Design verification method for long-life pump system inner balance disc and motor electromagnetic

Abstract

This application belongs to the field of pump design technology, and particularly relates to a design verification method for the balance disc and motor electromagnetic components in a long-life pump system. The design verification method includes: Step 1, after integrating the design of the balance disc and motor electromagnetic components in the centrifugal pump system, determining the motor air gap and the outer diameter of the balance disc; Step 2, designing the parameters to be optimized in the balance disc; Step 3, using a fault diagnosis model, verifying the sliding bearing eccentricity fault of the centrifugal pump system containing the designed balance disc under operating conditions. If the verification fails, return to Step 2; otherwise, the verification is considered successful. This application ensures that the designed motor rotor diameter meets electromagnetic performance requirements, and the balance disc also has stronger balancing capabilities. Furthermore, it can guarantee through verification that the designed balance disc will not cause sliding bearing eccentricity faults; significantly improving the overall performance and safety of the centrifugal pump system, while extending the lifespan of the centrifugal pump system.

Description

Technical Field

[0001] This application belongs to the field of pump design technology, and in particular relates to the design and verification methods of balance discs and motor electromagnetics in long-life pump systems. Background Technology

[0002] In a centrifugal pump system, the shaft rotates at high speed driven by the drive unit, while the bearings support the shaft and reduce rotational friction; the two work closely together. In a multistage centrifugal pump system, axial force balance is crucial for ensuring long-term stable operation of the equipment. Traditional hydraulic flexible balance discs balance axial forces using hydraulic principles and are typically located inside the pump body.

[0003] During the high-speed rotation of a centrifugal pump, an inherent product of hydrodynamic effects—axial force—exists, such as the pressure difference between the front and rear impeller shrouds. To ensure stable and continuous operation, current technology typically uses a balance disc to balance this axial force. This balance disc generates a fluid pressure equal in magnitude but opposite in direction to the axial force generated by the impeller (hereinafter referred to as the axial balancing force) to counteract the axial force acting on the shaft as much as possible. However, due to dynamic response delays, design margins, and manufacturing errors, the axial balancing force cannot completely counteract the axial force at all times. When the axial force becomes too large, exceeding the maximum axial balancing force provided by the balance disc, or when oil film failure occurs (due to insufficient lubricating oil, oil deterioration, or excessively high oil temperature), the oil film ruptures, disrupting the balance and causing metal-to-metal contact and rotational friction between the shaft and bearing. This continuous metal-to-metal contact and rotational friction not only shortens the lifespan of the balance disc but can also lead to its complete failure in a very short time, severely impacting the operating efficiency and reliability of the centrifugal pump.

[0004] Therefore, we need to design the balance disc to have a greater upper limit of axial balancing force, thereby improving the lifespan of the balance disc and its safety during use.

[0005] However, in some highly integrated designs, in order to shorten the axial dimension and improve the system stiffness and response speed, the balance disc is placed inside the rotor of the drive motor or in the space between the rotor and the stator; but currently the electromagnetic design of the motor and the design of the balance disc are still independent of each other.

[0006] The rotor diameter of a motor is primarily determined based on electromagnetic performance optimization, while the size of the internal space of the rotor directly determines the maximum possible size of the balance disc. When a motor is designed with a small rotor diameter to achieve high power density, its limited internal space may prevent it from accommodating a balance disc of the required size. Conversely, if too much space is reserved for the balance disc, resulting in an increased rotor diameter, the motor's electromagnetic performance and power density may be reduced. Therefore, the lifespan of the balance disc and the motor efficiency are often mutually restrictive. Designing the motor's electromagnetic components or the balance disc separately will severely limit the overall performance of the centrifugal pump.

[0007] Furthermore, while the purpose of designing the balance disc is to increase its axial balancing force and enhance its balancing ability, it may cause eccentricity failure in the sliding bearings at both ends of the pump shaft. The causes and consequences of this are mainly as follows: ① Over-balancing generates a reverse axial force. The reverse load will directly cause the Babbitt alloy layer of the unidirectional bearing to overload, wear, or even burn out.

[0008] ② After the balancing capability is improved, the gap control between the balance disc and the balance ring may become more sensitive, which can easily cause pressure fluctuations, leading to periodic changes in the axial position of the rotor (i.e., axial movement). Frequent axial impacts will damage the oil film stability of the sliding bearing, causing oil film oscillation and temperature rise.

[0009] ③ If the residual axial force is too small, it is easy to lose the oil film preload, which may cause scratches or bearing failure.

[0010] The operating condition of the sliding bearing directly determines the safety and reliability of the centrifugal pump system. Therefore, even if the balance disc is designed to have a stronger balancing ability, it cannot be adopted if it causes the sliding bearing to eccentrically deviate. Summary of the Invention

[0011] The purpose of this application is to overcome the shortcomings of the prior art and provide a design verification method for the balance disc and motor electromagnetics in a long-life pump system. This method combines the design requirements of the balance disc in the centrifugal pump system with the electromagnetic parameter optimization process of the motor, so that the designed motor rotor diameter meets the electromagnetic performance requirements and the balance disc has a stronger balancing ability. At the same time, the verification can also ensure that the designed balance disc will not cause sliding bearing eccentricity failure. This significantly improves the overall performance and safety of the centrifugal pump system and extends its service life.

[0012] To achieve the above objectives, this application adopts the following technical solution: The design verification method for the balance disc and motor electromagnetic components in a long-life pump system includes the following steps: Step 1, after integrating the balance disc and motor electromagnetic components in the centrifugal pump system, determine the motor air gap and the outer diameter of the balance disc; Step 2, design the parameters to be optimized in the balance disc; Step 3, using a fault diagnosis model, verify the sliding bearing eccentricity fault of the centrifugal pump system where the designed balance disc is located under operating conditions. If the verification fails, return to Step 2; otherwise, it is recorded as a successful verification.

[0013] Preferably, step 1 further includes the following sub-steps: Step 11, based on the outer diameter of the balance disc and the motor air gap, construct a relationship model between axial balancing force and additional shaft power, and use a genetic algorithm to solve for the set of alternative solutions for the motor air gap that maximizes the coupled axial balancing force objective function and minimizes the coupled additional shaft power objective function; Step 12, calculate the theoretical value of the minimum outer diameter of the balance disc and the maximum allowable outer diameter of the motor when the balance disc reaches the maximum value of the corresponding coupled axial balancing force objective function under each alternative solution for the motor air gap; then, based on the maximum allowable outer diameter of the motor, perform a spatial feasibility verification on the theoretical value of the minimum outer diameter of the balance disc corresponding to the alternative solution for the motor air gap; record the alternative solution for the motor air gap that has successfully passed the spatial feasibility verification as the reasonable value of the motor air gap; Step 13, after determining the optimal motor air gap among the reasonable values ​​of the motor air gap by solving for the maximum comprehensive objective function, use the optimal motor air gap as the motor air gap of the centrifugal pump system where the balance disc is located, and use the maximum allowable outer diameter of the motor corresponding to the optimal motor air gap as the outer diameter of the balance disc.

[0014] Preferably, step 2 further includes the following sub-steps: Step 21, obtaining the parameters to be optimized for the balance disk; Step 22, constructing a relationship model between a single parameter to be optimized and the axial balancing force and the additional shaft power; the additional shaft power refers to the additional power required by the main shaft to overcome additional resistance when the flow channel is set; Step 23, based on the relationship model between a single parameter to be optimized and the axial balancing force and the additional shaft power, constructing the final axial balancing force objective function and the final additional shaft power objective function, and then using a genetic algorithm to solve for the potential solution set corresponding to maximizing the final axial balancing force objective function and minimizing the final additional shaft power objective function; Step 24, selecting any set of potential solutions for the parameters to be optimized from the potential solution set, modifying the actual values ​​of the parameters to be optimized in the balance disk to the values ​​of the corresponding potential solutions for the parameters to be optimized, and completing the design of the balance disk.

[0015] Preferably, step 2 also includes the following: using a fault diagnosis model, performing a sliding bearing eccentricity fault check on the centrifugal pump system where the designed balance disc is located under operating conditions; if the check fails, return to step 24, select any set of potential solutions for the parameters to be optimized from the remaining sets of potential solutions in the potential solution set, modify the actual value of the parameter to be optimized in the balance disc to the value of the corresponding potential solution for the parameter to be optimized, and then perform the sliding bearing eccentricity fault check again until the check is successful.

[0016] Preferably, step 11 also includes the following: Step 111, construct the balance disc outer diameter Axial balancing force for variables and additional shaft power A relationship model between them was constructed; at the same time, a model based on the air gap of the motor was also constructed. Axial balancing force for variables and additional shaft power Relationship Model

[0017] Step 112, construct the objective function of coupled axial equilibrium force. and the coupled additional axis power objective function : ; ; in, This represents the first weighting function; Indicates the first modification term; This represents the second weighting function; Indicates the second modification term; Step 113: Use a genetic algorithm to solve for the spare solution set of the motor air gap corresponding to the objective function of maximizing the coupled axial balance force and minimizing the objective function of the coupled additional shaft power.

