Method and system for determining equivalent damping ratio of steam turbine base

Abstract

The invention relates to the technical field of turbine base dynamics calculation, and provides a turbine base equivalent damping ratio determination method and system.The turbine base equivalent damping ratio determination method comprises the steps that the structure size and the material attribute of a turbine base are obtained, and a mechanical model of the turbine base is established; based on the mechanical model, determining a mass matrix and a stiffness matrix of the structure so as to establish a free vibration differential equation composed of various materials and an equivalent free vibration differential equation of the overall structure; based on a free vibration differential equation composed of multiple materials and an equivalent free vibration differential equation of the overall structure, according to vibration mode orthogonality, strain energy of a system composed of the multiple materials and strain energy of an equivalent system in all orders of vibration modes are obtained; based on strain energy of a system composed of multiple materials and an equivalent system in each order of vibration mode, an equivalent complex damping coefficient of each order of vibration mode is solved, and the equivalent complex damping coefficient is converted into an equivalent damping ratio. The equivalent damping ratio of the turbine base can be quickly and accurately obtained, and powerful support is provided for engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of turbine foundation dynamics calculation technology, and particularly relates to a method and system for determining the equivalent damping ratio of a turbine foundation. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] As a crucial structure supporting the turbine generator unit, the turbine foundation's dynamic performance directly impacts the unit's safe and stable operation. The damping ratio is a vital parameter describing a structure's energy dissipation capacity during vibration, and it is essential for accurately calculating the turbine foundation's vibration response and dynamic stability.

[0004] However, turbine foundations are typically composite structures made of steel, concrete, piles, and soil. The damping performance of these different materials varies considerably, and the overall damping ratio cannot be simply taken as the damping ratio of a single material. Therefore, an accurate and reliable method is needed to determine the equivalent damping ratio of the turbine foundation.

[0005] Currently, although there are some studies on methods for calculating the damping ratio of composite structures, most of these methods are for specific structural forms or material combinations and lack universality; at the same time, existing methods rarely consider special composite structures such as turbine foundations composed of steel, concrete, piles and soil. Summary of the Invention

[0006] To address the technical problems mentioned above, this invention provides a method and system for determining the equivalent damping ratio of a steam turbine foundation. Combining material damping ratio, complex damping theory, and modal strain energy model, it fully considers the combined structural characteristics of the steam turbine foundation, which is composed of steel, concrete, piles, and soil. This method can more accurately reflect the actual damping performance of the structure and quickly and accurately obtain the equivalent damping ratio of the steam turbine foundation, providing strong support for engineering practice.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides a method for determining the equivalent damping ratio of a steam turbine foundation, comprising: Obtain the structural dimensions and material properties of the turbine base, and establish a mechanical model of the turbine base; Based on the mechanical model, the mass matrix and stiffness matrix of the structure are determined in order to establish the differential equation of free vibration of the material composed of multiple materials and the equivalent differential equation of free vibration of the whole structure. Based on the differential equation of free vibration of a system composed of multiple materials and the equivalent differential equation of free vibration of the overall structure, and according to the orthogonality of the vibration modes, the strain energy of the system composed of multiple materials and the equivalent system in each vibration mode is obtained respectively. Based on the strain energy of the system composed of multiple materials and the equivalent system in each mode, the equivalent complex damping coefficient of each mode is obtained and converted into the equivalent damping ratio.

[0008] Furthermore, based on the equivalent complex damping coefficients of each vibration mode, and combined with the relationship between the viscous damping ratio and the complex damping coefficients, the equivalent damping ratios of each vibration mode are calculated.

[0009] Furthermore, the material properties include the elastic modulus, density, Poisson's ratio, and material damping ratio of different materials.

[0010] Furthermore, the differential equation for free vibration composed of multiple materials is: ;in,[ M ] is the quality matrix. m It refers to the types and quantities of materials, { ÿ} represents the acceleration vector of the structural nodes. Indicates the first i The complex damping coefficient of the material, where i is the imaginary unit, [ K ] i For the first i The block stiffness matrix corresponding to the material, { y} represents the displacement vector of the structural node.

