CN112364459A - Method for obtaining optimized parameters of tungsten alloy flywheel sleeved with multiple rings - Google Patents
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Abstract
The invention discloses an optimized parameter acquisition method of a tungsten alloy flywheel sleeved with multiple rings, which comprises the steps of establishing a parameterized finite element model of the tungsten alloy flywheel sleeved with multiple rings by using ABAQUS software; establishing a parameterized finite element analysis file of the tungsten alloy flywheel sleeved with multiple rings by using ABAQUS software; building a DOE test design model by using ISIGHT optimization design software to obtain a test design matrix; the bat file calls ABAQUS software to analyze and calculate each data point in a test design matrix, and DOE sample data is generated; based on DOE sample data, a neural network proxy model is constructed by adopting RBF radial basis functions, a mathematical model between factors and responses is obtained, an interference magnitude optimization value between the tungsten alloy intermediate layer and the outer retaining ring when an allowable stress value is taken as an optimization target is obtained under a constraint condition by mining internal relations of data, and size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when energy storage density and rotational inertia are taken as optimization targets are obtained.
Description
Technical Field
The invention relates to the field of obtaining optimized parameters of a mechanical structure with the assistance of a computer, in particular to an optimized parameter obtaining method of a multi-ring sleeved tungsten alloy flywheel.
Background
The flywheel is a typical mechanical energy storage device, stores kinetic energy during high-speed rotation, releases the energy for use during low-speed rotation, achieves the purpose of energy storage and conversion, and is widely applied to the fields of automobiles, aerospace, power systems, nuclear power and the like. One of the important performance indexes of the energy storage flywheel is the energy storage density, namely, the kinetic energy which can be stored in unit mass, and the improvement of the energy storage density can improve the material utilization rate, reduce the self weight of the flywheel system and reduce the bearing burden. When the flywheel material and the working rotation speed are limited, the structural form determines the energy storage density. The traditional flywheel is composed of a solid disc, but because the energy storage density is low, the flywheel system is always overweight in order to meet the requirement of rotational inertia, and therefore, how to improve the energy storage density becomes one of the key technical problems in the optimization design of the flywheel structure.
Generally, there are two common methods for increasing the energy storage density: the cross section shape of the rotor along the radius direction is optimally designed into a non-uniform thickness cross section, and the topological structure of the rotating plane is optimally designed, namely, a through hole structure is introduced into the rotating plane. However, the two methods have the disadvantages that the flywheel is large in size, and when the size design space is limited, such as the radius and axial size of the energy storage flywheel in the pressure bearing boundary of the shielded nuclear main pump and the material selection are all strictly limited, the design of the flywheel with large rotational inertia and high energy storage density faces great difficulty. In recent years, a multi-ring nested tungsten alloy flywheel has been proposed (as shown in fig. 1, in which 1 in fig. 1 is a rotating shaft) which is composed of three layers of an inner hub (2), a tungsten alloy intermediate layer (3) and an outer retaining ring (4) along the radius direction. The tungsten alloy layer is evenly divided into 12 blocks and evenly distributed along the circumferential direction, and the tungsten alloy layer and the outer retaining ring are in interference fit to provide assembling prestress to ensure tight fit among the layers. Because the high-density characteristics of the tungsten alloy and the advantages of the sandwich structure are fully utilized, the novel flywheel is compact in structure, small in size, high in energy storage density and large in rotational inertia, the advanced pressurized water reactor AP1000 nuclear main pump in the third-generation nuclear power technology is adopted, and the novel flywheel is widely applied to structural design of large energy storage flywheels in engineering.
At present, the structural size design of the tungsten alloy flywheel sleeved by multiple rings is a difficult problem.
The overweight of the flywheel is easily caused by the oversize of the middle tungsten alloy layer, and the centrifugal force is increased along with the overweight, so that higher assembling prestress is required to ensure the close fit between the layers; on the other hand, the tungsten alloy cannot be efficiently utilized due to the undersize of the tungsten alloy layer, and the requirements of large rotational inertia and high energy storage density are difficult to meet.
In addition, if the initial interference (hereinafter referred to as interference) between the tungsten alloy layer and the outer retaining ring is too small, sufficient assembling prestress cannot be ensured to ensure effective matching between the layers, and if the interference is too large, the stress of the outer retaining ring is too large, which brings about the problem of structural strength safety.
Obviously, complex coupling relationships exist between the sizes of the layers of the flywheel and the interference, and how to optimally distribute the sizes of the layers and design the reasonable interference becomes one of the key technical problems of the structural design of the flywheel.
The existing literature has few researches on the structural design of the novel flywheel, how to optimally design the radial dimension of each layer of the flywheel and select proper interference is always a difficult problem, a method of repeated trial calculation and check is adopted in engineering, the workload is large, the efficiency is low, and a safe and efficient rapid design method is still lacked at present to solve the problems of size distribution and interference optimization of the multi-ring sleeved heavy metal flywheel.
Disclosure of Invention
The invention aims to provide an optimal parameter obtaining method for a tungsten alloy flywheel sleeved with multiple rings. By the method, the design scheme of the optimal size and the interference of the multi-ring sleeved tungsten alloy flywheel can be quickly obtained under the condition of meeting the structural strength safety requirement and the interlayer matching pressure, the maximum energy storage density or the rotary inertia can be obtained, and the design efficiency can be greatly improved. The method has important guiding significance for the structure optimization design of the multi-ring sleeved heavy metal flywheel in engineering.
