WO2020192623A2 - 一种旋转叶片非接触式动应变场测量方法及其*** - Google Patents

一种旋转叶片非接触式动应变场测量方法及其*** Download PDF

Info

Publication number
WO2020192623A2
WO2020192623A2 PCT/CN2020/080644 CN2020080644W WO2020192623A2 WO 2020192623 A2 WO2020192623 A2 WO 2020192623A2 CN 2020080644 W CN2020080644 W CN 2020080644W WO 2020192623 A2 WO2020192623 A2 WO 2020192623A2
Authority
WO
WIPO (PCT)
Prior art keywords
blade
strain
matrix
rotating blade
displacement
Prior art date
Application number
PCT/CN2020/080644
Other languages
English (en)
French (fr)
Other versions
WO2020192623A3 (zh
Inventor
乔百杰
敖春燕
陈雪峰
曹宏瑞
孙瑜
Original Assignee
西安交通大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 西安交通大学 filed Critical 西安交通大学
Priority to GB2105360.8A priority Critical patent/GB2592775B/en
Publication of WO2020192623A2 publication Critical patent/WO2020192623A2/zh
Publication of WO2020192623A3 publication Critical patent/WO2020192623A3/zh
Priority to US17/325,209 priority patent/US12007309B2/en

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G01M7/04—Monodirectional test stands
    • G01M7/045—Monodirectional test stands in a circular direction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M15/00—Testing of engines
    • G01M15/14—Testing gas-turbine engines or jet-propulsion engines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0016—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of aircraft wings or blades
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Definitions

