A turbine damping blade response solving method and system based on a correction coefficient

Abstract

The application discloses a turbine damping blade response solving method and system based on a correction coefficient, and the method comprises the following steps: obtaining a finite element analysis model of a turbine damping blade to be solved in response, and obtaining a total stiffness matrix, a total mass matrix and a total damping matrix based on the finite element analysis model; based on the total stiffness matrix, the total mass matrix and the total damping matrix, a frequency domain dynamics equation of the finite element analysis model is constructed; and the frequency domain dynamics equation is solved based on a displacement harmonic coefficient vector and a dry friction force harmonic coefficient vector, so that turbine damping blade response solving is completed. The method provided by the application can realize efficient solving of the nonlinear response of the turbine damping blade under the action of the dry friction force.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear motion characteristics research of turbine damping blades, and specifically relates to a method and system for solving the response of turbine damping blades based on correction coefficients. Background Technology

[0002] Currently, the most widely used solution methods for calculating the nonlinear motion characteristics of turbine damped blades generally include the time-frequency interaction method and the equivalent coefficient method. The time-frequency interaction method is generally combined with the multi-harmonic balance method, and the solution results of nonlinear forces are obtained through the interactive iterative process of frequency domain-time domain-frequency domain. The equivalent coefficient method is based on the idea of ​​engineering simplification, and uses the single harmonic assumption to obtain the equivalent stiffness coefficient and the equivalent damping coefficient, thereby realizing the rapid solution of nonlinear forces.

[0003] Because it takes into account the influence of higher-order harmonics, the time-frequency interaction method has relatively good accuracy. However, when solving the damped blade response, the method is prone to non-convergence when the dry friction dynamics model is complex. On the other hand, for different dry friction dynamics models, the time-frequency interaction method requires the derivation of different forms of Jacobian matrices, which makes the program scalability of the method relatively poor and difficult to combine with experimental data.

[0004] The equivalent coefficient method describes the nonlinear force at the interface using only equivalent stiffness and equivalent damping coefficient, which allows different dry friction dynamics models to be described by a unified equivalent coefficient. Therefore, this method has good versatility and is easy to combine with experimental data to complete model correction. However, when using the traditional equivalent coefficient method to solve the frequency response curve, it is necessary to continuously correct the equivalent stiffness coefficient and equivalent damping coefficient, resulting in low solution efficiency.

[0005] In summary, there is an urgent need for a new method for solving the nonlinear turbine damping blade response under dry friction. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for solving the response of turbine damping blades based on correction coefficients, in order to solve one or more of the aforementioned technical problems. The method provided by this invention can efficiently solve the nonlinear response of turbine damping blades subjected to dry friction.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention provides a method for solving the response of a turbine damping blade based on a correction coefficient, comprising the following steps:

[0009] Obtain the finite element analysis model of the turbine damping blade to be solved, and obtain the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model;

[0010] Based on the overall stiffness matrix, overall mass matrix, and overall damping matrix, the frequency domain dynamic equations of the finite element analysis model are constructed.

[0011] The frequency domain dynamic equation is solved based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the turbine damping blade response solution; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network.

[0012] A further improvement of the present invention lies in that, in the process of constructing the frequency domain dynamic equations of the finite element analysis model based on the overall stiffness matrix, the overall mass matrix, and the overall damping matrix,

[0013] The expression for the obtained frequency domain dynamic equation is:

[0014] SX-F e -F n =0;

[0015] In the formula, S represents the dynamic stiffness matrix, and F e F represents the vector of excitation force harmonic coefficients; n represents the dry friction harmonic coefficient vector, and X is the displacement harmonic coefficient vector;

[0016] In the formula, Λ i This represents the harmonic coefficient matrix corresponding to the i-th harmonic;

[0017] In the formula, ω e Let M represent the excitation frequency, K represent the overall mass matrix of the damping blade, C represent the overall stiffness matrix of the damping blade, and C represent the overall damping matrix of the damping blade.

[0018] A further improvement of the present invention is that the structure of the fully connected artificial neural network includes an input layer, a hidden layer 1, a hidden layer 2, and an output layer; the activation function of the hidden layer 1 is ReLU, and the activation function of the hidden layer 2 is Sigmoid;

[0019] The steps for obtaining the pre-trained fully connected artificial neural network include:

[0020] Obtain a training set of samples for the neural network, wherein each training sample includes a sample displacement harmonic coefficient vector and a sample dry friction harmonic coefficient vector; update the parameters of the fully connected artificial neural network to a preset convergence condition based on the training set of samples to obtain the pre-trained fully connected artificial neural network.

[0021] The specific steps for obtaining the training set of samples for the neural network include:

[0022] The equations are processed, including: defining amplitude and phase correction coefficients in the equation model based on the turbine damping blade; where, In the formula, x c,j A represents the time-domain relative displacement at the j-th contact element. c,j σ represents the time-domain amplitude at the j-th contact element, i represents the imaginary unit, ω represents the blade vibration angular frequency, and σ represents the time-domain amplitude at the j-th contact element. j This indicates that the relative displacement of the j-th contact element lags behind the excitation force in phase; f c,j This represents the dry friction force at the j-th contact unit. This represents the amplitude correction coefficient at the j-th contact unit. This represents the phase correction coefficient at the j-th contact unit;

[0023] The nonlinear terms in the equation model are made dimensionless and expressed using the frequency domain method; where the tangential stiffness k at the contact element is used. x The frictional force can be dimensionless by using the coefficient of friction μ and the normal pressure N0, and the expression is: In the formula, This represents dimensionless dry friction. This represents the dimensionless amplitude correction factor. Indicates dimensionless displacement. This represents the phase correction coefficient after dimensionless conversion for 1 rad;

[0024] By constructing the frequency domain dynamic equations and time-frequency interaction algorithm of the finite element model of the turbine damped blade, the harmonic coefficient vector F of dry friction force under multiple frequency excitation forces is obtained. n The displacement harmonic coefficient vector X is used as the training sample set.

