Multi-level optimization method and system for numerical control machine tool structure

Abstract

The invention relates to the technical field of numerical control machine tool structure optimization, and discloses a numerical control machine tool structure multi-level optimization method and system, and the method comprises the steps: building a to-be-optimized numerical control machine tool model; calculating a first weight value of each working condition of the to-be-optimized numerical control machine tool model based on statics analysis; performing first topological optimization on the to-be-optimized numerical control machine tool model according to the first weight value of each working condition to obtain a first numerical control machine tool model; calculating a second weight value of each working condition of the first numerical control machine tool model based on the kinetic analysis; performing second topological optimization on the first numerical control machine tool model according to the second weight value of each working condition to obtain a second numerical control machine tool model; performing design size optimization on the second numerical control machine tool model to obtain a plurality of groups of optimized design sizes; and redesigning the numerical control machine tool to be optimized to obtain an optimized numerical control machine tool. The optimized numerical control machine tool is good in stability and applicability and light in weight.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical control machine tool structure optimization, and in particular to a numerical control machine tool structure multi-level optimization method and system. Background Art

[0002] With the rapid development of the economic structure, the development of the CNC machine tool industry is moving towards high precision, high efficiency, high speed and intelligence. As one of the important indicators to measure the processing performance of machine tools, machine tool accuracy directly processes the accuracy and performance of parts, which has always been a hot and key direction of machine tool research. The strength and stiffness of large parts in the machine tool structure, such as columns and bed, have a great influence on the overall stability of the machine tool. Therefore, structural optimization of these large parts can greatly improve the stability of the whole machine and the stability of parts production and processing. In the prior art, the optimization of large parts of CNC machine tools mostly adopts one-time topology optimization, and generally only considers dynamic optimization or static optimization, and the optimization effect is limited; and the required performance ratio of CNC machine tools under different working conditions is different. The existing optimization methods rarely consider the impact of the required performance ratio of different working conditions on the optimization, and the final optimization effect is not comprehensive and applicable.

[0003] Therefore, there is an urgent need for a multi-level optimization method and system for CNC machine tool structures to solve the above problems. Summary of the invention

[0004] Based on the above, the purpose of the present invention is to provide a multi-level optimization method and system for CNC machine tool structure, which takes into account the weight of each working condition. After optimization, the CNC machine tool has better stability and applicability and lighter weight.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-level optimization method for a CNC machine tool structure, comprising:

[0007] Establishing a model of a CNC machine tool to be optimized according to the CNC machine tool to be optimized, wherein the CNC machine tool to be optimized has n working conditions;

[0008] Performing static analysis on the CNC machine tool model to be optimized under each working condition, and calculating a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis;

[0009] According to the first weight value of each working condition, the CNC machine tool model to be optimized is subjected to a first topological optimization with maximizing static stiffness and minimizing stress as optimization objectives and with the first volume as a constraint, to obtain a first CNC machine tool model;

[0010] Performing a dynamic analysis on the first CNC machine tool model under each working condition, and calculating a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis;

[0011] According to the second weight value of each working condition, performing a second topology optimization on the first CNC machine tool model with the first s-order natural frequency as the optimization target and the second volume as the constraint, to obtain a second CNC machine tool model;

[0012] Selecting the design dimension parameters to be optimized of the second CNC machine tool model, optimizing the design dimension of the second CNC machine tool model, and obtaining multiple groups of optimized design dimensions;

[0013] A set of the optimized design dimensions is selected according to the requirements, and the CNC machine tool to be optimized is redesigned to obtain the optimized CNC machine tool.

[0014] As a preferred solution of the multi-level optimization method for the structure of a CNC machine tool, static analysis is performed on the CNC machine tool model to be optimized under each working condition, and the first weight value of each working condition of the CNC machine tool model to be optimized is calculated based on the static analysis, including:

[0015] Performing static analysis on the CNC machine tool model to be optimized by finite element software to obtain the static stiffness value and maximum stress value of the CNC machine tool model to be optimized under each working condition;

[0016] Establishing a first single-layer evaluation index system consisting of n evaluated objects and m indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the m indicators include the static stiffness value and the maximum stress value of the CNC machine tool model to be optimized;

[0017] Calculating a first weight coefficient of each of the m indicators by an entropy weight method based on the first single-layer evaluation indicator system;

[0018] Calculate the second weight coefficient of each of the m indicators by a hierarchical method;

[0019] The first comprehensive indicator weight coefficient is calculated according to the first weight coefficient of each indicator and the second weight coefficient of each indicator, and then the first weight value of each working condition is calculated according to the first comprehensive indicator weight coefficient.

[0020] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, the first weight coefficient of each index is calculated by the entropy weight method based on the first single-layer evaluation index system, including:

[0021] The first original indicator data matrix X is established with the n evaluated objects and the m indicators. ij )n×m , and the values ​​in the first original indicator data matrix are dimensionless to obtain the second original indicator data matrix X′=(x′ ij ) n×m ;

[0022] The second original indicator data matrix X′=(x′ ij ) n×m Normalization processing obtains the third original indicator data matrix Y=(y ij ) n×m ;

[0023] The normalized information entropy E of the jth indicator is calculated according to the following formula: j :

[0024]

[0025] In the formula, p ij is the proportion of the index value of the i-th working condition under the j-th index to the index;

[0026] Through the information entropy E of each indicator j Calculate the first weight coefficient w of each indicator j1 :

[0027]

[0028] As a preferred solution of the multi-level optimization method for CNC machine tool structure, the second weight coefficient of each index calculated by the hierarchical method includes:

[0029] Compare the importance of the m indicators and establish a decision matrix based on them Indicates index j a For indicator j b The relative importance of, a = 1, 2, 3,,, m, b = 1, 2, 3,,,, m;

[0030] Calculate the eigenvector corresponding to the maximum eigenvalue of the decision matrix to obtain the second weight coefficient w of each indicator. j2 .

[0031] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, a first comprehensive index weight coefficient is calculated according to the first weight coefficient of each index and the second weight coefficient of each index, and then the evaluation value of the first comprehensive index weight coefficient for each working condition is calculated according to the first comprehensive index weight coefficient. The evaluation value includes:

[0032] Calculate the evaluation value s of the first index weight coefficient and the second index weight coefficient for n working conditions 1 、s 2 :

[0033]

[0034] Construct a linear programming model:

[0035]

[0036] Among them, α j - Weight coefficient of the first comprehensive indicator;

[0037] The first weight value of each working condition is obtained according to the following formula:

[0038]

[0039] Among them, l i is the first weight value of the i-th working condition.

[0040] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, a dynamic analysis is performed on the first CNC machine tool model under each working condition, and a second weight value of each working condition of the first CNC machine tool model is calculated based on the dynamic analysis, including:

[0041] Performing dynamic analysis on the first CNC machine tool model by using finite element software to obtain the first s-order natural frequencies of the first CNC machine tool model under each working condition;

[0042] Establishing a second single-layer evaluation index system consisting of n evaluated objects and s indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the s indicators include each natural frequency of the first s orders of the first CNC machine tool model;

[0043] Calculating a third weight coefficient of each of the s indicators by an entropy weight method based on the second single-layer evaluation indicator system;

[0044] Calculate the fourth weight coefficient of each of the s indicators by a hierarchical method;

[0045] The second comprehensive indicator weight coefficient is calculated according to the third weight coefficient of each indicator and the fourth weight coefficient of each indicator, and then the second weight value of each working condition is calculated according to the second comprehensive indicator weight coefficient.

