Turbomachinery blade tip clearance and vibration calculation method based on continuous Gaussian fitting

Abstract

The invention discloses a method for calculating blade tip clearance and vibration of a turbomachine blade based on continuous Gaussian fitting, and belongs to the technical field of fault diagnosis. A continuous Gaussian fitting (CGF) method is proposed to be used for obtaining a data signal which can be used for more accurately calculating a blade tip gap and a blade tip vibration characteristic. Compared with a conventional threshold value recognition method (TVM), the CGF method has the advantages that Gaussian fitting calibration is performed on blade tip state signals collected by the capacitive sensor, interference of environmental noise is greatly reduced, and the accuracy of blade tip clearance and vibration calculation is remarkably improved. Experimental results show that the CGF method shows better calculation stability under different rotating speed working conditions, especially at a low rotating speed, the calculation stability of blade tip vibration is 4.15 times that of a TVM method, and blade resonance can be recognized more accurately. According to the method, real-time monitoring can be realized, and more accurate blade tip clearance and vibration data can be provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault diagnosis, and relates to the identification and diagnosis of the blade tip clearance and blade tip vibration of turbomachinery blades. Specifically, it is a method for calculating the blade tip clearance and vibration of turbomachinery blades based on continuous Gaussian fitting. Background Technique

[0002] With the wide application of turbomachinery equipment in fields such as aerospace and energy, the monitoring of blade tip clearance (BTC) and blade tip vibration (BTV) has become a key means to ensure the stable operation of the equipment. Traditional monitoring means mainly rely on fiber optic sensors to capture blade tip vibration signals to evaluate the operating state of the blades. However, with the continuous improvement of the working performance requirements for large turbomachinery (such as compressors and steam turbines), simply monitoring blade tip vibration can no longer meet the needs of complex working conditions. Especially in high-performance equipment, the accurate monitoring of blade tip clearance has become increasingly important, while traditional fiber optic sensing technology lacks effective support for this. Therefore, a monitoring method that can accurately measure both blade tip vibration and blade tip clearance has become a new demand direction. This can not only provide more comprehensive equipment status information but also be crucial for the stable operation of turbomachinery under complex working conditions.

[0003] The basic function of a capacitive sensor is distance measurement, that is, the change in the distance between the sensor and the target measured surface will result in different voltage amplitudes. Usually, the Threshold Value Method (TVM) is used to determine the blade tip arrival time point. This method first filters the data using the Savitzky-Golay Filter method to obtain smoother corrected data, and then sets a voltage value as the threshold to screen out the highest peak point exceeding this threshold within a single signal cycle and uses it as the feature recognition point, thereby extracting information such as the arrival time and amplitude of the blade tip to calculate the blade tip clearance and vibration. The characteristic signals of the blade tip clearance and vibration can be obtained through existing blade tip timing calculation methods. This method uses the sensor to record the exact time when the blade passes (the actual arrival time of the blade tip), and by analyzing the deviation between the actual arrival time and the blade arrival time in the theoretically vibration-free state, information such as the amplitude, frequency, and phase of the blade vibration is extracted.

[0004] However, since the signals collected by capacitive sensors contain more information than fiber optic sensors, they are more susceptible to environmental noise. Even after filtering, it may still lead to relatively large characteristic recognition errors. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention proposes a Gaussian distribution non-linear fitting method based on a capacitance sensor, aiming to improve the calculation accuracy of tip state monitoring. This method calibrates the characteristic points of the capacitance test signal through continuous Gaussian fitting, extracts the characteristic parameter information of the fitted signal, and performs subsequent calculations, effectively avoiding environmental noise interference and greatly improving the calculation accuracy of the tip signal. Compared with the threshold recognition method, the recognition method based on continuous Gaussian fitting can not only work stably under complex working conditions, but also improve the overall accuracy of the test data, thus providing a more reliable technical means for the state monitoring of turbine mechanical blades.