  • the invention belongs to the technical field of non-contact vibration testing of rotating mechanical blades, in particular to a non-contact dynamic strain field measurement method and system of rotating blades.
  • the present invention proposes a non-contact dynamic strain field measurement method and system for rotating blades, which solves the problem that the tip timing technology can only measure the limited displacement and limited strain of the blade tip, and has simultaneous Reconstruct the advantages of dynamic strain on the surface and internal nodes of the rotating blade.
  • Non-contact measurement based on blade tip timing has become the most promising alternative to contact strain measurement.
  • Blade tip timing can measure all blade vibration information such as vibration frequency, amplitude, excitation order, resonance area, etc., and then use finite element The model can realize the estimation of dynamic strain at a specific position of the blade under specific modal vibration.
  • Dynamic strain inversion based on non-contact measurement is the key to determine whether blade tip timing can replace traditional strain gauge measurement.
  • the working environment of the rotating blade is harsh, and the vibration of the blade under complex load excitation is the result of the superposition of multiple modes.
  • the present invention reconstructs the overall strain field of the rotating blade through vibration inversion of finite measuring points based on the theory of modal reduction and expansion.
  • the core is to construct the blade displacement-strain conversion matrix.
  • a non-contact dynamic strain field measurement method of a rotating blade includes the following steps:
  • a three-dimensional finite element model of the rotating blade to be measured is established, and the modal parameters of the three-dimensional finite element model are extracted;
  • the conversion matrix between the displacement of the finite measuring point and the overall strain field is constructed
  • the dynamic strain is based on the conversion matrix modal processing to obtain the dynamic strain measurement of the rotating blade at any time, any position, and any direction.
  • the first n m- order modal parameters, modal frequency f i and the displacement mode vibration shape ⁇ i of n dof ⁇ 1 of the three-dimensional finite element model are extracted through modal analysis.
  • the strain mode mode shape ⁇ i with the size of 2n dof ⁇ 1 construct the full-field displacement mode mode matrix of the rotating blade
  • the size is n dof ⁇ n m
  • the number of model nodes are
  • the strain of each node of the finite element model of the rotating blade includes 3 normal strains ⁇ x , ⁇ y , ⁇ z and 3 shear strains ⁇ xy , ⁇ yz , and ⁇ xz . Strain component.
  • the number n d of timing measurement points at the axial tip of the rotating blade is greater than or equal to the number of modes n m .
  • the second step extract the displacement mode shape of the blade tip in the axial direction of the blade tip that can be installed with the blade tip timing sensor, and construct a measurement point selection matrix about the displacement mode shape
  • the size is n c ⁇ n m ; where n c represents the number of nodes in the finite element mesh of the blade tip, and each node selects the circumferential displacement mode mode; randomly selects n d measurement points from the measurement point selection matrix ⁇ p
  • the measurement point displacement mode matrix ⁇ d with size n d ⁇ n m is calculated, and its matrix condition number ⁇ is calculated; the random process is repeated R times and the measurement point layout when the matrix condition number ⁇ is the smallest is selected.
  • the conversion matrix The size is 2n dof ⁇ n d ; among them, Indicates the inverse of the mode matrix ⁇ d of the displacement mode of the measuring point; superscript Represents the inverse of the matrix; superscript T represents the transpose of the vector.
  • the blade tip timing non-contact measurement system obtains the displacement signals at n d positions in the axial direction of the rotating blade at t times.
  • the displacement signal u(t) is measured based on the conversion matrix T and the blade tip timing.
  • the strain S(t) includes normal strain and shear strain; where ⁇ i,x represents the normal strain in the x direction of the i-th node of the blade finite element model, and ⁇ i,y represents the i-th node y of the blade finite element model
  • the normal strain in the direction, ⁇ i, z represents the normal strain in the z direction at the i-th node of the blade finite element model, ⁇ i, xy represents the shear strain in the xy direction at the i-th node of the blade finite element model, and ⁇ i, yz represents the finite blade
  • the modal processing is based on the mode reduction and expansion of the strain mode.
  • a measurement system for implementing the method includes:
  • the blade tip timing vibration measurement module is connected to the blade tip timing sensor to measure the displacement signal at n d positions in the axial direction of the rotating blade at t times
  • a calculation unit connected to the blade tip timing vibration measurement module, and the calculation unit includes:
  • Modal analysis module which is configured to perform modal analysis based on the three-dimensional finite element model of the rotating blade to be measured to obtain the displacement mode ⁇ i of the first n m- order modal frequency f i of the rotating blade and construct the full-field displacement of the rotating blade Modal matrix
  • the measuring point optimization module is configured to optimize the number of measuring points of the tip timing sensor arranged on the rotating blade, wherein the measuring point selection matrix is constructed based on the displacement mode shape of the blade tip timing sensor that can be installed on the rotating blade From measuring point matrix ⁇ p randomly selects n d measuring points configured size of the displacement of the measuring point n d ⁇ n m is the mode shape matrix ⁇ d and calculating the condition number of matrix ⁇ , stochastic process is repeated R times and choose The arrangement of measuring points when the matrix condition number ⁇ is minimum,
  • Conversion matrix calculation module which is configured to construct a conversion matrix between the displacement of the finite measuring point of the blade tip and the strain of all nodes in the whole field
  • the strain S(t) includes normal strain and shear strain.
  • the non-contact dynamic strain field measurement method of the rotating blade provided by the invention can realize the measurement of the overall dynamic strain field of the rotating blade only by using a few blade tip timing measurement points. Not only can the dynamic strain of the blade surface be measured, but also the normal strain and shear strain of the internal nodes of the blade can be measured.
  • the method provided by the present invention breaks the limitation that the traditional dynamic strain inversion method based on blade tip timing can only approximate the reconstruction of the dynamic strain of a certain point of the blade under single-mode vibration.
  • the constructed displacement-strain conversion matrix is constant, and the frequency, Time and even boundary conditions are irrelevant.
  • the method provided by the invention can analyze the dynamic strain distribution of the key points of the rotating blade in two dimensions of time and space.
  • the calculation process is simple, easy to measure online, and can save a large number of strain gauges.
  • the method provided by the invention considers multi-modal vibration, has high measurement accuracy, has a simple process for the reconstruction of the dynamic strain field of the rotating blade and is easy to implement.
  • Figure 1 is a schematic flow diagram of a preferred example of a non-contact dynamic strain field measurement method for a rotating blade provided by the present invention
  • Figures 2(a) to 2(c) are structural schematic diagrams of a non-contact dynamic strain field measurement system for rotating blades provided by the present invention, in which Figure 2(a) consists of a rotating blade dynamic strain field reconstruction system; 2(b) Blade tip timing vibration measurement module; Figure 2(c) A schematic diagram of the axial installation of the blade tip timing sensor;
  • Fig. 3 is a schematic diagram of the dynamic load excitation position of the simulated rotating blade and the position of the measuring point of the blade tip timing sensor (BTT) in an embodiment
  • Figures 4(a) to 4(f) are the displacement mode and strain mode vibration modes of the rotating blade in an embodiment, in which, Figure 4(a) is a bending displacement mode; Figure 4(b) is a Bending strain mode; Fig. 4(c) a torsional displacement mode; Fig. 4(d) a torsional strain mode; Fig. 4(e) a second bending displacement mode; Fig. 4(f) a second bending strain mode;
  • Figure 5 shows the actual measurement of the blade tip displacement vibration signal of the three blade tip timing sensors of the rotating blade in an embodiment
  • Fig. 6(a) and Fig. 6(b) are the results of comparison between the dynamic strain and the real dynamic strain at the node 748 of the blade body in the reconstructed strain field of the rotating blade in an embodiment.
  • the three normal strain components in Fig. 6(a) and Comparison result of real dynamic strain Figure 6(b) Comparison result of three shear strain components and real dynamic strain;
  • Figures 7(a) and 7)(b) are the results of the comparison between the dynamic strain of the root node 1100 and the real dynamic strain in the reconstructed strain field of the rotating blade in an embodiment.
  • Figure 7(a) has three normal strain components Compared with the real dynamic strain;
  • Figure 7(b) compares the three shear strain components with the real dynamic strain.
  • Fig. 1 is a working flow chart of a non-contact dynamic strain field measurement method of a rotating blade.
  • a non-contact dynamic strain field measurement method of a rotating blade includes the following steps:
  • a three-dimensional finite element model of the rotating blade to be measured is established, and the modal parameters of the three-dimensional finite element model are extracted;
  • step S3 the conversion matrix between the displacement of the finite measuring point and the overall strain field is constructed
  • the limited position displacement of the tip of the rotating blade is acquired based on the tip timing sensor
  • the dynamic strain is based on the transformation matrix modal processing to obtain the dynamic strain measurement of the rotating blade at any time, any position, and any direction.
  • the first n m- order modal parameters, modal frequency f i, and displacement mode n dof ⁇ 1 of the three-dimensional finite element model are extracted through modal analysis.
  • State mode shape ⁇ i , strain mode mode shape ⁇ i of size 2n dof ⁇ 1 construct the full-field displacement mode mode matrix of the rotating blade
