Strain-gage-based multi-order dynamic stress measurement design method for engine blade

Abstract

The engine blade strain gauge-based multi-order dynamic stress measurement design method comprises the following steps: S1, determining the vibration range of the blade; S2, analyzing the strength of the blade and the vibration of the blade according to the vibration range of the blade; S3, determining the vibration monitoring order of the blade, the patch position of the strain gauge and the patch direction of the strain gauge; S4, calculating the limit value of the strain gauge according to the vibration principle and based on the maximum vibration risk factor; S5, calculating the strain gauge multi-order conversion coefficient and the multi-order limit value; and S6, determining the vibration order that can be simultaneously monitored by the strain gauge through sensitivity analysis. In the test, the number of strain gauges used is reduced.

Description

Technical Field

[0001] This invention belongs to the technical field of aero-engines, and particularly relates to a design method for measuring and designing multi-order dynamic stress of engine blades based on strain gauges. Background Technology

[0002] Aero-engines operate over a wide speed range, and their blades are subject to numerous direct excitation factors, making resonance points inevitable. Blade resonance generates significant vibrations, affecting high-cycle fatigue life and potentially leading to high-cycle fatigue failure. Therefore, dynamic stress monitoring of the blades must be incorporated into the testing process to ensure safe and successful execution, while simultaneously obtaining the blade's vibration characteristics. Currently, strain gauges remain the primary method for monitoring the vibration characteristics and high-cycle fatigue of aero-engine blades.

[0003] To prevent high-cycle fatigue failure of the blade due to resonance during the experiment, it is necessary to ensure that the vibration stress of the blade does not continuously exceed the allowable vibration stress. Therefore, the steady-state vibration stress limit value of the strain gauge needs to be provided. If the blade vibration stress measured by the strain gauge does not exceed or continuously exceed the steady-state vibration stress limit value during the experiment, the blade will not suffer high-cycle fatigue failure, thus ensuring the safe conduct of the experiment.

[0004] Because aero-engine blades have many stages, each stage has numerous resonance points within its operating speed range. If a strain gauge were designed to monitor each resonance point of each stage (considering strain gauge damage during testing and the reliability of the measured dynamic stress data, in practice, multiple blades would be selected circumferentially to attach strain gauges), a large number of strain gauges would be required. However, due to limitations in testing requirements, equipment, personnel, and economics, the actual number of strain gauges used for dynamic stress monitoring in a single test is finite. Therefore, it is entirely possible to design a single strain gauge to simultaneously monitor multiple vibration orders of the blade, thus achieving the goal of monitoring more vibration orders of the blade with a limited number of strain gauges. Since engines have many stages of blades, and each stage has many strain gauges, current methods of attaching strain gauges to the engine result in high testing costs. Summary of the Invention

[0005] In view of this, the present invention provides a design method for measuring and designing multi-order dynamic stress of engine blades based on strain gauges, which solves the technical problem of high cost in engine testing of existing methods.

[0006] A design method for measuring and designing multi-order dynamic stress in engine blades based on strain gauges, the method comprising:

[0007] S1: Determine the range of blade vibration;

[0008] S2: Analyze the blade's strength and vibration based on the range of blade vibration;

[0009] S3: Determine the vibration monitoring order of the blade, and the location and orientation of the strain gauges;

[0010] S4: Calculate the limit value of the strain gauge based on the vibration principle and the maximum vibration hazard factor;

[0011] S5: Calculate the multi-order conversion factor and multi-order limit value of the strain gauge;

[0012] S6: Determine the vibration order that the strain gauge can monitor simultaneously through sensitivity analysis.

[0013] The beneficial effects of this invention are:

[0014] In aero-engine testing, resistance strain gauges (hereinafter referred to as strain gauges) are generally used to monitor the vibration stress of blades. However, aero-engines need to monitor multiple blade orders during testing, and each blade order has many resonance points within its operating speed range. To address the problem of how to monitor more orders of blade vibration using a limited number of strain gauges, the design method presented in this invention can be used to determine the patch position and orientation of strain gauges for monitoring blade dynamic stress in aero-engine testing. It can enable a single strain gauge to monitor multiple orders of blade vibration simultaneously, and can help determine the vibration order by comparing the response magnitudes and limit values ​​of different strain gauges on the same blade, and can verify the accuracy of the modal analysis method used. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 Draw frequency lines connecting the static frequency and the dynamic frequency at multiple speeds (n1, n4, n5);

[0017] Figure 2 Calculate the frequency line from the static frequency and the dynamic frequency at the maximum speed n1;

[0018] Figure 3 The patch is placed at the point of maximum vibration stress;

[0019] Figure 4 The patch is placed at the location of the second largest stress with a relatively small stress gradient;

[0020] Figure 5 Determining the orientation of strain gauges;

[0021] Figure 6 Schematic diagram of strain gauge angle deviation;

[0022] Figure 7 Schematic diagram of strain gauge position deviation;

[0023] Figure 8 This is a schematic diagram of the static leaf patch scheme;

[0024] Figure 9 A flowchart of the method of the present invention. Detailed Implementation

[0025] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0026] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0027] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this invention, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0028] like Figure 9 The method shown is a design method for measuring and designing multi-order dynamic stress of engine blades based on strain gauges. The method includes:

[0029] S1: Determine the range of blade vibration, specifically:

[0030] The upper frequency limit f for vibration analysis of rotor and stator blades in aero-engines, or compressor and turbine blades. s satisfy:

[0031] fs =n max / 60*J max *S (1)

[0032] In the formula, n max J is the maximum operating speed of the blade. max Given the maximum dominant excitation order of the blade and the S-margin, the upper limit of the blade frequency, f, can be determined based on vibration calculations. s The corresponding highest vibration order.

