Beam optimization design method and system based on multi-scale topology and data driving

Abstract

The present application relates to the technical field of beam optimization design, and particularly relates to a beam optimization design method and system based on multi-scale topology and data driving, comprising the following steps: correlatively dividing a beam design domain according to overall box scale, internal rib plate scale and connecting detail scale, and setting non-removal areas in guide rail connecting areas, stand connecting areas and load acting areas; coupling each scale design domain based on load transmission continuity under mobile load action, and obtaining a multi-scale beam optimization domain; inputting a multi-scale topology iteration unit based on the multi-scale beam optimization domain, and determining a bending load main path at the overall box scale. The present application reconstructs the topology result into a wall plate-continuous rib plate structure, and implements cross-scale backfilling and rib plate connection correction through static force, modal and manufacturing constraint checking, so as to realize collaborative optimization of lightweight, structural performance and manufacturability.

Description

Technical Field

[0001] This invention relates to the field of beam optimization design technology, and in particular to a beam optimization design method and system based on multi-scale topology and data-driven approaches. Background Technology

[0002] As CNC machine tools develop towards higher speed, higher precision, and lighter weight, the crossbeam, as a crucial component bearing the spindle box, guide rails, and cutting loads, directly impacts machining accuracy and operational stability due to its mass, rigidity, torsional resistance, and dynamic performance. Existing crossbeam optimization methods often employ dimensional optimization, parameter optimization, or single-scale topology optimization, achieving weight reduction by adjusting wall thickness, stiffener quantity, and material distribution. However, these methods struggle to simultaneously consider the continuous force transmission relationships between different dimensions, including the overall machine body, internal stiffeners, and connection details, easily leading to problems such as stiffener breakage, insufficient local connections, or material isolation.

[0003] When the crossbeam is in actual operation, it bears multi-position loads formed by the movement of the spindle box along the guide rail. Existing methods do not adequately consider the stable force transmission region and the migration force transmission region, and the resulting structure is difficult to take into account the displacement, stress and torsional performance under the whole stroke.

[0004] Traditional topology optimization has limited utilization of existing design and finite element verification data, and the discrete optimization results need to be further reconstructed in engineering. After reconstruction, problems such as interruption of force transmission path, discontinuity of stiffeners and failure to meet manufacturing constraints are likely to occur. Therefore, it is necessary to study a beam optimization design method that takes into account multi-scale continuous force transmission, moving load conditions, data-driven correction and structural manufacturability. Summary of the Invention

[0005] This invention provides a method and system for beam optimization design based on multi-scale topology and data-driven principles.

[0006] The first aspect is a beam optimization design method based on multi-scale topology and data-driven approaches, which includes the following steps: The beam design domain is divided according to the overall box dimensions, internal stiffener dimensions, and connection detail dimensions. Non-removable areas are set in the guide rail connection area, column connection area, and load application area. Based on the load transfer continuity under moving load, the design domains of each scale are coupled to obtain the multi-scale beam optimization domain. Based on the multi-scale beam optimization domain input multi-scale topology iteration unit, the main path of bending load is determined at the overall box scale. Based on the internal stiffener dimensions, the torsional force transmission branch connected to the main bending load path is determined, and the local connection between the main bending load path and the torsional force transmission branch is corrected at the connection detail dimensions. Based on the data-driven performance prediction trained by the existing design scheme of the beam and the corresponding finite element verification results, the material retention priority in each round of topology iteration is corrected to obtain the cross-scale beam material layout. Based on the cross-scale beam material layout, the candidate beam structure is converted into a beam composed of wall panels and continuous stiffeners. The candidate beam structure is then subjected to static verification under moving load and low-order modal verification. Based on the verification results, cross-scale backfilling or stiffener plate connection correction is performed on the local areas that do not meet the requirements, and the beam optimization design results are output.

