Stress online calculation and fatigue evaluation method suitable for steam turbine rotor

Abstract

The invention relates to a stress on-line calculation and fatigue evaluation method suitable for a steam turbine rotor, and the method comprises the steps: collecting geometric parameters and material physical property parameters of the rotor, selecting a detection point, supposing the rotor to be an infinitely long hollow cylinder, building a displacement differential control equation through a heat conduction differential equation and thermoelastic mechanics, and calculating the fatigue of the rotor. And solving temperature distribution and radial displacement distribution of the rotor, and calculating stress based on the displacement. After a fourth strength theory is adopted to solve equivalent stress, equivalent strain is calculated through a Ramberg-Osgood model, fatigue loss of the rotor is evaluated based on a rain flow counting method and a Manson-Coffin-Basic relational expression, and finally accumulated fatigue loss in a specified period is obtained through a Miner linear damage accumulation method. According to the method, real-time monitoring of rotor stress and evaluation of fatigue loss can be realized, and an important basis is provided for safe operation and maintenance of a steam turbine.

Description

Technical Field

[0001] This invention belongs to the field of online monitoring and fatigue assessment technology for steam turbine rotors. Specifically, it relates to a method for online stress calculation and fatigue assessment of steam turbine rotors, which is used to monitor the stress of the rotor in real time under high temperature and high pressure conditions and assess the fatigue life loss of the rotor. Background Technology

[0002] With the development of intelligent and automated industrial equipment, steam turbines play a crucial role in power generation and industrial production. Because steam turbines are prone to stress concentration under prolonged, high-temperature, and high-pressure operation, potentially leading to structural fatigue failure, accurate monitoring of the stress distribution in the turbine rotor and assessment of its fatigue life are essential. However, existing methods are mostly based on periodic offline monitoring or rely on simplified stress models, making them unsuitable for real-time monitoring. Furthermore, existing fatigue assessment methods often neglect the nonlinear deformation characteristics of materials at high temperatures and lack reliable means of calculating fatigue loss. Summary of the Invention

[0003] To overcome the difficulties in online stress monitoring and insufficient accuracy in fatigue loss assessment in existing technologies, this invention aims to provide an online stress calculation and fatigue assessment method suitable for steam turbine rotors. By establishing a calculation model of temperature and stress distribution at the detection points, and combining the fourth strength theory and the Ramberg-Osgood model, a systematic online analysis of stress and fatigue loss is achieved, thereby providing a reliable basis for the safety management of rotor operation.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for online stress calculation and fatigue assessment of steam turbine rotors includes the following steps: Step 1: Collect the geometric parameters of the turbine rotor and the physical property parameters of the rotor material. The physical property parameters include Young's modulus, density, thermal conductivity, coefficient of thermal expansion, Poisson's ratio, and specific heat at constant pressure at different temperatures. Step 2: Select one or more detection points, and assume the turbine rotor to be an infinitely long hollow cylinder with the diameter of the detection point as the size; Step 3: Using the heat conduction differential equation of a hollow cylinder, with a third heat transfer boundary condition on the outer surface and an adiabatic boundary condition on the inner surface, solve for the radial temperature distribution at the rotor detection point. The discretization process of the heat conduction differential equation uses an implicit Crank-Nicolson difference scheme, and the temperature distribution is solved using... QR Decomposition method; details are as follows: i) Thermal conductivity differential equation: ,in: T Rotor temperature; tFor time; l The rotor's thermal conductivity; r Rotor density; c Rotor specific heat; r The radial coordinates of the rotor; As an internal heat source; ii) Discretize and rearrange the heat conduction differential equation according to the Crank-Nicolson difference scheme. The radial temperature distribution equation at the detection point satisfies the following matrix: The elements in the matrix a i , b i , c i These are the coefficients of the thermal conductivity differential equation, and the vector on the right-hand side. f i These are the constant terms and elements in the heat conduction differential equation. T i The nodal temperature to be solved, subscript i From 0 to n, where i =0 and i =n corresponds to the boundary point. i =1 to i = n -1 corresponds to an interior point; iii) The above matrix can be written as AT=B The form, for A conduct QR Decomposition, in which, Q It is an orthogonal matrix. R It is an upper triangular matrix, so we get: The temperature distribution can be obtained by iterative solution; Step 4: Based on the rotor's temperature distribution and the assumptions of thermoelasticity, establish the differential control equation for the displacement of the detection point along the rotor's radial direction. The boundary conditions for the differential control equation are the outer surface vapor pressure load and the inner surface zero displacement assumption. The differential control equation is discretized using an implicit Crank-Nicolson difference scheme, and the radial displacement distribution is determined using... QR Solve by decomposition; details are as follows: i) Displacement differential equation, ,in: u Radial displacement; m Poisson's ratio; α The coefficient of thermal expansion; v The viscosity coefficient; E It is the elastic modulus; oh The rotor's angular velocity; ii) Solve for the displacement using the same method as in step ii) of step 3 to solve for the temperature distribution; Step 5: Based on the geometric and physical equations in the cylindrical coordinate system of the detection point, solve for the stress at the detection point through displacement; Stress solution at the detection point ,in: Radial stress; For circumferential stress; This refers to the rotor temperature deviation. Step 6: Based on the stress at the detection point, calculate the equivalent stress at the detection point using the fourth strength theory. s The details are as follows: Fourth strength theory, ,in: s z This is axial stress; Step 7: Determine the fatigue loss assessment period and number of periods. Based on the equivalent stress in the past periods at the test point, calculate the equivalent strain corresponding to the equivalent stress using the Ramberg-Osgood model. ɛ ; Ramberg-Osgood model ,in K and n These are parameters related to the material type; Step 8: Based on the equivalent strain history, the equivalent strain is simplified into a cyclic strain history using the rainflow counting method, and the fatigue loss of the rotor is calculated using the Basquin-Coffin-Manson relation. Finally, the cumulative fatigue loss of each cycle history is calculated using the Miner linear damage accumulation method. i) Basquin-Coffin-Manson relation, ,in: It is the total strain amplitude; s f ′ is the fatigue strength coefficient; e f ′ is the fatigue ductility coefficient; b′ It is the fatigue strength index; c′ It is the fatigue ductility index; N f It is low-cycle fatigue loss; ii) Based on the obtained fatigue life of each cyclic load, the cumulative fatigue loss at the detection points during the evaluation cycle is calculated using the Miner linear damage accumulation method. ,in: m The number of loop types; n i For the first i The number of loops of each loop type, Nf,i It is the first i Low-cycle fatigue loss per cycle of a single cycle of a cycle type.