The invention is realized by the following technical scheme:
the method for obtaining the optimized parameters of the tungsten alloy flywheel sleeved with multiple rings comprises a main shaft, an inner hub, a tungsten alloy intermediate layer and an outer retaining ring which are sequentially sleeved from inside to outside, wherein interference magnitude is arranged between the tungsten alloy intermediate layer and the outer retaining ring for assembly,
the optimization parameter obtaining method is used for obtaining an interference magnitude optimization value between the tungsten alloy intermediate layer and the outer retaining ring when an allowable stress value is taken as an optimization target, and size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when energy storage density and rotational inertia are taken as optimization targets;
the optimization parameter obtaining method comprises the following steps:
s1, establishing a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s2, establishing an analysis file of a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s3, building a DOE test design model by using ISIGHT optimization design software to obtain a test design matrix;
s4, calling ABAQUS software to analyze and calculate each data point in a test design matrix by a bat file to generate DOE sample data;
s5, based on DOE sample data, a neural network proxy model is built by adopting RBF radial basis functions, a mathematical model between factors and responses is obtained, an interference magnitude optimization value between the tungsten alloy intermediate layer and the outer retaining ring when an allowable stress value is taken as an optimization target is obtained under a constraint condition by mining internal relations of data, and size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when energy storage density and rotational inertia are taken as optimization targets are obtained.
The parameterized finite element model is a 1/N basic structure finite element model, and the 1/N basic structure finite element model is 1 finite element model corresponding to a basic structure obtained by cutting out 1/N part of the tungsten alloy flywheel sleeved by the multi-ring; the 1/N basic unit structure finite element model comprises 2 adjacent tungsten alloy intermediate layers; the value of N is equal to the number of tungsten alloy intermediate layers in the multi-ring sleeved tungsten alloy flywheel;
the parameterized finite element model is a two-dimensional plane stress model.
The specific process of creating the parameterized finite element model comprises the following steps:
s11, under a graphic interface CAE of ABAQUS software, creating components required by a parameterized finite element model and corresponding to a main shaft, an inner hub, a tungsten alloy middle layer and an outer retaining ring; sleeving and assembling all the parts to form an assembly body corresponding to the tungsten alloy flywheel sleeved by multiple rings, and dividing each part into grids;
s12, setting parameters:
defining material properties and cross-sectional properties of each component;
create contacts for the parts and define contact attributes: establishing adjacent contact between the adjacent tungsten alloy intermediate layers, and establishing interference fit contact between the tungsten alloy intermediate layers and the outer retaining ring;
defining boundary conditions and applied loads;
defining an analysis step: selecting a general static analysis step;
open nonlinear analysis options: a corresponding incremental step is set.
The specific process of creating the analysis file of the parameterized finite element model comprises the following steps:
s21, establishing an analysis task aiming at the parameterized finite element model, and submitting the analysis task to ABAQUS kernel calculation;
s22, find the suffix under the ABAQUS working catalog: rpy, suffixing with: rpy, recording all operation commands under the graphical interface;
s23, modified suffix: the command stream of rpy parsing the contents of the file:
the suffix is: rpy, the projected dimensions in the radial direction of the spindle, inner hub, intermediate layer of tungsten alloy and outer retaining ring are defined as t0, t1, t2 and t3, respectively; the suffix is: rpy, the amount of interference between the tungsten alloy intermediate layer and the outer retaining ring in the command stream analysis file is defined as δ; the inner radius size and the outer radius size of the multi-ring sleeved tungsten alloy flywheel are respectively given as r1 and r4 and are set fixed values, and t1, t2, t3 and delta are given as variables; the inner radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the inner ring surface of the inner hub, and the outer radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the outer ring surface of the outer retaining ring;
in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum pressure value of the contact surface between the inner hub and the tungsten alloy intermediate layer is Pmax; in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum stress value of the outer retaining ring is σ max;
s24, saving the file;
and S25, changing the suffix rpy of the command stream analysis file into a py suffix to complete the creation of the analysis file of the parameterized finite element model.
The specific process of building the DOE test design model by using the ISIGHT optimization design software is as follows:
in the ISIGHT optimization design software, an analysis file of a parameterized finite element model of a tungsten alloy flywheel sleeved with multiple rings is used as an input file, and the projection size of the tungsten alloy middle layer in the radial direction and the projection size of the outer retaining ring in the radial direction in the analysis file of the parameterized finite element model and the interference between a tungsten alloy layer and the outer retaining ring are defined as factors; defining the weight of the flywheel, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer in the finite element analysis result file as responses by taking the finite element analysis result file as an output file; and generating a test design matrix by adopting an optimal Latin hypercube method.
And when the factors are set, setting the upper and lower limits of the factors according to the preset values and setting the horizontal number of the factors to be 21.
The specific process of generating the DOE sample data comprises the following steps:
using ABAQUS software to analyze and calculate the analysis file of the initial parameterized finite element model, recording the response value in the finite element analysis result file,
then, judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software: if not, automatically modifying the factors in the analysis file of the parameterized finite element model for re-assignment, submitting the modified analysis file of the parameterized finite element model to ABAQUS for continuous analysis and calculation, recording the response values in the finite element analysis result file, and judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software again; if not, the loop is repeated, and if complete, the loop is terminated and exited.
