CN111723506A - System-level analysis model each component dynamic contribution degree analysis method and system - Google Patents
System-level analysis model each component dynamic contribution degree analysis method and system Download PDFInfo
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Abstract
The invention discloses a method for analyzing the dynamic contribution of each component of a system-level analysis model, which comprises the following steps: establishing a dynamic analysis model of a reactor system, and extracting a global mass matrix and a global stiffness matrix; carrying out modal analysis on the dynamic analysis model; acquiring a modal strain energy equation of the dynamic analysis model, and acquiring modal strain energy of each single component under each order of mode; and acquiring normalized modal strain energy and acquiring the power contribution degree of each single component. The invention also discloses a system for analyzing the dynamic contribution of each component of the system-level analysis model. The calculation method provided by the invention can be used for quantitatively researching and investigating the power contribution degree of each device or component in the system-level power analysis model under a specific degree of freedom, and the dynamic contribution degree of each device or component under the system coupling effect can be fully mastered at the initial stage of device or component design, so that a quantitative reference basis is provided for the initial mechanical design and subsequent structure optimization of the devices and components.
Description
Technical Field
The invention relates to the field of reactor structure mechanics, in particular to a method and a system for analyzing the dynamic contribution of each component of a system-level analysis model.
Background
The dynamic analysis and load distribution calculation of the main system (coolant system, reactor system, purification system, auxiliary system, etc.) of the reactor are important links in the structural design of the reactor and the auxiliary systems thereof, and are the main technical means for evaluating the structural safety. The system level power analysis and calculation is upstream of the development of reactor system load distribution studies and safety analysis. The system level power analysis model generally comprises main equipment (such as a reactor pressure vessel, a coolant main pump, a steam generator and a pressure stabilizer), pipelines (such as a main pipeline and auxiliary pipelines), other auxiliary systems (such as a waste heat discharge system and a purification system) and the like in a reactor and a loop system. The system-level dynamic analysis model is usually established through a finite element method, and a mechanical model capable of describing main dynamic characteristics of the system is abstracted through simplification of each main device and each component. The method is mainly used for calculating the displacement and the reaction force of each main device and each component of a system under the action of external dynamic loads (such as earthquake, LOCA, impact and the like), and provides calculation input for further detailed analysis of the bearing strength and stress evaluation of each component.
The system-level dynamic analysis is mainly developed by mode analysis in a frequency domain, spectrum analysis, harmonic response analysis and nonlinear transient analysis in a time domain. Because a large number of non-linear factors are usually included in the system-level model, and the model is large in scale, it takes a lot of time and calculation cost to obtain the dynamic response contribution degree of a single component or device by simulating the system-level model in a full size. How to examine the power contribution degree of each component of the system-level model under a specific load condition through a rapid method is an important factor for analyzing the power characteristics of the components.
In the current stage of engineering, the dynamic characteristics of the whole system are mainly investigated by a modal analysis method. Although modal analysis can give the resonant frequency and the mode shape distribution of a system in a certain frequency band, the existing analysis method and calculation software cannot give the dominant resonant frequency and the main participating mass of a certain device or component in a system-level model. The method commonly used in engineering is to qualitatively judge a component with larger motion amplitude under a certain order of resonance frequency by observing the mode shape displacement of all nodes of the system under a specific mode. Because the mode shape function in modal analysis is usually normalized for the mass matrix of the system model, the qualitative judgment method cannot give a true description of the component power contribution degree on a physical coordinate, only can give a rough judgment according to the engineering experience of an analyst, and cannot give a quick mechanical design suggestion at the initial design stage of the equipment.
In summary, in the process of implementing the technical solution of the invention in the embodiment of the present application, the inventors found that at least the following problems exist in the current technology:
1. the existing published documents and data lack quantitative research aiming at the dynamic contribution degree of each component under a system-level dynamic analysis model.
2. The mode of determining the power contribution of the component by qualitatively observing the mode shape distribution of the system-level model in engineering lacks theoretical support and cannot give quantitative description.