[0006] The technical solution of the present invention is as follows:

[0007] A method for calculating the tip clearance and vibration of a turbine mechanical blade based on continuous Gaussian fitting, comprising the following steps:

[0008] Step 1: Acquisition of tip state signals based on capacitance sensors;

[0009] The signal waveform when the blade passes is collected through a single capacitance sensor installed on the rotating machine housing; the sensor is capacitive, fixed in the radial direction of the rotating machine housing, and maintains a specific gap with the blade tip to ensure that the sensor can capture the rotating blade signal in real time; the gap between the sensor and the blade tip is determined by the sensor sensitivity and the blade size, usually 0.5 - 3 mm, to prevent signal distortion or mechanical interference. The tip state monitoring depends on the signal generated when the blade passes through the sensor. Each time the blade passes, the sensor outputs a waveform signal similar to a Gaussian distribution related to the position of the blade tip. To ensure that the collected signal is in the form of a Gaussian-like distribution, the measured blade is required to be a straight blade with a blade width greater than the diameter of the capacitance sensor or a large turbine mechanical blade (regardless of the blade shape).

[0010] Step 2: Tip data feature extraction method based on continuous Gaussian fitting

[0011] The present invention proposes a continuous non-linear fitting method based on the Gaussian function (Continuous Gauss Fitting, abbreviated as CGF). This method calibrates the actual tip test data by generating a continuous Gaussian fitting curve, optimizes signal feature extraction, and improves the accuracy of peak feature recognition. Utilizing the characteristics of the Gaussian function, the CGF method can better avoid environmental interference, improve the reliability of data extraction, and provide a more accurate technical means for signal processing in complex environments.

[0012] (1) Definition of the fitting function

[0013] For a blade rotating n circles, the definition of the angular domain Gaussian function is as follows:

[0014]

[0015] Among them, is the angular domain value when the blade i rotates the nth circle, and the amplitude initializes an amplitude for each blade i rotating the nth circle, which makes each blade correspond to different initial peak voltages, thus more truly reflecting the characteristics under the calibration conditions. Set a fixed point on the circumference of the blade rotation as the reference point, is the angular position of the blade i in the nth circle based on the reference point. Considering the actual signal situation, the signal peak is formed at the moment when the blade tip intersects with the sensor. Therefore, the sensor is set at the angle based on the reference point The standard deviation parameter in the Gaussian function determines the width of the single-cycle signal. When: it is the moment for identifying the peak state of the blade tip.

[0016] Convert formula (1) into a complete form applicable to the generalized time-domain signal, and convert the angle difference into the relative time difference t relative , that is:

[0017]

[0018] Among them, is the actual time point of the rotating blade, and the Gaussian mean defines that the signal peak will be formed at a specific position of the blade i. Ω shaft is the rotational speed of the blade i under the rotational speed condition to be calculated, is the angular velocity at this rotational speed.

[0019] Since the rotational speed of the blade is a uniquely determined value at any independent moment, formula (2) can be substituted into formula (1) and then the whole is converted into a voltage amplitude function based on the time domain There is:

[0020]

[0021] By looping through each blade, calculate the Gaussian signal output generated by it at the sensor position. The Gaussian function of each blade is defined as:

[0022]

[0023] Among them, the offset Δx offset is used to correct the reference line of the signal to ensure the correctness of the final output signal.

[0024] (2) Minimize the difference fitting

[0025] To realize the fitting of the standard Gaussian signal to the real signal, the goal is to minimize the measured vibration signal of the blade i and the tip signal of the Gaussian fitting The difference between them is used to find appropriate fitting approximation parameters. Its core significance lies in finding the optimal fitting parameters for the tip signal by minimizing the difference between the measured signal and the theoretical signal. That is, by adjusting the model parameters to approximate the actual measured signal, extracting the characteristic parameters of the fitting signal, and achieving more accurate blade vibration monitoring and analysis in engineering applications.

[0026] Establish the objective formula:

[0027]

[0028] where is the discrete value of the measured signal, and ‖·‖2 represents the L2 norm, i.e., the Euclidean distance, which is used to measure the difference between two signals.

[0029] To accelerate the calculation efficiency, appropriate initial parameter Δx needs to be set according to the actual working conditions offset , where the initial value setting of can refer to the peak time point obtained by the threshold recognition method i.e.:

[0030]

[0031] Minimize the calculation of the error between the measured signal and the Gaussian fitting signal The L2 norm of the error is defined as:

[0032]

[0033] where N is the number of time points or the number of samples of the discrete signal.

