CN109558669B - Finite element model-based online calculation method for fatigue damage of steam turbine rotor - Google Patents
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Abstract
The invention provides a finite element model-based online calculation method for fatigue damage of a steam turbine rotor, which comprises the following steps: modeling a turbine rotor by using finite element software ADINA, and calculating a temperature field and a stress field; extracting temperature data and thermal stress data of key parts; calculating the resultant stress according to a fourth strength theory; normalizing the actually measured stress data; establishing a support vector regression model, and training and calculating input and output data; analyzing and fitting a stress-damage function relation, and calculating fatigue damage in real time; and establishing a fatigue damage online computing system architecture. The method can solve the problem that the rotor low-cycle fatigue damage online calculation and the high-precision calculation are difficult to be fused in the prior art.
Description
Technical Field
The invention relates to the field of calculation and evaluation of low-cycle fatigue damage of a steam turbine rotor, in particular to a finite element numerical calculation method and a support vector regression machine on-line calculation method.
Background
As one of the important parts of a steam turbine unit, a steam turbine rotor has a great influence on the safe operation of equipment due to various damages of metal materials. Because the steam turbine rotor is in the severe working environment of high temperature, high pressure and variable working condition for a long time, the stress condition is very complex, and the rotor metal is easy to generate low-cycle fatigue. According to engineering experience and existing experimental results, the low-cycle fatigue damage accounts for about 80% and is the main cause of damage to the steam turbine rotor. Therefore, in order to prevent safety problems caused by fatigue damage of the turbine rotor, it is important to perform online calculation on the fatigue damage of the turbine rotor.
At present, methods for calculating low cycle fatigue of a rotor mainly comprise an analytical method and a numerical algorithm. The analytic method is characterized in that the dimension reduction of a rotor model is simplified into a wireless long cylinder, a temperature field is solved according to an unstable heat conduction differential equation and an integral equation, and then the thermal stress is calculated according to a temperature difference average value, so that the calculation speed is high, and the method is suitable for on-line calculation. According to the structural characteristics, the physical parameters, the boundary conditions and the initial conditions of the rotor, the maximum stress calculation is carried out on the part of the rotor which is most easy to crack. The analytic method simplifies the model, neglects the influence of heat flow, only considers the radial temperature difference, and therefore the calculation accuracy is not high. The numerical analysis method does not perform dimension reduction processing, discretizes the geometric shape continuum on the basis of a two-dimensional model or a three-dimensional model, and considers the convective heat transfer coefficient and the physical property of the material changing along with space and time, so that the method has higher calculation precision. But the disadvantage is that the online calculation is difficult to realize due to large calculation amount.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide an online calculation method for fatigue damage of a steam turbine rotor based on a finite element model, which is used for solving the problem that the online calculation and the high-precision calculation of low cycle fatigue damage of the rotor in the prior art are difficult to be merged.
To achieve the above and other related objects, there is provided a support vector regression method based on finite element models, the method comprising: modeling a turbine rotor by using finite element software ADINA, and calculating a temperature field and a stress field; extracting temperature data and thermal stress data of key parts; calculating the resultant stress according to a fourth strength theory; carrying out normalization processing on the actually measured stress data; establishing a support vector regression model, and training and calculating input and output data; analyzing and fitting a stress-damage function relation, and calculating fatigue damage in real time; and establishing a fatigue damage online computing system architecture.
Preferably, finite element software ADINA is used for modeling the turbine rotor, and the temperature field and the stress field under each working condition are calculated. When the unstable temperature field of the turbine rotor is calculated, the boundary condition of the outer surface of the rotor is determined by the heat exchange speed of steam on the rotor surface, and belongs to the third type of boundary condition in heat transfer science, namely the heat exchange condition between the boundary and a medium is known:
wherein T is f -the temperature of the air in contact with the rotor surface, α -the heat release coefficient of the steam from the rotor surface.
Preferably, temperature data and thermal stress data of the critical locations are extracted. Regions of stress concentration are present in metallic materials when fatigue damage is calculated, such as conditioner roots, high pressure stage roots and spring force groove bottoms of turbine rotors. Fatigue failure generally occurs first at the maximum local strain from the point of strain concentration, and a certain amount of plastic strain is generated and accumulated before crack initiation. Therefore, when the actually measured stress data is extracted, corresponding thermal stress data is extracted at the root of the adjusting stage according to engineering experience.
Preferably, the resultant stress is calculated according to a fourth strength theory. In the numerical calculation method, in order to ensure the calculation accuracy, the effect of various stresses cannot be simply ignored, so that the calculation needs to be performed according to a fourth intensity theory:
wherein: sigma ∞m -and stress; y, θ, r-represent axial, tangential and radial, respectively; tau is yr -shear stress.
