CN109558669B - Finite element model-based online calculation method for fatigue damage of steam turbine rotor - Google Patents

Abstract

The present invention proposes an online calculation method for steam turbine rotor fatigue damage based on finite element model, including: modeling the steam turbine rotor with finite element software ADINA, calculating temperature field and stress field; extracting temperature data and thermal stress data of key parts ; Calculate the combined stress according to the fourth strength theory; normalize the measured stress data; establish a support vector regression model, and train and calculate the input and output data; analyze and fit the stress-damage function relationship, and calculate in real time Fatigue damage; establish an online calculation system architecture for fatigue damage. The invention can solve the problem in the prior art that the on-line calculation of the rotor low-cycle fatigue damage and the high-precision calculation are difficult to integrate.

Description

An online calculation method for turbine rotor fatigue damage based on finite element model

Technical Field

The invention relates to the field of calculation and evaluation of low cycle fatigue damage of a steam turbine rotor, and in particular to a finite element numerical calculation method and a support vector regression machine online calculation method.

Background Art

As one of the important components of the steam turbine unit, various damages to the metal materials of the steam turbine rotor will have a significant impact on the safe operation of the equipment. Since the steam turbine rotor is in a harsh working environment of high temperature, high pressure and variable working conditions for a long time, the stress conditions are very complicated, and the rotor metal is prone to low-cycle fatigue. According to engineering experience and existing experimental results, it can be determined that low-cycle fatigue damage accounts for about 80% and is the main cause of steam turbine rotor damage. Therefore, in order to prevent safety problems caused by fatigue damage of steam turbine rotors, it is particularly important to perform online calculation of fatigue damage of steam turbine rotors.

At present, the methods for calculating rotor low-cycle fatigue are mainly divided into analytical methods and numerical calculation methods. The analytical method is to simplify the rotor model into a long, infinite cylinder, calculate the temperature field based on the unstable heat conduction differential equation and integral equation, and then calculate the thermal stress based on the average temperature difference. The calculation speed is fast and suitable for online calculation. It calculates the maximum stress of the rotor's most prone to cracks based on the rotor's structural characteristics, material physical parameters, boundary conditions, and initial conditions. The analytical method simplifies the model, ignores the influence of heat flow, and only considers the radial temperature difference, so the calculation accuracy is not high. The numerical analysis method does not perform dimensionality reduction processing. On the basis of a two-dimensional model or a three-dimensional model, it discretizes the geometric shape continuum, and considers factors such as the changes in the convective heat transfer coefficient and the material physical properties with space and time, so it has a higher calculation accuracy. However, its disadvantage is that it is difficult to achieve online calculation due to the large amount of calculation.

Summary of the invention

In view of the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide an online calculation method for turbine rotor fatigue damage based on a finite element model, so as to solve the problem in the prior art that online calculation of rotor low-cycle fatigue damage and high-precision calculation are difficult to integrate.

To achieve the above purpose and other related purposes, a support vector regression machine method based on a finite element model is provided, the method comprising: using finite element software ADINA to model a steam turbine rotor and calculate temperature fields and stress fields; extracting temperature data and thermal stress data of key parts; calculating combined stress according to the fourth strength theory; normalizing the measured stress data; establishing a support vector regression machine model, and training and calculating input and output data; parsing and fitting the stress-damage function relationship, and calculating fatigue damage in real time; and establishing a fatigue damage online calculation system architecture.

Preferably, the finite element software ADINA is used to model the turbine rotor and calculate the temperature field and stress field under various working conditions. When calculating the unstable temperature field of the turbine rotor, the boundary condition of the outer surface of the rotor is determined by the heat exchange rate of steam to the rotor surface, which belongs to the third type of boundary condition in heat transfer, that is, the heat exchange condition between the boundary and the medium is known:

Where T _f is the air temperature in contact with the rotor surface, and α is the heat release coefficient between steam and the rotor surface.

Preferably, the temperature data and thermal stress data of key parts are extracted. When calculating fatigue damage of metal materials, there will be areas of stress concentration, such as the root of the regulator, the root of the high-pressure stage, and the bottom of the elastic force groove of the turbine rotor. Fatigue failure generally first appears at the maximum local strain of the strain concentration part. Before the crack initiates, a certain amount of plastic strain must be generated and accumulated. Therefore, when extracting the measured stress data, the corresponding thermal stress data is extracted at the root of the regulating stage based on engineering experience.