3. The calculation cost is high by carrying out the mode of carrying out the nonlinear transient analysis of the system-level model to obtain the power contribution of the single component, and the method is not beneficial to the quick iteration of the initial stage of the system design.
Disclosure of Invention
The invention aims to solve the technical problems that an analysis technology for the power contribution degree of each component under a system-level power analysis model is lacked in the prior art, and quantitative description cannot be given to the power contribution degree of each component, so that the invention aims to provide the analysis method and the analysis system for the power contribution degree of each component of the system-level power analysis model, and solve the problems.
The invention is realized by the following technical scheme:
a method for analyzing dynamic contribution degrees of components of a system-level analysis model comprises the following steps: s1: establishing a dynamic analysis model of a reactor system, and extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model; s2: performing modal analysis on the dynamic analysis model according to the global quality matrix and the global stiffness matrix; s3: acquiring a modal strain energy equation of the dynamic analysis model according to the modal analysis, and acquiring modal strain energy of each single component under each order of mode according to the modal strain energy equation; s4: and normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy.
When the method is applied, the dynamic analysis model of the reactor system can be established in a discrete model mode of finite elements, discrete elements and the like, and key components in the dynamic analysis model comprise: fuel Assemblies (FA), a Core Barrel (CB), an upper internals (UVI), a core barrel (CS), a Control Rod Drive Mechanism (CRDM), a Reactor Pressure Vessel (RPV), and an integrated reactor top structure (UVI). After the model is established, a global mass matrix M and a global stiffness matrix K can be extracted from the power analysis model; modal analysis can be carried out on the dynamic analysis model according to M and K, the fixed frequency and the vibration mode of each order of modal of the dynamic analysis model can be obtained through the modal analysis, and the fixed frequency and the vibration mode of each order of modal are basic data of subsequent analysis; the modal strain energy equation of the dynamic analysis model can be obtained through modal analysis, the modal strain energy equation comprises fixed frequency, vibration mode, global mass matrix and global rigidity matrix, on the basis of the equation, modal strain energy of each single component under each order of mode can be obtained through decomposition of the global rigidity matrix, and the dynamic contribution degree of each single component can be obtained after normalization of the modal strain energy of each single component. The calculation method provided by the invention only needs to examine the modal information of the system-level model and perform blocking operation on the global quality and stiffness matrix, thereby avoiding the high calculation cost and the machine time required for directly carrying out the transient analysis of the nonlinear system-level model. The method can deeply mine the dynamic characteristics and information of the system in the preprocessing stage before transient analysis is carried out, and can be popularized in the standard analysis process of reactor structure mechanics.
Further, the method also comprises the following steps:
s5: and obtaining the effective mass of the dynamic analysis model in the respective freedom degree direction according to the modal analysis, and obtaining the dynamic contribution degree of each single component in the respective freedom degree according to the effective mass in the respective freedom degree direction and the normalized modal strain energy.
When the method is applied, the effective mass in the respective freedom degree direction can be obtained by adding the displacement load vector, and the method can obtain the dynamic contribution degree of each single component in the respective freedom degree by using the effective mass and the normalized modal strain energy.
Further, the effective masses of the dynamic analysis models in the directions of the respective degrees of freedom are obtained according to the following formula:
in the formula
Effective mass of the dynamic analysis model under j-order mode; gamma rayjIs a modal engagement factor;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; d is a displacement load vector;
and acquiring the power contribution degree of each single component on each degree of freedom according to the following formula:
wherein X is the direction of freedom;
the power contribution of the p node in the direction of the jth order modal X degree of freedom is obtained; omegajIs the natural frequency of the j-th order mode;
the mode shape of a j-th order mode of a p node; kpqFor dynamic analysis of mouldA block matrix in the global stiffness matrix;
the effective mass of the dynamic analysis model in the X degree of freedom direction under the j-order mode is shown.
