CN117034536A - Rotor blade damping ratio calculation method - Google Patents

Rotor blade damping ratio calculation method Download PDF

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Publication number
CN117034536A
CN117034536A CN202310724433.0A CN202310724433A CN117034536A CN 117034536 A CN117034536 A CN 117034536A CN 202310724433 A CN202310724433 A CN 202310724433A CN 117034536 A CN117034536 A CN 117034536A
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rotor blade
blade
frequency
time
rotor
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杨志勃
李浩琪
胡华辉
陈雪峰
田绍华
张兴武
曹佳辉
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Xian Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H13/00—Measuring resonant frequency
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/12—Timing analysis or timing optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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Abstract

The present disclosure discloses a rotor blade damping ratio calculation method, comprising: the method comprises the steps of collecting time pulse signals of blade tips by using two blade tip timing sensors, collecting rotating speed reference pulse signals of blades by using one OPR sensor, and obtaining the rotating period of the rotor blades according to the rotating speed signalsT OPR The method comprises the steps of carrying out a first treatment on the surface of the Based on the actual arrival time of the bladeAnd a rotation period T OPR Calculating displacement data for a rotor blade tipTip-based displacement dataExtracting displacement trend curves of two sensors, calculating standard deviation of first derivatives of the two displacement trend curves, and searching for the time t of the resonance center of the blade m The method comprises the steps of carrying out a first treatment on the surface of the Incorporating known first order modal frequencies f of rotor blades n Calculating the resonant frequency F of the blade; performing time-frequency analysis on the time pulse signals of the rotor blade to obtain a frequency response curve of the rotor blade; the frequency response curve is fitted by nonlinear least squares based on the resonance frequency F to obtain the damping ratio ζ of the rotor blade.