[0007] Secondly, the beam optimization design system based on multi-scale topology and data-driven principles includes the following modules: A multi-scale optimization domain construction module is used to divide the beam design domain into an overall box-shaped scale design domain, an internal stiffener scale design domain, and a connection detail scale design domain, set non-removal areas and scale connection areas, and construct a multi-scale beam optimization domain based on the load transfer continuity under moving loads. A multi-scale topology iteration module is used to identify the main path of bending load and the branch of torsional force transmission based on the multi-scale beam optimization domain, perform local continuity correction on the cross-scale connection area, and use the performance contribution prediction results and structural constraint risk prediction results output by the data-driven performance prediction model to correct the material retention priority, and obtain the cross-scale beam material layout through iterative updates. The structural reconstruction and verification module is used to convert the cross-scale beam material layout into a candidate beam structure composed of wall panels and continuous stiffeners. The module performs static verification of moving loads and low-order modal verification on the candidate beam structure, and performs cross-scale backfilling, stiffener connectivity correction or connection area correction according to the structural verification results, until the preset mass, displacement, stress, natural frequency and manufacturing constraints are met, and outputs the beam optimization design results.

[0008] The beneficial effects of this invention are: This invention divides the crossbeam into an overall box-shaped dimension, an internal stiffener dimension, and a connection detail dimension. Under moving load conditions, it identifies the main path of bending load and the branch path of torsional force transmission. By using dimension connection and local continuity correction, it achieves continuous force transmission across dimensions, solving the problems of stiffener breakage, insufficient connection, and interruption of force transmission path that are prone to occur in traditional single-scale topology optimization.

[0009] This invention utilizes existing beam design schemes and finite element verification data to train performance prediction, dynamically adjusts material retention priorities based on performance contribution and structural constraint risks, and reconstructs the topology results into a wall panel-continuous stiffener structure. Through static, modal, and manufacturing constraint verification, cross-scale backfilling and stiffener connectivity correction are implemented to achieve synergistic optimization of lightweighting, structural performance, and manufacturability. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic diagram of the method flow of Embodiment 1 of the present invention; Figure 2 This is a diagram of the multi-scale topological iterative unit architecture of Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the method flow for S2 in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the system modules in Embodiment 2 of the present invention. Detailed Implementation

[0012] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. For some well-known technologies, those skilled in the art may also use other alternative methods to implement the invention. Moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0013] Example 1 like Figures 1-4 As shown, the beam optimization design method based on multi-scale topology and data-driven approach includes the following steps: S1. The beam design domain is divided into related dimensions according to the overall box size, internal stiffener size, and connection detail size. Non-removable areas are set in the guide rail connection area, column connection area, and load action area. The design domains of each size are coupled by the load transfer continuity under moving load to obtain the multi-scale beam optimization domain.

[0014] S11. Based on the three-dimensional geometric model of the beam, the outer wall panel, inner wall panel, cross-sectional outline, internal stiffener arrangement space, and connection areas of the beam are identified in layers. According to the three structural functions of overall load bearing, internal force transmission, and local connection, the beam design domain is divided into the overall box-shaped scale design domain, the internal stiffener scale design domain, and the connection detail scale design domain.

[0015] The solid space within the outer contour of the beam section, occupied by the outer and inner wall panels, is defined as the overall box-shaped design domain, represented as follows: ; in, Design domain for overall enclosure dimensions; This refers to the spatial area corresponding to the outer wall panel. This refers to the spatial region corresponding to the inner wall panel.

[0016] First, the geometric information of the wall panels in the 3D solid model of the beam is read. Then, based on the outer contour of the beam section, the normal direction of the wall panels, and the thickness of the wall panels, the inner and outer layers of the double-wall structure are identified. The continuous solid region that is directly adjacent to the outer contour of the beam section, whose outer surface constitutes the outer surface of the beam and extends into the beam along the thickness direction of the wall panels is determined as the spatial region corresponding to the outer wall panel. The spatial region corresponding to the outer wall panel includes a continuous box-shaped wall panel region formed by the top wall, bottom wall, front and rear side walls, and end outer walls of the beam; and then... The inner boundary is the starting boundary, and the search proceeds along the inner direction of the beam. A second layer of wall panel, which is spaced apart, extends continuously around the internal cavity of the crossbeam, and is used to connect with the internal stiffening plate, is defined as the spatial region corresponding to the inner wall panel. .

