force. Ultimately, 10% of the critical speed was selected as the first balancing speed based on engineering experience.

[0100] Furthermore, since the initial large imbalance is concentrated in the switched reluctance rotor body, the most direct way to eliminate it is to apply a corrective force at both ends of the rotor (left / right cross-section). Therefore, the balance plane is locked to the left and right counterweight plates installed at both ends of the switched reluctance rotor.

[0101] The first vibration parameter represents the original vibration response generated on the shaft surface by the superposition of all the inherent defects of the flexible rotor itself in its original state without any trial weight or correction mass applied.

[0102] The second vibration parameter represents the combined vibration response of the flexible rotor under the combined action of the original imbalance and the first test weight at the left end, after a first test weight of known size and phase has been added to the outer ring counterweight hole of the left counterweight disk. The second vibration parameter reflects the result of the vector superposition of the first vibration parameter and the vibration caused solely by the first test weight at the left end.

[0103] The third vibration parameter represents the combined vibration response of the flexible rotor under the combined action of the original imbalance and the second test weight on the right end, after adding a second test weight of known size and phase only to the outer ring counterweight hole of the right counterweight disk. The third vibration parameter reflects the result of the vector superposition of the first vibration parameter and the vibration caused solely by the second test weight on the right end.

[0104] The influence coefficient method is an analytical and experimental approach based on the linear system assumption, used to establish the vibration equations of dynamic systems for dynamic balance correction. Its core idea is to describe the system's response under specific conditions using influence coefficients: the vibration response of the system at other measuring points when a unit mass is applied to a certain coordinate or plane.

[0105] The first influence coefficient represents the magnitude of vibration change in the measurement surface caused by applying a unit test weight to the left and right counterweight disks at the first equilibrium rotational speed. The first correction mass includes the correction mass of the left counterweight disk and the correction mass of the right counterweight disk. The correction mass includes its specific magnitude and phase.

[0106] The fourth vibration parameter represents the final synthesized vibration response of the flexible rotor under the combined effect of the initial imbalance and the correction masses at both ends after adding balancing weights to the left and right counterweight plates. This fourth vibration parameter no longer includes the temporary effects of the trial weight process; instead, it represents the vibration caused by residual defects in the flexible rotor that have not yet been eliminated after this round of balancing correction. All vibration parameters can be obtained using displacement sensors.

[0107] The first residual imbalance represents the quantified value of the uncounted centrifugal force remaining in the rotor after the first round of balancing (added to the left and right counterweight plates). The first residual imbalance also includes both magnitude and phase. When grinding away material from the corresponding edge positions of the left and right counterweight plates, the specific grinding location is determined by the phase of the first residual imbalance, and the specific degree of grinding is determined by the magnitude of the first residual imbalance.

[0108] The first balancing accuracy requirement is a preset condition for ending the first low-speed dynamic balancing phase. This requirement represents the maximum allowable residual imbalance before entering the second low-speed dynamic balancing phase. The first balancing accuracy requirement is derived from engineering experience and safety calculations. In the first low-speed dynamic balancing phase, the goal is not to achieve extreme precision, but rather to achieve a sufficiently safe coarse adjustment. The first balancing accuracy requirement is a set threshold; if the first residual imbalance is less than this threshold, it indicates that the first residual imbalance meets the first balancing accuracy requirement.

[0109] If the first remaining imbalance meets the first balancing accuracy requirement, it means that the residual defects are within the safe allowable range, and the result is deemed qualified. The first low-speed dynamic balancing stage ends, and the next stage, the second low-speed dynamic balancing stage, begins.

[0110] If the initial residual imbalance does not meet the initial balance accuracy requirement, it indicates that the residual defects are still significant, and directly increasing the speed poses a risk. In this case, it is necessary to grind away the material, change the physical mass distribution of the rotor, then restart the vibration parameter monitoring, and recalculate the new initial residual imbalance until the initial balance accuracy requirement is met.