  • the size is n dof ⁇ n m , construct the full-field strain mode mode matrix of the rotating blade
  • the number of model nodes are used to generate modal analysis.
  • the strain of each node of the finite element model of the rotating blade includes three normal strains ⁇ x , ⁇ y , and ⁇ z and three shear strains ⁇ xy , ⁇ yz , ⁇ xz has 6 strain components.
  • the number n d of timing measurement points at the axial tip of the rotating blade is greater than or equal to the number of modes n m .
  • the second step S2 extract the displacement mode shape of the blade tip in the axial direction of the blade tip that can be installed with the blade tip timing sensor, and construct a measurement point selection matrix about the displacement mode shape.
  • the size is n c ⁇ n m ; where n c represents the number of nodes in the finite element mesh of the blade tip, and each node selects the circumferential displacement mode mode; randomly selects n d measurement points from the measurement point selection matrix ⁇ p
  • the measurement point displacement mode matrix ⁇ d with size n d ⁇ n m is calculated, and its matrix condition number ⁇ is calculated; the random process is repeated R times and the measurement point layout when the matrix condition number ⁇ is the smallest is selected.
  • the conversion matrix The size is 2n dof ⁇ n d ; among them, Indicates the inverse of the mode matrix ⁇ d of the displacement mode of the measuring point.
  • the blade tip timing non-contact measurement system obtains the displacement signals at n d positions in the axial direction of the rotating blade at t times
  • the strain S(t) includes normal strain and shear strain.
  • the modal processing is based on the mode reduction and expansion of the strain mode.
  • Figure 1 is a schematic flow chart of a non-contact dynamic strain field measurement method of a rotating blade completed by the present invention.
  • the method is based on the modal reduction and expansion theory to construct the conversion between the limited displacement measurement point of the blade tip of the rotating blade and the strain of all nodes in the whole field Reconstruction of the dynamic strain field of the rotating blade by using very little blade tip timing information.
  • Figures 2(a) to 2(c) are schematic diagrams of the measurement system provided by the present invention. Among them, 1-blade tip timing sensor; 2 -Rotor casing; 3- rotor blades; 4- rotor; 5- wheel disc; 6-speed sensor.
  • the specific steps of the method are as follows:
  • strain includes 3 normal strains ⁇ x , ⁇ y , ⁇ z and 3 shear strains ⁇ xy , ⁇ yz , and ⁇ xz, totaling 6 strain components, That is, each node has 6 strain modes.
  • the number n d of the axial blade tip timing measurement points of the rotating blade should not be less than the number of modes of interest n m , that is, n d ⁇ n m ; in this case, focus on the simulated rotor
  • n m 3
  • n d 3
  • the optimal results of the measurement points are shown in Figure 3.
  • the selected three measurement points are node 1135 near the inlet edge, node 1127 near the midpoint of the blade end, and node 1119 near the exhaust edge, corresponding to the displacement mode matrix of the measurement points
  • the condition number of ⁇ d is 208.41.
  • Timing vibration measurement of blade tip Transient analysis of the rotating blade in ANSYS finite element software.
  • the speed is 15000RPM
  • the strain S(t) includes normal strain and shear strain.
  • Fig. 6(a) and Fig. 6(b) are the results of comparison between the dynamic strain of the blade body No. 748 and the real dynamic strain in the reconstructed rotating blade strain field in an embodiment; Fig. 7(a) and Fig. 7(b) It is the result of comparing the dynamic strain of the blade root No. 1100 node with the real dynamic strain in the reconstructed strain field of the rotating blade in an embodiment. From Fig. 6(a), Fig. 6(b) and Fig. 7(a), Fig.
  • the reconstructed dynamic strain signal is highly consistent with the real dynamic strain; in order to quantitatively evaluate the dynamic strain of the rotating blade of the present invention
  • the performance of the field measurement method is to calculate the relative error between the reconstructed signal and the real strain in the interval t ⁇ [0, 0.3]s.
  • the three normal strains of the blade body 748 nodes ⁇ x , ⁇ y and ⁇ z
  • the relative errors are 10.76%, 11.35%, and 12.35%, respectively.
  • the relative errors of the three shear strains of the leaf body 748 node ⁇ xy , ⁇ yz and ⁇ xz are 12.52%, 2.13% and 8.27%, respectively;
  • 7(a) The relative errors of the three normal strains of ⁇ x , ⁇ y , and ⁇ z at No. 1100 middle leaf root are 12.24%, 12.28% and 12.36%, respectively.
  • Fig. 7(b) No. 1100 leaf root node ⁇ xy and ⁇ yz the relative error of three shear strain ⁇ xz were 12.20%, 0.20% and 5.34%. Therefore, the non-contact dynamic strain field measurement method of the rotating blade provided by the present invention can reconstruct the dynamic strain field of the blade with high precision.
  • the method provided by the invention realizes the reconstruction of the overall strain field of the rotating blade only by using the limited measuring point displacement of the blade tip, which not only realizes the measurement of the dynamic strain of the blade surface, but also realizes the measurement of the normal strain and shear strain of the internal node of the blade, and the calculation process is simple , High measurement accuracy, easy to measure online.
  • the above descriptions are only preferred embodiments of the present invention, which can be applied to the vibration test of fan/compressor/turbine blades of rotating machinery such as aero-engines, gas turbines, steam turbines, etc., and are not intended to limit the present invention.
  • the method includes the following steps:
  • step 2) The number n d of timing measurement points at the axial tip of the rotating blade shall not be less than the number of modes of interest n m , that is, n d ⁇ n m ;
  • n c represents the number of nodes in the finite element mesh of the blade tip, and each node only selects the mode shape of the circumferential displacement
  • step 3 Construct the conversion matrix between the displacement of the finite measuring point of the blade tip and the strain of all nodes in the whole field
  • the size is 2n dof ⁇ n d ; among them, Indicates the inverse of the mode matrix ⁇ d of the displacement mode of the measuring point.
  • step 4) Use the blade tip timing non-contact measurement system to obtain the displacement signals at n d positions in the axial direction of the rotating blade at t times
  • the strain S(t) includes normal strain and shear strain.
  • a measurement system for implementing the method includes:
  • the blade tip timing vibration measurement module is connected to the blade tip timing sensor to measure the displacement signal at n d positions in the axial direction of the rotating blade at t times
  • a calculation unit connected to the blade tip timing vibration measurement module, and the calculation unit includes:
  • Modal analysis module which is configured to perform modal analysis based on the three-dimensional finite element model of the rotating blade to be measured to obtain the displacement mode ⁇ i of the first n m- order modal frequency f i of the rotating blade and construct the full-field displacement of the rotating blade Modal matrix
  • the measuring point optimization module is configured to optimize the number of measuring points of the tip timing sensor arranged on the rotating blade, wherein the measuring point selection matrix is constructed based on the displacement mode shape of the blade tip timing sensor that can be installed on the rotating blade From measuring point matrix ⁇ p randomly selects n d measuring points configured size of the displacement of the measuring point n d ⁇ n m is the mode shape matrix ⁇ d and calculating the condition number of matrix ⁇ , stochastic process is repeated R times and choose The arrangement of measuring points when the matrix condition number ⁇ is minimum,
  • Conversion matrix calculation module which is configured to construct a conversion matrix between the displacement of the finite measuring point of the blade tip and the strain of all nodes in the whole field
  • the strain S(t) includes normal strain and shear strain.
  • the dynamic strain measurement module includes a telemetry unit, a slip ring unit and a signal acquisition module.
  • the measurement system further includes a display unit and a wireless communication device, and the wireless communication device includes a 4G/GPRS or Internet communication module.
  • the modal analysis module, the measurement point optimization module, the conversion matrix calculation module or the dynamic strain field reconstruction module is a general-purpose processor, a digital signal processor, an application specific integrated circuit ASIC or a field programmable gate array FPGA,
  • the modal analysis module, the measurement point optimization module, the conversion matrix calculation module or the dynamic strain field reconstruction module includes a memory, and the memory includes one or more read-only memory ROM, random access memory RAM, flash Memory or electronically erasable programmable read-only memory EEPROM.
  • a system for a non-contact dynamic strain field measurement method of a rotating blade includes:
  • Measurement point optimization module used to determine the number of timing measurement points n d of the axial blade tip of the rotating blade shall not be less than the number of modalities n m of interest , that is, n d ⁇ n m ; used to extract the blade tip axial direction for installation of the blade tip
  • the displacement mode vibration shape of the timing sensor, and the measurement point selection matrix about the displacement mode vibration shape is constructed The size is n c ⁇ n m ; where n c represents the number of finite element mesh nodes at the blade tip, and each node only selects the circumferential displacement mode mode; n d measurement points are randomly selected from the measurement point selection matrix ⁇ p ; Construct the displacement mode matrix ⁇ d of the measuring point with size n d ⁇ n m , and calculate its matrix condition number ⁇ ; this random process is repeated R times, and the measuring point layout plan when the condition number ⁇ is the smallest is selected.
  • Conversion matrix calculation module used to construct the conversion matrix between the displacement of the finite measuring point of the blade tip and the strain of all nodes in the whole field The size is 2n dof ⁇ n d ; among them, Indicates the inverse of the mode matrix ⁇ d of the displacement mode of the measuring point.
  • Blade tip timing vibration measurement module contains several blade tip timing sensors and signal acquisition modules; the blade tip timing non-contact measurement system is used to obtain displacement signals at n d positions and t moments in the axial direction of the rotating blade
  • the strain S(t) includes normal strain and shear strain.