[0025] A further improvement of the present invention lies in that the frequency domain dynamic equations and time-frequency interaction algorithm of the constructed turbine damping blade finite element model are used to obtain the dry friction force harmonic coefficient vector F under multiple frequency excitation forces. n The steps of using the displacement harmonic coefficient vector X as the training sample set include:

[0026] (1) Obtain the excitation force frequency, amplitude, and relative displacement between the contact surfaces of the turbine damping blades;

[0027] (2) The time-domain solution of the nonlinear friction force is obtained by calculating the relative displacement between the contact surfaces of the turbine damping blades through the friction model; the frequency-domain solution of the nonlinear friction force is obtained by Fourier transform; the frequency-domain dynamic equation of the obtained turbine damping blade finite element model is solved, and the calculated overall displacement field of the damping blade is subjected to inverse Fourier transform to update the relative displacement between the contact surfaces of the turbine damping blades.

[0028] (3) Repeat step (2) to update until the error of the relative displacement iteration value between the contact surfaces meets the preset requirements, and obtain the dry friction harmonic coefficient vector Fn and the displacement harmonic coefficient vector X at the excitation frequency.

[0029] (4) Change the excitation force frequency and amplitude, and repeat steps (1) to (3) to obtain multiple sets of dry friction force harmonic coefficient vectors Fn and displacement harmonic coefficient vectors X as training sample sets.

[0030] A further improvement of the present invention lies in that the steps of solving the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the solution of the turbine damping blade response specifically include:

[0031] For a given frequency f, determine whether it exceeds the solution range. If it does not exceed the range, iterate the expression of the update vector X according to the arc length extension method, so that the magnitude of the residual vector ||R|| is less than a certain given error range ε. If it exceeds the range, input a new frequency f and re-determine until the turbine damping blade response solution within the frequency range is completed.

[0032] The residual vector R is expressed as R = SX - F. e -F n During the iterative solution process, the displacement harmonic coefficient vector X and the dry friction harmonic coefficient vector F are continuously updated. n This ensures that the magnitude of the residual vector, ||R||, is less than a given error range ε; during the iteration process, for a given initial displacement vector or the result X of the k-th iteration step... (k) The expression for updating vector X is: Specifically, for a given displacement harmonic coefficient vector X, after dimensionless subtraction, it is fed into a pre-trained fully connected artificial neural network to obtain the dry friction harmonic coefficient vector F. n .

[0033] This invention provides a turbine damping blade response solution system based on correction coefficients, comprising:

[0034] The matrix acquisition module is used to acquire the finite element analysis model of the turbine damping blade to be solved, and to acquire the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model;

[0035] The equation construction module is used to construct the frequency domain dynamic equations of the finite element analysis model based on the overall stiffness matrix, overall mass matrix, and overall damping matrix.

[0036] The response solving module is used to solve the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the response solution of the turbine damping blade; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network.

[0037] A further improvement of the present invention lies in that, in the process of constructing the frequency domain dynamic equations of the finite element analysis model based on the overall stiffness matrix, the overall mass matrix, and the overall damping matrix,

[0038] The expression for the obtained frequency domain dynamic equation is:

[0039] SX-F e -F n =0;

[0040] In the formula, S represents the dynamic stiffness matrix, and F e F represents the vector of excitation force harmonic coefficients; n represents the dry friction harmonic coefficient vector, and X is the displacement harmonic coefficient vector;

[0041] In the formula, Λ i This represents the harmonic coefficient matrix corresponding to the i-th harmonic;

[0042] In the formula, ω e Let M represent the excitation frequency, K represent the overall mass matrix of the damping blade, C represent the overall stiffness matrix of the damping blade, and C represent the overall damping matrix of the damping blade.

[0043] A further improvement of the present invention is that the structure of the fully connected artificial neural network includes an input layer, a hidden layer 1, a hidden layer 2, and an output layer; the activation function of the hidden layer 1 is ReLU, and the activation function of the hidden layer 2 is Sigmoid;

[0044] The steps for obtaining the pre-trained fully connected artificial neural network include:

[0045] Obtain a training set of samples for the neural network, wherein each training sample includes a sample displacement harmonic coefficient vector and a sample dry friction harmonic coefficient vector; update the parameters of the fully connected artificial neural network to a preset convergence condition based on the training set of samples to obtain the pre-trained fully connected artificial neural network.