[0034] Substitute the Gaussian function formula (5) into formula (8) to get:

[0035]

[0036] Formula (9) represents the cumulative difference of all sample points and takes its square root. The goal is to adjust each parameter: the total offset Δx offset , amplitude signal width and mean value (associated with the initial peak point) to minimize the result.

[0037] Finally, based on the time series, accumulate the fitting curves of each blade to form a continuous fitting data curve, that is, obtain the continuous Gaussian fitting function

[0038]

[0039] The continuous Gaussian fitting function can be used as a substitute for the original data for the overall analysis of continuous data. Based on the parameters in the fitting curve and Combined with the Blade Tip Timing (BTT) theory, the tip clearance and vibration amplitude can be calculated respectively. The principle of the BTT method is that the peak moment of the signal waveform corresponds to the moment when the blade tip passes through the center of the sensor. The two core calculation parameters of this method are the theoretical time for the blade tip to reach the sensor under the non-vibrating state at the current rotational speed and the actual time for the blade tip to reach the sensor under the vibrating state at the current rotational speed The time difference between the two is converted into the deflection angle difference at the current rotational speed, and the deflection arc length obtained by multiplying by the length of the current blade is the tip vibration value. For the continuous Gaussian fitting function at when the value of is the actual time for the blade tip to reach the sensor, which is the characteristic value for calculating the tip vibration value. At the same time, at this the value of

[0040] in the period to which it belongs represents the tip clearance voltage amplitude at the moment when the blade tip actually arrives, which is the characteristic value for calculating the tip clearance value. The corresponding clearance value can be calculated through the voltage amplitude - clearance value calibration formula of the capacitive sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flowchart of the method for monitoring the tip clearance and tip vibration of a rotating blade based on a capacitive sensor provided by the present invention.

[0042] Figure 2It is the BTC and BTV calculation processes of the method used in the present invention and the TVM method.

[0043] Figure 3 It is the residual calculation result after the step of minimizing the difference fitting using the Gaussian fitting signal and the correction signal proposed by the present invention.

[0044] Figure 4 It is the adjacent blade identification time difference traversal verification result of the peak position results after the filtered correction signal and the continuous Gaussian fitting signal provided by the present invention are respectively identified and calculated by the BTT method.

[0045] Figure 5 It is the calculation results of the tip clearances of 9 blades based on the identification method TVM of the correction signal and the continuous Gaussian fitting identification method CGF provided by the present invention.

[0046] Figure 6 It is the calculation results of the tip vibrations of 4 blades based on the identification method TVM of the correction signal and the continuous Gaussian fitting identification method CGF provided by the present invention.

[0047] Figure 7 It is the calculation result of the single blade tip clearance sweep frequency based on the identification method TVM of the correction signal and the continuous Gaussian fitting identification method CGF provided by the present invention.

[0048] Figure 8 It is the calculation result of the single blade tip vibration sweep frequency based on the identification method TVM of the correction signal and the continuous Gaussian fitting identification method CGF provided by the present invention.

[0049] Figure 9 It is the calculation result of the standard deviation of the tip vibration and tip clearance data at each fixed rotational speed using two different identification and calculation methods provided by the present invention. Detailed implementation manners

[0050] The following details the specific implementation manners of the present invention in combination with the technical solutions and the drawings.

[0051] A method for calculating the tip clearance and vibration of turbine blades based on continuous Gaussian fitting in the present invention, the specific process is as Figure 1 shown.

[0052] The data of this embodiment comes from a rotating bladed disk test bench, which mainly consists of a capacitive sensor tip data generation system and a data acquisition system. The capacitive sensor tip data generation system mainly consists of a motor, a frequency converter, a steel shaft, a bladed disk, blades, etc. The blade material is 45# steel, and the diameter of the entire bladed disk with blades is 140 mm. The main equipment of the data acquisition system includes a capacitive sensor, a capacitive signal demodulation and modulation chassis, an NI-9223 analog voltage input acquisition card, and a host computer for installing data acquisition software.