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Chemical & Material Sciences (AREA)
  • General Engineering & Computer Science (AREA)
  • Geometry (AREA)
  • Evolutionary Computation (AREA)
  • Computer Hardware Design (AREA)
  • Combustion & Propulsion (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
  • Turbine Rotor Nozzle Sealing (AREA)
  • Measurement Of Length, Angles, Or The Like Using Electric Or Magnetic Means (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

本发明公开了一种旋转叶片非接触式动应变场测量方法及其***，所述方法包括以下步骤：建立待测量旋转叶片的三维有限元模型，提取所述三维有限元模型的模态参数；确定叶端定时传感器数目与轴向安装位置；构造有限测点位移与整体应变场的转换矩阵；基于所述叶端定时传感器获取旋转叶片叶端有限位置位移，所述动应变基于所述转换矩阵模态处理得到所述旋转叶片任意时刻、任意位置及任意方向的动应变。本发明提供的方法仅利用叶端有限测点位移实现旋转叶片整体应变场的重构，不仅可实现叶片表面动应变的测量，还可实现叶片内部节点正应变、剪应变的测量，计算过程简单，测量精度高，易于在线测量。

Description

一种旋转叶片非接触式动应变场测量方法及其*** 技术领域
本发明属于旋转机械叶片非接触式振动测试技术领域，特别是一种旋转叶片非接触式动应变场测量方法及其***。
背景技术
高速旋转叶片的完整性直接影响航空发动机整体结构的安全运行，受工作环境苛刻、载荷强交变等因素的影响，其在服役过程中极易产生振动疲劳裂纹而导致严重事故。叶片振动过大导致的高周疲劳是航空发动机叶片主要失效模式。叶片高周疲劳主要由各种气动载荷、机械载荷导致的动应力引起，在短时间内便可累计大量循环产生疲劳裂纹，特别是当叶片发生共振时动应力极易导致叶片疲劳失效。在航空发动机研制、生产过程中，为了掌握叶片振动特性，需要对叶片振动进行测量。长期以来，航空发动机叶片是通过在旋转叶片表面粘贴应变片的方式实现动应变测量，这仅能测量有限叶片有限位置动应变，其可靠性和持续工作时间较低，特别是高温环境下在涡轮叶片布置大量应变片常常只有很少的应变片可以获取有效信息，存活率极低。由于航空发动机叶片高速旋转的特点，基于叶端定时的非接触式测量成为叶片振动测试领域研究的发展方向。利用安装在靠近机匣内侧的传感器感知叶尖振动信息，被称为“叶端定时”。当前叶端定时技术(Blade Tip Timing，BTT)是航空 发动机制造、测试巨头关注热点，比如美国空军阿诺德工程研发中心(AEDC)推出了叶片非侵入式应力测试***(Non-Intrusive Stress Measurement System，NSMS)。
在背景技术部分中公开的上述信息仅仅用于增强对本发明背景的理解，因此可能包含不构成在本国中本领域普通技术人员公知的现有技术的信息。
发明内容
针对现有技术中存在的问题，本发明提出一种旋转叶片非接触式动应变场测量方法及其***，解决了叶端定时技术仅能测量叶端有限位移与有限应变的难题，并具备同时重构旋转叶片表面与内部所有节点动应变的优势。
基于叶端定时的非接触式测量成为接触式应变测量最有前景的替代方法，叶端定时可以测量所有叶片的振动信息如振动频率、幅值、激励阶次、共振区域等，进而借助有限元模型可实现特定模态振动下叶片特定位置动应变的估算。基于非接触式测量的动应变反演是决定叶端定时能否取代传统应变片测量的关键。旋转叶片工作环境苛刻，复杂载荷激励下叶片的振动是多个模态叠加的结果，此时最大动应力点位置不固定，位移-应变没有固定的转换关系；当前的动应变重构方法仅适用于单模态振动下的叶片动应变估计，无法实现任意时刻多模态振动下的动应变场重构。为此，本发明基于模态降阶与扩展理论通过有限测点的振动反演重构旋转叶片整体应变场，核心是构造叶片位移-应变的转换矩阵。
本发明的目的是通过以下技术方案予以实现，一种旋转叶片非接触式动应变场测量方法包括以下步骤：
第一步骤中，建立待测量旋转叶片的三维有限元模型，提取所述三维有限元模型的模态参数；
第二步骤中，确定叶端定时传感器数目与轴向安装位置；
第三步骤中，构造有限测点位移与整体应变场的转换矩阵；
第四步骤中，基于所述叶端定时传感器获取旋转叶片叶端有限位置位移；
第五步骤中，所述动应变基于所述转换矩阵模态处理得到所述旋转叶片任意时刻、任意位置及任意方向的动应变测量。
所述的方法中，第一步骤中，通过模态分析提取所述三维有限元模型前n m阶模态参数、模态频率f i和大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i，构造旋转叶片全场位移模态振型矩阵
Figure PCTCN2020080644-appb-000001
大小为n dof×n m，构造旋转叶片全场应变模态振型矩阵
Figure PCTCN2020080644-appb-000002
大小为2n dof×n m；其中，n m表示模态数目，i表示模态阶次，n dof表示旋转叶片有限元模型的自由度数目，n dof＝3n n，n n表示旋转叶片有限元模型节点数目。
所述的方法中，第一步骤中，每个旋转叶片有限元模型节点的应变包含3个正应变ε x、ε y、ε z与3个剪应变γ xy、γ yz、γ xz共6个应变分量。
所述的方法中，第二步骤中，旋转叶片轴向叶端定时测点数目n d 大于等于模态数目n m。
所述的方法中，第二步骤中，提取叶片叶端轴向方向可安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
Figure PCTCN2020080644-appb-000003
大小为n c×n m；其中n c表示叶片叶端有限元网格节点数目，每个节点选周向位移模态振型；从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；随机过程重复R次并从中选择矩阵条件数κ最小时的测点布置。
所述的方法中，第三步骤中，转换矩阵
Figure PCTCN2020080644-appb-000004
大小为2n dof×n d；其中，
Figure PCTCN2020080644-appb-000005
表示测点位移模态振型矩阵Φ d的逆；上标
Figure PCTCN2020080644-appb-000006
表示矩阵的逆；上标T表示矢量的转置。
所述的方法中，第四步骤中，叶端定时非接触式测量***获得旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000007
其中u j(t)表示第j(j＝1，...，n d)个叶端定时传感器实测信号。
所述的方法中，第五步骤中，基于转换矩阵T和叶端定时测量位移信号u(t)，旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000008
，所述应变S(t)包括正应变和剪应变；其中，ε i，x表示叶片有限元模型第i个节点x方向的正应变，ε i，y表示叶片有限元模型第i个节点y方向的正应变，ε i，z表示叶片有限元模型第i个节点z方向的正应变，γ i，xy 表示叶片有限元模型第i个节点x-y方向的剪应变，γ i，yz表示叶片有限元模型第i个节点y-z方向的剪应变，γ i，xz表示叶片有限元模型第i个节点x-z方向的剪应变。
所述的方法中，第五步骤中，所述模态处理基于所述应变模态振型模态降阶与扩展。
根据本发明的另一方面，一种实施所述方法的测量***包括，
多个叶端定时传感器，其布置在旋转叶片机匣上；
叶端定时测振模块，其连接所述叶端定时传感器以测量旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000009
计算单元，其连接所述叶端定时测振模块，所述计算单元包括，
模态分析模块，其配置成基于待测量旋转叶片的三维有限元模型进行模态分析以获取旋转叶片前n m阶模态频率f i的位移模态振型φ i以及构造旋转叶片全场位移模态振型矩阵
Figure PCTCN2020080644-appb-000010
测点优选模块，其配置成优化布置在所述旋转叶片上的叶端定时传感器的测点数目，其中，基于旋转叶片可安装叶端定时传感器的位移模态振型构造测点选择矩阵
Figure PCTCN2020080644-appb-000011
从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d并计算其矩阵条件数κ，随机过程重复R次并从中选择矩阵条件数κ最小时的测点布置，
转换矩阵计算模块，其配置成构造叶端有限测点位移与全场所有节点应变的转换矩阵，
应变场重构模块，其配置成旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000012
，所述应变S(t)包括正应变和剪应变。
有益效果
本发明提供的旋转叶片非接触式动应变场测量方法仅利用极少叶端定时测点便可实现旋转叶片整体动应变场的测量。不仅可实现叶片表面动应变的测量，还可以实现叶片内部节点正应变、剪应变的测量。本发明提供的方法突破了基于叶端定时的传统动应变反演方法仅能近似重构单模态振动下叶片某点动应变的局限，构造的位移-应变转换矩阵是恒定的，与频率、时间、甚至边界条件无关。发明提供的方法可在时间-空间两个维度分析旋转叶片关键点动应变分布，计算过程简单，易于在线测量，可节约大量应变片。本发明提供的方法考虑了多模态振动，测量精度高，旋转叶片动应变场重构***过程简单，易于实现。