[0046] The specific steps for obtaining the training set of samples for the neural network include:

[0047] The equations are processed, including: defining amplitude and phase correction coefficients in the equation model based on the turbine damping blade; where, In the formula, x c,j A represents the time-domain relative displacement at the j-th contact element. c,j σ represents the time-domain amplitude at the j-th contact element, i represents the imaginary unit, ω represents the blade vibration angular frequency, and σ represents the time-domain amplitude at the j-th contact element. j This indicates that the relative displacement of the j-th contact element lags behind the excitation force in phase; f c,j This represents the dry friction force at the j-th contact unit. This represents the amplitude correction coefficient at the j-th contact unit. This represents the phase correction coefficient at the j-th contact unit;

[0048] The nonlinear terms in the equation model are made dimensionless and expressed using the frequency domain method; where the tangential stiffness k at the contact element is used. x The frictional force can be dimensionless by using the coefficient of friction μ and the normal pressure N0, and the expression is: In the formula, This represents dimensionless dry friction. This represents the dimensionless amplitude correction factor. Indicates dimensionless displacement. This represents the phase correction coefficient after dimensionless conversion for 1 rad;

[0049] By constructing the frequency domain dynamic equations and time-frequency interaction algorithm of the finite element model of the turbine damped blade, the harmonic coefficient vector F of dry friction force under multiple frequency excitation forces is obtained. n The displacement harmonic coefficient vector X is used as the training sample set.

[0050] A further improvement of the present invention lies in that the frequency domain dynamic equations and time-frequency interaction algorithm of the constructed turbine damping blade finite element model are used to obtain the dry friction force harmonic coefficient vector F under multiple frequency excitation forces. n The steps of using the displacement harmonic coefficient vector X as the training sample set include:

[0051] (1) Obtain the excitation force frequency, amplitude, and relative displacement between the contact surfaces of the turbine damping blades;

[0052] (2) The time-domain solution of the nonlinear friction force is obtained by calculating the relative displacement between the contact surfaces of the turbine damping blades through the friction model; the frequency-domain solution of the nonlinear friction force is obtained by Fourier transform; the frequency-domain dynamic equation of the obtained turbine damping blade finite element model is solved, and the calculated overall displacement field of the damping blade is subjected to inverse Fourier transform to update the relative displacement between the contact surfaces of the turbine damping blades.

[0053] (3) Repeat step (2) to update until the error of the relative displacement iteration value between the contact surfaces meets the preset requirements, and obtain the dry friction harmonic coefficient vector Fn and the displacement harmonic coefficient vector X at the excitation frequency.

[0054] (4) Change the excitation force frequency and amplitude, and repeat steps (1) to (3) to obtain multiple sets of dry friction force harmonic coefficient vectors Fn and displacement harmonic coefficient vectors X as training sample sets.

[0055] A further improvement of the present invention lies in that the steps of solving the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the solution of the turbine damping blade response specifically include:

[0056] For a given frequency f, determine whether it exceeds the solution range. If it does not exceed the range, iterate the expression of the update vector X according to the arc length extension method, so that the magnitude of the residual vector ||R|| is less than a certain given error range ε. If it exceeds the range, input a new frequency f and re-determine until the turbine damping blade response solution within the frequency range is completed.

[0057] The residual vector R is expressed as R = SX - F. e -F n During the iterative solution process, the displacement harmonic coefficient vector X and the dry friction harmonic coefficient vector F are continuously updated. n This ensures that the magnitude of the residual vector, ||R||, is less than a given error range ε; during the iteration process, for a given initial displacement vector or the result X of the k-th iteration step... (k) The expression for updating vector X is: Specifically, for a given displacement harmonic coefficient vector X, after dimensionless subtraction, it is fed into a pre-trained fully connected artificial neural network to obtain the dry friction harmonic coefficient vector F. n .

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The method provided in this invention obtains the mapping relationship between the relative displacement harmonic coefficient vector and the dry friction harmonic coefficient vector by constructing a fully connected artificial neural network framework. Amplitude correction coefficients and phase correction coefficients are used to replace the traditional equivalent coefficients, simplifying the time-frequency transformation process in the original calculation flow into a direct mapping relationship in the frequency domain. Related calculations can be completed through highly parallelized matrix operations, resulting in high solution efficiency. Furthermore, the fully connected artificial neural network framework used in this invention has good fitting performance and is suitable for the two major types of dry friction dynamics models widely used in engineering for solving the response of damped blades. It can establish a unified representation structure for dry friction dynamics models with different forms, eliminating the need to modify the code every time the dry friction dynamics model is changed, facilitating debugging, and making it easy to integrate with experimental data. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; obviously, the drawings described below are some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0061] Figure 1 This is a flowchart illustrating a method for solving the response of a turbine damping blade based on a correction coefficient, provided in an embodiment of the present invention.

[0062] Figure 2 This is a flowchart illustrating a method for solving the response of a turbine damping blade based on a correction coefficient, provided in an embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram of a turbine damping blade response solution system based on a correction coefficient, provided in an embodiment of the present invention. Detailed Implementation

[0064] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0065] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0066] The present invention will now be described in further detail with reference to the accompanying drawings:

[0067] Please see Figure 1 The present invention provides a method for solving the response of a turbine damping blade based on a correction coefficient, comprising the following steps:

[0068] Step 1: Obtain the finite element analysis model of the turbine damping blade to be solved, and obtain the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model;

[0069] Step 2: Based on the overall stiffness matrix, overall mass matrix, and overall damping matrix, construct the frequency domain dynamic equations of the finite element analysis model;

[0070] Step 3: Solve the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the turbine damping blade response solution; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network.

