CN114528743A - Method for calculating dynamic stress monitoring limit value of rotor blade in wide rotating speed range - Google Patents

Method for calculating dynamic stress monitoring limit value of rotor blade in wide rotating speed range Download PDF

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CN114528743A
CN114528743A CN202210432808.1A CN202210432808A CN114528743A CN 114528743 A CN114528743 A CN 114528743A CN 202210432808 A CN202210432808 A CN 202210432808A CN 114528743 A CN114528743 A CN 114528743A
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rotor blade
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CN114528743B (en
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王永明
刘香
吴绵绵
王春健
杜文军
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AECC Sichuan Gas Turbine Research Institute
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Abstract

The invention provides a method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range, which comprises the steps of determining a plurality of analysis rotating speeds of the rotor blade in the wide rotating speed range; calculating the static frequency f of the rotor blade and the dynamic frequency f at each analysis rotation speedDAnd intensity results; establishing a rotor blade resonance rotating speed diagram, and acquiring the vibration monitoring order of the rotor blade; determining the position and the direction of a patch of a strain gauge for monitoring the vibration stress on a rotor blade; according to the maximum vibration risk factor KmaxCalculating the dynamic response of each strain gauge at each analysis rotating speed and vibration monitoring orderChanging the monitoring limit value; and establishing a strain gauge rotating speed-dynamic strain monitoring limit value curve from the slow vehicle rotating speed of the engine to the maximum rotating speed range of the engine. The method can obtain more reliable dynamic strain monitoring limit values under different rotating speed conditions, and realizes reliable monitoring of the dynamic stress of the rotor blade.

Description

Method for calculating dynamic stress monitoring limit value of rotor blade in wide rotating speed range
Technical Field
The invention belongs to the technical field of engine blade monitoring, and relates to a method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range.
Background
The dynamic stress of the rotor blade is monitored in the performance test and the whole machine test process of the parts of the aircraft engine, so that the test is ensured to be carried out safely and smoothly, and the vibration characteristic of the rotor blade is obtained.
At present, a strain gauge resistance type strain gauge (referred to as a strain gauge for short) is widely used for monitoring the vibration stress of an aircraft engine blade so as to judge the vibration characteristic and high cycle fatigue of the blade, the strain gauge mainly comprises five parts, namely a sensitive grid, a substrate, a lead wire, an adhesive and a surface covering, the principle is that the structural deformation actually measured by the strain gauge in the dynamic test is converted into a strain value of the strain gauge in the test and direction, and the dynamic stress limit value is calculated according to the hooke's law under the elastic assumption condition.
In the conventional monitoring method, in order to ensure that the blade does not generate high-cycle fatigue failure caused by resonance in a test, the vibration stress of the blade needs to be ensured not to continuously exceed the allowable vibration stress of the blade, so that a steady-state vibration stress limit value of a strain gauge needs to be given. And if the vibration stress of the blade measured by the strain gauge does not exceed or does not continuously exceed the limit value of the steady-state vibration stress in the test, the blade cannot be subjected to high-cycle fatigue failure, so that the safe test is ensured. Because the static stress of the blade body of the rotor blade is closely related to the rotating speed, the dynamic stress limiting value can also change along with the rotating speed, but in the calculation of the dynamic stress limiting value at present, the working condition of the vibration mode calculation of the rotor blade mostly adopts the working condition with larger rotating speed of an engine (usually, the maximum aerodynamic working condition is selected) to calculate the dynamic stress limiting value, so that the dynamic stress limiting value of the working condition with large rotating speed is used for limiting the vibration stress of the rotor blade for the working condition with lower rotating speed, the test is over conservative, the test cannot be normally carried out, and the real vibration characteristic of the rotor blade under the working condition with low rotating speed cannot be expressed.
Moreover, in an aircraft engine test, when a strain gauge is adopted to monitor the vibration stress of a rotor blade of the compressor, the problem of false overrun alarm frequently occurs in the test due to the fact that the safety margin is too large in a wide rotating speed range.
Disclosure of Invention
The invention discloses a method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range, which aims to solve the problems that a dynamic stress limit value (also called a dynamic stress monitoring limit value) of the rotor blade in the wide rotating speed range is calculated by adopting a working condition with a larger rotating speed in a test, frequent false overrun alarm is caused in the test process due to overlarge safety margin, and the real vibration characteristic of the rotor blade in the low rotating speed working condition cannot be expressed.
The technical scheme for realizing the purpose of the invention is as follows: a method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range comprises the following steps:
s1, determining a plurality of analysis rotating speeds of the rotor blade within the range from the slow-moving rotating speed of the engine to the maximum rotating speed of the engine;
s2, calculating the static frequency f of the rotor blade and the dynamic frequency f at each analysis rotating speedDAnd intensity results;
s3, according to static frequency f and dynamic frequency fDEstablishing a rotor blade resonance rotating speed diagram, and acquiring the vibration monitoring order of the rotor blade based on the rotor blade resonance rotating speed diagram;
s4, determining the patch position and the patch direction of a strain gauge for monitoring the vibration stress on the rotor blade based on the modal vibration stress distribution of the vibration monitoring order of the rotor blade;
s5 maximum vibration risk factor KmaxCalculating each strain gauge in eachAnalyzing dynamic strain monitoring limit values under the rotation speed and vibration monitoring order;
and S6, establishing a strain gauge rotating speed-dynamic strain monitoring limit value curve from the slow vehicle rotating speed of the engine to the maximum rotating speed of the engine based on each analysis rotating speed and the dynamic strain monitoring limit value thereof.
The method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotating speed range can obtain more reliable dynamic strain monitoring limit values under different rotating speed conditions in a test, realize reliable monitoring of the dynamic stress of the rotor blade, avoid the problem of false overrun alarm, ensure smooth running of an engine test and avoid high cycle fatigue failure of the rotor blade.
Further, in step S1, there are at least 3 analysis rotation speeds, and the rotation speed difference between adjacent analysis rotation speeds is greater than zero and less than 10% of the maximum rotation speed of the engine.