附图说明
通过阅读下文优选的具体实施方式中的详细描述，本发明各种其他的优点和益处对于本领域普通技术人员将变得清楚明了。说明书附图仅用于示出优选实施方式的目的，而并不认为是对本发明的限制。显而易见地，下面描述的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。而且在整个附图中，用相同的附图标记表示 相同的部件。
在附图中：
图1是本发明提供的一种旋转叶片非接触式动应变场测量方法优先实例的流程示意图；
图2(a)至图2(c)是本发明提供的一种旋转叶片非接触式动应变场测量***的结构示意图，其中，图2(a)旋转叶片动应变场重构***组成；图2(b)叶端定时测振模块；图2(c)叶端定时传感器轴向安装示意图；
图3是一个实施例中模拟旋转叶片动载荷激励位置与叶端定时传感器(BTT)测点位置示意图；
图4(a)至图4(f)是一个实施例中旋转叶片的位移模态振型与应变模态振型，其中，图4(a)一弯位移振型；图4(b)一弯应变振型；图4(c)一扭位移振型；图4(d)一扭应变振型；图4(e)二弯位移振型；图4(f)二弯应变振型；
图5是一个实施例中旋转叶片三个叶端定时传感器实测叶端位移振动信号；
图6(a)、图6(b)是一个实施例中重构的旋转叶片应变场中叶身748号节点动应变与真实动应变比较结果，其中，图6(a)三个正应变分量与真实动应变比较结果；图6(b)三个剪应变分量与真实动应变比较结果；
图7(a)、图7)(b)是一个实施例中重构的旋转叶片应变场中叶根1100号节点动应变与真实动应变比较结果，其中，图7(a)三 个正应变分量与真实动应变比较结果；图7(b)三个剪应变分量与真实动应变比较结果。
以下结合附图和实施例对本发明作进一步的解释。
具体实施方式
下面将参照附图1至附图7(b)更详细地描述本发明的具体实施例。虽然附图中显示了本发明的具体实施例，然而应当理解，可以以各种形式实现本发明而不应被这里阐述的实施例所限制。相反，提供这些实施例是为了能够更透彻地理解本发明，并且能够将本发明的范围完整的传达给本领域的技术人员。
需要说明的是，在说明书及权利要求当中使用了某些词汇来指称特定组件。本领域技术人员应可以理解，技术人员可能会用不同名词来称呼同一个组件。本说明书及权利要求并不以名词的差异来作为区分组件的方式，而是以组件在功能上的差异来作为区分的准则。如在通篇说明书及权利要求当中所提及的“包含”或“包括”为一开放式用语，故应解释成“包含但不限定于”。说明书后续描述为实施本发明的较佳实施方式，然所述描述乃以说明书的一般原则为目的，并非用以限定本发明的范围。本发明的保护范围当视所附权利要求所界定者为准。
为便于对本发明实施例的理解，下面将结合附图以具体实施例为例做进一步的解释说明，且各个附图并不构成对本发明实施例的限定。
为了更好地理解，图1为一个旋转叶片非接触式动应变场测量方法工作流程图，如图1所示，一种旋转叶片非接触式动应变场测量方法包括以下步骤：
第一步骤S1中，建立待测量旋转叶片的三维有限元模型，提取所述三维有限元模型的模态参数；
第二步骤S2中，确定叶端定时传感器数目与轴向安装位置；
第三步骤S3中，构造有限测点位移与整体应变场的转换矩阵；
第四步骤S4中，基于所述叶端定时传感器获取旋转叶片叶端有限位置位移，
第五步骤S5中，所述动应变基于所述转换矩阵模态处理得到所述旋转叶片任意时刻、任意位置及任意方向的动应变测量。
所述的方法的一个实施方式中，第一步骤S1中，通过模态分析提取所述三维有限元模型前n m阶模态参数、模态频率f i和大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i，构造旋转叶片全场位移模态振型矩阵
Figure PCTCN2020080644-appb-000013
大小为n dof×n m，构造旋转叶片全场应变模态振型矩阵
Figure PCTCN2020080644-appb-000014
大小为2n dof×n m；其中，n m表示模态数目，i表示模态阶次，n dof表示旋转叶片有限元模型的自由度数目，n dof＝3n n，n n表示旋转叶片有限元模型节点数目。
所述的方法的一个实施方式中，第一步骤S1中，每个旋转叶片有限元模型节点的应变包含3个正应变ε x、ε y、ε z与3个剪应变 γ xy、γ yz、γ xz共6个应变分量。
所述的方法的一个实施方式中，第二步骤S2中，旋转叶片轴向叶端定时测点数目n d大于等于模态数目n m。
所述的方法的一个实施方式中，第二步骤S2中，提取叶片叶端轴向方向可安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
Figure PCTCN2020080644-appb-000015
大小为n c×n m；其中n c表示叶片叶端有限元网格节点数目，每个节点选周向位移模态振型；从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；随机过程重复R次并从中选择矩阵条件数κ最小时的测点布置。
所述的方法的一个实施方式中，第三步骤S3中，转换矩阵
Figure PCTCN2020080644-appb-000016
大小为2n dof×n d；其中，
Figure PCTCN2020080644-appb-000017
表示测点位移模态振型矩阵Φ d的逆。
所述的方法的一个实施方式中，第四步骤S4中，叶端定时非接触式测量***获得旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000018
所述的方法的一个实施方式中，第五步骤S5中，旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000019
，所述应变S(t)包括正应变和剪应变。
所述的方法的一个实施方式中，其中，第五步骤S5中，所述模态处理基于所述应变模态振型模态降阶与扩展。
为了进一步理解本发明，下面结合附图1至附图7(b)及具体实施例对本发明作进一步描述，应该强调的是，下述说明仅仅是示例性的，而本发明的应用对象不局限下述示例。
图1是本发明完成的一种旋转叶片非接触式动应变场测量方法的流程示意图，该方法基于模态降阶与扩展理论构造旋转叶片叶端有限位移测点与全场所有节点应变的转换关系，利用极少叶端定时信息实现旋转叶片动应变场重构，图2(a)至图2(c)是本发明提供的测量***的结构示意图，其中，1-叶端定时传感器；2-转子机匣；3-转子叶片；4-转子；5-轮盘；6-转速传感器。方法具体步骤如下：
1)提取叶片三维有限元模型的模态参数：参见图3，利用ANSYS有限元分析软件建立模拟转子直板叶片的三维有限元模型，其中材料为铝，密度2700kg/m 3，泊松比0.33，弹性模量72000MPa；叶片长48mm，厚度1mm，宽20mm；有限元单元类型为实体单元SOLID185，节点总数为3153；叶根两侧面固定约束，模拟转子叶片实际工作状态；
利用ANSYS模态分析模态提取前3阶模态参数，即n m＝3：模态频率f i、大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i，其中，前三阶模态频率分别为f 1＝333.08Hz、f 2＝1806.03Hz、f 3＝2076.52Hz；构造转子叶片全场应变模态振型矩阵
Figure PCTCN2020080644-appb-000020
大小为2n dof×n m，应变模态振型见图4(a)至图4(f)；i表示模态阶次，n dof＝9459表示叶片有限元模型的自 由度数目，则n dof＝3n n，n n＝3153表示叶片有限元模型节点的数目；应变包含3个正应变ε x、ε y、ε z与3个剪应变γ xy、γ yz、γ xz共6个应变分量，即每个节点有6个应变模态振型。
2)确定叶端定时传感器数目与轴向安装位置：旋转叶片轴向叶端定时测点数目n d不得小于关注的模态数目n m，即n d≥n m；本案例中，关注模拟转子叶片前三阶振动模态，取n m＝3；叶端定时传感器数目取最少，即n d＝3；
提取叶片叶端轴向可供安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
Figure PCTCN2020080644-appb-000021
大小为n c×n m＝21×3；其中n c＝21表示叶片单面叶端有限元网格节点数目，每个节点仅选周向位移模态振型，本案例中为X轴方向；本案例中旋转叶片叶端节点[1118：1136，66，1117]。从测点选择矩阵Φ p中随机选择n d＝3个测点；构造大小为n d×n m＝3×3的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；这个随机过程重复R＝200次，并从中选择条件数κ最小时的测点布局方案。测点优选结果见图3，选中的三个测点分别为进气边附近1135号节点、叶端中点1127号节点、排气边附近1119号节点，对应的测点位移模态振型矩阵Φ d的条件数为208.41。
3)构造叶端有限测点位移与全场所有节点应变的转换矩阵
Figure PCTCN2020080644-appb-000022
大小为2n dof×n d＝18918×3；其中，
Figure PCTCN2020080644-appb-000023
表示测点位移模态振型矩阵Φ d的逆。
4)叶端定时测振：在ANSYS有限元软件中对旋转叶片进行瞬 态分析质量阻尼系数设定为α＝12.1380，刚度阻尼系数设定为β＝8.1986×10 -8，转速为15000RPM，模拟气动载荷对转子叶片的多模态振动，对转子叶片叶端1117号节点X方向施加多频简谐激励f(t)＝cos(2πf 1t)+10cos(2πf 2t)+20cos(2πf 3t)，获得叶片真实的应变场，作为重构结果的参考；图3中三个叶端定时传感器获取旋转叶片叶端轴向t个时刻(75转)欠采样离散信号u(t)＝[u 1(t)，u 2(t)，u 3(t)] T，实测结果参见图5；其中，采样频率f s＝15000/60＝250Hz，即与转速相同，信号的数据长度为N＝75，采样时间为t＝N/f s＝0.3s。