[0053] The specific steps for monitoring the tip state of a rotating blade are as follows:

[0054] Step 1: Acquisition of tip signals based on capacitance sensors;

[0055] The sensor is fixed in the radial direction of the rotating machinery housing. To ensure that the tip distance from the capacitance sensor is within the test range, the installation distance needs to be between 0.5 and 3 mm. After passing through the supporting capacitance sensor signal demodulation and gain module, the modulated output signal is connected to the NI-9223 acquisition card on the cRIO-9031, and then transmitted to the host computer through the network interface on the cRIO-9031.

[0056] Step 2: Calculate the tip clearance and vibration by using different methods for the obtained original data respectively;

[0057] Select a set of test data with multiple periods and perform calculations using the following different methods respectively, such as Figure 5 .

[0058] (1) The traditional TVM method is to perform Savitzky-Golay filtering on the original data to eliminate noise and irregular fluctuations, so as to obtain smooth corrected data. The corrected data is used for peak identification to extract the current time and amplitude when the tip passes by the sensor. The extracted current time can be used to calculate the tip vibration through the BTT theory, and the extracted amplitude can be used to calculate the tip clearance according to the voltage amplitude-clearance value calibration formula of the capacitance sensor when leaving the factory.

[0059] (2) The flow of calculating the tip vibration and tip clearance is as Figure 2 shown.

[0060] The original data is used for multi-period data fitting by using the continuous Gaussian fitting method (CGF) of the present invention to directly obtain the amplitudes and times of multiple tips passing by the sensor after fitting. According to the capacitance sensor calibration formula, the tip clearance value is calculated, and the tip vibration value is calculated by using the tip timing BTT theory. Figure 3 The residual calculation result after the minimization difference fitting step using the Gaussian fitting signal and the corrected signal for the Gaussian fitting data and the corrected data shows the fitting effect at the peak point.

[0061] Step 3: Compare the vibration calculation results of CGF with those of the TVM method;

[0062] With Figure 3An example of fitting the actual test signals under a certain conventional test condition is shown. By calculating the residuals between the actual signals and the Gaussian fitting signals when the sensor passes over a certain blade, it can be observed that in the main feature extraction part of the signals, the fitting signals are basically consistent with the original signals. The residual results show that although there are certain deviations between the data at both edges and the central feature extraction points, since they are far from the central position of the feature extraction, they have almost no impact on the final calculation results of the tip state features. This indicates that the Gaussian fitting signals can effectively represent the features of the original signals, demonstrating that it has better anti-noise and other environmental interference capabilities. Therefore, it can be used for standardized calculations to improve the accuracy and stability of signal processing.

[0063] Compare the recognition effects of using the TVM and CGF methods. The calculation results of traversing the differences after peak moment recognition, and the calculation results of the tip clearance and tip vibration of the TVM method and the CGF method under constant speed and swept frequency conditions are shown in Figures 4 to 8 . Figure 4 In it, the number of interval data points identified between adjacent blades is the traversing difference calculation, which can also be equivalently understood as the proportion of the angle values of adjacent blades inversely calculated through feature recognition on the total circumference of the blade. In addition Figures 5 to 6 also shows the BTC / BTV calculation results of multi-channel data using the two methods under a certain constant speed condition. Figures 7 to 8 It shows the tip clearance and tip vibration results of blade No. 9 calculated using the two methods under the swept frequency condition. These 4 comparison diagrams all show that the CGF method has better recognition stability than the TVM method, and Figure 8 it can be seen from it that the CGF method can more accurately identify blade resonance. The Y-axis on the right side of the figure is the rotational speed coordinate axis. Figure 9 The standard deviations of the recognition results of BTC / BTV calculated using two different methods at different constant rotational speeds (1000 RPM, 2000 RPM, 3000 RPM, 4000 RPM) are shown. From the numerical results of the standard deviations, it can be seen that the CGF method has better recognition effects under any conditions. The gray bar chart in the figure is the calculation result of the standard deviation of BTV, corresponding to the left Y-axis coordinate, and the black bar chart is the calculation result of the standard deviation of BTC, corresponding to the right Y-axis coordinate.

