CN114354112A - Blade multi-order coupling vibration fatigue analysis method - Google Patents

Blade multi-order coupling vibration fatigue analysis method Download PDF

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CN114354112A
CN114354112A CN202210267061.9A CN202210267061A CN114354112A CN 114354112 A CN114354112 A CN 114354112A CN 202210267061 A CN202210267061 A CN 202210267061A CN 114354112 A CN114354112 A CN 114354112A
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vibration
strain
blade
order
coupling
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CN114354112B (en
Inventor
李鑫
王永明
陈官峰
秦秀云
史剑
王春健
潘容
罗辅欢
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AECC Sichuan Gas Turbine Research Institute
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AECC Sichuan Gas Turbine Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M15/00—Testing of engines
    • G01M15/14—Testing gas-turbine engines or jet-propulsion engines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G01M7/025—Measuring arrangements
    • 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
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G06F17/156—Correlation function computation including computation of convolution operations using a domain transform, e.g. Fourier transform, polynomial transform, number theoretic transform

Abstract

The application provides a blade multi-order coupling vibration fatigue analysis method, which specifically comprises the steps of analyzing coupling vibration danger orders; determining the dangerous order of the coupled vibration of the blade through a test; carrying out a multi-order displacement-strain calibration test on the blade, wherein the calibration order is a determined coupling vibration danger order, and obtaining a conversion function of displacement results and strain results of each order; performing a coupling vibration high-cycle fatigue pre-test to obtain a coupling vibration displacement frequency spectrum function of the blade under a specific load; calculating to obtain a coupling vibration strain spectrum function according to a conversion function of the displacement result and the strain result and the coupling vibration displacement spectrum function; calculating to obtain a time domain signal of the coupling vibration stress; obtaining high cycle fatigue equivalent stress of the blade under a specific stress ratio; the number of cycles of the blade under high cycle fatigue equivalent stress is determined. Through the processing scheme, the accuracy of the coupling vibration fatigue analysis is improved.

Description

Blade multi-order coupling vibration fatigue analysis method
Technical Field
The application relates to the technical field of aero-engines, in particular to a blade multi-order coupling vibration fatigue analysis method.
Background
The engine blade is used as a key component in an aircraft engine, and along with the continuous improvement of the performance of the engine, the load borne by the engine blade in the working process is larger and larger. Blade vibration problems occur almost all the time during the development and use of all engines, blade vibration failures account for about one third of structural failures of the engines, and therefore sufficient experimental verification of high cycle fatigue of the engine blades is necessary during the engine development stage.
When a high-cycle fatigue test is carried out, the vibration stress level of the test generally exceeds the range of the strain gauge, and meanwhile, the test frequency is high, the measurement time is long, and the reliability of a strain test system is poor, so that the vibration stress of the blade is indirectly measured in a non-contact displacement measurement mode. At present, the high-cycle fatigue vibration stress of the blade is generally subjected to excitation under a certain order of natural vibration mode, and the vibration stress of the blade is indirectly measured by adopting a laser displacement sensor through calibrating the relation between displacement and strain under the excitation frequency of a test.
When the high-order natural frequency of the blade is close to the integral multiple of the excitation order natural frequency of the high-cycle fatigue test, and the excitation order natural frequency is adopted for excitation, the phenomenon of coupled vibration can occur between the blade test excitation order vibration mode and the high-order vibration mode, and the condition that the blade simultaneously vibrates under a plurality of frequencies can occur. When multi-order coupling vibration occurs, only the test excitation order is calibrated, the vibration stress obtained by measuring the displacement is only the vibration stress under the test excitation order, the vibration stress of the coupling order is not considered, and the obtained vibration stress is seriously low. The existing high cycle fatigue test method cannot acquire the vibration characteristics of each order when the blade generates coupling vibration, and cannot acquire the vibration stress level after multi-order coupling, so that the high cycle fatigue limit of the blade cannot be determined.
Disclosure of Invention
In view of this, the embodiment of the present application provides a method for analyzing blade multi-order coupling vibration fatigue, and in order to solve the problem that a conventional test analysis method cannot obtain vibration characteristics of each order when a blade generates coupling vibration and a determination method of vibration stress level after multi-order coupling when the blade generates multi-mode coupling vibration, displacement-strain calibration is performed on the multi-order of the blade at the same time, vibration characteristics of each order of the blade during coupling vibration are obtained through multi-order calibration conversion, a method for determining equivalent vibration stress of the blade is provided based on a vibration mode superposition method, a high cycle fatigue limit of the blade is finally obtained, and a basic support is provided for design of the high cycle fatigue life of an engine blade.