[0017] The overall box-shaped design domain is used to characterize the overall bending load-bearing space formed by the external enclosed box of the beam and the double-layer wall panels; for the beam ends, guide rail mounting surfaces or other areas that need to maintain cross-sectional integrity, the corresponding physical boundaries are retained within the overall box-shaped design domain, and such boundaries are not included as part of the internal stiffener design domain.

[0018] The internal space between the outer and inner wall panels, where stiffeners can be arranged and which is not occupied by functional passages, is defined as the internal stiffener dimension design domain, expressed as: ; in, Design domain for internal stiffener dimensions; This refers to the internal cavity region formed between the outer and inner wall panels; There is no space reserved for ribs in assembly channels, maintenance channels, and chip removal channels.

[0019] The internal stiffener dimensional design domain is used to define the possible arrangement range of subsequent torsional force transmission branches and local support stiffeners. The internal stiffener dimensional design domain is adjacent to the overall box dimensional design domain, but does not use the same design resolution. The overall box dimensional design domain uses a relatively large design unit, while the internal stiffener dimensional design domain uses a relatively small design unit, so as to refine the position and orientation of the stiffeners while maintaining the stability of the overall load-bearing path.

[0020] The areas where stiffening slabs connect to outer or inner wall panels, the areas where two or more stiffening slabs intersect, the guide rail connection areas, and the column connection areas are defined as the connection detail dimension design domains, represented as follows: ; in, Design domains for connecting detailed scales; This is the area where the stiffening slab connects to the wall panel; This is the area where the stiffening plates intersect; This is the guide rail connection area; This is the area where the columns connect.

[0021] First, the connection points are identified based on the contact interfaces and assembly references in the 3D solid model of the beam. The location where each stiffener end or side makes solid contact, welding connection, or geometric penetration with the outer or inner wall panel is taken as the stiffener-wall panel connection interface. A preset connection influence distance is then extended along this connection interface to both sides of the stiffener and wall panel. The continuous solid area formed after the extension is defined as the stiffener-wall panel connection area. The location where the solid boundaries of two or more stiffening slabs intersect, overlap, or share a common connecting edge is taken as the stiffening slab intersection center. Based on the intersection center, the area is extended along the direction of each participating stiffening slab until the stiffening slab cross-section returns to stability. The union of the corresponding extended areas is determined as the stiffening slab intersection area. Based on the distribution range of the guide rail mounting surface, guide rail fastening holes or mounting grooves, the contact projection range between the guide rail and the crossbeam, and the diffusion range of the spindle box load input to the crossbeam via the guide rail, the continuous solid area covered by the guide rail installation and force transmission is determined, and this area is defined as the guide rail connection area. Based on the welding surfaces, bolted connection surfaces, support contact surfaces, or geometrically fixed interfaces between the two ends of the beam and the column, identify the actual connection range at the ends of the beam. Then, extend the load from the beam to the column inwards until the stress or strain energy distribution tends to be flat. This connection interface and its extended area are defined as the column connection area. .

[0022] The boundary of the connection detail-scale design domain is obtained by extending the corresponding connection interface outwards by a preset connection influence distance; the connection influence distance is expressed as: ; in, The connection affects the distance; For the corresponding wall panel thickness; For the corresponding stiffener thickness; The equivalent coverage width required for the weld and its heat-affected zone; The coefficient representing the influence of wall panel thickness; The coefficient representing the influence of stiffener thickness is... and All are set to 2-4, and priority is given to ensuring that the connection detail scale design domain covers at least two stiffener thickness ranges and two wall panel thickness ranges.