[0011] Furthermore, the equivalent free vibration differential equation of the overall structure is: ;in,[ M ] is the mass matrix, { ÿ} represents the acceleration vector of the structural nodes, where i is the imaginary unit, [ K [ ] represents the overall stiffness matrix of the equivalent system. For the equivalent complex damping coefficient, { y} represents the displacement vector of the structural node.

[0012] Furthermore, the strain energy of a system composed of multiple materials after one cycle of vibration in each mode is as follows: ;in, T For the first j The vibration period of the mode shape, m It refers to the types and quantities of materials. For modal vectors, For the first j Generalized coordinates of mode shapes For the first l The material corresponds to the first j The damping coefficient of the mode shape, where i is the imaginary unit, [K ] l For the first l The block stiffness matrix corresponding to each material.

[0013] Furthermore, the strain energy of the equivalent system during one cycle of vibration in each mode is: ;in, T For the first j The vibration period of the mode shape, m It refers to the types and quantities of materials. For modal vectors, For the first j Generalized coordinates of mode shapes, where i is the imaginary unit, [ K [ ] represents the overall stiffness matrix of the equivalent system. The first equivalent damping j Mode-of-motion complex damping coefficient.

[0014] A second aspect of the present invention provides a system for determining the equivalent damping ratio of a steam turbine foundation, comprising: The model building module is configured to: obtain the structural dimensions and material properties of the turbine base, and establish a mechanical model of the turbine base; The differential equation establishment module is configured to: determine the mass matrix and stiffness matrix of the structure based on the mechanical model, in order to establish the free vibration differential equations composed of multiple materials and the equivalent free vibration differential equations of the overall structure; The strain energy calculation module is configured to: based on the free vibration differential equation of the system composed of multiple materials and the equivalent free vibration differential equation of the overall structure, and according to the mode orthogonality, obtain the strain energy of the system composed of multiple materials and the equivalent system in each mode. The damping ratio determination module is configured to: solve for the equivalent complex damping coefficient of each mode based on the strain energy of the system composed of multiple materials and the equivalent system in each mode, and convert it into the equivalent damping ratio.

[0015] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for determining the equivalent damping ratio of a steam turbine foundation as described above.

[0016] A fourth aspect of the present invention provides a computer device including a computer-readable storage medium, a processor, and a computer program stored on the computer-readable storage medium and executable on the processor, wherein the processor executes the program to implement the steps in the method for determining the equivalent damping ratio of a steam turbine foundation as described above.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This invention combines material damping ratio, complex damping theory, and modal strain energy model, fully considering the combined structural characteristics of the turbine foundation composed of steel, concrete, piles, and soil. It can more accurately reflect the actual damping performance of the structure and quickly and accurately obtain the equivalent damping ratio of the turbine foundation, providing strong support for engineering practice. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] Figure 1 This is a flowchart of a method for determining the equivalent damping ratio of a steam turbine foundation according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the structure of a computer device according to Embodiment 4 of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] Example 1 This embodiment provides a method for determining the equivalent damping ratio of a steam turbine base.

[0023] This embodiment provides a method for determining the equivalent damping ratio of a turbine foundation, specifically for a turbine foundation with a composite structure consisting of steel, concrete, piles, and soil.

[0024] This embodiment provides a method for determining the equivalent damping ratio of a steam turbine foundation, comprising: establishing a mechanical model of the steam turbine foundation; determining the mass matrix and stiffness matrix of the structure based on the established mechanical model, so as to establish the differential equation of free vibration composed of multiple materials and the equivalent differential equation of free vibration of the overall structure; obtaining the strain energy of the system composed of multiple materials and the equivalent system in each mode based on the differential equation and the orthogonality of the mode shapes; obtaining the equivalent complex damping coefficient based on the strain energy, thereby converting it into the equivalent damping ratio.