5)利用基于模态降阶与扩展理论计算旋转叶片t时刻叶片表面和内部所有节点正应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000024
，所述应变S(t)包括正应变和剪应变。
取旋转叶片叶身748号节点和叶根1100号节点作为动应变场高精度重构的典型代表(见图3)，结论同样适用于其他节点。其中，图6(a)、图6(b)是一个实施例中重构的旋转叶片应变场中叶身748号节点动应变与真实动应变比较结果；图7(a)、图7(b)是一个实施例中重构的旋转叶片应变场中叶根1100号节点动应变与真实动应变比较结果。从图6(a)、图6(b)和图7(a)、图7(b)中可知，重构的动应变信号与真实动应变高度吻合；为了定量评价本发明的旋转叶片动应变场测量方法的性能，在t∈[0，0.3]s区间计算重构信号与真实应变的相对误差，图6(a)中叶身748号节点ε x、ε y、ε z三个正应变的相对误差分别为10.76％、11.35％和12.35％，图6(b)中叶身748号节点γ xy、γ yz、γ xz三个剪应变的相对 误差分别为12.52％、2.13％和8.27％；图7(a)中叶根1100号节点ε x、ε y、ε z三个正应变的相对误差分别为12.24％、12.28％和12.36％，图7(b)中叶根1100号节点γ xy、γ yz、γ xz三个剪应变的相对误差分别为12.20％、0.20％和5.34％。因此，本发明提供的一种旋转叶片非接触式动应变场测量方法，可以高精度地重构叶片动应变场。
本发明提供的方法仅利用叶端有限测点位移实现旋转叶片整体应变场的重构，不仅可实现叶片表面动应变的测量，还可实现叶片内部节点正应变、剪应变的测量，计算过程简单，测量精度高，易于在线测量。以上所述仅为本发明的较佳实施例而已，可应用在航空发动机、燃气轮机、汽轮机等旋转机械的风扇/压气机/涡轮叶片振动测试中，并不用以限制本发明。
在另一个实施例中，方法包括以下步骤：
提取叶片三维有限元模型的模态参数；
2)确定叶端定时传感器数目与轴向安装位置；
3)构造有限测点位移与整体应变场的转换矩阵；
4)利用叶端定时传感器获取旋转叶片叶端有限位置位移；
5)基于模态降阶与扩展理论实现旋转叶片任意时刻、任意位置、任意方向的动应变测量。
进一步地，步骤1)建立转子叶片的有限元模型，通过模态分析提取前n m阶模态参数：模态频率f i、大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i；构造转子叶片全场位移模态 振型矩阵
Figure PCTCN2020080644-appb-000025
大小为n dof×n m；构造转子叶片全场应变模态振型矩阵
Figure PCTCN2020080644-appb-000026
大小为2n dof×n m；i表示模态阶次，n dof表示叶片三维有限元模型的自由度数目；每个节点的位移包含3个位移u x、u y、u z分量，即每个节点有3个位移模态振型，则n dof＝3n n，n n表示叶片有限元模型节点的数目；应变包含3个正应变ε x、ε y、ε z与3个剪应变γ xy、γ yz、γ xz共6个应变分量，即每个节点有6个应变模态振型。
进一步地，步骤2)旋转叶片轴向叶端定时测点数目n d不得小于关注的模态数目n m，即n d≥n m；
提取叶片叶端轴向可供安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
Figure PCTCN2020080644-appb-000027
大小为n c×n m；其中n c表示叶片叶端有限元网格节点数目，每个节点仅选周向位移模态振型；
从测点选择矩阵Φ p中随机选择n d个测点；构造大小为n d×n m的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；这个随机过程重复R次，并从中选择条件数κ最小时的测点布局方案。
进一步地，步骤3)构造叶端有限测点位移与全场所有节点应变的转换矩阵
Figure PCTCN2020080644-appb-000028
大小为2n dof×n d；其中，
Figure PCTCN2020080644-appb-000029
表示测点位移模态振型矩阵Φ d的逆。
进一步地，步骤4)利用叶端定时非接触式测量***获得旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000030
进一步地，步骤5)基于模态降阶与扩展理论计算旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000031
，所述应变S(t)包括正应变和剪应变。
另一方面，一种实施所述方法的测量***包括，
多个叶端定时传感器，其布置在旋转叶片机匣上；
叶端定时测振模块，其连接所述叶端定时传感器以测量旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000032
计算单元，其连接所述叶端定时测振模块，所述计算单元包括，
模态分析模块，其配置成基于待测量旋转叶片的三维有限元模型进行模态分析以获取旋转叶片前n m阶模态频率f i的位移模态振型φ i以及构造旋转叶片全场位移模态振型矩阵
Figure PCTCN2020080644-appb-000033
测点优选模块，其配置成优化布置在所述旋转叶片上的叶端定时传感器的测点数目，其中，基于旋转叶片可安装叶端定时传感器的位移模态振型构造测点选择矩阵
Figure PCTCN2020080644-appb-000034
从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d并计算其矩阵条件数κ，随机过程重复R次并从中选择矩阵条件数κ最小时的测点布置，
转换矩阵计算模块，其配置成构造叶端有限测点位移与全场所有节点应变的转换矩阵，
应变场重构模块，其配置成旋转叶片t时刻叶片表面和内部所有 节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000035
，所述应变S(t)包括正应变和剪应变。
在一个实施例中，动应变测量模块包括遥测单元、滑环单元和信号采集模块。
在一个实施例中，测量***还包括显示单元和无线通信设备，无线通信设备包括4G/GPRS或互联网通信模块。
在一个实施例中，模态分析模块、测点优选模块、转换矩阵计算模块或动应变场重构模块为通用处理器、数字信号处理器、专用集成电路ASIC或现场可编程门阵列FPGA，
在一个实施例中模态分析模块、测点优选模块、转换矩阵计算模块或动应变场重构模块包括存储器，所述存储器包括一个或多个只读存储器ROM、随机存取存储器RAM、快闪存储器或电子可擦除可编程只读存储器EEPROM。
在一个实施例中，一种旋转叶片非接触式动应变场测量方法用***包括：
模态分析模块：利用商用有限元分析软件对叶片的三维有限元模型进行模态分析，用于获取前n m阶模态参数：模态频率f i、大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i；构造转子叶片全场位移模态振型矩阵
Figure PCTCN2020080644-appb-000036
大小为n dof×n m；构造转子叶片全场应变模态振型矩阵
Figure PCTCN2020080644-appb-000037
大小为2n dof×n m；i表示模态阶次，n dof表示叶 片三维有限元模型的自由度数目；每个节点的位移包含3个位移u x、u y、u z分量，即每个节点有3个位移模态振型，则n dof＝3n n，n n表示叶片有限元模型节点的数目；应变包含3个正应变ε x、ε y、ε z与3个剪应变γ xy、γ yz、γ xz共6个应变分量，即每个节点有6个应变模态振型。
测点优选模块：用于确定旋转叶片轴向叶端定时测点数目n d不得小于关注的模态数目n m，即n d≥n m；用于提取叶片叶端轴向可供安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
Figure PCTCN2020080644-appb-000038
大小为n c×n m；其中n c表示叶片叶端有限元网格节点数目，每个节点仅选周向位移模态振型；从测点选择矩阵Φ p中随机选择n d个测点；构造大小为n d×n m的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；这个随机过程重复R次，并从中选择条件数κ最小时的测点布局方案。
转换矩阵计算模块：用于构造叶端有限测点位移与全场所有节点应变的转换矩阵
Figure PCTCN2020080644-appb-000039
大小为2n dof×n d；其中，
Figure PCTCN2020080644-appb-000040
表示测点位移模态振型矩阵Φ d的逆。
叶端定时测振模块：包含若干叶端定时传感器、信号采集模块；利用叶端定时非接触式测量***获得旋转叶片轴向n d个位置t个时刻的位移信号
Figure PCTCN2020080644-appb-000041
应变场重构模块：用于计算旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
Figure PCTCN2020080644-appb-000042
，所述应变S(t)包括正应变和剪应变。
尽管以上结合附图对本发明的实施方案进行了描述，但本发明并不局限于上述的具体实施方案和应用领域，上述的具体实施方案仅仅是示意性的、指导性的，而不是限制性的。本领域的普通技术人员在本说明书的启示下和在不脱离本发明权利要求所保护的范围的情况下，还可以做出很多种的形式，这些均属于本发明保护之列。