[0046] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, the design dimension parameters to be optimized of the second CNC machine tool model are selected, and the design dimension of the second CNC machine tool model is optimized to obtain multiple sets of optimized design dimensions including:

[0047] Constructing an approximate model, wherein the approximate model reflects the relationship between design variables and objective function values, wherein the design variables include design size parameters to be optimized and uncertainty factor parameters, wherein the uncertainty factor parameters include density, elastic modulus, and Poisson's ratio of the second CNC machine tool model, and the objective function value includes one or more of deformation, stress, volume, and several-order natural frequencies of the second CNC machine tool model after optimization;

[0048] A double-layer nested algorithm is used to optimize the approximate model to obtain a Pareto optimal solution set, wherein the Pareto optimal solution set includes multiple groups of optimized design dimensions and objective function values ​​corresponding to each group of optimized design dimensions.

[0049] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, the double-layer nested algorithm includes an outer non-dominated sorting genetic algorithm and an inner generation-interval mapping genetic algorithm. The double-layer nested algorithm is used to optimize the approximate model, including:

[0050] An outer non-dominated sorting genetic algorithm is used to optimize the approximate model in a design dimension space formed by a first design range of the design dimension parameters to be optimized;

[0051] For each group of design dimensions with certain values, an inner-layer intergenerational mapping genetic algorithm is used to search for the optimum in the uncertain parameter space formed by the second design range of the uncertain factor parameters, and an upper limit value and a lower limit value of the objective function value response are obtained through the approximate model, and a midpoint value and a radius value of the objective function value response are obtained according to the upper limit value and the lower limit value, and a multi-objective evaluation function value is obtained according to the midpoint value and the radius value;

[0052] The multi-objective evaluation function value is fed back to the outer non-dominated sorting genetic algorithm, and the outer non-dominated sorting genetic algorithm continues to search for the best solution, and outputs the Pareto optimal solution set if the stopping criterion is met.

[0053] As a preferred solution of a multi-level optimization method for a CNC machine tool structure, constructing the approximate model includes:

[0054] Acquire multiple groups of sample points of the design variables within the design range by using an experimental design method;

[0055] The response value of the second CNC machine tool model corresponding to each of the sample points is calculated by finite element analysis software, wherein the response value is the objective function value corresponding to the second CNC machine tool model under the design variable, thereby obtaining a plurality of sets of data sets of design variable-objective function values;

[0056] Based on the Kriging model, a non-analytical function expression of the design variables and the objective function values ​​is constructed, and the Kriging model is trained using the data set of the design variables-objective function values ​​to obtain the approximate model reflecting the relationship between the design variables and the objective function values.

[0057] A multi-level optimization system for CNC machine tool structure, comprising:

[0058] A model building module is used to build a CNC machine tool model to be optimized;

[0059] A first analysis module, configured to perform a static analysis on the CNC machine tool model to be optimized under each working condition, and calculate a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis;

[0060] A first topology optimization module is used to perform a first topology optimization on the CNC machine tool model to be optimized according to the first weight value of each working condition, taking static stiffness maximization and stress minimization as objective functions and volume as a constraint, to obtain a first CNC machine tool model;

[0061] a second analysis module, configured to perform a dynamic analysis on the first CNC machine tool model under each working condition, and calculate a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis;

[0062] A second topology optimization module is used to perform a second topology optimization on the first CNC machine tool model according to the second weight value of each working condition, taking the first s-order natural frequency as the objective function and the volume as the constraint, to obtain a second CNC machine tool model;

[0063] The design dimension optimization module is used to optimize the design dimension parameters of the second CNC machine tool model to obtain multiple groups of optimized design dimensions.

[0064] The beneficial effects of the present invention are:

[0065] The present invention provides a multi-level optimization method for the structure of a numerically controlled machine tool. The method first performs a topology optimization based on statics and then performs a topology optimization based on dynamics. The static and dynamic performances of the second numerically controlled machine tool model obtained after optimization are both better. At the same time, the weights of various working conditions are considered during the two topology optimizations, so that the optimization results are more scientific and reliable, that is, the static and dynamic performances of the optimized second numerically controlled machine tool model under various working conditions are both better, and the applicability is better. After the two topology optimizations, the design dimensions are further optimized, so that the various design dimensions of the numerically controlled machine tool after optimization are more accurate, convenient for processing and manufacturing, and convenient for selecting a certain set of optimized design dimensions according to demand, which can provide a direct and effective reference for the production design of the numerically controlled machine tool.

[0066] The present invention also provides a multi-level optimization system for the structure of a CNC machine tool, which can realize multi-level structural optimization of the CNC machine tool, reduce the weight of the CNC machine tool, and improve the design efficiency and performance of the CNC machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the contents of the embodiments of the present invention and these drawings without paying any creative work.

[0068] Figure 1 is a flow chart of a multi-level optimization method for a CNC machine tool structure provided by an embodiment of the present invention;

[0069] Figure 2 is a schematic diagram of a bed structure to be optimized provided by an embodiment of the present invention;

[0070] Figure 3 is a schematic diagram of two topology optimizations provided by an embodiment of the present invention;

[0071] Figure 4 is a schematic diagram of the topological structure of the bed after the first topological optimization based on statics provided by an embodiment of the present invention;

[0072] Figure 5 It is a schematic diagram of the topological structure of the bed after the second topological optimization based on statics and dynamics provided by an embodiment of the present invention;

[0073] Figure 6 It is a schematic diagram of the bed structure after two topological optimizations and regular designs provided by an embodiment of the present invention;

[0074] Figure 7 It is a side view of a bed after two topological optimizations and regular designs provided by an embodiment of the present invention;

[0075] Figure 8 yes Figure 7 Cross-section from the perspective of the middle BB;

[0076] Fig. 9 is a flow chart of a double-layer nesting algorithm provided by an embodiment of the present invention;

[0077] Fig.10 is a deformation cloud diagram of the bed before optimization provided by an embodiment of the present invention;

[0078] Fig.11 is a stress cloud diagram of a bed before optimization provided by an embodiment of the present invention;

[0079] Fig.12 It is a cloud diagram of the first-order harmonic response value of the bed before optimization provided by an embodiment of the present invention;

[0080] Fig.13 is a deformation cloud diagram of the optimized bed provided by an embodiment of the present invention;

[0081] Fig.14 is a stress cloud diagram of the optimized bed provided by an embodiment of the present invention;

[0082] Fig.15 It is a cloud diagram of the first-order harmonic response value of the optimized bed provided in an embodiment of the present invention.

[0083] In the figure:

[0084] 1′, bed to be optimized; 1, bed after two topology optimizations. DETAILED DESCRIPTION

[0085] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0086] In the embodiments of the present application, the terms "first" and "second" are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise specified, "plurality" means two or more.

[0087] The term "at least one" in this application means one or more, and the term "multiple" in this application means two or more, for example, multiple second messages means two or more second messages. The terms "system" and "network" are often used interchangeably herein.

[0088] It should be understood that the terms used in the description of the various examples herein are only for describing specific examples and are not intended to be limiting. As used in the description of the various examples and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0089] It should also be understood that the term "and / or" used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. The term "and / or" is a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this application generally indicates that the associated objects before and after are in an "or" relationship.

[0090] It should also be understood that in the various embodiments of the present application, the size of the serial number of each process does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0091] It should be understood that determining B based on A does not mean determining B only based on A. B can also be determined based on A and / or other information.

[0092] It should also be understood that the term “comprise” (also known as “includes,” “including,” “comprises” and / or “comprising”) when used in this specification specifies the presence of stated features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0093] It should also be understood that the term "if" may be interpreted to mean "when" or "upon" or "in response to determining" or "in response to detecting." Similarly, the phrase "if it is determined that ..." or "if [a stated condition or event] is detected" may be interpreted to mean "upon determining that ..." or "in response to determining that ..." or "upon detecting [a stated condition or event]" or "in response to detecting [a stated condition or event]," depending on the context.

