A part structure topology optimization method with geometric characteristics and manufacturing process constraints

Abstract

The application belongs to the field of equipment structure topology optimization and processing, and discloses a part structure topology optimization method with geometric characteristics and manufacturing process constraints, a topology optimization method based on double constraints and dynamic punishment, and the key lies in that according to the manufacturing process constraints, the overhanging angle of additive manufacturing and the wall thickness of machining are taken as the punishment items and embedded in the objective function of optimization in advance, the influence of different constraints is balanced by dynamically adjusting the punishment factor, and finally the optimization structure meeting the mechanical performance and process manufacturing constraints is designed through multiple rounds of iterative optimization and feedback correction.

Description

Technical Field

[0001] This invention belongs to the field of equipment structure topology optimization and processing, and particularly relates to a part structure topology optimization method based on geometric features and manufacturing process constraints. Background Technology

[0002] Currently, the main technical solutions in the field of structural topology optimization are based on density methods or level set methods to achieve lightweight design. The core idea is to improve structural stiffness or reduce material deformation by adjusting the material distribution within the design region through finite element analysis and iterative calculations. Common density methods simulate material distribution using a continuous density field (0 for cavities, 1 for solids), rely on image-like filtering techniques to suppress numerical noise, and then generate the structural profile through threshold projection. However, this method is prone to boundary blunting due to over-smoothing. Level set methods define boundaries using implicit function zero isosurfaces and drive the boundaries through velocity fields. While this can create naturally transitioning geometric shapes, it is sensitive to the initial shape and requires repeated function resetting, increasing computational costs. Most current topology optimization methods do not incorporate manufacturing process constraints (such as overhang angles in additive manufacturing and wall thickness in machining) into the optimization design process simultaneously. This can lead to excessively large overhang angles and unmanufacturable thin-walled structures after optimization, requiring manual repair through post-processing. This "optimize first, process later" approach typically prolongs the development cycle and disrupts the integrity of structural force transmission paths, resulting in localized stress concentrations. It can even trigger interlayer separation and collapse during manufacturing. For example, patent CN117574543A discloses a spacecraft support topology design method based on additive manufacturing process constraints, which considers these constraints and smooths the results after optimization. Furthermore, traditional methods lack effective locking mechanisms during the optimization iteration of some key assembly hole features, easily leading to positional offsets or geometric deformations that affect the assembly accuracy of parts. When dealing with the transition between the design space and the non-design space, the discontinuity of the boundary function easily leads to stress abrupt change zones at the material-non-material interface, significantly reducing the fatigue resistance of the structure. Furthermore, conventional filtering techniques lack sufficient control over the minimum feature size, resulting in numerous unstable thin-walled or fragmented structures in the optimization results. These structures are prone to deformation and instability under dynamic conditions, threatening the long-term operational reliability of equipment in harsh environments. These shortcomings collectively limit the application value of topology optimization technology in high-precision, high-reliability equipment components. Summary of the Invention

[0003] The technical problem to be solved by this invention is: how to design an optimized structure that simultaneously satisfies mechanical performance and manufacturing constraints.

[0004] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows: A method for topology optimization of part structures constrained by geometric features and manufacturing processes includes the following steps: S1. Initialization: Define the design domain and non-design domain, and identify key geometric feature constraint domains. Set minimum wall thickness Maximum overhang angle Grid size ; S2. Construct a composite objective function:

[0005] in, It is a structural performance target. It is a structural wall thickness constraint penalty term. It is a penalty term for the overhang angle constraint. These are the dynamic penalty factors for constrained wall thickness and overhang angle, respectively; S3. Iterative optimization: Lock the geometric feature constraint domain, calculate and correct the objective function and sensitivity, dynamically update the penalty factor, and terminate the iteration after the convergence condition is met. S4. Boundary transition processing: After the penalty term converges, the radial gradient field is activated to achieve a smooth transition between the design domain and the non-design domain. S5, Post-Repair: Maintaining Under the premise of unchanged node coordinates, geometric filtering is used to repair the non-compliant areas of thin walls and overhang angles; S6. Output results: Output the topology optimization structure that satisfies geometric feature locking, process constraints and boundary continuity.

[0006] Furthermore, the wall thickness constraint penalty term Through the gradient magnitude of the level set function Map local wall thickness and base it on a minimum wall thickness threshold.

