Water turbine runner blade crack identification method based on PSDT

Abstract

The invention discloses a water turbine runner blade crack identification method based on PSDT, and belongs to the technical field of water turbine blade crack identification. A mixed-flow turbine runner blade is used as a research object, finite element analysis software is used for establishing a kinetic model of the cracked mixed-flow turbine runner blade under the fluid action, and damage response signals of different crack positions of a structure under environmental excitation are simulated under the fluid-solid coupling action in combination with solid mechanics. The method comprises the following steps: extracting acceleration time-history signals of a crack blade, carrying out PSDT modal parameter identification on the acceleration time-history signals to obtain two groups of PSDT function curves, comparing the two groups of PSDT function curves, constructing a PSDT difference function reciprocal, extracting modal frequency of the crack of the blade according to the PSDT difference function reciprocal curve, and carrying out structure modal parameter identification by using a PSDT method. Whether the runner blade cracks or not can be judged according to the PSDT method, and the method is applied to structural health monitoring, recognition and the like of large rotating machinery and has high engineering practical value.

Description

Technical Field

[0001] The invention belongs to the technical field of crack identification of water turbine blades, and in particular relates to a crack identification method of a water turbine runner blade based on PSDT. Background Art

[0002] With the increasing demand for renewable energy, peak-shaving and frequency-regulating hydropower stations play an important role in renewable energy power systems, which can effectively regulate the peak load of the power grid and maintain frequency stability. The frequent start and stop of the turbine unit will cause drastic changes in pressure pulsation and flow, causing the turbine to frequently pass through the vibration zone during operation, resulting in cracks in the runner blades. With the growing demand for renewable energy.

[0003] The presence of cracks will reduce the rigidity of the blade or increase the local flexibility. If they are not monitored and repaired in time, the cracks will continue to extend from surface cracks to through cracks, causing devastating damage to the turbine unit. Therefore, effective detection of cracks in turbine units can reduce the occurrence of accidents and economic losses.

[0004] The prior art CN112116587A uses image detection technology to identify and analyze whether there are cracks on the blades. This method requires shutdown and the amount of analysis is too large. CN117554498A discloses that the frequency-doubling law of the blades is obtained by analyzing multiple different types of crack models, and then applying external excitation to it when the unit is shut down, extracting the response frequency, and then converting it and comparing it with the frequency-doubling law to determine whether the blades have cracks and which model the cracks belong to. This method greatly simplifies the identification method, but requires shutdown, which is difficult to implement for large turbine units. Summary of the invention

[0005] The purpose of the present invention is to provide a PSDT-based method for identifying cracks in turbine runner blades, so as to solve the problem that the existing analysis method requires external excitation, resulting in a small scope of application and is difficult to implement on large turbine units.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solution: a method for identifying cracks in a turbine runner blade based on PSDT, characterized in that it comprises the following steps:

[0007] Step 1: Take 1 set of normal blade runner models and 2 sets of blade runner models with through-cracks, where the through-cracks are located at the connection between the water inlet and the upper crown and at the connection between the water outlet and the lower ring;

[0008] Step 2: According to the actual operating conditions of the turbine unit, the boundary conditions for numerical simulation of the turbine flow field and structural field are set, and the interface between the water body and the runner is set as the fluid-solid coupling surface;

[0009] Step 3: The turbine unit is meshed using finite element software, and then a fluid-solid coupling numerical simulation is performed on the turbine unit. The impact of water acts on the runner blades as an environmental load, and the acceleration time history signals of normal blades and cracked blades are extracted respectively;

[0010] Step 4: Perform PSDT modal parameter identification on the acceleration time history signal to obtain two sets of PSDT function curves and compare them, construct the inverse of the PSDT difference function, and extract the reference modal frequency of the blade crack according to the inverse curve of the PSDT difference function;

[0011] Step 5: Collect the vibration signal of the turbine runner blade in the running state, refer to steps 2-4 and use the PSDT method to obtain the blade modal frequency, and compare the blade modal frequency with the reference modal frequency to determine whether the blade has cracks.

[0012] A further technical solution is that the turbine model is a mixed flow turbine.

[0013] A further technical solution is that in actual engineering applications, the flow of fluid in the turbine is a three-dimensional non-steady-state flow with water as the medium, which is an incompressible fluid. There is almost no heat exchange in the turbine, and the micro-heat can be ignored. Therefore, when adding boundary conditions in step 2, the flow of fluid in the turbine unit follows the law of conservation of mass and the law of conservation of momentum:

[0014] (1) Mass conservation equation

[0015] The mass conservation equation follows the law of mass conservation and is essentially the continuity equation of flow. It is based on the continuous medium model, and the flow velocity, density, and space and time coordinates in the flow domain are continuous. The expression is as follows:

[0016]

[0017] When the water flow inside the fluid machinery is an incompressible fluid, the equation is simplified to:

[0018]

[0019] u i is the fluid velocity vector in the i direction; ρ is the fluid density; x i is the coordinate component in the x direction.