[0094] It should be understood that the references to "one embodiment", "an embodiment", or "a possible implementation" throughout the specification mean that specific features, structures, or characteristics related to the embodiment or implementation are included in at least one embodiment of the present application. Therefore, the references to "in one embodiment" or "in an embodiment", or "a possible implementation" appearing throughout the specification do not necessarily refer to the same embodiment. In addition, these specific features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0095] CNC machine tools are short for Computer numerical control machine tools. They are automated machine tools equipped with a program control system. They can better solve the problems of complex, precise, small batch, and multi-variety parts processing. They are flexible and efficient automated machine tools. Among them, the main machine is the main body of the CNC machine tool. It includes mechanical parts such as the bed, base, column, beam, slide, workbench, spindle box, feed mechanism, tool holder, and automatic tool changer. It is the mechanical part that automatically completes various cutting processes on the CNC machine tool. Among them, the strength and rigidity of large parts in the machine tool structure, such as columns and bed, have a great influence on the overall stability of the machine tool. Therefore, structural optimization of these large parts can greatly improve the stability of the whole machine and the stability of parts production and processing. In the prior art, the optimization of large components of CNC machine tools mostly adopts a one-time topology optimization, and generally only considers dynamic optimization or static optimization, and the optimization effect is limited; and the required performance ratio of CNC machine tools under different working conditions is different, and the existing optimization methods rarely consider the impact of the required performance ratio of different working conditions on the optimization, and the final optimization effect is not comprehensive and applicable.

[0096] Based on the above problems, this embodiment provides a multi-level optimization method for CNC machine tool structure, such as Figure 1 As shown, the specific steps include:

[0097] S1: Establish a CNC machine tool model to be optimized according to the CNC machine tool to be optimized, and the CNC machine tool to be optimized has n working conditions;

[0098] In this embodiment, it is optional but not limited to using finite element software to establish the CNC machine tool model to be optimized, for example, using ANSYS software to establish the CNC machine tool model to be optimized.

[0099] When establishing the CNC machine tool model to be optimized based on the CNC machine tool to be optimized, the CNC machine tool to be optimized is simplified to reduce the difficulty of subsequent meshing and reduce the occupation of computer resources, thereby reducing the simulation operation time and improving efficiency while ensuring the accuracy of the finite element analysis results. Figure 2 As shown, in this embodiment, the structure of the bed of the CNC machine tool is optimized, that is, other components are omitted during modeling, and the geometric model of the bed 1′ is established using finite element software. The CNC machine tool model to be optimized refers to the geometric model of the bed 1′ here.

[0100] Furthermore, after the CNC machine tool model to be optimized is established, it also includes pre-processing: including defining material properties and dividing the finite element grid; for example, the bed material is HT300 (gray cast iron), the cell size is set to 5mm, and the six anchor bolts at the bottom are used as constraints to analyze the actual force load, such as the gravity of the bed, the positive pressure of other components, and the cutting force during the cutting process.

[0101] Among them, different types of CNC machine tools have different working conditions. Taking a dual-spindle CNC machine tool as an example, the main and secondary axes of the dual-spindle CNC machine tool have different force conditions during the machining process. It is defined that the dual-spindle CNC machine tool has four working conditions during the machining process, namely, main roughing and secondary roughing (main axis roughing and secondary axis roughing), main roughing and secondary fine (main axis roughing and secondary axis fine machining), main fine and secondary roughing (main axis fine machining and secondary axis rough machining), main fine and secondary fine (main axis fine machining and secondary axis fine machining), that is, n is 4.

[0102] S2: performing static analysis on the CNC machine tool model to be optimized under each working condition, and calculating a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis;

[0103] When performing structural optimization on a CNC machine tool to be optimized, in order to improve the overall performance of the CNC machine tool to be optimized and ensure that the optimized CNC machine tool can adapt to various working conditions, n working conditions need to be considered during optimization, that is, multiple objectives are optimized during optimization, and each working condition is a sub-objective. In order to deal with multi-objective optimization problems, this embodiment adopts a compromise programming method to convert the multi-objective optimization problem into a compromise solution to the multi-objective optimization problem, and requires that the Euclidean distance between the solution and the optimal solution of each single-objective optimization problem be minimized, so that each objective can reach its optimal value to the greatest extent. Among them, the specific steps for allocating sub-objective weights in the compromise programming method are as follows:

[0104] S21: Perform static analysis on the CNC machine tool model to be optimized by using finite element software to obtain the static stiffness value and maximum stress value of the CNC machine tool model to be optimized under each working condition;

[0105] After establishing the CNC machine tool model to be optimized through finite element software, define the topological domain X 1 , load different working conditions and boundary conditions under each working condition respectively. Under different working conditions, such as the movement of the main spindle and the sub-spindle, the cutting parameters, etc. are different. In the optimization process, by applying forces of different positions and sizes, as boundary conditions under different working conditions. For example, finite element simulation calculation and analysis are performed on the bed of the dual-spindle CNC machine tool under the above four working conditions, and the static stiffness value and maximum stress value of the bed of the dual-spindle CNC machine tool under each working condition are obtained respectively, wherein the static stiffness value includes the static stiffness values ​​in the three directions of X, Y, and Z, as shown in the following Table 1 for example:

[0106] Table 1 Static analysis results of the bed of the dual-spindle CNC machine tool under four different working conditions

[0107]

[0108] S22: Establish a first single-layer evaluation index system consisting of n evaluated objects and m indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the m indicators include the static stiffness value and the maximum stress value of the CNC machine tool model to be optimized. Taking Table 1 as an example, the n evaluated objects are the four working conditions of main roughing and auxiliary roughing, main roughing and auxiliary fine 4, main fine and auxiliary roughing, and main fine and auxiliary fine, and the m indicators are the four indicators of X-direction static stiffness, Y-direction static stiffness, Z-direction static stiffness and maximum stress value.

[0109] S23: Calculating a first weight coefficient of each of the m indicators by an entropy weight method based on the first single-layer evaluation indicator system;

[0110] Specifically, the steps include:

[0111] S231: Establish a first original indicator data matrix X=(x ij ) n×m , that is, the index value sequence of the i-th working condition is recorded as X i ={X i The index value sequences corresponding to the n working conditions are combined to obtain the first original index data matrix X = (x ij ) n×m :

[0112]

[0113] S232: Dimensionless processing is performed on the values ​​in the first original index data matrix to obtain a second original index data matrix X′=(x′ ij ) n×m , by the following formula X=(x ij ) n×m Dimensionless:

[0114]

[0115] The second original indicator data matrix X′=(x′ ij ) n×m for:

[0116]

[0117] S233: The second original index data matrix X′=(x′ ij ) n×mNormalization processing obtains the third original indicator data matrix Y=(y ij ) n×m :

[0118]

[0119] S234: Calculate the normalized information entropy E of the j-th indicator according to the following formula: j The larger the value, the smaller the index variation, and the smaller the weight coefficient of the index.

[0120]

[0121] In the formula, p ij is the proportion of the index value of the i-th working condition under the j-th index to the index;

[0122] Through the information entropy E of each indicator j Calculate the first weight coefficient w of each indicator j1 :

[0123]

[0124] Finally, we calculate ω j1 =(0.0967,0.0894,0.7272,0.0867) T , that is, the first weight coefficient of the first indicator is 0.0967, the first weight coefficient of the second indicator is 0.0894, the first weight coefficient of the third indicator is 0.7272, and the first weight coefficient of the fourth indicator is 0.0867.

[0125] The first weight coefficient of each indicator is calculated by the entropy weight method, which is more objective and can effectively reduce the subjective proportion of human assignment, making the first weight value finally calculated more reasonable and reliable.

[0126] S24: Calculate the second weight coefficient of each indicator of the m indicators by a hierarchical method;

[0127] The specific steps include:

[0128] S241: Compare the importance of m indicators and establish a decision matrix based on them Indicates index j a For indicator j b The relative importance of, where,a=1,2,3,,,m, and b=1,2,3,,,m;

[0129] Among them, the comparison of the pairwise importance of m indicators can refer to the following Table 2:

[0130] Table 2 Reference definition of importance between decision matrix indicators

[0131]

[0132]

[0133] Note: a For b The relative importance of is between the above two importance ratios. Corresponding pairs are 2, 4, 6, 8, 1 / 2, 1 / 4, 1 / 6, 1 / 8.