[0007]

[0008] in , It is a grid size correlation factor. ; and then This is the penalty index.

[0009] Furthermore, the hanging angle constraint penalty term via boundary normal vector With manufacturing printing direction inner product Constrain the overhang angle and introduce a smooth transition function. Control the scope of punishment:

[0010] , in For the transition steepness parameter, The penalty intensity index is initialized. This is the critical overhang angle.

[0011] Furthermore, the dynamic penalty factor is characterized in that... Adopt a tiered update strategy: Step 301: Build Bayesian prior distribution ,in , The molten pool coefficient of the material; Step 302: Update the distribution based on MCMC sampling, with sampling weights determined by the target sensitivity. With constraint violation Joint decision; Step 303: Generate cooperative functions , The spatial average value of the gradient magnitude within the design domain reflects the structural boundary complexity. It is a coordination coefficient used to dynamically adjust the weight of manufacturing process constraints in the topology optimization objective function, with a value range of... ,initialization The overhang angle threshold; Step 304: Adjust using a tiered strategy The global layer updates the Bayesian prior parameters every 10 steps; the local layer is scaled appropriately using a proportional method. ,but ;like ,but ; Step 305: Convergence check. If the convergence is satisfied for 10 consecutive steps... Freeze .

[0012] Furthermore, after the penalty term in step S3 converges, a smoothing process is performed between the optimized design domain and the non-design domain, including the following steps: Step 401: Construct a radial transition region between the design domain and the non-design domain, with the density distribution function being...

[0013] in, Density of the material at the edge of the mounting hole; To design the target density; To calculate the distance from the point to the center of the hole; The radius of the mounting hole; The width of the transition zone is 1.5 to 2 times the aperture. For gradient regulation index; Step 402: Transform the draft constraint into a vector field equation; Step 403: Achieve material property transition through nodal variable interpolation.

[0014] Furthermore, the geometric feature locking is achieved through the following steps: identifying bolt holes, mounting surfaces, and substrate contours; constructing a boundary normalized distance; and correcting the sensitivity with an exponentially decaying field.

[0015] Furthermore, the post-repair includes: Thin-walled repair: Identifying thicknesses less than In areas where the material density is increased, the thickness is enhanced. Overhang Angle Correction: Detects whether there are excessively large overhang angles in the optimization results, and corrects angles exceeding the maximum allowable angle through geometric transformation. Adjust the overhang area; The repair process remains The coordinates of the internal nodes remain unchanged.

[0016] Furthermore, the optimized key indicators meet the following requirements: bolt hole deformation ≤ 0.05 mm, substrate flatness ≤ 0.08 mm.

[0017] Furthermore, the method is applicable to the topology optimization of parts in additive manufacturing and machining composite processes, and can simultaneously satisfy the minimum wall thickness and overhang angle manufacturing constraints.

[0018] This invention offers the following advantages: By embedding manufacturing process constraints into the topology optimization process, it achieves integrated design and manufacturing technologies. Distance field-driven dynamic locking technology effectively ensures the geometric accuracy of key assembly features; the early introduction of additive manufacturing overhang constraints and machining wall thickness control significantly improves part manufacturability; gradient control mechanisms eliminate stress abrupt changes at design boundaries, and hybrid filtering strategies effectively suppress the generation of thin-walled structures. This method greatly reduces manual repair work after optimization, ensuring the integrity of the structure along the force transmission path and the manufacturability of the parts. Attached Figure Description

[0019] Figure 1 This is a flowchart of the topology optimization design method; Figure 2 This is a schematic diagram of the penalty mechanism for the composite objective function; Figure 3 This is a schematic diagram of the radial gradient field; Figure 4 It is a geometric dynamic feature locking map; Figure 5 It is a double-repaired image. Detailed Implementation

[0020] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0021] This embodiment presents a topology optimization design method for part structures based on geometric features and manufacturing process constraints. It utilizes distance-field driven dynamic locking technology to ensure the pose accuracy of key assembly features (such as bolt holes and mounting surfaces). Simultaneously, it embeds additive manufacturing overhang constraints and machining wall thickness control requirements into the objective function beforehand. Furthermore, it employs gradient modulation to eliminate abrupt stress changes at the design / non-design domain interfaces and constructs a hybrid filtering strategy to suppress the generation of thin-walled structures. Ultimately, it achieves four-dimensional synergy in topology optimization: geometric feature protection, process constraint satisfaction, boundary structure continuity, and dimensional stability control. This reduces post-processing after optimization, realizes integrated "design-manufacturing" design for special equipment components, improves optimization design efficiency, and ensures part reliability.