[0071] The method provided by this invention obtains the mapping relationship between the relative displacement harmonic coefficient vector and the dry friction harmonic coefficient vector by building a fully connected artificial neural network framework, and uses amplitude correction coefficient and phase correction coefficient to replace the traditional equivalent coefficient, so that the time-frequency transformation process in the original calculation process can be simplified to a direct mapping relationship in the frequency domain. The relevant calculations can be completed through highly parallelized matrix operations, which has high solution efficiency.

[0072] Please see Figure 2 The present invention provides a method for solving the response of a turbine damping blade based on a correction coefficient, the specific steps of which include:

[0073] Step 1: Construct the corresponding finite element analysis model for the actual turbine damping blade model to be studied.

[0074] In a specific and exemplary embodiment of the present invention, in order to obtain the response characteristics of the turbine damping blade under study, it is first necessary to construct a finite element model of the turbine damping blade; the blade model can be an actual operating unit or a blade for laboratory research. Based on the obtained blade design parameters and other information, a 3D model of the blade's true shape is constructed using 3D modeling software, such as SolidWorks or CATIA; subsequently, finite element modeling is performed on the blade and impeller models using mesh generation software; during finite element modeling, attention should be paid to preserving the local shape features of the blade, such as the blade's fillets and the contact surfaces of the damping components.

[0075] Based on the node numbers, relative positions of the nodes, and properties of the blade's metallic material (such as density and elasticity) in the three-dimensional finite element model of the blade obtained through modeling, the overall stiffness matrix, overall mass matrix, and overall damping matrix corresponding to the three-dimensional finite element model of the blade can be obtained through element assembly.

[0076] Step 2: By constructing the corresponding finite element analysis model in Step 1, obtain the frequency domain dynamic equation of the finite element model of the turbine damping blade to be studied.

[0077] Specifically, in this embodiment of the invention, the dynamic equations of the turbine damping blade in the time domain, obtained by discretization using the finite element method, are as follows:

[0078]

[0079] In the formula, M represents the overall mass matrix of the flat damping blade; K represents the overall stiffness matrix of the damping blade; C represents the overall damping matrix of the damping blade; and x represents the vector of displacement of each node in the finite element model of the blade in each degree of freedom. This represents the velocity vector of each node in the finite element model of the blade at each degree of freedom; f represents the acceleration vector of each node in the finite element model of the blade at each degree of freedom; e f represents the periodic low-frequency airflow excitation force vector acting on the nodes of the finite element model surface of the blade; n This represents the nonlinear frictional force vector introduced at the nodes on the contact interface between the damping components in the finite element model of the blade.

[0080] Generally, periodic excitation force is caused by periodic airflow disturbance between the moving and stationary rotors, and belongs to a type of harmonic excitation force with a specific order. Based on this assumption, in this embodiment of the invention, the periodic low-frequency airflow excitation force vector f is considered to be... e The components have the following form:

[0081]

[0082] In the formula, ω represents the amplitude component of the excitation force in the i-th degree of freedom of the j-th sector; e N represents the excitation force frequency; t represents time; N b The number of blades is represented by r; r represents the excitation force order, used to describe the action of excitation forces with different inter-blade phase angles.

[0083] Under periodic loads, the blade response generally also exhibits periodicity. According to the harmonic balance method, when considering the influence of higher-order harmonics, its steady-state response is composed of the superposition of multiple harmonic components, and therefore has the following form:

[0084]

[0085] In the formula, x j N represents the magnitude of the displacement of the j-th degree of freedom at time t; h Indicates the highest harmonic order retained; i represents the harmonic index; Let represent the phase of the i-th harmonic component corresponding to the j-th degree of freedom, and have

[0086] Expanding equation (3), we obtain the harmonic coefficients X of the sine and cosine terms, respectively. s and X c Based on this, equation (3) can be expressed as:

[0087]

[0088] In the formula, X0 represents the constant term harmonic coefficient vector of each degree of freedom displacement; X si X represents the sinusoidal harmonic coefficient of the i-th harmonic; ci This represents the cosine harmonic coefficient of the i-th harmonic.

[0089] To simplify the representation, they are combined into a single displacement harmonic coefficient vector X:

[0090]

[0091] Substituting equations (4) and (5) into equation (1), considering that the coefficients of the same harmonic terms on both sides of the equation should be equal, and neglecting the harmonic terms while retaining only the harmonic coefficients, we obtain the dynamic equation expressed by the displacement harmonic coefficient vector X as follows:

[0092] SX-F e -F n =0 (6)

[0093] Here, matrix S represents the dynamic stiffness matrix, which depends on the excitation frequency ω. e ;F e F represents the vector of excitation force harmonic coefficients; nThis represents the vector of harmonic coefficients of nonlinear friction force. The dynamic stiffness matrix S has the following form:

[0094]

[0095] In the formula: Λ i The harmonic coefficient matrix representing the i-th harmonic has the following form:

[0096]

[0097] Excitation force harmonic vector F e In the excitation force vector f e Once given, it is already determined. According to equation (2), the harmonic vector has a non-zero term only at the linear force degree of freedom of the first harmonic. The dry friction harmonic coefficient vector F... n Because of the influence of the shifted harmonic coefficient vector X, in order to obtain the shifted harmonic coefficient vector X, it is necessary to analyze and obtain the harmonic coefficient vector F of the model. n The relationship with X.