[0111] In this embodiment, after the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balancing speed and the second balancing surface, including:

[0112] After the first low-speed dynamic balancing is completed, start the flexible rotor to the second balancing speed, detect the fifth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0113] Add a third test weight to the outer ring counterweight hole of the turbine disk, start the flexible rotor to the second equilibrium speed, detect the sixth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0114] Remove the third test weight, add the fourth test weight to the outer ring counterweight hole of the coupling disc, start the flexible rotor to the second equilibrium speed, detect the seventh vibration parameter at the shaft measuring surface, and then stop the machine.

[0115] Remove the fourth test weight, and calculate the second influence coefficient and the second correction mass using the influence coefficient method based on the fifth, sixth, and seventh vibration parameters. Add balancing weights to the turbine disk and coupling disk respectively based on the second correction mass, start the flexible rotor to the second equilibrium speed, detect the eighth vibration parameter at the shaft measuring surface, and then stop the machine.

[0116] The second residual unbalance is calculated using the influence coefficient method based on the second influence coefficient and the eighth vibration parameter.

[0117] If the second remaining imbalance meets the preset second balance accuracy requirement, the second low-speed dynamic balancing ends.

[0118] If the second remaining imbalance does not meet the second balance accuracy requirement, the material is ground off at the corresponding edge positions of the turbine disk and coupling disk according to the second remaining imbalance until the second balance accuracy requirement is met.

[0119] After the initial low-speed dynamic balancing, the initial large imbalance has been significantly reduced. At this point, the rotational speed needs to be appropriately increased to expose the inherent rigidity imbalances of other components after assembly. However, the rotational speed still needs to be below the critical speed to prevent significant bending deformation of the rotor. Therefore, 30% of the critical speed, which is higher than 10% of the critical speed but still far from the resonance zone, is selected.

[0120] In addition to the switched reluctance rotor, the turbine disk and coupling disk themselves also have inherent eccentricities during machining and assembly. At this point, the concentration of the imbalance has shifted to these two disks, so the balance surface in the second low-speed dynamic balancing is switched to the turbine disk and coupling disk to specifically eliminate the residual rigid imbalance at these locations.

[0121] The fifth vibration parameter represents the total vibration remaining in the rotor after the first low-speed dynamic balancing process, caused by the rigid imbalance between the turbine disk and the coupling disk. The fifth vibration parameter reflects the original vibration during the second low-speed dynamic balancing process and is the target to be eliminated in this round.

[0122] The sixth vibration parameter represents the combined vibration response of the rotor under the combined action of the original vibration of the rotor and the third test weight of the turbine disk after adding a third test weight of known size and phase to the outer ring counterweight hole of the turbine disk. The sixth vibration parameter reflects the result of the vector superposition of the fifth vibration parameter and the vibration caused solely by the third test weight of the turbine disk.

[0123] The seventh vibration parameter represents the combined vibration response of the rotor under the combined action of the original vibration of the rotor and the fourth test weight of the coupling disc after adding a fourth test weight of known size and phase to the outer ring counterweight hole of the coupling disc. The seventh vibration parameter reflects the result of the vector superposition of the fifth vibration parameter and the vibration caused solely by the fourth test weight of the coupling disc.

[0124] The second influence coefficient indicates the magnitude of vibration change on the measuring surface caused by applying a unit test weight to the turbine disk and coupling disk at the second equilibrium speed. The second correction mass includes the correction mass of the turbine disk and the correction mass of the coupling disk.

[0125] The eighth vibration parameter represents the final synthesized vibration response of the rotor under the combined effect of the original imbalance and the corrective mass after adding balancing weights to the turbine disk and coupling disk. The eighth vibration parameter no longer includes the temporary effects of the trial weight process, but represents the vibration caused by the residual defects of the rotor that have not yet been eliminated after the current balancing correction.

[0126] The second residual imbalance represents the equivalent unbalanced mass torque remaining on the rotor after the second round of balancing (added to the turbine disk and coupling disk), contributed by the turbine disk and coupling disk side. The second residual imbalance also includes both magnitude and phase. When grinding away material from the corresponding edge positions of the turbine disk and coupling disk, the specific grinding location is determined by the phase of the second residual imbalance, and the specific grinding degree is determined by the magnitude of the second residual imbalance.