[0023] First, determine the type of fillet weld, butt weld, or combined weld used at the connection between the stiffener and the wall panel based on the beam welding process documents or joint design drawings, and obtain the actual coverage width of the weld in the direction perpendicular to the weld length. For fillet welds, the projected width between the weld toes on both sides of the weld is taken as the weld coverage width, with the weld root as the reference. For butt welds, the width of the weld fusion zone on the base metal surface is taken as the weld coverage width. Then, perform cross-sectional macroscopic inspection, hardness gradient testing, or metallographic testing on welding process qualification specimens of the same material, plate thickness, and welding parameters. Identify the position where the microstructure or hardness recovers to the stable value of the base metal from the weld fusion line towards both sides of the base metal, and take the maximum distance from the fusion line to this position as the width of the heat-affected zone on one side. Add the weld coverage width to the width of the heat-affected zone on both sides of the weld to obtain the actual total coverage width of the weld and its heat-affected zone. To use this total coverage area for the expansion of the connection interface, take half of the actual total coverage width as... That is, the distance is extended to both sides based on the weld centerline or the connection interface.

[0024] After obtaining the three design domains, a spatial mapping relationship is established between them based on their geometric positions; for the first design domain of the overall box-shaped structure... The first design unit, the internal stiffener dimension design domain The design unit and the first design domain in the connection detail scale design domain Each design unit is represented by a scale mapping matrix as follows: ; ; in, The spatial mapping matrix between the overall box-shaped design domain and the internal stiffening plate design domain; The spatial mapping matrix between the internal stiffener scale design domain and the connection detail scale design domain; The first in the overall box-shaped design domain Design unit; The first in the internal stiffener dimensional design domain Design unit; To connect the first in the detailed scale design domain Design unit.

[0025] Connection relationship refers to the direct contact between the physical boundaries of two design units. Projection correspondence relationship refers to the overlapping area after the design unit in the internal stiffener scale design domain is projected along its candidate stiffener normal to the overall box scale design domain. Coverage relationship refers to the connection detail scale design domain covering the end of the stiffener or the intersection of stiffeners.

[0026] When the overlap ratio between the projected area and the corresponding design unit is not less than the spatial mapping threshold At that time, a projection correspondence is established between the two, and the overlap ratio is expressed as: ; in, This refers to the spatial overlap ratio; The projected volume of the design unit to be mapped; The volume of the target design unit.

[0027] First, determine the scale of the design unit to be mapped and its mapping direction with the target design unit. The mapping direction is determined based on the local normal of the design unit to be mapped, the extension direction of the candidate stiffener, or the shortest connection direction between adjacent scales. Then, project the geometric entity of the design unit to be mapped onto the scale space of the target design unit along the mapping direction, and make the projection depth equal to the effective thickness of the target design unit along the mapping direction. The projection contour of the design unit to be mapped and the projection depth together form a three-dimensional projection entity. The volume of this three-dimensional projection entity is determined as the projection volume of the design unit to be mapped. .for The system directly reads the solid boundary of the target design unit in the finite element model or geometric discrete model of the beam, calculates the volume of its closed solid according to the coordinates of each vertex, the element type, and the actual geometric dimensions of the target design unit, and determines the volume of the closed solid as the volume of the target design unit. .

[0028] Spatial mapping threshold Set to 0.3-0.6; the spatial mapping threshold is obtained by comparing the mapping results at different grid scales: the spatial mapping threshold is gradually adjusted, and the corresponding threshold is adopted when the mapped stiffener path can continuously connect the corresponding wall panel and will not misjudge the design units that are far apart as related units; preferably, 0.5 is used as the initial spatial mapping threshold.

[0029] when At that time, the corresponding design unit is determined to have a projection correspondence, and it is mapped in the spatial mapping matrix. or The value is assigned to 1; when When the value is zero, no corresponding mapping relationship is established, and the value is assigned to 0.

[0030] Based on the spatial mapping relationship between the overall box-shaped dimension design domain, the internal stiffener dimension design domain, and the connection detail dimension design domain, another dimension design domain that has a connection, projection correspondence, or coverage relationship with any dimension design domain is determined as the adjacent dimension design domain of that dimension design domain, resulting in the beam sub-dimension design domain as follows: ;in, The design domain is defined by the dimensions of the beam.