[0025] This embodiment provides a method for determining the equivalent damping ratio of a steam turbine foundation, such as... Figure 1 As shown, it includes the following steps: Step S1: Establish a mechanical model of the turbine base.

[0026] Step 101: Establish a mechanical model based on the actual structural dimensions and material properties of the turbine base.

[0027] The turbine base is a frame structure made of steel and concrete, and the base plate is embedded in the soil by piles. Therefore, it can be regarded as a composite structure composed of steel, concrete, piles and soil.

[0028] Step 102: In the mechanical model, define the material properties of steel, concrete, piles and soil respectively, including elastic modulus, density, Poisson's ratio and their respective material damping ratio.

[0029] Step 103: Mesh the mechanical model by dividing it into elements within different damping materials and using the material boundaries as the boundaries of the elements.

[0030] Step S2: Based on the established mechanical model, determine the mass matrix and stiffness matrix of the turbine base structure in order to establish the free vibration differential equation composed of multiple materials and the equivalent free vibration differential equation of the overall structure.

[0031] In the example, the free vibration differential equation is established through the following steps: Based on the established mechanical model, the mass matrix of the structure and the stiffness matrix of each material are obtained; based on the mass matrix and stiffness matrix, the free vibration differential equation composed of multiple materials is established; based on the mass matrix and the equivalent complex damping coefficient of the overall structure, the equivalent free vibration differential equation of the overall structure of the turbine base is established.

[0032] (1) First, the mass matrix of the structure can be obtained based on the mechanical model. M ] and stiffness matrix [ K ] i .

[0033] In this embodiment, the mass matrix and stiffness matrix are obtained based on general finite element theory.

[0034] Specifically, calculate the unit mass matrix. and ,in, For material density, N For shape functions, D For the material constitutive matrix, B The strain-displacement matrix, V e Indicates the first e The volume of each element is calculated; then the element mass matrix and element stiffness matrix are assembled according to the relative positions of the elements to form the mass matrix of the structure. and stiffness matrix ,in, n eThis represents the total number of units.

[0035] Among them, after optimizing the sorting of the nodes of each material damping element, [ K ] i Most of the elements will be 0.

[0036] For example, the materials used to construct a turbine foundation include steel, concrete, piles, and soil, each with a complex damping coefficient of [missing information]. , , and Their respective stiffness matrices are [ K ] 11 、[ K ] 22 、[ K ] 33 and[ K ] 44 Then we can get: ; ; ; .

[0037] (2) Based on the mass matrix and stiffness matrix, establish the differential equation for free vibration composed of multiple materials: ;in,[ M ] is the quality matrix; m It refers to the types and quantities of different materials; ÿ} represents the acceleration vector of the structural node, { ÿ} is displacement y The second derivative with respect to time; Indicates the first i The complex damping coefficient of the material; i is the imaginary unit; [ K ] i For the first i The block stiffness matrix corresponding to the material; { y} represents the displacement vector of the structural nodes, indicating the vibration displacement state of each node.

[0038] (3) Based on the mass matrix and the equivalent complex damping coefficient of the overall structure, the equivalent free vibration differential equation of the overall structure is established: Among them, the overall stiffness matrix of the equivalent system ; This is the equivalent complex damping coefficient.

[0039] Step S3: Based on the vibration differential equations (the free vibration differential equations of the system composed of multiple materials and the equivalent free vibration differential equations of the overall structure), and according to the mode orthogonality, obtain the strain energy of the system composed of multiple materials and the equivalent system in each mode.

[0040] Specifically, the strain energy is obtained through the following steps: based on the vibration differential equation, the modal frequencies and modal vectors of each order of the structure are obtained; based on the modal frequencies and modal vectors, the strain energy of the system composed of multiple materials and the equivalent system in each mode of vibration is calculated.