Preferably, the combined stress is calculated according to the fourth strength theory. In the numerical calculation method, in order to ensure the calculation accuracy, the effects of various stresses cannot be simply ignored, so it is necessary to calculate according to the fourth strength theory:

Among them: σ _∞m —— stress; y, θ, r——represent axial, tangential and radial directions respectively; τ _yr —— shear stress.

其中min和max为原始数据的最小值和最大值。Preferably, the measured stress data is normalized. The essence of normalization is to obtain dimensionless numbers by linear normalization of all dimensional numbers, eliminating the influence of different units on the calculation units. The original data x is linearly transformed so that the result falls into the interval [0,1]. The conversion function is

Where min and max are the minimum and maximum values of the original data.

Preferably, a support vector regression machine model is established, and the input and output data are trained and calculated. The constraint function of the SVM regression model has the following form:

加入松弛变量ε_i≥0，则SVM回归模型的约束函数具体为：Define the objective function:

By adding the slack variable ε _i ≥ 0, the constraint function of the SVM regression model is:

Preferably, the stress-damage function relationship is analyzed and fitted to calculate fatigue damage in real time. The cyclic stress-strain relationship is as follows:

Among them, E is Young's modulus, K' is cyclic strength coefficient, and n' is cyclic strain hardening index. The low-cycle fatigue damage of the rotor has the following relationship when the steam temperature is 538℃:

ε＝0.00332(N _f ) ^-0.0697 +0.6264(2N _f ) ^-0.7553

Where: N _f ——Number of cyclic fractures. Through the multinomial fitting method, strain can be used as input and cyclic fracture as output. The relationship between damage and strain is obtained:

Wherein: fitting coefficients P ₁ =9.7904×10 ¹² , P ₂ =-3.8943×10 ¹¹ , P ₃ =6.011×10 ⁹ , P ₄ =-4.6037×10 ⁷ , P ₅ =1.8292×10 ⁵ , P ₆ =-3.3086×10 ² , P ₇ =0.27029, P ₈ =0.

Preferably, an online calculation system architecture for fatigue damage is established. Under any operating condition, thermal stress is obtained through ADINA simulation. Thermal stress, pressure and centrifugal force are used to calculate the combined stress on the turbine rotor through the fourth strength theory. The measured temperature, pressure and speed are used as input, and the combined stress calculated by the fourth strength theory is used as output to obtain a support vector regression model. The measured temperature, pressure and speed are used as inputs of the SVR model to calculate the combined stress of key parts of the turbine rotor online. Fatigue damage is calculated online based on the stress-strain relationship and the strain-fatigue damage relationship.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic flow chart of an online calculation method for turbine rotor fatigue damage based on a finite element model.

FIG2 shows a curve of the root temperature of the cold start regulating stage changing with time.

FIG3 shows a curve showing the change of thermal stress at the root of the regulating stage during cold start-up with time.

Figure 4 shows the SVR stress training curve under cold start conditions.

Figure 5 shows the online calculation curve of SVR stress under cold start condition.

Figure 6 shows the online calculation curve of rotor low-cycle fatigue damage under cold start conditions.

FIG7 shows the block diagram of the online calculation system for low-cycle fatigue damage of a steam turbine rotor.

DETAILED DESCRIPTION

The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

Please refer to Figures 1 to 7. It should be noted that the illustrations provided in this embodiment are only used to illustrate the basic concept of the present invention in a schematic manner, and the illustrations only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the form, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

In the field of turbine rotor damage assessment, calculation methods can be mainly divided into one-dimensional analytical method and numerical analysis method. The one-dimensional analytical method performs calculations based on the simplified rotor model, material physical properties and initial conditions. It has a fast calculation speed and is suitable for online calculations. However, due to the dimensionality reduction and simplification of the model, many parameters are simplified to constants, and the complex structure of the rotor and the load application cannot be effectively taken into account, so the calculation accuracy is not high; while the numerical analysis method, based on the two-dimensional or three-dimensional model of the rotor, fully considers the physical properties of the material, the temporal and spatial changes of parameters, the operating boundary conditions, etc., and the calculation accuracy is high and can even be close to the actual situation. However, since the calculation method mostly uses algebraic equations to solve, the solution process is complicated and slow, and it is only suitable for offline calculations. At present, there is a need to seek an online calculation method for rotor low-cycle fatigue damage with a certain accuracy, and the present invention is formed based on these concepts.