[0031] S12, in the crossbeam subdivision design domain, the guide rail connection area, column connection area and load application area are marked without removal, and the scale connection area used to transfer load between adjacent scales is further identified.

[0032] The guide rail connection area is determined based on the mounting surface of the crossbeam guide rail, the fastening connection range, and the load diffusion range of the guide rail; the column connection area is determined based on the welding surface, bolt connection surface, or support contact surface between the end of the crossbeam and the column; and the load application area is determined based on the contact position and load diffusion range of the spindle box when it moves along the guide rail.

[0033] The non-removed region is represented as: ; in, This is the area that will not be removed. This is the guide rail connection area; This is the area where the columns connect; This refers to the area where the load is applied.

[0034] For design units within non-removed areas, a non-removed identifier is set as follows: ; in, For the first The non-removal identifier of each design unit; when At that time, the first Each design unit maintains its solid state during subsequent topology optimization.

[0035] The width of the guide rail connection area is extended outwards according to the actual installation width of the guide rail, with a preset guide rail load diffusion distance. It is determined that the guide rail load diffusion distance is obtained based on the strain energy distribution of the guide rail connection area under typical load, that is, the guide rail installation boundary is extended layer by layer to the surrounding area until the average strain energy density of the design unit outside the extended boundary is lower than the preset ratio of the average strain energy density of the guide rail connection area.

[0036] The preset ratio is denoted as The value is set to 0.1-0.2; the basis for this setting is to ensure that the guide rail connection area covers the main load input range, rather than setting the large area in the middle of the crossbeam as a non-removal area; specifically, it is calibrated by the guide rail surface displacement change rate under different expansion distances. When the maximum displacement change of the guide rail surface is less than 2% after further expanding the non-removal area, the current expansion distance is taken as the guide rail load diffusion distance. .

[0037] The column connection area is extended into the beam by a predetermined column load diffusion distance according to the actual connection interface. The column load diffusion distance The distance is determined based on the attenuation of principal stress or strain energy density near the connection interface; specifically, taking the peak strain energy density at the connection interface as a benchmark, the distance corresponding to the point where the strain energy density decreases to 15%-25% of the peak value is taken as the column load diffusion distance. .

[0038] The load application area is determined based on the contact projection area between the spindle box and the crossbeam guide rail at each moving load position; for the first... The sub-regions corresponding to the locations of moving loads are represented as follows: ; in, For the first The load action sub-region corresponding to each moving load location; This indicates that the area will expand outwards at a preset distance. Extend the distance of the load application area; The main spindle box in the first The contact projection area at the first moving load position; first, based on the allowable movement trajectory of the spindle box along the crossbeam guide rail, translate the three-dimensional geometric model of the spindle box to the first... The system is positioned at a moving load location, maintaining the actual assembly posture of the spindle box, slide, slider, rolling elements, or pressure plate relative to the guide rail. Then, all contact surfaces that directly contact or transmit force between the spindle box side guide rail pair and the crossbeam guide rail are extracted from the 3D geometric model. These include the bottom surface of the slider, the equivalent contact surface of the rolling elements, the pressure plate bearing surface, and other connecting surfaces bearing normal or lateral forces. The contact surfaces are then projected onto the crossbeam guide rail mounting surface along the normal direction. The projected contours formed by each contact surface are then combined, deleting scattered projections formed only by assembly gaps, chamfers, or non-load-bearing edges, and retaining the effective projection portion bearing the weight of the spindle box, cutting reaction force, eccentric bending moment, or torque according to the actual contact state. When rolling guide rails are used and the actual contact is point-like or line-like, discrete contact points or contact lines are equivalently expanded into continuous load-bearing projection surfaces based on the rated contact length of the slider and the effective arrangement width of the rolling elements. When the spindle box is connected to the crossbeam guide rail via multiple sliders, the projection area corresponding to each slider is obtained, and the union of these projection areas is determined as the spindle box's position at the [missing information]. The contact projection area at the location of each moving load.