[0018] Preferably, step 12 also includes the following: Step 121, denote the spare air gap solution of a certain motor as The theoretical minimum outer diameter of the balance disc when it reaches the maximum value of the objective function of the coupled axial balance force is then... ( ); the air gap of the motor is Maximum allowable outer diameter of the motor for: ; in, Indicates the air gap of the motor is Correcting the rotor outer diameter at that time; Indicates a safety margin; Step 122, if If the space feasibility verification is successful, then the space feasibility verification is successful; otherwise, the space feasibility verification is unsuccessful. The spare solution for the motor air gap that has successfully passed the space feasibility verification is recorded as the reasonable value of the motor air gap. In step 13, based on the efficiency potential of the motor air gap and the modified rotor outer diameter change index, a comprehensive objective function with the motor air gap as the variable is constructed. .

[0019] Preferably, in step 21, the parameters to be optimized for the balancing disk include: the length of the short side of the first sub-channel. Length of the long side of the first sub-channel First sub-channel short side eccentricity distance 1. Eccentricity of the long side of the first sub-channel The short side bending angle of the first sub-channel connection end The bending angle of the long side of the first sub-channel connection end Angle between adjacent first sub-channels Flow channel depth .

[0020] Preferably, in step 22: construct the first sub-channel with the short side length respectively. Axial balancing force for variables and additional shaft power The relationship model, with the length of the first sub-channel long side Axial balancing force for variables and additional shaft power The relationship model, with the short side eccentricity distance of the first sub-channel Axial balancing force for variables and additional shaft power The relationship model, with the eccentric distance of the long side of the first sub-channel Axial balancing force for variables and additional shaft power The relationship model, with the short side bending angle of the first sub-channel connection end Axial balancing force for variables and additional shaft power The relationship model, with the long side bending angle of the first sub-channel connection end Axial balancing force for variables and additional shaft power The relationship model, based on the angle between adjacent first sub-channels Axial balancing force for variables and additional shaft power Relationship model based on channel depth Axial balancing force for variables and additional shaft power The relationship model.

[0021] Preferably, step 23 further includes the following: The final objective function F for the axial equilibrium force is expressed as: ; The final expression for the objective function P of the additional shaft power is: ; in, ~ These represent the first to the eighth equilibrium force coefficients, respectively. ~ These represent the first power coefficient to the eighth power coefficient, respectively. Indicates the amount of correction for the balancing force; This indicates the amount of additional shaft power correction.

[0022] The preferred method for obtaining the fault diagnosis model includes the following sub-steps: Step 31: Generate voltage signals for different degrees of eccentricity of the faulty bearing. The voltage signals include the fundamental frequency, the third harmonic related to the bearing eccentricity, and Gaussian white noise with different signal-to-noise ratios. Step 32: The generated voltage signal is subjected to wavelet denoising based on the improved soft threshold function and EMD decomposition to extract IMF energy features. The resulting seven-dimensional fusion features, consisting of five-dimensional IMF energy features, pulse amplitude, and harmonic distortion rate, are then input into the neural network and a loss function containing pulse weight coefficients and harmonic weight coefficients is used. Step 33: First, fix the wavelet denoising parameters, train the neural network by combining multiple sets of pulse weight coefficients and harmonic weight coefficients, and determine the optimal pulse weight coefficients and harmonic weight coefficients; then fix the pulse weight coefficients and harmonic weight coefficients, train the neural network, and determine the optimal threshold parameters. Step 34: Assign the optimal pulse weight coefficient, harmonic weight coefficient and threshold parameter to the loss function. The resulting neural network is the bearing eccentricity fault diagnosis model.

[0023] The beneficial effects of this application are as follows: (1) The design verification method of this application combines the design requirements of the balance disc with the electromagnetic parameter optimization process of the motor, so that the rotor diameter of the motor meets the electromagnetic performance requirements and provides the optimal design space for the balance disc. Thus, under the premise of ensuring high efficiency and high power density of the motor, the balance disc has a larger upper limit of axial balance force, improves the life of the balance disc and the safety during use, and thus greatly improves the overall performance of the centrifugal pump system.

[0024] (2) The design verification method of this application, during the design process of the motor air gap (i.e., the process of obtaining the optimal motor air gap): ① Not only were the coupling effects of changes in the outer diameter of the balance disc and the motor air gap on the axial balancing force and additional shaft power considered, but the goal was always to improve the performance of the balance disc (i.e., to use a genetic algorithm to solve for the objective function that maximizes the coupled axial balancing force and minimizes the coupled additional shaft power) before obtaining the alternative solution set for the motor air gap. This is the first layer of screening for the motor air gap in the integrated design process.

[0025] ②Then, through spatial feasibility verification, a reasonable value for the motor air gap is obtained from the spare solution set of motor air gaps. Sufficient radial installation space is provided for the balance disc in the motor to avoid limiting the upper limit of the balance disc's subsequent optimization performance due to the initial limitation on the balance disc's outer diameter. This is the second layer of screening for the motor air gap in the integrated design process.

[0026] ③ Finally, a comprehensive objective function is constructed using various factors of the centrifugal pump system, such as cost, lifespan, space importance, motor efficiency, and rotor outer diameter variation. By solving for the maximum comprehensive objective function, the optimal motor air gap among reasonable values ​​is determined. This is the third layer of screening for the motor air gap in the integrated design process.

[0027] (3) In this application, once the optimal motor air gap is determined, the optimal motor air gap is used as the motor air gap of the centrifugal pump system where the balance disc is located. This ensures that the motor has high efficiency and high power density. Since the appropriate outer diameter of the balance disc can only be determined after the optimal motor air gap is determined, it also ensures that the subsequent design of the balance disc other than the diameter will not affect the motor performance. The subsequent design of the balance disc will only further optimize the balance disc, so that the balance disc has a larger upper limit of axial balancing force, a longer life and higher safety. Finally, the fault diagnosis model is used for verification to ensure the safety of the centrifugal pump system applied in the integrated design (that is, to ensure that the centrifugal pump system applied in the integrated design will not cause sliding bearing eccentricity failure), which greatly improves the overall performance and safety of the centrifugal pump system and extends the life of the centrifugal pump system.

[0028] (4) The design verification method of this application is applicable to the optimization of centrifugal pump systems with any type of motor and balance disc. It has a high degree of universality and strong applicability, so that the designed centrifugal pump system has better performance, higher safety and longer life compared with the undesigned centrifugal pump system.

[0029] (5) The balance disc designed by the design verification method of this application not only increases the upper limit of the maximum axial balance force that the optimized balance disc can provide, but also minimizes the additional shaft power of the optimized balance disc, greatly reduces the probability of metal contact and rotational friction between the shaft and the bearing, improves the safety of the optimized balance disc during use, reduces the wear of the flow channel on the optimized balance disc, and extends the life of the optimized balance disc.

[0030] (6) The design verification method of this application adopts an arc connection structure at the bend of the flow channel. Compared with the straight line flow channel formed by directly connecting the straight parts of the first sub-flow channel and the second sub-flow channel, the arc connection structure can effectively reduce the stress concentration at the connection end of the two sub-flow channels, reduce the wear of the flow channel, and extend the life of the balance disc.

[0031] (7) In the process of designing the balance disk, the verification method of this application focuses on the influence of multiple related parameters of the flow channel on the axial balance force and the additional shaft power (i.e., "constructing a relationship model between a single parameter to be optimized and the axial balance force and the additional shaft power"). Considering the mutual interference between these influences, the objective function is constructed by combining the relationship model with the correction amount. The genetic algorithm is used to solve the potential solution set that satisfies the objective function of "maximizing the final axial balance force and minimizing the objective function of the final additional shaft power". The fault diagnosis model is used to verify the sliding bearing eccentricity fault of the centrifugal pump system to further confirm whether the selected potential solution set can simultaneously ensure the safe operation of the sliding bearing in the centrifugal pump system. This ensures that the potential solution set of the parameter to be optimized that is successfully verified by the fault diagnosis model has not only made the balance disk have a stronger balancing ability, but also ensured that the designed balance disk will not cause the sliding bearing eccentricity fault, provided that the rotor diameter of the motor meets the electromagnetic performance requirements.

[0032] (8) The design verification method of this application results in a more uniform axial balancing force distribution on the optimized balance disk and a smaller span of axial balancing force in each flow channel, which reduces the dynamic response delay of the optimized balance disk in the dynamic adaptive process, improves the balancing accuracy, further reduces the risk of metal contact and rotational friction between the shaft and the bearing, improves the safety of the optimized balance disk in use and extends the life of the optimized balance disk.

[0033] (9) The design verification method of this application, the method for obtaining the fault diagnosis model, and the obtained fault diagnosis model: ① A comprehensive methodology covering "fault voltage signal generation—feature extraction—parameter optimization—model determination" was constructed, organically integrating key steps such as signal generation, wavelet denoising, EMD decomposition, neural network training, and parameter optimization. This formed a highly targeted system for establishing diagnostic models for sliding bearing eccentricity faults. This process ensures logical coherence from raw data to the diagnostic model and, through multi-stage collaborative design, ensures that the model can accurately identify the three states of bearing normal, slight eccentricity, and severe eccentricity. It solves the problems of insufficient targeting and fragmented processes in traditional diagnostic methods, providing a systematic solution for improving the accuracy of bearing eccentricity fault diagnosis.