[0020] (2) Energy conservation equation

[0021] According to the law of conservation of momentum, we get the Navier-Stokes equation (NS equation). The resultant force is the rate of change of momentum over time, so the momentum conservation equation can be expressed as the NS equation:

[0022]

[0023] Where u is the fluid velocity vector; ρ is the fluid density; f is the mass force; p is the fluid pressure; μ is the turbulence intensity, and x is i is the coordinate component.

[0024] From the theory of classical mechanics, we know that the dynamic equation of the structure is:

[0025] Mx″+Cx′+Kx=F(t) (4)

[0026] Wherein, M is the mass matrix of the runner; C is the damping matrix of the runner; K is the stiffness matrix of the runner; x is the displacement vector; F is the external excitation force; x″ is the velocity vector; x′ is the acceleration vector; and t is the time.

[0027] A further technical solution is to satisfy the following relationship when performing fluid-solid coupling numerical simulation in step 3:

[0028]

[0029] In the formula, τ f n f is the fluid normal stress; τ s n s is the solid normal stress; d f is the fluid displacement; d s is the solid displacement; q f is the fluid heat flow; q s is the solid heat flow; T f is the fluid temperature; T s is the solid temperature.

[0030] A further technical solution is that step 4 is to perform PSDT operation on the acceleration time history data of the two measuring points to obtain two sets of PSDT function curves, and construct the inverse of the PSDT difference function. The function peak is the modal frequency of the wheel, as follows:

[0031] For the responses at any two output points i and j, the power spectral density transfer ratio about the reference point p is defined as the power spectrum S ip (ω) and power spectrum S jp (ω) ratio

[0032]

[0033] If the reference point q is transformed, the power spectrum density transfer ratio of the reference point q is:

[0034]

[0035] It can also be expressed as:

[0036]

[0037] When s approaches the system r-order pole λ r When , its limit satisfies:

[0038]

[0039] Where: φ ir and φ jr are the r-order vibration modes corresponding to the degrees of freedom i and j respectively.

[0040] According to the proportional function limit theorem (8), it can be proved that for the terms t with the same subscripts k and n in the numerator and denominator kn The limiting ratios of (ω) are equal, so we can conclude that:

[0041]

[0042] Similarly, the PSDT function corresponding to the reference point q is satisfy

[0043]

[0044] Under the same loading condition, subtracting the response power spectrum density transfer ratio functions of two different reference output measurement points yields:

[0045]

[0046] In other words, the extremes of the system are The zero point of . Therefore, according to The inverse of the amplitude can determine the function pole, that is, the function peak, that is,

[0047]

[0048] A further technical solution is that in step 5, when the blade modal frequency includes the normal blade frequency and has no high-order frequency, it is determined that the turbine runner blade has no cracks; otherwise, it is determined that the turbine runner blade has cracks.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] Taking the Francis turbine runner blade as the research object, the dynamic model of the cracked Francis turbine runner blade under the action of fluid was established using finite element software, and the damage response signals of different crack positions of the structure under environmental excitation were simulated under the action of fluid-solid coupling in combination with solid mechanics. The acceleration signal of the cracked blade was extracted and the modal parameters of the structure were identified using the PSDT method. According to the PSDT method, it can be determined whether the runner blade has cracks. It is applied to the structural health monitoring and identification of large rotating machinery, and has high engineering practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of cracks at different positions in the embodiment.

[0052] Figure 2 The measurement point arrangement of blade cracks in the embodiment

[0053] Figure 3 This is a diagram for setting the boundary condition parameters of the runner structure in the embodiment.

[0054] Figure 4 This is a verification diagram of the PSDT method of the present invention.

[0055] Figure 5 1 is the acceleration time history diagram of different measuring points of the blade crack under environmental excitation in the embodiment.

[0056] Figure 6 It is a PSDT function curve diagram of different reference points under the blade crack in the embodiment.