[0134] For example, the decision matrix A is obtained by comparing the four indicators under four working conditions:

[0135]

[0136] S242: Calculate the eigenvector corresponding to the maximum eigenvalue of the decision matrix to obtain the second weight coefficient w of each indicator j2 .

[0137] The maximum eigenvalue of A is 4.0201, and the corresponding eigenvector is (0.8503, 0.4851, 0.1772, 0.1017) T ,In order to simplify the calculation, the eigenvector corresponding to the maximum eigenvalue is normalized to obtain ω j2 =(0.0496, 0.0397, 0.8896, 0.0211). That is, the first weight coefficient of the first indicator is 0.0496, the first weight coefficient of the second indicator is 0.0397, the first weight coefficient of the third indicator is 0.8896, and the first weight coefficient of the fourth indicator is 0.0211.

[0138] Preferably, in order to ensure the reliability of the decision matrix, a consistency test is also required for the decision matrix. If its consistency ratio CR<0.1, it is acceptable, where:

[0139]

[0140] Where: CI-test consistency index; RI-consistency index of random matrix generation; μ max - the maximum eigenvalue of the decision matrix A;

[0141] Among them, RI is determined by the following Table 3:

[0142] Table 3 Random consistency index RI

[0143]

[0144] In this embodiment, the matrix order is 4, then RI is 0.9, n is 4, and CR=0.0074<0.1 is calculated. The above decision matrix A is acceptable, and the second weight coefficient of each indicator finally calculated is acceptable.

[0145] S25: Calculate a first comprehensive indicator weight coefficient according to the first weight coefficient of each indicator and the second weight coefficient of each indicator, and then calculate a first weight value of each working condition according to the first comprehensive indicator weight coefficient;

[0146] Specifically include:

[0147] Calculate the evaluation value s of the first index weight coefficient and the second index weight coefficient for n working conditions 1 、s 2 :

[0148]

[0149] For example, according to the above obtained w j1 、w j2 Find s 1 、s 2 They are s 1 =[0.1576,0.1492,0.9089,0.1395] T ,s 2 =[0.1396, 0.1265, 0.8999, 0.1675] T .

[0150] Will s 1 、s 2 As two vectors in n-dimensional space, that is, (s 1 ) n*1 、(s 2 ) n*1 , define an n-dimensional vector (l i ) n*1 Make it to (s 1 ) n*1 、(s 2 ) n*1 The spatial Euclidean distance and the minimum are taken as the objective function, and a linear programming model is constructed to transform the integration problem of the first indicator weight coefficient and the second indicator weight coefficient obtained by the two methods into an optimization problem:

[0151] Construct a linear programming model:

[0152]

[0153] Among them, α j - Weight coefficient of the first comprehensive indicator;

[0154] The first weight value of each working condition is obtained according to the following formula:

[0155]

[0156] l i is the first weight value of the i-th working condition. Preferably, l i After normalization, it is used as the first weight value of each working condition.

[0157] For example, according to the above calculation, s 1 、s 2 Calculate l i =(0.3334,0.3290,0.6859,0.3482), i After normalization, the first weight values ​​of each working condition are 0.1965, 0.1939, 0.4043, and 0.2053 respectively.

[0158] This embodiment combines the entropy weight method and the hierarchical method to calculate the weight of each operating condition, which can effectively overcome the shortcomings caused by using the subjective or objective assignment method alone, and make the weight of each operating condition more scientific and reasonable.

[0159] S3: According to the first weight value of each working condition, the CNC machine tool model to be optimized is subjected to a first topology optimization with maximizing static stiffness and minimizing stress as optimization objectives and taking the first volume as a constraint, to obtain a first CNC machine tool model;

[0160] In order to improve the static performance of the CNC machine tool to be optimized, strengthen its static stiffness and reduce stress concentration, the weight (since the bed of the machine tool to be optimized is an isodensity body, the mass can be equivalent to the volume) and the optimization objective function are considered in the static topology optimization. That is, at this stage, for example, the maximization of the static stiffness and minimization of the stress of the bed are taken as the optimization objectives, and the bed volume is taken as the constraint function. Based on the compromise programming method, a comprehensive objective function is established, and the topology optimization mathematical model of the bed is obtained as follows:

[0161]

[0162] Where: R n - Initial structural design area; x i -unit relative density vector, which is a design variable and represents the density value of each unit after discretization; u-the total number of grid units after discretization; w i -The weight of the i-th order objective function, which is the first weight value of the i-th working condition mentioned above; f i min 、f i max , is the maximum and minimum value of the single objective optimization of the i-th order objective function; f i(x)- objective function of the i-th order; v(x) - objective function of the volume, where v i - optimized unit volume; v min 、v max -Maximum and minimum values ​​of volume single-objective optimization; V * -Total volume constraints of the structure.

[0163] like Figure 3 As shown, in the specific operation, after obtaining the first weight value of each working condition, the first topological domain X is defined in the topological optimization module of the finite element software. 1 , set the topology optimization penalty factor, for example, to 3, and use the first volume as the constraint function, that is, the constraint target is min: V(X 1 ), for example, retaining 75% of the volume ratio. Of course, in other embodiments, the penalty factor and volume ratio may also be other, such as retaining 80% or 70% of the volume ratio, which is set according to actual needs. And set four working conditions and the first weight value of each working condition and the boundary conditions of each working condition in the finite element software, and start iterative optimization until the convergence condition is reached, for example Figure 4 As shown, a topology optimization model based on static indicators can be obtained, that is, the first CNC machine tool model is obtained.

[0164] In order to improve the dynamic performance of the CNC machine tool to be optimized and reduce the probability of resonance with the outside world, a second topology optimization is performed after a rounding design is performed on the basis of the first CNC machine tool model. The rounding design refers to the regular design of the holes formed by the optimization in the first CNC machine tool model obtained after the first topology optimization, such as designing irregular holes into circles or squares. The specific steps of the second topology optimization are as follows:

[0165] S4: performing a dynamic analysis on the first CNC machine tool model under each working condition, and calculating a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis;

[0166] The method for obtaining the second weight value is the same as the method for obtaining the first weight value in the static optimization stage, both of which use the compromise planning method to allocate sub-goal weights. The specific steps refer to S21-S25, which are briefly described below:

[0167] S41: Performing dynamic analysis on the first CNC machine tool model through finite element software to obtain the first s-order natural frequencies of the first CNC machine tool model under each working condition; then establishing the CNC machine tool model to be optimized through finite element software, loading different working conditions and boundary conditions under each working condition, for example, performing finite element simulation calculation and analysis on the bed of the dual-spindle CNC machine tool under the above-mentioned 4 working conditions, respectively, and obtaining the first 4-order natural frequencies of the dual-spindle CNC machine tool under each working condition, as shown in the following Table 4 for example:

[0168] Table 4 The first four natural frequencies of the dual-spindle CNC machine tool under four different working conditions

[0169]

[0170] S42: establishing a second single-layer evaluation index system consisting of n evaluated objects and s indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the s indicators include each natural frequency of the first s orders of the first CNC machine tool model, for example, s is 4;

[0171] S43: calculating a third weight coefficient of each of the s indicators by an entropy weight method based on the second single-layer evaluation indicator system;

[0172] S44: Calculate the fourth weight coefficient of each indicator of the s indicators by a hierarchical method;

[0173] S45: Calculate a second comprehensive indicator weight coefficient according to the third weight coefficient of each indicator and the fourth weight coefficient of each indicator, and then calculate a second weight value of each working condition according to the second comprehensive indicator weight coefficient.

[0174] Steps S42-S45 refer to steps S22-S25, which will not be described in detail. For example, the second weight values ​​of each working condition are calculated to be 0.2498, 0.2596, 0.2763, and 0.2152, respectively.