The embodiment of the application provides a blade multi-order coupling vibration fatigue analysis method, which comprises the following steps:
analyzing coupling vibration danger orders, and selecting all orders which are located in an analysis frequency range and can generate coupling vibration as danger orders;
determining a strain test position according to the dangerous order obtained by vibration analysis, and determining the coupling vibration dangerous order of the blade through an excitation test of a specific order;
carrying out multi-order displacement-strain calibration test on the blade, wherein the calibration order is the determined coupling vibration danger order, and obtaining the conversion function of the displacement result and the strain result of each order
Figure 503494DEST_PATH_IMAGE001
；
Carrying out a coupling vibration high-cycle fatigue pre-test, wherein the load of the high-cycle fatigue pre-test is larger than that of the calibration test, and obtaining a coupling vibration displacement frequency spectrum function of the blade under a specific load
Figure 79969DEST_PATH_IMAGE002
；
According to the conversion function of the displacement result and the strain result
Figure 6336DEST_PATH_IMAGE001
And the coupled vibration displacement spectrum function
Figure DEST_PATH_IMAGE003
Calculating to obtain a coupling vibration strain spectrum function
Figure 617446DEST_PATH_IMAGE004
；
Based on the coupled vibration mode superposition method, according to the coupled vibration strain frequency spectrum function
Figure 439909DEST_PATH_IMAGE004
Calculating to obtain time domain signal of coupled vibration stress
Figure DEST_PATH_IMAGE005
；
Calculating high cycle fatigue equivalent stress, and measuring time domain signals of vibration stress obtained by different blades
Figure 270724DEST_PATH_IMAGE005
The equivalent stress of the blade is converted to the same stress ratio to obtain the high cycle fatigue equivalent stress of the blade at the specific stress ratio
Figure 735203DEST_PATH_IMAGE006
；
Determining blade fatigue equivalent stress at high cycle
Figure 935240DEST_PATH_IMAGE006
The number of cycles N below.
According to a specific implementation manner of the embodiment of the present application, the selecting the order in which all vibration modes within the analysis frequency range can generate coupled vibration as the dangerous order is obtained by the following steps:
analyzing and obtaining theoretical calculation results of the natural frequency and the natural vibration mode of the blade;
and calculating the relative vibration stress of the blade at each order vibration mode.
According to a specific implementation manner of the embodiment of the application, the determining the dangerous order of the coupled vibration of the blade comprises:
strain sensors are arranged on the blades according to the vibration stress distribution of dangerous orders analyzed theoretically, and the strain frequency monitoring bandwidth is set to be the excitation frequency range of the blades in the working environment of the engine;
selecting a certain natural frequency of the blade as a test excitation frequency to excite the blade, gradually increasing the excitation load from zero, and determining the order of the coupling vibration according to a strain amplitude-frequency characteristic curve, wherein the order of the coupling vibration is the dangerous order of the coupling vibration.
According to a specific implementation manner of the embodiment of the application, the conversion function of the displacement result and the strain result
Figure DEST_PATH_IMAGE007
The calculation formula of (2) is as follows:
Figure 256500DEST_PATH_IMAGE008
，
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE009
to calibrate the displacement spectrum function of the test,
Figure 73147DEST_PATH_IMAGE010
is a function of the strain spectrum of the calibration test.
According to a specific implementation manner of the embodiment of the application, the coupling vibration displacement frequency spectrum function
Figure DEST_PATH_IMAGE011
The method is characterized in that a displacement time domain signal measured through a high-cycle fatigue pre-test is obtained through Fourier transform.
According to a specific implementation manner of the embodiment of the application, the coupling vibration strain spectrum function
Figure 639519DEST_PATH_IMAGE004
The calculation process of (2) includes:
according to the blade vibration principle, the phase-frequency characteristic curve of displacement and strain of the same blade is consistent, and the following results are obtained:
Figure 694063DEST_PATH_IMAGE012
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE013
，
then the process of the first step is carried out,
Figure 920645DEST_PATH_IMAGE014
，
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE015
is the mode of the displacement spectrum function and represents the amplitude of the displacement;
Figure 224588DEST_PATH_IMAGE016
is the mode of the strain spectrum function and represents the amplitude of the strain;
Figure DEST_PATH_IMAGE017
representing the phase of the displacement as the argument of the displacement spectrum function;
Figure 329072DEST_PATH_IMAGE018
the argument of the strain spectrum function represents the phase of the strain.