Further, the analysis rotational speed includes a maximum engine rotational speed, a dangerous resonance rotational speed obtained by resonance analysis, and an operating rotational speed obtained in a conventional test when vibration is large.
Further, in step S2, the dynamic frequency f at each analysis rotational speed isDAnd the intensity result calculation method comprises the following steps: and establishing a finite element model of the rotor blade, and performing strength analysis and modal analysis by adopting the same finite element model.
Further, in step S3, the vibration monitoring order includes one or more of a bending vibration of the first three steps of the blade, a torsional vibration of the first two steps of the blade, a chord bending vibration of the first two steps of the blade, an estimated resonance order, and a preset vibration order. The estimated resonance order is a resonance order excited in the range from the slow vehicle rotating speed of the engine to the maximum rotating speed of the engine according to an excitation factor, and the preset vibration order is a vibration order with large monitoring response in the previous test.
Furthermore, in step S3, the method for determining the frequency line of the rotor blade resonance speed map includes:
according to the static frequency f and dynamic frequency f of the rotor bladeDThe static frequency f and the dynamic frequency f at each analysis rotating speed are comparedDConnected into a rotorA frequency line of the blade varying with the rotation speed;
or, calculating the static frequency f of the rotor blade and the dynamic frequency f at a preset rotating speed nDAccording to the formula
Figure 745805DEST_PATH_IMAGE001
Inversely solving the dynamic frequency coefficient B; according to the formula
Figure 432001DEST_PATH_IMAGE002
Calculating the dynamic frequency f at each analysis rotating speedDAccording to the static frequency f and the dynamic frequency f at each analysis rotating speedDA frequency line of the rotor blade variation with the rotational speed is formed.
Further, in step S4, the method for determining the position and the direction of the strain gauge patch for monitoring the vibration stress on the rotor blade includes: calculating the dynamic frequency f of the vibration monitoring order of the engine at a certain rotating speed according to the rotor blade resonance rotating speed diagramDAnd determining the patch position and the patch direction of the strain gauge for monitoring the vibration stress on the rotor blade according to the relative vibration stress distribution of the vibration monitoring order.
Further, in the step S5, the maximum vibration risk factor K is usedmaxThe method for calculating the dynamic strain monitoring limit value of each strain gauge at each analysis rotating speed comprises the following steps:
s501, based on the strength results of the analysis at the rotating speeds, the allowable vibration stress sigma of each node of the rotor blade is calculatedai；
S502, according to the relative vibration stress sigmaxziAnd allowable vibration stress σaiCalculating the maximum vibration risk factor K under a certain order of vibration of the rotor blade at a set rotating speedmax；
S503, according to the maximum vibration risk factor KmaxCalculating a dynamic stress monitoring limit value of the strain gauge;
and S504, converting the dynamic stress monitoring limit value of the strain gauge into a dynamic strain monitoring limit value.
In an improved embodiment of the present invention, the method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotation speed range further includes step S7, and an overrun alarm is performed on the strain gauge based on the strain gauge rotation speed-dynamic strain monitoring limit value curve.
In another modified embodiment of the present invention, the method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotation speed range further includes step S8, which is to calculate the position (generally mainly focused on K) of the rotor blade other than the position of the strain gauge patch based on the dynamic strain response measured by the strain gauge on the rotor blade during the testmaxPoint, point of maximum vibrational stress or location of crack occurrence) vibrational stress at the vibration monitoring order.
Compared with the prior art, the invention has the beneficial effects that: the dynamic stress monitoring limit value analysis and overrun judgment method of the rotor blade considering the wide rotating speed range can be used for calculating the dynamic stress monitoring limit value of the blade in the design aeroengine test, and can obtain a more reliable dynamic stress monitoring limit value of the rotor blade under different rotating speed conditions in the wide rotating speed range, so that the dynamic stress of the blade is reliably monitored in the test, the false overrun alarm problem is avoided, the smooth running of the engine test is ensured, and the high-cycle fatigue failure of the rotor blade is also avoided.
Drawings
In order to more clearly illustrate the technical solution of the embodiment of the present invention, the drawings used in the description of the embodiment will be briefly introduced below.
FIG. 1 is a flow chart of a method for calculating a dynamic stress monitoring limit for a rotor blade over a wide range of rotational speeds in accordance with an embodiment of the present invention;
FIG. 2 shows a first method in the embodiment, i.e. depending on the dead frequency f and the different rotational speeds (n)1~n5) Lower dynamic frequency fDFrequency lines of the drawn rotor blade resonance speed map;
FIG. 3 shows a second method of implementing the second embodiment, i.e. a dynamic frequency f according to a static frequency f and a preset rotation speedDFrequency lines of the drawn rotor blade resonance speed map;
FIG. 4 is a schematic illustration of a patch position of a strain gage of a rotor blade according to an exemplary embodiment;
FIG. 5 is a schematic illustration of another patch position of a strain gage of a rotor blade according to an exemplary embodiment;
FIG. 6 is a 1 st order vibratory rotation speed-microstrain curve for a rotor blade strain gage at multiple rotation speeds obtained using an independent algorithm in an exemplary embodiment;
FIG. 7 is a 1 st order oscillatory rotation speed-microstrain curve of a strain gage of a rotor blade at multiple rotation speeds obtained using a simplified algorithm in an exemplary embodiment;
FIG. 8 is a second flowchart of a method for calculating a dynamic stress monitoring limit for a rotor blade over a wide range of rotational speeds according to an embodiment;
FIG. 9 is a third flowchart of a method for calculating a dynamic stress monitoring limit for a rotor blade over a wide speed range in accordance with an embodiment.
Detailed Description
The invention will be further described with reference to specific embodiments, and the advantages and features of the invention will become apparent as the description proceeds. These examples are illustrative only and do not limit the scope of the present invention in any way. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention, and that such changes and modifications may be made without departing from the spirit and scope of the invention.
The specific embodiment discloses a method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range, as shown in fig. 1, comprising the following steps:
and S1, determining a plurality of analysis rotating speeds of the rotor blade within the range from the slow vehicle rotating speed of the engine to the maximum rotating speed of the engine.