[0057] Figure 7 It is the inverse curve graph of the PSDT difference function at different reference points under the blade crack in the embodiment. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0059] First of all, hydraulic factors are the main cause of cracks in runner blades. Hydraulic loads usually cause high stress concentration on the runner crown and water inlet, lower ring and water outlet, which can easily lead to cracks in runner blades. However, in the operating state, the vibration signal of the crack cannot be extracted and if the traditional experimental analysis method is used, it is necessary to add external excitation as input data manually, but in actual working conditions, it is difficult to apply excitation manually, which has great limitations on the identification of structural damage of turbine units. Therefore, the present invention uses the PSDT method to identify the modal characteristics of the structure using only the output data. Using finite element software to simulate the vibration signal of blade cracks in the working state for modal identification is the most convenient and more effective and reduces economic losses. Figure 1 A normal blade and two blade cracks at different locations studied in the present invention are shown. Figure 2 Arrange the measuring points of blade cracks.

[0060] The PSDT-based method for identifying cracks in a turbine runner blade in this embodiment includes the following steps:

[0061] Step 1: Use the corresponding 1 set of normal blade runner models and 2 sets of blade runner models with through cracks. The through cracks are located at the connection between the water inlet and the upper crown, and the connection between the water outlet and the lower ring. The specific measurement points are as follows: Figure 2 shown.

[0062] Step 2: According to the actual operating conditions of the turbine unit, the numerical simulation boundary conditions of the turbine flow field and structural field are set, and the interface between the water body and the runner is set as the fluid-solid coupling surface. The inlet is the mass flow inlet, with a value of 199.550082kg / s; the outlet is the pressure outlet, with a value of 0. There is almost no heat exchange in the turbine, so the solid wall is adiabatic and has no slip. The fluid-solid coupling interface of the rotating domain is processed by sliding mesh. The total running time is 800s, and the time step is 0.5X10 -3 s, and the rotor speed is 332.59 rpm.

[0063] In actual engineering applications, the flow of fluid in a turbine is a three-dimensional non-steady-state flow with water as the medium. It is an incompressible fluid. There is almost no heat exchange in the turbine, and the micro-heat can be ignored. Therefore, when adding boundary conditions, the flow of fluid in the turbine unit follows the law of conservation of mass and momentum:

[0064] (1) Mass conservation equation

[0065] The mass conservation equation follows the law of mass conservation and is essentially the continuity equation of flow. It is based on the continuous medium model, and the flow velocity, density, and space and time coordinates in the flow domain are continuous. The expression is as follows:

[0066]

[0067] When the water flow inside the fluid machinery is an incompressible fluid, the equation is simplified to:

[0068]

[0069] u i is the fluid velocity vector in the i direction; ρ is the fluid density; x i is the coordinate component in the x direction.

[0070] (2) Energy conservation equation

[0071] According to the law of conservation of momentum, we get the Navier-Stokes equation (NS equation). The resultant force is the rate of change of momentum over time, so the momentum conservation equation can be expressed as the NS equation:

[0072]

[0073] Where u is the fluid velocity vector; ρ is the fluid density; f is the mass force; p is the fluid pressure; μ is the turbulence intensity, and x is i is the coordinate component.

[0074] From the theory of classical mechanics, we know that the dynamic equation of the structure is:

[0075] Mx″+Cx′+Kx=F(t) (4)

[0076] Wherein, M is the mass matrix of the runner; C is the damping matrix of the runner; K is the stiffness matrix of the runner; x is the displacement vector; F is the external excitation force; x″ is the velocity vector; x′ is the acceleration vector; and t is the time.

[0077] Step 3: The turbine unit is meshed using finite element software, and then a fluid-solid coupling numerical simulation is performed on the turbine unit. The impact of water acts on the runner blades as an environmental load, and the acceleration time history signals of normal blades and cracked blades are extracted respectively;

[0078] Transfer the flow field load to the structural field. The structural field settings are as follows: Figure 3 As shown, the working modal analysis of the structure is realized. When considering the fluid-solid coupling, the temperature, stress, displacement and heat flow should be equal at the interface of the fluid-solid coupling. Therefore, the fluid domain and the structural domain can be coupled through the physical quantities at the interface. The following relationship is satisfied:

[0079]

[0080] In the formula, τ f n f is the fluid normal stress; τ s n s is the solid normal stress; d f is the fluid displacement; d s is the solid displacement; q f is the fluid heat flow; q s is the solid heat flow; T f is the fluid temperature; T s is the solid temperature.