[0039] The load application area corresponding to all moving load locations is represented as follows: ; in, This represents the total number of locations where the load has been moved.

[0040] Load application area extension distance Take 0.25-0.5 times the contact width of the spindle box; when the contact stress or strain energy density decreases to below 20% of the peak value, use the corresponding distance as... This is to prevent the formation of excessively thin or fractured material structures near the contact edges.

[0041] After marking the non-removed areas, identify the scale connection areas from the design units directly adjacent to the non-removed areas; for any material area adjacent to the non-removed area, if it has a spatial mapping relationship with the adjacent scale design domain and is located in the direction of load transfer from the non-removed area to the internal stiffener scale design domain or the overall box scale design domain, then mark the material area as a scale connection area.

[0042] The scale transition region is represented as: ; in, This is the area where scales connect; For the first The shortest distance between each design unit and the non-removed area; The distance between scale connections; For scale-related identifiers, when the first When establishing a spatial mapping relationship between a design unit and an adjacent scale design domain .

[0043] Scale connection distance Set to 2-5 times the size of the local design unit; specifically determined through mesh independence analysis: gradually increase the scale connection distance, calculate the number of load transfer interruptions between the non-removed area and the adjacent scale design domain, and select the corresponding distance when the number of load transfer interruptions no longer decreases after the scale connection distance increases, and the volume growth rate of the scale connection area begins to increase significantly; preferably set to 3 times the size of the local design unit.

[0044] For design units within the scale transition area, the scale transition identifier is set as follows: ; in, For the first Scale connection markers for each design unit.

[0045] Design units within non-removable regions must not be removed during subsequent topology iterations; design units within scale connection regions are allowed to adjust their material density based on topology iteration results, but their material density must not be lower than the preset lower limit for connection material density. .

[0046] The lower limit of the density of the connecting material The lower limit of the connection material density is set to 0.5-0.8. The lower limit of the connection material density is obtained by comparing the connection stiffness and material usage corresponding to different lower limits of the connection material density. When the increase in connection stiffness due to further increasing the lower limit of the connection material density is less than 5%, while the increase in material usage exceeds 5%, the previous value is selected as the lower limit of the connection material density. Preferably, the initial lower limit of the connection material density is set to 0.6.

[0047] The beam's subscale constraint domain, containing both non-removal constraints and scale connection constraints, is represented as follows: ; in, This is the dimensional constraint domain for the beam.

[0048] S13. Multiple moving load positions are set along the direction of the crossbeam guide rail. Static finite element analysis is performed on the crossbeam subscale constraint domain at each moving load position to determine the load transfer area extending from the load action area to the column connection area, and the stable force transmission area and the migrating force transmission area are identified accordingly.

[0049] The locations of the moving loads, arranged at equal intervals, are represented as follows: ; in, For the first The coordinates of the moving load position in the direction of the crossbeam guide rail; The starting position of the allowable range of movement of the spindle box; The end position of the allowable movement range of the spindle box; This represents the total number of moving load locations. .

[0050] Total number of moving load locations The determination is based on the beam length, load contact width, and critical location identification accuracy. In specific settings, the moving load positions are first arranged at intervals not greater than the spindle box contact width. If the maximum displacement change rate corresponding to two adjacent moving load positions exceeds the preset position refinement threshold, then moving load positions are added between the adjacent positions.

[0051] The maximum rate of change of displacement can be expressed as: ; in, For the first The location of the moving load is related to the first The maximum rate of displacement change between the locations of the moving loads; and These represent the maximum displacement at the corresponding moving load position.

[0052] The location refinement threshold is set to 0.08-0.15. The location refinement threshold is determined based on the smoothness of the moving load response curve. When the difference in response between adjacent locations exceeds this range, it indicates that there may be unidentified local dangerous locations in the middle area, and it is necessary to increase the number of sampling locations. The preferred location refinement threshold is set to 0.1.