[0127] The second balancing accuracy requirement is the upper limit of the residual imbalance that is pre-set for the second low-speed dynamic balancing before entering high-speed dynamic balancing. The second balancing accuracy requirement is also a set threshold, which is usually more stringent (smaller in value) than the first balancing accuracy requirement. This is because the first low-speed dynamic balancing is a coarse adjustment, and the second low-speed dynamic balancing is a medium adjustment. In order to safely pass through the critical speed, the residual imbalance of the turbine disc and coupling disc must also be suppressed to a sufficiently low level.

[0128] If the second remaining imbalance meets the second balance accuracy requirement, it is deemed qualified, the second low-speed dynamic balancing stage ends, and preparation begins for the high-speed dynamic balancing stage.

[0129] If the second residual imbalance does not meet the second balancing accuracy requirement, it indicates that the residual defect is still significant, and directly increasing the speed poses a risk. In this case, it is necessary to grind away the material, change the physical mass distribution of the rotor, then restart the vibration parameter monitoring, and recalculate the new second residual imbalance until the second balancing accuracy requirement is met.

[0130] In this embodiment, the preset balance conditions include a first balance condition and a second balance condition. High-speed dynamic balancing of the flexible rotor includes:

[0131] If the flexible rotor does not meet the first balance condition, the third balance speed is determined according to the critical speed. Based on the third balance speed and the first balance surface, the flexible rotor is subjected to the first high-speed dynamic balance to eliminate the unbalance of the flexible vibration mode.

[0132] If the flexible rotor satisfies the first balance condition, determine whether the flexible rotor satisfies the second balance condition.

[0133] If the flexible rotor does not meet the second balance condition, a second high-speed dynamic balance is performed on the flexible rotor based on the operating speed of the flexible rotor and the second balance surface to eliminate the residual imbalance at the operating speed.

[0134] Specifically, determining the third equilibrium speed based on the critical speed includes:

[0135] After the second low-speed dynamic balancing is completed, the flexible rotor is started. During the speed-up process of the flexible rotor, the ninth vibration parameter at the measuring surface of the shaft is detected until the ninth vibration parameter reaches the first vibration limit value or the speed of the flexible rotor exceeds the critical speed, then the rotor is stopped.

[0136] If the ninth vibration parameter reaches the first vibration limit value before the speed of the flexible rotor reaches the critical speed, record the target speed corresponding to the first time the ninth vibration parameter reaches the first vibration limit value, and determine the third equilibrium speed as 90% of the target speed;

[0137] If the rotational speed of the flexible rotor exceeds the critical speed, the ninth vibration parameter does not exceed the first vibration limit, and the difference between the maximum value of the ninth vibration parameter and the first vibration limit is less than the vibration threshold, the third equilibrium speed is determined to be 95% of the critical speed.

[0138] The ninth vibration parameter is the vibration signal measured in real time during the continuous acceleration of the flexible rotor past the critical speed after the second low-speed dynamic balancing is completed. The ninth vibration parameter reflects whether the flexible rotor can safely pass the critical speed.

[0139] The first vibration limit value is a pre-determined critical zone acceleration vibration limit value, used to determine whether a flexible unbalance is needed for balancing when the rotor crosses the critical speed and whether further acceleration is allowed. Its value should ensure that the rotor does not experience rubbing or support overload during transient over-critical conditions. Before formal balancing, the first vibration limit value is pre-determined based on rotor-static clearance, overall machine vibration standards, and test data of similar rotors.

[0140] If the ninth vibration parameter reaches the first vibration limit value during the acceleration of the flexible rotor, it indicates a risk, and the operation must be stopped immediately; acceleration cannot continue. If the speed of the flexible rotor exceeds the critical speed, it indicates successful acceleration, and further analysis can be performed after stopping the operation.

