Thermal bearing stable structure topological optimization method for high-precision coordinate boring machine

Abstract

The invention discloses a thermal bearing stable structure topological optimization method for a high-precision coordinate boring machine, and relates to the field of machine tool structure topological optimizing.The method comprises the steps that a design domain and a non-design domain are defined according to the appearance requirement of the coordinate boring machine structure, and a thermal coupling finite element model is established; performing density filtering and projection on the design variable field to obtain a physical variable field, and parameterizing to represent a machine tool complete machine and component integrated model; establishing a design response of a mean value and a variance of the maximum displacement amplitudes of multiple working conditions; constructing a heat bearing stable structure topological optimization model for the high-precision coordinate boring machine; solving a finite element model under various thermal coupling working conditions, calculating each design response, and carrying out sensitivity analysis; and solving the topological optimization model by adopting a moving asymptote algorithm to obtain a topological optimization result. According to the method, the integral expression of the whole machine tool and the bearing part structure is applied to the structure topology optimization model, the multi-gear mechanical performance of a moving part is comprehensively considered, and the thermal bearing stability of an optimization result is improved.

Description

Technical Field

[0001] This invention relates to the field of machine tool structure topology optimization, and in particular to a method for optimizing the thermal load-bearing stable structure topology of a high-precision coordinate boring machine. Background Technology

[0002] High precision, high speed, and high stability are the eternal themes of precision machine tool research and development. Currently, the precision indicators of domestically produced machine tools are close to international advanced levels, but during long-term service, the precision of these machines deteriorates rapidly and significantly, resulting in insufficient precision retention. In complex thermal conditions during long-term service, insufficient thermal stability leads to large fluctuations in thermal deformation, causing a decline in precision over extended periods. Improving the thermal stability of machine tools is crucial for ensuring their precision retention. The thermal load stability of machine tools during long-term service is influenced by factors such as structural configuration, process control, thermal compensation, and the workshop environment. Among these, the structural configuration determines the thermal deformation of the machine tool under thermal conditions; improper configuration design easily leads to a decline in structural performance and is the core factor affecting the thermal load stability of machine tools.

[0003] Structural topology optimization methods can achieve rational and accurate material configuration within a given design space, based on established load conditions, constraints, and optimization objectives, to obtain structural configurations with superior performance. Due to its high degree of design freedom and ability to automate design, it has been widely applied in aerospace, complex equipment, and other fields in recent years, providing a new direction for designing high-performance components. It is a suitable design tool for machine tool structures considering thermal load stability. Existing research on structural topology optimization considering thermo-mechanical coupling establishes reasonable optimization models based on simplified heat sources or optimization objects, focusing on engineering requirements. Current research mainly focuses on improving the load-bearing capacity of machine tool structures.

[0004] To address the problem of machine tool structural optimization design, Chinese patent CN102063540 A discloses a method for optimizing the design of machine tool bed structures, which performs multi-objective optimization on the bed wall thickness and stiffener geometry. This method establishes a parametric model of the bed based on feature references, using bed mass, maximum deformation, maximum equivalent stress, and first and second natural frequencies as objective functions to establish a multi-objective optimization model. This invention improves the dynamic and static stiffness characteristics of the machine tool bed structure and reduces manufacturing costs. However, this invention only addresses the optimization design of the machine tool bed structure under specific working conditions and cannot universally solve the thermal load stability of machine tool structures under multiple working conditions. Especially considering the high sensitivity of machine tool structures to thermal influences, the thermal effects of their internal heat sources are closely related to machining conditions, and the external ambient temperature exhibits long-term fluctuations, there is still a lack of structural optimization design methods that consider the thermal load stability of machine tools under multiple working conditions.

[0005] Therefore, those skilled in the art are dedicated to developing a topology optimization method for thermally stable structures of high-precision coordinate boring machines. Summary of the Invention

[0006] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that the existing structural topology optimization design methods for machine tools are based on specific working conditions, do not consider the changes in the thermal effects of internal heat sources in the machine tool structure and the temperature fluctuation characteristics of the external environment, ignore the influence of internal and external heat sources under multiple working conditions, and usually aim at stiffness optimization, making it difficult to grasp the thermal load stability performance of the machine tool structure under multiple working conditions.