In this step, because the excitation factors of the rotor blades are more, the span of the rotation speed range in which resonance may occur is larger, so that at least 3 analysis rotation speeds are selected in the range from the slow turning rotation speed of the engine to the maximum rotation speed of the engine, and the rotation speed difference between adjacent analysis rotation speeds is larger than zero and smaller than 10% of the maximum rotation speed of the engine.
Preferably, the analysis rotation speed includes a maximum rotation speed of the engine (which may also be referred to as a maximum operating state rotation speed of the rotor blade), a dangerous resonance rotation speed obtained by resonance analysis, and an operating rotation speed obtained in a conventional test when vibration is large, and may further include other operating rotation speeds that need attention, such as a long-term operating rotation speed of the engine, a maximum aerodynamic rotation speed, a maximum operating rotation speed of the temperature, a rotation speed with a small surge margin, and the like.
S2, calculating the static frequency f of the rotor blade and the dynamic frequency f at each analysis rotating speedDAnd strength results.
In this step, the dynamic frequency f at each analysis rotational speedDAnd the intensity result calculation method comprises the following steps: and establishing a finite element model of the rotor blade, and performing strength analysis and modal analysis by adopting the same finite element model.
When establishing a finite element model (for example, establishing a finite element model of a vertical rotor blade or a blade disc structure for a tenon joint; establishing a finite element model of a blade disc structure for a whole blade disc), the following requirements are required to be met in addition to the requirement of performing strength analysis and modal analysis by using the same finite element model (in order to facilitate the analysis of a dynamic strain monitoring limit value by a subsequent program):
a. in the test, the vibration of the blade is mainly monitored for dynamic stress, the grid of the disk body of the blisk can be sparse when a finite element model is established, and the grids of the leading edge, the trailing edge and the blade root of the blade are refined to ensure the quality of each grid of the finite element model;
b. in order to reduce the workload of dynamic strain monitoring limit values during modal analysis and establishment of a strain gauge rotating speed-dynamic strain monitoring limit value curve, the grid scale should be properly controlled, and the number of grid units in a finite element model of a blisk is usually tens of thousands to twenty-three hundred thousands;
c. the mesh at the fault location or crack location is refined as needed for troubleshooting.
The dynamic frequency f of the rotor blade is obtained by calculating modes at different rotating speedsDAnd strength results, it is also necessary to calculate the mode of the rotor blade without considering the loads such as the rotating speed, the aerodynamic force, the temperature field and the like to obtain the static frequency f of the rotor blade.
It should be noted that the static frequency f of the rotor blade is determined without considering the loads such as the rotational speed, the aerodynamic force, the temperature field, etcModal derived, static frequency f of rotor blades and dynamic frequency f at analytic speedDAnd the intensity results are calculated using existing general methods.
S3, according to static frequency f and dynamic frequency fDAnd establishing a rotor blade resonance rotating speed diagram, and acquiring the vibration monitoring order of the rotor blade based on the rotor blade resonance rotating speed diagram.
In this step, since the number of resonance orders that may exist in the operating speed range of the rotor blade is large, in order to avoid an excessively large calculation amount, it is necessary to determine the resonance order that the rotor blade needs to be monitored in an important manner in the test as the vibration monitoring order. The screened vibration monitoring order comprises one or more of bending vibration of the first three steps of the blade, torsional vibration of the first two steps of the blade, string bending vibration of the first two steps of the blade, an estimated resonance order and a preset vibration order, wherein the estimated resonance order is a resonance order excited in the range from the slow rotating speed of the engine to the maximum rotating speed of the engine according to excitation factors, and the preset vibration order is a vibration order with large monitoring response in the previous test.
Wherein the vibration monitoring order of the rotor blade is resonance analysis of the rotor blade, and the static frequency f and the dynamic frequency f at a certain rotating speed are usedDThe method for establishing the rotor blade resonance rotating speed diagram includes two methods:
the first one is: according to the static frequency f and dynamic frequency f of the rotor bladeDThe static frequency f and the dynamic frequency f at each analysis rotating speed are comparedDThe frequency lines of the rotor blades as a function of the rotational speed are connected, and the frequency lines of the rotor blades as a function of the rotational speed are shown in fig. 2.
The second method is as follows: calculating the static frequency f of the rotor blade and the dynamic frequency f at a predetermined speed nDAccording to the formula
Figure 966887DEST_PATH_IMAGE002
(formula 1), inversely solving the dynamic frequency coefficient B; according to the formula
Figure 345916DEST_PATH_IMAGE002
Calculating the dynamic frequency f at each analysis rotating speedDAccording to the static frequencyf and dynamic frequency f at each analysis rotational speedDA frequency line of the rotor blades as a function of the rotational speed is formed, which is shown in fig. 3. The preset rotation speed n is preferably the rotation speed of the rotor blade under the highest temperature condition or the maximum rotation speed of the engine (i.e. the maximum working rotation speed).
Furthermore, when establishing a rotor blade resonance speed map, excitation factors to be considered include:
a. 1 st to 4 th order engine airflow distortion and low order excitation;
b. defining the number of the first two stages of stator blades of the rotor blade of the engine and the number of the later stage of stator blades of the rotor blade as S;
c. defining the difference value between the numbers of the stator blades of the first two stages of the rotor blades of the engine and the difference value between the number of the stator blades of the first stage and the number of the stator blades of the next stage of the rotor blades as C;
d. for structural factors with small quantity, such as engine support plates, 2-frequency doubling excitation of the engine support plates needs to be considered;
e. some non-structural factor excitations with larger vibration appear in the early test.
S4, determining the patch position and the patch direction of the strain gauge for monitoring the vibration stress on the rotor blade based on the modal vibration stress (also called relative vibration stress, two expression modes of the modal vibration stress and the relative vibration stress which are the vibration calculation results) distribution of the vibration monitoring order of the rotor blade.
In this step, the method for determining the patch position and the patch direction of the strain gauge for monitoring the vibration stress on the rotor blade comprises the following steps: calculating the dynamic frequency f of the vibration monitoring order of the engine at a certain rotating speed according to the rotor blade resonance rotating speed diagramDAnd determining the patch position and the patch direction of a strain gauge for monitoring the vibration stress on the rotor blade according to the relative vibration stress distribution of the vibration monitoring order.