The purpose of the present invention is to provide an online calculation method for fatigue damage of a steam turbine rotor based on a finite element model, so as to solve the problem that the existing methods are difficult to integrate online calculation and high-precision calculation of low-cycle fatigue damage of the rotor. The principle and implementation method of the online calculation method for fatigue damage of a steam turbine rotor based on a finite element model of the present invention will be described in detail below, so that those skilled in the art can understand the online calculation method for fatigue damage of a steam turbine rotor based on a finite element model of the present invention without creative labor.

As shown in FIG1 , the present invention provides an online calculation method for fatigue damage of a steam turbine rotor based on a finite element model, the method comprising the following steps:

S1, use finite element software ADINA to model the turbine rotor and calculate the temperature field and stress field;

S2, extracting temperature data and thermal stress data of key parts;

S3, calculate the resultant stress according to the fourth strength theory;

S4, normalizing the measured stress data;

S5, establish a support vector regression model, and train and calculate the input and output data;

S6, analyzes and fits the stress-damage function relationship, calculates fatigue damage in real time, and the results have high accuracy;

S7, establish the fatigue damage online calculation system architecture.

The present invention is described in detail below in conjunction with a specific embodiment. This embodiment is completed in the environment of ADINA8.5 software and matlab2013. The specific method is as follows: The steam turbine rotor used is based on the No. 1 unit of a certain power plant. The steam turbine is a single-shaft, condensing steam turbine. The material of the rotor is 30Cr1Mo1V. The length of the high-pressure rotor is about 4800mm, with a single-row regulating stage and 11 pressure stages. A two-dimensional model of the rotor is established by ADINA, and according to the "Domestic 300MW Steam Turbine Operation Guidelines", operating condition simulation is applied to the regulating stage and the high-pressure stage.

First, execute step S1, use finite element software ADINA to model the turbine rotor and calculate the temperature field and stress field; the rotor is symmetrical in shape, and an appropriate geometric model is established. The amount of calculation can be reduced by appropriately simplifying the model, for example, simplifying the gas seal system device into a line.

In step S2, the temperature data and thermal stress data of the key parts are extracted. The stress data of the corresponding working condition is extracted in the finite element software ADINA. Fatigue damage is first initiated from the maximum local strain of the part where the strain is concentrated, and a certain plastic deformation will occur before the crack initiation. Therefore, as long as the local stress and strain are the same, the fatigue damage is the same. The temperature change at the root of the cold start regulating stage is shown in Figure 2, and the thermal stress change at the root of the cold start regulating stage is shown in Figure 3.

In step S3, the resultant stress is calculated according to the fourth strength theory. The rotor surface is subjected to multiple stresses. When calculating the resultant stress, the fourth strength theory needs to be used for analysis. The outer surface and the center hole of the rotor are subjected to tangential and axial stresses, that is, σ _r and τ _rs are zero, and the resultant stress is:

Where: σ _eq ——the total stress acting on the rotor, σ _θ ——the tangential stress, σ _y ——the axial stress.

The sum of tangential stresses:

σ _θ =σ _th +σ _t

Where: σ _th —— thermal stress of the rotor, σ _t —— centrifugal tangential stress at the calculation location.

其中min和max为原始数据的最小值和最大值。建立样本数据集，数据的每一列都是一个样本，每一行是多个样本的同一维，即对于一个M·N的矩阵来说，样本的维度是M，样本数目是N。In step S4, the measured stress data is normalized. For the convenience of subsequent data processing, linear normalization is performed to obtain dimensionless numbers to eliminate the influence of different units on the calculation units. The original data x is linearly transformed so that the result falls into the interval [0,1]. The conversion function is

Where min and max are the minimum and maximum values of the original data. Create a sample data set, where each column of the data is a sample and each row is the same dimension of multiple samples, that is, for an M·N matrix, the sample dimension is M and the number of samples is N.