[0141] If the ninth vibration parameter reaches the first vibration limit value before the flexible rotor reaches the critical speed, it indicates that the rotor's current residual imbalance is amplified sharply as it approaches the critical region, making it unsafe to pass through. At this point, the target speed corresponding to when the ninth vibration parameter first reaches the first vibration limit value is recorded, and the third balancing speed is set to 90% of the target speed. This method leaves a 10% safety margin.

[0142] The third balancing speed needs to be selected within the speed range where the vibration has not yet reached a dangerous value. This allows the operator to safely add trial weights, measure vibration, and perform balancing calculations at the third balancing speed. If the target speed is directly used as the third balancing speed, performing dynamic balancing at the target speed will pose a safety hazard. After completing flexible balancing at 90% of the target speed, the critical vibration peak value of the rotor will be significantly reduced, thus allowing the critical speed to be safely exceeded.

[0143] The vibration threshold is a relatively small vibration value. If the difference between the maximum value of the ninth vibration parameter and the first vibration limit value is less than the vibration threshold, it indicates that the ninth vibration parameter is close to the first vibration limit value. On the other hand, if the rotor successfully exceeds the critical speed, and the ninth vibration parameter does not exceed the first vibration limit value but is close to it throughout the acceleration process, it indicates that the rotor condition is acceptable, but the vibration peak value near the critical region is still too large. In this case, the third balancing speed is taken as 95% of the critical speed, and the third balancing speed is selected at a position slightly lower than the critical speed. At this speed, the rotor is already close to the critical region, and the flexible bending deformation is already quite obvious. Applying correction at this time can effectively suppress the flexible vibration mode. If a lower speed is selected, such as 50% or even lower of the critical speed, the rotor is still in a rigid state, and the correction effect cannot be effectively transferred to the flexible vibration mode. After completing the flexible balancing at 95% of the critical speed, the critical peak value is further reduced, and the rotor can run more smoothly.

[0144] In this embodiment, the first high-speed dynamic balancing of the flexible rotor is performed based on the third balance speed and the first balance surface, including:

[0145] Add the fifth test weight to the inner ring counterweight hole of the left counterweight plate, start the flexible rotor to the third equilibrium speed, detect the tenth vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0146] Remove the fifth test weight, add the sixth test weight to the inner ring counterweight hole of the right counterweight plate, start the flexible rotor to the third equilibrium speed, detect the eleventh vibration parameter at the measuring surface of the rotating shaft, and then stop the machine.

[0147] The sixth test weight is removed. The third correction mass is calculated using the influence coefficient method based on the first original vibration parameter, the tenth vibration parameter and the eleventh vibration parameter. The first original vibration parameter is the vibration parameter when the flexible rotor is started to reach the third equilibrium speed after the second low-speed dynamic balancing state is completed.

[0148] Based on the third correction mass, balance weights are added to the left and right counterweights respectively. The flexible rotor is started to pass through the critical speed, and the twelfth vibration parameter at the measuring surface of the rotating shaft is detected.

[0149] Whether the first balance condition is met is determined based on the twelfth vibration parameter during the speed-up process of the flexible rotor. The first balance condition is that the twelfth vibration parameter is lower than the first vibration limit value.

[0150] If the first balance condition is not met, repeat the first high-speed dynamic balancing steps described above until the first balance condition is met.

[0151] The first original vibration parameter represents the residual vibration of the rotor at the third equilibrium speed after the first two rounds of low-speed dynamic balancing. It includes the uncorrected unbalanced flexible mode. The first original vibration parameter serves as the reference for this round of calculation.

[0152] The tenth vibration parameter represents the combined vibration response of the rotor under the combined action of the first original vibration parameter and the fifth test weight of the left counterweight plate after adding a fifth test weight of known size and phase to the inner ring counterweight hole of the left counterweight plate. The tenth vibration parameter reflects the result of the vector superposition of the first original vibration parameter and the vibration caused solely by the fifth test weight of the left counterweight plate.

[0153] The eleventh vibration parameter represents the combined vibration response of the rotor under the combined action of the first original vibration parameter and the sixth test weight of the right counterweight plate after adding a sixth test weight of known size and phase to the inner ring counterweight hole of the right counterweight plate. The eleventh vibration parameter reflects the result of the vector superposition of the first original vibration parameter and the vibration caused solely by the sixth test weight of the right counterweight plate.