[0022] The topology optimization method based on dual constraints and dynamic penalties is key to embedding the overhang angle of additive manufacturing and the wall thickness of machining as penalty terms into the objective function of optimization in advance according to the manufacturing process constraints. The penalty factor is dynamically adjusted to balance the influence of different constraints. Through multiple rounds of iterative optimization and feedback correction, an optimized structure that simultaneously satisfies mechanical performance and manufacturing process constraints is finally designed.

[0023] The smooth transition between the optimized design space and the non-design space is achieved by automatically activating the radial gradient field after the penalty term converges. A transition zone is constructed based on elasticity principles, and the density parabolic gradient is achieved using an exponential function to combine the edge density of the mounting holes and the target density. The draft constraint is transformed into a vector equation, and the checkerboard effect is suppressed through nodal interpolation combined with a power function, thus realizing gradient fusion between the design space and the non-design space.

[0024] The boundary processing based on geometric feature constraints is used for optimizing initially designed parts. Due to installation and other requirements, the geometric features of the part's dimensional boundaries and critical dimensions cannot be changed. This provides a method for dynamically locking critical boundary dimensions during topology optimization by defining geometric constraint domains. The boundary distance field is constructed, and the sensitivity field is dynamically corrected to achieve precise control of key dimensions.

[0025] The geometric filtering method addresses the possibility that the optimization results may contain a few areas that do not meet manufacturing characteristics (such as extremely thin sections or excessively large overhang angles). While keeping the node coordinates within the domain unchanged, geometric filtering is used to repair them, thereby satisfying the characteristics of manufacturing constraints.

[0026] This embodiment, in conjunction with specific parameters, elaborates on the implementation steps of the above optimization method as follows: S1. Initialization Settings (1) Define the design domain and non-design domain (such as unmodifiable areas such as assembly holes and mounting surfaces); (2) Identify key geometric feature constraint domains (Bolt holes, substrate outline, etc.); (3) Set process parameters: minimum wall thickness Maximum overhang angle Grid size .

[0027] S2. Constructing a composite objective function (1) Define the objective function: Specifically, a penalty term for thickness and overhang angle constraints is introduced into the objective function to construct a composite objective function:

[0028] in, .

[0029] Specifically:

[0030]

[0031] .

[0032]

[0033]

[0034]

[0035] Minimum wall thickness threshold =1.0mm, which meets the minimum process requirements for structural components of special military equipment according to ISO 2768-mK precision machining standards; T max The value of 5mm is obtained from the formula for the critical thickness of thin plate instability. cr

[0036] Verification (D is the bending stiffness coefficient, E is the elastic modulus, (Poisson's ratio), to avoid deformation of the optimized structure during processing.

[0037]

[0038] S3, Iterative Optimization Loop Transition steepness parameters and penalty intensity index Dynamically adjust with each iteration step: ,

[0039] in, The number of iterations, the initial value. .

[0040] The normal vector After Gaussian filtering, the filter radius is The filter function is: .

[0041] The dynamic penalty factor is dynamically updated through a hierarchical strategy, and the specific steps are as follows: Step 3.1: Building Bayesian prior distribution ,in , The molten pool coefficient of the material (steel) Titanium alloy ); Step 3.2: Update the distribution based on MCMC sampling, with sampling weights determined by the target sensitivity. With constraint violation Joint decision; Step 3.3: Generate Cooperative Functions , The spatial average value of the gradient magnitude within the design domain reflects the structural boundary complexity. It is a coordination coefficient used to dynamically adjust the weight of manufacturing process constraints in the topology optimization objective function, with a value range of... ,initialization The overhang angle threshold; Step 3.4: Adjust using a tiered strategy The global layer updates the Bayesian prior parameters every 10 steps; the local layer is scaled appropriately using a proportional method. ,but ,like ,but ; Step 3.5: Convergence check. If the convergence is satisfied for 10 consecutive steps... Freeze .

[0042] The value of the molten pool coefficient K is determined by the thermophysical properties of the material. ,in Laser absorption rate (0.35 for steel, 0.25 for titanium alloy). Density (steel 7850) Titanium alloy 4500 ), Specific heat capacity (steel 500 Titanium Alloy 520 ), calculated steel Titanium alloy , and the heat conduction equation ( For laser power, The exposure time is consistent with theoretical predictions.