[0007] To achieve the above objectives, this invention provides a topology optimization method for the thermally load-bearing stable structure of a high-precision coordinate boring machine, the method comprising the following steps: S101: Based on the shape requirements of the coordinate boring machine structure, define the design domain and the non-design domain, and establish a thermo-coupled finite element model; S103: The design variable field is filtered by density and projected to obtain the physical variable field, which is parametrically represented as an integrated model of the machine tool and its components. S105: Based on the obtained physical variable field, establish the design response with mean and variance of the maximum displacement amplitude under multiple working conditions; S107: Constructing a topology optimization model for the thermal load-bearing stable structure of a high-precision coordinate boring machine; S109: Solve the finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions, calculate the design response, and perform sensitivity analysis; S111: The moving asymptote algorithm is used to solve the topology optimization model to obtain the topology optimization results that satisfy the constraints and convergence conditions.

[0008] Furthermore, in step S101, in the finite element model, all nodes on the bottom surface of the coordinate boring machine are fixed, a horizontal point load to the right is applied at a predetermined position on the top centerline of the coordinate boring machine, and various working conditions are determined based on the top surface temperature and bottom surface temperature of the coordinate boring machine.

[0009] Further, in step S103, the density filtering is performed using the following method:

[0010] in, For unit Design variable field, For unit Intermediate variable field, Representation unit The set of adjacent cells within a distance range of the filtering radius r. For unit coordinates For unit coordinates These are the coefficients of the weighting function.

[0011] Furthermore, in step S103, the projection is performed using the following method:

[0012] in, For unit Intermediate variable field, For unit Physical variable field, For unit identification, For projection threshold, The steepness of the projection.

[0013] Further, in step S103, the integrated model includes fixed components and moving components, and a design variable field is established for the fixed components and the moving components, wherein: The fixed components include a column and a bed, and the moving components include a worktable, a moving beam, and a spindle box. The design variable fields include the column and bed design variable fields, the worktable design variable fields, the moving beam design variable fields, and the spindle box design variable fields.

[0014] Furthermore, in step S103, a parameterized model of element density and stiffness is established using a penalized solid isotropic material method, and element density interpolation is integrated into the finite element analysis.

[0015] Further, in step S103, the interpolation model for the material's elastic modulus is:

[0016] in, For unit The elasticity matrix, To avoid minima introduced by the singularity of the matrix in the finite element solution, The elasticity matrix of the solid structure. This is the penalty value.

[0017] Further, step S105 includes the following sub-steps: S1051: Calculate the maximum displacement amplitude of the structure in the target region under a single load condition:

[0018] S1052: Construct the mean response and variance response of the maximum displacement amplitude under multiple working conditions;

[0019]

[0020] S1053: Establish the overall volume constraints of the design domain required for optimization:

[0021] in, For the design domain, The total number of design domain units, For unit identification, For unit displacement amplitude, As a characterization unit A column vector representing the activation status of the core region. For the P-norm parameter, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For operating condition indication, For the number of working conditions, For the overall volume, This represents the upper limit of the overall volume fraction.

[0022] Further, in step S107, the topology optimization model is:

[0023]

[0024]

[0025]

[0026]

[0027] in, This is a weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions. As a weighting factor, This is the average of the maximum displacement amplitude under multiple working conditions. The variance of the maximum displacement amplitude under multiple working conditions. Due to overall volume constraints, Here is the thermal stiffness matrix. For temperature field, For thermal load, Here is the stiffness matrix. For displacement field, For external mechanical loads, This is the thermal expansion load.

[0028] Furthermore, in step S109, during the sensitivity analysis, the analytical sensitivity formula of the objective function to the design variables is derived as follows:

[0029]

[0030]

[0031] norm For design variables The sensitivity is:

[0032] in, Let be the objective function. For design variables, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For unit identification, This represents the number of units.