[0033] Furthermore, the margin is generally taken as 1.1 (1.2 may be used for special engines). The value of Jmax is generally determined by considering the following:

[0034] a) The number of adjacent stages (previous stage and next stage) of the rotor (stationary) blades;

[0035] b) For turbine moving blades, excitation of twice the number of stationary blades in adjacent stages should be considered;

[0036] c) If the adjacent stages of the rotor blades have a small number of support plates, then excitation with twice the number of support plates should be considered.

[0037] Determine f s After obtaining the value, the vibration order corresponding to the upper limit of the blade frequency fs can be determined based on vibration calculations.

[0038] S2: Analyze the blade's intensity and vibration based on the range of blade vibration, specifically:

[0039] A finite element model of the aero-engine blade was established, and strength and modal analyses were conducted under the engine's maximum speed condition or the maximum condition of this test. Specifically, the vibration order in the modal analysis was determined by the upper frequency f. s Sure;

[0040] Strength analysis and modal analysis both use the same finite element model to calculate the dynamic frequency f of the blade at different rotational speeds. D The static frequency f of the blade is obtained by calculating the modes of the blade without considering rotational speed, aerodynamic force and temperature field load.

[0041] Furthermore, the following requirements should be followed when establishing a finite element model:

[0042] a) For the integral bladed disk, the disk mesh can be appropriately sparse when establishing the finite element model, while the mesh of the leading and trailing edges of the blades and the blade root should be appropriately refined to ensure the quality of the mesh.

[0043] b) The mesh size should be appropriately controlled according to the performance of the computer used. The mesh size should not be too large, which would lead to excessive time consumption for modal analysis and subsequent constraint value analysis. For example, for a workstation with 20 cores and 64GB of memory, the number of elements in the finite element model of a fan, compressor blade, or integral bladed disk is generally tens of thousands to two or three hundred thousand. When performing strength and vibration analysis of hollow turbine blades before patch design, the air film pores in the blade body can be ignored, and the small fillets and chamfers in the blade body cavity can be neglected. The size of the finite element model should be controlled as much as possible (the number of nodes should preferably be controlled within one million).

[0044] c) To facilitate subsequent limit value analysis via the program, the same finite element model is required for both strength analysis and modal analysis.

[0045] d) Based on the need for troubleshooting, the mesh at the location of the fault or crack should be further refined.

[0046] Generally, in addition to calculating the modes at different speeds to obtain the dynamic frequency f of the blade, it is also necessary to... D Furthermore, it is necessary to calculate the blade's modal characteristics without considering loads such as rotational speed, aerodynamic forces, and temperature field to obtain the blade's static frequency f. D .

[0047] S3: Determine the vibration monitoring order of the blade, and the placement and orientation of the strain gauges. Specifically...

[0048] Vibration monitoring order

[0049] Since there may be many resonance orders within the blade's operating speed range, the vibration orders that need to be monitored in the test should be determined. The vibration orders that should be focused on include:

[0050] f) The first three bending vibrations, the first two torsional vibrations, and the first two chord bending vibrations of the fan / compressor rotor blades;

[0051] g) The first two bending vibrations, the first two torsional vibrations, and the first chord bending vibration of the fan / compressor stator blades.

[0052] h) The first four beam modes of the turbine blade with non-obvious chord bending characteristics and the first two flat plate modes with chord bending characteristics;

[0053] i) Spanwise bending mode of a single turbine guide vane;

[0054] j) The resonance order induced by the excitation factor near the important rotational speed;

[0055] To determine the monitoring order of the blade, resonance analysis of the blade is required. There are two ways to determine the frequency line in the resonance rotation speed diagram of the blade:

[0056] a. Connect the static frequency of the blade and the dynamic frequency at different speeds to form a frequency line showing the change of the blade with speed. Figure 1 b. Calculate only the stationary frequency f of the blade and the dynamic frequency n at a single rotational speed. Then, solve the dynamic frequency coefficient B by inversely solving the relationship between the dynamic frequency and the stationary frequency. Calculate the dynamic frequency at different rotational speeds using equation (2). Finally, draw the frequency line of the blade, as shown in the figure. Figure 2 As shown, the speed selected for calculating the dynamic frequency is either the speed at which the blade temperature is highest or the maximum operating speed. The relationship between the dynamic frequency and the static frequency satisfies:

[0057]

[0058] The main excitation factors to be considered on the rotor (stator) blade resonance speed diagram are:

[0059] a) Orders 1-4 (engine airflow distortion and low-order excitation);

[0060] b) Number of stationary (rotor) blades S in the first two stages and the last stage;

[0061] c) The difference in the number of stationary (rotor) blades between the first two stages, and the difference in the number of stationary (rotor) blades between the first and second stages, C;

[0062] d) For structural factors such as support plates, which are relatively few in number, their second harmonic excitation on the rotor blades should also be considered. Some non-structural factors that caused significant vibrations in the previous tests also contributed to the vibration.

[0063] The placement and orientation of the strain gauges include:

[0064] The strain gauge placement is determined by monitoring multiple vibrations and synthesizing the results of these vibrations. This includes:

[0065] Based on the stress distribution of multi-order vibration, determine the patch position that can simultaneously monitor multi-order vibration;

[0066] The location where the ratio of the multi-order vibration stress to the maximum vibration stress of each order is greater than a preset value (0.7) is used as the strain gauge placement position. When the stress gradient at the location of the maximum modal vibration stress of the designed monitoring order is small or less than the preset value, the strain gauge can be placed at the maximum vibration stress location. When the maximum vibration stress point of the designed monitoring order is located at a guide circle, sharp corner, or location with a large stress gradient where the strain gauge cannot be placed, the strain gauge placement position is selected at the second largest stress point with a gradient less than the preset value. When a single strain gauge is designed to monitor multiple orders of blade vibration, the location where all multi-order vibration stresses are greater than the preset value is selected as the strain gauge placement position based on the modal vibration stress distribution of the vibration monitoring order.