According to a specific implementation manner of the embodiment of the application, the coupling vibration strain spectrum function is obtained
Figure DEST_PATH_IMAGE019
Calculating to obtain time domain signal of coupled vibration stress
Figure 769281DEST_PATH_IMAGE005
The method comprises the following steps:
to the coupled vibration strain spectrum function
Figure 901185DEST_PATH_IMAGE004
Performing inverse Fourier transform to obtain strain measurement time domain result
Figure 895685DEST_PATH_IMAGE020
The analysis frequency is 0-fm，fmThe highest frequency in the coupled vibration mode;
by hooke's law:
Figure 771238DEST_PATH_IMAGE021
wherein E is the elastic modulus, and the time domain signal of the vibration stress of the high cycle fatigue test is calculated
Figure 800373DEST_PATH_IMAGE005
。
According to a specific implementation of the embodiments of the present application, the determining blade fatigue equivalent stress at high cycle
Figure 837600DEST_PATH_IMAGE006
The following steps of cycle number N include:
converting the strain time domain curve into a plurality of sine wave loads by adopting a rain flow meter method;
the damage accumulation principle is adopted to convert the cycle number corresponding to each sine wave load into high cycle fatigue equivalent stress
Figure 86441DEST_PATH_IMAGE006
The number of cycles N below.
According to a specific implementation manner of the embodiment of the application, the coupling vibration strain spectrum function is obtained through calculation
Figure 500104DEST_PATH_IMAGE019
Further comprising after the step of:
analyzing a coupling coefficient, wherein the coupling coefficient is defined as the strain ratio of each coupling vibration order to the test excitation order when the coupling vibration occurs;
analyzing the frequency difference between each coupling vibration order frequency and the multiple of the test excitation frequency;
and carrying out correlation analysis on the coupling coefficient and the frequency difference based on a plurality of blade test results to determine a coupling vibration frequency difference threshold value, wherein the coupling vibration frequency difference threshold value is used in the high-cycle fatigue design of the engine blade in the later period, and the coupling vibration frequency difference of the blade needs to be larger than the coupling vibration frequency difference threshold value in order to avoid the coupling vibration.
According to a specific implementation manner of the embodiment of the present application, the calculation formula of the coupling coefficient is:
Figure DEST_PATH_IMAGE022
，
wherein m is a coupling coefficient,
Figure 914905DEST_PATH_IMAGE023
is the vibration strain of the nth order natural mode,
Figure DEST_PATH_IMAGE024
to test the frequency value of the excitation order, fnFrequency value of nth order natural mode, f1The frequency value of the test excitation order;
the calculation formula of the frequency difference is as follows:
Figure 654191DEST_PATH_IMAGE025
，
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE026
k is a multiple of the frequency difference between the coupled vibration order frequency and the excitation frequency multiple.
Advantageous effects
The blade multi-order coupling vibration fatigue analysis method in the embodiment of the application provides a multi-order calibration high-cycle fatigue test method and a vibration stress analysis method for blade coupling vibration, solves the problem that the conventional blade high-cycle fatigue test method cannot obtain vibration characteristics of each order and vibration stress levels after multi-order coupling when the blades generate coupling vibration, and finally determines the high-cycle fatigue limit of the blades.
The method is successfully applied to the rotor blade of the compressor of a certain type of engine, and a complete design, test and analysis process is established on the basis. The method provides theoretical and engineering test basis for the calculation of the vibration stress of the blades under the coupled vibration, and provides basic support for the high-cycle fatigue design of the blades.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for analyzing fatigue of multi-step coupled vibrations of a blade according to an embodiment of the present invention;
FIG. 2 is a frequency spectrum diagram of a coupled vibrating blade according to an embodiment of the present invention;
FIG. 3 shows the displacement-strain calibration results of 1 st and 2 nd order modes of a certain type of blade according to an embodiment of the present invention;
FIG. 4 is a graph of certain blade displacement and strain-coupled vibration responses according to an embodiment of the present invention;
FIG. 5 is a calculated strain amplitude-frequency characteristic according to an embodiment of the present invention;
FIG. 6 is a calculated time domain plot of strain according to an embodiment of the present invention;
FIG. 7 is a graph illustrating high cycle fatigue life of a material according to an embodiment of the present invention;
FIG. 8 is a flow chart of a method for analyzing fatigue of multi-step coupled vibrations of a blade according to another embodiment of the present invention;
FIG. 9 is a graph illustrating the relationship between a blade coupling coefficient and a coupled vibration frequency difference according to an embodiment of the present invention.