[0033] In a preferred embodiment of the present invention, compared with the prior art, the following advantages are achieved: 1. This invention constructs the maximum displacement amplitude response of the core region under multiple working conditions, and considers the variance of the maximum displacement amplitude of the core region under multiple working conditions in the structural topology optimization model. By minimizing the weighted value of the mean and variance, the thermal load stability of the optimization result is improved. Compared with the single working condition optimization result, the machine tool structure optimized by this patent method has stable deformation fluctuation in the core region under the thermo-mechanical coupling multi-working condition environment, and has thermal load stability. 2. This invention integrates the structure of the machine tool and the load-bearing components into a structural topology optimization model, thereby obtaining an optimized structure that considers the changes in multiple positions of the moving parts of the machine tool. It comprehensively considers the mechanical performance of the moving parts in multiple positions and has thermal load-bearing stability under multiple positions of the moving beam and spindle box. 3. For coordinate boring machines operating in complex environments with multiple gear positions and thermo-coupling conditions, this invention employs a structural topology optimization design method to obtain a machine tool structure with stable thermal load under multiple gear positions and conditions. This can shorten the design cycle, achieve reasonable material allocation within the design domain of the coordinate boring machine, and improve the thermal load stability of the machine tool structure.

[0034] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0035] Figure 1 This is a step diagram of a preferred embodiment of the thermal load-bearing stable structure topology optimization method for high-precision coordinate boring machines; Figure 2 This is a flowchart of a preferred embodiment of the method for optimizing the topology of a thermally load-bearing stable structure for a high-precision coordinate boring machine. Figure 3 This is a schematic diagram of an integrated parametric modeling of a machine tool and its components according to a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of the overall structural design domain, loads, and boundary conditions of a preferred embodiment of the present invention; Figure 5 This is a schematic diagram comparing the overall structure of the machine under different operating conditions and without considering thermal load stability, according to a preferred embodiment of the present invention. Figure 6 This is a schematic diagram of the overall structural design domain and the optimization results considering the thermal load stability under multiple operating conditions, according to a preferred embodiment of the present invention. Detailed Implementation

[0036] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0037] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0038] like Figure 1 , Figure 2 As shown, existing structural topology optimization design methods for machine tools focus on specific working conditions, failing to consider the changes in the thermal effects of internal heat sources and the temperature fluctuations of the external environment. They also ignore the influence of multiple working conditions on internal and external heat sources. Typically, they aim at stiffness optimization, making it difficult to grasp the thermal load stability performance of machine tool structures under multiple working conditions. This invention provides a thermal load stability structural topology optimization method for high-precision coordinate boring machines, aiming to obtain a thermally stable machine tool structure under multi-working-condition thermo-mechanical coupling.

[0039] The method includes the following steps: S101: Based on the shape requirements of the coordinate boring machine structure, define the design domain and the non-design domain, and establish a thermo-mechanical coupled finite element model.

[0040] In this embodiment, based on the shape requirements of the coordinate boring machine structure, the design domain and non-design domain of the structure are defined. Based on the actual working conditions of the structure, the loads and boundary conditions are determined, a finite element model is established, and optimization parameters and design variables are completed. Initialization.

[0041] In this embodiment, in the finite element model, all nodes on the bottom surface of the coordinate boring machine are fixed, a horizontal point load to the right is applied at a predetermined position on the top centerline of the coordinate boring machine, and various working conditions are determined based on the top and bottom surface temperatures of the coordinate boring machine.

[0042] S103: The design variable field is filtered by density and projected to obtain the physical variable field, which is then parametrically represented as an integrated model of the machine tool and its components.

[0043] In this embodiment, based on the density filtering formula and the Heaviside projection formula, the design variable field is sequentially... The intermediate variable field is obtained after density filtering. Then, the physical variables are obtained from the projection. A penalized solid isotropic material method (SIMP) is used to establish a parametric model of element density and stiffness, and element density interpolation is integrated into the finite element analysis.

[0044] In this embodiment, the density filtering formula is as follows:

[0045] in, For unit Design variable field, For unit Intermediate variable field, Representation unit The set of adjacent cells within a distance range of the filtering radius r. For unit coordinates For unit coordinates These are the coefficients of the weighting function.

[0046] The Heaviside projection formula is as follows:

[0047] in, For unit Intermediate variable field, For unit Physical variable field, For unit identification, For projection threshold, The steepness of the projection.