[0067] For example, after determining the vibration order of the blade that needs to be monitored in the test, the strain gauge placement position is determined based on the modal vibration stress distribution:

[0068] a) If the stress gradient at the location of the maximum relative vibration stress in the design monitoring order is also small, and the strain gauge can be easily attached, then the strain gauge can be attached at the location of the maximum vibration stress, such as... Figure 3 The location of the maximum value of the third principal stress in the modal vibration of the blade is region A. The stress gradient is also relatively small in this region, and the structure is flat, which facilitates the application of strain gauges. Therefore, the strain gauge is placed in region A.

[0069] b) If the maximum vibration stress point of the designed monitoring order is located at a guide circle, sharp corner, or location with a large stress gradient where strain gauges cannot be attached, then the strain gauge attachment point should be selected at the second largest stress point with a smaller stress gradient. For example... Figure 4 The location of the maximum value of the third principal stress of the relative vibration of the blade is region B. However, the stress gradient is large here and it is in the rounded corner area of ​​the blade root, so strain gauges cannot be attached. Therefore, the second largest stress region, C, with a smaller stress gradient and easier strain gauge attachment, is determined as the strain gauge attachment location.

[0070] c) When designing a single strain gauge to monitor multiple vibrations of a blade, the location where the stress of all vibration orders is relatively large should be selected as the strain gauge placement location based on the relative vibration stress distribution of the vibration orders to be monitored. For example:

[0071] The maximum modal vibration stresses of the 6th-8th and 10th orders of the adjustable guide vane are all located on the front side of the root boss. It is possible to initially design a strain gauge at the bottom of the blade to simultaneously monitor the 6th-8th and 10th orders of the adjustable guide vane.

[0072] The placement direction includes:

[0073] Based on the modal vibration stress distribution, the initial placement position of a strain gauge can be determined when it can simultaneously monitor multiple orders of blade vibration. Since the principal stress directions of different orders of vibration may differ at the same location, the strain gauge's placement orientation needs to be further determined after the initial placement position is determined. That is, based on the modal vibration stress distribution, the initial placement position of a strain gauge can be determined when it can simultaneously monitor multiple orders of blade vibration. Since the principal stress directions of different orders of vibration may differ at the same location, the strain gauge's placement orientation needs to be further determined after the initial placement position is determined, satisfying the following:

[0074] a) If a strain gauge is designed to monitor only a certain order of vibration, the strain gauge's mounting direction can be determined as the first / third principal strain direction of the modal vibration at the mounting position of that order of vibration.

[0075] b) If the initial design of the strain gauge simultaneously monitors multiple vibrations, and the direction of the strain gauge is chosen as the patch direction based on the principal stress directions of the vibrations at the patch location, and the angle between the principal stress directions of each vibration monitored in the initial design and the determined patch direction is no greater than 30°, then the strain gauge can simultaneously monitor the corresponding multiple vibrations. See [reference needed]. Figure 5As shown;

[0076] c) If the strain gauge is initially designed to monitor multiple vibrations simultaneously, but the angle between the principal stress direction of a certain vibration at the patch position and the principal stress directions of the other vibrations is greater than 40°, then the strain gauge cannot monitor that vibration simultaneously.

[0077] S4: The limit value of the strain gauge is calculated based on the vibration principle and the maximum vibration hazard factor. Specifically, the limit value is not the maximum value, but the alarm value of a single vibration order monitored during the test. According to the vibration principle, when the blade vibrates according to a certain mode during the test, its actual vibration mode is similar to the mode shape, and the actual vibration stress distribution is similar to the modal vibration stress distribution.

[0078] Calculate the limits for strain gauges, including the allowable vibration stress at each node, where:

[0079] Based on the steady-state equivalent stress σ at the i-th node in the blade static strength calculation results mi The minimum tensile limit σ of the material at the operating temperature of node i. bi The fatigue limit σ when the stress ratio at the operating temperature of the i-th node is -1 -1i The allowable vibration stress σ at the i-th node on the blade can be obtained from the formula shown in equation (3). ai Fatigue limit σ- 1i Take the fatigue limit test value of the component; if there is no fatigue limit, take the fatigue limit test value of a component with the same performance or function; if neither is available, take the fatigue limit of the material minus 3σ; for stainless steel blades, take the fatigue life N. f =1×10 7 The fatigue limit; for non-ferrous metal alloy blades, take the fatigue life N. f =3×10 7 The fatigue limit; for titanium alloy blades, take the fatigue life N. f =1×10 9 The fatigue limit; if not, take the fatigue life N. f =3×10 7 The fatigue limit;

[0080]

[0081] The calculation of the maximum vibration hazard factor includes:

[0082] The vibration stress σ at any node on the blade in the experiment zi Not greater than the corresponding allowable vibration stress σ ai , i.e. σ ai ≥σ ziWhen a blade experiences a certain level of resonance, the node on the blade where the vibration stress first exceeds its allowable vibration stress is the most dangerous point for high-cycle fatigue. The high-cycle fatigue risk at any node on the blade depends on the magnitude of the vibration stress and the allowable vibration stress value at that node. This is determined by the allowable vibration stress σ at any node on the blade. ai and relative modal stress σ xzi The vibration hazard factor K of the node is defined as shown in Equation (4). The larger the value of K, the more dangerous the node is under the resonance of this order. The maximum value of the vibration hazard factor in the blade node is Kmax as shown in Equation (5). The corresponding node is the Kmax point. The Kmax point is the most dangerous point of high cycle fatigue of the blade under this vibration order.