[0034] ② By refining the voltage signal generation rules, accurate simulation of different bearing eccentricity states was achieved. The fixed fundamental frequency parameter provides a stable benchmark for the signal; the direct proportionality between the third harmonic amplitude and the eccentricity directly correlates with the fault severity; and the differentiated signal-to-noise ratio Gaussian white noise settings (10dB for normal, 15dB for mild, and 20dB for severe eccentricity) closely reflect the characteristic in actual operating conditions that "the more severe the fault, the stronger the signal interference." The signal generated by this design contains clear fault characteristics (harmonic variations) and simulates noise interference in the real environment, providing high-quality, high-fidelity sample data for subsequent model training and avoiding insufficient model generalization ability due to data distortion.

[0035] ③ The seven-dimensional fusion feature acquisition method achieves comprehensive capture of fault information. Wavelet denoising preprocessing effectively filters noise interference; the first five IMF energy features extracted by EMD decomposition reflect the energy distribution of the signal at different frequency scales, capturing multi-scale fluctuations caused by the fault; pulse amplitude features quantify the mechanical impact intensity, while harmonic distortion rate features reflect the degree of anomalous harmonic components. The fusion of these three features preserves both the time and frequency domain information of the signal and integrates the physical characteristics of the fault (impact, harmonic distortion), overcoming the shortcomings of single features in providing a comprehensive fault representation. This significantly improves the correlation between features and bearing eccentricity, laying the foundation for accurate model classification.

[0036] ④ The improved soft thresholding function solves the signal distortion problem caused by hard truncation in traditional soft thresholding functions through exponential decay. This function smooths the original wavelet coefficients, and instead of directly zeroing coefficients close to the threshold, it preserves some information through exponential decay. This effectively suppresses noise while maximizing the preservation of weak features related to bearing eccentricity (such as the third harmonic signal of early faults). Simultaneously, its continuously differentiable characteristic makes the processed signal smoother, avoiding artifacts that may occur with traditional functions, improving the fidelity of the denoised signal, and providing more reliable basic data for subsequent feature extraction.

[0037] ⑤ By calculating the correlation between the fundamental amplitude and the amplitudes of each harmonic, the change in the proportion of harmonic components caused by bearing eccentricity is intuitively reflected. That is, the more severe the eccentricity, the larger the amplitude of the third harmonic and the higher the THD value. This quantitative indicator not only has a clear physical meaning (directly related to the degree of failure), but also provides the model with comparable and calculable characteristic parameters, avoiding subjective judgment of harmonic characteristics and enhancing the objectivity and accuracy of fault diagnosis.

[0038] ⑥ Based on the traditional cross-entropy loss function, the weighting coefficients α and β are used to enhance the influence of pulse (mechanical shock) and harmonic distortion (electrical characteristics) on the loss calculation. This allows the model to focus more on features directly related to bearing eccentricity during training, rather than irrelevant noise. This design solves the problem of insufficient attention to fault features in traditional loss functions, improves the model's ability to distinguish between different degrees of eccentricity, and especially enhances the sensitivity to identify early faults such as mild eccentricity.

[0039] ⑦ By employing the process of "optimizing feature weights with fixed wavelet denoising parameters → optimizing denoising parameters with fixed feature weights," the impact of each parameter on model performance can be evaluated individually, eliminating optimization biases caused by parameter interactions. Furthermore, through comparative experiments using the same training set and validation set, combined with averaging multiple simulations, the reliability of parameter selection is further improved, ultimately determining the optimal parameters. α , β , λ It can maximize the performance of the model and solve the problem of determining the optimal combination when optimizing multiple parameters simultaneously.

[0040] ⑧ By performing simulations on the optimal parameter combination more than three times and taking the average accuracy, the result deviation caused by random factors (such as noise fluctuations and differences in neural network initialization) in a single experiment can be effectively offset. If the mean does not meet the requirements, iterative adjustments can be made by repeating the parameter optimization process to further improve the model accuracy. This design avoids "pseudo-optimal" models caused by accidental factors, ensuring that the output diagnostic model can stably perform in practical applications and improving the engineering practical value of the model. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the design verification method for the balance disc and motor electromagnetic components in the long-life pump system of this application. Figure 2 This is a schematic diagram of the balance disc; Figure 3 The pressure distribution diagram of the working surface of the optimized balance disc under extreme conditions is shown in the design diagram. Figure 4 The diagram shows the pressure distribution on the working surface of the balance disc before and after optimization under the same normal operating conditions. Detailed Implementation

[0042] To make the technical solution of this application clearer and more explicit, the application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Solutions derived by those skilled in the art through equivalent substitution and conventional reasoning of the technical features of the technical solution of this application without creative effort all fall within the protection scope of this application.

[0043] The design verification method for the balance disc and motor electromagnetic components in the long-life pump system of this application, such as... Figure 1 As shown, it includes the following steps: Step 1: After integrating the balance disc and motor solenoid in the centrifugal pump system into a single design, determine the motor air gap and the outer diameter of the balance disc. Step 2: Design the parameters to be optimized in the balance disc; Step 3: Using the fault diagnosis model, perform sliding bearing eccentricity fault verification on the centrifugal pump system where the designed balance disc is located under operating conditions. If the verification fails, return to step 2; otherwise, it is recorded as successful verification.

[0044] If the verification is successful, the centrifugal pump system will be manufactured and put into use according to the current motor air gap, balance disc outer diameter, and the designed parameters to be optimized.

[0045] Step 1 also includes the following sub-steps: Step 11: Based on the outer diameter of the balance disc and the air gap of the motor, construct a relationship model between the axial balancing force and the additional shaft power, and use a genetic algorithm to solve for the alternative solution set of the motor air gap corresponding to the objective function of maximizing the coupled axial balancing force and minimizing the objective function of the coupled additional shaft power. Step 12: Calculate the theoretical minimum outer diameter of the balance disc when the balance disc reaches the maximum value of the objective function of the corresponding coupled axial balance force under the spare solution of the air gap for each motor, as well as the maximum allowable outer diameter of the motor; then, based on the maximum allowable outer diameter of the motor, perform a spatial feasibility verification on the theoretical minimum outer diameter of the balance disc corresponding to the spare solution of the air gap for the corresponding motor; record the spare solution of the air gap for the motor that has successfully passed the spatial feasibility verification as the reasonable value of the air gap for the motor. Step 13: After determining the optimal motor air gap among the reasonable values ​​of motor air gap by solving the maximum comprehensive objective function, the optimal motor air gap is used as the motor air gap of the centrifugal pump system where the balance disc is located. At the same time, the maximum allowable outer diameter of the motor corresponding to the optimal motor air gap is used as the outer diameter of the balance disc.

[0046] This completes the integrated design of the balance disc and motor solenoid within the centrifugal pump system.

[0047] Step 11 also includes the following sub-steps: Step 111, construct the outer diameter of the balance disc The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent the first to the twenty-first parameters, respectively.

[0048] In this embodiment ~ The values ​​were 523.471256, -8.315427, 0.204312, 157.842179, -0.042127, 0.003456, and 4.18×10⁻⁶ respectively. -5 12.345678, 0.098765, 5.678912, 0.123456, 2345.678912, 0.567834, 0.104567, 456.782345, -0.034512, 0.012345, 20.123456, 0.103456, 10.567834, 1.234×10 -3 .

[0049] Constructing the air gap of the motor The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent parameters 22 through 44, respectively.

[0050] In this embodiment ~ Take respectively , , , , , , , , , , , , , , , , , , , , , , .

[0051] Step 112, Couple the axial equilibrium force objective function The expression is: ; ; ; in, This represents the first weighting function; Indicates the first modification term; ~ These represent parameters forty-fifth to fifty-fifth, respectively.

[0052] In this embodiment ~ Take values ​​of 0.031456, 0.126789, and 1.237 × 10⁻⁶ respectively. -3 5.12×10 -4 , 0.842567, -0.021487, 9.827456, 0.103456, 0.214567, 5.678912, 0.098765.

[0053] Coupled additional axis power objective function The expression is: ; ; ; in, This represents the second weighting function; Indicates the second modification term; ~ These represent parameters from the fifty-sixth to the sixty-fourth, respectively.

[0054] In this embodiment ~ The values ​​were 0.025678, 0.089123, 0.012345, 4.218765, 0.008765, 12.345678, 0.053456, 0.212345, and 0.573412, respectively.

[0055] Step 113: Use a genetic algorithm to solve for the spare solution set of the motor air gap corresponding to the objective function of maximizing the coupled axial balance force and minimizing the objective function of the coupled additional shaft power.

[0056] Step 12 includes the following sub-steps: Step 121, denote the spare air gap solution of a certain motor as The theoretical minimum outer diameter of the balance disc is the value at which the balance disc reaches the maximum value of the objective function of the coupled axial balance force. ( )for: ; in, Indicates the air gap of the motor At that time, the balance disc reaches the maximum value of the objective function of the corresponding coupled axial balance force.