[0053] For the The strain energy density of each design element is obtained from the location of the moving load using finite element analysis. Design units with strain energy density not less than the preset force transmission identification threshold at the current moving load position are identified as candidate force transmission units.

[0054] No. The set of candidate force transmission elements at each moving load location is represented as follows: ; in, For the first A set of candidate force transmission units at each moving load location; For the first The design unit in the first Strain energy density at each moving load location; For the first The maximum strain energy density in all design units at each moving load location; The threshold ratio for force transmission identification.

[0055] Force transmission recognition threshold ratio Set to 0.05-0.2; the force transmission identification threshold is obtained through load transfer area connectivity calibration; starting from a higher threshold, it is gradually reduced. When the candidate force transmission unit can form a continuous connection structure extending from the load application area to at least one column connection area, and no large area of ​​low strain energy is simultaneously included, the corresponding force transmission identification threshold is adopted; the preferred force transmission identification threshold ratio is set to 0.1.

[0056] First, a finite element model is established using the beam's segmented constraint domain. Corresponding material parameters and element properties are assigned to the outer wall panel, inner wall panel, internal stiffeners, and connection detail areas. Then, displacement constraints consistent with the actual support method are applied to the column connection area. The load action sub-region corresponding to each moving load position is subjected to the bending moment and torque generated by the spindle box gravity, cutting force, and eccentricity. After completing the static solution, the stress and strain components at each integration point of each design element are read. Half of the sum of the products of the corresponding stress and strain components is calculated to obtain the elastic strain energy density at each integration point. Then, the elastic strain energy density inside the design element is integrated by volume according to the integration point weight and the Jacobian determinant to obtain the total strain energy of the design element. The total strain energy is then divided by the actual volume of the design element to obtain the first... The design unit in the first Strain energy density at each moving load location .

[0057] When establishing the finite element model based on the crossbeam's segmented constraint domain, the overall box-shaped design domain, the internal stiffener design domain, and the connection detail design domain are first placed in the same crossbeam coordinate system. The positional correspondence between different design domains is then corrected based on the spatial mapping relationship established in S11. Subsequently, the outer and inner wall panels in the overall box-shaped design domain are discretized using shell or solid elements capable of characterizing wall panel bending and in-plane deformation. The internal stiffener design domain is discretized using shell or solid elements adapted to the actual thickness and extension direction of the stiffeners. The areas connecting stiffeners and wall panels, stiffener intersections, guide rail connections, and column connections are discretized using locally refined elements with dimensions smaller than the adjacent mesh sizes. At the boundaries of different mesh sizes, common node connections, node coupling, and constraint methods are used. Displacement and load are transferred using process or interface mapping to ensure cross-scale finite element mesh continuity. Non-removable regions corresponding to the guide rail connection area, column connection area, and load application area are set as always-retained solid material elements. Scale transition areas are set as continuous material elements that must not form cross-scale fractures. The remaining optimizable regions are set as design elements whose material states can be adjusted during topology iteration. Based on the actual materials of each component of the beam, the corresponding elements are assigned elastic modulus, Poisson's ratio, density, and yield strength. The element thickness or solid geometry is set according to the actual dimensions of the wall panels and stiffeners. Welds and heat-affected zones are characterized using equivalent connection elements, equivalent material parameters, or connection interface stiffness. Finally, according to the actual installation method between the beam end and the column, fixed, elastic supports, or connection stiffness constraints are set in the column connection area. The spindle box gravity, cutting reaction force, bending moment, and torque are applied to the contact projection area corresponding to each moving load position, and load conditions are established for each moving load position. This forms a beam finite element model that maintains the spatial correspondence of the three-scale design domains and can characterize non-removed constraints, scale connection constraints, and moving load transmission characteristics.