[0083]

[0084] K max =max(K) i (5);

[0085] The calculation of dynamic stress limits includes: ensuring that the vibration stress at all nodes on the blade does not exceed the corresponding allowable vibration stress when a certain order of resonance occurs; and when the vibration stress at point Kmax equals the allowable vibration stress, the vibration stress at other nodes on the blade is the maximum allowable vibration stress σ at that node under that order of resonance. azi At this point, σ of any node azi The modal vibration stress σ of this node can be determined. xzi The Kmax value is obtained from equation (6), and the maximum allowable vibration stress of any node is obtained from equation (6):

[0086]

[0087] A) For point Kmax, the maximum allowable vibration stress σ az It is equal to its allowable vibration stress σ a ;

[0088] B) For nodes other than Kmax, the maximum allowable vibration stress σ azi Less than its allowable vibration stress σ ai ;

[0089] The maximum allowable vibration stress corresponding to the node at the strain gauge attachment location obtained from equation (5) is the dynamic stress limit value of the strain gauge under that vibration order. Since strain gauges are generally attached according to the principal stress direction of the monitoring order, σ is used when calculating the dynamic stress limit value of the strain gauge. xzi Generally, the stress absolute value of the larger of the first or third principal stress of the patch node is taken;

[0090] The conversion of dynamic strain limit values ​​includes:

[0091] Since the strain gauges actually measured the dynamic strain at the patch location during the experiment, the dynamic stress limit value was converted to the dynamic strain limit value, including:

[0092] a) For blades made of isotropic materials, and when the stress state at the strain gauge location is close to a uniaxial stress state, the corresponding dynamic strain limit value can be obtained from the dynamic stress limit value according to Hooke's law.

[0093] b) Under service conditions, the strain gauge patch location on the blade is usually not under uniaxial stress, and the dynamic strain limit ε xz The relative vibration strain ε at the strain gauge patch location can be directly obtained. xz According to equation (7),

[0094] Due to the dynamic strain limit ε az Since the values ​​are generally small, they are inconvenient to use in experiments, and are usually converted into micro-strain (με) for use.

[0095] Calculation of multi-order limit values ​​for strain gauges: When using a single strain gauge to monitor multiple resonances in a blade, it is necessary to calculate the multi-order vibration limit values ​​for each strain gauge separately. The main difference between this method and the method for calculating the limit values ​​of a single-order strain gauge is that, since the strain gauge needs to monitor multiple vibrations simultaneously, the strain gauge placement direction is not completely consistent with the first or third principal stress direction of each vibration. Therefore, it is necessary to establish a local coordinate system and extract the modal vibration stress and strain of each vibration in the strain gauge monitoring direction (i.e., the strain gauge placement direction), including:

[0096] A local coordinate system is established, and the relative vibration stress and strain components of each vibration order in the strain gauge patch direction are extracted to determine the maximum relative vibration stress and strain of the blade within one cycle; the strain components ε of each vibration order in the strain gauge monitoring direction at the strain gauge patch location are obtained. x Then, the dynamic strain limit value of each vibration is calculated using equation (8) (each vibration corresponds to a limit value);

[0097]

[0098] c) Since the strain values ​​are generally very small and not convenient to monitor and use in experiments, the dynamic strain limit value is converted into a micro-strain με before use;

[0099] d) Due to patch error, differences between actual vibration and calculated results, and factors related to the actual engine operating history, in order to ensure test safety, the dynamic strain limit value needs to be used with a certain reserve N. The reserve coefficient N can be selected with reference to the following different situations, that is, the selection range of the reserve coefficient N:

[0100] 1. If the strain gauge readings during the test are effective values, N is taken as 2.5;

[0101] 2. If the strain gauge measures the amplitude during the test, N is taken as 1.67;

[0102] 3. Since the fatigue limit value is generally used for calculation, the -3σ value is generally used. Therefore, in specific tests such as dynamic stress measurement tests, N can be taken as 1.0. During the test, monitoring should be strengthened, and it is sufficient to ensure that the vibration response does not continuously exceed the limit.

[0103] S5: Calculate the multi-order conversion factors and multi-order limit values ​​for the strain gauge. Specifically,

[0104] Calculate the multi-order conversion factors of the strain gauge, including:

[0105] Establish the vibration stress relationship between the strain gauge measurement position and the preset position, where the preset position is the location of interest for the strain gauge, such as the maximum vibration stress point and Kmax point, and satisfy the following:

[0106] In the formula, σ' eqm - Equivalent stress value of modal vibration at the preset position; σ eqm - The measured equivalent vibration stress at the preset position; σ' xt - Modal vibration stress value in the direction of the strain gauge at the patch location; σ xt - Measured vibration stress values ​​in the direction of the strain gauge at the patch location;

[0107] The strain gauge angle sensitivity analysis method includes: the impact of changes in strain gauge position and angle on the limit value; when performing strain gauge angle sensitivity analysis, the difference between the actual strain gauge angle and the designed strain gauge angle is assumed to be β, see... Figure 6 In the figure, the angle being too large or too small refers to the angle between the strain gauge direction and the marking line. The corresponding limit value of the strain gauge is obtained by calculating the angle after deviation at the designed patch position. For strain gauges attached close to the leading and trailing edges of the blade, the deviation angle β-3° is used, and β=5° is used for the rest of the analysis.