[0175] S5: performing a second topology optimization on the first CNC machine tool model according to the second weight value of each working condition, taking the first s-order natural frequency as the optimization target and the second volume as the constraint, to obtain a second CNC machine tool model;

[0176] For example, in the topology optimization stage based on dynamic indicators, the first four natural frequencies of the bed are taken as optimization targets, and the bed volume is taken as the constraint function. A comprehensive objective function is established based on the compromise programming method, and the topology optimization mathematical model of the bed is obtained as follows:

[0177]

[0178] Where: R n - Initial structural design area; x i -unit relative density vector, which is a design variable and represents the density value of each unit after discretization; u-the total number of grid units after discretization; w i -The weight of the i-th order objective function, which is the second weight value of the i-th working condition mentioned above; h i min 、h i max is the maximum and minimum value of the single-objective optimization of the i-th order objective function; h i(x)- objective function of the i-th order; v(x) - objective function of the volume, where v i - optimized unit volume; v min 、v max -Maximum and minimum values ​​of volume single-objective optimization; V * -Total volume constraints of the structure.

[0179] like Figure 3 As shown, in the specific operation, after obtaining the second weight value of each working condition, the second topological domain X is defined in the topological optimization module of the finite element software. 2 , set the topology optimization penalty factor, for example, to 3, and take the second volume as the constraint target, for example, retaining 75% of the volume ratio. Of course, in other embodiments, the penalty factor and volume ratio can also be other, such as retaining 80% or 70% of the volume ratio, which is set according to actual needs. And set four working conditions and the second weight value of each working condition and the boundary conditions of each working condition in the finite element software, and start iterative optimization until the convergence condition is reached, for example Figure 5 As shown, a secondary topology optimization model based on dynamic indicators can be obtained, that is, the second CNC machine tool model is obtained.

[0180] The multi-level optimization method for the CNC machine tool structure provided in this embodiment fully considers the impact of changes in machining conditions on the static and dynamic characteristic parameters of the machine tool during the machining process, and adopts a combination of subjective and objective methods to determine the weight of each working condition. It takes into account both the frequency of use of the working condition in the actual process and the actual force of each working condition, so that the second CNC machine tool model obtained after two topology optimizations can be more in line with actual usage requirements.

[0181] S6: Selecting the design dimension parameters to be optimized of the second CNC machine tool model, optimizing the design dimension of the second CNC machine tool model, and obtaining multiple groups of optimized design dimensions;

[0182] like Figure 6 As shown in the figure, the shape obtained after topology optimization is the shape after removing some materials. Most of them are irregular shapes and do not meet the actual production requirements. Therefore, in full consideration of the production process, the topology optimized parts should be remodeled with the help of 3D software and the design dimensions should be determined. For example, after the second CNC machine tool module is designed regularly, the bed manufacturing and processing technology are comprehensively considered to determine the design dimensions including the middle funnel-shaped support, the front and rear X-shaped reinforcement ribs, and the vertical support at the beam as the optimized space, such as Figure 7 and Figure 8 As shown, x 1 -x 6That is, the design size parameter to be optimized. Since large machine tool components are generally manufactured by casting, there are many uncertainties in their material property parameters, boundary conditions, measurement errors, etc. The cross-coupling of multiple uncertain errors will cause large deviations in the system response. Therefore, when optimizing the design size, these uncertainties must be fully considered to obtain the sample point space and build an approximate model. For example, the density x of the bed 7 , elastic modulus x 8 and Poisson's ratio x 9 is an uncertain factor parameter. The specific steps for design size optimization are as follows:

[0183] S61: Construct an approximate model, which reflects the relationship between the parameters to be optimized and the objective function value. The parameters to be optimized include the design size parameters to be optimized and the uncertain factor parameters. The uncertain factor parameters include the density, elastic modulus and Poisson's ratio of the second CNC machine tool model. The objective function value includes one or more of the deformation, stress, volume and several orders of natural frequencies of the second CNC machine tool model after optimization. For example, in this embodiment, the objective function value includes deformation, stress and volume.

[0184] Specifically, the specific steps of building an approximate model are as follows:

[0185] S611: Obtain multiple groups of sample points of design variables within the design range through experimental design methods;

[0186] like Figure 7 and Figure 8 As shown, determine the X in bed 1 1 -X 6 is the design size parameter of the design variable, and determines the density X of the bed. 7 , elastic modulus X 8 and Poisson's ratio X 9 is the uncertainty factor parameter of the design variable, and the range of each design variable is:

[0187] Table 5 The first design range of design dimension parameters

[0188]

[0189] Table 6 Determine the second design range of factor variable parameters

[0190]

[0191]

[0192] Based on the design range of the above-mentioned design variables, sample points are obtained through experimental design methods. Each group of sample points is the value of each design variable within the design range each time. For example, the central composite design method is adopted. Since the central composite design method is a relatively mature existing technology, it will not be described here one by one.

[0193] S612: Calculate the response value of the second CNC machine tool model at each sample point using finite element analysis software, where the response value is the objective function value of the second CNC machine tool model under the design variable, thereby obtaining multiple sets of data sets of dimensional parameters to be optimized-objective function values;

[0194] In the specific operation, the range of the design variables is set in the finite element software, and multiple groups of experimental sample points are generated through the experimental design module. In this embodiment, the static stiffness, stress and mass (equivalent to volume) of the bed are the main optimization targets. The finite element software simulates and calculates the response values ​​corresponding to each group of experimental sample points. Each group of response values ​​is each group of objective function values ​​corresponding to the second CNC machine tool model under each group of design variables, such as the minimum stress value y of the bed. 1 , maximum deformation y 2 and minimum mass y 3 , thereby obtaining multiple sets of data sets of design variables-objective function values. For example, as shown in the following Table 7:

[0195] Table 7 Dataset of design variables and objective function values

[0196]

[0197] S613: Based on the Kriging model, a non-analytical function expression of the design variables and the objective function values ​​is constructed, and the Kriging model is trained using the data set of the design variables-objective function values ​​to obtain an approximate model reflecting the relationship between the design variables and the objective function values:

[0198] The above-mentioned data set of design variables and objective function values ​​is divided into a training set and a validation set according to a ratio of 7:3 or other ratios. The training set is used to train the Kriging model, and the validation set is used to verify the accuracy of the Kriging model.

[0199] The theoretical analysis basis of the Kriging approximation model is the variogram, which is an unbiased optimal estimate of the value of the regionalized variable in a limited area. It is a spatial local interpolation method. This method uses weighted interpolation weight design for the design variable data and uses the distance as the variogram of the independent variable to calculate the value. Therefore, it can not only reflect the spatial structure characteristics of the design variables, but also reflect the random distribution characteristics of the design variables. The Kriging model is composed of the superposition of the global model and the local deviation, which can be expressed as

[0200] y(x)=f(x)+z(x)

[0201] Where: y(x) is the unknown approximate model; f(x) is the known polynomial function, namely Taylor's formula; z(x) is a random process with zero mean, non-zero variance and covariance, and has the following statistical characteristics:

[0202] E[z(x)]=0

[0203] Var[z(x)]=σ 2

[0204] Cov[z(x i ,x j )]=σ 2 [R(x i ,x j )]

[0205] R(x i ,x j ) represents the spatial correlation function between any two sample points in the sampling points. In this embodiment, a Gaussian function is used:

[0206]

[0207] Once the correlation function is determined, the approximate response of y(x) can be established An expression for the observation point x.

[0208] Specifically, this embodiment establishes an approximate model through Matlab. For example, the dimension is specified in Matlab. In this embodiment, the input is 9 dimensions and the output is 3 dimensions. The training data, that is, the above-mentioned data set of design variables-objective function values, is imported, and the Gaussian function is called. Through iterative training, an approximate model reflecting the relationship between the design variables and the objective function values ​​is obtained.