Detailed Description
The embodiments of the present application will be described in detail below with reference to the accompanying drawings.
The following description of the embodiments of the present application is provided by way of specific examples, and other advantages and effects of the present application will be readily apparent to those skilled in the art from the disclosure herein. It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. The present application is capable of other and different embodiments and its several details are capable of modifications and/or changes in various respects, all without departing from the spirit of the present application. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It is noted that various aspects of the embodiments are described below within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present application, one skilled in the art should appreciate that one aspect described herein may be implemented independently of any other aspects and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. Additionally, such an apparatus may be implemented and/or such a method may be practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present application, and the drawings only show the components related to the present application rather than the number, shape and size of the components in actual implementation, and the type, amount and ratio of the components in actual implementation may be changed arbitrarily, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
The embodiment of the application provides a blade multi-order coupling vibration fatigue analysis method, which comprises the steps of blade vibration mode testing and analysis, multi-order calibration test, high-cycle fatigue pre-test, frequency spectrum analysis and high-cycle fatigue test, and is described in detail with reference to the attached drawings 1 to 9.
Referring to fig. 1, the method for analyzing the fatigue of the blade in the embodiment of the invention includes the following steps:
and S1, analyzing the dangerous order of the coupled vibration, and selecting the order of the coupled vibration of all vibration modes in the analysis frequency range as the dangerous order. Analyzing the blade, and before calculation, firstly, according to the working environment of the engine, the frequency analysis range is from zero to the highest excitation frequency f of the blade which can appear in the working state of the enginemaxI.e. vibration frequency analysis range of 0-fmax. Obtaining theoretical calculation results of natural frequency and natural vibration mode of the blade through analysis, and calculating relative vibration stress of the blade under each order vibration mode (
Figure 154443DEST_PATH_IMAGE027
) All orders within the analysis frequency range where coupled vibrations occur are selected as dangerous orders.
And S2, performing a sensor test according to the dangerous order obtained by the vibration analysis, and determining the coupling vibration dangerous order of the blade. Specifically, firstly, strain gauges (strain sensors) are arranged on selected vibration stress monitoring points, and it is noted that the vibration characteristics of the blade after the strain gauges are arranged cannot be greatly changed due to the mass of an additional testing device, the frequency change of the excitation order is recommended to be not more than 10Hz, and if the frequency change is larger than 10Hz, the testing scheme is recommended to be changed after the number of the sensors is reduced. During the test, the detection bandwidth of the strain measurement is that a certain-order natural frequency (generally 1 order) of the blade is selected as an excitation frequency to excite the blade, the excitation load is gradually increased from zero, and the order of the coupled vibration is determined according to the amplitude-frequency characteristic curve of the strain. Fig. 4 shows the displacement and strain amplitude responses of a certain blade under 1 st order excitation, and it can be seen that coupled vibration occurs in multiple orders of the blade.
S3, carrying out multi-order displacement-strain calibration test on the blade, wherein the calibration order is the determined coupling vibration danger order, and obtaining the conversion function of the displacement result and the strain result of each order
Figure 873262DEST_PATH_IMAGE001
. In particular, a scaling function of the displacement result and the strain result
Figure DEST_PATH_IMAGE028
The calculation formula of (2) is as follows:
Figure 345832DEST_PATH_IMAGE029
，
in the formula (I), the compound is shown in the specification,
Figure 990440DEST_PATH_IMAGE009
to calibrate the displacement spectrum function of the test,
Figure 712408DEST_PATH_IMAGE010
for calibrating the tested strain spectrum function, the two functions are complex variable functions, the mode and the argument of the functions reflect the respective amplitude and phase,
Figure 467875DEST_PATH_IMAGE001
as a scaled function of displacement and strain magnitude.