The mathematical model between the factors and the responses includes:
and a mathematical model is formed among the projection size of the tungsten alloy intermediate layer in the radius direction, the projection size and the interference magnitude of the outer retaining ring in the radius direction, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer.
The process of obtaining the interference magnitude optimized value between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as the optimized target is as follows:
and (3) constructing according to a mathematical model:
a relation graph A between the maximum stress of the outer retaining ring and the projection size and the interference of the outer retaining ring in the radius direction;
a relation graph B between the maximum stress of the outer retaining ring and the projection size and the interference of the tungsten alloy layer in the radius direction;
obtaining an upper limit value A1 and a lower limit value A2 of the interference according to the relation graph A, and obtaining another upper limit value A3 and another lower limit value A4 of the interference according to the relation graph B;
selecting the minimum value from the upper limit value A1 and the upper limit value A3 as an upper limit optimized value for the interference between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as an optimization target;
selecting the maximum value from the lower limit value A2 and the lower limit value A4 as a lower limit optimized value of the interference magnitude between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as an optimization target;
the process of obtaining the size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when the energy storage density and the rotational inertia are taken as optimization targets comprises the following steps:
and (3) constructing according to a mathematical model:
a relation graph C between the energy storage density increasing rate of the flywheel and the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction;
a relation graph D between the flywheel rotation inertia lifting rate around the shaft center and the projection size of the tungsten alloy in the middle radius direction and the projection size of the outer retaining ring in the radius direction;
taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as the corresponding values when the energy storage density lifting rate of the flywheel reaches the maximum from the relation chart C, and regarding the values as the size optimization values of the inner hub, the tungsten alloy middle layer and the outer retaining ring when the energy storage density is taken as the optimization target;
and taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as the corresponding values when the flywheel reaches the maximum moment of inertia lifting rate around the shaft center from the relation graph D, and regarding the values as the size optimization values of the inner hub, the tungsten alloy middle layer and the outer retaining ring when the energy storage density is taken as the optimization target.
The projected dimension in the radial direction is understood as the difference between the inner and outer diameters of the ring.
The invention provides a method for optimally designing a multi-ring sleeved tungsten alloy flywheel structure, which is realized by mutually matching a plurality of pieces of software and adopts basic data such as ISIGHT and ABAQUS for constructing finite elements and the like and constraint conditions to form basic coupling data. And finally, obtaining simulation data in the neural network agent model, and finally performing statistical analysis on the obtained simulation data to find the optimal data parameters.
That is to say: the invention provides a method for optimally designing a multi-ring sleeved tungsten alloy flywheel structure, aiming at an energy storage flywheel which is formed by taking stainless steel as an inner layer and an outer layer and taking high-density tungsten alloy as an intermediate layer along the radius direction and has a multi-ring sleeved structural formula, under the constraint condition of meeting the requirements of structural strength safety and interlayer matching pressure,
the optimal design of size distribution and interference of each layer is quickly obtained,
the maximum energy storage density (unit mass energy storage) or the rotary inertia is realized, and the design efficiency is greatly improved.
The method can be summarized as the following steps:
establishing a parameterized finite element model of the flywheel, defining the radial dimension of each layer of the flywheel and the interference magnitude between the tungsten alloy layer and the outer retaining ring as design variables, and adding a command line to output performance parameters such as the weight, the rotational inertia, the structural stress, the contact pressure and the like of the flywheel;
building a test design model, defining design parameters as factors and performance parameters as responses, and selecting a proper sampling method to generate a test design matrix;
executing a test plan by calling a finite element program, and calculating sample points;
based on experimental design data, by constructing a proxy model mathematical method, mining the relation between factors and responses, and combining constraint conditions and variable design space, the optimal design scheme of size design and interference is obtained with the goal of maximizing energy storage density or rotational inertia.
Specifically, the method comprises the following steps:
firstly, establishing a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel based on an ABAQUS script language parameterized modeling function. Based on the plane stress hypothesis and the rotational symmetry periodic structure characteristics, intercepting the 1/12 structure of the multi-ring sleeved tungsten alloy flywheel to establish a finite element model, and simplifying the finite element model into a plane stress model; the radial dimension of each layer of the flywheel, the interference magnitude between the tungsten alloy layer and the outer retaining ring are defined as design variables, and the weight, the rotational inertia, the maximum structural stress, the contact pressure and the like of the flywheel are target performance parameters.
And secondly, building a DOE (design of experiment) test design model based on an ISIGHT multidisciplinary optimization design software platform. The method comprises the steps that a multi-ring sleeved tungsten alloy flywheel parameterized finite element model analysis file is used as an input file, and the radial sizes of a tungsten alloy layer and an outer retaining ring in the file and the interference magnitude between the tungsten alloy layer and the outer retaining ring are defined as factors; taking a finite element analysis result file as an output file, and defining the mass, the rotational inertia, the energy storage density, the structural maximum stress and the interlayer contact pressure of the flywheel in the file as responses; and generating a test design matrix by adopting an optimal Latin hypercube method.
And thirdly, executing a test plan, calculating each data point in the matrix and obtaining test design sample data. And (3) calling commercial software ABAQUS analysis to calculate sample points by writing a bat file, namely performing calculation analysis on each data point in a design matrix to generate DOE sample data.