[0043] S4, Radial gradient field boundary transition processing After the penalty term converges, the radial gradient field is automatically activated for boundary transition, smoothing the optimized design space from the non-design space. This includes the following steps: Step 4.1.1: Construct a radial transition zone between the design space and the non-design space, with the density distribution function being...

[0044] To calculate the distance from the point to the center of the hole; .

[0045] Step 4.1.2: Transform the draft constraint into a vector field equation: ; Where: n is the boundary normal vector; d is the draft direction vector; Minimum draft angle, with a value ≥3°; Step 4.1.3: Achieve material property transition through nodal variable interpolation, specifically including: (a) Defining nodal variables (a) Indicates whether the material is in a certain state; (b) The properties of any point within the element are interpolated using shape functions: ;in It is a shape function, which determines Within the cell The influence of point weights; (c) Introducing power functions Suppress the checkerboard effect.

[0046] The width of the transition zone It is 1.8 times the aperture. Gradient control index. The density changes parabolically, and the regulation index... Timely satisfaction ( This ensures that the stress gradient is minimized. The value of is determined by the following mechanical principles: (1) Based on the stress continuity criterion of elasticity, when the density distribution function satisfies ,( When is a non-zero constant, the rate of change of stress gradient in the transition region is minimized. Analytical calculations show that only when When the second derivative of the density distribution function is constant, the second derivative of the density distribution function is constant. (2) Based on the dynamic system stability theory, through the Lyapunov function Proof of the stability criterion for the construction: when The real parts of all eigenvalues ​​of the time-Jacobi matrix are negative, satisfying the global asymptotic stability condition; When using When combining parameters, based on the Saint-Venant principle of elasticity, the range of boundary stress disturbance is controlled within... It can achieve: Bolt hole deformation (Meets ASME Y14.5-2018 IT7 tolerance level) substrate flatness (Meets the vibration resistance requirements of MIL-STD-810H Method 514.6) The draft direction vector The vertical direction is [0,0,1].

[0047] Locking critical boundary dimensions during topology optimization to achieve precise control of critical dimensions includes the following steps: Step 4.2.1: Geometric Constraint Domain Identification. Identify key geometric feature regions (such as bolt holes, mounting surfaces, and substrate contours) in the structure to be optimized that require dimensional preservation, and define them as geometric constraint domains. ; Step 4.2.2: Boundary distance field construction. Compute any point in the computation space. to the boundary of the constraint domain Normalized distance function:

[0048] To affect the radius, The finite element mesh size is...

[0049] Step 4.2.3: Dynamic correction of sensitivity field: Correct the original sensitivity using an exponentially decaying suppression field.

[0050]

[0051] The geometric constraint domain One of the following conditions must be met: Bolt hole structure: hole diameter d∈[6mm,12mm] and hole depth h>8mm; Substrate outline: Length L≥100mm and flatness error≤0.1mm.

[0052] The influence radius parameter k=5 is used to control the boundary displacement ≤0.05mm under random vibration conditions (vibration spectrum: 20–2000Hz@12Grms).

[0053] S5, Post-repair processing For the few areas that do not meet the manufacturing characteristics in the optimization results, geometric filtering is used for repair, characterized by the following steps: Step 5.1: Thickness Inspection and Repair Calculate the spatial region of the optimized design using numerical integration methods. Local thickness of each element By scanning the optimized density distribution, thicknesses less than [a certain value] were identified. In certain areas, the thickness is increased by increasing the material density.

[0054] ; in, This indicates the material density before adjustment. This indicates the preset density gain, used to compensate for areas with insufficient thickness.

[0055] Step 5.2: Overhang Angle Correction If the optimization results show excessive overhang angles, geometric transformations can be used to address angles exceeding the maximum allowable value. Adjust the overhang area.

[0056]

[0057] in, It is the original coordinate vector of the point to be corrected. Vertical downward vector (manufacturing direction). This represents the corrected position. It involves moving the point upwards or downwards to reduce the sag angle. These are angle-related displacements, as shown below:

[0058] This is the preset maximum adjustment height. It is the current overhang angle. It is the maximum permissible overhang angle.

[0059] when hour, Displacement direction At this point, move upwards; when hour, Displacement direction At this point, move downwards; when hour, No displacement occurs.