According to the analysis of the blade vibration principle, the displacement and the strain of the blade are in a linear relation under single-mode vibration, and the vibration stress of the blade is indirectly measured in a displacement mode due to the problems of the measuring range and the testing reliability of a strain gauge when a high-cycle fatigue test is carried out. Therefore, a calibration test is required before the high cycle fatigue test is performed.
Because the blade has the coupled vibration, therefore need mark respectively to the vibration of a plurality of orders when the mark, when carrying out the calibration test, increase excitation load step by step until the foil gage is invalid, need carry out filtering process to the signal of gathering simultaneously in the testing process, eliminate the interference of environmental noise and other factors to the test result.
Compared with the traditional high-cycle fatigue calibration method which only monitors the vicinity of the excitation frequency, the method firstly widens the monitoring frequency to the excitation frequency range under the working environment of the blade according to the vibration mode test result, and simultaneously monitors the vibration of multiple orders. And simultaneously, calibrating the displacement and the strain under each order according to the orthogonality of each vibration mode of the blade vibration during calibration, and the test result also proves that the displacement and the strain under each order are in a linear relation. FIG. 3 shows the calibration results of 1-order and 2-order modes of a certain type of blade.
S4, carrying out a coupling vibration high cycle fatigue pre-test to obtain a coupling vibration displacement frequency spectrum function of the blade under a specific load
Figure 60530DEST_PATH_IMAGE011
. When the high-cycle fatigue pre-test is carried out, the load of the high-cycle fatigue pre-test is larger than that of the calibration test, the displacement result measured by the high-cycle fatigue test is subjected to spectrum analysis, the time domain signal d (t) of the displacement of the monitoring point is obtained through the high-cycle fatigue pre-test, and the amplitude characteristic curve and the phase angle characteristic curve of the displacement signal are obtained through Fourier transform. FIG. 2 shows time domain and frequency domain measurement results of displacement of certain engine compressor blades at excitation frequency.
S5, according to the conversion function of the displacement result and the strain result
Figure 876039DEST_PATH_IMAGE001
And the coupled vibration displacement spectrum function
Figure 554145DEST_PATH_IMAGE003
Meter for measuringCalculating to obtain a coupling vibration strain frequency spectrum function
Figure 626486DEST_PATH_IMAGE004
。
From the nature of the complex function:
Figure 339227DEST_PATH_IMAGE013
，
in the formula (I), the compound is shown in the specification,
Figure 591217DEST_PATH_IMAGE015
is the mode of the displacement spectrum function and represents the amplitude of the displacement;
Figure DEST_PATH_IMAGE030
is the mode of the strain spectrum function and represents the amplitude of the strain;
Figure 553357DEST_PATH_IMAGE031
representing the phase of the displacement as the argument of the displacement spectrum function;
Figure DEST_PATH_IMAGE032
the argument of the strain spectrum function represents the phase of the strain.
According to the blade vibration principle, the phase-frequency characteristic curves of displacement and strain of the same blade are consistent, so that the amplitude of the strain spectrum function can be obtained through the amplitude of the displacement spectrum function and the displacement-strain conversion function, and the strain spectrum function can be obtained through the amplitude of the strain spectrum function and the phase angle of the displacement spectrum function. Namely:
Figure 916205DEST_PATH_IMAGE033
，
then:
Figure 749032DEST_PATH_IMAGE014
。
fig. 5 shows the calculated strain amplitude-frequency characteristic curve.
S6、Calculating the coupling vibration stress: based on the coupled vibration mode superposition method, according to the coupled vibration strain frequency spectrum function
Figure 407808DEST_PATH_IMAGE004
Calculating to obtain time domain signal of coupled vibration stress
Figure 60507DEST_PATH_IMAGE005
Comprises the following steps.
Specifically, based on the coupled vibration mode superposition method, the strain spectrum function of the coupled vibration is subjected to
Figure 961467DEST_PATH_IMAGE004
Performing inverse Fourier transform to obtain strain measurement time domain result
Figure DEST_PATH_IMAGE034
The analysis frequency is 0-fm，fmThe highest frequency in the coupled vibration mode; by hooke's law:
Figure 179958DEST_PATH_IMAGE021
wherein E is the elastic modulus, and the time domain signal of the vibration stress of the high cycle fatigue test is calculated
Figure 508171DEST_PATH_IMAGE005
. The calculated strain time domain curve is given in fig. 6. The influence of phases of different orders of vibration modes is considered during calculation, and the amplitudes of all vibration modes cannot be directly linearly superposed, so that the calculated vibration stress is seriously high.