[0098] Through the above transformations, the frequency domain dynamic equation of the finite element model of the turbine damping blade is obtained, namely equation (6). Solving equation (6) yields the displacement harmonic coefficient vector X. Based on this, the time domain displacement vector x is obtained through transformation using equation (4), and thus the actual response characteristics of the turbine damping blade can be obtained. In this embodiment of the invention, in order to solve equation (6), the mapping relationship between the relative displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained through a pre-trained fully connected artificial neural network framework, that is, the dry friction harmonic coefficient vector F is obtained. n The mapping relationship with the displacement harmonic coefficient vector X.

[0099] In this embodiment of the invention, the equations to be processed in order to obtain the neural network training set include:

[0100] First, for the turbine damping blade under study, the amplitude correction coefficient and phase correction coefficient are defined in the turbine damping blade response solution equation model.

[0101] Based on the single-harmonic balance method, the airflow excitation force on the blade has the form of a first harmonic. Correspondingly, the relative displacement and dry friction force at the interface of the blade damper can also be expressed in the form of a first harmonic, as shown in the following equation:

[0102]

[0103]

[0104] In the formula, x c,j f represents the time-domain relative displacement at the j-th contact element; c,jA represents the dry friction force at the j-th contact unit; c,j F represents the time-domain amplitude at the j-th contact unit; c,j The value represents the amplitude of the dry friction force at the j-th contact unit; i represents the imaginary unit; ω represents the angular frequency of the blade vibration; σ j This indicates that the relative displacement of the j-th contact element lags behind the excitation force in phase. This indicates that the dry friction force at the j-th contact unit lags behind the excitation force in phase.

[0105] Considering the relative displacement of the contact surface of the damping element between adjacent blades of the turbine damping blade and the determination of the dry friction dynamics model, the dry friction force at the damping element will also be determined. Therefore, the invention believes that the dry friction force can be completely determined by the relative displacement after the given friction model. Thus, the turbine damping blade equation (10) can be further expressed in the following form:

[0106]

[0107] In the formula: This represents the amplitude correction coefficient at the j-th contact unit; This represents the phase correction coefficient at the j-th contact unit.

[0108] Secondly, the nonlinear terms in the turbine damping blade response solution equation model are made dimensionless and expressed using the frequency domain method.

[0109] Using the tangential stiffness k at the contact element x The frictional force can be made dimensionless using the coefficient of friction μ and the normal pressure N0:

[0110]

[0111] In the formula, This represents dimensionless dry friction. This represents the dimensionless amplitude correction factor; Indicates dimensionless displacement; This represents the phase correction coefficient after dimensionless transformation with respect to 1 rad. For ease of representation, the subscripts of the dimensionless quantities in the above formula have been removed.

[0112] Correspondingly, the relationship between the nonlinear force at the j-th contact element and the relative displacement at the interface can be expressed as:

[0113]

[0114] In this invention, to further optimize the solution efficiency, both the time-domain nonlinear friction force and displacement are expressed in frequency domain form, and time-dependent terms are discarded. The relationship between the harmonic coefficients of dry friction force and displacement harmonic coefficients can be obtained as follows:

[0115]

[0116] In the formula, Indicates the harmonic coefficient of dry friction; This represents the displacement harmonic coefficient.

[0117] In a further embodiment of the present invention, a neural network training set is obtained through a time-frequency interaction algorithm. Using the dynamic equations of the turbine damping blade finite element model constructed in step 2 and the time-frequency interaction algorithm, the nonlinear force harmonic coefficient vector F under multiple frequency excitation forces is obtained. n The displacement harmonic coefficient vector X.

[0118] First, given the excitation force frequency and amplitude, the relative displacement between the excitation force and the contact surface of the turbine damping blade;

[0119] Secondly, by calculating the time-domain solution of the nonlinear friction force through the relative displacement between the contact surfaces of the turbine damping blades using a friction model;

[0120] Subsequently, the frequency domain solution of the nonlinear friction force was obtained through Fourier transform;

[0121] Then, the frequency domain dynamic equation of the turbine damping blade finite element model obtained in step 2 is solved, and the inverse Fourier transform is performed on the calculated overall displacement field of the damping blade to update the relative displacement between the contact surfaces of the turbine damping blade.

[0122] Repeat the above steps until the error between the two iterations of the relative displacement between the contact surfaces meets the requirements, thus obtaining the nonlinear force harmonic coefficient vector F at the excitation frequency. n With the displacement harmonic coefficient vector X;

[0123] By changing the excitation force frequency and amplitude, repeat the above steps to obtain multiple sets of nonlinear force harmonic coefficient vectors F. n The displacement harmonic coefficient vector X.

[0124] Through the above dimensionless processing, multiple sets of dimensionless amplitude correction coefficients are obtained. and dimensionless phase correction coefficient With the corresponding dimensionless displacement

[0125] In a further embodiment of the present invention, a neural network is constructed and trained to obtain the dimensionless amplitude correction coefficient. and dimensionless phase correction coefficient Regarding dimensionless displacement Based on the changing relationship, a fully connected neural network framework with two hidden layers was established to obtain the dimensionless correction coefficient curves of different dry friction dynamic models, thereby obtaining the nonlinear fitting functions of the dimensionless amplitude and phase correction coefficients with respect to the dimensionless amplitude. The specific network structure is shown in Table 1 below, containing one input layer, two hidden layers, and one output layer. The network parameters were trained using a mini-batch Adam optimizer, and the loss function was chosen as mean squared error.