[0048] When performing parametric representation of the integrated model of the machine tool and its components, the integrated model includes fixed parts and moving parts, and design variable fields are established for the fixed parts and moving parts, wherein: Fixed components include the column and bed, while moving components include the worktable, moving beam, and spindle box; The design variable fields include multiple fields: column and bed design variable fields, worktable design variable fields, moving beam design variable fields, and spindle box design variable fields.

[0049] In this embodiment, element density interpolation modeling is used, and a penalized solid isotropic material method is adopted to establish a parameterized model of element density and stiffness, integrating element density interpolation into finite element analysis.

[0050] The interpolation model for the elastic modulus of a material is:

[0051] in, For unit The elasticity matrix, To avoid minima introduced by the singularity of the matrix in the finite element solution, The elasticity matrix of the solid structure. This is the penalty value.

[0052] S105: Based on the obtained physical variable field, establish the design response with mean and variance of the maximum displacement amplitude under multiple working conditions.

[0053] In this embodiment, after obtaining the physical variable field, it is necessary to model and constrain the mean and variance responses of the maximum displacement amplitude under multiple working conditions, calculate the maximum displacement amplitude of the structure in the target region under a single working condition, and on this basis, construct the mean response of the maximum displacement amplitude under multiple working conditions respectively. and variance response of maximum displacement amplitude under multiple operating conditions Among them, the response It can assess the thermal load stability of the structure and establish an overall volume constraint model for the coordinate boring machine design domain.

[0054] Specifically, it includes the following sub-steps: S1051: Calculate the maximum displacement amplitude of the structure in the target region under a single load condition:

[0055] S1052: Construct the mean response and variance response of the maximum displacement amplitude under multiple working conditions;

[0056]

[0057] S1053: Establish the overall volume constraints of the design domain required for optimization:

[0058] in, For the design domain, The total number of design domain units, For unit identification, For unit displacement amplitude, As a characterization unit A column vector representing the activation status of the core region. For the P-norm parameter, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For operating condition indication, For the number of working conditions, For the overall volume, This represents the upper limit of the overall volume fraction.

[0059] S107: Construct a topology optimization model for thermally stable structures of high-precision coordinate boring machines.

[0060] When establishing a topology optimization model for a thermally stable structure oriented towards a coordinate boring machine, the objective function is to minimize the weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions, ensuring the overall volume constraint of the structure. The constraints are met.

[0061] In this embodiment, the topology optimization model is:

[0062]

[0063]

[0064]

[0065]

[0066] in, This is a weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions. As a weighting factor, This is the average of the maximum displacement amplitude under multiple working conditions. The variance of the maximum displacement amplitude under multiple working conditions. Due to overall volume constraints, Here is the thermal stiffness matrix. For temperature field, For thermal load, Here is the stiffness matrix. For displacement field, For external mechanical loads, This is the thermal expansion load.

[0067] S109: Solve the finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions, calculate the design response, and perform sensitivity analysis.

[0068] In this embodiment, based on the structural density information under the current optimization iteration step, and considering the loads and boundary conditions under multiple working conditions, a finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions is established to obtain structural deformation information. Then, the mean response of the maximum displacement amplitude under multiple working conditions within the target area is calculated. and variance response Simultaneously, the constraint function response is calculated to complete the design response solution.

[0069] After solving for the design responses, sensitivity analysis needs to be performed on each design response. This involves analyzing the impact of each design response on the design variables. The analytical sensitivity formula is used to solve for the objective function and the effect of each constraint function on the design variables in the current iteration step. The differential sensitivity value.

[0070] When performing sensitivity analysis, the objective function For design variables The derivation of the analytical sensitivity formula is as follows:

[0071]

[0072]

[0073] norm For design variables The sensitivity is:

[0074] in, Let be the objective function. For design variables, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For unit identification, This represents the number of units.

[0075] S111: The moving asymptote algorithm is used to solve the topology optimization model, and the topology optimization results that satisfy the constraints and convergence conditions are obtained.

[0076] In this embodiment, the Moving Asymptote Algorithm (MMA) is used to solve the optimization function, thereby solving the topology optimization model of the thermally stable structure oriented towards the coordinate boring machine, and updating the design variables. .