Preferably, the measured stress data is normalized. The essence of normalization is that all the dimensional numbers are subjected to linear normalization processing to obtain dimensionless numbers, and the influence of different units on the calculation unit is eliminated. The original data x is linearly transformed so that the result falls to [0,1]Interval, transfer function of
In which min and max are raw dataA minimum value and a maximum value.
Preferably, a support vector regression model is established, and input and output data are trained and calculated. The constraint function of the SVM regression model has the form:
defining an objective function:
adding the relaxation variable ε i If the value is greater than or equal to 0, the constraint function of the SVM regression model is specifically as follows:
preferably, the stress-damage function relationship is analyzed and fitted, and the fatigue damage is calculated in real time. The cyclic stress-strain relationship is as follows:
wherein E is Young's modulus, K ' is cyclic strength coefficient, n ' is cyclic strain hardening index. The low cycle fatigue damage of the rotor has the following relationship at a steam temperature of 538 ℃:
ε＝0.00332(N f ) -0.0697 +0.6264(2N f ) -0.7553
wherein: n is a radical of f -cycle cracking times. By means of a polynomial fitting method, strain can be used as input, and cyclic cracking can be used as output. Obtaining the relationship between damage and strain:
wherein: coefficient of fit 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, a fatigue damage online computing system architecture is established. Under any working condition, the heat stress, the pressure and the centrifugal force are obtained through ADINA simulation, and the resultant stress of the steam turbine rotor is obtained through fourth intensity theory calculation. And (4) taking the actually measured temperature, pressure and rotating speed as input, and taking the resultant stress obtained by the fourth strength theory as output to obtain a support vector regression model. And the actually measured temperature, pressure and rotating speed are used as the input of the SVR model, and the resultant stress of the key part of the turbine rotor is calculated on line. And calculating the fatigue damage on line according to the stress-strain relation and the strain-fatigue damage relation.
Drawings
FIG. 1 is a schematic flow chart of a finite element model-based online calculation method for fatigue damage of a steam turbine rotor.
Fig. 2 shows the root temperature of the cold start regulation stage as a function of time.
FIG. 3 shows the thermal stress at the root of the cold start regulation stage as a function of time.
FIG. 4 shows an SVR stress training curve under cold start conditions.
FIG. 5 shows an on-line calculated SVR stress curve for cold start conditions.
FIG. 6 shows an online calculated curve of low cycle fatigue damage of a rotor under cold start conditions.
FIG. 7 shows a block diagram of an online calculation system for low cycle fatigue damage of a steam turbine rotor.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.
Please refer to fig. 1 to 7. It should be noted that the drawings provided in the present embodiment are only for illustrating the basic idea of the present invention, and the drawings only show the components related to the present invention rather than being drawn according to the number, shape and size of the components in actual implementation, and the form, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
In the field of damage assessment of steam turbine rotors, calculation methods can be mainly divided into one-dimensional analytical methods and numerical analysis methods. The one-dimensional analytical method carries out calculation according to the rotor simplified model, the physical properties of the material and the initial conditions, has high calculation speed and is suitable for on-line calculation. However, due to the fact that the model is reduced in dimension and simplified, many parameters are simplified into constants, and meanwhile, the complex structure of the rotor and the load applying condition cannot be taken into consideration effectively, and therefore the calculation accuracy is not high; and the numerical analysis method fully considers the physical characteristics of materials, the space-time variation of parameters, the boundary conditions of working conditions and the like on the basis of a two-dimensional or three-dimensional model of the rotor, and has high calculation accuracy even close to the actual condition. However, the calculation method mostly adopts an algebraic equation system to solve, so that the solving process is complex and slow, and is only suitable for off-line calculation. The invention is formed based on the concepts that the method for calculating the low-cycle fatigue damage of the rotor on line with certain precision needs to be found.
The invention aims to provide a finite element model-based online calculation method for fatigue damage of a steam turbine rotor, which is used for solving the problem that the conventional method is difficult to realize the online calculation and high-precision calculation of low-cycle fatigue damage of the rotor. The principle and embodiment of the present invention will be described in detail below, so that those skilled in the art can understand the present invention without creative efforts.
As shown in FIG. 1, the invention provides a finite element model-based online calculation method for fatigue damage of a steam turbine rotor, which comprises the following steps:
s1, modeling a steam turbine rotor by using finite element software ADINA, and calculating a temperature field and a stress field;
s2, extracting temperature data and thermal stress data of key parts;
s3, calculating the resultant stress according to a fourth strength theory;
s4, carrying out normalization processing on actually measured stress data;
s5, establishing a support vector regression model, and training and calculating input and output data;
s6, analyzing and fitting a stress-damage function relation, calculating fatigue damage in real time, and enabling the result to have higher accuracy;
and S7, establishing a fatigue damage online computing system architecture.