[0126]

[0127] In the formula: l represents the loss function; N batch Indicates batch size; The dimensionless correction coefficient represents the prediction and can be either an amplitude or a phase correction coefficient. This represents the actual dimensionless correction factor.

[0128] Table 1. Fully connected neural network structures used for fitting dimensionless correction coefficient curves

[0129]

[0130]

[0131] Through the above training, the dimensionless amplitude correction coefficient can be obtained. and dimensionless phase correction coefficient and dimensionless displacement The correspondence.

[0132] In this embodiment of the invention, given the frequency range to be solved, the arc-length extension method is used to solve the frequency domain dynamic equation, thereby obtaining the nonlinear response results of the turbine damping blade.

[0133] The process of solving the frequency domain dynamic equations using the arc-length extension method is as follows:

[0134] When solving for the maximum response amplitude curve of a turbine blade within a swept frequency range, a significant turning point often appears at the peak value, and in some cases, even a jump occurs. This makes it difficult for the traditional Newton-Raphson iteration method to converge or accurately describe this jump phenomenon. Therefore, this invention employs an arc-length extension method to solve for the response curve of the blade under the nonlinear coupling effect of the damping element.

[0135] First, for equation (6), define a residual vector R, which has the following form:

[0136] R = SX - F e -F n (16)

[0137] During the iteration process, the displacement harmonic coefficient vector X and the nonlinear force harmonic coefficient vector F are continuously updated.n That is, given the displacement harmonic coefficient vector X, after dimensionless transformation, it is fed into the neural network trained in step 3 to obtain the nonlinear force harmonic coefficient vector F. n .

[0138] This ensures that the magnitude of the residual vector, ||R||, is less than a given error range ε. For a given initial displacement vector or the result of the k-th iteration, X... (k) The traditional Newton-Raphson iteration method updates vector X using the following formula:

[0139]

[0140] The arc length extension method is used to track the trajectory of the response curve within the frequency sweep range of equation (17). The excitation force frequency is regarded as a variable, and the dynamic stiffness matrix S and the initial displacement harmonic coefficient vector X are continuously changed in a way similar to variable load to obtain the convergent solution.

[0141] In this embodiment of the invention, after specifying the solution range for the turbine damping blade's response frequency, the response analysis process is as follows:

[0142] First, for a given frequency f, determine whether it exceeds the solution range;

[0143] If the error does not exceed the range, then according to the arc length extension method described above, equation (17) is iterated to make the magnitude of the residual vector ||R|| less than a given error range ε. In this invention, ε can be taken as 1×10 -3 .

[0144] Output and save the results;

[0145] If the frequency exceeds the range, input a new frequency f and perform the above judgment. Continue until the turbine damping blade response within the specified frequency range is solved.

[0146] By following the above steps, the solution for the nonlinear response of the turbine damping blade can be obtained.

[0147] In the technical method provided by this invention, the dry friction harmonic coefficient vector is calculated from the displacement harmonic coefficient vector using correction coefficients instead of a time-frequency transformation process. This eliminates the need for repeated time-domain-frequency-time-domain transformations during the iterative solution of the nonlinear dynamic equations. The relevant calculations can be completed through highly parallelized matrix operations, resulting in high solution efficiency. Furthermore, by defining amplitude and phase correction coefficients instead of traditional equivalent coefficients, the time-frequency transformation process in the original calculation flow can be simplified to a direct mapping relationship in the frequency domain. Moreover, the fully connected artificial neural network framework constructed in this invention has good fitting performance and is suitable for the two major types of dry friction dynamic models widely used in engineering for solving the response of damped blades. It can establish a unified representation structure for dry friction dynamic models with different forms, eliminating the need to modify the code every time the dry friction dynamic model is changed, thus facilitating debugging and integration with experimental data. The method provided by this invention can accurately track the frequency response curves of the two dry friction dynamic models. In engineering, considering only the influence of the first harmonic is sufficient to describe the effect of dry friction at the damping component on the blade frequency response curve.

[0148] The following are embodiments of the apparatus of the present invention, which can be used to execute embodiments of the method of the present invention. For details not omitted in the apparatus embodiments, please refer to the embodiments of the method of the present invention.

[0149] Please see Figure 3 In another embodiment of the present invention, a turbine damping blade response solution system based on correction coefficients is provided, comprising:

[0150] The matrix acquisition module is used to acquire the finite element analysis model of the turbine damping blade to be solved, and to acquire the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model;

[0151] The equation construction module is used to construct the frequency domain dynamic equations of the finite element analysis model based on the overall stiffness matrix, overall mass matrix, and overall damping matrix.

[0152] The response solving module is used to solve the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the response solution of the turbine damping blade; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network.