[0057] The air gap of the motor is Maximum allowable outer diameter of the motor for: ; ; ; ; ; in, Indicates the air gap of the motor is Air gap magnetic flux density correction coefficient at that time; Indicates the air gap of the motor is Input power correction factor at that time; Indicates the air gap of the motor is Correcting the rotor outer diameter at that time; Indicates the motor input power; Indicates rated power; This indicates the power loss of the rotor ring; Copper loss power of the coil; Indicates other power losses; This indicates the calculation of the polar arc coefficient; Indicates the motor winding coefficient; Indicates the waveform coefficient of the air gap magnetic field; Indicates the rated speed of the motor; This represents the ratio between the armature length and the armature diameter. Indicates the estimated line load; Indicates magnetic load; Indicates relative permeability; Indicates the leakage flux coefficient; Indicates remanence; This indicates a safety margin; in this embodiment, it is taken as 5mm.

[0058] Step 122, if If the space feasibility verification is successful, then the space feasibility verification is successful; otherwise, the space feasibility verification is unsuccessful. The spare solution for the motor air gap that has successfully passed the space feasibility verification is recorded as the reasonable value of the motor air gap.

[0059] The space feasibility check failed, indicating that the current air gap of the motor does not provide enough space for the balance disc. If the balance disc is installed in this space, its outer diameter will definitely be smaller than [the required space]. ( This means that no matter how the parameters on the balance disc are optimized subsequently, they are limited by the outer diameter of the balance disc. This directly prevents the balance disc from having a larger upper limit for axial balancing force, thus limiting the optimization of the overall performance of the entire centrifugal pump system. In step 1, we obtained more than one alternative solution for the motor air gap. In step 2, we retained only the alternative solution for the motor air gap that passed the spatial feasibility check. In other words, this application further screens the alternative solutions for the motor air gap through spatial feasibility check to obtain several reasonable values ​​for the motor air gap.

[0060] In step 13, the formula for calculating the comprehensive objective function is as follows: ; ; ; ; ; in, Represent the overall objective function; and These represent the first weighting coefficient and the second weighting coefficient, respectively. and These represent the efficiency potential and the corrected rotor outer diameter variation index, respectively. and These represent the minimum and maximum values ​​of the corrected rotor outer diameter, respectively; and X and Y represent the maximum and minimum air gap magnetic flux density correction coefficients, respectively, which are the maximum and minimum values ​​calculated within the feasible range of the motor air gap. The feasible range of the motor air gap is known, and all alternative solutions and reasonable values ​​of the motor air gap in this application are within the feasible range. X and Y represent the first adjustment coefficient and the second adjustment coefficient, respectively, which are used to make... and Key constants that match orders of magnitude and reflect industry experience can be obtained by analyzing historical successful design cases. The proportions are set in accordance with the typical value orientation of this type of product; for example, for high-efficiency energy-saving pumps, X and Y may be set to be larger; for miniature compact pumps, X and Y may be set to be smaller. This indicates the rated power of the motor, in kW. The higher the power, the greater the absolute value of energy savings; therefore, efficiency should be given more importance (to increase...). (relative influence) In the calculation formula Located in the denominator, the overall sensitivity is adjusted via X; This indicates the expected total operating hours of the equipment, in hours. The longer the operating time, the greater the cumulative energy saving benefit, and the higher the efficiency weight should be. This represents the electricity cost coefficient, in yuan / kWh. The higher the electricity price, the higher the value of efficiency. This indicates the maximum allowable envelope diameter of the centrifugal pump system, in millimeters. The more limited the installation space, the higher the value of compactness (increases). The relative impact), since its impact is related to the area, is taken as a power of two; This represents the space cost coefficient. For situations where space is extremely precious, such as ships, this coefficient is very large; for fixed factory buildings, this coefficient is relatively small.

[0061] Step 2 also includes the following sub-steps: Step 21: Obtain the parameters to be optimized for the balancing disc.

[0062] Step 22: Construct a relationship model between a single parameter to be optimized, the axial balancing force, and the additional shaft power. The additional shaft power refers to the extra power required by the main shaft to overcome additional resistance when the flow channel is set up. The additional resistance is caused by factors such as pumping water and compressing gas.

[0063] Step 23: Based on the relationship model between a single parameter to be optimized, the axial balancing force, and the additional shaft power, construct the objective function of the final axial balancing force and the objective function of the final additional shaft power. Then, use a genetic algorithm to solve for the potential solution set corresponding to maximizing the objective function of the final axial balancing force and minimizing the objective function of the final additional shaft power. The potential solution set contains several sets of potential solutions for the parameters to be optimized, and each set of potential solutions for the parameters to be optimized contains all the parameters to be optimized.

[0064] Step 24: Select any set of potential solutions for the parameters to be optimized from the potential solution set, and then modify the actual values ​​of the parameters to be optimized in the balance disk to the values ​​of the corresponding potential solutions for the parameters to be optimized, thus completing the design of the balance disk.

[0065] Different types of balance discs are applicable to different scenarios. You can select the appropriate balance disc based on the applicable scenario and then modify the parameters of the balance disc to be optimized.

[0066] In step 21: The constant parameters of the balance disc include: the diameter of the shaft used in conjunction with the balance disc; the safety clearance between the shaft and the inner circle of the balance disc; the upper limit of the outer diameter of the blades; the inner diameter of the balance disc; the outer diameter of the balance disc; and the thickness of the balance disc.

[0067] In this embodiment, the safety clearance between the shaft and the inner circle of the balance disk is 1mm; the diameter of the shaft used in conjunction with the balance disk is 11mm; the upper limit of the outer diameter of the blades is 38mm; and the inner diameter of the balance disk is 12mm (in...). Figure 2 middle The inner diameter of the balance disc is indicated; the outer diameter of the balance disc is 30mm (in...). Figure 2 middle (This indicates the outer diameter of the balance disc); the thickness of the balance disc is 2mm. The height of the inner circular boss extending towards the high-pressure side of the balance disc is 5mm; the height of the inner circular boss extending towards the low-pressure side of the balance disc is 2mm.

[0068] like Figure 2 The diagram shown is a schematic of the balance disk of this application. All channels on the balance disk have the same depth. Each channel is composed of two sub-channels connected sequentially, with the first sub-channel and the second sub-channel arranged sequentially from the inner edge to the outer edge of the balance disk. The two ends of the first sub-channel are the inner end and the connecting end, respectively, and the two ends of the second sub-channel are the outer end and the connecting end, respectively. The inner end of the first sub-channel extends to the inner edge of the balance disk, and the connecting end of the first sub-channel connects to the connecting end of the second sub-channel. The two sides of the first sub-channel used to connect the inner end and the connecting end are the long side and the short side, respectively, forming a sealing dam between the long side of one first sub-channel and the short side of an adjacent first sub-channel. All connecting ends of the first sub-channels are arc-shaped, curving towards their own short sides, and connect to the connecting end of the second sub-channel. The outer end of the second sub-channel extends to the outer edge of the balance disk. The included angle between adjacent first sub-channels is the same, and the depths of both the first and second sub-channels are the same.

[0069] The parameters to be optimized for the balance disk include: the length of the short side of the first sub-channel. Unit: mm; Length of the long side of the first sub-channel Unit: mm; eccentricity distance of the short side of the first sub-channel Unit: mm; Distance between the long side and the center of the first sub-channel Unit: mm; Short side bending angle of the first sub-channel connection end. Unit: °; Bending angle of the long side of the first sub-channel connection end. Unit: °; Angle between adjacent first sub-channels Unit: °; channel depth , Unit: mm.

[0070] For a given first sub-channel: The intersection point between the geometric center line of the first sub-channel and the inner edge of the balance disk at the inner end of the first sub-channel is recorded as the tangent point of the current first sub-channel. The intersection point between the long side of the first sub-channel and the inner edge of the balance disk is denoted as... The intersection point between the short side of the first sub-channel and the inner edge of the balance disk is denoted as... The midpoint of the arc connecting the long side of the first sub-channel is denoted as... The midpoint of the arc connecting the short side of the first sub-channel is denoted as... ; Passing through the tangent point And the straight line tangent to the inner edge of the balance disc is denoted as After the intersection And with the straight line Parallel lines are denoted as After the intersection And with the straight line Parallel lines are denoted as Passing through the midpoint of the connecting end arc And with the straight line Parallel lines are denoted as Passing through the midpoint of the connecting end arc And with the straight line Parallel lines are denoted as For easier viewing, in Figure 2 midpoint ~ Black dots, straight lines ~ The line is solid red.

[0071] First sub-channel short side length It refers to a straight line With a straight line The distance between them; the length of the long side of the first sub-channel It refers to a straight line With a straight line The distance between them; the short side eccentricity distance of the first sub-channel This refers to the distance between the geometric center line of the first sub-channel and the straight section of the short side of the first sub-channel; the eccentricity distance of the long side of the first sub-channel. This refers to the distance between the geometric center line of the first sub-channel and the straight section of the long side of the first sub-channel; the bending angle of the short side at the connection end of the first sub-channel. This refers to the obtuse angle between the extended straight section of the short side of the first sub-channel and the extended straight section of the second sub-channel on the same side within the same flow channel; the bending angle of the long side at the connection end of the first sub-channel. This refers to the obtuse angle between the extended straight section of the long side of the first sub-channel and the extended straight section of the second sub-channel on the same side within the same flow channel; the angle between adjacent first sub-channels. This refers to the acute angle between the geometric center lines of adjacent first sub-channels. For easier viewing, in Figure 2 In the diagram, the extension lines and the geometric center line are represented by red dashed lines.