[0064] Through comparison, it is found that the CGF method of the present invention effectively improves the fluctuation stability of the calculation results, improves the accuracy of the calculation results, and can realize more accurate monitoring of the tip clearance and tip vibration.

Claims

1. A method for calculating the tip clearance and vibration of a turbomachinery blade based on continuous Gaussian fitting, characterized in that Including the following steps: Step 1: Acquisition of tip state signals based on capacitance sensors; Collect the signal waveforms when the blades pass through by using a single capacitance sensor installed on the rotating machinery housing; Step 2: Feature extraction method for tip data based on continuous Gaussian fitting (1) Definition of fitting function For the blades rotating n circles, the definition of the angular domain Gaussian function is as follows: Among them, is the angular domain value when the blade i rotates the nth circle, and the amplitude initializes an amplitude for each blade i rotating the nth circle; a certain fixed point on the circumference of the blade rotation is set as the reference point, is the angular position of the blade i in the nth circle based on the reference point; considering the actual signal situation, a signal peak is formed at the moment when the blade tip intersects with the sensor, so the sensor is set to be the angle of the standard deviation parameter in the Gaussian function determines the width of the single-cycle signal. When: it is the moment for identifying the peak state of the blade tip; Convert the formula (1) into a time-domain signal, and convert the angular difference into a relative time difference t relative , that is: Among them, is the actual time point of the rotating blade, and the Gaussian mean defines the signal peak formed by blade i at a specific position, and Ω shaft is the rotational speed of blade i under the rotational speed condition to be calculated, and is the angular velocity at this rotational speed; After substituting Equation (2) into Equation (1), it is overall converted into a voltage amplitude function based on the time domain We get: By looping through each blade, calculate the Gaussian signal output generated at the sensor position; the Gaussian function for each blade is defined as: Among them, the offset Δx offset is used to correct the reference line of the signal to ensure the correctness of the final output signal; (2) Minimization of difference fitting To fit the real signal with a standard Gaussian signal, the goal is to minimize the vibration signal of the measured blade i and the tip signal of the Gaussian fit to find the fitting approximation parameters; Establish the objective formula: Among them, is the discrete value of the measured signal, and ‖·‖2 represents the L2 norm, that is, the Euclidean distance, which is used to measure the difference between two signals; Set the initial parameters according to the actual working conditions Among them The initial value setting can refer to the peak time point obtained by the threshold recognition method That is: Minimize the computational measurement signal and the Gaussian-fitted signal The error between them, and the L2 norm of the error is defined as: Where N is the number of time points or the number of samples of the discrete signal; Substitute the Gaussian function formula (5) into formula (8) to obtain: The objective of formula (9) is to minimize the result by adjusting various parameters: total offset Δx offset , amplitude , signal width , and mean value ; Finally, based on the time series, the fitting curves of each blade are accumulated to form a continuous fitting data curve, that is, a continuous Gaussian fitting function is obtained. Based on the parameters in the fitting curve and Combined with the blade tip timing BTT theory, the blade tip clearance and the vibration amplitude are calculated respectively.

2. The calculation method of the tip clearance and vibration of a turbomachinery blade based on a capacitance sensor according to claim 1, characterized in that In Step 2, the BTT method is as follows: The peak moment of the signal waveform corresponds to the instant when the blade tip passes through the center of the sensor. The calculation parameter is the time when the blade tip theoretically reaches the sensor in the non-vibrating state of the current rotational speed. And the time when the blade tip actually reaches the sensor in the vibrating state of the current rotational speed. The time difference between the two is converted into the deflection angle difference at the current rotational speed. The deflection arc length obtained by multiplying the time difference by the length of the current blade is the blade tip vibration value. For the continuous Gaussian fitting function In When The value of Belonging to the current cycle The value of represents the blade tip clearance voltage amplitude at the actual arrival moment of the blade tip and is the characteristic value for calculating the blade tip clearance value. The corresponding clearance value can be calculated through the voltage amplitude-clearance value calibration formula of the capacitive sensor.

3. A calculation method for the tip clearance and vibration of a turbomachinery blade based on a capacitance sensor according to claim 1, characterized in that, In Step 1, the blades to be measured are required to be straight blades or turbomachinery blades with a blade width greater than the diameter of the capacitance sensor.

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