Description

Rotor blade damping ratio calculation method
Technical Field
The disclosure belongs to the field of rotor blade online monitoring and dynamic parameter identification, and particularly relates to a rotor blade damping ratio calculation method.
Background
Turbomachinery is widely used in industry, particularly in the fields of aviation, navigation and electrical energy. The blade is an important part for ensuring performance and operation safety of the turbine machinery, but because the blade is impacted by high temperature and high pressure, alternating load and foreign objects for a long time, the service life of the blade is influenced, and the operation safety of the whole machine is threatened, so that the vibration state detection of the blade is very important.
The traditional contact type measuring method, such as strain gauge measurement, has high system complexity and low efficiency, is difficult to apply to the actual industrial environment, and Blade Tip Timing (BTT) is a non-contact type method, which records the arrival time pulse of the Blade by using a probe (capacitive type, optical fiber type, electric vortex type and the like) installed in a casing, converts the theoretical arrival angle and the actual arrival angle difference under the condition of not considering the vibration of the Blade into Blade Tip displacement, thereby obtaining the vibration displacement of the Blade Tip, and analyzes the health condition of the Blade according to the vibration displacement. The traditional rotor blade damping ratio estimation can only be measured through a strain gauge, but the undersampling characteristic of the blade tip timing signal causes that the method is difficult to collect the maximum displacement of blade resonance, so that a larger error occurs in the amplitude response curve fitting result.
Disclosure of Invention
In view of the shortcomings in the prior art, an object of the present disclosure is to provide a rotor blade damping ratio calculation method, which can obtain a natural frequency and a damping ratio from strictly undersampled tip timing data, so as to realize health monitoring of a blade.
In order to achieve the above object, the present disclosure provides the following technical solutions:
a method of rotor blade damping ratio calculation, comprising the steps of:
step 1: collecting time pulse signals of the rotor blade by using two blade end timing sensors, and obtaining the actual arrival time of the rotor blade according to the time pulse signalsCollecting a rotation speed reference pulse signal of the rotor blade by using an OPR sensor, and obtaining a rotation period T of the rotor blade according to the rotation speed reference pulse signal OPR ；
Step 2: based on actual arrival time of rotor bladesAnd a rotation period T OPR Calculating the actual angle of arrival of the rotor blade>
Step 3: based on the radius R of the rotor blade and the actual angle of arrival of the rotor bladeAngle of arrival from theoryAngle difference of +.>Calculating tip displacement data +.>
Step 4: tip-based displacement dataExtracting displacement trend curves of two leaf-end timing sensors, calculating standard deviation of first derivatives of the two displacement trend curves, and taking time corresponding to the maximum standard deviation as resonance center time t of the rotor blade m ；
Step 5: searching for the resonance center time t of a rotor blade based on the time-frequency curve of the rotational speed reference pulse signal m Corresponding resonant frequency f r In combination with known first-order modal frequencies f of the rotor blade n Calculating a resonance frequency F of the rotor blade;
step 6: performing time-frequency analysis on the time pulse signals of the rotor blades to obtain a time-frequency diagram;
step 7: the formant ridge lines in the time-frequency diagram are extracted to obtain a frequency response curve of the rotor blade, and the frequency response curve is fitted through nonlinear least squares based on the resonance frequency F of the rotor blade in the step 5 to obtain the damping ratio zeta of the rotor blade.
Preferably, in step 1, the installation angle of the two dual sensors satisfies the following formula:
wherein k is such thatSatisfy->Positive integer set of EO p Is the resonance order of interest in the test.
Preferably, in step 2, the actual angle of arrival of the rotor bladeCalculated by the following formula:
wherein,representing the actual arrival time of the rotor blade, T OPR Representing the period of rotation of the rotor blade.
Preferably, in step 3, the theoretical angle of arrival of the rotor bladeCalculated by the following formula:
wherein the subscript i denotes the number of the rotor blade, the subscript j denotes the number of the sensor, n denotes the number of rotations of the rotor blade, and M denotes that the rotor blade has rotated M rotations.
Preferably, in step 3, the displacement data of the rotor bladeCalculated by the following formula:
wherein R represents the radius of the rotor blade, pi represents the circumference ratio,representing the actual angle of arrival of a rotor bladeAngle of arrival from theory->Angle difference of>
Preferably, in step 4, the standard deviation of the first derivative of the displacement trend curve is calculated by the following formula:
wherein,representing the first derivative of the signal of the ith blade at the nth turn measured by the jth sensor,/->Standard deviation of the derivative of the two sensor signals representing the ith blade at the nth turn,/->Representing the mean of the first derivatives of the two sensor trend signals.
Preferably, in step 5, the resonance frequency F of the rotor blade i Calculated by the following formula:
F i ＝f ri EO
wherein f n Representing the first order modal frequencies of the rotor blade, f ri Indicating that the rotor blade is at t i The frequency of revolution corresponding to the moment EO represents the order of the resonant frequency of the rotor blade, [. Cndot.]Rounding values of the representation.
Preferably, in step 7, the damping ratio ζ of the rotor blade is calculated by:
where m denotes the mass of the rotor blade, c denotes the damping of the rotor blade, k denotes the stiffness of the rotor blade, ω n Representing the natural frequency of the rotor blade.
The present disclosure also provides an electronic device, characterized by comprising:
a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein,
the processor, when executing the program, implements a method as described in any of the preceding.