The method for determining the position of the strain gauge patch for monitoring the vibration stress comprises the following steps:
a. for each vibration stress monitoring position, if the stress gradient at the position of the maximum relative vibration stress is smaller and the patch operation is convenient, the strain foil is attached at the position of the maximum vibration stress. Referring to FIG. 4, the maximum position of the third principal stress value of the relative vibration of a certain order of the rotor blade is in the region A, where the stress gradient is also small, and the patch operation is convenient, so that the position of the region A where the strain gauge for monitoring the vibration stress on the rotor blade is attached is determined.
b. For each vibration stress monitoring position, if the maximum vibration stress point is at the position of a radius and a sharp corner which can not be adhered with the strain gauge or the position with larger stress gradient, the position of the strain gauge patch is selected at the position of the second maximum stress point with smaller gradient. Referring to fig. 5, the maximum position of the third principal stress value of the relative vibration of a certain order of vibration of the rotor blade is a region B, but since the stress gradient is large and is located in the root fillet region, the surface mounting operation cannot be performed or is difficult to perform, and a stress secondary large region C which has a small stress gradient and is convenient for the surface mounting operation needs to be used as the surface mounting position of a strain gauge for monitoring the vibration stress on the rotor blade.
c. For each vibration stress monitoring position, if the fault elimination requirement is considered, the strain gauge can be directly attached to the position where the crack appears.
The method for determining the patch direction of the strain gauge comprises the following steps: and after the position of the strain gauge patch is determined, determining the direction of the larger one of the first main stress value and the third main stress value of the vibration monitoring order relative vibration at the position of the patch as the patch direction of the strain gauge.
S5 maximum vibration risk factor KmaxAnd calculating the dynamic strain monitoring limit value of each strain gauge at each analysis rotating speed and vibration monitoring order.
According to the vibration principle, when the rotor blade vibrates according to a certain order of mode at a rotating speed n in the test, the actual vibration mode is similar to the mode vibration mode, namely the actual vibration stress distribution is similar to the mode vibration stress distribution, so that in the step, according to the maximum vibration risk factor KmaxThe method for calculating the dynamic strain monitoring limit value of each strain gauge at each analysis rotating speed comprises the following steps:
s501, based on the strength results of the analysis at the rotating speeds, the allowable vibration stress sigma of each node of the rotor blade is calculatedai。
Specifically, the steady-state equivalent stress sigma of the ith node (namely, the grid node in the finite element model) of the rotor blade in the static strength calculation result at the rotating speed nmi(i.e., strength resultant stress), ith node, minimum tensile limit σ of the material at operating temperaturebiThe lowest value sigma of the stretching limit of the material at the i-th node at the working temperaturebiFatigue limit sigma of ith node at stress ratio of-1 at working temperature-1iAccording to the formula
Figure DEST_PATH_IMAGE003
(equation 2) the allowable vibrational stress σ at the ith node on the rotor blade can be determinedai。
Wherein the fatigue limit [ sigma ]-1iFirstly, selecting a fatigue limit test value of a rotor blade; if not, selecting a fatigue limit test value of a similar rotor blade; if neither of the two is available, selecting the fatigue limit-3 sigma value of the rotor blade material; if only the median fatigue limit of the material is present, the median value is used as an approximate-3 σ value, taking into account certain reserves. The number of cycles corresponding to the fatigue limit may follow the following principle: fatigue life N of rotor blade made of stainless steelf=1×107Fatigue limit of (d); for non-ferrous metal alloy blade, fatigue life N is takenf=3×107Fatigue limit of (d); for titanium alloy blade, fatigue life N is takenf=1×109If not, the fatigue life N is taken as the fatigue limit off=3×107The fatigue limit of (2).
S502, according to the relative vibration stress sigmaxziAnd allowable vibration stress σaiCalculating the maximum vibration risk factor K under a certain order of vibration of the rotor blade at a set rotating speedmax。
Specifically, the vibration stress sigma of any node on the blade body of the rotor blade in the general testziNot greater than the corresponding allowable vibration stress sigmaaiI.e. sigmaai≥σzi. When the rotor blade generates certain-order resonance, the vibration stress of all nodes on the blade body does not exceed the corresponding allowable vibration stress at the same time, and along with the increase of the resonance amplitude,when the vibration stress on the blade body firstly exceeds the node of the allowable vibration stress, the node is the most dangerous point of the fatigue of the blade body with the vibration of the order. The high cycle fatigue risk of any node on the blade body depends on the vibration stress magnitude and the allowable vibration stress value of the node, so that the allowable vibration stress sigma of any node of the rotor blade is based onaiAnd the relative vibratory stress (generally, taking the relative vibratory equivalent stress) σxziDefining vibration risk factor K of nodes, and passing the vibration risk factor K of each node through a formula
Figure 818617DEST_PATH_IMAGE004
(equation 3) the calculation yields that the node is more dangerous at this order of resonance as the value of K is larger. The maximum value of the vibration risk factor in the blade node is Kmax through a formula Kmax=max(Ki) (equation 4) obtain the corresponding node (denoted as K)maxPoint) is the most dangerous point of high cycle fatigue of the rotor blade under the vibration of the order.
S503, according to the maximum vibration risk factor KmaxAnd calculating the dynamic stress monitoring limit value of the strain gauge.
In particular, when a certain order of resonance occurs in the rotor blade, the vibration stress sigma of all the nodes on the rotor blade should be ensuredziNot greater than its corresponding allowable vibration stress sigmaaiSince the true vibratory stress distribution of the rotor blade is similar to the modal relative vibratory stress distribution, when K ismaxVibration stress sigma of pointziIs equal to its allowable vibration stress sigmaaiWhile, the vibratory stress σ of other nodes on the blade bodyziIs the maximum allowable vibration stress sigma of the node under the order resonanceaziAt this time, σ of an arbitrary nodeaziFrom the relative vibrational stress σ of the nodexziAnd KmaxValue according to formula
Figure 308504DEST_PATH_IMAGE005
(equation 5).