Claims (10)

  1. 一种旋转叶片非接触式动应变场测量方法，所述方法包括以下步骤：
    第一步骤(S1)中，建立待测量旋转叶片的三维有限元模型，提取所述三维有限元模型的模态参数；
    第二步骤(S2)中，确定叶端定时传感器数目与轴向安装位置；
    第三步骤(S3)中，构造有限测点位移与整体应变场的转换矩阵；
    第四步骤(S4)中，基于所述叶端定时传感器获取旋转叶片叶端有限位置位移；
    第五步骤(S5)中，所述动应变基于所述转换矩阵模态处理得到所述旋转叶片任意时刻、任意位置及任意方向的动应变。
  2. 根据权利要求1所述的方法，其中，第一步骤(S1)中，通过模态分析提取所述三维有限元模型前n m阶模态参数、模态频率f i和大小为n dof×1的位移模态振型φ i、大小为2n dof×1的应变模态振型ψ i，构造旋转叶片全场位移模态振型矩阵
    Figure PCTCN2020080644-appb-100001
    大小为n dof×n m，构造旋转叶片全场应变模态振型矩阵
    Figure PCTCN2020080644-appb-100002
    大小为2n dof×n m；其中，n m表示模态数目，i表示模态阶次，n dof表示旋转叶片有限元模型的自由度数目，n dof＝3n n，n n表示旋转叶片有限元模型节点数目。
  3. 根据权利要求2所述的方法，其中，第一步骤(S1)中，每个旋转叶片有限元模型节点的应变包含3个正应变ε x、ε y、ε z与3个剪应变γ xy、γ yz、γ xz共6个应变分量。
  4. 根据权利要求1所述的方法，其中，第二步骤(S2)中，旋转 叶片轴向叶端定时测点数目n d大于等于模态数目n m。
  5. 根据权利要求1所述的方法，其中，第二步骤(S2)中，提取叶片叶端轴向方向可安装叶端定时传感器的位移模态振型，构造关于位移模态振型的测点选择矩阵
    Figure PCTCN2020080644-appb-100003
    大小为n c×n m；其中n c表示叶片叶端有限元网格节点数目，每个节点选周向位移模态振型；从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d，并计算其矩阵条件数κ；随机过程重复R次并从中选择矩阵条件数κ最小时的测点布置。
  6. 根据权利要求2所述的方法，其中，第三步骤(S3)中，转换矩阵
    Figure PCTCN2020080644-appb-100004
    大小为2n dof×n d；其中，
    Figure PCTCN2020080644-appb-100005
    表示测点位移模态振型矩阵Φ d的逆；上标
    Figure PCTCN2020080644-appb-100006
    表示矩阵的逆；上标T表示矢量的转置。
  7. 根据权利要求6所述的方法，其中，第四步骤(S4)中，叶端定时非接触式测量***获得旋转叶片轴向n d个位置t个时刻的位移信号
    Figure PCTCN2020080644-appb-100007
    其中u j(t)表示第j(j＝1，...，n d)个叶端定时传感器实测信号。
  8. 根据权利要求7所述的方法，其中，第五步骤(S5)中，基于转换矩阵T和叶端定时测量位移信号u(t)，旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
    Figure PCTCN2020080644-appb-100008
    ，所述应变S(t)包括正应变和剪应变；其中，ε i，x表示叶片有限元模 型第i个节点x方向的正应变，ε i，y表示叶片有限元模型第i个节点y方向的正应变，ε i，z表示叶片有限元模型第i个节点z方向的正应变，γ i，xy表示叶片有限元模型第i个节点x-y方向的剪应变，γ i，yz表示叶片有限元模型第i个节点y-z方向的剪应变，γ i，xz表示叶片有限元模型第i个节点x-z方向的剪应变。
  9. 根据权利要求2所述的方法，其中，第五步骤(S5)中，所述模态处理基于所述应变模态振型模态降阶与扩展。
  10. 一种实施权利要求1-9中任一项所述方法的测量***，所述测量***包括，
    多个叶端定时传感器，其布置在旋转叶片机匣上；
    叶端定时测振模块，其连接所述叶端定时传感器以测量旋转叶片轴向n d个位置t个时刻的位移信号
    Figure PCTCN2020080644-appb-100009
    计算单元，其连接所述叶端定时测振模块，所述计算单元包括，
    模态分析模块，其配置成基于待测量旋转叶片的三维有限元模型进行模态分析以获取旋转叶片前n m阶模态频率f i的位移模态振型φ i以及构造旋转叶片全场位移模态振型矩阵
    Figure PCTCN2020080644-appb-100010
    测点优选模块，其配置成优化布置在所述旋转叶片上的叶端定时传感器的测点数目，其中，基于旋转叶片可安装叶端定时传感器的位移模态振型构造测点选择矩阵
    Figure PCTCN2020080644-appb-100011
    从测点选择矩阵Φ p中随机选择n d个测点构造大小为n d×n m的测点位移模态振型矩阵Φ d并计算其矩阵条件数κ，随机过程重复R次并从中选择矩阵条件数 κ最小时的测点布置，
    转换矩阵计算模块，其配置成构造叶端有限测点位移与全场所有节点应变的转换矩阵，
    应变场重构模块，其配置成旋转叶片t时刻叶片表面和内部所有节点应变，经由公式S(t)＝Tu(t)计算得出，
    Figure PCTCN2020080644-appb-100012
    ，所述应变S(t)包括正应变和剪应变。
PCT/CN2020/080644 2019-03-22 2020-03-23 一种旋转叶片非接触式动应变场测量方法及其*** WO2020192623A2 (zh)

Priority Applications (2)

Application Number Priority Date Filing Date Title
GB2105360.8A GB2592775B (en) 2019-03-22 2020-03-23 Non-contact dynamic strain field measuring method and system for rotating blade
US17/325,209 US12007309B2 (en) 2019-03-22 2021-05-20 Non-contact dynamic strain field measuring method and system for rotating blade

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN201910226767.9A CN109870134B (zh) 2019-03-22 2019-03-22 一种旋转叶片非接触式动应变场测量方法及其***
CN201910226767.9 2019-03-22

Related Child Applications (1)

Application Number Title Priority Date Filing Date
US17/325,209 Continuation US12007309B2 (en) 2019-03-22 2021-05-20 Non-contact dynamic strain field measuring method and system for rotating blade

Publications (2)

Publication Number Publication Date
WO2020192623A2 true WO2020192623A2 (zh) 2020-10-01
WO2020192623A3 WO2020192623A3 (zh) 2021-02-11

Family

ID=66921125

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2020/080644 WO2020192623A2 (zh) 2019-03-22 2020-03-23 一种旋转叶片非接触式动应变场测量方法及其***

Country Status (4)

Country Link
US (1) US12007309B2 (zh)
CN (1) CN109870134B (zh)
GB (1) GB2592775B (zh)
WO (1) WO2020192623A2 (zh)

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112287580A (zh) * 2020-10-27 2021-01-29 中国船舶重工集团公司第七0三研究所 一种基于全三维数值模拟的轴流压气机喘振边界计算方法
CN112464535A (zh) * 2020-11-27 2021-03-09 西安交通大学 一种转子叶片动应变测量数据一致性评估方法
CN114034487A (zh) * 2022-01-11 2022-02-11 成都中科翼能科技有限公司 基于数字板卡的发动机转子叶片动态信号输出方法和设备
CN114136643A (zh) * 2021-10-20 2022-03-04 中国航发四川燃气涡轮研究院 一种航空发动机空气流量测点布局方法
CN114414223A (zh) * 2021-12-16 2022-04-29 华中科技大学 一种非接触式车架怠速振动传感监测***
CN115114721A (zh) * 2022-06-02 2022-09-27 西安交通大学 基于非接触测量的叶片多模态最大应力预测方法及***