[0077] Determine if the convergence condition is met; if not, repeat the optimization steps. The objective function's rate of change is less than 0.2% within the current 5 iterations, and the projection sharpness of the Heaviside function used for parameterization is [value missing]. As the optimization iterations reach the preset maximum value... If the convergence condition is not met, repeat steps S105-S111 until the convergence condition is met.

[0078] For the optimization results with a small number of gray units, a projection method with a density field threshold of 0.5 is used to convert the gray optimization results into optimization results with a density of 0 or 1, thereby obtaining a coordinate boring machine optimization structure that meets the thermal load stability performance.

[0079] Compared with existing technologies, the thermal load-bearing stability structure topology optimization method for high-precision coordinate boring machines provided in this invention has the following characteristics: 1. Existing structural topology optimization design methods for machine tools primarily focus on specific operating conditions, neglecting the variations in thermal effects of internal heat sources and the temperature fluctuations of the external environment. They ignore the impact of multiple operating conditions on internal and external heat sources and typically prioritize stiffness optimization, making it difficult to grasp the thermal load stability of the machine tool structure under various operating conditions. This invention addresses the complex multi-operating conditions of coordinate boring machine structures with thermo-mechanical coupling. It uses the weighted average of the mean and variance of the maximum displacement amplitude under multiple operating conditions as the objective function, integrating this into the topology optimization model. This yields a machine tool structure with thermal load stability that considers thermo-mechanical coupling under multiple operating conditions. By constructing the maximum displacement amplitude response of the core region under multiple operating conditions and considering the variance of the maximum displacement amplitude of the core region under multiple operating conditions in the structural topology optimization model, the thermal load stability of the optimization result is improved by minimizing the weighted average of the mean and variance. Compared with single-condition optimization results, the machine tool structure optimized by this invention exhibits stable deformation fluctuations in its core region under thermo-mechanical coupling multi-operating conditions, demonstrating thermal load stability.

[0080] 2. Existing structural topology optimization design methods for machine tools only address the fixed positions of the moving beam and spindle box of coordinate boring machines, and do not yet include a thermally stable structural design method that considers the changing positions of the moving parts. This invention constructs a parametric model of the coordinate boring machine and its load-bearing components within a topology optimization model, achieving integrated design of the entire machine tool and its components. This breaks through the traditional design approach that only considers the fixed positions of the moving parts, resulting in a structural configuration with superior mechanical performance that considers multiple positions of the moving parts. This invention integrates the structure of the entire machine tool and its load-bearing components into a structural topology optimization model, obtaining an optimized structure that considers multiple positions of the moving parts. This invention comprehensively considers the mechanical performance of the moving parts across multiple positions, and the optimized machine tool structure exhibits thermal stability under multiple positions of the moving beam and spindle box.

[0081] 3. Existing traditional machine tool structure optimization design methods rely on the designer's experience, requiring repeated trial and error iterations, resulting in long design cycles and high material redundancy. This invention utilizes a simulation-driven structural topology optimization design method to optimize the structure of coordinate boring machines. It can achieve a rational allocation of materials within the design domain of the coordinate boring machine while meeting the design constraints of the coordinate boring machine's multi-condition thermo-coupling environment. For the complex service environment of coordinate boring machines with multiple gear positions and thermo-coupling conditions, a structural topology optimization design method is employed to obtain a machine tool structure with stable thermal load under multiple gear positions and conditions. Compared with existing traditional machine tool structure optimization design methods, this invention can shorten the design cycle, achieve a rational allocation of materials within the coordinate boring machine's design domain, and improve the thermal load stability of the machine tool structure.

[0082] The present invention will now be described in detail with reference to preferred embodiments.

[0083] like Figure 1 , Figure 2 As shown, this invention provides a topology optimization method for thermally stable structures of high-precision coordinate boring machines, aiming to obtain thermally stable machine tool structures under multi-condition thermo-mechanical coupling environments, and includes the following steps: Step 1: Parameter initialization.

[0084] Based on the shape requirements of the coordinate boring machine structure, the design domain and non-design domain of the structure are defined; based on the actual working conditions of the structure, the loads and boundary conditions are determined, and a finite element model is established; the optimization parameters and design variables are initialized.