At the same time, in the channels
Figure 901159DEST_PATH_IMAGE005
Any section obtainedMaximum allowable vibrational stress of the point: for KmaxPoint of maximum allowable vibration stress σazIs equal to its allowable vibration stress sigmaai(ii) a For removing KmaxNodes other than the point having the maximum allowable vibration stress σaziLess than its permissible vibration stress sigmaai。
According to
Figure 451090DEST_PATH_IMAGE005
The maximum allowable vibration stress sigma corresponding to the node at the position of the strain gauge patch is obtainedaziNamely, the dynamic stress monitoring limit value of the strain gauge under the vibration of the order is obtained.
Furthermore, since the strain gauge is usually mounted in the primary stress direction of the monitoring order, σ is the limit value for monitoring the dynamic stress of the strain gauge when calculating the limit valuexziThe larger of the absolute value of the first principal stress or the absolute value of the third principal stress of the patch node of the strain gauge is generally taken as the stress absolute value.
And S504, converting the dynamic stress monitoring limit value of the strain gauge into a dynamic strain monitoring limit value.
Specifically, the actual measurement of the strain gauge on the rotor blade in the test is the dynamic strain at the position of the patch, and for convenience of judgment of the vibration response magnitude in the test, the dynamic stress monitoring limit value needs to be converted into the dynamic strain monitoring limit value.
The method for converting the dynamic stress monitoring limit value into the dynamic strain monitoring limit value comprises the following two methods:
the first one is: and for the isotropic material blade, when the stress state at the position of the strain gauge is close to the unidirectional stress state, obtaining a corresponding dynamic strain monitoring limit value according to the Hooke's law and the dynamic stress monitoring limit value.
The second method is as follows: because the patch position of the blade strain gauge is not in a unidirectional stress state under the service working condition, the dynamic strain monitoring limit value epsilon is obtained at the momentazCan be directly influenced by the relative vibration strain epsilon at the position of the strain foil patchxzAccording to the formula
Figure 129196DEST_PATH_IMAGE006
(equation 6), it should be further noted that the limit value ε is monitored due to dynamic strainazThe value of (a) is generally small and inconvenient to use in experiments, and therefore it is generally used by converting it into micro strain (. mu. epsilon.).
And S6, establishing a strain gauge rotating speed-dynamic strain monitoring limit value curve from the slow vehicle rotating speed of the engine to the maximum rotating speed of the engine based on each analysis rotating speed and the dynamic strain monitoring limit value thereof.
Specifically, the following two methods are used for obtaining the rotating speed-limit value curve of the strain gauge of the inner rotor blade in a wide rotating speed range (namely the range from the slow rotating speed of the engine to the maximum rotating speed of the engine):
the first one is: and independently calculating limit values at multiple rotating speeds (the method is simply called as an independent algorithm).
Specifically, the independent algorithm method comprises the following steps: with rotor blades at different speeds (see fig. 6 for speed n)1、n2、n3Wherein n is1>n2>n3) And (3) respectively calculating the dynamic strain monitoring limit values of the strain gauge at different rotating speeds according to the strength result and the modal calculation result in the steps S1-S5, converting the dynamic strain monitoring values into micro strain mu epsilon, and then drawing a strain gauge rotating speed-micro strain curve, for example, referring to a 1-order vibration rotating speed-micro strain curve of the strain gauge of a certain compressor rotor blade at different rotating speeds in fig. 6.
The second method is as follows: and (3) a simplified algorithm (simplified algorithm for short) of the dynamic stress monitoring limit value of the strain gauge at low rotating speed based on the dynamic stress monitoring limit value at maximum rotating speed.
In the method for respectively calculating the dynamic strain monitoring limit values under the multiple rotating speeds of the rotor blade, the calculation process has more repeated work and larger workload, so in order to reduce the workload, the strength result and the large state (namely the rotating speed n in the maximum working state) of the rotor blade under different working conditions are adopted1) Lower vibration and patch (position and orientation) design, using a simplified algorithm to approximate strain gage operating at other lower speeds (e.g., speed n as shown in FIG. 6)2、n3… …) is monitored. Rotor blade strain gageSame rotational speed (n)1>n2) The method of the simplified algorithm of the lower dynamic stress monitoring limit value is as follows:
rotor blades at n1Rotational speed and n2The static stress distribution of the blade body and the relative vibration stress distribution of a certain order of vibration in a rotating speed state are basically unchanged. By the above formula
Figure 430296DEST_PATH_IMAGE005
(equation 5) it can be seen that the dynamic stress monitoring limit of the rotor blade strain gauge and the rotor blade KmaxThe values are inversely proportional, from the formula
Figure 143037DEST_PATH_IMAGE004
(equation 3) can show KmaxValue of and KmaxAllowable vibration stress sigma of pointaInversely proportional, therefore the dynamic stress monitoring limit of the strain gauge is KmaxThe allowable vibrational stress of a point is proportional, therefore at n1Dynamic stress monitoring limit at speed (i.e. n)1Limit value) and n2The ratio between the limit values for monitoring the dynamic stress at a rotational speed is equal to n1At a rotational speed and n2At rotational speed KmaxAllowable vibration stress sigma of pointan1And σan2Ratio of (i.e. formula)
Figure 598289DEST_PATH_IMAGE007
(equation 7).
Due to KmaxAllowable vibration stress of point can be KmaxPoint is at n1Rotational speed and n2Fatigue limit sigma at rotational speed-1n1And σ-1n2Strength resultant stress σmn1And σmn2Tensile Limit σbn1And σbn2Obtained by the GOODMAN formula
Figure 763691DEST_PATH_IMAGE008
(equation 7) variable to (equation 8)
Figure 860960DEST_PATH_IMAGE009
At this time n2Strain gauge under rotating speed stateThe dynamic stress monitoring limit value can be based on n1The dynamic stress monitoring limit value under the rotating speed is according to the formula
Figure 428208DEST_PATH_IMAGE010
(equation 9).