[0005] In step 3, the heat transfer coefficient of the outer surface is obtained by the convective heat transfer correlation of the rotor, which includes correlation 1), Westinghouse correlation, Alstom correlation and Harbin Turbine-Nanjing Machinery correlation. 1) Heat transfer coefficient at the rotor surface: ; 2) Heat transfer coefficient at the rotor shaft: 3) Heat transfer coefficient at the rotor impeller: in: h 1, h 2, h 3 represents the heat transfer coefficients at the rotor surface, rotor optical axis, and rotor impeller, respectively. It is the thermal conductivity of steam; R b It is the radius of the rotor; w It is the rotor's angular velocity; It is the kinematic viscosity of air; Re It is the Reynolds number.

[0006] If the material-related parameters of the Ramberg-Osgood model are missing in step 7, they can be obtained from the readily available material coefficients using the following formula: 1) Constant fitting relationship: ,in, e 1 and s 1 represents the strain at the material's yield point and its yield strength; 2) Coefficients in the relation A and n , , s 2 represents the ultimate strength of the material. ψ It is the reduction of area of ​​the material.

[0007] If the material-related parameters of the Basquin-Coffin-Manson relation are missing in step 8, then the material-related parameters can be obtained from the readily available material coefficients through the relation: 1) Fatigue strength coefficient s f ′ and fatigue ductility coefficient ɛ f ′ When fatigue test data is lacking, the fatigue strength coefficient and fatigue ductility coefficient can be approximated using the actual fracture strength and actual fracture ductility. However, they are not the same in terms of physical concepts; 2) Solving for the fatigue strength index. ; 3) Solving for the fatigue ductility index. ; 4) Among them: .

[0008] in: s f It is the actual fracture strength; ɛ f It is true fracture ductility; s u It is the tensile strength of the material; It is the reduction of area of ​​the material; A and A are intermediate calculation variables.

[0009] The beneficial effects of this invention include: (1) Real-time: Realizes online monitoring of rotor stress and can obtain stress change information in a timely manner.

[0010] (2) Reliable fatigue assessment: The fatigue loss is accurately assessed by the Ramberg-Osgood model and the Basquin-Coffin-Manson relation, providing a method for assessing rotor fatigue life.

[0011] (3) Strong applicability: It is suitable for various types of steam turbine rotors, especially for high-temperature rotor structures that operate continuously for a long time. Attached Figure Description

[0012] Figure 1 This is a flowchart of an online stress calculation and fatigue assessment method for steam turbine rotors according to the present invention.