When the method is applied, d is a displacement load vector, which is a displacement vector of other nodes of the system when unit displacement is applied in a certain degree of freedom direction at the system constraint, and X is a degree of freedom which is characterized in that X represents all degrees of freedom which may appear, including but not limited to the degrees of freedom of three translation directions and an upper rotation direction of each node; the components in the dynamic analysis model are discretized, and when each component is discretized into a plurality of units, each unit has a plurality of nodes, and the characteristics of the components can be represented through the nodes. In the above formula, n is the number of the node sets corresponding to the different components under consideration and the different degrees of freedom thereof. p (p 1., n) is the node set number corresponding to the part under consideration in the system level model.
Further, step S5 includes the following sub-steps:
s51: carrying out non-dimensionalization processing on the effective masses in the respective degree directions to obtain the percentage of the effective masses participating in the total mass in each order of modes;
s52: and when the power contribution degree of each single component on the corresponding degree of freedom is obtained, the mode that the percentage of the effective mass participating in the total mass is lower than the threshold value is ignored.
When the method is applied, the dynamic response analysis is a calculation process with huge calculation amount, particularly, after the freedom degree direction is added, the calculation amount is increased in a geometric multiple mode, so in order to improve the calculation efficiency, the method also carries out non-dimensionalization processing on the effective mass in the respective freedom degree direction to obtain the percentage of the effective mass participating in the total mass under each order of modes, and ignores the mode that the percentage of the effective mass participating in the total mass is lower than the threshold value, thereby improving the calculation efficiency.
Further, in step S2, the kinetic analysis model is modal-analyzed according to the following formula:
in the formula of omegajIs the natural frequency of the j-th order mode;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model.
Further, step S3 includes the following sub-steps: and partitioning the global stiffness matrix in the modal strain energy equation, and acquiring the modal strain energy of each single component under each order of mode according to the multiplication rule of the partitioned matrix.
When the method is applied, one block matrix can represent the rigidity of one node, one unit or one component, and required data can be extracted from the global rigidity matrix in a block matrix mode.
Further, the modal strain energy equation is:
in the formula of omegajIs the natural frequency of the j-th order mode;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model;
blocking a global stiffness matrix in the modal strain energy equation according to:
in the formula K11To KnnAll are block matrixes in the global stiffness matrix;
obtaining modal strain energy of each single component in each order of mode according to the following formula:
in the formula
The modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
Further, in step S4, the modal strain energy of each single component is normalized to obtain the normalized modal strain energy, which is obtained by using the following formula:
in the formula
Normalized modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
A system-level analysis model component dynamic contribution degree analysis system, comprising:
a modeling unit: the dynamic analysis model is used for establishing a reactor system;
an extraction unit: the system is used for extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model;
an analysis unit: the modal analysis module is used for carrying out modal analysis on the dynamic analysis model according to the global quality matrix and the global rigidity matrix;
a processing unit: the modal strain energy equation of the dynamic analysis model is obtained according to the modal analysis, and the modal strain energy of each single component under each order of mode is obtained according to the modal strain energy equation;
a normalization unit: the device is used for normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy;
a freedom degree analysis unit: the dynamic analysis module is used for obtaining effective masses of the dynamic analysis model in the respective freedom degrees according to the modal analysis and obtaining dynamic contribution degrees of the single components in the respective freedom degrees according to the effective masses in the respective freedom degrees and the normalized modal strain energy.