[0085] like Figure 4 As shown, the dimensions are defined as The overall design domain of the inverted L-shaped coordinate boring machine, of which the bed area is The outer contour of the whole machine is arranged with The non-design domains are marked as the core optimization areas, along with the column guide rails and bed guide rails.

[0086] A finite element model is established, with all nodes on the bottom surface fixed, and a horizontal point load is applied to the right at a point 1 / 5 of the side length downwards from the top centerline. .

[0087] Temperature boundary of the top surface of the whole machine Bottom surface temperature boundary Three operating conditions are designed in total: Operating Condition 1: ; Operating Condition 2: ; Operating Condition 3: .

[0088] The optimization parameters are initialized as follows: Overall volume fraction upper limit The density filter and weighting coefficients are respectively The material is low-carbon steel Q235, with an elastic modulus of [missing value]. Poisson's ratio thermal conductivity coefficient of thermal expansion The maximum sharpness of the Heaviside function. .

[0089] Step 2: Element density interpolation modeling.

[0090] Based on the density filtering formula and the Heaviside projection formula, the design variable fields are sequentially... The intermediate variable field is obtained after density filtering. Then, the physical variables are obtained from the projection. A penalized solid isotropic material method (SIMP) is used to establish a parametric model of element density and stiffness, and element density interpolation is integrated into the finite element analysis.

[0091] like Figure 3 As shown, design variable field The intermediate variable field is obtained after density filtering. Then, the physical variables are obtained from the projection. The expressions for density filtering and projection are as follows:

[0092] in, Representation unit The set of adjacent cells within a distance range of filter radius r. For unit The coordinates; These are the coefficients of the weighting function; The projection threshold; The projection steepness is used to ensure smooth convergence during the optimization process. The projection sharpness parameter... It gradually changes from the initial value to the maximum value.

[0093] Based on this, considering the multi-position changes of the various load-bearing components of the machine tool during actual machining and service, each component is divided into fixed parts and moving parts. The column and bed are fixed parts, while the worktable, moving beam, and spindle box are moving parts. Based on the above parametric model, four types of design variable fields are established. , , , The design space for the columns and bed frame is The design space of the workbench is... The design space for the field and the moving beam is The design space of the spindle box is... The four types of design variable fields were then subjected to density filtering and projection to obtain four types of physical variables. , , , The assembly forms the complete machine tool model. Simultaneously, as the moving beam and worktable components change positions, the overall machine design space is dynamically constructed.

[0094] Based on the above variable field, an interpolation model for the elastic modulus of QT600-3 material is established using the SIMP (Solid Isotropic Material with Penalization) formula:

[0095] in, To avoid the minimum value introduced by the singularity of the matrix in the finite element solution; is the elasticity matrix of the solid structure; p is the penalty value, usually taken as 3.

[0096] Step 3: Modeling the mean and variance response of the maximum displacement amplitude under multiple working conditions and modeling the constraints.

[0097] The maximum displacement amplitude of the structure in the target region under a single working condition is calculated. Based on this, the mean response of the maximum displacement amplitude under multiple working conditions is constructed. and variance response of maximum displacement amplitude under multiple operating conditions Among them, the response It can assess the thermal load stability of the structure and establish an overall volume constraint model for the coordinate boring machine design domain.

[0098] In obtaining physical variable fields Based on this, the mean and variance responses of the maximum displacement amplitude under multiple working conditions are established. The specific process is as follows: First, calculate the maximum displacement amplitude of the structure in the target area under a single working condition j.

[0099]

[0100] Where n is the total number of design domain elements; This refers to the displacement amplitude; This is a column vector representing the activation status of the core region. The cell is marked as 1 if it belongs to the core region, and 0 otherwise. For the P-norm parameter, .

[0101] Based on this, mean responses of the maximum displacement amplitude under multiple working conditions are constructed respectively. and variance response of maximum displacement amplitude under multiple operating conditions .

[0102]

[0103] Where N=3 represents the number of operating conditions.

[0104] Based on this, establish the constraint model required for optimization, such as the overall volume constraint.

[0105] Step 4: Topology optimization modeling.

[0106] A topology optimization model for the thermally stable structure of a coordinate boring machine is established. The objective function is to minimize the weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions, while ensuring the overall volume constraint of the structure. The constraints are met.