The present disclosure also provides a computer storage medium storing computer executable instructions for performing a method as described in any one of the preceding claims.
Compared with the prior art, the beneficial effects that this disclosure brought are: the method does not need to be adhered with a strain gauge and a complex electricity leading slip ring system, and can achieve extraction of blade resonance frequency and damping ratio only by using two blade end timing sensors.
Drawings
FIG. 1 is a flow chart of a method of rotor blade damping ratio calculation provided by one embodiment of the present disclosure;
FIG. 2 is a variable operating mode rotary blade test stand for a tip timing sensor provided in one embodiment of the present disclosure;
FIG. 3 is a tip displacement simulation signal acquired by a dual tip timing sensor provided by one embodiment of the present disclosure;
FIG. 4 (a) is a graph showing a displacement trend of a dual tip timing sensor according to one embodiment of the present disclosure;
FIG. 4 (b) is a standard deviation plot of the first derivative of the displacement trend plot provided by one embodiment of the present disclosure;
FIG. 4 (c) is a schematic diagram of a time-to-frequency plot of a rotational speed reference pulse signal provided by one embodiment of the present disclosure;
FIG. 5 is a graph of blade tip frequency response provided by one embodiment of the present disclosure;
FIG. 6 (a) is a time-frequency diagram of a dual leaf end timing sensor signal provided by one embodiment of the present disclosure;
FIG. 6 (b) is a frequency response plot of a rotor blade provided by an embodiment of the present disclosure;
FIG. 7 is a graph of frequency response curve fitting results provided by one embodiment of the present disclosure;
fig. 8 is a frequency response curve acquisition schematic provided by one embodiment of the present disclosure.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 8. While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. Those of skill in the art will understand that a person may refer to the same component by different names. The specification and claims do not identify differences in terms of components, but rather differences in terms of the functionality of the components. As used throughout the specification and claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description hereinafter sets forth the preferred embodiments for carrying out the present disclosure, but is not intended to limit the scope of the disclosure in general, as the description proceeds. The scope of the present disclosure is defined by the appended claims.
For the purposes of promoting an understanding of the embodiments of the disclosure, reference will now be made to the embodiments illustrated in the drawings and specific examples, without the intention of being limiting the embodiments of the disclosure.
In one embodiment, as shown in FIG. 1, the present disclosure provides a rotor blade damping ratio calculation method comprising the steps of:
step 1: as shown in FIG. 2, two blade tip timing sensors with specific mounting angles and one OPR sensor are used to respectively collect the time pulse signal and the rotation speed reference pulse signal of the rotating blade, and then the actual arrival time of the rotor blade is obtained according to the time pulse signalObtaining the rotation period T of the rotor blade according to the rotation speed reference pulse signal OPR ；
Assuming that the blade vibrates at a single frequency, the blade resonance order of interest is 4, and 2 optical fiber type blade tip timing sensors are fixed on the casing, then the following formula is used:
wherein k is such thatSatisfy->Is herein 1, EO p Is the resonance order of interest in the test.
The included angle of the two leaf end timing sensors is 20 degrees and 65 degrees. Setting the initial rotation frequency as 70Hz, the rotation speed change rate as 1Hz/s and the time length as 30s. Setting the natural frequency F of the blade n =354 Hz, damping ratio ζ 0 =0.01, the resulting simulation signal is shown in fig. 3, specifically expressed as:
where λ represents the order of resonance, pi represents the circumferential rate, noise represents gaussian white noise, N represents the number of components, subscript i represents the vibration component, where the simulation signal vibrates only one component of the 4 th order, thus n=1, λ 1 =4, θ represents the phase of the vibration component, here only one vibration component, and thus is set to 0 at the time of simulation.
In addition, in order to excite 4-order resonance (i.e., eo=4), the resonance frequency is f n Eo=88.5 Hz, so the frequency range is set to 70-100Hz to ensure that the frequency range contains resonant frequency transitions.
Step 2: based on actual arrival time of rotor bladesAnd a rotation period T OPR Calculating the actual angle of arrival of the rotor blade>
In this step, the actual angle of arrival of the rotor bladeCalculated by the following formula:
wherein,representing the actual arrival time of the rotor blade, T OPR Representing the period of rotation of the rotor blade.
Step 3: based on the radius R of the rotor blade and the actual angle of arrival of the rotor bladeAngle of arrival from theoryAngle difference of +.>Calculating tip displacement data +.>
In the step, the blade end timing sensor acquires the arrival time of the rotor blade at constant speed as(n is the number of rotation turns, i is the number of blades, j is the number of sensors), and calculating the theoretical arrival angle of the rotor blade by taking the average of the data of the previous M turns +.>The method comprises the following steps:
wherein the subscript i denotes the number of the rotor blade, the subscript j denotes the number of the sensor, n denotes the number of rotations of the rotor blade, and M denotes that the rotor blade has rotated M rotations.
The actual angle of arrival of the rotor bladeAnd theoretical angle of arrival->Angle difference of +.>Further, the displacement data of the rotor blade +.>The method comprises the following steps:
wherein R represents the radius of the rotor blade, pi represents the circumference ratio,representing the actual angle of arrival of the rotor blade>Angle of arrival from theory->Is provided.