[0154] The third calibration mass includes the calibration mass of the left and right counterweight plates, and also includes specific mass magnitudes and phases. Unlike the outer ring counterweight holes used in the low-speed dynamic balancing stage, the inner ring counterweight holes are used in the high-speed balancing stage for fine adjustments.

[0155] The twelfth vibration parameter represents the vibration data measured in real time as the rotor accelerates past the critical speed after adding balancing weights to the left and right counterweights. This twelfth vibration parameter is used to determine whether the rotor can safely and smoothly pass the critical speed.

[0156] If the twelfth vibration parameter is lower than the first vibration limit, it means the rotor can smoothly pass through the critical zone without damaging the support or rotor body due to excessive vibration. If it does not meet the requirement, it means the critical vibration is still too large, and flexible balancing needs to be performed again.

[0157] In this embodiment, a second high-speed dynamic balancing of the flexible rotor is performed based on the operating speed of the flexible rotor and the second balancing surface, including:

[0158] Add the seventh test weight to the inner ring counterweight hole of the turbine disk, start the flexible rotor to the working speed, detect the thirteenth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0159] Remove the seventh test weight, add the eighth test weight to the inner ring counterweight hole of the coupling disc, start the flexible rotor to the working speed, detect the fourteenth vibration parameter at the measuring surface of the shaft, and then stop the machine.

[0160] The eighth test weight was removed, and the fourth correction mass was calculated using the influence coefficient method based on the second original vibration parameter, the thirteenth vibration parameter, and the fourteenth vibration parameter. The second original vibration parameter was the vibration parameter at the shaft measurement surface detected when the flexible rotor reached the working speed after the first high-speed dynamic balancing was completed.

[0161] Based on the fourth correction mass, balance weights are added to the turbine disk and coupling disk respectively. The flexible rotor is started to the operating speed, and the fifteenth vibration parameter is detected.

[0162] The second balance condition is determined based on the fifteenth vibration parameter, wherein the second balance condition is that the fifteenth vibration parameter at the flexible rotor operating speed is less than the second vibration limit value.

[0163] If the second equilibrium condition is not met, repeat the above second high-speed dynamic balancing steps until the second equilibrium condition is met.

[0164] If the second balance condition is met, the entire balancing process for the flexible rotor is complete.

[0165] The second original vibration parameter represents the residual vibration of the rotor at the operating speed after the first two rounds of low-speed dynamic balancing and the first high-speed dynamic balancing. This is the target that needs to be eliminated in this round of balancing.

[0166] The thirteenth vibration parameter represents the combined vibration response of the rotor under the combined action of the second original vibration parameter and the seventh test weight of the turbine disk after adding a seventh test weight of known size and phase to the inner ring counterweight hole of the turbine disk. The thirteenth vibration parameter reflects the result of the vector superposition of the second original vibration parameter and the vibration caused solely by the seventh test weight of the turbine disk.

[0167] The fourteenth vibration parameter represents the combined vibration response of the rotor under the combined action of the second original vibration parameter and the eighth test weight of the coupling disc, after adding an eighth test weight of known size and phase to the inner ring counterweight hole of the coupling disc. The fourteenth vibration parameter reflects the result of the vector superposition of the second original vibration parameter and the vibration caused solely by the eighth test weight of the coupling disc.

[0168] The fourth calibration mass includes the calibration mass of the turbine disk and the coupling disk, and also includes specific mass magnitude and phase. Similar to the first high-speed dynamic balancing stage, the inner ring counterweight hole is used here for fine adjustment.

[0169] The fifteenth vibration parameter represents the vibration data measured at the rotor's operating speed after adding balancing weights to the turbine disk and coupling disk. The fifteenth vibration parameter is used to determine whether the rotor can operate normally.