[0107] Establish a topology optimization model for the thermal load-bearing stability structure of a high-precision coordinate boring machine:

[0108] in, It is a weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions. =0.3 is the weighting factor. This is the average of the maximum displacement amplitude under multiple working conditions. The variance of the maximum displacement amplitude under multiple working conditions; The overall volume is constrained. The displacement response is determined by first solving the temperature field. Then solve for the displacement field. get.

[0109] Step 5: Design response solution.

[0110] Based on the structural density information at the current optimization iteration step, and considering the loads and boundary conditions under multiple working conditions, a finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions is established to obtain structural deformation information. Then, the mean response of the maximum displacement amplitude under multiple working conditions within the target area is calculated. and variance response Simultaneously, the constraint function response is calculated.

[0111] Based on the density information of the structure under the current optimization iteration step, and considering the loads and boundary conditions under multiple working conditions, a finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions is established to obtain structural deformation information, and then the objective function and constraint function are calculated.

[0112] Step 6: Sensitivity analysis.

[0113] Based on each design response, the design variables The analytical sensitivity formula is used to solve for the objective function and the effect of each constraint function on the design variables in the current iteration step. The differential sensitivity value.

[0114] objective function For design variables The derivation of the analytical sensitivity formula is as follows:

[0115]

[0116]

[0117] Among them, the P norm For design variables Sensitivity:

[0118] Among them, displacement is a design variable The sensitivity is obtained by solving the adjoint equation.

[0119] Step 7: Optimize the solution.

[0120] Using the Moving Asymptote Algorithm (MMA), the topology optimization model of the thermally stable structure for a coordinate boring machine is solved, and the design variables are updated. .

[0121] Step 8: Convergence conditions.

[0122] The rate of change of the objective function is less than 0.2% within the current 5 iterations, and the projected sharpness of the Heaviside function used for parameterization is... As the optimization iterations reach the preset maximum value... If the convergence condition is not met, repeat steps 3-7.

[0123] This invention employs the Moving Moving Asymptote Algorithm (MMA) to solve the topology optimization model, obtaining topology optimization results that satisfy the constraints and convergence conditions, such as... Figure 5 As shown in (a). For comparison, Figure 5 (b), (c), and (d) represent the overall structural optimization results with the objective function of minimizing the maximum displacement amplitude under a single working condition (for three working conditions in total). These results do not consider the thermal load stability.

[0124] Step 9: Post-processing.

[0125] After executing steps 1-8, an optimization result with a small number of grayscale units is obtained. Using a projection method with a density field threshold of 0.5, the grayscale optimization result is converted into an optimization result with a density of 0 or 1.

[0126] Simulation results show that the maximum displacement amplitudes considering thermal stability under the three operating conditions are 112.47 μm, 112.19 μm, and 113.18 μm, with a variance of 0.417. In contrast, the variances of the single-condition optimization results without considering thermal stability under the three operating conditions are 1.183, 2.286, and 6.292, respectively. Compared with the single-condition optimization results without considering thermal stability, this optimization method reduces the variance by 64.8%.

[0127] In addition, such as Figure 6 The diagram shown is a schematic representation of the 3D overall structure design domain and the optimization results considering thermal load stability under multiple operating conditions in an example of this invention. Figure 6 In section (a), the 3D overall structure design domain is shown. Figure 6 (b) shows the 3D whole machine optimization result. The optimization implementation method follows steps 1 to 9.

[0128] Compared with existing technologies, this invention integrates the machine tool and its load-bearing components into a structural topology optimization model to obtain an optimized structure that considers the multi-position changes of the machine tool's moving parts. Compared with traditional optimization designs that focus on the fixed positions of the moving beam and spindle box of coordinate boring machines, this invention comprehensively considers the mechanical properties of the moving parts at multiple positions, resulting in a machine tool structure with thermal load stability under multiple positions of the moving beam and spindle box. Furthermore, this invention considers the variance of the maximum displacement amplitude in the core region under multiple working conditions in the structural topology optimization model, improving the thermal load stability of the optimization results. Compared with existing machine tool structure topology optimization design methods that primarily focus on specific working conditions, the machine tool structure optimized using this invention exhibits stable deformation fluctuations in its core region under thermo-mechanical coupling multi-working-condition environments, demonstrating better thermal load stability.