Step 4: tip-based displacement dataAnd extracting displacement trend curves of the two leaf-end timing sensors according to SG smoothing filtering (as shown in fig. 4 (a)), calculating standard deviation of first derivatives of the two displacement trend curves (as shown in fig. 4 (b)), and taking time corresponding to the maximum standard deviation as resonance center time t of the rotor blade m ；
In this step, let the width of the filter window be n=2m+1, each measurement point be x= (-m, -m+1, …,0,1, …, m-1, m), fit the data points within the window using a k-1 th order polynomial:
wherein x is data to be fitted, y is output data after fitting, and a is a parameter to be solved.
There are then n such equations that constitute a system of k-element linear equations. To solve the equation set, should n.gtoreq.k, n > k is generally chosen, and parameter A is determined by least squares fit:
the above is written in matrix form:
Y＝XA+B
least squares solution for AThe method comprises the following steps:
model predicted or filtered values of YI.e. the trend term for signal x:
E＝X(X T X) -1 X T
trend signalIndicating ++trend signal>First derivative of time t is determined>And calculates the standard deviation of the first derivatives of the two sensor trend signals:
wherein,representing the first derivative of the signal of the ith blade at the nth turn measured by the jth sensor,/->Standard deviation of the derivative of the two sensor signals representing the ith blade at the nth turn,/->Representing the mean of the first derivatives of the two sensor trend signals.
For the ith leaf, find its vectorMaximum value of +.>The number of turns corresponding to the maximum value is n m ，n m Corresponding time t m Then the resonance center time of the rotor blade No. i.
Step 5: finding the blade resonance center time t of the rotor based on the time-to-frequency curve of the rotational speed reference pulse signal as shown in fig. 4 (c) m Corresponding resonant frequency f r In combination with known first-order modal frequencies f of the rotor blade n Calculating a resonance frequency F of the rotor blade;
in this step, it can be recognized from FIG. 4 (b) that the resonance time of the rotor blade is 18.52 seconds, the initial rotation frequency is 70Hz, the rotation speed change rate is 1Hz/s, and the resonance rotation frequency corresponding to the moment of 18.52 seconds is 88.52Hz.
Further, in the present disclosure, the blade is made of aluminum alloy 6061, and the material parameters and the dimensional parameters of the blade are shown in table 1 and table 2 respectively:
TABLE 1 blade Material parameters
Number plate Young's modulus Density of Poisson's ratio
Al6061 69GPa 2750kgm -3 0.33
TABLE 2 blade size parameters
Blade tip radius Blade length Blade thickness Blade width
68mm 48mm 1mm 20mm
The first-order natural frequency of the blade is 345Hz (shown in figure 5) through finite element simulation.
Therefore, the resonance order of the blade can be calculated as follows:
the resonant frequency of the rotor blade is:
F＝f ri EO＝4×88.52＝354.08Hz。
wherein f n Representing the first order modal frequencies of the rotor blade, f ri Indicating that the rotor blade is at t i The frequency of revolution corresponding to the moment EO represents the order of the rotor blade resonance frequency.
Step 6: performing time-FrEquency analysis on the time pulse signal of the rotor blade by using any one of a least square estimation of a variable window length, a SAFE graph (Sampling Aliasing FrEquency, SAFE) method, a circumferential Fourier fitting (Circle Fourier Fitting, CFF) and other spectrum analysis methods to obtain a time-FrEquency graph as shown in FIG. 6 (a);
step 7: the formant ridge line in the time-frequency diagram is extracted to obtain a frequency response curve of the rotor blade as shown in fig. 6 (b) (the time-frequency diagram shown in fig. 6 (a) is projected to the amplitude-frequency plane according to the method shown in fig. 8 to obtain 6 (b)), and the frequency response curve is fitted by nonlinear least square based on the resonance frequency F of the rotor blade in step 5 to obtain the damping ratio ζ of the rotor blade.
In this step, the single degree of freedom vibration equation for the rotor blade is as follows:
wherein m, c, k, x represent the mass, damping, stiffness and tip displacement of the blade, respectively,first order derivative representing tip displacement, +.>Representing the second order differential of tip displacement. Natural frequency ω of the blade n And damping ratio ζ is defined as:
where m denotes the mass of the rotor blade, c denotes the damping of the rotor blade, k denotes the stiffness of the rotor blade, ω n Representing the natural frequency of the rotor blade.
The tip displacement response Y (ω) is obtained by averaging the time-frequency results of the measurement signals in the frequency domain. The transfer function H (ω) can be defined as:
where X (ω) is the excitation function, it is difficult for a rotor blade to achieve a measurement of the aerodynamic excitation of the blade surface, so the excitation function is assumed to be constant at blade resonance. The amplitude response of the single degree of freedom system is therefore |H (ω) | 2 Can be given by:
omega based on this model n It has been determined that k and ζ are obtained by sampling a nonlinear square fit to curve fit the measured data points. The variance between the curve fit and the data points was minimized using a Nonlinear Least Squares Fit (NLSF) method. A non-linear least squares fit is performed on the response curve shown in fig. 6 (b) to obtain a fitted response curve shown in fig. 7. The damping ratio of the rotor blade obtained by fitting is ζ=0.0112. Compared with the damping ratio of 0.01 introduced by the modal simulation, the error is 12%.
In another embodiment, the present disclosure further provides an electronic device, including:
a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein,
the processor, when executing the program, implements a method as described in any of the preceding.
In another embodiment, the present disclosure also provides a computer storage medium storing computer-executable instructions for performing the method of any one of the preceding claims.
According to the method disclosed by the disclosure, a strain gauge and a complex electricity-guiding slip ring system are not required to be pasted, and only two leaf end timing sensors are required to extract the resonant frequency and the damping ratio of the leaf.
The foregoing description is only of preferred embodiments of the invention and is not intended to limit the invention to the particular embodiments disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