This will be described in detail with reference to specific examples. This example was done in the context of the ADINA8.5 software and matlab 2013. The specific method comprises the following steps: the used steam turbine rotor is a prototype of No. 1 unit of a certain power plant, and the steam turbine is a single-shaft condensing steam turbine. The material of the rotor is 30Cr1Mo1V. The high pressure rotor is approximately 4800mm in length with a single row of regulation stages and 11 pressure stages. A two-dimensional model of the rotor is established through ADINA, and working condition simulation is applied to a regulating stage and a high-pressure stage according to the national 300MW steam turbine operation guide rule.
Firstly, executing a step S1, modeling a turbine rotor by using finite element software ADINA, and calculating a temperature field and a stress field; the rotor is in a symmetrical shape, a proper geometric model is established, and the calculated amount can be reduced by a proper simplified model, for example, the gas seal system device is simplified into a line.
In step S2, temperature data and thermal stress data of the key portion are extracted. And extracting stress data corresponding to the working conditions from finite element software ADINA. Fatigue damage is initiated first from the maximum local strain at the site of strain concentration, and before cracks initiate, some plastic deformation occurs. Therefore, as long as the local stress strain is the same, the fatigue damage is the same. The cold start regulation stage root temperature variation is shown in fig. 2, and the cold start regulation stage root thermal stress variation is shown in fig. 3.
In step S3, the resultant stress is calculated according to a fourth intensity theory. The rotor surface is subjected to a plurality of stresses, and a fourth strength theory is needed for analysis when calculating the resultant stress. The outer surface of the rotor and the central bore are subjected to tangential and axial stresses, i.e. σ r And τ rs Zero, the resultant stress is:
wherein: sigma eq The resultant stress to which the rotor is subjected, σ θ -tangential stress, σ y -axial stress.
Sum of tangential stresses:
σ θ ＝σ th +σ t
wherein: sigma th Thermal stress of the rotor, σ t -calculating the centrifugal tangential stress of the site.
In step S4, the measured stress data is normalized. In order to facilitate subsequent data processing, dimensionless numbers are obtained through linear normalization processing, and the influence of different units on calculation units is eliminated. The original data x is linearly transformed so that the result falls to [0,1]Interval of conversion function of
Where min and max are the minimum and maximum values of the raw data. A sample data set is established, each column of the data is a sample, each row is the same dimension of a plurality of samples, namely for an M.N matrix, the dimension of the sample is M, and the number of the samples is N.
In step S5, a support vector regression model is established, and input/output data is trained and calculated. And finishing the functions of data reading, data writing, model training and damage calculation. The read function is mainly used for reading data; the write function stores the known data; the training function is used for training data to establish an SVR model; the computation function uses the trained model to compute the data type. The tuning stage root stress training data is shown in fig. 4 and the test data is shown in fig. 5.
In step S6, the stress-damage function relationship is analyzed and fitted, and the fatigue damage is calculated on line. Knowing the maximum stress, the low cycle fatigue damage can be calculated from the number of processes. The cyclic stress-strain relationship is as follows:
wherein E is Young's modulus, K ' is cyclic strength coefficient, and n ' is cyclic strain hardening index. Low cycle fatigue damage of the rotor at a steam temperature of 538 ℃:
ε＝0.00332(N f ) -0.0697 +0.6264(2N f ) -0.7553
wherein: n is a radical of f -number of cyclic fracturing cycles. And (4) taking strain as an input and taking cycle fracturing cycles as an output through multiple fitting. Obtaining the relationship between damage and strain:
wherein: coefficient of fit 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 And =0. The calculation results are shown in fig. 6.
In step S7, a fatigue damage online computing system architecture is established. Under any working condition, the heat stress, the pressure and the centrifugal force are obtained through ADINA simulation, and the resultant stress of the steam turbine rotor is obtained through fourth intensity theory calculation. And taking the actually measured temperature, pressure and rotating speed as input, and taking the resultant stress calculated by the fourth intensity theory as output to obtain a support vector regression model. And establishing a low-cycle fatigue damage online computing system framework of the steam turbine rotor according to the stress-strain relation and the strain-fatigue damage relation.
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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| CN107145687A (en) * | 2017-06-07 | 2017-09-08 | 上海电力学院 | The method that turbine rotor start up curve optimizes and creep fatigue life is assessed |
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| CN107145687A (en) * | 2017-06-07 | 2017-09-08 | 上海电力学院 | The method that turbine rotor start up curve optimizes and creep fatigue life is assessed |
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| 135 MW汽轮机无中心孔转子热应力有限元计算及低周疲劳寿命分析;楼晓阳等;《浙江电力》;20070420(第02期);1-6 * |
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