[0129] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for optimizing the topology of a thermally load-bearing stable structure for a high-precision coordinate boring machine, characterized in that, The method includes the following steps: S101: Based on the shape requirements of the coordinate boring machine structure, define the design domain and the non-design domain, and establish a thermo-coupled finite element model; S103: The design variable field is filtered by density and projected to obtain the physical variable field, which is parametrically represented as an integrated model of the machine tool and its components. S105: Based on the obtained physical variable field, establish the design response with mean and variance of the maximum displacement amplitude under multiple working conditions; S107: Constructing a topology optimization model for the thermal load-bearing stable structure of a high-precision coordinate boring machine; S109: Solve the finite element model of the coordinate boring machine structure under various thermo-mechanical coupling conditions, calculate the design response, and perform sensitivity analysis; S111: The moving asymptote algorithm is used to solve the topology optimization model to obtain the topology optimization results that satisfy the constraints and convergence conditions.

2. The method as described in claim 1, characterized in that, In step S101, in the finite element model, all nodes on the bottom surface of the coordinate boring machine are fixed, a horizontal point load to the right is applied at a predetermined position on the top centerline of the coordinate boring machine, and various working conditions are determined based on the top surface temperature and bottom surface temperature of the coordinate boring machine.

3. The method as described in claim 2, characterized in that, In step S103, the density filtering is performed using the following method: in, For unit Design variable field, For unit Intermediate variable field, Representation unit The set of adjacent cells within a distance range of the filtering radius r. For unit coordinates For unit coordinates These are the coefficients of the weighting function.

4. The method as described in claim 3, characterized in that, In step S103, the projection is performed using the following method: in, For unit Intermediate variable field, For unit Physical variable field, For unit identification, For projection threshold, The steepness of the projection.

5. The method as described in claim 4, characterized in that, In step S103, the integrated model includes fixed components and moving components, and a design variable field is established for the fixed components and the moving components, wherein: The fixed components include a column and a bed, and the moving components include a worktable, a moving beam, and a spindle box. The design variable fields include the column and bed design variable fields, the worktable design variable fields, the moving beam design variable fields, and the spindle box design variable fields.

6. The method as described in claim 5, characterized in that, In step S103, a parameterized model of element density and stiffness is established using a penalized solid isotropic material method, and element density interpolation is integrated into the finite element analysis.

7. The method as described in claim 6, characterized in that, In step S103, the interpolation model for the material's elastic modulus is: in, For unit The elasticity matrix, To avoid minima introduced by the singularity of the matrix in the finite element solution, The elasticity matrix of the solid structure. This is the penalty value.

8. The method as described in claim 7, characterized in that, Step S105 includes the following sub-steps: S1051: Calculate the maximum displacement amplitude of the structure in the target region under a single load condition: S1052: Construct the mean response and variance response of the maximum displacement amplitude under multiple working conditions; S1053: Establish the overall volume constraints of the design domain required for optimization: in, For the design domain, The total number of design domain units, For unit identification, For unit displacement amplitude, As a characterization unit A column vector representing the activation status of the core region. For the P-norm parameter, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For operating condition indication, For the number of working conditions, For the overall volume, This represents the upper limit of the overall volume fraction.

9. The method as described in claim 8, characterized in that, In step S107, the topology optimization model is: in, This is a weighted average of the mean and variance of the maximum displacement amplitude under multiple working conditions. As a weighting factor, This is the average of the maximum displacement amplitude under multiple working conditions. The variance of the maximum displacement amplitude under multiple working conditions. Due to overall volume constraints, Here is the thermal stiffness matrix. For temperature field, For thermal load, Here is the stiffness matrix. For displacement field, For external mechanical loads, This is the thermal expansion load.

10. The method as described in claim 9, characterized in that, In step S109, during the sensitivity analysis, the analytical sensitivity formula of the objective function to the design variables is derived as follows: norm For design variables The sensitivity is: in, Let be the objective function. For design variables, This is the average response of the maximum displacement amplitude under multiple operating conditions. The variance response of the maximum displacement amplitude under multiple operating conditions. For unit identification, This represents the number of units.

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