Families Citing this family (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109870134B (zh) * 2019-03-22 2020-01-31 西安交通大学 一种旋转叶片非接触式动应变场测量方法及其***
CN110851963A (zh) * 2019-10-25 2020-02-28 西安交通大学 叶端定时传感器的机匣周向布置方法
CN110807283B (zh) * 2019-10-31 2023-08-15 中电工业互联网有限公司 基于有限元计算模型的多载荷应变测量点获取方法及***
CN110807284B (zh) * 2019-10-31 2023-08-25 中电工业互联网有限公司 基于有限元和应变测量的载荷谱识别方法、***及装置
CN111507042A (zh) * 2020-04-29 2020-08-07 西安交通大学 基于叶端定时的旋转叶片动应力测量方法及其***
CN114441125B (zh) * 2021-12-24 2022-10-28 北京化工大学 一种非接触式透平机械高转速叶片振动多模态分解方法
CN114218841A (zh) * 2021-12-29 2022-03-22 北京航空航天大学 一种热-离心载荷作用下多层薄膜耦合应力仿真计算方法
CN115455790B (zh) * 2022-06-01 2024-01-30 北京理工大学 一种运载火箭发射动力学有限元智能后处理方法
CN115062410A (zh) * 2022-06-02 2022-09-16 西安交通大学 单传感器转子叶片多模态应变场重构方法及测量***
CN115371627A (zh) * 2022-08-10 2022-11-22 山东大学 一种轻量化舱体结构应变场重构方法及***
CN115510713A (zh) * 2022-09-29 2022-12-23 哈电发电设备国家工程研究中心有限公司 汽轮机超低负荷叶片动应力三维计算***及其计算方法
US11898453B1 (en) * 2022-10-20 2024-02-13 Xi'an Jiaotong University Method for extracting natural frequency difference between blades by single blade tip timing sensor or uniformly distributed blade tip timing sensors
CN118168791B (zh) * 2024-05-16 2024-07-16 中国航发四川燃气涡轮研究院 一种压气机静子叶片的最大应力等效测量方法

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7574338B1 (en) * 2005-01-19 2009-08-11 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Finite-difference simulation and visualization of elastodynamics in time-evolving generalized curvilinear coordinates
US9530209B2 (en) * 2014-01-15 2016-12-27 Siemens Energy, Inc. Method of determining the location of tip timing sensors during operation
CN104794284B (zh) * 2015-04-22 2017-08-22 西安电子科技大学 一种基于嵌入光纤光栅的智能蒙皮天线电补偿方法
CN107103111B (zh) * 2017-03-02 2019-07-26 西安电子科技大学 基于应变传感器电子装备功能形面特征点位移场重构方法
CN107515980B (zh) * 2017-08-18 2021-03-23 西安电子科技大学 面向结构形变重构的两步序列应变传感器优化布局方法
CN107741312B (zh) * 2017-09-27 2020-01-14 中国舰船研究设计中心 一种非均布式结构振动场工程测试方法
CN108895974B (zh) * 2018-05-08 2020-06-09 航天东方红卫星有限公司 一种结构变形光纤监测与重构方法及***
CN109870134B (zh) * 2019-03-22 2020-01-31 西安交通大学 一种旋转叶片非接触式动应变场测量方法及其***

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112287580A (zh) * 2020-10-27 2021-01-29 中国船舶重工集团公司第七0三研究所 一种基于全三维数值模拟的轴流压气机喘振边界计算方法
CN112464535A (zh) * 2020-11-27 2021-03-09 西安交通大学 一种转子叶片动应变测量数据一致性评估方法
CN112464535B (zh) * 2020-11-27 2024-04-05 西安交通大学 一种转子叶片动应变测量数据一致性评估方法
CN114136643A (zh) * 2021-10-20 2022-03-04 中国航发四川燃气涡轮研究院 一种航空发动机空气流量测点布局方法
CN114136643B (zh) * 2021-10-20 2024-01-09 中国航发四川燃气涡轮研究院 一种航空发动机空气流量测点布局方法
CN114414223A (zh) * 2021-12-16 2022-04-29 华中科技大学 一种非接触式车架怠速振动传感监测***
CN114034487A (zh) * 2022-01-11 2022-02-11 成都中科翼能科技有限公司 基于数字板卡的发动机转子叶片动态信号输出方法和设备
CN115114721A (zh) * 2022-06-02 2022-09-27 西安交通大学 基于非接触测量的叶片多模态最大应力预测方法及***
CN115114721B (zh) * 2022-06-02 2024-02-23 西安交通大学 基于非接触测量的叶片多模态最大应力预测方法及***

Also Published As

Publication number Publication date
WO2020192623A3 (zh) 2021-02-11
US20210389207A1 (en) 2021-12-16
CN109870134B (zh) 2020-01-31
US12007309B2 (en) 2024-06-11
GB202105360D0 (en) 2021-06-02
GB2592775A (en) 2021-09-08
CN109870134A (zh) 2019-06-11
GB2592775B (en) 2023-11-08

Similar Documents

Publication Publication Date Title
WO2020192623A2 (zh) 一种旋转叶片非接触式动应变场测量方法及其***
WO2020192621A1 (zh) 一种基于叶端定时的转子叶片动应变场测量方法及其***
CN109883380B (zh) 一种基于叶端定时的转子叶片位移场测量方法及其***
CN108895974B (zh) 一种结构变形光纤监测与重构方法及***
CN109883389B (zh) 一种旋转叶片动应变场测量方法及其***
CN110375690B (zh) 一种旋转叶片非接触式位移场测量方法及其***
CN110006563B (zh) 直升机桨叶挥舞与摆振弯矩分布式光纤解耦测量方法
CN110032776B (zh) 基于模态解耦的叶片动应变场与位移场重构方法及其***
CN111507042A (zh) 基于叶端定时的旋转叶片动应力测量方法及其***
CN110851963A (zh) 叶端定时传感器的机匣周向布置方法
CN111507043A (zh) 一种基于叶端定时的转子叶片动应力场测量方法及其***
CN109766617B (zh) 一种基于应变传感器的位移场重构方法
CN111563342B (zh) 一种转子叶片的应变片测点布局优化方法
CN111563340A (zh) 一种转子叶片动应力重构方法及其***
CN112464535A (zh) 一种转子叶片动应变测量数据一致性评估方法
CN109885976A (zh) 一种旋转叶片位移场反演重构方法及其***
CN109733641A (zh) 一种飞机全尺寸结构件多轴疲劳试验方法
Zhu et al. Full-field dynamic strain reconstruction of rotor blades under multi-mode vibration
Kaszynski et al. Accurate blade tip timing limits through geometry mistuning modeling
CN113504025B (zh) 一种大迎角低频结构风洞动载荷测试方法
CN105404740B (zh) 一种基于联合指标与有限信息的修正灵敏度结构损伤识别方法
CN115435894A (zh) 基于模拟退火算法的叶尖定时振动应力反演方法
WO2024073899A1 (zh) 一种考虑两端半刚性约束的拉索索力识别算法
CN115062410A (zh) 单传感器转子叶片多模态应变场重构方法及测量***
Hartung et al. A Practical Approach for Evaluation of Equivalent Linear Damping From Measurements of Mistuned and/or Non-Linear Stages and Forced Response Validation

Legal Events

Date Code Title Description
ENP Entry into the national phase

Ref document number: 202105360

Country of ref document: GB

Kind code of ref document: A

Free format text: PCT FILING DATE = 20200323

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 20779683

Country of ref document: EP

Kind code of ref document: A2

121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 20779683

Country of ref document: EP

Kind code of ref document: A2

122 Ep: pct application non-entry in european phase

Ref document number: 20779683

Country of ref document: EP

Kind code of ref document: A2

32PN Ep: public notification in the ep bulletin as address of the adressee cannot be established

Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205A DATED 27/05/2022)