[0108] Determine the deviation between the designed and actual positions, including: when performing strain gauge position sensitivity analysis, assuming the offset distance between the actual and designed strain gauge positions is R, see... Figure 7 Four points on a circle with radius R are selected as possible deviation locations for the strain gauges, as shown in the diagram, at the designed strain gauge placement locations. The corresponding limit values ​​for the strain gauges are then calculated at these possible deviation locations using the designed strain gauge angle. The magnitude R of the strain gauge position deviation should be determined based on the specific problem.

[0109] a) For fan blades with attached room temperature strain gauges, R = 2mm can be used as a reference.

[0110] b) For turbine blades with high-temperature strain gauges, R = 1 mm can be used as a reference.

[0111] Sensitivity quantification indicators include: the deviation Δ between the limit value calculated according to formula (10) of the strain gauge angle or position deviation and the limit value of the patch design result, satisfying:

[0112] The limit value after deviation is recalculated using Formula 8, and ε is re-extracted after determining the angle and position after deviation. x .

[0113] S6: Determine the vibration order that the strain gauge can simultaneously monitor through sensitivity analysis. Specifically,

[0114] For solid blades, if the projection of the relative vibration stress value of the multi-order vibration at the strain gauge location onto the monitoring direction is much smaller than the relative vibration stress value at the preset location, the conversion factor ranges from 2 to 3.

[0115] However, for hollow blades and adjustable blades, since the maximum vibration stress of many vibration orders is located in areas where blade supports cannot be applied, such as rounded corners or the interior of the hollow structure, the minimum conversion factor for suitable blade support locations may not be less than 2. In such cases, the conversion factor requirement should be determined based on the specific structural characteristics and vibration stress distribution. A preferred conversion factor is between 3 and 5. For example... Figure 3 The adjustable guide vane shown was ultimately determined to have a strain gauge attached at point A parallel to the lower edge of the blade, which could simultaneously monitor the 6th-8th and 10th order vibrations of the adjustable guide vane. The conversion factors of the strain gauge at the location of the maximum vibration stress for these four orders of vibration were 3.2, 3.0, 4.2 and 2.3, respectively.

[0116] Sensitivity bias requirements include:

[0117] The sensitivity quantification index deviation Δ is calculated according to formula (10) in step 9.3. If the deviation Δ is too large, it means that it is no greater than (33%), indicating that the strain gauge pasting position and angle have a great influence on the limit value. The error in manual patching will cause a large change in the dynamic stress limit value, which is not conducive to vibration monitoring and test result analysis. Therefore, if the sensitivity quantification index Δ of the strain gauge to a certain order of vibration is too large, it means that the strain gauge is not suitable for monitoring that order of vibration.

[0118] Since the limit values given in the patch design generally consider the limit values with a 2.5-fold safety factor, and when the measured signal in the test is the maximum transient value, a safety factor of 1.67 is sufficient to meet the test monitoring requirements. Therefore, when the limit value of the strain gauge after patch deviation is greater than the designed patch limit value (i.e., Δ>0), it is on the safe side to monitor with the designed limit value in the test; when the limit value after patch deviation is less than the designed patch limit value (i.e., Δ<0), it is required that the actual patch limit value after deviation is not less than 2 / 3 of the designed patch limit value (at this time, the actual safety factor of the originally given designed limit value considering a 2.5-fold safety factor is not less than 1.67, still meeting the requirements), that is, it is required that the deviation |Δ| of the sensitivity quantification index ≯33%.

[0119] Secondly, a design method for determining the priority of the reliability of the strain gauge measurement results is provided. Using some or all of the above methods, the priority of the reliability of the strain gauge measurement results can be determined according to the magnitude of the conversion coefficient. It is characterized in that it includes:

[0120] Calculate the limit values and conversion coefficients of the strain gauges under each order of vibration of the blade. For the same order of vibration, multiple strain gauges at different positions are used for monitoring. In actual analysis, the results measured by the strain gauge with the smallest conversion coefficient are the most reliable.

[0121] Example: 1) Determine the order

[0122] At a measured response frequency, the responses of different strain gauges (numbered A, B, C, D...) on the same blade are a, b, c, d,... respectively;

[0123] The limit values of the strain gauges for vibration order A are A1, B1, C1, D1,...

[0124] The limit values of the strain gauges for vibration order B are A2, B2, C2, D2,...

[0125] Definition: Response vector = (a, b, c, d,...)

[0126] Limit value vector A (A, for example, is the 3rd order vibration) = (A1, B1, C1, D1,...)

[0127] Limit value vector B (B, for example, is the 4th order vibration) = (A2, B2, C2, D2,...) <000**********336>The included angle between the response vector and the limit value vector A is θ

[0129] The included angle between the response vector and the limit value vector B is η

[0130] Then the cosines of θ and η can be obtained from the following formula

[0131]

[0132]

[0133] The vibration order corresponding to the smaller of θ and η is taken as the vibration order of a certain response frequency. If there is a significant difference between the actual mode shape and the calculated mode shape, the cause of this phenomenon should be analyzed, such as model deviation, inaccuracy of existing modal analysis methods, or the presence of factors other than resonance.

[0134] Secondly, a method for identifying vibration orders is provided. Using the above method and based on the design results of multi-order constraint values, this method is applicable to the identification of vibration orders corresponding to the measured response frequencies of blades, including:

[0135] For strain gauges at different positions on the same blade, the response values ​​of strain gauges at different positions are measured at a certain response frequency, and the interval order of blade vibration corresponding to the response frequency is determined. The interval order includes the first order point and the second order point.

[0136] The response values ​​of strain gauges at different positions on the same blade at the aforementioned response frequency are defined as the response vector;

[0137] The constraint values ​​of strain gauges at different positions on the blade corresponding to the first-order point are defined as the first-order point constraint value vector, and the constraint values ​​of strain gauges at different positions on the blade corresponding to the second-order point are defined as the second-order point constraint value vector.