[0072] Step 22 also includes the following: Construct the short side length of the first sub-channel The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent the first to eighth coefficients, respectively; k represents the first intermediate parameter.

[0073] In this embodiment ~ The values ​​were 330.943, 21.995, 15.179, 3.16, 2.921, 2.08, 0.834, and 0.205, respectively.

[0074] Construct the length of the long side of the first sub-channel The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent the ninth to twentieth coefficients, respectively.

[0075] In this embodiment ~ The values ​​are 577.59, 377.257, 262.617, 102.485, 531.1, 278.46, 172.239, 56.389, 619.97, 194.32, 54.835, and 7.755 respectively.

[0076] Construct the short side eccentricity distance of the first sub-channel The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent coefficients 21 through 28, respectively.

[0077] In this embodiment ~ The values ​​were 344.253, 0.198, 0.132, 94.4858, 1.387, 0.141, 3.797, and 41.369, respectively.

[0078] Construct the eccentricity distance of the long side of the first sub-channel The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent the twenty-ninth to thirty-ninth coefficients, respectively.

[0079] In this embodiment ~ The values ​​were 0.2358, 1.8386, 34.11, 342.6, 58.086, 889.519, 7674.772, 1.389, 0.02, 4.908, and 71.63, respectively.

[0080] Construct the short-side bending angle of the first sub-channel connection end The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent the 40th to 48th coefficients, respectively.

[0081] In this embodiment ~ Take 7.654 and 3.73 × 10 respectively. 6, 100, 79489.98, 967.36, 12.4129, 0.3355, 0.0041, 2.48×10 -5 .

[0082] Constructing the long side bending angle of the first sub-channel connection end The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent coefficients 49 through 55, respectively.

[0083] In this embodiment ~ The values ​​were 7933.56, 207.358, 1.93918, 0.00802, 1.34107, 0.0018, and 2.222 × 10⁻⁶, respectively. -5 .

[0084] Construct the angle between adjacent first sub-channels The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent coefficients 56 through 63, respectively.

[0085] In this embodiment ~ The values ​​were 0.711, 0.209, 0.027, 0.0019, 339.463, 1.101, 0.1329, and 0.00898, respectively.

[0086] Constructing channel depth The relationship model between the axial balancing force and the additional shaft power: ; ; in, and They represent respectively with The variables reflect the axial balancing force and additional shaft power; ~ These represent coefficients sixty-four to seventy-nine, respectively.

[0087] In this embodiment ~ The values ​​were 632.63, 3813.19, 9754.15, 13708, 830.574, 2608.62, 2164.465, 796.66, 17.889, 81.84, 137.568, 114.352, 122.56, 271.034, 226.495, and 83.785, respectively.

[0088] Step 23 also includes the following: The final objective function F for the axial equilibrium force is expressed as: ; ; in, ~ These represent the first to the eighth equilibrium force coefficients, respectively. Indicates the amount of correction for the balancing force; ~ These represent coefficients 80 through 84, respectively.

[0089] The final expression for the objective function P of the additional shaft power is: ; ; in, ~ These represent the first power coefficient to the eighth power coefficient, respectively. Indicates the amount of additional shaft power correction; ~ These represent coefficients 85 through 90, respectively.

[0090] In this embodiment ~ The values ​​were 347.0, 5.2, 3.8, 2.1, 1.5, 47.53, 4.2, 2.8, 1.9, 1.2, and 0.7, respectively.

[0091] Optionally, obtain the constraint relationship between the coefficients in the objective function and the parameters to be optimized, as follows: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; in, ~ These represent coefficients 91 through 115, respectively.

[0092] In this embodiment ~ The values ​​were 0.28, 0.02, 0.01, 0.22, 0.03, 0.20, 0.015, 0.12, 0.10, 0.008, 0.04, 0.006, 0.004, 0.003, 0.002, 0.25, 0.24, 0.025, 0.018, 0.08, 0.06, 0.005, 0.05, 0.001, and 0.012, respectively.

[0093] In this embodiment, the balance disc rotates together with the shaft, the rotational speed is set to n=6000rpm, the pressure inlet is set to 320000Pa, the outlet is set to free outflow, and the flow field is set to laminar flow.

[0094] The specific values ​​of the coefficients in this application can be determined by fitting the values ​​of the corresponding axial balancing force and additional shaft power obtained by adjusting the parameters to be optimized based on the specific balance disc parameters.

[0095] In step 23, a non-dominated solution set on the Pareto front is obtained using a genetic algorithm, which is the potential solution set. The starting point for obtaining the potential solution set is to make the final axial balance force objective function and the final additional shaft power objective function reach their respective theoretical optimal values ​​(i.e., maximize the final axial balance force objective function and minimize the final additional shaft power objective function). However, there is usually no set of optimization parameters that can simultaneously make both objectives reach their respective theoretical optimal values. These two objectives are in conflict, so the potential solution set is actually several sets of trade-off solutions.

[0096] In step 24, we randomly select a set from the potential solution set. Alternatively, based on actual engineering requirements, we can use the requirement that "the final axial balance force objective function and / or the final additional shaft power objective function must be within a set interval" as a screening criterion to select a corresponding set of potential solutions for the parameters to be optimized from the potential solution set.

[0097] Step 3 also includes the following: Using a fault diagnosis model, the sliding bearing eccentricity fault of the centrifugal pump system containing the balancing disc after design is checked under operating conditions. If the check fails, return to step 24. From the remaining potential solutions in the potential solution set, select any one set of potential solutions for the parameter to be optimized. Modify the actual value of the parameter to be optimized in the balancing disc to the value of the corresponding potential solution for the parameter to be optimized. Then, check the sliding bearing eccentricity fault again until the check is successful.

[0098] The method for obtaining the fault diagnosis model includes the following sub-steps: Step 31: Generate voltage signals for different degrees of eccentricity of the faulty bearing. The voltage signals include the fundamental frequency, the third harmonic related to the bearing eccentricity, and Gaussian white noise with different signal-to-noise ratios. Step 32: The generated voltage signal is subjected to wavelet denoising based on the improved soft threshold function and EMD decomposition to extract IMF energy features, forming a seven-dimensional fusion feature: five-dimensional IMF energy features + pulse amplitude + harmonic distortion rate; then the seven-dimensional fusion feature is input into the neural network and a loss function containing pulse weight coefficient and harmonic weight coefficient is used. Step 33: First, fix the wavelet denoising parameters, train the neural network by combining multiple sets of pulse weight coefficients and harmonic weight coefficients, and determine the optimal pulse weight coefficients and harmonic weight coefficients; then fix the pulse weight coefficients and harmonic weight coefficients, train the neural network, and determine the optimal threshold parameters. Step 34: Assign the optimal pulse weight coefficient, harmonic weight coefficient and threshold parameter to the loss function. The resulting neural network is the bearing eccentricity fault diagnosis model.

[0099] In step 31, the voltage signal acquisition process is as follows: Step 311, Set the frequency of the fundamental signal and amplitude ; Step 312, set the frequency of the third harmonic as And determine the harmonic amplitude. With eccentricity Relationship The degree of eccentricity is divided into normal state, mild eccentricity and severe eccentricity, and the corresponding eccentricity increases in that order. Step 313, determine the added Gaussian white noise: Normal state: Adding a signal-to-noise ratio of [value missing] to a pure signal consisting of the fundamental frequency and the third harmonic. Gaussian white noise; Slight eccentricity: Adding a signal-to-noise ratio of [value missing] to a pure signal consisting of the fundamental frequency and the third harmonic. Gaussian white noise; Severe eccentricity: Adding a signal-to-noise ratio of [value missing] to a pure signal consisting of the fundamental frequency and the third harmonic. Gaussian white noise; Step 314: The fundamental wave, the third harmonic wave and the corresponding Gaussian white noise signal are superimposed to generate a voltage signal for the faulty bearing that includes three categories of labels: normal state, slight eccentricity and severe eccentricity.

[0100] In step 32, the process of obtaining the seven-dimensional fusion features is as follows: Step 321: Apply wavelet denoising based on an improved soft thresholding function to the voltage signal; Step 322: Decompose the wavelet-denoised voltage signal into multiple intrinsic mode functions (IMFs) and arrange them in descending order of frequency. Step 323: Obtain the first five IMFs and calculate the energy characteristics of these five IMFs, then fuse them to form a five-dimensional IMF energy characteristic; Step 324: Calculate the maximum absolute value of the difference between the voltage signal and the pure signal. This maximum value is the pulse amplitude. At the same time, calculate the harmonic distortion rate based on the harmonic amplitude and the fundamental amplitude. Step 325: Integrate the five-dimensional IMF energy characteristics, pulse amplitude, and harmonic distortion rate to form a seven-dimensional fused characteristic.

[0101] In step 32, the improved soft threshold function is expressed as follows: ; In the formula, Represents the original wavelet coefficients; Indicates the improved wavelet coefficients; This represents the threshold parameter.

[0102] In step 32, the formula for calculating the harmonic distortion rate is as follows: ; In the formula, Indicates harmonic distortion rate; express Second harmonic amplitude.