And fourthly, mining and analyzing the test design sample data based on a neural network agent model method to obtain the final design. Based on test design sample data, an agent model is constructed by adopting RBF (radial Basis functions) radial Basis functions, a mathematical model between factors (radial size of a tungsten alloy layer, radial size of an outer retaining ring and interference magnitude) and responses (maximum structural stress, interlayer contact pressure, rotational inertia and energy storage density) is obtained, and an optimal design scheme is finally obtained by mining an internal relation of data and fully considering structural strength safety and interlayer matching pressure constraint conditions.
According to the invention, the optimal design scheme of the optimal size and the interference of the multi-ring sleeved tungsten alloy flywheel can be quickly obtained under the condition of meeting the safety requirement of the structural strength of the flywheel and the interlayer matching pressure, and the maximum energy storage density or the maximum rotational inertia can be obtained. The method can provide important guidance for the structural size design of the multi-ring sleeved heavy metal flywheel in engineering.
The invention has the beneficial effects that:
compared with the conventional method of repeated trial calculation and check in engineering, the method provided by the invention can quickly and directly obtain the optimal design scheme of the radial dimension and the interference of each layer of the multi-ring sleeved heavy metal flywheel, can greatly improve the design efficiency, and has strong universality and easy mastering and implementation.
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 side sectional view of an overall structure of a tungsten alloy flywheel sleeved with multiple rings.
FIG. 2 is a schematic top view of the overall structure of a tungsten alloy flywheel with multiple rings nested therein.
FIG. 3 is a schematic diagram of the basic structure of a tungsten alloy flywheel sleeved with multiple rings.
FIG. 4 is a flow chart of an optimized design of a multi-ring nested tungsten alloy flywheel.
FIG. 5 is a graph of maximum stress of the structure versus radial dimension and interference of the outer retaining ring: (a) a 3D relationship diagram, and (b) a 2D relationship diagram.
FIG. 6 is a graph of the relationship between the maximum stress of the structure and the radial dimension and the interference of the tungsten alloy layer: (a) a 3D relationship diagram, and (b) a 2D relationship diagram.
FIG. 7 is a graph of energy storage density versus radial dimension of a tungsten alloy layer, outer retaining ring: (a) a 3D relationship diagram, and (b) a 2D relationship diagram.
FIG. 8 is a graph of the moment of inertia versus the radial dimensions of the tungsten alloy layer and the outer retaining ring: (a) a 3D relationship diagram, and (b) a 2D relationship diagram.
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. 1-8:
the method for obtaining the optimized parameters of the tungsten alloy flywheel sleeved with multiple rings comprises a main shaft, an inner hub, a tungsten alloy intermediate layer and an outer retaining ring which are sequentially sleeved from inside to outside, wherein interference magnitude is arranged between the tungsten alloy intermediate layer and the outer retaining ring for assembly,
the optimization parameter obtaining method is used for obtaining an interference magnitude optimization value between the tungsten alloy intermediate layer and the outer retaining ring when an allowable stress value is taken as an optimization target, and size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when energy storage density and rotational inertia are taken as optimization targets;
the optimization parameter obtaining method comprises the following steps:
s1, establishing a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s2, establishing an analysis file of a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s3, building a DOE test design model by using ISIGHT optimization design software to obtain a test design matrix;
s4, calling ABAQUS software to analyze and calculate each data point in a test design matrix by a bat file to generate DOE sample data;
s5, based on DOE sample data, a neural network proxy model is built by adopting RBF radial basis functions, a mathematical model between factors and responses is obtained, an interference magnitude optimization value between the tungsten alloy intermediate layer and the outer retaining ring when an allowable stress value is taken as an optimization target is obtained under a constraint condition by mining internal relations of data, and size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when energy storage density and rotational inertia are taken as optimization targets are obtained.
Example 2
As shown in fig. 1-8:
on the basis of the above-described embodiments,
the parameterized finite element model is a 1/N basic structure finite element model, and the 1/N basic structure finite element model is 1 finite element model corresponding to a basic structure obtained by cutting out 1/N part of the tungsten alloy flywheel sleeved by the multi-ring; the 1/N basic unit structure finite element model comprises 2 adjacent tungsten alloy intermediate layers; the value of N is equal to the number of tungsten alloy intermediate layers in the multi-ring sleeved tungsten alloy flywheel;
the parameterized finite element model is a two-dimensional plane stress model.
The specific process of creating the parameterized finite element model comprises the following steps:
s11, under a graphic interface CAE of ABAQUS software, creating components required by a parameterized finite element model and corresponding to a main shaft, an inner hub, a tungsten alloy middle layer and an outer retaining ring; sleeving and assembling all the parts to form an assembly body corresponding to the tungsten alloy flywheel sleeved by multiple rings, and dividing each part into grids;
s12, setting parameters:
defining material properties and cross-sectional properties of each component;
create contacts for the parts and define contact attributes: establishing adjacent contact between the adjacent tungsten alloy intermediate layers, and establishing interference fit contact between the tungsten alloy intermediate layers and the outer retaining ring;
defining boundary conditions and applied loads;
defining an analysis step: selecting a general static analysis step;
open nonlinear analysis options: a corresponding incremental step is set.