Further, the processing unit blocks the global stiffness matrix in the modal strain energy equation, and obtains the modal strain energy of each single component in each order of mode according to a multiplication rule of the block matrix.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention discloses an analysis method and a system for the power contribution degree of each component of a system-level analysis model, provides a calculation method for inspecting the power contribution degree of each component in the system-level analysis model, and solves the problem that the power contribution degree of each component cannot be quantitatively calculated on a specific degree of freedom in the current engineering. The method is suitable for dynamic analysis and calculation of a reactor coolant system. The method can analyze the dynamic response contribution degree of each part under the condition that coupling exists among different devices or parts in the system, and the applicable dynamic analysis load working conditions comprise common earthquake, LOCA, impact and the like in the reactor structure mechanical analysis. The calculation method provided by the invention only needs to examine the modal information of the system-level model and perform blocking operation on the global quality and stiffness matrix, thereby avoiding the high calculation cost and the machine time required for directly carrying out the transient analysis of the nonlinear system-level model. The method can deeply mine the dynamic characteristics and information of the system in the preprocessing stage before transient analysis is carried out, and can be popularized in the standard analysis process of reactor structure mechanics.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic diagram of the process steps of the present invention;
FIG. 2 is a schematic diagram of the method steps of an embodiment of the present invention;
FIG. 3 is a schematic diagram of a reactor system dynamics analysis calculation model according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a reactor system according to an embodiment of the present invention;
FIG. 5 is a seismic load response spectrum of a reactor system according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating the distribution of modal effective mass in different directions in a reactor system according to an embodiment of the present invention;
FIG. 7 is a graph of power contribution distributions of various components of a reactor system according to an embodiment of the present invention;
FIG. 8 is a diagram illustrating different degree-of-freedom power contribution distributions of individual components of a reactor system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1
As shown in FIG. 1, the method for analyzing the dynamic contribution of each component of the system-level analysis model comprises the following steps: s1: establishing a dynamic analysis model of a reactor system, and extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model; s2: performing modal analysis on the dynamic analysis model according to the global quality matrix and the global stiffness matrix; s3: acquiring a modal strain energy equation of the dynamic analysis model according to the modal analysis, and acquiring modal strain energy of each single component under each order of mode according to the modal strain energy equation; s4: and normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy.
In this embodiment, the power analysis model of the reactor system may be established in a discrete model manner such as a finite element or a discrete element, and the key components in the power analysis model include: fuel Assemblies (FA), a Core Barrel (CB), an upper internals (UVI), a core barrel (CS), a Control Rod Drive Mechanism (CRDM), a Reactor Pressure Vessel (RPV), and an integrated reactor top structure (UVI). After the model is established, a global mass matrix M and a global stiffness matrix K can be extracted from the power analysis model; modal analysis can be carried out on the dynamic analysis model according to M and K, the fixed frequency and the vibration mode of each order of modal of the dynamic analysis model can be obtained through the modal analysis, and the fixed frequency and the vibration mode of each order of modal are basic data of subsequent analysis; the modal strain energy equation of the dynamic analysis model can be obtained through modal analysis, the modal strain energy equation comprises fixed frequency, vibration mode, global mass matrix and global rigidity matrix, on the basis of the equation, modal strain energy of each single component under each order of mode can be obtained through decomposition of the global rigidity matrix, and the dynamic contribution degree of each single component can be obtained after normalization of the modal strain energy of each single component. The calculation method provided by the invention only needs to examine the modal information of the system-level model and perform blocking operation on the global quality and stiffness matrix, thereby avoiding the high calculation cost and the machine time required for directly carrying out the transient analysis of the nonlinear system-level model. The method can deeply mine the dynamic characteristics and information of the system in the preprocessing stage before transient analysis is carried out, and can be popularized in the standard analysis process of reactor structure mechanics.
For further explaining the working process of the embodiment, the method further comprises the following steps:
s5: and obtaining the effective mass of the dynamic analysis model in the respective freedom degree direction according to the modal analysis, and obtaining the dynamic contribution degree of each single component in the respective freedom degree according to the effective mass in the respective freedom degree direction and the normalized modal strain energy.
In the implementation of the embodiment, the effective masses in the directions of the respective degrees of freedom can be obtained by adding the displacement load vector, and the dynamic contribution degrees of the single components in the respective degrees of freedom can be obtained by using the effective masses and the normalized modal strain energy.
To further illustrate the operation of the present embodiment, the effective mass of the dynamical analysis model in the direction of each degree of freedom is obtained according to the following formula:
in the formula
Effective mass of the dynamic analysis model under j-order mode; gamma rayjIs a modal engagement factor;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; d is a displacement load vector;
and acquiring the power contribution degree of each single component on each degree of freedom according to the following formula:
wherein X is a degree of freedom;
the power contribution of the p node under the j-th order modal X degree of freedom is obtained; omegajIs the natural frequency of the j-th order mode;
the mode shape of a j-th order mode of a p node; kpqA block matrix in the dynamic analysis model global rigidity matrix;
is the effective mass of the dynamic analysis model in the X degree of freedom under the j-order mode.