[0209] The approximate model has the characteristic of local estimation, and has a relatively ideal fitting effect for the problem with a high degree of nonlinearity and a large number of design variable dimensions in this embodiment.

[0210] S614: The approximate model is an approximate modeling of the relationship between the sample points and the response values. It cannot fully express the relationship between the sample points and the response values. Therefore, after the approximate model is successfully constructed, the fitting accuracy of the approximate model needs to be evaluated. Common evaluation indicators for approximate models include R 2 (coefficient of determination), RMSE (root mean square error), MAE (mean absolute error), MRE (mean relative error), etc., and their expressions are:

[0211]

[0212] Where: n-the total number of experimental sample points; yi -Actual response value of the experimental sample; - The approximate model predicts the response value.

[0213] For example, the approximate model obtained according to the data in Table 6 is evaluated for its fitting accuracy, and the results are as follows:

[0214] Table 8 Evaluation results of the fitting accuracy of the approximate model

[0215]

[0216] If R 2 If the values ​​of RMSE, MAE, and MRE are within the preset range, the approximate model is judged to have reached the preset accuracy. For example, R 2 If the R is above 0.95, the RMSE is below 0.1, the MAE is below 0.1, and the MRE is below 0.1, the fitting accuracy of the approximate model reaches the preset accuracy. 2 , RMSE, MAE, and MRE do not all need to reach the preset range. If three of them reach the preset range, it can be judged that the fitting accuracy of the approximate model reaches the preset accuracy.

[0217] S62: Figure 7 As shown, a double-layer nested algorithm is used to optimize the approximate model and obtain the Pareto optimal solution set. The Pareto optimal solution set includes multiple groups of optimized design dimensions and the objective function value corresponding to each group of optimized design dimensions.

[0218] The design dimensions and material parameters are optimized respectively through a double-layer nested algorithm. For each specific value of a set of design dimensions, the material properties are considered to satisfy the Pareto frontier solution within an interval, and the set of design dimensions is output as a set of solutions in the Pareto optimal solution set.

[0219] It can be understood that this embodiment describes the uncertainty of uncertain factors in the optimization process based on interval numbers, and the uncertain multi-objective optimization problem can be described as:

[0220]

[0221] Where: X is the multi-dimensional design size parameter vector to be optimized. In this embodiment, X=(x 1 , x 2 , x 3 , x 4 , x 5 , x 6 ), whose value range is Ω n , I, R, L represent the interval, the upper and lower bounds of the interval respectively, and U is a multidimensional uncertain vector. In this embodiment, U = (x 7 , x8 , x 9 ). f and g are the objective function and constraint respectively, which are continuous functions of X and U. is the allowable interval of the i-th uncertain constraint.

[0222] The interval order relation is used to judge whether one interval is better or worse than another interval. It is usually used to deal with uncertainty optimization problems in linear interval number optimization. Intervals are used to describe uncertainties. During the optimization process, the objective function value obtained will be an interval rather than a definite real value. In this way, in uncertainty optimization based on interval numbers, it is necessary to compare the advantages and disadvantages of the objective function intervals under different design variables, so as to judge the advantages and disadvantages of the corresponding design variables and finally obtain the optimal design variables.

[0223] For any design size parameter X to be optimized, due to the existence of the uncertain vector U and f is a continuous function of U, the possible value range of f(X,U) is an interval:

[0224] f I (X) = [f L (X),f R (X)]={f C (X),f W (X)}

[0225]

[0226] In the optimization process, the midpoint value and radius of the objective function interval are used to judge the advantages and disadvantages of different design size parameter vectors to be optimized: the design size parameter vector to be optimized X 1 Better than the design size parameter vector X to be optimized 2 , then X 1 The objective function interval at is better than X 2 The objective function interval at f C (X 1 )≤f C (X 2 ),f W (X 1 )≤f W (X 2 ), for interval uncertainty optimization problems, we hope to obtain a design variable that makes the interval of the objective function have both the minimum midpoint value and the minimum radius value. This design size is the optimal solution of the objective function. Therefore, the uncertain multi-objective optimization problem can be transformed into the following deterministic multi-objective optimization problem:

[0227]

[0228] For this deterministic multi-objective optimization problem, in the process of solving the design size optimization, for each design size parameter vector to be optimized, it is necessary to solve the midpoint value and radius value of its objective function.

[0229] By optimizing the midpoint value of the objective function, the average design performance of the objective function under the influence of uncertainty factors is improved; and by optimizing the radius value of the objective function, the sensitivity of the objective function to uncertainty can be reduced, thereby ensuring the robustness of the design.

[0230] Specifically, the two-layer nested algorithm is used to optimize the approximate model including:

[0231] S62: The double-layer nested algorithm includes an outer non-dominated sorting genetic algorithm (NSGA-II) and an inner intergenerational mapping genetic algorithm (IP-GA), and the outer non-dominated sorting genetic algorithm is used to optimize the approximate model in the design size space constituted by the first design range of the design size parameter to be optimized;

[0232] Randomly generate the initial population P in the design size space 0 After that, the initial population P 0 It includes a given number of individuals, each individual refers to each design size vector, and the element value in each design size vector is a gene; for the initial population P 0 Sort the individuals in the parent population P t , then the parent population P t Genetically generated offspring population Q t , the offspring population Q t and the parent population P t The new population R generated by the merger t , for example, by the parent population P t Any two individuals of the same species undergo gene crossover, and any one of them undergoes gene mutation, and the offspring population Q is obtained. t ; According to population R t The objective function value corresponding to each individual in the , calculates the number of dominated individuals, and classifies the individuals according to the number of dominated individuals, and estimates the crowding degree between the individuals, and puts the lowest level into the new generation parent population P first t+1 Until this generation is full of the given population, the new generation of parent population P is placed in the order of ranking from large to small according to the degree of crowding. t+1 In; by the new generation of parent population P t+1 Genetically generate a new generation of offspring population Q t+1 , and repeat until the termination condition is reached, such as the population generation number reaches the set generation number. In this way, a Pareto frontier solution with a better fitting design size space can be obtained.

[0233] In this embodiment, Matlab programming or calling an existing program is used to realize the optimization in the design dimension space, and the initialization parameters are set, such as the population number, fitness calculation function, mutation probability, crossover probability, number of iterations, etc. Exemplarily, in the optimization process, the population number is set to 100, and after 200 iterations, the Pareto solution set is obtained.

[0234] Since the influence of the uncertainty factor parameters is considered in this embodiment, in step S62, according to the population R t When calculating the dominated number of each individual based on the function response value of each individual, due to the existence of uncertain factor parameters, the objective function value corresponding to the individual cannot be directly obtained through the approximate model. This embodiment uses the inner-layer intergenerational mapping genetic algorithm to find the optimal solution in the uncertain parameter space formed by the second design range of the uncertain factor parameters. By finding the optimal Pareto frontier solution of the uncertain parameter space when each individual is determined, the objective function value of the corresponding individual can be determined, so that the dominated number of each individual in the outer design dimension space can be calculated, so that the outer non-dominated sorting genetic algorithm can proceed smoothly and find the optimal Pareto frontier solution of the design dimension space. The details are as follows:

[0235] S63: For each group of design dimensions with a certain value, that is, when calculating the number of dominated individuals in each generation of the outer non-dominated sorting genetic algorithm, the inner layer intergenerational mapping genetic algorithm seeks the optimal solution in the uncertain parameter space formed by the second design range of the uncertain factor parameters, and obtains the upper and lower bounds of the objective function value response through the approximate model, and obtains the midpoint value and radius value of the objective function value response according to the upper and lower bounds, and obtains the multi-objective evaluation function value according to the midpoint value and radius value:

[0236]

[0237] Among them, f d is the value of the multi-objective evaluation function, f C (X,U) is the midpoint value of the objective function response, f W (X,U) is the radius value of the objective function value response, is the multi-objective weight coefficient, for example Set to 0.5, and set it according to specific needs. For example, when robustness has little effect on the problem, a relatively large weight coefficient can be selected to increase the preference for the midpoint value of the objective function, thereby obtaining a better average design performance under the influence of uncertainty factors to a certain extent; when very stable performance is required, especially when the performance fluctuates greatly due to the influence of uncertainty and has a greater impact on the objective function, it is generally considered to select a relatively small weight coefficient, thereby reducing the fluctuation of the uncertain objective function at the expense of the average design performance, and ultimately obtaining better design robustness.