Claims (10)

1. A method of rotor blade damping ratio calculation, comprising the steps of:
step 1: collecting time pulse signals of the rotor blade by using two blade end timing sensors, and obtaining the actual arrival time of the rotor blade according to the time pulse signalsCollecting a rotation speed reference pulse signal of the rotor blade by using an OPR sensor, and obtaining a rotation period T of the rotor blade according to the rotation speed reference pulse signal OPR ；
Step 2: based on actual arrival time of rotor bladesAnd a rotation period T OPR Calculating an actual angle of arrival of a rotor blade
Step 3: according to the radius R of the rotor blade and the actual practice of the rotor bladeAngle of arrivalAngle of arrival from theory->Angle difference of +.>Calculating tip displacement data +.>
Step 4: tip-based displacement dataExtracting displacement trend curves of two leaf-end timing sensors, calculating standard deviation of first derivatives of the two displacement trend curves, and taking time corresponding to the maximum standard deviation as resonance center time t of the rotor blade m ；
Step 5: searching for the resonance center time t of a rotor blade based on the time-frequency curve of the rotational speed reference pulse signal m Corresponding resonant frequency f r In combination with known first-order modal frequencies f of the rotor blade n Calculating a resonance frequency F of the rotor blade;
step 6: performing time-frequency analysis on the time pulse signals of the rotor blades to obtain a time-frequency diagram;
step 7: the formant ridge lines in the time-frequency diagram are extracted to obtain a frequency response curve of the rotor blade, and the frequency response curve is fitted through nonlinear least squares based on the resonance frequency F of the rotor blade in the step 5 to obtain the damping ratio zeta of the rotor blade.
2. The method according to claim 1, wherein, preferably, in step 1, the mounting angles of the two dual sensors satisfy the following formula:
wherein k is such that it satisfiesPositive integer set of EO p Is the resonance order of interest in the test.
3. The method according to claim 1, wherein in step 2, the actual angle of arrival of the rotor bladeCalculated by the following formula:
wherein,representing the actual arrival time of the rotor blade, T OPR Representing the period of rotation of the rotor blade.
4. The method of claim 1, wherein in step 3, the theoretical angle of arrival of the rotor bladeCalculated by the following formula:
wherein the subscript i denotes the number of the rotor blade, the subscript j denotes the number of the sensor, n denotes the number of rotations of the rotor blade, and M denotes that the rotor blade has rotated M rotations.
5. The method of claim 1, wherein in step 3, the displacement data of the rotor bladeCalculated by the following formula:
wherein R represents the radius of the rotor blade, pi represents the circumference ratio,representing the actual angle of arrival of the rotor blade>Angle of arrival from theory->Angle difference of>
6. The method of claim 1, wherein in step 4, the standard deviation of the first derivative of the displacement trend curve is calculated by:
wherein,representing the first derivative of the signal of the ith blade at the nth turn measured by the jth sensor,/->Standard deviation of the derivative of the two sensor signals representing the ith blade at the nth turn,/->Representing the mean of the first derivatives of the two sensor trend signals.
7. The method according to claim 1, wherein in step 5, the resonance frequency F of the rotor blade i Calculated by the following formula:
F i ＝f ri EO
wherein f n Representing the first order modal frequencies of the rotor blade, f ri Indicating that the rotor blade is at t i The frequency of revolution corresponding to the moment EO represents the order of the resonant frequency of the rotor blade, [. Cndot.]Rounding values of the representation.
8. The method of claim 1, wherein in step 7, the damping ratio ζ of the rotor blade is calculated by:
where m denotes the mass of the rotor blade, c denotes the damping of the rotor blade, k denotes the stiffness of the rotor blade, ω n Representing the natural frequency of the rotor blade.
9. An electronic device, comprising:
a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein,
the processor, when executing the program, implements the method of any one of claims 1 to 8.
10. A computer storage medium having stored thereon computer executable instructions for performing the method of any of claims 1 to 8.
CN202310724433.0A 2023-05-15 2023-06-19 Rotor blade damping ratio calculation method Pending CN117034536A (en)

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CN202310539259 2023-05-15

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