[0170] The second vibration limit value is a predetermined steady-state vibration limit value allowed at the rotor operating speed, used to determine whether the residual unbalance at the operating speed meets the long-term operation requirements. This is the final accuracy requirement in the entire balancing process, because the operating speed represents the actual operating conditions of the rotor during long-term operation.

[0171] If the fifteenth vibration parameter is lower than the second vibration limit value, it indicates that the rotor meets the requirements for long-term operation. Then, the second high-speed dynamic balancing is completed, and the entire balancing process is finished.

[0172] This invention addresses the initial large imbalance of aerospace flexible rotors. First, modal calculations determine the critical speed, mode shape, critical zone, and vibration limits at operating speed. Then, balancing is performed in stages: initial large imbalance of the switched reluctance rotor is eliminated at 10% of the critical speed, and overall assembly rigidity imbalance is eliminated at 30% of the critical speed. Subsequently, based on measured vibrations during acceleration and the limits, it is determined whether high-speed dynamic balancing should be performed at the critical zone and operating speed. This method reduces the risk of acceleration through staged pre-balancing, avoiding severe vibrations caused by large initial imbalances; grouping the inner and outer ring counterweight holes avoids trial weight conflicts and reduces material damage; it balances safety and efficiency, has good repeatability, and can achieve stable operation of aerospace flexible rotors with large initial imbalances at all speeds.

[0173] While specific embodiments of the present invention have been described in detail by way of examples, those skilled in the art should understand that the above examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should understand that modifications can be made to the above embodiments without departing from the scope and spirit of the invention.

[0174] Those skilled in the art will recognize that the modules and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0175] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the above-described apparatus and equipment can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0176] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0177] The modules described as separate components may or may not be physically separate. Similarly, the components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the objectives of the embodiments of the present invention, depending on actual needs.

[0178] In addition, the functional modules in the embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0179] If the functionality is implemented as a software module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, ROM, RAM, magnetic disks, or optical disks.

[0180] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

[0181] It should be understood that the sequence numbers of the steps in the invention's content and embodiments do not absolutely imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention. The foregoing description of embodiments of this disclosure has been provided for illustrative and descriptive purposes. The foregoing description is not exhaustive and is not intended to limit this disclosure to the exact form disclosed. Various modifications and variations may exist based on the foregoing teachings, or various modifications and variations may be derived from the practice of this disclosure. These embodiments were chosen and described to illustrate the principles of this disclosure and its practical application, so that those skilled in the art can utilize this disclosure in various implementations and modifications suitable for the specific purpose of the concept.

Claims

1. A flexible rotor balancing method, characterized in that, include: Finite element analysis is performed based on the structural parameters of the flexible rotor to determine the critical speed and target location where the flexible rotor undergoes bending deformation. Based on the critical speed, target location, and initial imbalance concentration location of the flexible rotor, determine multiple equilibrium speeds of the flexible rotor and the equilibrium surface corresponding to each equilibrium speed. The flexible rotor is subjected to multi-stage balancing treatment based on multiple balancing speeds and the balancing surface corresponding to each balancing speed, in order to eliminate the imbalance of the flexible rotor.

2. The flexible rotor balancing method according to claim 1, characterized in that, The flexible rotor has a switched reluctance rotor, which is a multi-salient pole structure made of magnetic steel sheets bonded and pressed together. The target part is the switched reluctance rotor.

3. The flexible rotor balancing method according to claim 2, characterized in that, The balancing speed includes a first balancing speed and a second balancing speed, and the balancing surface includes a first balancing surface and a second balancing surface; Based on multiple balancing speeds and the balancing surface corresponding to each balancing speed, a multi-stage balancing process is performed on the flexible rotor, including: Based on the first equilibrium speed and the first equilibrium surface, a first low-speed dynamic balance is performed on the flexible rotor to eliminate large initial imbalance. After the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balance speed and the second balance surface to eliminate rigid imbalance. At the end of the second low-speed dynamic balancing, determine whether the flexible rotor meets the preset balance conditions. High-speed dynamic balancing is performed on the flexible rotor when the preset balance conditions are not met.