[0238] S64: The multi-objective evaluation function value is fed back to the outer non-dominated sorting genetic algorithm, and the outer non-dominated sorting genetic algorithm continues to search for the best solution. If the stopping criterion is met, the Pareto optimal solution set is output.

[0239] The multi-objective evaluation function value obtained by optimizing the inner-layer intergenerational mapping genetic algorithm is fed back to the outer-layer non-dominated sorting genetic algorithm. The multi-objective evaluation function value is the objective function value corresponding to the individual. The dominated number of each individual in the population is calculated through the objective function value corresponding to the individual, and then the individuals in the population are sorted and the crowding degree is calculated to obtain a new generation of population. This iterative cycle is repeated until the termination condition is reached, such as the population generation number reaches the set generation number, so that a Pareto solution set with a better fitting design size space can be obtained.

[0240] In this embodiment, the inner layer intergenerational mapping genetic algorithm is similar to the outer layer non-dominated genetic algorithm in the design size space. The difference is that the inner layer intergenerational mapping genetic algorithm is based on a small population micro genetic algorithm. When the population is initialized, the number of individuals in the population is small, for example, 5-8 individuals, so as to improve the convergence speed, thereby improving the calculation speed. At the same time, the restart strategy is used to avoid local convergence while also improving the convergence speed of the population. The individual here is the uncertainty factor parameter vector, and the elements in the uncertainty factor parameter vector are genes. Among them, the restart strategy means that once the current generation meets the convergence requirements, a population of the same size is randomly generated, and this population will contain the best individuals of the previous generation, and operations such as selection and crossover are performed until the evolution process finds the global optimal point (or reaches a pre-set number of generations). The basic standard for restarting is: when the genes of less than 5% of the individuals in the population except the best individual are different from the best individual, restart. In the evolution process, the inner-layer intergenerational mapping genetic algorithm also includes mutation operators and intergenerational mapping operators. The mutation operator is to mutate individual genes when the parent population is inherited to generate the offspring population, thereby increasing the individual diversity in the population; the intergenerational mapping operator is to use the two best individuals in the current generation and the parent generation to calculate two IP operators, and use the two calculated IP operators to replace the two worst individuals in the current generation, thereby achieving the purpose of specific search performance. Specifically, if the two best individuals in the current generation and the parent generation are respectively used and Indicates that the IP operator is and Three new individuals found nearby 1 、new 2 and new 3 It can be obtained by the following formula:

[0241]

[0242] Where α, β, and γ represent the control parameters of the IP operator, and 0<α, β, γ<1.0

[0243] Then calculate new 1 、new 2 and new 3 If the maximum value among them is greater than the fitness of the worst individual in the current generation, the worst individual in the current generation is replaced by a new individual with the maximum fitness. 1 、new 2 and new 3 The best two individuals in the generation replace the worst two individuals in the current generation to obtain a new generation of population.

[0244] Understandably, a small population of 5-8 individuals is randomly generated at the beginning of evolution, and is used as the parent population after sorting and selection using the niche technology; then the parent population is subjected to crossover and mutation, and the child population is obtained after the optimal preservation strategy is implemented, and the IP operator is obtained by performing IP calculation on the two best individuals in the current child population and the parent population, and the two IP operators are used to replace the two worst individuals in the current child population to obtain a new generation population; then the new generation population is restarted and judged, if the population is concentrated, it is restarted, otherwise it is judged whether the convergence condition is met, if it is met, it is terminated, if not, the above cycle is continued.

[0245] By adopting the inner-layer intergenerational mapping genetic algorithm and using a small population strategy, the difficulty of complex problems is simplified and the convergence performance and search efficiency of the algorithm are enhanced; the restart strategy is introduced to increase the diversity of individuals in the population and avoid local convergence; the IP operator is added to construct individuals with higher fitness to replace the individuals with the worst fitness in the offspring, so as to improve the average fitness of individuals in the population and improve the local search ability of the algorithm.

[0246] After the above optimization, multiple sets of optimized design dimensions are obtained, as shown in the following table:

[0247] Table 9 Design size reference table

[0248]

[0249] S7: Select a set of optimized design dimensions according to the requirements, and redesign the CNC machine tool to be optimized to obtain the optimized CNC machine tool.

[0250] In actual production, for example, a set of design dimensions can be selected according to Table 9. Appropriate design dimensions can be selected based on the expected value of the target and engineering experience. For example, for design criteria with relatively high stress requirements, groups 2 and 5 can be referred to. For design criteria with relatively high static stiffness requirements, groups 1 and 2 can be considered. Taking both design criteria into consideration, group 2 can be considered.

[0251] Taking the fourth group of design dimensions in Table 9 as an example, the quality and performance values ​​of the optimized bed are obtained through finite element simulation analysis. Figures 8 to 13 , can be found in Table 10 below. By comparing the data before and after optimization, it can be seen that through the multi-level optimization of the above steps S1-S7, the static stiffness of the bed can be improved, the stress concentration phenomenon can be improved, and the quality of the bed can be reduced. At the same time, the selection of various design dimensions can be efficiently realized to meet different performance control requirements.

[0252] Table 10 Comparison of quality and performance of the bed before and after optimization

[0253]

[0254] This embodiment also provides a multi-level optimization system for CNC machine tool structures, which can implement the above steps S1-S6, and specifically includes a model building module, a first analysis module, a first topology optimization module, a second analysis module, a second topology optimization module and a design size optimization module. The model building module is used to establish the CNC machine tool model to be optimized, the first analysis module is used to perform static analysis on the CNC machine tool model to be optimized under each working condition, and calculate the first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis; the first topology optimization module is used to perform the first topology optimization on the CNC machine tool model to be optimized according to the first weight value of each working condition, with the static stiffness maximization and stress minimization as the objective function and the volume as the constraint, to obtain the first CNC machine tool model; the second analysis module is used to perform dynamic analysis on the first CNC machine tool model under each working condition, and calculate the second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis; the second topology optimization module is used to perform the second topology optimization on the first CNC machine tool model according to the second weight value of each working condition, with the first s-order natural frequency as the objective function and the volume as the constraint, to obtain the second CNC machine tool model; the design size optimization module is used to optimize the design size parameters of the second CNC machine tool model, and obtain multiple sets of optimized design sizes. Among them, the first analysis module and the second analysis module can be one module, and the first topology optimization module and the second topology optimization module can be one module, which is not specifically limited here.

[0255] The multi-level structural optimization system for CNC machine tools provided in this embodiment can realize multi-level structural optimization of CNC machine tools, reduce the weight of CNC machine tools, and improve the design efficiency and performance of CNC machine tools.

[0256] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A multi-level optimization method for CNC machine tool structure, characterized in that: include: Establishing a model of a CNC machine tool to be optimized according to the CNC machine tool to be optimized, wherein the CNC machine tool to be optimized has n working conditions; Performing static analysis on the CNC machine tool model to be optimized under each working condition, and calculating a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis; According to the first weight value of each working condition, the CNC machine tool model to be optimized is subjected to a first topological optimization with maximizing static stiffness and minimizing stress as optimization objectives and with the first volume as a constraint, to obtain a first CNC machine tool model; Performing a dynamic analysis on the first CNC machine tool model under each working condition, and calculating a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis; According to the second weight value of each working condition, performing a second topology optimization on the first CNC machine tool model with the first s-order natural frequency as the optimization target and the second volume as the constraint, to obtain a second CNC machine tool model; Selecting the design dimension parameters to be optimized of the second CNC machine tool model, optimizing the design dimension of the second CNC machine tool model, and obtaining multiple groups of optimized design dimensions; A set of the optimized design dimensions is selected according to the requirements, and the CNC machine tool to be optimized is redesigned to obtain the optimized CNC machine tool.