In this embodiment, d is a displacement load vector, which is a displacement vector of other nodes of the system when a unit displacement is applied in a direction of a certain degree of freedom at the system constraint, and X is a degree of freedom which is a characteristic and represents all degrees of freedom that may occur, including but not limited to degrees of freedom in three translational directions and an upper rotational direction of each node; the components in the dynamic analysis model are discretized, and when each component is discretized into a plurality of units, each unit has a plurality of nodes, and the characteristics of the components can be represented through the nodes. In the above formula, n is the number of the node sets corresponding to the different components under consideration and the different degrees of freedom thereof. p (p 1., n) is the node set number corresponding to the part under consideration in the system level model.
To further explain the operation of the present embodiment, step S5 includes the following sub-steps:
s51: carrying out non-dimensionalization processing on the effective masses in the respective degree directions to obtain the percentage of the effective masses participating in the total mass in each order of modes;
s52: and when the power contribution degree of each single component on the corresponding degree of freedom is obtained, the mode that the percentage of the effective mass participating in the total mass is lower than the threshold value is ignored.
In the implementation of this embodiment, the dynamic response analysis is a calculation process with huge computation amount, and especially after the degree of freedom direction is added, the computation amount will increase in geometric times, so in order to improve the computation efficiency, the present invention further performs non-dimensionalization on the effective masses in the respective degree of freedom directions to obtain the percentage of the effective masses participating in the total mass in each order of modes, and ignores the mode in which the percentage of the effective masses participating in the total mass is lower than the threshold, thereby improving the computation efficiency.
To further illustrate the operation of the present embodiment, in step S2, the kinetic analysis model is modal-analyzed according to the following formula:
in the formula of omegajIs the natural frequency of the j-th order mode;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model.
To further explain the operation of the present embodiment, step S3 includes the following sub-steps: and partitioning the global stiffness matrix in the modal strain energy equation, and acquiring the modal strain energy of each single component under each order of mode according to the multiplication rule of the partitioned matrix.
In this embodiment, one blocking matrix may represent the stiffness of one node, one unit, or one component, and the required data may be extracted from the global stiffness matrix by means of the blocking matrix.
To further illustrate the operation of this embodiment, the modal strain energy equation is:
in the formula of omegajIs the natural frequency of the j-th order mode;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model;
blocking a global stiffness matrix in the modal strain energy equation according to:
in the formula K11To KnnAll are block matrixes in the global stiffness matrix;
obtaining modal strain energy of each single component in each order of mode according to the following formula:
in the formula
The modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
Further, in step S4, the modal strain energy of each single component is normalized to obtain the normalized modal strain energy, which is obtained by using the following formula:
in the formula
Normalized modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
Example 2
The embodiment provides a system for analyzing dynamic contribution of each component of a system-level analysis model, which comprises:
a modeling unit: the dynamic analysis model is used for establishing a reactor system;
an extraction unit: the system is used for extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model;
an analysis unit: the modal analysis module is used for carrying out modal analysis on the dynamic analysis model according to the global quality matrix and the global rigidity matrix;
a processing unit: the modal strain energy equation of the dynamic analysis model is obtained according to the modal analysis, and the modal strain energy of each single component under each order of mode is obtained according to the modal strain energy equation;
a normalization unit: the device is used for normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy;
a freedom degree analysis unit: the dynamic analysis module is used for obtaining effective masses of the dynamic analysis model in the respective freedom degrees according to the modal analysis and obtaining dynamic contribution degrees of the single components in the respective freedom degrees according to the effective masses in the respective freedom degrees and the normalized modal strain energy.
To further illustrate the working process of this embodiment, the processing unit blocks the global stiffness matrix in the modal strain energy equation, and obtains the modal strain energy of each single component in each order of modes according to a multiplication rule of the block matrix.