S7, calculating the high cycle fatigue equivalent stress according to the time domain signal of the vibration stress
Figure 851428DEST_PATH_IMAGE005
Obtaining the peak-valley value of the vibration stress, and measuring the time domain signals of the vibration stress obtained by different blades
Figure 290500DEST_PATH_IMAGE005
Conversion to the same stress ratioCalculating the high cycle fatigue equivalent stress of the blade under a specific stress ratio through the service life curve
Figure 97919DEST_PATH_IMAGE006
。
Due to processing, the frequencies of different blades are not identical, and the coupled vibration frequency difference of different vibration orders
Figure 98498DEST_PATH_IMAGE035
The coupling coefficients are not completely consistent, so that the coupling vibration characteristics are completely inconsistent, and the vibration stress-stress ratio is also different. The vibration stress under different stress ratios cannot be directly compared, so that the data under different stress ratios need to be converted into the same stress ratio by adopting an equal life curve, and a life curve of a certain material, such as high cycle fatigue, is given in fig. 7.
S8, determining the fatigue equivalent stress of the blade in the high cycle
Figure 725788DEST_PATH_IMAGE006
The number of cycles N below.
Because of the multi-order coupled vibration, the time-domain waveform of the vibration of the blade is not a pure sine wave (fig. 2), and N cannot be used as the equivalent stress of the blade
Figure 171813DEST_PATH_IMAGE006
The high cycle fatigue life of the lower blade needs to adopt a rain flow counting method to convert time domain waveforms into a plurality of sine wave loads, and then adopts a damage accumulation principle to convert the cycle number corresponding to the sine wave loads into equivalent stress
Figure DEST_PATH_IMAGE036
The corresponding cycle number is obtained, thereby determining the fatigue equivalent stress of the blade at high cycle
Figure 896056DEST_PATH_IMAGE006
The number of cycles N below.
Specifically, the time domain curve is decomposed into time domain curves by adopting a rain flow methodAnd a plurality of cyclic loads, wherein the cyclic loads comprise a main load and a plurality of branch loads, and the branch cyclic loads are converted to the main load by adopting a damage principle. The sum of the number of cyclic loading cycles is the fatigue equivalent stress of the blade at high cycle
Figure 831651DEST_PATH_IMAGE006
The number of cycles N below.
In another embodiment, the following steps are further included after step S5:
and S9, analyzing the coupling coefficient, wherein the coupling coefficient is defined as the strain ratio of each coupling vibration order to the test excitation order when the coupling vibration occurs, and simultaneously analyzing the frequency difference between each coupling vibration order frequency and the test excitation frequency multiple.
Through further analysis of the frequency spectrum result of the coupling vibration high-cycle fatigue test, a coupling coefficient and a frequency difference between the coupling vibration order frequency and the excitation frequency multiple are obtained through calculation, and the calculation formula of the coupling coefficient is as follows:
Figure 680658DEST_PATH_IMAGE022
，
wherein m is a coupling coefficient,
Figure 727111DEST_PATH_IMAGE037
is the vibration strain of the nth order natural mode,
Figure 745008DEST_PATH_IMAGE024
to test the frequency value of the excitation order, fnFrequency value of nth order natural mode, f1The frequency value of the test excitation order;
the calculation formula of the frequency difference is as follows:
Figure 585925DEST_PATH_IMAGE025
，
in the formula (I), the compound is shown in the specification,
Figure 922229DEST_PATH_IMAGE026
k is a multiple of the frequency difference between the coupled vibration order frequency and the excitation frequency multiple.
S10, coupled vibration frequency difference threshold analysis: based on the test results of a plurality of blades, the coupling coefficient m and the frequency difference are adjusted
Figure 506794DEST_PATH_IMAGE026
Performing correlation analysis, and obtaining m and m by means of data point curve fitting
Figure 877732DEST_PATH_IMAGE026
The function relationship between the two is that the critical value of each order coupling coefficient is determined according to the vibration stress level (the coupling coefficient exceeds the critical value, and the obvious coupling vibration effect is considered to be generated). Further determining the threshold value of the coupling vibration frequency difference through a function relation curve obtained by fitting
Figure DEST_PATH_IMAGE038
Fig. 9 shows the relationship between a certain blade coupling coefficient and the coupling vibration frequency difference. The coupling vibration frequency difference threshold value
Figure 420709DEST_PATH_IMAGE039
The method is used for the high cycle fatigue design of the engine blade in the later period, and the coupling vibration frequency difference of the blade needs to be larger than the coupling vibration frequency difference threshold value in order to avoid the coupling vibration.