[0060] The geometric filtering process does not cover certain areas; these areas must be identified before repair. The domain will not change due to restoration, that is... .

[0061] The method is applicable to additive manufacturing structure optimization, eliminating areas of non-compliant overhang constraints through directional filtering.

[0062] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art will be able to make various modifications and improvements without departing from the principles of the present invention, and these modifications and improvements should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for topology optimization of part structures based on geometric features and manufacturing process constraints, characterized in that, Includes the following steps: S1. Initialization: Define the design domain and non-design domain, and identify key geometric feature constraint domains. Set minimum wall thickness Maximum overhang angle Grid size ; S2. Construct a composite objective function: in, It is a structural performance target. It is a structural wall thickness constraint penalty term. It is a penalty term for the overhang angle constraint. These are the dynamic penalty factors for constrained wall thickness and overhang angle, respectively; S3. Iterative optimization: Lock the geometric feature constraint domain, calculate and correct the objective function and sensitivity, dynamically update the penalty factor, and terminate the iteration after the convergence condition is met. S4. Boundary transition processing: After the penalty term converges, the radial gradient field is activated to achieve a smooth transition between the design domain and the non-design domain. S5, Post-Repair: Maintaining Under the premise of unchanged node coordinates, geometric filtering is used to repair the non-compliant areas of thin walls and overhang angles; S6. Output results: Output the topology optimization structure that satisfies geometric feature locking, process constraints and boundary continuity.

2. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The wall thickness constraint penalty item Through the gradient magnitude of the level set function Map local wall thickness and base it on a minimum wall thickness threshold. in , It is a grid size correlation factor. ; and then This is the penalty index.

3. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, Overhang angle constraint penalty via boundary normal vector With manufacturing printing direction inner product Constrain the overhang angle and introduce a smooth transition function. Control the scope of punishment: ， in For the transition steepness parameter, The penalty intensity index is initialized. This is the critical overhang angle.

4. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The dynamic penalty factor Adopt a tiered update strategy: Step 301: Build Bayesian prior distribution ,in , The molten pool coefficient of the material; Step 302: Update the distribution based on MCMC sampling, with sampling weights determined by the target sensitivity. With constraint violation Joint decision; Step 303: Generate cooperative functions , The spatial average value of the gradient magnitude within the design domain reflects the structural boundary complexity. It is a coordination coefficient used to dynamically adjust the weight of manufacturing process constraints in the topology optimization objective function, with a value range of... ,initialization The overhang angle threshold; Step 304: Adjust using a tiered strategy The global layer updates the Bayesian prior parameters every 10 steps; the local layer is scaled appropriately using a proportional method. ,but ;like ,but ; Step 305: Convergence check. If the convergence is satisfied for 10 consecutive steps... Freeze .

5. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, After the penalty term in step S3 converges, a smoothing process is performed between the optimized design domain and the non-design domain, including the following steps: Step 401: Construct a radial transition region between the design domain and the non-design domain, with the density distribution function being... in, Density of the material at the edge of the mounting hole; To design the target density; To calculate the distance from the point to the center of the hole; The radius of the mounting hole; The width of the transition zone is 1.5 to 2 times the aperture. For gradient regulation index; Step 402: Transform the draft constraint into a vector field equation; Step 403: Achieve material property transition through nodal variable interpolation.

6. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The geometric feature locking is achieved through the following steps: identifying bolt holes, mounting surfaces, and substrate contours; constructing a boundary normalized distance; and correcting the sensitivity with an exponentially decaying field.

7. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The post-repair includes: Thin-walled repair: Identifying thicknesses less than In areas where the material density is increased, the thickness is enhanced. Overhang Angle Correction: Detects whether there are excessively large overhang angles in the optimization results, and corrects angles exceeding the maximum allowable angle through geometric transformation. Adjust the overhang area; The repair process remains The coordinates of the internal nodes remain unchanged.

8. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The optimized key indicators meet the following requirements: bolt hole deformation ≤ 0.05 mm, substrate flatness ≤ 0.08 mm.

9. The part structure topology optimization method based on geometric features and manufacturing process constraints according to claim 1, characterized in that, The method is applicable to the topology optimization of parts in additive manufacturing and machining composite processes, and can simultaneously meet the manufacturing constraints of minimum wall thickness and overhang angle.

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