Example 3
This example on the basis of example 1 and example 2,
the embodiment of the application provides a method for analyzing dynamic contribution of several key components in a reactor system in the direction along the axis of a reactor pressure vessel, which comprises the following steps:
1. and carrying out dynamic analysis modeling on the reactor system by using a finite element calculation program. The model includes key components including: fuel Assemblies (FA), a Core Barrel (CB), an upper internals (UVI), a core barrel (CS), a Control Rod Drive Mechanism (CRDM), a Reactor Pressure Vessel (RPV), and an integrated reactor top structure (UVI).
2. And extracting global mass and rigidity matrixes in the system-level dynamic analysis model, recording the global mass and rigidity matrixes as M and K, and recording the mass and rigidity matrixes of the system-level model in a text file in a storage form of a sparse matrix.
3. Modal analysis was performed based on the mass and stiffness matrix of the system level model, as shown in equation (1). And calculating the effective masses of the system-level model in the respective degree directions by using the mode shape function, as shown in formula (2), and carrying out non-dimensionalization on the effective masses, as shown in formula (3).
4. From the modal analysis, it can be known that the modal strain energy of the system-level model has a relationship as shown in equation (4). By performing blocking operation on the global stiffness matrix K, the modal strain energy of a single component in a certain order of modes can be obtained according to the multiplication rule of the blocking matrix, as shown in formula (6). And the partitioning of the matrix is carried out according to the finite element model node set to which the inspected component and the degree of freedom thereof belong. The key technique of the matrix blocking operation is shown in equation (5).
5. The component modal strain energy shown in formula (6) can be normalized by utilizing the orthogonality and normalization properties of the mode shape function so as to examine the power contribution degree of the component, as shown in formula (7).
6. Further, when considering the weight of the modal importance of the component in different degrees of freedom directions, the examination can be made in combination with the modal effective mass and the normalized modal strain energy, as shown in equation (8).
When the power contribution degree of a certain component in the system-level model under a specific degree of freedom is considered in quantification, the quantification distribution of the formulas (7) and (8) under different modes is output in the form of a histogram.
Wherein:
in the above formulas, M and K in formula (1) are the global mass matrix and stiffness matrix, ω, of the finite element model for the system-level dynamic analysis respectivelyjAnd
the natural frequency and the mode shape of the j-th order mode; the vector d in the formula (2) is the displacement vector of other nodes of the system when unit displacement is applied in a certain degree of freedom direction at the system constraint, and gammajAs a modal engagement factor, meffIs a modal effective mass; m in formula (3)totIs the total mass of the system level model; in the formula (5), n is the number of the node sets corresponding to the different examined components and the different degrees of freedom thereof.
The effective mass of the j-th order mode participates in the total mass percentage
R ═ d constrained vector, displacement load vector
Further, when the r value in the formula (3) is lower than a certain small threshold value, the mode corresponding to the direction of the degree of freedom does not dominate the overall response of the system, so that the mode with a relatively small mass ratio in each direction can be ignored when considering the component power contribution degree.
Further, the directions of freedom include three translational directions X, Y, Z and three rotational directions ROTX, ROTY, ROTZ for each node in the finite element model.
Further, in equations (6) and (7), p (p ═ 1.., n) is the node set number corresponding to the part under consideration in the system level model.
Further, the subscript X of the variable WRMSE in the formula (8) represents a component dynamic contribution index when the effective mass of the X degree-of-freedom direction mode is weighted, and the calculation of other degrees-of-freedom directions is the same as the formula (8).
By utilizing the calculation method provided by the invention, the power contribution degree of each device or component in the system-level power analysis model under a specific degree of freedom can be quantitatively researched and examined. The method provided by the invention does not need to carry out nonlinear transient analysis aiming at a system-level dynamic analysis model, and can grasp the dynamic characteristics of the component only by modal information. By applying the method provided by the invention, the dynamic contribution degree of the equipment or the component under the system coupling effect can be fully mastered at the initial stage of the equipment or the component design, and a quantitative reference basis is provided for the initial mechanical design and the subsequent structural optimization of the equipment or the component. All the processes are realized by computer programs, the calculation result is reliable, and the analysis process can be integrated in the mechanical standard analysis process of the reactor structure.