During the derivation, the rotor blade is at n1Rotational speed and n2K under the working condition of rotating speedmaxHowever, in the actual condition of the rotor blade with a small rotation speed, the blade body strength result stress overall level is not high, the K value of the strength result maximum position is small, and the blade body maximum relative vibration equivalent stress point (recorded as sigma ') is formed at the moment'eqmaxPoint) has a K value that is large or even equal to Kmax. Meanwhile, under the condition that the rotor blade vibrates at a high rotating speed and a low order (such as one-bending vibration), the blade body KmaxPoint is often not at σ'eqmaxPoint, where the strength results in larger stress, and the vibration risk factor K of the two may be greatly different, so it should be determined according to n1Sigma 'at rotating speed'eqmaxThe intensity result of the point is n under different rotating speed states1Calculating n by monitoring limit value of dynamic stress of strain gauge at rotating speed2The dynamic stress of the strain gauge at the rotating speed is monitored and limited, and the above formula 9 is formed by n1At rotational speed KmaxThe intensity results of the points at different rotational speeds are calculated, so that n should be taken into account1At rotational speed KmaxClick to sigma'eqmaxPoint (sigma'eqmaxThe K value of the point is recorded as Keqmax) Then equation 9 is transformed into equation
Figure 70673DEST_PATH_IMAGE011
(equation 10). Wherein for n1Low order vibration (especially a bending vibration) of the rotor blade at rotational speed, usually KmaxDot and σ'eqmaxThe points do not coincide (at this time)
Figure 723371DEST_PATH_IMAGE012
) (ii) a For its higher order vibrations, usually KmaxDot and σ'eqmaxThe points coincide (at this time)
Figure 624331DEST_PATH_IMAGE013
) Or they do not coincide but KmaxAnd KeqmaxValue is close (at this time)
Figure 780506DEST_PATH_IMAGE014
) At this time, the above equation 10 is substantially the same as the calculation result of equation 9.
Generally speaking, the difference of the rotating speed between the working conditions needing to calculate the dynamic stress monitoring limit value is larger, the higher the rotating speed of the rotor is, the higher the temperature of the blade body under the corresponding working conditions is, and the tensile limit of the material is reduced along with the temperature increase, so that the rotating speed of the rotor is higher, and the tensile limit of the material is higher along with the temperature increase, so that the rotating speed of the rotor is higher, and the dynamic stress monitoring limit value is larger along with the temperature increase
Figure 108719DEST_PATH_IMAGE015
The above equation 10 can be processed according to the change rule of the fatigue limit of the material with the temperature according to the following conditions:
a. if the fatigue limit of the material does not have a monotonous rule along with the change of the temperature, the fatigue limit and the tensile limit at the corresponding temperature are respectively substituted into the formula 10 to be calculated according to the temperatures of the blade body at different rotating speeds;
b. if the fatigue limit of the material decreases with increasing temperature (
Figure 733867DEST_PATH_IMAGE016
) Or when the fatigue limit values at different temperatures do not vary much (
Figure 172938DEST_PATH_IMAGE017
) In this case, the formula 10 can be simplified as the formula
Figure 714778DEST_PATH_IMAGE018
(formula 11); when in use
Figure 948313DEST_PATH_IMAGE016
The calculation result of the above equation 11 is more conservative than the calculation result by equation 10. For example: certain compressor rotor blades at n1Rotational speed n2Rotational speed n3Intensity results at speed of rotation and n1The vibration result under the rotating speed state is respectively calculated by a formula 10 and a formula 11 to obtain the 1-order vibration of the strain gauge at the rotating speed n1Rotational speed n2Rotational speed n3Dynamic strain monitoring limit value epsilon at rotating speedazSimilarly, the limit value ε is monitored due to dynamic strainazThe value of (a) is generally small and inconvenient to use in experiments, so that the strain gauge is generally converted into micro strain (mu epsilon) for use, namely, a strain gauge vibration rotation speed-micro strain curve in 1 st order is shown in the attached figure 7, and can be known from the attached figure 7:
1. the limiting values of the strain gauges at low rotating speed obtained by the formula 10 and the formula 11 are both larger than the micro strain value of the strain gauge obtained by an independent algorithm (namely obtained after conversion of the dynamic strain monitoring limiting value);
2. the microstrain value (obtained after the conversion of the dynamic strain monitoring limit value) under the low rotating speed calculated by the formula 10 is 22.4 percent larger than the result obtained by adopting an independent algorithm to the maximum;
3. the microstrain value (obtained after the conversion of the dynamic strain monitoring limit value) under the low rotating speed calculated by the formula 11 is 5.3 percent larger than the result obtained by adopting an independent algorithm to the maximum;
4. theoretically, the calculation result of formula 11 is more conservative than that of formula 10, but actually, the calculation result of formula 11 has smaller deviation;
5. because the lowest value of the tensile limit and the value of the fatigue limit-3 sigma of the material are adopted when the micro-strain value is calculated (namely, the micro-strain value is obtained after conversion of the dynamic strain monitoring limit value), and because a certain reserve is generally considered when the dynamic strain monitoring limit value is used, the maximum deviation of the calculation result of the formula 11 can meet the use requirement of the test when the maximum deviation is 5%.
The dynamic stress monitoring limit value calculation method provided by the specific embodiment is suitable for monitoring dynamic stress of various rotor blades, such as a fan rotor blade, a gas compressor rotor blade, a turbine rotor blade, a gas turbine gas compressor rotor blade, a turbine rotor blade and the like of a turbine engine.
In a modified example of the specific embodiment, in order to ensure the smooth progress of the experiment, as shown in fig. 8, the method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotation speed range further includes a step S7 of alarming the strain gauge over-limit based on the strain gauge rotation speed-dynamic strain monitoring limit value curve, in addition to the steps S1 to S6.