It should be noted that steps S9-S10 are not limited to be performed after step S8 is performed, and steps S6-S7 may be performed in synchronization with steps S9-S10 after step S5 is performed, as shown in the flow chart of fig. 8, to finally obtain the coupled vibration characteristic and the vibration fatigue performance.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (10)

1. A blade multi-order coupling vibration fatigue analysis method is characterized by comprising the following steps:
analyzing coupling vibration danger orders, and selecting all orders which are located in an analysis frequency range and can generate coupling vibration as danger orders;
determining a strain test position according to the dangerous order obtained by vibration analysis, and determining the coupling vibration dangerous order of the blade through an excitation test of a specific order;
carrying out multi-order displacement-strain calibration test on the blade, wherein the calibration order is the determined coupling vibration danger order, and obtaining the conversion function of the displacement result and the strain result of each order
Figure 92059DEST_PATH_IMAGE001
；
Carrying out a coupling vibration high-cycle fatigue pre-test, wherein the load of the high-cycle fatigue pre-test is larger than that of the calibration test, and obtaining a coupling vibration displacement frequency spectrum function of the blade under a specific load
Figure 471088DEST_PATH_IMAGE002
；
According to the conversion function of the displacement result and the strain result
Figure 927477DEST_PATH_IMAGE001
And the coupled vibration displacement spectrum function
Figure 682943DEST_PATH_IMAGE003
Calculating to obtain a coupling vibration strain spectrum function
Figure 744440DEST_PATH_IMAGE004
；
Based on the coupled vibration mode superposition method, according to the coupled vibration strain frequency spectrum function
Figure 61414DEST_PATH_IMAGE004
Calculating to obtain time domain signal of coupled vibration stress
Figure 5100DEST_PATH_IMAGE005
；
Calculating high cycle fatigue equivalent stress, and measuring time domain signals of vibration stress obtained by different blades
Figure 298678DEST_PATH_IMAGE005
The equivalent stress of the blade is converted to the same stress ratio to obtain the high cycle fatigue equivalent stress of the blade at the specific stress ratio
Figure 11419DEST_PATH_IMAGE006
；
Determining blade fatigue equivalent stress at high cycle
Figure 997829DEST_PATH_IMAGE006
The number of cycles N below.
2. The method for analyzing the fatigue of the blades by the multistage coupling vibration as claimed in claim 1, wherein the step of selecting the orders in which the coupled vibration occurs in all vibration modes in the analysis frequency range as dangerous orders is obtained by the following steps:
analyzing and obtaining theoretical calculation results of the natural frequency and the natural vibration mode of the blade;
and calculating the relative vibration stress of the blade at each order vibration mode.
3. The method of claim 1, wherein determining the dangerous order of coupled vibration of the blade comprises:
strain sensors are arranged on the blades according to the vibration stress distribution of dangerous orders analyzed theoretically, and the strain frequency monitoring bandwidth is set to be the excitation frequency range of the blades in the working environment of the engine;
selecting a certain natural frequency of the blade as a test excitation frequency to excite the blade, gradually increasing the excitation load from zero, and determining the order of the coupling vibration according to a strain amplitude-frequency characteristic curve, wherein the order of the coupling vibration is the dangerous order of the coupling vibration.
4. The method of claim 1, wherein the scaling function of the displacement result and the strain result is a function of the multi-order coupling vibration fatigue of the blade
Figure 694390DEST_PATH_IMAGE001
The calculation formula of (2) is as follows:
Figure 526080DEST_PATH_IMAGE007
，
in the formula (I), the compound is shown in the specification,
Figure 93327DEST_PATH_IMAGE008
to calibrate the displacement spectrum function of the test,
Figure 752104DEST_PATH_IMAGE009
is a function of the strain spectrum of the calibration test.