The specific process of creating the analysis file of the parameterized finite element model comprises the following steps:
s21, establishing an analysis task aiming at the parameterized finite element model, and submitting the analysis task to ABAQUS kernel calculation;
s22, find the suffix under the ABAQUS working catalog: rpy, suffixing with: rpy, recording all operation commands under the graphical interface;
s23, modified suffix: the command stream of rpy parsing the contents of the file:
the suffix is: rpy, the projected dimensions in the radial direction of the spindle, inner hub, intermediate layer of tungsten alloy and outer retaining ring are defined as t0, t1, t2 and t3, respectively; the suffix is: rpy, the amount of interference between the tungsten alloy intermediate layer and the outer retaining ring in the command stream analysis file is defined as δ; the inner radius size and the outer radius size of the multi-ring sleeved tungsten alloy flywheel are respectively given as r1 and r4 and are set fixed values, and t1, t2, t3 and delta are given as variables; the inner radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the inner ring surface of the inner hub, and the outer radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the outer ring surface of the outer retaining ring;
in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum pressure value of the contact surface between the inner hub and the tungsten alloy intermediate layer is Pmax; in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum stress value of the outer retaining ring is σ max;
s24, saving the file;
and S25, changing the suffix rpy of the command stream analysis file into a py suffix to complete the creation of the analysis file of the parameterized finite element model.
The specific process of building the DOE test design model by using the ISIGHT optimization design software is as follows:
in the ISIGHT optimization design software, an analysis file of a parameterized finite element model of a tungsten alloy flywheel sleeved with multiple rings is used as an input file, and the projection size of the tungsten alloy middle layer in the radial direction and the projection size of the outer retaining ring in the radial direction in the analysis file of the parameterized finite element model and the interference between a tungsten alloy layer and the outer retaining ring are defined as factors; defining the weight of the flywheel, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer in the finite element analysis result file as responses by taking the finite element analysis result file as an output file; and generating a test design matrix by adopting an optimal Latin hypercube method.
And when the factors are set, setting the upper and lower limits of the factors according to the preset values and setting the horizontal number of the factors to be 21.
The specific process of generating the DOE sample data comprises the following steps:
using ABAQUS software to analyze and calculate the analysis file of the initial parameterized finite element model, recording the response value in the finite element analysis result file,
then, judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software: if not, automatically modifying the factors in the analysis file of the parameterized finite element model for re-assignment, submitting the modified analysis file of the parameterized finite element model to ABAQUS for continuous analysis and calculation, recording the response values in the finite element analysis result file, and judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software again; if not, the loop is repeated, and if complete, the loop is terminated and exited.
The mathematical model between the factors and the responses includes:
and a mathematical model is formed among the projection size of the tungsten alloy intermediate layer in the radius direction, the projection size and the interference magnitude of the outer retaining ring in the radius direction, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer.
The process of obtaining the interference magnitude optimized value between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as the optimized target is as follows:
and (3) constructing according to a mathematical model:
a relation graph A between the maximum stress of the outer retaining ring and the projection size and the interference of the outer retaining ring in the radius direction;
a relation graph B between the maximum stress of the outer retaining ring and the projection size and the interference of the tungsten alloy layer in the radius direction;
obtaining an upper limit value A1 and a lower limit value A2 of the interference according to the relation graph A, and obtaining another upper limit value A3 and another lower limit value A4 of the interference according to the relation graph B;
selecting the minimum value from the upper limit value A1 and the upper limit value A3 as an upper limit optimized value for the interference between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as an optimization target;
selecting the maximum value from the lower limit value A2 and the lower limit value A4 as a lower limit optimized value of the interference magnitude between the tungsten alloy intermediate layer and the outer retaining ring when the allowable stress value is taken as an optimization target;
the process of obtaining the size optimization values of the inner hub, the tungsten alloy intermediate layer and the outer retaining ring when the energy storage density and the rotational inertia are taken as optimization targets comprises the following steps:
and (3) constructing according to a mathematical model:
a relation graph C between the energy storage density increasing rate of the flywheel and the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction;
a relation graph D between the flywheel rotation inertia lifting rate around the shaft center and the projection size of the tungsten alloy in the middle radius direction and the projection size of the outer retaining ring in the radius direction;
taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as the corresponding values of the inner hub 2, the tungsten alloy middle layer 3 and the outer retaining ring 4 with the energy storage density as the optimization target when the energy storage density lifting rate of the flywheel reaches the maximum from the relation graph C;
and taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as the corresponding values when the flywheel reaches the maximum moment of inertia lifting rate around the shaft center from the relation graph D, and regarding the values as the size optimization values of the inner hub 2, the tungsten alloy middle layer 3 and the outer retaining ring 4 when the energy storage density is taken as the optimization target.
Example 3
As shown in fig. 1-8:
the following description will be made of a concrete embodiment of the present invention by taking a pressurized water reactor AP1000 nuclear main pump multi-ring sleeved tungsten alloy flywheel as an example (as shown in fig. 1 and 2) and combining the technical scheme and the accompanying drawings. The radial dimension described below is a projected dimension in the radial direction, and may be regarded as a difference between the inner diameter and the outer diameter of the ring.
Firstly, establishing a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel based on an ABAQUS script language parameterized modeling function.