Example 4
On the basis of the embodiments 1-3, the dynamic response analysis of the pressurized water reactor system under the earthquake load is performed by the embodiment, and the dynamic contribution degrees of different key components of the reactor system in the axial direction of the pressure vessel are analyzed and calculated. Reactor system key components include: fuel Assemblies (FA), core hangers (CB), upper internals (UVI), core barrels (CS), Control Rod Drive Mechanisms (CRDM), Reactor Pressure Vessels (RPV), integrated reactor dome structures (UVI), and the like. The schematic structural diagram of the reactor system and the abstract representation of the finite element model for dynamic analysis are shown in fig. 3 and 4. The dynamic load input for seismic analysis of the reactor system is given in the form of seismic response spectra in three horizontal directions, see fig. 5, the position of the response spectrum as the interface position of the reactor inlet nozzle.
As shown in fig. 2, the method comprises the following steps:
and S10, establishing a system-level dynamic analysis finite element model through finite analysis software or a program, extracting a global quality matrix M and a rigidity matrix K of the model, and storing the global quality matrix and the rigidity matrix in a text file in a sparse matrix storage mode.
After step S10, the method of the embodiment of the present application proceeds to step S20, i.e.: and (3) carrying out modal analysis on the system level model, wherein the basic technology of the modal analysis is shown in formula (1), and meanwhile, the effective mass of each order of modal in different freedom directions is calculated, and is shown in formula (2). The distribution of the modal effective mass in different directions of the reactor system in this example is shown in fig. 6.
After step S20, the method of the embodiment of the present application proceeds to step S30, i.e.: according to the distribution of dimensionless effective mass in each degree of freedom direction under different modes, as shown in formula (3), selecting the dominant mode of the system level model to conduct component power contribution degree investigation. In this embodiment, the dominant mode corresponds to the mode in fig. 5 in which the effective mass is at a higher level.
After step S30, the method of the embodiment of the present application proceeds to step S40, i.e.: according to different apparatus or partsNode distribution in system-level finite element model, global stiffness matrix K and each order matrix type
The blocking operation is performed as shown in equation (5).
After step S40, the method of the embodiment of the present application proceeds to step S50, i.e.: according to the formulas (6) and (7), the modal strain energy of the single component in the system-level model and the normalization index thereof are calculated, and the modal strain energy distribution of different components of the reactor system after normalization under the dominant mode is shown in figure 7.
After step S50, the method of the embodiment of the present application proceeds to step S60, i.e.: and (4) according to a formula (8), taking the dimensionless modal effective mass in each degree of freedom direction as a weight, and calculating the distribution condition of the weighted modal strain energy of each part under the dominant mode. The present embodiment takes a Fuel Assembly (FA) as an example, and the distribution of the dynamic contribution of each degree of freedom of the component taking into account the modal effective mass weighting along the reactor pressure vessel axis is given in fig. 8.
After step S60, the method of the embodiment of the present application proceeds to step S70, i.e.: the distribution of the dynamic contribution of each part under the dominant mode is shown in a histogram or a bar graph.
After step S70, the method of the embodiment of the present application proceeds to step S80, i.e.: and outputting the analysis result of the power contribution of the component.
Among the respective degree of freedom dynamic contributions shown in fig. 8, UX, UY, and UZ represent the respective translational displacements of the investigation nodes; ROT denotes a set of displacements in each rotational direction.
In practical application, the commercial finite element software comprises: ANSYS, ABAQUS, etc., numerical calculation software and programming languages include: MATLAB, FORTRAN, C/C + +, PYTHON, and the like.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for analyzing dynamic contribution degrees of components of a system-level analysis model is characterized by comprising the following steps:
s1: establishing a dynamic analysis model of a reactor system, and extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model;
s2: performing modal analysis on the dynamic analysis model according to the global quality matrix and the global stiffness matrix;
s3: acquiring a modal strain energy equation of the dynamic analysis model according to the modal analysis, and acquiring modal strain energy of each single component under each order of mode according to the modal strain energy equation;
s4: and normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy.