[0041] (1) Based on the vibration differential equation, the modal frequencies of each order of the structure are obtained. and mode vector .

[0042] (2) Based on the modal frequencies and modal vectors, calculate: The strain energy of a system composed of multiple materials after one cycle of vibration in each mode: ; in, For the first j Generalized coordinates of mode shapes; T For the first j The vibration period of a mode; For the first l The material corresponds to the first j Damping coefficient of the mode shape; The strain energy of the equivalent system after one cycle of vibration in each mode is: ; in, The first equivalent damping j Mode-of-motion complex damping coefficient.

[0043] Step S4: Based on the principle that the two strain energies are equal, the equivalent complex damping coefficients of each order can be obtained, and thus the equivalent damping ratio can be calculated.

[0044] Specifically, the equivalent damping ratio is determined through the following steps: based on the principle of equal strain energy, the equivalent complex damping coefficients of each mode are obtained; based on the equivalent complex damping coefficients, the equivalent damping ratio of each mode is determined.

[0045] Based on the principle that the strain energy of a system composed of multiple materials and an equivalent system is equal in one cycle of vibration at each order, the equivalent complex damping coefficients for each vibration mode are obtained: ; Based on the equivalent complex damping coefficient and the relationship between the viscous damping ratio and the complex damping coefficient, the equivalent viscous damping ratio, i.e., the equivalent damping ratio, of each vibration mode can be determined: ;in, For the first l The viscous damping ratio of a material corresponding to the j-th mode of vibration.

[0046] The method described in this embodiment can accurately calculate the equivalent damping ratio of the turbine foundation, improving the accuracy of dynamic calculations. Specifically, the method of this embodiment has the following beneficial effects: By combining material damping ratio, complex damping theory and modal strain energy model, the combined structural characteristics of the turbine base, which is composed of steel, concrete, piles and soil, are fully considered, which can more accurately reflect the actual damping performance of the structure. It is not only suitable for steam turbine bases, but can also be applied to other composite structures composed of multiple materials, and has a wide range of applications; Using the finite element method, the equivalent damping ratio of the turbine foundation can be obtained quickly and accurately, providing strong support for engineering practice.

[0047] Example 2 This embodiment provides a system for determining the equivalent damping ratio of a steam turbine foundation, comprising: The model building module is configured to: obtain the structural dimensions and material properties of the turbine base, and establish a mechanical model of the turbine base; The differential equation establishment module is configured to: determine the mass matrix and stiffness matrix of the structure based on the mechanical model, in order to establish the free vibration differential equations composed of multiple materials and the equivalent free vibration differential equations of the overall structure; The strain energy calculation module is configured to: based on the free vibration differential equation of the system composed of multiple materials and the equivalent free vibration differential equation of the overall structure, and according to the mode orthogonality, obtain the strain energy of the system composed of multiple materials and the equivalent system in each mode. The damping ratio determination module is configured to: solve for the equivalent complex damping coefficient of each mode based on the strain energy of the system composed of multiple materials and the equivalent system in each mode, and convert it into the equivalent damping ratio.

[0048] It should be noted that each module in this embodiment corresponds one-to-one with each step in Embodiment 1, and their specific implementation processes are the same, so they will not be repeated here.

[0049] Example 3 This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the method for determining the equivalent damping ratio of a steam turbine foundation as described in Embodiment 1 above.

[0050] Example 4 This embodiment provides a computer device, such as... Figure 2As shown, the system includes a computer-readable storage medium 1003, a processor 1001, a communication interface 1002, and a computer program stored on the computer-readable storage medium 1003 and executable on the processor 1001. The processor 1001, communication interface 1002, and computer-readable storage medium 1003 can be connected via a bus or other means. The communication interface 1002 is used to receive and transmit data. When the processor 1001 executes the program, it implements the steps in the method for determining the equivalent damping ratio of a steam turbine foundation as described in Embodiment 1 above.