[0138] The angles between the response vector and the first-order point (vibration order of the strain gauge) limit value vector, and the angle between the response vector and the second-order point (vibration order monitored by the strain gauge and adjacent to the first order) limit value vector are calculated respectively. The vibration order corresponding to the smaller angle is taken as the blade vibration order corresponding to a certain response frequency. And / or, after determining that the measured response frequency is a specific order of vibration based on the vibration analysis results, the angle between the response vector and the limit value vector under that order is calculated. If the angle is less than 10°, it indicates that the measured vibration mode and the modal vibration mode are well combined. If it is greater than 20°, it indicates that there is a significant difference between the measured vibration mode and the modal vibration mode. The reasons for this phenomenon may be that the model is out of tolerance, the existing modal analysis method is inaccurate, or there are other factors other than resonance.

[0139] Example 1:

[0140] The calculated third-order frequency of a certain blade is 1200Hz and the fourth-order frequency is 1700Hz. ABCD strain gauges are attached to the same blade. The third-order vibration limit values ​​of the ABCD strain gauges are 100με, 80με, 30με, and 120με, respectively; the fourth-order vibration limit values ​​of the ABCD strain gauges are 100με, 50με, 120με, and 50με, respectively.

[0141] In the experiment, the measured responses of strain gauges ABCD at a resonance response frequency of 1500 Hz were 90 με, 80 με, 45 με, and 90 με, respectively.

[0142] Response vector = (90, 80, 45, 90)

[0143] Third-order constraint value vector = (100, 80, 30, 120)

[0144] Fourth-order constraint value vector = (100, 50, 120, 50)

[0145] Using formula 11 or 12 above, the angle between the response vector and the third-order constraint vector is 9.6°, and the angle between the response vector and the fourth-order constraint vector is 31.7°. Therefore, the measured resonance at 1500Hz should be the third-order vibration of the blade.

[0146] Example 2:

[0147] The calculated first-order frequency of a certain blade is 200Hz, the second-order frequency is 1000Hz, and the third-order frequency is 2000Hz.

[0148] The resonance at a frequency of 1050 Hz was actually measured in the experiment. According to the vibration analysis results, 1050 Hz is the second-order vibration of the blade. The second-order vibration limit values ​​of strain gauges ABCD on the same blade are 100 με, 90 με, 50 με, and 120 με, respectively.

[0149] 1) If the responses of strain gauges ABCD at the measured resonance response frequency of 1050Hz are 80με, 80με, 30με, and 120με respectively, then the angle between the response vector and the second-order constraint vector is 7.4°, indicating that the measured mode shape and the calculated mode shape (mode shape) of the second-order vibration are in good agreement.

[0150] 2) If the measured response of strain gauges ABCD at a resonance response frequency of 1050Hz in the experiment is 80με, 90με, 80με, and 50με respectively, then the angle between the response vector and the second-order constraint vector is 24.2°. This indicates that there is a significant difference between the measured mode shape and the calculated mode shape (mode shape) of the second-order vibration. It is necessary to analyze the reasons for this phenomenon, such as model deviation, inaccuracy of existing modal analysis methods, or the existence of other factors besides resonance.

[0151] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A design method for measuring and controlling multi-order dynamic stress in engine blades based on strain gauges, characterized in that, The method includes: S1: Determine the range of blade vibration, wherein the blade is a compressor rotor / stator blade or a turbine rotor / stator blade, and the vibration range is defined by the upper frequency f. s This means that the following conditions are met: f s =n max / 60 J max S (1) In the formula, n max J is the maximum operating speed of the blade. max The maximum primary excitation order of the blade, S-margin; The upper limit of the blade frequency can be determined by vibration calculations. s The corresponding highest vibration order; S2: Analyze the blade's strength and vibration based on the range of blade vibration; S3: Determine the vibration monitoring order of the blade, and the location and orientation of the strain gauges. The placement and orientation of the strain gauges in S3 include: The strain gauge placement is determined by monitoring multiple vibrations and synthesizing the results of these vibrations. This includes: Based on the stress distribution of multi-order vibration, determine the patch position that can simultaneously monitor multi-order vibration; The location where the ratio of the multi-order vibration stress to the maximum vibration stress of each order is greater than a preset value is used as the strain gauge placement position. When the stress gradient at the location of the maximum modal vibration stress of the designed monitoring order is small or less than the preset value, the strain gauge can be placed at the maximum vibration stress. When the maximum vibration stress point of the designed monitoring order is at the guide circle, sharp corner, or location with a large stress gradient where the strain gauge cannot be placed, the strain gauge placement position is selected at the second largest stress point with a gradient less than the preset value. When a single strain gauge is designed to monitor multiple orders of blade vibration, the location where all multi-order vibration stresses are greater than the preset value is selected as the placement position based on the modal vibration stress distribution of the vibration monitoring order. The placement direction includes: Based on the modal vibration stress distribution, the initial placement position of a strain gauge can be determined when it can simultaneously monitor multiple orders of blade vibration. Since the principal stress directions of different orders of vibration may differ at the same location, after initially determining the placement position, it is necessary to further determine the strain gauge placement orientation to satisfy the following conditions: a) If a strain gauge is designed to monitor only a certain order of vibration, the strain gauge's mounting direction can be determined as the first / third principal strain direction of the modal vibration at the mounting position of that order of vibration. b) If the strain gauge is designed to monitor multiple vibrations simultaneously, and the direction of the strain gauge is chosen as the middle direction based on the principal stress direction of the vibrations at the patch position, and the angle between the principal stress direction of each vibration monitored in the preliminary design and the determined patch direction is no greater than 30°, then the strain gauge can monitor the corresponding multiple vibrations simultaneously. c) If the strain gauge is initially designed to monitor multiple vibrations simultaneously, but the angle between the principal stress direction of a certain vibration at the patch position and the principal stress direction of the other vibrations is greater than 40°, then the strain gauge cannot monitor that vibration simultaneously. S4: Calculate the limit value of the strain gauge based on the vibration principle and the maximum vibration hazard factor; S5: Calculate the multi-order conversion factor and multi-order limit value of the strain gauge; S6: Determine the vibration order that the strain gauge can monitor simultaneously through sensitivity analysis.