4. The flexible rotor balancing method according to claim 3, characterized in that, The first balance speed is 10% of the critical speed, the second balance speed is 30% of the critical speed, the first balance surface is the left and right counterweight discs, and the second balance surface is the turbine disc and the coupling disc.

5. The flexible rotor balancing method according to claim 4, characterized in that, The first low-speed dynamic balancing of the flexible rotor is performed based on the first equilibrium speed and the first equilibrium surface, including: The left and right counterweights are installed at both ends of the switched reluctance rotor using a hot-fitting process. In the initial state, the flexible rotor is started to the first equilibrium speed, the first vibration parameter at the measuring surface of the shaft is detected, and then the rotor is stopped. Add the first test weight to the outer ring counterweight hole of the left counterweight plate, start the flexible rotor to the first equilibrium speed, detect the second vibration parameter at the measuring surface of the rotating shaft, and then stop the machine. Remove the first test weight, add the second test weight to the outer ring counterweight hole of the right counterweight plate, start the flexible rotor to the first equilibrium speed, detect the third vibration parameter at the measuring surface of the rotating shaft, and then stop the machine. After removing the second test weight, the first influence coefficient and the first correction mass are calculated using the influence coefficient method based on the first vibration parameter, the second vibration parameter, and the third vibration parameter. Based on the first correction mass, balance weights are added to the left and right counterweight plates respectively. The flexible rotor is started to the first balance speed, the fourth vibration parameter at the measuring surface of the rotating shaft is detected, and then the rotor is stopped. The first residual unbalance is calculated using the influence coefficient method based on the first influence coefficient and the fourth vibration parameter. If the first remaining imbalance meets the preset first balance accuracy requirement, the first low-speed dynamic balancing ends. If the first remaining imbalance does not meet the first balance accuracy requirement, the material is ground off at the corresponding edge positions of the left and right counterweight plates according to the first remaining imbalance until the first balance accuracy requirement is met.

6. The flexible rotor balancing method according to claim 4, characterized in that, After the first low-speed dynamic balancing is completed, a second low-speed dynamic balancing is performed on the flexible rotor based on the second balance speed and the second balance surface, including: After the first low-speed dynamic balancing is completed, start the flexible rotor to the second balancing speed, detect the fifth vibration parameter at the measuring surface of the shaft, and then stop the machine. Add a third test weight to the outer ring counterweight hole of the turbine disk, start the flexible rotor to the second equilibrium speed, detect the sixth vibration parameter at the measuring surface of the shaft, and then stop the machine. Remove the third test weight, add the fourth test weight to the outer ring counterweight hole of the coupling disc, start the flexible rotor to the second equilibrium speed, detect the seventh vibration parameter at the shaft measuring surface, and then stop the machine. Remove the fourth test weight, and calculate the second influence coefficient and the second correction mass using the influence coefficient method based on the fifth, sixth, and seventh vibration parameters. Add balancing weights to the turbine disk and coupling disk respectively based on the second correction mass, start the flexible rotor to the second equilibrium speed, detect the eighth vibration parameter at the shaft measuring surface, and then stop the machine. The second residual unbalance is calculated using the influence coefficient method based on the second influence coefficient and the eighth vibration parameter. If the second remaining imbalance meets the preset second balance accuracy requirement, the second low-speed dynamic balancing ends. If the second remaining imbalance does not meet the second balance accuracy requirement, the material is ground off at the corresponding edge positions of the turbine disk and coupling disk according to the second remaining imbalance until the second balance accuracy requirement is met.

7. The flexible rotor balancing method according to claim 4, characterized in that, The preset equilibrium conditions include a first equilibrium condition and a second equilibrium condition; High-speed dynamic balancing of flexible rotors includes: If the flexible rotor does not meet the first balance condition, the third balance speed is determined according to the critical speed. Based on the third balance speed and the first balance surface, the flexible rotor is subjected to the first high-speed dynamic balance to eliminate the unbalance of the flexible vibration mode. If the flexible rotor satisfies the first balance condition, determine whether the flexible rotor satisfies the second balance condition. If the flexible rotor does not meet the second balance condition, a second high-speed dynamic balance is performed on the flexible rotor based on the operating speed of the flexible rotor and the second balance surface to eliminate the residual imbalance at the operating speed.