[0103] In step 32, the loss function It is expressed as follows: ; ; In the formula, Indicates the number of training samples; Indicates the loss coefficient; Indicates the first The pulse amplitude corresponding to each voltage signal; Indicates the first Harmonic distortion rate corresponding to each voltage signal; Indicates the pulse weighting coefficient; Indicates the harmonic weighting coefficient; ; Indicates the first The true value of the degree of eccentricity corresponding to each voltage signal; Indicates the first Predicted value of eccentricity corresponding to each voltage signal; Represents the logarithmic function with base 10; , Represents the sine function. Represents pi; Indicates the time.

[0104] In step 33, the optimal pulse weighting coefficient, harmonic weighting coefficient, and threshold parameter are obtained as follows: Step 331, maintain the threshold parameter of wavelet denoising. This is the default value; Step 332: Determine the combination of pulse weight coefficients and harmonic weight coefficients, and train the neural network using the same training set for each combination. Step 333: Test the accuracy of the neural network trained in step 332 on the same validation set; Step 334: Select the pulse weighting coefficient and harmonic weighting coefficient combination with the highest accuracy as the corresponding optimal pulse weighting coefficient and harmonic weighting coefficient. Step 335: Keep the pulse weighting coefficient and harmonic weighting coefficient at their optimal values; Step 336, for each Values, using the same training set to train the neural network; Step 337: Test the accuracy of the neural network trained in step 336 on the same validation set; Step 338: Select the one with the highest accuracy. The value is used as the corresponding optimal threshold parameter.

[0105] Step 34 also includes the following: after obtaining the optimal pulse weight coefficient, harmonic weight coefficient and threshold parameters, they are input into the neural network for a set number of tests, and the average accuracy is taken; if the average value meets the requirements, the bearing eccentricity fault diagnosis model is obtained; otherwise, the process is carried out in accordance with the contents of steps 331 to 338 until the set number of processing times is reached or the accuracy requirements are met.

[0106] To facilitate understanding, the following description, using specific experimental data, illustrates the method for obtaining the fault diagnosis model: 1. Generate fault bearing voltage signal The voltage signals under normal and eccentric fault conditions are simulated to provide training data for the model.

[0107] 1. Fundamental signal settings The fundamental signal is a sine wave, and its expression is: Among them, the fundamental frequency 50Hz t At that moment, the amplitude was 220V (the core signal component during normal operation).

[0108] 2. Third harmonic signal setting (related to eccentricity) Third harmonic frequency 150Hz, amplitude and eccentricity Proportional, the expression is: The degree of eccentricity is categorized as follows: Normal state: ,at this time Mild eccentricity: ,at this time V; Severe eccentricity: ,at this time V.

[0109] 3. Add Gaussian white noise Adding Gaussian white noise to a pure signal consisting of "fundamental frequency + harmonics" increases the signal-to-noise ratio (SNR). SNR Set according to fault severity: Normal state: Mild eccentricity: Severe eccentricity: (The more severe the fault, the stronger the noise interference, closely reflecting actual working conditions).

[0110] 4. Synthesize voltage signal The fundamental frequency, the third harmonic, and the corresponding noise are superimposed to generate a voltage signal dataset labeled "normal state / slight eccentricity / severe eccentricity".

[0111] II. Extracting Seven-Dimensional Fusion Features Through noise reduction and decomposition, the original signal is transformed into a feature vector that can be used for model training.

[0112] 1. Wavelet noise reduction processing An improved soft threshold function is used to reduce noise in the voltage signal. The function expression is as follows: .in: These are the original wavelet coefficients. For the improved wavelet coefficients, This is the threshold parameter (initially set to the default value, to be optimized later). The coefficients are smoothed using exponential decay to avoid signal distortion associated with traditional soft thresholding functions, while preserving fault characteristics such as the third harmonic.

[0113] 2. Extraction of IMF energy characteristics from EMD decomposition The denoised signal is decomposed into multiple intrinsic mode functions (IMFs) and sorted from high to low frequency. The first 5 IMFs are selected, and the energy (sum of squares) of each IMF is calculated to form a 5-dimensional IMF energy feature (reflecting the multi-scale fluctuation characteristics of the signal).

[0114] 3. Calculate pulse amplitude and harmonic distortion rate Pulse amplitude: The maximum absolute value of the difference between the noisy voltage signal and the clean signal (fundamental frequency + third harmonic). Physical meaning: Reflects the intensity of mechanical impact caused by eccentric faults.

[0115] Harmonic distortion rate (THD): quantifies the proportion of harmonic components, and the formula is: .

[0116] in, express The amplitude of the second harmonic is of primary concern, with a focus on the third harmonic. . The value represents the fundamental frequency amplitude; the more severe the eccentricity, the higher the THD value.

[0117] 4. Integration of seven-dimensional features The five-dimensional IMF energy features, pulse amplitude, and THD are combined to form a seven-dimensional fusion feature, which is used as the input to the neural network.

[0118] III. Training the Neural Network and Optimizing its Parameters By optimizing the loss function and threshold parameters, the model's accuracy in identifying eccentric faults can be improved.

[0119] 1. Neural Network Structure Input layer: 7-dimensional fused features; Hidden layer: 2 layers (containing 128 and 64 neurons respectively), using the ReLU activation function; Output layer: 3-class labels (0=normal state, 1=slight eccentricity, 2=severe eccentricity), using the Softmax function to output classification probabilities.

[0120] 2. Loss Function Design The weighted cross-entropy loss function is used to enhance the focus on impulse and THD features, and its expression is: Loss coefficient .

[0121] 3. Parameter optimization process optimization and :fixed As the default value, 9 test groups were used. Combinations (from 0.1 & 0.9 to 0.9 & 0.1, with a step size of 0.1) were used. After training each combination, the accuracy was calculated on the validation set, and the combination with the highest accuracy was selected (experimental results showed...). , At this point, the model pays more attention to the pulse characteristics, matching the impact characteristics of the eccentric fault.

[0122] optimization :fixed , ,test (Step size 0.5), the average of 5 experiments (removing extreme values) is taken, and the one with the highest accuracy is selected. At this point, the noise reduction effect is optimal, and the third harmonic characteristics are fully preserved.

[0123] IV. Determining the final diagnostic model Verify parameter stability and output a model that can be applied in practice.

[0124] Model validation will optimize parameters , , Substitute the data into the neural network and perform at least three simulations using the test set, taking the average accuracy (the experimental average accuracy was 91.53%). If the average accuracy of the model output meets the preset threshold (e.g., ≥90%), then the model is determined to be the final sliding bearing eccentricity fault diagnosis model; if it does not meet the threshold, repeat the parameter optimization process until the target is met.

[0125] V. Experimental Results The model constructed using this implementation method demonstrates significantly higher accuracy in identifying eccentricity faults in sliding bearings compared to traditional methods: the accuracy rate for identifying normal conditions is increased to over 95%, while the accuracy rates for identifying mild and severe eccentricity reach 92% and 94%, respectively; noise resistance is also enhanced. SNR It can still stably identify early fault characteristics even in a strong noise environment of 10dB.

[0126] The method for obtaining the fault diagnosis model, and the obtained fault diagnosis model, have the following effects: ① A comprehensive methodology covering "fault voltage signal generation—feature extraction—parameter optimization—model determination" was constructed, organically integrating key steps such as signal generation, wavelet denoising, EMD decomposition, neural network training, and parameter optimization. This formed a highly targeted system for establishing diagnostic models for sliding bearing eccentricity faults. This process ensures logical coherence from raw data to the diagnostic model and, through multi-stage collaborative design, ensures that the model can accurately identify the three states of bearing normal, slight eccentricity, and severe eccentricity. It solves the problems of insufficient targeting and fragmented processes in traditional diagnostic methods, providing a systematic solution for improving the accuracy of bearing eccentricity fault diagnosis.

[0127] ② By refining the voltage signal generation rules, accurate simulation of different bearing eccentricity states was achieved. The fixed fundamental frequency parameter provides a stable benchmark for the signal; the direct proportionality between the third harmonic amplitude and the eccentricity directly correlates with the fault severity; and the differentiated signal-to-noise ratio Gaussian white noise settings (10dB for normal, 15dB for mild, and 20dB for severe eccentricity) closely reflect the characteristic in actual operating conditions that "the more severe the fault, the stronger the signal interference." The signal generated by this design contains clear fault characteristics (harmonic variations) and simulates noise interference in the real environment, providing high-quality, high-fidelity sample data for subsequent model training and avoiding insufficient model generalization ability due to data distortion.

[0128] ③ The seven-dimensional fusion feature acquisition method achieves comprehensive capture of fault information. Wavelet denoising preprocessing effectively filters noise interference; the first five IMF energy features extracted by EMD decomposition reflect the energy distribution of the signal at different frequency scales, capturing multi-scale fluctuations caused by the fault; pulse amplitude features quantify the mechanical impact intensity, while harmonic distortion rate features reflect the degree of anomalous harmonic components. The fusion of these three features preserves both the time and frequency domain information of the signal and integrates the physical characteristics of the fault (impact, harmonic distortion), overcoming the shortcomings of single features in providing a comprehensive fault representation. This significantly improves the correlation between features and bearing eccentricity, laying the foundation for accurate model classification.