Specifically, the dynamic stress monitoring limit value overrun alarm method for the strain gauge comprises the following steps:
s701, setting a reserve coefficient of a dynamic stress monitoring limit value
The calculation of the dynamic stress monitoring limit value of the strain gauge is carried out according to the strength result and the modal relative vibration stress result of the rotor blade at different rotating speeds, the actual working process of the engine is more complex, and when the rotor blade actually generates certain-order resonance, the vibration mode and the vibration stress distribution of the rotor blade are different from the modal vibration mode and the modal relative vibration stress distribution of the rotor blade, so that the dynamic stress monitoring limit value obtained by the process is used in the test after certain reserves (safety measures taken for the factors not considered in the design) are considered, and the selection method of the reserve coefficient N comprises the following steps: if the effective value is measured by the strain gauge in the test process, N is generally 2.5; if the amplitude value is measured by the strain gauge in the test process, N is generally 1.67; as the-3 sigma value of the fatigue limit is generally used for calculating the dynamic stress monitoring limit value, N can be only 1.0 in special purpose tests such as special measurement tests, and the vibration response can be ensured not to be continuously overrun by strengthening monitoring in the test process.
S702, alarm of overrun
After determining a dynamic stress monitoring limit value of the strain gauge under a design monitoring vibration order, focusing on the strain gauge response of the strain gauge under the design monitoring vibration order frequency in a test, and considering that the order resonance of the rotor blade occurs and the order vibration response is continuously focused if the response of the strain gauge under the order vibration frequency is obviously increased under a certain rotating speed and the strain gauge response is rapidly reduced after the rotating speed is crossed; if the response of the strain gauge under a certain rotating speed continuously exceeds the limit value under the rotating speed on the rotating speed-dynamic strain monitoring limit value curve, overrun alarm is required to be carried out, and the engine does not stop at the rotating speed. And after the test, carrying out dynamic test data analysis and feeding back a dynamic test result.
Whether the response measured by the rotor blade strain gauge at different rotating speeds in the test exceeds the limit value is judged by the limit value at the corresponding rotating speed on the strain gauge rotating speed-dynamic strain monitoring limit value curve, so that the problem that the response measured by the rotor blade strain gauge at different rotating speeds is judged to be false overrun alarm by the dynamic stress monitoring limit value at the maximum rotating speed is solved.
In addition, strain responses of a plurality of frequency components can be measured by the strain gauge in the test, but generally, only the response of the monitoring order of the strain gauge design is subjected to overrun alarm, and only the larger response of other frequency components is measured and recorded, and then analysis is carried out subsequently. Therefore, the resistance and insulation state of the strain gauge should be detected before the test to ensure that the strain gauge can work normally. When the response measured by the strain gauge is large in the test process, the resistance and the insulation state of the strain gauge in the test are timely confirmed on the test site, a waterfall graph and a step response curve of the strain gauge are obtained through rapid analysis, and the effectiveness of the vibration response signal acquired by the strain gauge is comprehensively judged. If the response of the rotor blade strain gauge under the design monitoring vibration frequency is measured for multiple times at a certain rotation speed in the test, the avoidance requirement can be provided for the rotation speed in the subsequent test.
In another improved embodiment of the invention, in the steps S1-S6, the strain gauge in the test is the dynamic strain response information, and the dynamic strain e measured by the strain gauge after the test is finishedxtConverted into dynamic stress sigma at the strain gaugextOther positions on the rotor blade can be obtained by converting the vibration stress at the strain gauge in the test (for example, comparing the Kmax point, sigma 'under the monitoring vibration order of the strain gauge'eqmaxPoints and locations where cracks occur, etc.), as shown in fig. 9, the above-described wide rotation speed rangeThe method for calculating the dynamic stress monitoring limit value of the blade of the rotor in the enclosure comprises the step S8 of calculating the positions (generally mainly concerning K) of the blade of the rotor except the position of the patch of the strain gauge on the basis of the dynamic strain response measured by the strain gauge on the blade of the rotor in the test on the basis of the steps S1 to S6maxPoint, point of maximum vibrational stress or location of crack occurrence) vibrational stress at the vibration monitoring order.
Wherein the dynamic strain extAnd dynamic stress sigmaxtThe conversion method comprises the following two methods:
the first one is: for the isotropic material rotor blade, when the stress state at the position of the strain gauge is close to the unidirectional stress state, the elastic modulus E at the position of the strain gauge at the test rotating speed is combined to measure the dynamic strain E of the strain gauge in the testxtBy the expression Hooke's law
Figure 575604DEST_PATH_IMAGE019
(equation 12) calculating the dynamic stress σ measured by the strain gaugext。
The second method is as follows: under the working condition of service, the surface mounting position of the blade strain gauge is not in a unidirectional stress state generally, and then the limiting value is combined to calculate the relative vibration stress sigma' in the direction of the strain gauge at the surface mounting positionxtAnd relative vibration strain e ″xtAnd elastic modulus E' and elastic modulus E at test rotating speedxtBy the formula
Figure 569099DEST_PATH_IMAGE020
(equation 13) calculating the dynamic stress σ measured by the strain gaugext。
Further, since the position of the strain gauge attached to the blade is not generally a vibration stress concern of a certain stage of vibration on the blade, for example, the maximum position σ 'of the vibration stress of the blade at the stage of vibration'eqmaxPoint or high cycle fatigue most dangerous location KmaxIn this regard, it is therefore also necessary to convert the dynamic stress measured by the strain gauges to σ 'on the rotor blade'eqmaxDot or KmaxThe vibrational stress of the spot. Since the actual vibration stress distribution of the blade body is similar to the modal relative vibration stress, according toRelative vibration equivalent stress σ' of vibration stress focus pointeqmIs' corresponding to the relative vibration stress in the direction of the strain gauge at the position of the strain gauge patchxtTo define a stress conversion coefficient alpha, the calculation formula of alpha is
Figure 699866DEST_PATH_IMAGE021
(equation 14). After the dynamic stress of the strain gauge of the rotor blade is obtained in the test, the vibration stress sigma of the vibration stress focus point of the blade in the test can be calculated and obtained by combining the conversion coefficient alpha of the vibration stress focus pointeqm. Vibrational stress σ of vibrational stress concerneqmThe conversion includes the following two cases:
the first method is as follows: for the isotropic material blade, when the stress state at the position of the strain gauge is close to the unidirectional stress state, a formula is adopted