[0081] Step 4: Perform PSDT modal parameter identification on the acceleration time history signal to obtain two sets of PSDT function curves and compare them, construct the inverse of the PSDT difference function, and extract the reference modal frequency of the blade crack according to the inverse curve of the PSDT difference function;

[0082] The acceleration time history data of the two measuring points are subjected to PSDT operation to obtain two sets of PSDT function curves, and the inverse of the PSDT difference function is constructed. The function peak is the modal frequency of the wheel, as follows:

[0083] For the responses at any two output points i and j, the power spectral density transfer ratio about the reference point p is defined as the power spectrum S ip (ω) and power spectrum S jp (ω) ratio

[0084]

[0085] If the reference point q is transformed, the power spectrum density transfer ratio of the reference point q is:

[0086]

[0087] It can also be expressed as:

[0088]

[0089] When s approaches the system r-order pole λ r When , its limit satisfies:

[0090]

[0091] Where: φ ir and φ jr are the r-order vibration modes corresponding to the degrees of freedom i and j respectively.

[0092] According to the proportional function limit theorem (8), it can be proved that for the terms t with the same subscripts k and n in the numerator and denominator kn The limiting ratios of (ω) are equal, so we can conclude that:

[0093]

[0094] Similarly, the PSDT function corresponding to the reference point q satisfy

[0095]

[0096] Under the same loading condition, subtracting the response power spectrum density transfer ratio functions of two different reference output measurement points yields:

[0097]

[0098] In other words, the extremes of the system are The zero point of . Therefore, according to The inverse of the amplitude can determine the function pole, that is, the function peak, that is,

[0099]

[0100] Using the above method, the Welch response spectrum of the acceleration time history data of any measuring point around the crack is estimated. The window function is Kaiser window, the signal length is 512, and the overlap rate is 256. Two sets of PSDT function curves under different reference outputs are obtained. It is found that the peak position of the PSDT amplitude is equal to the structural resonance frequency. The inverse of the PSDT difference function is constructed, and the system pole just corresponds to the peak position of the function, and the modal frequency of the runner structure is obtained.

[0101] because At the system poles, they are independent and invariant and converge to the same value, so the function ΔT -1 The value of (ω) at the system pole is obviously prominent, and the system pole λ r That is, in the function ΔT -1 (ω) is found. Figure 4 The peak curve of the frequency identified by the power spectrum density transfer ratio method is shown in Figure 1. The correctness of the PSDT method is verified by the above equation, and the identification results of this method are compared with the finite element identification results. The comparison results show that the maximum error of the natural frequency of the cantilever beam calculated by the power spectrum density transfer ratio method is 2%. Therefore, the power spectrum density transfer ratio method can be used as a reliable data processing method to obtain the modal parameters of the structure, and the results obtained are accurate and effective.

[0102] Step 5: Collect the vibration signal of the turbine runner blade in the running state, refer to steps 2-4 to obtain the blade modal frequency using the PSDT method, and compare the blade modal frequency with the reference modal frequency to determine whether the blade has cracks. When the blade modal frequency contains the normal blade frequency and no high-order frequency, it is determined that the turbine runner blade has no cracks; otherwise, it is determined that the turbine runner blade has cracks.

[0103] The cracked blade was numerically simulated by the finite element analysis method in step 3, and the pressure pulsation in the fluid domain was applied to the runner blade in the structural domain, such as Figure 5 As shown in the figure, the acceleration time history diagrams of different measuring points of the blade crack under environmental excitation are extracted, and there are 800 data in each acceleration signal.

[0104] Finally, the acceleration time history signal described above is subjected to the PSDT method for modal parameter identification. First, the power spectrum is estimated using the Welch method to obtain two sets of PSDT function curves: For comparison, Figure 6 As shown, the PSDT curves overlap at the structural resonance frequency, and then the inverse of the PSDT difference function is constructed, as Figure 7 As shown, it can be seen that the trends of different blade crack measurement points are consistent, but the amplitudes are different. The modal frequencies of blade cracks are extracted as shown in Table 1. Regardless of the crack position at B or C, due to the appearance of cracks, the vibration signal near the crack will contain specific frequency components. Compared with normal blades, it is found that the frequency peaks of 532 Hz, 660 Hz, and 720 Hz appear in the 3rd, 5th, and 7th order modes, respectively. It is found that cracks mainly appear in the high frequency range of 500-800 Hz. Therefore, 532 Hz, 660 Hz, and 720 Hz are identified as the structural modal frequencies caused by blade cracks. At the same time, the modal frequencies are identified by the PSDT method. It is believed that cracks appear in the turbine runner blades as long as the normal blade frequency does not appear and is a high-order frequency.

[0105] Table 1. Modal parameters of blade cracks identified by PSDT

[0106]

[0107] In summary, the PSDT method does not rely on external excitation, but only relies on the effect of water pressure pulsation on the turbine unit to extract the acceleration data output by the runner structure to identify the modal parameters of the blade crack, and the frequency peak does not change with the change of the measurement point position. At the same time, it is found that the crack frequency can be captured at a high order. Therefore, the PSDT method is used to identify the crack model of the blade at the inlet and outlet of the turbine unit with strong robustness, and can fully identify the modal characteristic results under the working state, which solves the shortcomings of traditional identification methods and is used to solve problems such as structural health monitoring and load identification. This has great progressive significance for rotating machinery fault identification.