First, the flywheel model is simplified:
the load borne by the multi-ring sleeved tungsten alloy flywheel mainly comprises four parts: the gravity load has small influence on the structural stress relative to other loads and can be ignored, and in addition, the size of the flywheel along the axial direction is small relative to the size of the flywheel along the radius direction, so that the flywheel can be simplified into a two-dimensional plane stress model by introducing the plane stress assumption.
On the other hand, the 12 fan-shaped tungsten alloy blocks are uniformly distributed on the periphery of the inner hub along the circumferential direction, so that the multi-ring sleeved tungsten alloy flywheel is of a typical rotational symmetry periodic structure. In summary, considering that the structural shape, boundary conditions and loads meet the requirements of the rotationally symmetric periodic structure, the flywheel base structure (1/12) can be truncated for finite element modeling (as shown in FIG. 3).
Then, flywheel finite element modeling is performed under the ABAQUS graphical interface CAE. The method comprises the steps of creating a Part (Part), defining a material Property (Property) and a Section Property (Section), and endowing the Part with the Section Property; assembling each component in an Assembly module (Assembly) to form an Assembly body, and dividing each component into grids; establishing a contact pair and defining contact attributes, setting adjacent tungsten alloy blocks to be in contact, and defining boundary conditions and applied loads, wherein the tungsten alloy layers and the outer retaining ring are in interference fit; defining analysis steps (Step), wherein the flywheels are all subjected to Static loads, selecting General Static analysis steps (Static, General), opening a nonlinear analysis (NLgel) option, and setting corresponding increment steps (increment).
And finally, creating an analysis task and submitting ABAQUS kernel calculation to find a rpy file under an ABAQUS working directory, wherein all operation commands under a graphical interface are recorded, and the file is a command stream analysis file. Opening this document, the radial dimensions of the spindle, the inner hub, the tungsten alloy layer and the outer retaining ring are parameterized (as shown in fig. 1, 2 and 3) and defined as the variables r1, t1, t2 and t3, respectively, and the interference between the tungsten alloy layer and the outer retaining ring is defined as δ. In this case the flywheel inside and outside radii, r1 and r4, are constant values, thus setting the independent design parameters t2, t3 and δ. And because the minimum contact pressure between the flywheel layers always appears between the inner hub and the tungsten alloy layer, adding a post-processing command to output the maximum pressure value Pmax of the contact surface. The maximum flywheel structural stress σ max is always located in the outer retaining ring, and the structural maximum stress σ max of the outer retaining ring is output by adding the post-processing command. And saving the file, changing the suffix name into a py format, and completing the creation of the parameterized model analysis file.
And secondly, building a DOE test design model based on an ISIGHT multidisciplinary optimization design software platform.
Firstly, defining a parameterized model analysis file as an input file, defining a finite element analysis result file as an output file, compiling a batch file, and adding and calling an ABAQUS calculation analysis command;
then, integrating the input analysis files, the batch processing files and the output result files, building a test design model and making a test plan: design variables such as the radial dimension t2 of the tungsten alloy layer, the radial dimension t3 of the outer retaining ring, and the interference delta between the tungsten alloy layer and the outer retaining ring are defined as factors, and target performance parameters such as the overall weight of the flywheel, the moment of inertia I, the maximum contact pressure Pmax between the inner hub and the tungsten alloy layer, and the structural maximum stress sigma max of the outer retaining ring are defined as responses (as shown in Table 1). The upper and lower limits of the factor are set and the number of levels of the factor given is 21,
and then, selecting an optimal Latin hypercube method with a better space filling effect to uniformly distribute the design points in the design space, generating a test design matrix based on different level combinations of factors, and completing the construction of a test design model.
Table 1 multi-ring nested tungsten alloy flywheel test design model:
and thirdly, executing a test plan, calculating each data point in the matrix and obtaining test design sample data.
The adopted method is to call commercial software ABAQUS to analyze and calculate sample points, namely, each data point in the design matrix is calculated and analyzed to generate DOE sample data. As shown in fig. 3, first, ABAQUS performs an analysis calculation on an initial input file, records response values in a finite element analysis result file,
then, judging whether all the sample points are calculated by ISIGHT: if not, automatically modifying the variable parameters in the input file, namely re-assigning the factors, submitting the modified file to ABAQUS for continuous analysis and calculation, recording the response value in the result file, and judging whether all the sample points are completely calculated by ISIGHT again; if not (N), the loop is repeated, and if (Y) is complete, the loop is terminated and exited. And finally obtaining DOE sample data.
And fourthly, mining and analyzing the test design sample data based on a neural network agent model method to obtain the final design.
As shown in fig. 3, based on the test design sample data, a proxy model is constructed by using the RBF radial basis function, and a mathematical model between the radial size of the tungsten alloy layer, the radial size and the interference of the outer retaining ring, the maximum stress of the outer retaining ring, the maximum pressure between the inner hub and the tungsten alloy layer, the rotational inertia and the energy storage density is established. A graph of the maximum stress of the outer retaining ring in relation to the radial dimension of the outer retaining ring and the interference is shown in fig. 5, and an upper limit value of the interference of 1.35mm can be obtained from the graph, namely the interference is ensured to be lower than the value, and the maximum stress of the outer retaining ring does not exceed the allowable stress value of 576.0 MPa. In the same way, fig. 6 constructs a graph of the maximum stress of the outer retaining ring and the radial dimension and the interference of the tungsten alloy layer, and another upper limit value of the interference is 1.25 mm. The two upper limit values are combined, namely the upper limit value of the interference is 1.25mm, namely, the upper limit requirement of the interference is met in a given design space, and the structural stress of the flywheel can be ensured not to exceed the allowable stress value. Similarly, aiming at the requirement of the maximum matching pressure between the inner hub and the tungsten alloy layer, two lower limit values of the interference magnitude are searched by the same analysis method, wherein the two lower limit values are 1.15mm and 0.65mm respectively, and the obtained lower limit value of the interference magnitude is 1.15mm, which is not described herein again. In conclusion, the complete design range of the interference magnitude can be determined, namely 1.15-1.25 mm, and the design requirements of the structural strength safety of the flywheel and the matching pressure between flywheel layers can be met.