2. The design method according to claim 1, characterized in that, S2 include: A finite element model of the aero-engine blade was established, and strength and modal analyses were conducted under the engine's maximum speed condition or the maximum condition of this test. Specifically, the vibration order in the modal analysis was determined by the upper frequency f. s Sure; Strength analysis and modal analysis both use the same finite element model to calculate the dynamic frequency f of the blade at different rotational speeds. D The static frequency f of the blade is obtained by calculating the modes of the blade without considering rotational speed, aerodynamic force and temperature field load.

3. The design method according to claim 2, characterized in that, In S3, the vibration monitoring order of the blade is determined. Since there may be many resonance orders within the operating speed range of the blade, the vibration orders that need to be focused on during the test are identified. The vibration orders that should be focused on the blade include: a) The first three bending vibrations, the first two torsional vibrations, and the first two chord bending vibrations of the fan / compressor rotor blades; b) The first two bending vibrations, the first two torsional vibrations, and the first chord bending vibration of the fan / compressor stator blades. c) The first four beam modes of the turbine blade that do not exhibit obvious chord bending characteristics and the first two flat plate modes that exhibit chord bending characteristics; d) Spanwise bending mode of a single turbine guide vane; e) The resonance order induced by the excitation factor near the important rotational speed; To determine the monitoring order of the blade, resonance analysis of the blade is required. There are two ways to determine the frequency line in the resonance rotation speed diagram of the blade: a) Connect the static frequency of the blade and the dynamic frequency at different speeds to form a frequency line of the blade as the speed changes; b) Calculate only the stationary frequency f of the blade and the dynamic frequency n at a single rotational speed. Then, solve the dynamic frequency coefficient B inversely based on the relationship between the dynamic frequency and the stationary frequency. Calculate the dynamic frequency at different rotational speeds using equation (2). Finally, plot the frequency line of the blade. The rotational speed for calculating the dynamic frequency is selected based on the highest operating temperature of the blade or the maximum operating speed. The relationship between the dynamic frequency and the stationary frequency satisfies: (2)。 4. The design method according to claim 3, characterized in that, The limits for calculating strain gauge values ​​in S4 include: The allowable vibration stress calculation for each node includes: Based on the steady-state equivalent stress at node i in the blade static strength calculation results Minimum tensile strength of the material at the operating temperature of node i Fatigue limit when the stress ratio at the operating temperature of node i is -1 The allowable vibration stress at the i-th node on the blade can be obtained from the formula shown in equation (3). Fatigue limit Take the fatigue limit test value of the component; if there is no fatigue limit, take the fatigue limit test value of a component with the same performance or function; if neither is available, take the fatigue limit of the material minus 3σ; for stainless steel blades, take the fatigue life N. f =1×10 7 The fatigue limit; for non-ferrous metal alloy blades, take the fatigue life N. f =3×10 7 The fatigue limit; for titanium alloy blades, take the fatigue life N. f =1×10 9 The fatigue limit; if not, take the fatigue life N. f =3×10 7 The fatigue limit; （3）； The calculation of the maximum vibration hazard factor includes: Vibration stress at any node on the blade during the experiment Not greater than the corresponding allowable vibration stress ,Right now When a blade experiences a certain level of resonance, the node on the blade where the vibration stress first exceeds its allowable vibration stress is the most dangerous point for high-cycle fatigue. The high-cycle fatigue risk at any node on the blade depends on the magnitude of the vibration stress and the allowable vibration stress value at that node. and modal vibration stress The vibration hazard factor K of the node is defined as shown in equation (4). The larger the value of K, the more dangerous the node is under the resonance of this order. The maximum value of the vibration hazard factor in the blade node is Kmax as shown in equation (5). The corresponding node is the Kmax point. The Kmax point is the most dangerous point of high cycle fatigue of the blade under this vibration order. （4） K max =max(K i )(5); The calculation of dynamic stress limits includes: ensuring that the vibration stress at all nodes on the blade does not exceed the corresponding allowable vibration stress when a certain order of resonance occurs; and when the vibration stress at point Kmax equals the allowable vibration stress, the vibration stress at other nodes on the blade is the maximum allowable vibration stress at that node under that order of resonance. At this point, any node's The modal vibration stress of this node can be determined. The Kmax value is obtained from equation (6), and the maximum allowable vibration stress of any node is obtained from equation (6): A) For point Kmax, the maximum allowable vibration stress Equal to its allowable vibration stress ; B) For nodes other than Kmax, the maximum allowable vibration stress Less than its allowable vibration stress ; The maximum allowable vibration stress corresponding to the node at the strain gauge patch location obtained from equation (5) is the dynamic stress limit value of the strain gauge under that vibration order. The conversion of dynamic strain limit values ​​includes: Since the strain gauges actually measured the dynamic strain at the patch location during the experiment, the dynamic stress limit value was converted to the dynamic strain limit value, including: a) For blades made of isotropic materials, and when the stress state at the strain gauge location is close to a uniaxial stress state, the corresponding dynamic strain limit value can be obtained from the dynamic stress limit value according to Hooke's law. b) Under service conditions, the strain gauge patch location on the blade is usually not under uniaxial stress, and the dynamic strain limit value is... The relative vibration strain at the strain gauge patch location can be directly obtained. According to equation (7), （7）； Calculation of multi-order limit values ​​for strain gauges, including: A local coordinate system is established, and the modal vibration stress and strain components of each vibration order in the strain gauge patch direction are extracted to determine the maximum relative vibration stress and strain of the blade within one cycle; the strain components of each vibration order in the strain gauge monitoring direction at the strain gauge patch location are obtained. Then, the dynamic strain limit values ​​for each order of vibration are calculated using equation (8). Limit value = (8); a) Since the strain values ​​are generally very small and not convenient to monitor and use in experiments, the dynamic strain limit value is converted into a micro-strain με before use; b) Due to patch error, the difference between actual vibration and calculated results, and factors related to the actual engine operating history, in order to ensure test safety, the dynamic strain limit value needs to be used with a certain reserve N. The reserve coefficient N can be selected with reference to the following different situations, that is, the selection range of the reserve coefficient N:

1. If the strain gauge readings during the test are effective values, N is taken as 2.5; 2. If the strain gauge measures the amplitude during the test, N is taken as 1.67; 3. Since the calculation limit value uses the fatigue limit value of -3σ, N is taken as 1.0 in the dynamic stress measurement test.

5. The design method according to claim 4, characterized in that, S5 calculates the multi-order conversion factors for strain gauges, including: Establish the vibration stress relationship between the strain gauge measurement position and the preset position, satisfying: In the formula, - Equivalent stress value of modal vibration at preset position; - Measured equivalent vibration stress at the preset location; - Modal vibration stress values ​​in the direction of the strain gauge at the patch location; - Measured vibration stress values ​​in the direction of the strain gauge at the patch location; The strain gauge angle sensitivity analysis method includes: the impact of changes in strain gauge position and angle on the limit value; when performing strain gauge angle sensitivity analysis, the difference between the actual strain gauge angle and the designed strain gauge angle is set to β. The corresponding limit value of the strain gauge is obtained at the designed strain gauge position by the angle after the deviation. For strain gauges attached close to the leading and trailing edges of the blade, the deviation angle β = 3°, and α = 5° is taken for the rest of the analysis. Determine the deviation between the design position and the actual position, including: when performing strain gauge position sensitivity analysis, set the offset distance between the actual patch position and the design patch position as R, select 4 points on the circle with radius R on the blade surface where the patch is designed to be patched as the deviation position of the strain gauge, and obtain the corresponding limit value of the strain gauge at the deviation position with the design patch angle. For fan blades with room temperature strain gauges, R=2mm can be taken as a reference. For turbine blades with high-temperature strain gauges, R=1mm can be used as a reference. Sensitivity quantification indicators include: the deviation Δ between the limit value calculated according to formula (10) of the strain gauge angle or position deviation and the limit value of the patch design result, satisfying: The deviation limit value is recalculated using Formula 8, and the angle and position after deviation are determined and then extracted again. .

6. The design method according to claim 5, characterized in that, The methods in S6 include: For solid blades, the conversion factor for the maximum vibration stress point of the strain gauge design monitoring order should not be greater than 3. For hollow blades and adjustable blades, the conversion factor for the maximum vibration stress point of the strain gauge design monitoring order is between 3 and 5. Sensitivity bias requirements include: If the sensitivity quantification index deviation Δ is greater than 33%, it indicates that the strain gauge placement position and angle have a significant impact on the limit value. Errors in manual strain gauge placement will cause a large change in the dynamic stress limit value, which is not conducive to vibration monitoring and test result analysis. Therefore, it means that the strain gauge is not suitable for monitoring this order of vibration. When the measured signal in the experiment is the maximum transient value, the reserve coefficient is taken as 1.

67.

7. A design method for determining the reliability priority of strain gauge measurement results, characterized in that, Using the method described in any one of claims 1 to 6, the reliability priority of strain gauge measurement results can be determined according to the magnitude of the conversion factor, characterized in that it includes: The limiting values ​​and conversion factors of strain gauges under each order of blade vibration were calculated. The same order of vibration was monitored by multiple strain gauges at different locations. In actual analysis, the results measured by the strain gauge with the smallest conversion factor are the most reliable.

8. A method for identifying vibration orders, characterized in that, Using the method described in any one of claims 1 to 6, and based on the design results of multi-order constraint values, it is applicable to the identification of the vibration order corresponding to the measured response frequency of the blade, including: For strain gauges at different positions on the same blade, the response values ​​of strain gauges at different positions are measured at a certain response frequency, and the interval order of blade vibration corresponding to the response frequency is determined. The interval order includes the first order point and the second order point. The response values ​​of strain gauges at different positions on the same blade at the aforementioned response frequency are defined as the response vector; The constraint values ​​of strain gauges at different positions on the blade corresponding to the first-order point are defined as the first-order point constraint value vector, and the constraint values ​​of strain gauges at different positions on the blade corresponding to the second-order point are defined as the second-order point constraint value vector. The angles between the response vector and the first-order point constraint vector, and the angle between the response vector and the second-order point constraint vector are respectively obtained. The vibration order corresponding to the smaller angle is taken as the blade vibration order corresponding to a certain response frequency. And / or, after determining that the measured response frequency is a certain order of vibration based on the vibration analysis results, the angle between the response vector and the constraint vector of that order is calculated. If the angle is less than 10°, it indicates that the measured vibration mode and the modal vibration mode are well combined; if it is greater than 20°, it indicates that there is a significant difference between the measured vibration mode and the modal vibration mode.

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