[0108] Although the present invention is described herein with reference to a number of illustrative embodiments of the present invention, it will be appreciated that those skilled in the art may devise numerous other modifications and implementations that fall within the scope of the present disclosure. More specifically, within the scope of the present disclosure, drawings, and claims, a variety of variations and modifications may be made to the components or layout. In addition to variations and modifications to the components or layout, other uses will be apparent to those skilled in the art.

Claims

1. A PSDT-based method for identifying cracks in turbine runner blades, characterized in that: The following steps are involved: Step 1: Take 1 set of normal blade runner models and 2 sets of blade runner models with through-cracks, where the through-cracks are located at the connection between the water inlet and the upper crown and at the connection between the water outlet and the lower ring; Step 2: According to the actual operating conditions of the turbine unit, the boundary conditions for numerical simulation of the turbine flow field and structural field are set, and the interface between the water body and the runner is set as the fluid-solid coupling surface; Step 3: The turbine unit is meshed using finite element software, and then a fluid-solid coupling numerical simulation is performed on the turbine unit. The impact of water acts on the runner blades as an environmental load, and the acceleration time history signals of normal blades and cracked blades are extracted respectively; Step 4: Perform PSDT modal parameter identification on the acceleration time history signal to obtain two sets of PSDT function curves and compare them, construct the inverse of the PSDT difference function, and extract the reference modal frequency of the blade crack according to the inverse curve of the PSDT difference function; Step 5: Collect the vibration signal of the turbine runner blade in the running state, refer to steps 2-4 and use the PSDT method to obtain the blade modal frequency, and compare the blade modal frequency with the reference modal frequency to determine whether the blade has cracks.

2. The method according to claim 1, characterized in that The water turbine model is a Francis turbine.

3. The method according to claim 1, characterized in that When adding boundary conditions in step 2, the fluid flow in the turbine unit follows the law of conservation of mass and the law of conservation of momentum: (1) Mass conservation equation The mass conservation equation follows the law of mass conservation and is essentially the continuity equation of flow. It is based on the continuous medium model, and the flow velocity, density, and space and time coordinates in the flow domain are continuous; the expression is as follows: u i is the fluid velocity vector in the i direction; ρ is the fluid density; x i is the coordinate component in the x direction; (2) Energy conservation equation Express the momentum conservation equation as the Navier-Stokes equations: Where u is the fluid velocity vector; ρ is the fluid density; f is the mass force; p is the fluid pressure; μ is the turbulence intensity, and x is i is the coordinate component; The dynamic equation of the structure is: Mx″+Cx′+Kx=F(t) Wherein, M is the mass matrix of the runner; C is the damping matrix of the runner; K is the stiffness matrix of the runner; x is the displacement vector; F is the external excitation force; x″ is the velocity vector; x′ is the acceleration vector; and t is the time.

4. The method according to claim 1, characterized in that: When performing fluid-solid coupling numerical simulation in step 3, the following relationship is satisfied: In the formula, τ f n f is the fluid normal stress; τ s n s is the solid normal stress; d f is the fluid displacement; d s is the solid displacement; q f is the fluid heat flow; q s is the solid heat flow; T f is the fluid temperature; T s is the solid temperature.

5. The method according to claim 1, characterized in that Step 4 is to perform PSDT operation on the acceleration time history data of the two measuring points to obtain two sets of PSDT function curves, and construct the inverse of the PSDT difference function. The function peak is the modal frequency of the wheel, as follows: For the responses at any two output points j and k, the power spectral density transfer ratio at the reference point p is defined as the power spectrum S ip (ω) and power spectrum S jp (ω) ratio: The power spectral density transfer ratio at the reference point q is: Also expressed as: When s approaches the system r-order pole λ r When Where: φ ir and φ jr are the r-order vibration modes corresponding to the degrees of freedom i and j respectively; Similarly, the PSDT function of the reference point q is satisfy Under the same loading condition, subtracting the response power spectrum density transfer ratio functions of two different reference output measurement points yields: according to The inverse of the amplitude can determine the function pole, that is, the function peak, that is, 6. The method according to claim 1, characterized in that In step 5, when the blade modal frequency includes the normal blade frequency and has no high-order frequency, it is determined that the turbine runner blade has no cracks; otherwise, it is determined that the turbine runner blade has cracks.

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