Then, a proxy model is constructed by using the RBF radial basis function, and a relation graph (shown in FIG. 7) between the energy storage density improvement rate (Re) and the radial dimension of the tungsten alloy layer and the radial dimension of the outer retaining ring is established. As can be seen from fig. 6, when the inner hub, the tungsten alloy layer and the outer retaining ring have the dimensions of 215mm, 100mm and 35mm, the energy storage density increase rate is maximized, and compared with the flywheel made of the same-size all-steel material, the optimal size design can increase the energy storage density by 11.6%. Similarly, fig. 8 is a graph of the relationship between the moment of inertia lifting Rate (RI) and the radial dimensions of the tungsten alloy layer and the outer retaining ring, where RI is relative to an all-steel solid disc flywheel of the same dimensions. It can be seen that the optimum dimensions of the inner hub, tungsten alloy layer and outer retaining ring are 120mm, 195mm and 35mm, with a maximum rise in rotational inertia of up to 80.8%.
The invention can guide the structural size optimization design of the multi-ring sleeved structural energy storage flywheel in practical engineering, can effectively improve the utilization rate of flywheel materials, and achieves the effects of reducing the dead weight, lightening the bearing load and the like. Compared with the conventional method of trial calculation and check frequently used in engineering, the method provided by the invention can quickly and directly obtain the optimal design scheme of the radial dimension and the interference magnitude of each layer of the multi-ring sleeved heavy metal flywheel, greatly improves the design efficiency, and has strong universality and easy mastering and implementation.
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. The method for obtaining the optimized parameters of the tungsten alloy flywheel sleeved with multiple rings comprises a main shaft (1), an inner hub (2), a tungsten alloy intermediate layer (3) and an outer retaining ring (4) which are sequentially sleeved from inside to outside, wherein interference is arranged between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) for assembly,
it is characterized in that the preparation method is characterized in that,
the optimization parameter obtaining method is used for obtaining an interference magnitude optimization value between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when a permissible stress value is taken as an optimization target, and size optimization values of the inner hub (2), the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when energy storage density and rotational inertia are taken as optimization targets;
the optimization parameter obtaining method comprises the following steps:
s1, establishing a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s2, establishing an analysis file of a parameterized finite element model of the multi-ring sleeved tungsten alloy flywheel by using ABAQUS software;
s3, building a DOE test design model by using ISIGHT optimization design software to obtain a test design matrix;
s4, calling ABAQUS software to analyze and calculate each data point in a test design matrix by a bat file to generate DOE sample data;
s5, based on DOE sample data, a neural network proxy model is built by adopting RBF radial basis functions, a mathematical model between factors and responses is obtained, an interference optimization value between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when allowable stress values are taken as optimization targets is obtained by mining internal relations of data under constraint conditions, and size optimization values of the inner hub (2), the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when energy storage density and rotational inertia are taken as optimization targets are obtained.
2. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 1,
the parameterized finite element model is a 1/N basic structure finite element model, and the 1/N basic structure finite element model is 1 finite element model corresponding to a basic structure obtained by cutting out 1/N part of the tungsten alloy flywheel sleeved by the multi-ring; the 1/N basic unit structure finite element model comprises 2 adjacent tungsten alloy intermediate layers (3); the value of N is equal to the number of tungsten alloy intermediate layers (3) in the multi-ring sleeved tungsten alloy flywheel;
the parameterized finite element model is a two-dimensional plane stress model.
3. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 1,
the specific process of creating the parameterized finite element model comprises the following steps:
s11, under a graphic interface CAE of ABAQUS software, creating components required by a parameterized finite element model and corresponding to the main shaft (1), the inner hub (2), the tungsten alloy intermediate layer (3) and the outer retaining ring (4); sleeving and assembling all the parts to form an assembly body corresponding to the tungsten alloy flywheel sleeved by multiple rings, and dividing each part into grids;
s12, setting parameters:
defining material properties and cross-sectional properties of each component;
create contacts for the parts and define contact attributes: establishing adjacent contact between the adjacent tungsten alloy intermediate layers (3), and establishing interference fit contact between the tungsten alloy intermediate layers (3) and the outer retaining ring (4);
defining boundary conditions and applied loads;
defining an analysis step: selecting a general static analysis step;
open nonlinear analysis options: a corresponding incremental step is set.
4. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 1,
the specific process of creating the analysis file of the parameterized finite element model comprises the following steps:
s21, establishing an analysis task aiming at the parameterized finite element model, and submitting the analysis task to ABAQUS kernel calculation;
s22, find the suffix under the ABAQUS working catalog: rpy, suffixing with: rpy, recording all operation commands under the graphical interface;
s23, modified suffix: the command stream of rpy parsing the contents of the file:
the suffix is: rpy, the projected dimensions in the radial direction of the spindle, inner hub, intermediate layer of tungsten alloy and outer retaining ring are defined as t0, t1, t2 and t3, respectively; the suffix is: rpy, the amount of interference between the tungsten alloy intermediate layer and the outer retaining ring in the command stream analysis file is defined as δ; the inner radius size and the outer radius size of the multi-ring sleeved tungsten alloy flywheel are respectively given as r1 and r4 and are set fixed values, and t1, t2, t3 and delta are given as variables; the inner radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the inner ring surface of the inner hub, and the outer radius of the multi-ring sleeved tungsten alloy flywheel is equal to the radius of the outer ring surface of the outer retaining ring;
in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum pressure value of the contact surface between the inner hub and the tungsten alloy intermediate layer is Pmax; in the suffix: rpy adding a post-processing command output to the command stream analysis file: the maximum stress value of the outer retaining ring is σ max;
s24, saving the file;
and S25, changing the suffix rpy of the command stream analysis file into a py suffix to complete the creation of the analysis file of the parameterized finite element model.
5. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 1,
the specific process of building the DOE test design model by using the ISIGHT optimization design software is as follows:
in the ISIGHT optimization design software, an analysis file of a parameterized finite element model of a tungsten alloy flywheel sleeved with multiple rings is used as an input file, and the projection size of the tungsten alloy middle layer in the radial direction and the projection size of the outer retaining ring in the radial direction in the analysis file of the parameterized finite element model and the interference between a tungsten alloy layer and the outer retaining ring are defined as factors; defining the weight of the flywheel, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer in the finite element analysis result file as responses by taking the finite element analysis result file as an output file; and generating a test design matrix by adopting an optimal Latin hypercube method.
6. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 5,
and when the factors are set, setting the upper and lower limits of the factors according to the preset values and setting the horizontal number of the factors to be 21.
7. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 5,
the specific process of generating the DOE sample data comprises the following steps:
using ABAQUS software to analyze and calculate the analysis file of the initial parameterized finite element model, recording the response value in the finite element analysis result file,
then, judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software: if not, automatically modifying the factors in the analysis file of the parameterized finite element model for re-assignment, submitting the modified analysis file of the parameterized finite element model to ABAQUS for continuous analysis and calculation, recording the response values in the finite element analysis result file, and judging whether all the data points in the test design matrix are calculated by ISIGHT optimization design software again; if not, the loop is repeated, and if complete, the loop is terminated and exited.
8. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 7,
the mathematical model between the factors and the responses includes:
and a mathematical model is formed among the projection size of the tungsten alloy intermediate layer in the radius direction, the projection size and the interference magnitude of the outer retaining ring in the radius direction, the rotational inertia of the flywheel around the shaft center, the energy storage density of the flywheel, the maximum stress of the outer retaining ring and the maximum interlayer pressure of the inner hub and the tungsten alloy intermediate layer.
9. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 8,
the process of obtaining the interference magnitude optimized value between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when the allowable stress value is taken as an optimized target is as follows:
and (3) constructing according to a mathematical model:
a relation graph A between the maximum stress of the outer retaining ring and the projection size and the interference of the outer retaining ring in the radius direction;
a relation graph B between the maximum stress of the outer retaining ring and the projection size and the interference of the tungsten alloy layer in the radius direction;
obtaining an upper limit value A1 and a lower limit value A2 of the interference according to the relation graph A, and obtaining another upper limit value A3 and another lower limit value A4 of the interference according to the relation graph B;
selecting the minimum value from the upper limit value A1 and the upper limit value A3 as an upper limit optimized value for the interference between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when the allowable stress value is taken as an optimization target;
the selection of the largest value from the lower limit values A2 and A4 is regarded as the lower optimized value for the interference between the tungsten alloy intermediate layer (3) and the outer retaining ring (4) with the permissible stress values as the optimization target.
10. The method for obtaining optimized parameters of a multi-ring nested tungsten alloy flywheel of claim 8,
the process of obtaining the size optimization values of the inner hub (2), the tungsten alloy intermediate layer (3) and the outer retaining ring (4) when the energy storage density and the rotational inertia are used as optimization targets is as follows:
and (3) constructing according to a mathematical model:
a relation graph C between the energy storage density increasing rate of the flywheel and the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction;
a relation graph D between the flywheel rotation inertia lifting rate around the shaft center and the projection size of the tungsten alloy in the middle radius direction and the projection size of the outer retaining ring in the radius direction;
taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as the corresponding values when the energy storage density lifting rate of the flywheel reaches the maximum from the relation graph C, and regarding the values as the size optimization values of the inner hub (2), the tungsten alloy middle layer (3) and the outer retaining ring (4) when the energy storage density is taken as the optimization target;
and taking the projection size of the inner hub in the radius direction, the projection size of the tungsten alloy middle in the radius direction and the projection size of the outer retaining ring in the radius direction as corresponding values when the flywheel reaches the maximum moment of inertia lifting rate around the shaft center from the relation graph D, and regarding the values as size optimization values of the inner hub (2), the tungsten alloy middle layer (3) and the outer retaining ring (4) when the energy storage density is taken as an optimization target.
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