8. A flexible rotor balancing method according to claim 7, characterized in that, Determining the third equilibrium speed based on the critical speed includes: After the second low-speed dynamic balancing is completed, the flexible rotor is started. During the speed-up process of the flexible rotor, the ninth vibration parameter at the measuring surface of the shaft is detected until the ninth vibration parameter reaches the first vibration limit value or the speed of the flexible rotor exceeds the critical speed, then the rotor is stopped. If the ninth vibration parameter reaches the first vibration limit value before the speed of the flexible rotor reaches the critical speed, record the target speed corresponding to the first time the ninth vibration parameter reaches the first vibration limit value, and determine the third equilibrium speed as 90% of the target speed; If the rotational speed of the flexible rotor exceeds the critical speed, the ninth vibration parameter does not exceed the first vibration limit, and the difference between the maximum value of the ninth vibration parameter and the first vibration limit is less than the vibration threshold, the third equilibrium speed is determined to be 95% of the critical speed.

9. A flexible rotor balancing method according to claim 8, characterized in that, The first high-speed dynamic balancing of the flexible rotor is performed based on the third balance speed and the first balance surface, including: Add the fifth test weight to the inner ring counterweight hole of the left counterweight plate, start the flexible rotor to the third equilibrium speed, detect the tenth vibration parameter at the measuring surface of the rotating shaft, and then stop the machine. Remove the fifth test weight, add the sixth test weight to the inner ring counterweight hole of the right counterweight plate, start the flexible rotor to the third equilibrium speed, detect the eleventh vibration parameter at the measuring surface of the rotating shaft, and then stop the machine. The sixth test weight is removed. The third correction mass is calculated using the influence coefficient method based on the first original vibration parameter, the tenth vibration parameter and the eleventh vibration parameter. The first original vibration parameter is the vibration parameter when the flexible rotor is started to reach the third equilibrium speed after the second low-speed dynamic balancing state is completed. Based on the third correction mass, balance weights are added to the left and right counterweights respectively. The flexible rotor is started to pass through the critical speed, and the twelfth vibration parameter at the measuring surface of the rotating shaft is detected. Whether the first balance condition is met is determined based on the twelfth vibration parameter during the speed-up process of the flexible rotor. The first balance condition is that the twelfth vibration parameter is lower than the first vibration limit value. If the first balance condition is not met, repeat the first high-speed dynamic balancing steps described above until the first balance condition is met.

10. A flexible rotor balancing method according to claim 9, characterized in that, A second high-speed dynamic balancing of the flexible rotor is performed based on its operating speed and a second balancing surface, including: Add the seventh test weight to the inner ring counterweight hole of the turbine disk, start the flexible rotor to the working speed, detect the thirteenth vibration parameter at the measuring surface of the shaft, and then stop the machine. Remove the seventh test weight, add the eighth test weight to the inner ring counterweight hole of the coupling disc, start the flexible rotor to the working speed, detect the fourteenth vibration parameter at the measuring surface of the shaft, and then stop the machine. The eighth test weight was removed, and the fourth correction mass was calculated using the influence coefficient method based on the second original vibration parameter, the thirteenth vibration parameter, and the fourteenth vibration parameter. The second original vibration parameter was the vibration parameter at the shaft measurement surface detected when the flexible rotor reached the working speed after the first high-speed dynamic balancing was completed. Based on the fourth correction mass, balance weights are added to the turbine disk and coupling disk respectively. The flexible rotor is started to the operating speed, and the fifteenth vibration parameter is detected. The second balance condition is determined based on the fifteenth vibration parameter, wherein the second balance condition is that the fifteenth vibration parameter at the flexible rotor operating speed is less than the second vibration limit value. If the second equilibrium condition is not met, repeat the above second high-speed dynamic balancing steps until the second equilibrium condition is met. If the second balance condition is met, the entire balancing process for the flexible rotor is complete.

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