[0051] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the equivalent damping ratio of a steam turbine foundation, characterized in that, include: Obtain the structural dimensions and material properties of the turbine base, and establish a mechanical model of the turbine base; Based on the mechanical model, the mass matrix and stiffness matrix of the structure are determined in order to establish the differential equation of free vibration of the material composed of multiple materials and the equivalent differential equation of free vibration of the whole structure. Based on the differential equation of free vibration of a system composed of multiple materials and the equivalent differential equation of free vibration of the overall structure, and according to the orthogonality of the vibration modes, the strain energy of the system composed of multiple materials and the equivalent system in each vibration mode is obtained respectively. Based on the strain energy of the system composed of multiple materials and the equivalent system in each mode, the equivalent complex damping coefficient of each mode is obtained and converted into the equivalent damping ratio.

2. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, Based on the equivalent complex damping coefficients of each vibration mode, and combined with the relationship between the viscous damping ratio and the complex damping coefficients, the equivalent damping ratios of each vibration mode are calculated.

3. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, The material properties include the elastic modulus, density, Poisson's ratio, and material damping ratio of different materials.

4. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, The differential equation for free vibration composed of multiple materials is: ;in,[ M ] is the quality matrix. m It refers to the types and quantities of materials, { ÿ } represents the acceleration vector of the structural nodes. Indicates the first i The complex damping coefficient of the material, where i is the imaginary unit, [ K ] i For the first i The block stiffness matrix corresponding to the material, { y } represents the displacement vector of the structural node.

5. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, The equivalent free vibration differential equation of the overall structure is: ;in,[ M ] is the mass matrix, { ÿ } represents the acceleration vector of the structural nodes, where i is the imaginary unit, [ K [ ] represents the overall stiffness matrix of the equivalent system. For the equivalent complex damping coefficient, { y } represents the displacement vector of the structural node.

6. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, The strain energy of a system composed of multiple materials after one cycle of vibration in each mode: ;in, T For the first j The vibration period of the mode shape, m It refers to the types and quantities of materials. For modal vectors, For the first j Generalized coordinates of mode shapes For the first l The material corresponds to the first j The damping coefficient of the mode shape, where i is the imaginary unit, [ K ] l For the first l The block stiffness matrix corresponding to each material.

7. The method for determining the equivalent damping ratio of a steam turbine foundation as described in claim 1, characterized in that, The strain energy of the equivalent system after one cycle of vibration in each mode is: ;in, T For the first j The vibration period of the mode shape, m It refers to the types and quantities of materials. For modal vectors, For the first j Generalized coordinates of mode shapes, where i is the imaginary unit, [ K [ ] represents the overall stiffness matrix of the equivalent system. The first equivalent damping j Mode-of-motion complex damping coefficient.

8. A system for determining the equivalent damping ratio of a steam turbine foundation, characterized in that, include: The model building module is configured to: obtain the structural dimensions and material properties of the turbine base, and establish a mechanical model of the turbine base; The differential equation establishment module is configured to: determine the mass matrix and stiffness matrix of the structure based on the mechanical model, in order to establish the free vibration differential equations composed of multiple materials and the equivalent free vibration differential equations of the overall structure; The strain energy calculation module is configured to: based on the free vibration differential equation of the system composed of multiple materials and the equivalent free vibration differential equation of the overall structure, and according to the mode orthogonality, obtain the strain energy of the system composed of multiple materials and the equivalent system in each mode. The damping ratio determination module is configured to: solve for the equivalent complex damping coefficient of each mode based on the strain energy of the system composed of multiple materials and the equivalent system in each mode, and convert it into the equivalent damping ratio.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the method for determining the equivalent damping ratio of a steam turbine base as described in any one of claims 1-7.

10. A computer device comprising a computer-readable storage medium, a processor, and a computer program stored on the computer-readable storage medium and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the method for determining the equivalent damping ratio of a steam turbine base as described in any one of claims 1-7.

Images