[0153] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0154] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0155] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0156] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for solving the response of a turbine damping blade based on a correction coefficient, characterized in that, Includes the following steps: Obtain the finite element analysis model of the turbine damping blade to be solved, and obtain the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model; Based on the overall stiffness matrix, overall mass matrix, and overall damping matrix, the frequency domain dynamic equations of the finite element analysis model are constructed. The frequency domain dynamic equation is solved based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the turbine damping blade response solution; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network. in, In the frequency domain dynamic equations of the finite element analysis model constructed based on the overall stiffness matrix, overall mass matrix, and overall damping matrix, The expression for the obtained frequency domain dynamic equation is: ； In the formula, S Represents the dynamic stiffness matrix. F e Represents the vector of excitation force harmonic coefficients; F n This represents the vector of harmonic coefficients of dry friction. X This is the displacement harmonic coefficient vector; In the formula, Indicates the first i The harmonic coefficient matrix corresponding to the first harmonic; To indicate the highest harmonic order retained; In the formula, ω e Indicates the frequency of the excitation force. M This represents the total mass matrix of the flat-damped blade. K This represents the overall stiffness matrix of the damping blade. C This represents the overall damping matrix of the damping blade; The structure of the fully connected artificial neural network includes an input layer, hidden layer 1, hidden layer 2, and an output layer; the activation function of hidden layer 1 is ReLU, and the activation function of hidden layer 2 is Sigmoid. The steps for obtaining the pre-trained fully connected artificial neural network include: obtaining a training set of samples for the neural network, wherein each training sample includes a sample displacement harmonic coefficient vector and a sample dry friction harmonic coefficient vector; updating the parameters of the fully connected artificial neural network to a preset convergence condition based on the training set of samples to obtain the pre-trained fully connected artificial neural network. The specific steps for obtaining the training set of samples for the neural network include: The equations are processed, including: defining amplitude and phase correction coefficients in the equation model based on the turbine damping blade; where, , In the formula, Indicates the first j The relative displacement in the time domain at each contact unit Indicates the first j Time-domain amplitude at each contact unit i Represents the imaginary unit. ω Indicates the angular frequency of blade vibration. Indicates the first j The relative displacement of each contact element lags behind the phase of the excitation force; Indicates the first j Dry friction at each contact unit Indicates the first j Amplitude correction coefficient at each contact unit Indicates the first j Phase correction coefficient at each contact unit; t represents time; The nonlinear terms in the equation model are made dimensionless and expressed using the frequency domain method; where the tangential stiffness at the contact element is used. k x coefficient of friction µ and normal pressure N To make friction dimensionless, we have the expression: ; In the formula, This represents dimensionless dry friction. This represents the dimensionless amplitude correction factor. Indicates dimensionless displacement. This represents the phase correction coefficient after dimensionless conversion for 1 rad; By constructing the frequency domain dynamic equations and time-frequency interaction algorithm of the finite element model of the turbine damped blade, the harmonic coefficient vectors of dry friction force under multiple frequency excitation forces are obtained. F n With displacement harmonic coefficient vector X As a training sample set.

2. The method for solving the response of a turbine damping blade based on a correction coefficient according to claim 1, characterized in that, The frequency domain dynamic equations and time-frequency interaction algorithm of the constructed turbine damping blade finite element model are used to obtain the dry friction harmonic coefficient vectors under multiple frequency excitation forces. F n With displacement harmonic coefficient vector X The steps for creating a training sample set include: (1) Obtain the excitation force frequency, amplitude, and relative displacement between the contact surfaces of the turbine damping blades; (2) The time-domain solution of the nonlinear friction force is obtained by calculating the relative displacement between the contact surfaces of the turbine damping blades through the friction model; the frequency-domain solution of the nonlinear friction force is obtained by Fourier transform; the frequency-domain dynamic equation of the obtained turbine damping blade finite element model is solved, and the calculated overall displacement field of the damping blade is subjected to inverse Fourier transform to update the relative displacement between the contact surfaces of the turbine damping blades. (3) Repeat step (2) to update until the error of the relative displacement iteration value between the contact surfaces meets the preset requirements, and obtain the dry friction harmonic coefficient vector Fn and the displacement harmonic coefficient vector X at the excitation force frequency. (4) Change the excitation force frequency and amplitude, and repeat steps (1) to (3) to obtain multiple sets of dry friction force harmonic coefficient vectors Fn and displacement harmonic coefficient vectors X as training sample sets.

3. The method for solving the response of a turbine damping blade based on a correction coefficient according to claim 2, characterized in that, The specific steps for solving the frequency domain dynamic equations based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the turbine damping blade response solution include: For a given frequency f Determine if it exceeds the solution range. If it does not exceed the range, update the displacement harmonic coefficient vector according to the arc length extension method. X Iterate over the expression to make the magnitude of the residual vector... Less than a given error range ε If the frequency is outside the range, enter a new frequency. f The determination is repeated until the turbine damping blade response within the frequency range is solved. Among them, the residual vector R The expression is, The displacement harmonic coefficient vector is continuously updated during the iterative solution process. X and the vector of harmonic coefficients of dry friction F n This makes the magnitude of the residual vector Less than a given error range ε During the iteration process, for a given initial displacement vector or the first... k Step iteration results X (k) Update the displacement harmonic coefficient vector X The expression is, Wherein, for a given displacement harmonic coefficient vector X After dimensionless substituents are fed into a pre-trained fully connected artificial neural network, the dry friction harmonic coefficient vector is obtained. F n .