Figure 369882DEST_PATH_IMAGE022
(equation 15) dynamic stress σ measured by strain gaugextConverting to obtain the dynamic stress sigma of the point of interesteqm。
The second method is as follows: when the position of the blade strain gauge patch is not in a unidirectional stress state, a formula is adopted
Figure 484468DEST_PATH_IMAGE023
(equation 16) dynamic stress σ measured by strain gaugextConverting to obtain the dynamic stress sigma of the point of interesteqm。
The method for analyzing the dynamic stress monitoring limit value and judging the overrun of the rotor blade considering the wide rotating speed range, which is designed by the specific embodiment, can be used for calculating the dynamic stress monitoring limit value of the blade in the design of an aircraft engine test, and can obtain a more reliable dynamic stress monitoring limit value of the rotor blade under different rotating speed conditions in the wide rotating speed range, so that the dynamic stress of the blade is reliably monitored in the test, the false overrun alarm problem is avoided, the engine test is ensured to be carried out smoothly, and the rotor blade is ensured not to have high-cycle fatigue failure.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (10)

1. A method for calculating a dynamic stress monitoring limit value of a rotor blade in a wide rotating speed range is characterized by comprising the following steps of:
s1, determining a plurality of analysis rotating speeds of the rotor blade within the range from the slow turning rotating speed of the engine to the maximum rotating speed of the engine;
s2, calculating the static frequency f of the rotor blade and the dynamic frequency f at each analysis rotating speedDAnd intensity results;
s3, according to static frequency f and dynamic frequency fDEstablishing a rotor blade resonance rotating speed diagram, and acquiring the vibration monitoring order of the rotor blade based on the rotor blade resonance rotating speed diagram;
s4, determining the patch position and the patch direction of a strain gauge for monitoring the vibration stress on the rotor blade based on the modal vibration stress distribution of the vibration monitoring order of the rotor blade;
s5 maximum vibration risk factor KmaxCalculating dynamic strain monitoring limit values of each strain gauge at each analysis rotating speed and vibration monitoring order;
and S6, establishing a strain gauge rotating speed-dynamic strain monitoring limit value curve from the slow vehicle rotating speed of the engine to the maximum rotating speed of the engine based on each analysis rotating speed and the dynamic strain monitoring limit value thereof.
2. The dynamic stress monitoring limit value calculation method according to claim 1, wherein: in step S1, there are at least 3 analysis rotation speeds, and the rotation speed difference between adjacent analysis rotation speeds is greater than zero and less than 10% of the maximum rotation speed of the engine.
3. The dynamic stress monitoring limit value calculation method according to claim 2, wherein: the analysis rotating speed comprises the maximum rotating speed of the engine, dangerous resonance rotating speed obtained according to resonance analysis, and working rotating speed obtained in the past test when vibration is large.
4. The dynamic stress monitoring limit value calculation method according to claim 1, wherein: in step S2, the dynamic frequency f at each analysis rotational speedDAnd the intensity result calculation method comprises the following steps: and establishing a finite element model of the rotor blade, and performing strength analysis and modal analysis by adopting the same finite element model.
5. The dynamic stress monitoring limit value calculation method according to claim 1, wherein: in step S3, the vibration monitoring order includes one or more of bending vibration of the first three steps of the blade, torsional vibration of the first two steps of the blade, chord bending vibration of the first two steps of the blade, an estimated resonance order, and a preset vibration order, where the estimated resonance order is a resonance order excited in a range from a slow-speed rotation speed of the engine to a maximum rotation speed of the engine according to an excitation factor, and the preset vibration order is a vibration order with a large monitoring response in a previous test.
6. The dynamic stress monitoring limit value calculation method according to claim 5, wherein: in step S3, the method for determining the frequency line of the rotor blade resonance speed map includes:
according to the static frequency f and dynamic frequency f of the rotor bladeDThe static frequency f and the dynamic frequency f at each analysis rotating speed are comparedDConnecting into a frequency line of the rotor blade changing with the rotating speed;
or, calculating the static frequency f of the rotor blade and the dynamic frequency f at a preset rotating speed nDAccording to the formula
Figure 381664DEST_PATH_IMAGE001
Inversely solving the dynamic frequency coefficient B; then according toFormula (II)
Figure 589791DEST_PATH_IMAGE002
Calculating the dynamic frequency f at each analysis rotating speedDAccording to the static frequency f and the dynamic frequency f at each analysis rotation speedDA frequency line of the rotor blade variation with the rotational speed is formed.
7. The dynamic stress monitoring limit value calculation method according to claim 1, wherein: in step S4, the method for determining the position and direction of the patch of the strain gauge for monitoring the vibration stress on the rotor blade includes: calculating the dynamic frequency f of the vibration monitoring order of the engine at a certain rotating speed according to the rotor blade resonance rotating speed diagramDAnd determining the patch position and the patch direction of a strain gauge for monitoring the vibration stress on the rotor blade according to the relative vibration stress distribution of the vibration monitoring order.
8. The dynamic stress monitoring limit value calculation method according to claim 1, wherein: in step S5, based on the maximum vibration risk factor KmaxThe method for calculating the dynamic strain monitoring limit value of each strain gauge at each analysis rotating speed comprises the following steps:
s501, based on the strength results of the analysis at the rotating speeds, the allowable vibration stress sigma of each node of the rotor blade is calculatedai；
S502, according to the relative vibration stress sigmaxziAnd allowable vibration stress σaiCalculating the maximum vibration risk factor K under a certain order of vibration of the rotor blade at a set rotating speedmax；
S503, according to the maximum vibration risk factor KmaxCalculating a dynamic stress monitoring limit value of the strain gauge;
and S504, converting the dynamic stress monitoring limit value of the strain gauge into a dynamic strain monitoring limit value.
9. The dynamic stress monitoring limit value calculation method according to any one of claims 1 to 8, wherein: the method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotating speed range further comprises the step S7 of alarming the strain gauge in an overrun mode based on the strain gauge rotating speed-dynamic strain monitoring limit value curve.
10. The dynamic stress monitoring limit value calculation method according to any one of claims 1 to 8, wherein: the method for calculating the dynamic stress monitoring limit value of the rotor blade in the wide rotating speed range further comprises the step S8 of calculating the vibration stress of the rotor blade at the vibration monitoring order except the position of the strain gauge patch based on the dynamic strain response measured by the strain gauge patch in the rotor blade in the test.
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