In step S5, a support vector regression model is established, and the input and output data are trained and calculated. The functions of data reading, data writing, model training, and damage calculation are completed. The read function is mainly used to read data; the write function stores known data; the training function is used to train data to establish the SVR model; the calculation function uses the trained model to calculate the data type. The training data of the root stress of the regulating level is shown in Figure 4, and the test data is shown in Figure 5.

In step S6, the stress-damage function relationship is parsed and fitted, and fatigue damage is calculated online. Given the maximum stress, low-cycle fatigue damage can be calculated based on the number of processes. The cyclic stress-strain relationship is as follows:

Among them, E is Young's modulus, K' is cyclic strength coefficient, and n' is cyclic strain hardening index. The low-cycle fatigue damage of the rotor when the steam temperature is 538℃:

ε＝0.00332(N _f ) ^-0.0697 +0.6264(2N _f ) ^-0.7553

Where: _Nf is the number of cycles to fracture. Through multiple fitting, strain is used as input and the number of cycles to fracture is used as output. The relationship between damage and strain is obtained:

Among them: fitting coefficients P ₁ =9.7904×10 ¹² , P ₂ =-3.8943×10 ¹¹ , P ₃ =6.011×10 ⁹ , P ₄ =-4.6037×10 ⁷ , P ₅ =1.8292×10 ⁵ , P ₆ =-3.3086×10 ² , P ₇ =0.27029, P ₈ =0. The calculation results are shown in FIG6 .

In step S7, the online calculation system architecture of fatigue damage is established. Under any working condition, the thermal stress is obtained by ADINA simulation. The combined stress of the steam turbine rotor is obtained by the fourth strength theory calculation of thermal stress, pressure and centrifugal force. The measured temperature, pressure and speed are used as input, and the combined stress calculated by the fourth strength theory is used as output to obtain the support vector regression machine model. According to the stress-strain relationship and the strain-fatigue damage relationship, the online calculation system architecture of the low-cycle fatigue damage of the steam turbine rotor is established.

Claims (1)

1. A finite element model-based online calculation method for fatigue damage of a steam turbine rotor is characterized by comprising the following steps:

1.1, modeling a steam turbine rotor by using finite element software ADINA, and calculating a temperature field and a stress field, wherein the temperature field and the stress field under each working condition are calculated, and the heat exchange conditions of a boundary and a medium are specifically as follows:

wherein T is _f -the air temperature in contact with the rotor surface, α -the heat release coefficient of the steam from the rotor surface;

1.2, extracting temperature data and thermal stress data of key parts;

1.3, calculating the resultant stress according to a fourth intensity theory, wherein the calculation according to the fourth intensity theory specifically comprises:

wherein: sigma _∞m -and stress; y, θ, r-represent axial, tangential and radial, respectively; tau is _yr -shear stress;

1.4, carrying out normalization processing on the actually measured stress data, which is characterized in that the normalization processing on the actually measured stress data specifically comprises the following steps:

wherein min and max are the minimum and maximum values of the original data;

1.5, establishing a support vector regression model, and training and calculating input and output data, wherein the constraint function for establishing the SVM regression model is specifically as follows:

1.6, analyzing and fitting the stress-damage functional relation, and calculating the fatigue damage in real time, wherein the analyzing and fitting the stress-damage functional relation specifically comprises the following steps:

(1)

(2)ε＝0.00332(N _f ) ^-0.0697 +0.6264(2N _f ) ^--0.7553 ，

(3)

wherein E-Young's modulus, K ' -cyclic strength coefficient, N ' -cyclic strain hardening index, N _f -number of cyclic fracturing events, P ₁ ＝9.7904×10 ¹² ，P ₂ ＝-3.8943×10 ¹¹ ，P ₃ ＝6.011×10 ⁹ ，P ₄ ＝-4.6037×10 ⁷ ，P ₅ ＝1.8292×10 ⁵ ，P ₆ ＝-3.3086×10 ² ，P ₇ ＝0.27029，P ₈ ＝0。

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