[0013] Figure 2 A comparison diagram of stress obtained by finite element analysis and solution method of the present invention is provided during the peak shaving process of a certain unit from 100% THA to 75% THA. Detailed Implementation

[0014] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] like Figure 1 As shown, the present invention provides a method for online stress calculation and fatigue assessment of steam turbine rotors, comprising the following steps: Step 1: First, collect the geometric parameters and material properties of the turbine rotor. The material properties mainly include Young's modulus, density, thermal conductivity, coefficient of thermal expansion, Poisson's ratio, and specific heat at constant pressure at different temperatures. These parameters provide the basic data for subsequent calculations.

[0016] Step 2: Select one or more detection points, and assume the turbine rotor to be an infinitely long hollow cylinder with the diameter of the detection points as the size, to ensure that the calculation model matches the actual structure.

[0017] Step 3: Establish the heat conduction differential equation for the hollow cylinder, assuming no internal heat source. Set the outer surface as a third-type heat transfer boundary condition and the inner surface as an adiabatic boundary condition. To solve the heat conduction differential equation, an implicit Crank-Nicolson difference scheme is used for discretization. The temperature distribution is obtained through... QR The solution is obtained by decomposition; the heat transfer coefficient of the outer surface is obtained through the convection heat transfer correlation (including the correlations of Westinghouse, Alstom and Harbin Turbine-Nanjing Institute of Technology).

[0018] Step 4: Based on the rotor's temperature distribution, establish the differential control equation for the displacement of the detection point along the rotor's radial direction according to the fundamental assumptions of thermoelasticity. The boundary conditions for the differential control equation are the steam pressure load on the outer surface and the zero displacement assumption on the inner surface. This differential control equation is also discretized using the Crank-Nicolson difference scheme and... QR The radial displacement distribution of the rotor is solved by decomposition method.

[0019] Step 5: Calculate the stress at the detection point based on the geometric and physical equations in the cylindrical coordinate system of the detection point, and then calculate the equivalent stress using the fourth strength theory.

[0020] Step 6: Determine the fatigue assessment cycle and number of cycles. Based on the equivalent stress, use the Ramberg-Osgood model to solve for the equivalent strain. If the material parameters required for the model are missing, they can be estimated by fitting the relevant relationships.

[0021] Step 7: The equivalent strain history is simplified into several cyclic strain histories by applying the rainflow counting method. The fatigue loss in each cyclic strain history is calculated using the Basquin-Coffin-Manson relation, and the cumulative fatigue loss of the test point in the specified period is obtained by accumulating the results using the Miner linear damage accumulation method.

[0022] The above methods enable online stress calculation and fatigue life loss assessment of turbine rotors under complex operating conditions, providing effective support for ensuring the safety of equipment operation.

[0023] Figure 2A comparison chart of stress components and equivalent stress obtained by finite element analysis and the method of this invention during the peak shaving process of a certain unit from 100% THA to 75% THA is provided. It can be seen that during the entire transient process, the radial stress and axial stress calculated by this invention are close to the trend and values ​​of the finite element simulation calculation, which meets the requirements of simulation calculation.