5. The method of claim 1, wherein the displacement spectrum function of the coupled vibration is a function of the coupled vibration displacement
Figure 670381DEST_PATH_IMAGE002
The method is characterized in that a displacement time domain signal measured through a high-cycle fatigue pre-test is obtained through Fourier transform.
6. The method of claim 4, wherein the coupled vibration strain spectrum function is a function of a multi-step coupled vibration fatigue of the blade
Figure 571341DEST_PATH_IMAGE004
The calculation process of (2) includes:
according to the blade vibration principle, the phase-frequency characteristic curve of displacement and strain of the same blade is consistent, and the following results are obtained:
Figure 258675DEST_PATH_IMAGE010
，
wherein the content of the first and second substances,
Figure 586888DEST_PATH_IMAGE011
，
then the process of the first step is carried out,
Figure 726882DEST_PATH_IMAGE012
，
in the formula (I), the compound is shown in the specification,
Figure 431533DEST_PATH_IMAGE013
is the mode of the displacement spectrum function and represents the amplitude of the displacement;
Figure 973373DEST_PATH_IMAGE014
is the mode of the strain spectrum function and represents the amplitude of the strain;
Figure 962233DEST_PATH_IMAGE015
representing the phase of the displacement as the argument of the displacement spectrum function;
Figure 589524DEST_PATH_IMAGE016
the argument of the strain spectrum function represents the phase of the strain.
7. The method of claim 1, wherein the function of the strain spectrum of the coupled vibration is used as a function of the strain spectrum of the coupled vibration
Figure 566707DEST_PATH_IMAGE004
Calculating to obtain time domain signal of coupled vibration stress
Figure 228632DEST_PATH_IMAGE005
Included：
To the coupled vibration strain spectrum function
Figure 898648DEST_PATH_IMAGE004
Performing inverse Fourier transform to obtain strain measurement time domain result
Figure 13235DEST_PATH_IMAGE017
The analysis frequency is 0-fm，fmThe highest frequency in the coupled vibration mode;
by hooke's law:
Figure 794109DEST_PATH_IMAGE018
wherein E is the elastic modulus, and the time domain signal of the vibration stress of the high cycle fatigue test is calculated
Figure 310541DEST_PATH_IMAGE005
。
8. The method of claim 7, wherein the fatigue equivalent stress at high cycle fatigue of the blade is determined
Figure 652923DEST_PATH_IMAGE006
The following steps of cycle number N include:
converting the strain time domain curve into a plurality of sine wave loads by adopting a rain flow meter method;
the damage accumulation principle is adopted to convert the cycle number corresponding to each sine wave load into high cycle fatigue equivalent stress
Figure 254805DEST_PATH_IMAGE006
The number of cycles N below.
9. The method as claimed in claim 1, wherein the calculation is performed to obtain a strain spectrum function of the coupled vibration
Figure 839370DEST_PATH_IMAGE004
Further comprising after the step of:
analyzing a coupling coefficient, wherein the coupling coefficient is defined as the strain ratio of each coupling vibration order to the test excitation order when the coupling vibration occurs;
analyzing the frequency difference between each coupling vibration order frequency and the multiple of the test excitation frequency;
and carrying out correlation analysis on the coupling coefficient and the frequency difference based on a plurality of blade test results to determine a coupling vibration frequency difference threshold value, wherein the coupling vibration frequency difference threshold value is used in the high-cycle fatigue design of the engine blade in the later period, and the coupling vibration frequency difference of the blade needs to be larger than the coupling vibration frequency difference threshold value in order to avoid the coupling vibration.
10. The method for analyzing the multi-step coupled vibration fatigue of the blades as claimed in claim 1, wherein the calculation formula of the coupling coefficient is as follows:
Figure 413571DEST_PATH_IMAGE019
，
wherein m is a coupling coefficient,
Figure 425390DEST_PATH_IMAGE020
is the vibration strain of the nth order natural mode,
Figure 248989DEST_PATH_IMAGE021
to test the frequency value of the excitation order, fnFrequency value of nth order natural mode, f1The frequency value of the test excitation order;
the calculation formula of the frequency difference is as follows:
Figure 637245DEST_PATH_IMAGE022
，
in the formula (I), the compound is shown in the specification,
Figure 862690DEST_PATH_IMAGE023
k is a multiple of the frequency difference between the coupled vibration order frequency and the excitation frequency multiple.
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