[0129] ④ The improved soft thresholding function solves the signal distortion problem caused by hard truncation in traditional soft thresholding functions through exponential decay. This function smooths the original wavelet coefficients, and instead of directly zeroing coefficients close to the threshold, it preserves some information through exponential decay. This effectively suppresses noise while maximizing the preservation of weak features related to bearing eccentricity (such as the third harmonic signal of early faults). Simultaneously, its continuously differentiable characteristic makes the processed signal smoother, avoiding artifacts that may occur with traditional functions, improving the fidelity of the denoised signal, and providing more reliable basic data for subsequent feature extraction.

[0130] ⑤ By calculating the correlation between the fundamental amplitude and the amplitudes of each harmonic, the change in the proportion of harmonic components caused by bearing eccentricity is intuitively reflected. That is, the more severe the eccentricity, the larger the amplitude of the third harmonic and the higher the THD value. This quantitative indicator not only has a clear physical meaning (directly related to the degree of failure), but also provides the model with comparable and calculable characteristic parameters, avoiding subjective judgment of harmonic characteristics and enhancing the objectivity and accuracy of fault diagnosis.

[0131] ⑥ Based on the traditional cross-entropy loss function, the weighting coefficients α and β are used to enhance the influence of pulse (mechanical shock) and harmonic distortion (electrical characteristics) on the loss calculation. This allows the model to focus more on features directly related to bearing eccentricity during training, rather than irrelevant noise. This design solves the problem of insufficient attention to fault features in traditional loss functions, improves the model's ability to distinguish between different degrees of eccentricity, and especially enhances the sensitivity to identify early faults such as mild eccentricity.

[0132] ⑦ By employing the process of "optimizing feature weights with fixed wavelet denoising parameters → optimizing denoising parameters with fixed feature weights," the impact of each parameter on model performance can be evaluated individually, eliminating optimization biases caused by parameter interactions. Furthermore, through comparative experiments using the same training set and validation set, combined with averaging multiple simulations, the reliability of parameter selection is further improved, ultimately determining the optimal parameters. α , β , λ It can maximize the performance of the model and solve the problem of determining the optimal combination when optimizing multiple parameters simultaneously.

[0133] ⑧ By performing simulations on the optimal parameter combination more than three times and taking the average accuracy, the result deviation caused by random factors (such as noise fluctuations and differences in neural network initialization) in a single experiment can be effectively offset. If the mean does not meet the requirements, iterative adjustments can be made by repeating the parameter optimization process to further improve the model accuracy. This design avoids "pseudo-optimal" models caused by accidental factors, ensuring that the output diagnostic model can stably perform in practical applications and improving the engineering practical value of the model.

[0134] For ease of description, the design verification method of this application is used. After completing the design and verification of the balance disk, the resulting balance disk is called the optimized balance disk.

[0135] The design verification method of this application adopts an arc connection structure at the bend of the flow channel (that is, "the first sub-flow channel connection ends are all arc-shaped, bent towards their own short sides, and connected to the second sub-flow channel connection ends" as described above). Compared with the broken-line flow channel formed by directly connecting the straight parts of the first and second sub-flow channels, the arc connection structure can effectively reduce the stress concentration at the connection ends of the two sub-flow channels, reduce the wear of the flow channel, and extend the life of the balance disc.

[0136] We hope to increase the upper limit of the maximum axial balancing force that the balance disc can provide, so that during use, the balance disc will not cause metal-to-metal contact and rotational friction between the shaft and the bearing due to insufficient axial balancing force.

[0137] At the same time, we also want the additional shaft power to be as small as possible. Because the working principle of the balance disc inevitably causes the medium to flow from the high-pressure side to the low-pressure side, impacting the rotating disc surface and consuming additional spindle power, there will inevitably be additional shaft power. The existence of additional shaft power has the following drawbacks, and the greater the additional shaft power, the more serious the drawbacks: ① It increases costs such as electricity and fuel, and also reduces the share of effective power, thus lowering the overall efficiency of the centrifugal pump system.

[0138] ② The power consumption caused by the additional shaft power will be converted into heat energy, triggering a series of vicious cycles such as oil temperature rise and seal failure, and will further increase the probability of metal contact and rotational friction between the shaft and the bearing.

[0139] ③ Under variable speed or regulating conditions, the presence of additional shaft power may cause unstable load disturbances, affecting control accuracy.

[0140] These two optimization directions are not positively correlated, and the flow channel of the balance disc has many related parameters. Optimizing different related parameters of the flow channel may have different effects on these two optimization directions. Therefore, the design verification method of this application focuses on the influence of multiple related parameters of the flow channel on the axial balancing force and the additional shaft power (i.e., "constructing a relationship model between a single parameter to be optimized and the axial balancing force and the additional shaft power"). Considering the mutual interference between these influences, the objective function is constructed by combining the relationship model with the correction amount. A genetic algorithm is used to solve for the potential solution set that satisfies the objective function of "maximizing the final axial balancing force and minimizing the final additional shaft power". The centrifugal pump system is then checked for sliding bearing eccentricity faults using a fault diagnosis model to further confirm whether the currently selected set of potential solutions can simultaneously ensure the safe operation of the sliding bearings in the centrifugal pump system. This ensures that the set of potential solutions for the parameters to be optimized that has been successfully verified by the fault diagnosis model not only makes the balance disc have a stronger balancing ability, but also ensures that the designed balance disc will not cause sliding bearing eccentricity faults, provided that the rotor diameter of the motor meets the electromagnetic performance requirements.

[0141] The balance disc designed using the verification method in this application, compared to the balance disc before optimization, not only increases the upper limit of the maximum axial balancing force that the optimized balance disc can provide, but also minimizes the additional shaft power of the optimized balance disc, significantly reducing the probability of metal-to-metal contact and rotational friction between the shaft and bearing, improving the safety of the optimized balance disc during use, reducing wear on the flow channel of the optimized balance disc, and extending the life of the optimized balance disc.

[0142] like Figure 3 The figure shows the pressure distribution on the action surface of the balance disk before and after optimization under the extreme conditions obtained from simulation. Figure 3 (a) in the figure represents the working surface of the balance disc before optimization design. Figure 3 (b) in the diagram represents the optimized working surface of the balance disc. By continuously increasing the impeller axial force, even exceeding the maximum axial balancing force of the balance disc, the maximum axial balancing force of the balance disc can be obtained. The limiting case refers to the maximum axial balancing force provided by the balance disc. Therefore, from... Figure 3 visible, Figure 3 In (b), the outermost ring is dark red and wider. Figure 3 In (a), the outermost ring is a very narrow and almost discontinuous bright red color, and the maximum axial balancing force that the optimized balance disk obtained by the design verification method of this application can provide is greatly improved.

[0143] like Figure 4 The figure shows the pressure distribution on the working surface of the balance disc before and after optimization under the same normal operating conditions, obtained from simulation. Figure 4 (a) in the figure represents the working surface of the balance disc before optimization design. Figure 4 (b) in the diagram represents the working surface of the optimized balance disc. (From...) Figure 4 It can be seen that, compared to Figure 4 Regarding (a) in the text, Figure 4 In (b), the pressure distribution is more uniform and the span of the axial balance force in each flow channel is smaller.

[0144] Due to dynamic response delays and other factors, disturbances to the balance relationship between axial balancing forces can be amplified by uneven distribution of axial balancing forces on the balance disc or excessive span of axial balancing forces within the flow channels. Therefore, the design verification method of this application results in a more uniform distribution of axial balancing forces on the optimized balance disc, with smaller spans of axial balancing forces within each flow channel. This reduces the dynamic response delay of the optimized balance disc during dynamic adaptation, improves balancing accuracy, and further reduces the risk of metal-to-metal contact and rotational friction between the shaft and bearings, thereby enhancing the safety of the optimized balance disc during use and extending its lifespan.

[0145] The design verification method of this application combines the design requirements of the balance disc with the electromagnetic parameter optimization process of the motor. This ensures that the motor rotor diameter meets the electromagnetic performance requirements while also providing optimal design space for the balance disc. As a result, while ensuring high efficiency and high power density of the motor, the balance disc has a larger upper limit of axial balancing force, which improves the lifespan of the balance disc and the safety during use, thereby significantly improving the overall performance of the centrifugal pump system.

[0146] The design verification method of this application, during the design process of the motor air gap (i.e., the process of obtaining the optimal motor air gap): ① Not only were the coupling effects of changes in the outer diameter of the balance disc and the motor air gap on the axial balancing force and additional shaft power considered, but the goal was always to improve the performance of the balance disc (i.e., to use a genetic algorithm to solve for the objective function that maximizes the coupled axial balancing force and minimizes the coupled additional shaft power) before obtaining the alternative solution set for the motor air gap. This is the first layer of screening for the motor air gap in the integrated design process.

[0147] ②Then, through spatial feasibility verification, a reasonable value for the motor air gap is obtained from the spare solution set of motor air gaps. Sufficient radial installation space is provided for the balance disc in the motor to avoid limiting the upper limit of the balance disc's subsequent optimization performance due to the initial limitation on the balance disc's outer diameter. This is the second layer of screening for the motor air gap in the integrated design process.

[0148] ③ Finally, a comprehensive objective function is constructed using various factors of the centrifugal pump system, such as cost, lifespan, space importance, motor efficiency, and rotor outer diameter variation. By solving for the maximum comprehensive objective function, the optimal motor air gap among reasonable values ​​is determined. This is the third layer of screening for the motor air gap in the integrated design process.