2. The method for analyzing the dynamic contribution of each component of the system-level analysis model according to claim 1, further comprising the steps of:
s5: and obtaining the effective mass of the dynamic analysis model in the respective freedom degree direction according to the modal analysis, and obtaining the dynamic contribution degree of each single component in the respective freedom degree according to the effective mass in the respective freedom degree direction and the normalized modal strain energy.
3. The method according to claim 2, wherein the effective mass of each component of the dynamical analysis model in the direction of each degree is obtained according to the following formula:
in the formula
Effective mass of the dynamic analysis model under j-order mode; gamma rayjIs a modal engagement factor;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; d is a displacement load vector;
and acquiring the power contribution degree of each single component on each degree of freedom according to the following formula:
wherein X is the direction of freedom;
the power contribution of the p node in the direction of the jth order modal X degree of freedom is obtained;
the mode shape of the j-th order mode of the p node; kpqA block matrix in the dynamic analysis model global rigidity matrix;
the effective mass of the dynamic analysis model in the X degree of freedom direction under the j-order mode is shown.
4. The method for analyzing the dynamic contribution of each component of the system-level analysis model as claimed in claim 2, wherein the step S5 comprises the following sub-steps:
s51: carrying out non-dimensionalization treatment on the effective masses in the respective degree directions to obtain the percentage of the effective mass in each order of mode to the total mass of the structure;
s52: and when the power contribution degree of each single component on the corresponding degree of freedom is obtained, the mode that the percentage of the effective mass participating in the total mass is lower than the threshold value is ignored.
5. The method of claim 1, wherein in step S2, the modal analysis of the dynamical analysis model is performed according to the following formula:
in the formula of omegajIs the natural frequency of the j-th order mode;
the mode shape is the j order mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model.
6. The method for analyzing the dynamic contribution of each component of the system-level analysis model as claimed in claim 1, wherein the step S3 comprises the following sub-steps:
and partitioning the global stiffness matrix in the modal strain energy equation, and acquiring the modal strain energy of each single component under each order of mode according to the multiplication rule of the partitioned matrix.
7. The method of claim 6, wherein the modal strain energy equation is as follows:
wherein omega is the j-th order natural frequency of the system;
is the j order vibration mode; m is a global quality matrix of the dynamic analysis model; k is a global rigidity matrix of the dynamic analysis model;
blocking a global stiffness matrix in the modal strain energy equation according to:
in the formula K11To KnnAll are block matrixes in the global stiffness matrix;
obtaining modal strain energy of each single component in each order of mode according to the following formula:
in the formula
The modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
8. The method of claim 1, wherein the step S4 of normalizing the modal strain energy of each single component to obtain the normalized modal strain energy is obtained by the following formula:
in the formula
Normalized modal strain energy of the p node in the j-th order mode; kpqAnd the block matrix in the global rigidity matrix of the dynamic analysis model.
9. The system adopting the method for analyzing the dynamic contribution of each part of the system-level analysis model according to any one of claims 1 to 8, is characterized by comprising the following steps:
a modeling unit: the dynamic analysis model is used for establishing a reactor system;
an extraction unit: the system is used for extracting a global mass matrix and a global stiffness matrix in the dynamic analysis model;
an analysis unit: the modal calculation is carried out on the dynamic analysis model according to the global quality matrix and the global rigidity matrix;
a processing unit: the modal strain energy equation of the dynamic analysis model is obtained according to the modal analysis, and the modal strain energy of each single component under each order of mode is obtained according to the modal strain energy equation;
a normalization unit: the device is used for normalizing the modal strain energy of each single component to obtain normalized modal strain energy, and obtaining the power contribution degree of each single component according to the normalized modal strain energy;
a freedom degree analysis unit: the dynamic analysis module is used for obtaining effective masses of the dynamic analysis model in the respective freedom degrees according to the modal analysis and obtaining dynamic contribution degrees of the single components in the respective freedom degrees according to the effective masses in the respective freedom degrees and the normalized modal strain energy.
10. The system for analyzing the dynamic contribution of each component of the system-level analysis model according to claim 9, wherein the processing unit blocks the global stiffness matrix in the modal strain energy equation and obtains the modal strain energy of each single component in each order of mode according to a multiplication rule of the block matrix.
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