2. The multi-level optimization method for CNC machine tool structure according to claim 1, characterized in that: Performing static analysis on the CNC machine tool model to be optimized under each working condition, and calculating a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis includes: Performing static analysis on the CNC machine tool model to be optimized by finite element software to obtain the static stiffness value and maximum stress value of the CNC machine tool model to be optimized under each working condition; Establishing a first single-layer evaluation index system consisting of n evaluated objects and m indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the m indicators include the static stiffness value and the maximum stress value of the CNC machine tool model to be optimized; Calculating a first weight coefficient of each of the m indicators by an entropy weight method based on the first single-layer evaluation indicator system; Calculate the second weight coefficient of each of the m indicators by a hierarchical method; The first comprehensive indicator weight coefficient is calculated according to the first weight coefficient of each indicator and the second weight coefficient of each indicator, and then the first weight value of each working condition is calculated according to the first comprehensive indicator weight coefficient.

3. The multi-level optimization method for CNC machine tool structure according to claim 2, characterized in that: Calculating the first weight coefficient of each indicator by the entropy weight method based on the first single-layer evaluation indicator system includes: The first original indicator data matrix X is established with the n evaluated objects and the m indicators. ij ) n×m , and the values ​​in the first original indicator data matrix are dimensionless processed to obtain the second original indicator data matrix X′=(x i ' j ) n×m ; The second original indicator data matrix X′=(x i ' j ) n×m Normalization processing obtains the third original indicator data matrix Y=(y ij ) n×m ; The normalized information entropy E of the jth indicator is calculated according to the following formula: j : In the formula, p ij is the proportion of the index value of the i-th working condition under the j-th index to the index; Through the information entropy E of each indicator j Calculate the first weight coefficient w of each indicator j1 :

4. The multi-level optimization method for CNC machine tool structure according to claim 3 is characterized in that: The second weight coefficients of each indicator calculated by the hierarchical method include: Compare the importance of the m indicators and establish a decision matrix based on them Indicates index j a For indicator j b The relative importance of, a = 1, 2, 3,,, m, b = 1, 2, 3,,,, m; Calculate the eigenvector corresponding to the maximum eigenvalue of the decision matrix to obtain the second weight coefficient w of each indicator. j2 .

5. The multi-level optimization method for CNC machine tool structure according to claim 4, characterized in that: The first comprehensive indicator weight coefficient is calculated according to the first weight coefficient of each indicator and the second weight coefficient of each indicator, and then the evaluation value of the first comprehensive indicator weight coefficient for each working condition is calculated according to the first comprehensive indicator weight coefficient. The evaluation value includes: Calculate the evaluation values ​​s1 and s2 of the first index weight coefficient and the second index weight coefficient for n working conditions: Construct a linear programming model: Among them, α j - Weight coefficient of the first comprehensive indicator; The first weight value of each working condition is obtained according to the following formula: Among them, l i is the first weight value of the i-th working condition.

6. The multi-level optimization method for CNC machine tool structure according to any one of claims 1 to 5, characterized in that: Performing a dynamic analysis on the first CNC machine tool model under each working condition, and calculating a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis includes: Performing dynamic analysis on the first CNC machine tool model by using finite element software to obtain the first s-order natural frequencies of the first CNC machine tool model under each working condition; Establishing a second single-layer evaluation index system consisting of n evaluated objects and s indicators, wherein the n evaluated objects are n working conditions of the CNC machine tool to be optimized, and the s indicators include each natural frequency of the first s orders of the first CNC machine tool model; Calculating a third weight coefficient of each of the s indicators by an entropy weight method based on the second single-layer evaluation indicator system; Calculate the fourth weight coefficient of each of the s indicators by a hierarchical method; The second comprehensive indicator weight coefficient is calculated according to the third weight coefficient of each indicator and the fourth weight coefficient of each indicator, and then the second weight value of each working condition is calculated according to the second comprehensive indicator weight coefficient.

7. The multi-level optimization method for CNC machine tool structure according to any one of claims 1 to 5, characterized in that: Selecting the design dimension parameters to be optimized of the second CNC machine tool model, optimizing the design dimension of the second CNC machine tool model, and obtaining multiple groups of optimized design dimensions including: Constructing an approximate model, wherein the approximate model reflects the relationship between design variables and objective function values, wherein the design variables include design size parameters to be optimized and uncertainty factor parameters, wherein the uncertainty factor parameters include density, elastic modulus, and Poisson's ratio of the second CNC machine tool model, and the objective function value includes one or more of deformation, stress, volume, and several-order natural frequencies of the second CNC machine tool model after optimization; A double-layer nested algorithm is used to optimize the approximate model to obtain a Pareto optimal solution set, wherein the Pareto optimal solution set includes multiple groups of optimized design dimensions and objective function values ​​corresponding to each group of optimized design dimensions.

8. The multi-level optimization method for CNC machine tool structure according to claim 7, characterized in that: The double-layer nested algorithm includes an outer non-dominated sorting genetic algorithm and an inner intergenerational mapping genetic algorithm. The double-layer nested algorithm is used to optimize the approximate model, including: An outer non-dominated sorting genetic algorithm is used to optimize the approximate model in a design dimension space formed by a first design range of the design dimension parameters to be optimized; For each group of design dimensions with certain values, an inner-layer intergenerational mapping genetic algorithm is used to search for the optimum in the uncertain parameter space formed by the second design range of the uncertain factor parameters, and an upper limit value and a lower limit value of the objective function value response are obtained through the approximate model, and a midpoint value and a radius value of the objective function value response are obtained according to the upper limit value and the lower limit value, and a multi-objective evaluation function value is obtained according to the midpoint value and the radius value; The multi-objective evaluation function value is fed back to the outer non-dominated sorting genetic algorithm, and the outer non-dominated sorting genetic algorithm continues to search for the best solution, and outputs the Pareto optimal solution set if the stopping criterion is met.

9. The multi-level optimization method for CNC machine tool structure according to claim 7, characterized in that: Constructing the approximate model includes: Acquire multiple groups of sample points of the design variables within the design range by using an experimental design method; The response value of the second CNC machine tool model corresponding to each of the sample points is calculated by finite element analysis software, wherein the response value is the objective function value corresponding to the second CNC machine tool model under the design variable, thereby obtaining a plurality of sets of data sets of design variable-objective function values; Based on the Kriging model, a non-analytical function expression of the design variables and the objective function values ​​is constructed, and the Kriging model is trained using the data set of the design variables-objective function values ​​to obtain the approximate model reflecting the relationship between the design variables and the objective function values.

10. A multi-level optimization system for CNC machine tool structure, characterized in that: include: A model building module is used to build a CNC machine tool model to be optimized; A first analysis module, configured to perform a static analysis on the CNC machine tool model to be optimized under each working condition, and calculate a first weight value of each working condition of the CNC machine tool model to be optimized based on the static analysis; A first topology optimization module is used to perform a first topology optimization on the CNC machine tool model to be optimized according to the first weight value of each working condition, taking static stiffness maximization and stress minimization as objective functions and volume as a constraint, to obtain a first CNC machine tool model; a second analysis module, configured to perform a dynamic analysis on the first CNC machine tool model under each working condition, and calculate a second weight value of each working condition of the first CNC machine tool model based on the dynamic analysis; A second topology optimization module is used to perform a second topology optimization on the first CNC machine tool model according to the second weight value of each working condition, taking the first s-order natural frequency as the objective function and the volume as the constraint, to obtain a second CNC machine tool model; The design dimension optimization module is used to optimize the design dimension parameters of the second CNC machine tool model to obtain multiple groups of optimized design dimensions.

Images