4. A turbine damping blade response solution system based on correction coefficients, characterized in that, include: The matrix acquisition module is used to acquire the finite element analysis model of the turbine damping blade to be solved, and to acquire the overall stiffness matrix, overall mass matrix and overall damping matrix based on the finite element analysis model; The equation construction module is used to construct the frequency domain dynamic equations of the finite element analysis model based on the overall stiffness matrix, overall mass matrix, and overall damping matrix. The response solving module is used to solve the frequency domain dynamic equation based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the response solution of the turbine damping blade; wherein, when solving the frequency domain dynamic equation, the mapping relationship between the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector is obtained based on a pre-trained fully connected artificial neural network. In the frequency domain dynamic equations of the finite element analysis model constructed based on the overall stiffness matrix, overall mass matrix, and overall damping matrix, The expression for the obtained frequency domain dynamic equation is: ； In the formula, S Represents the dynamic stiffness matrix. F e Represents the vector of excitation force harmonic coefficients; F n This represents the vector of harmonic coefficients of dry friction. X This is the displacement harmonic coefficient vector; In the formula, Indicates the first i The harmonic coefficient matrix corresponding to the first harmonic; To indicate the highest harmonic order retained; In the formula, ω e Indicates the frequency of the excitation force. M This represents the total mass matrix of the flat-damped blade. K This represents the overall stiffness matrix of the damping blade. C This represents the overall damping matrix of the damping blade; The structure of the fully connected artificial neural network includes an input layer, hidden layer 1, hidden layer 2, and an output layer; the activation function of hidden layer 1 is ReLU, and the activation function of hidden layer 2 is Sigmoid. The steps for obtaining the pre-trained fully connected artificial neural network include: Obtain a training set of samples for the neural network, wherein each training sample includes a sample displacement harmonic coefficient vector and a sample dry friction harmonic coefficient vector; update the parameters of the fully connected artificial neural network to a preset convergence condition based on the training set of samples to obtain the pre-trained fully connected artificial neural network. The specific steps for obtaining the training set of samples for the neural network include: The equations are processed, including: defining amplitude and phase correction coefficients in the equation model based on the turbine damping blade; where, , In the formula, Indicates the first j The relative displacement in the time domain at each contact unit Indicates the first j Time-domain amplitude at each contact unit i Represents the imaginary unit. ω Indicates the angular frequency of blade vibration. Indicates the first j The relative displacement of each contact element lags behind the phase of the excitation force; Indicates the first j Dry friction at each contact unit Indicates the first j Amplitude correction coefficient at each contact unit Indicates the first j Phase correction coefficient at each contact unit; t represents time; The nonlinear terms in the equation model are made dimensionless and expressed using the frequency domain method; where the tangential stiffness at the contact element is used. k x coefficient of friction µ and normal pressure N To make friction dimensionless, we have the expression: ; In the formula, This represents dimensionless dry friction. This represents the dimensionless amplitude correction factor. Indicates dimensionless displacement. This represents the phase correction coefficient after dimensionless conversion for 1 rad; By constructing the frequency domain dynamic equations and time-frequency interaction algorithm of the finite element model of the turbine damped blade, the harmonic coefficient vectors of dry friction force under multiple frequency excitation forces are obtained. F n With displacement harmonic coefficient vector X As a training sample set.

5. The turbine damping blade response solution system based on correction coefficients according to claim 4, characterized in that, The frequency domain dynamic equations and time-frequency interaction algorithm of the constructed turbine damping blade finite element model are used to obtain the dry friction harmonic coefficient vectors under multiple frequency excitation forces. F n With displacement harmonic coefficient vector X The steps for creating a training sample set include: (1) Obtain the excitation force frequency, amplitude, and relative displacement between the contact surfaces of the turbine damping blades; (2) The time-domain solution of the nonlinear friction force is obtained by calculating the relative displacement between the contact surfaces of the turbine damping blades through the friction model; the frequency-domain solution of the nonlinear friction force is obtained by Fourier transform; the frequency-domain dynamic equation of the obtained turbine damping blade finite element model is solved, and the calculated overall displacement field of the damping blade is subjected to inverse Fourier transform to update the relative displacement between the contact surfaces of the turbine damping blades. (3) Repeat step (2) to update until the error of the relative displacement iteration value between the contact surfaces meets the preset requirements, and obtain the dry friction harmonic coefficient vector Fn and the displacement harmonic coefficient vector X at the excitation force frequency. (4) Change the excitation force frequency and amplitude, and repeat steps (1) to (3) to obtain multiple sets of dry friction force harmonic coefficient vectors Fn and displacement harmonic coefficient vectors X as training sample sets.

6. The turbine damping blade response solution system based on correction coefficients according to claim 5, characterized in that, The specific steps for solving the frequency domain dynamic equations based on the displacement harmonic coefficient vector and the dry friction harmonic coefficient vector to complete the turbine damping blade response solution include: For a given frequency f Determine if it exceeds the solution range. If it does not exceed the range, update the displacement harmonic coefficient vector according to the arc length extension method. X Iterate over the expression to make the magnitude of the residual vector... Less than a given error range ε If the frequency is outside the range, enter a new frequency. f The determination is repeated until the turbine damping blade response within the frequency range is solved. Among them, the residual vector R The expression is, The displacement harmonic coefficient vector is continuously updated during the iterative solution process. X and the vector of harmonic coefficients of dry friction F n This makes the magnitude of the residual vector Less than a given error range ε During the iteration process, for a given initial displacement vector or the first... k Step iteration results X (k) Update the displacement harmonic coefficient vector X The expression is, Wherein, for a given displacement harmonic coefficient vector X After dimensionless substituents are fed into a pre-trained fully connected artificial neural network, the dry friction harmonic coefficient vector is obtained. F n .

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