Claims

1. A method for stress on-line calculation and fatigue assessment of a rotor of a steam turbine, characterized in that, Comprise the following steps: Step 1: Collect the geometric parameters of the rotor of the steam turbine and the physical parameters of the rotor material, wherein the physical parameters include Young's modulus, density, thermal conductivity, thermal expansion coefficient, Poisson's ratio and specific heat at constant pressure at different temperatures; Step 2: Select one or more detection points, and assume the steam turbine rotor as an infinite hollow cylinder with the diameter of the detection point as the size; Step 3: The temperature distribution of the rotor detection point along the radial direction is solved by using the heat conduction differential equation of the hollow cylinder, the outer surface adopts the third heat exchange boundary condition, and the inner surface adopts the adiabatic boundary condition. The implicit Crank-Nicolson difference format is adopted in the discretization process of the heat conduction differential equation, and the temperature distribution is solved by using QR Decomposition method; Specifically as follows: i) Heat conduction partial differential equation: where: T is the rotor temperature; t is time; λ is the rotor thermal conductivity; ρ is the rotor density; c is the rotor specific heat; r is the rotor radial coordinate; is the internal heat source; ii) Discretize and arrange the heat conduction differential equation according to the Crank-Nicolson difference format, and the temperature distribution equation of the detection point along the radial direction satisfies the following matrix: where the elements of the matrix a i , b i , c i are the coefficients of the heat conduction differential equation, the right end vector f i are the constant terms of the heat conduction differential equation, the elements T i are the node temperatures to be solved, the subscript i from 0 to n, where i = 0 and i = n correspond to the boundary points, i = 1 to i = n - 1 correspond to the internal points; iii) The above matrix can be written in the form AT=B A QR Q is an orthogonal matrix, R is an upper triangular matrix, resulting in:​​​ The temperature distribution can be obtained by iterative solution; Step 4: Based on the temperature distribution of the rotor, a displacement differential control equation of the detection point along the radial direction of the rotor is established according to the assumption of thermoelasticity, the boundary condition of the displacement differential control equation is the steam pressure load of the outer surface and the zero displacement assumption of the inner surface, the implicit Crank-Nicolson difference format is used for the discretization of the displacement differential control equation, and the radial displacement distribution is obtained by using QR Decomposition method; specifically as follows: i) a differential equation of displacement, where: u is the radial displacement; μ is the Poisson ratio; α is the thermal expansion coefficient; v is the viscosity coefficient; E is the elastic modulus; ω is the rotor angular velocity of rotation; ii) The displacement is solved by the means for solving the temperature distribution in ii) of step 3; Step 5: Based on the geometric equation and the physical equation of the detection point in the cylindrical coordinate system, the stress of the detection point is solved through the displacement; Detection point stress solution, wherein: is the radial stress; is the circumferential stress; is the rotor temperature deviation; Step 6: Based on the stress of the detection point, the equivalent stress of the detection point is calculated by the fourth strength theory σ ; Specifically as follows: Fourth strength theory, wherein: σ z is the axial stress; Step 7: Determine fatigue damage assessment period and number of periods, calculate equivalent strain corresponding to equivalent stress using Ramberg-Osgood model based on equivalent stress of the past periods for the point of interest ɛ ; Ramberg-Osgood model, wherein K and n are material type dependent parameters; Step 8: Based on the equivalent strain history, the rainflow counting method is used to simplify the equivalent strain history into a cyclic strain history, and the fatigue loss of the rotor is calculated through the Basquin-Coffin-Manson relationship, and finally the cumulative fatigue loss of each cycle is calculated by using the Miner linear damage accumulation method; i) Basquin-Coffin-Manson relationship, where: is the total strain amplitude; σ f is the fatigue strength coefficient; ε f is the fatigue ductility coefficient; b′ is the fatigue strength exponent; c′ is the fatigue ductility exponent; N f is the low cycle fatigue loss; ii) based on the fatigue life of each cycle load, the cumulative fatigue damage of the evaluation period detection point is obtained based on the Miner linear damage accumulation method, wherein: m is the number of cycle types; n i is the number of cycles of the i th cycle type, N f,i is the low cycle fatigue damage of the single cycle of the i th cycle type.

2. A method for on-line stress calculation and fatigue assessment of a rotor of a steam turbine according to claim 1, characterized in that The heat transfer coefficient of the outer surface in step 3 is obtained from the convective heat transfer correlation of the rotor, and the convective heat transfer correlation includes correlation 1), Westinghouse correlation, Alstrom correlation and Haqi-Nan Gong correlation; 1) Heat transfer coefficient at the rotor surface: ; 2) Heat transfer coefficient at rotor optical axis: 3) Heat transfer coefficient at the rotor impeller: wherein: h 1, h 2, h 3is the heat transfer coefficient at the rotor surface, the optical axis of the rotor and the rotor impeller, respectively; is the thermal conductivity of the steam; R b is the radius of the rotor; w is the angular velocity of the rotor; is the kinematic viscosity of the air; Re is the Reynolds number.

3. A method for on-line stress calculation and fatigue assessment of a rotor of a steam turbine according to claim 1, characterized in that If the material-related parameters of the Ramberg-Osgood model are missing in step 7, the material-related parameters are obtained from the easily obtained material coefficients through the relationship: 1) Constant fit relationship: where, ε 1 and σ 1 are the strain and yield strength of the material yield point. 2) Coefficients in the relationship A and n , , σ 2 is the ultimate strength of the material, ψ is the reduction of area of the material.

4. A method for on-line stress calculation and fatigue assessment of a rotor of a steam turbine according to claim 1, characterized in that If the material-related parameters of the Basquin-Coffin-Manson relationship are missing in step 8, the material-related parameters are obtained from the easily obtained material coefficients through the relationship: 1) fatigue strength coefficient σ f ′ and fatigue ductility coefficient ɛ f ′ solved, when lacking fatigue test data, by approximating the fatigue strength coefficient and the fatigue ductility coefficient with the real fracture strength and the real fracture ductility, ; but they are not the same in physical concept; 2) fatigue strength index solution, ; 3) Fatigue ductility index solution, ; 4) wherein: wherein: σ f is the true fracture strength; ɛ f is the true fracture ductility; σ u is the tensile strength of the material; is the reduction of area of the material; and A is an intermediate calculation variable.

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