[0149] Once the optimal motor air gap is determined, it is used as the motor air gap for the centrifugal pump system containing the balance disc. This ensures high motor efficiency and high power density. Furthermore, since the optimal motor air gap is necessary to determine the appropriate outer diameter of the balance disc, subsequent design adjustments to parameters other than the diameter will not affect motor performance. Subsequent design work on the balance disc will only further optimize it, resulting in a higher axial balancing force limit, longer lifespan, and enhanced safety. Finally, a fault diagnosis model is used for verification to guarantee the safety of the centrifugal pump system used in the integrated design (i.e., ensuring that the integrated design will not cause sliding bearing eccentricity failure), significantly improving the overall performance and safety of the centrifugal pump system and extending its lifespan.

[0150] The design verification method in this application is applicable to the optimization of centrifugal pump systems with any type of motor and balance disc. It has high versatility and strong applicability, resulting in a centrifugal pump system with better performance, higher safety and longer lifespan after design compared to an undesigned centrifugal pump system.

[0151] The technologies, shapes, and structures not described in detail in this application are all well-known technologies. It should also be noted that the above are merely preferred embodiments of this application and are not intended to limit the scope of this application. The components or steps in the embodiments of this application can be decomposed and / or recombined, and these decompositions and / or recombinations should be considered as equivalent solutions of this application and should all fall within the protection scope of this application.

Claims

1. A design verification method for the balance disc and motor electromagnetic components in a long-life pump system, characterized in that, Includes the following steps: Step 1: After integrating the balance disc and motor solenoid in the centrifugal pump system into a single design, determine the motor air gap and the outer diameter of the balance disc. Step 2: Design the parameters to be optimized in the balance disc; Step 3: Using the fault diagnosis model, perform sliding bearing eccentricity fault verification on the centrifugal pump system where the designed balance disc is located under operating conditions. If the verification fails, return to step 2; otherwise, the verification is considered successful. Step 1 also includes the following sub-steps: Step 11: Based on the outer diameter of the balance disc and the air gap of the motor, construct a relationship model between the axial balancing force and the additional shaft power, and use a genetic algorithm to solve for the alternative solution set of the motor air gap corresponding to the objective function of maximizing the coupled axial balancing force and minimizing the objective function of the coupled additional shaft power. Step 12: Calculate the theoretical minimum outer diameter of the balance disc when the balance disc reaches the maximum value of the objective function of the corresponding coupled axial balance force under the spare solution of the air gap for each motor, as well as the maximum allowable outer diameter of the motor; then, based on the maximum allowable outer diameter of the motor, perform a spatial feasibility verification on the theoretical minimum outer diameter of the balance disc corresponding to the spare solution of the air gap for the corresponding motor; record the spare solution of the air gap for the motor that has successfully passed the spatial feasibility verification as the reasonable value of the air gap for the motor. Step 13: After solving the maximum comprehensive objective function, determine the optimal motor air gap among the reasonable values ​​of motor air gap, and use the optimal motor air gap as the motor air gap of the centrifugal pump system where the balance disc is located. At the same time, use the maximum allowable outer diameter of the motor corresponding to the optimal motor air gap as the outer diameter of the balance disc. Additional shaft power refers to the extra power required by the spindle to overcome additional resistance due to the flow channel configuration. Based on the efficiency potential of the motor air gap and the modified rotor outer diameter change index, a comprehensive objective function with the motor air gap as the variable is constructed. : ; and These represent the first weighting coefficient and the second weighting coefficient, respectively. and These represent the efficiency potential and the corrected rotor outer diameter variation index, respectively.

2. The design and verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 1, characterized in that, Step 2 also includes the following sub-steps: Step 21: Obtain the parameters to be optimized for the balancing disc; Step 22: Construct relationship models between individual parameters to be optimized, axial balancing force, and additional shaft power; Step 23: Based on the relationship model between a single parameter to be optimized, the axial balance force, and the additional shaft power, construct the final axial balance force objective function and the final additional shaft power objective function, and then use a genetic algorithm to solve for the potential solution set corresponding to maximizing the final axial balance force objective function and minimizing the final additional shaft power objective function. Step 24: Select any set of potential solutions for the parameters to be optimized from the potential solution set, and then modify the actual values ​​of the parameters to be optimized in the balance disk to the values ​​of the corresponding potential solutions for the parameters to be optimized, thus completing the design of the balance disk.

3. The design and verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 2, characterized in that, Step 2 also includes the following: Using a fault diagnosis model, the sliding bearing eccentricity fault of the centrifugal pump system containing the designed balance disc is verified under operating conditions. If the verification fails, return to step 24. From the remaining potential solutions in the potential solution set, select any one potential solution for the parameter to be optimized. Then, modify the actual value of the parameter to be optimized in the balance plate to the value of the corresponding potential solution for the parameter to be optimized. Then, re-verify the sliding bearing eccentricity fault until the verification is successful.

4. The design and verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 1, characterized in that, Step 11 also includes the following: Step 111, construct the balance disc outer diameter Axial balancing force for variables and additional shaft power A relationship model between them was constructed; at the same time, a model based on the air gap of the motor was also constructed. Axial balancing force for variables and additional shaft power Relationship model; Step 112, construct the objective function of coupled axial equilibrium force. and the coupled additional axis power objective function : ; ; in, This represents the first weighting function; Indicates the first modification term; This represents the second weighting function; Indicates the second modification term; Step 113: Use a genetic algorithm to solve for the spare solution set of the motor air gap corresponding to the objective function of maximizing the coupled axial balance force and minimizing the objective function of the coupled additional shaft power.

5. The design verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 4, characterized in that: Step 12 also includes the following: Step 121, denote the spare air gap solution of a certain motor as The theoretical minimum outer diameter of the balance disc when it reaches the maximum value of the objective function of the coupled axial balance force is then... ( ); the air gap of the motor is Maximum allowable outer diameter of the motor for: ;in, Indicates the air gap of the motor is Correcting the rotor outer diameter at that time; Indicates a safety margin; Step 122, if If the space feasibility verification is successful, then the space feasibility verification is successful; otherwise, the space feasibility verification is unsuccessful. The spare solution for the motor air gap that has successfully passed the space feasibility verification is recorded as the reasonable value of the motor air gap.

6. The design and verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 2, characterized in that, In step 21, the parameters to be optimized for the balancing disk include: the length of the short side of the first sub-channel. Length of the long side of the first sub-channel First sub-channel short side eccentricity distance 1. Eccentricity of the long side of the first sub-channel The short side bending angle of the first sub-channel connection end The bending angle of the long side of the first sub-channel connection end Angle between adjacent first sub-channels Flow channel depth ; Each flow channel is composed of two sub-flow channels connected in sequence, with the first sub-flow channel and the second sub-flow channel in the direction from the inner edge of the balance plate to the outer edge.

7. The design verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 6, characterized in that, In step 22: Construct the first sub-channel with the short side length respectively. Axial balancing force for variables and additional shaft power The relationship model, with the length of the first sub-channel long side Axial balancing force for variables and additional shaft power The relationship model, with the short side eccentricity distance of the first sub-channel Axial balancing force for variables and additional shaft power The relationship model, with the eccentric distance of the long side of the first sub-channel Axial balancing force for variables and additional shaft power The relationship model, with the short side bending angle of the first sub-channel connection end Axial balancing force for variables and additional shaft power The relationship model, with the long side bending angle of the first sub-channel connection end Axial balancing force for variables and additional shaft power The relationship model, based on the angle between adjacent first sub-channels Axial balancing force for variables and additional shaft power Relationship model based on channel depth Axial balancing force for variables and additional shaft power The relationship model.

8. The design verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 7, characterized in that, In step 23, also Includes the following: The final objective function F for the axial equilibrium force is expressed as: ; The final expression for the objective function P of the additional shaft power is: ; in, ~ These represent the first to the eighth equilibrium force coefficients, respectively. ~ These represent the first power coefficient to the eighth power coefficient, respectively. Indicates the amount of correction for the balancing force; This indicates the amount of additional shaft power correction.

9. The design verification method for the balance disc and motor electromagnetic components in a long-life pump system according to claim 3, characterized in that, The method for obtaining the fault diagnosis model includes the following sub-steps: Step 31: Generate voltage signals for different degrees of eccentricity of the faulty bearing. The voltage signals include the fundamental frequency, the third harmonic related to the bearing eccentricity, and Gaussian white noise with different signal-to-noise ratios. Step 32: The generated voltage signal is subjected to wavelet denoising based on the improved soft threshold function and EMD decomposition to extract IMF energy features. The resulting seven-dimensional fusion features, consisting of five-dimensional IMF energy features, pulse amplitude, and harmonic distortion rate, are then input into the neural network and a loss function containing pulse weight coefficients and harmonic weight coefficients is used. Step 33: First, fix the wavelet denoising parameters, train the neural network by combining multiple sets of pulse weight coefficients and harmonic weight coefficients, and determine the optimal pulse weight coefficients and harmonic weight coefficients; then fix the pulse weight coefficients and harmonic weight coefficients, train the neural network, and determine the optimal threshold parameters. Step 34: Assign the optimal pulse weight coefficient, harmonic weight coefficient and threshold parameter to the loss function. The resulting neural network is the bearing eccentricity fault diagnosis model.

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