[0058] From the candidate force transmission element set, design elements that are connected to the corresponding load application area and can extend to the column connection area are retained, resulting in the first... The load transfer area at each moving load location is represented as follows: ; in, For the first Load transfer area at each moving load location; This indicates the extraction of design elements from candidate force transmission elements that are simultaneously connected to both the load application area and the column connection area; first, the first... Design units whose strain energy density reaches the force transmission identification threshold at each moving load location constitute a candidate force transmission unit set. An adjacency graph of the candidate force transmission units is established based on the coplanar, edge-sharing, or node-sharing relationships between design units in the finite element mesh. Each candidate force transmission unit is treated as a node. When two candidate force transmission units have effective geometric contact and their contact range reaches a preset minimum connection scale, a connection edge is established between the corresponding nodes. Subsequently, this is combined with the... Candidate force transmission units that directly contact, project and overlap with, or are connected through scale connection areas corresponding to the load application areas of each moving load location are marked as load initiation units. Starting from the load initiation units, adjacent candidate force transmission units are searched layer by layer according to the candidate force transmission unit adjacency diagram, forming one or more connected components extending from the load application area to both ends of the beam. For each connected component, it is determined whether there are candidate force transmission units that directly contact, project and overlap with, or are connected through the connection detail scale design domain of the column connection area. If so, all candidate force transmission units in the connected component are retained; if not, the connected component is discarded as an isolated material area that cannot transfer the load to the column connection area. When the column connection area is located at both ends of the beam, the connectivity relationship between the connected component and the left and right column connection areas can be determined separately, and design units that are connected to at least one column connection area are retained. Thus, a set of design units that continuously extend from the corresponding load application area to the column connection area is obtained, and this set is determined as the first set. Load transfer area at each moving load location.

[0059] For any design element in the multi-dimensional constraint domain of the beam, the frequency of its identification as a load transfer region under all moving load locations is represented as follows: ; in, For the first The frequency of force transmission in each design unit; For the indicator function; first, select the design unit number to be counted one by one according to the design unit number in the beam segmentation constraint domain. Each design unit is read sequentially from the first to the second. The load transfer area corresponding to the position of the moving load; for the first... The moving load location will be the first The affiliation relationship between the design unit number, geometric entity, or unit center coordinates and the load transfer area at the location of the moving load is determined. When the first design unit number, geometric entity, or unit center coordinates are used to determine the affiliation relationship with the load transfer area at the location of the moving load, the affiliation relationship is determined. When a design unit belongs to the load transfer region, or is the same unit as a design unit in the load transfer region, the indicator function will be used. Assigning a value of 1 indicates that this design unit is in the [number]th [year]. Participating in load transfer at the location of the moving load; when the first... When a design unit does not belong to the load transfer area, the indicator function is set to 0, indicating that the design unit did not participate in load transfer at the moving load position.

[0060] When the The frequency of force transmission in each design unit is not less than the stable force transmission threshold. When this design unit is defined as part of a stable force transmission region, it is represented as follows: ; in, To stabilize the force transmission area; To stabilize the force transmission threshold.

[0061] Stable force transmission threshold The value is set to 0.6-0.8, based on the premise that the stable force transmission area should continuously bear the load transmission function under most moving load positions. Specifically, it is determined according to the connectivity and volume change of the stable force transmission area under different stable force transmission thresholds. When the stable force transmission area can continuously connect the load action zone and the connection area of ​​the two end columns, and the path breaks after the stable force transmission threshold is further increased, the stable force transmission threshold before the path breaks is used. The optimal stable force transmission threshold is set to 0.7.

[0062] When the If a design unit belongs to the load transfer region at at least one moving load location, but its force transmission frequency is less than the stable force transmission threshold, then the design unit is defined as part of the migrating force transmission region, as follows: ; in, For the migration of force transmission area.

[0063] To avoid discrepancies appearing only at a single abnormal load location being misidentified as migration force transmission regions, a minimum occurrence threshold for migration force transmission can be set. The force transmission region is then represented as: ; in, This is the minimum threshold for force transmission during migration.

[0064] Minimum threshold for force transmission during migration Set to 0.1-0.3; the specific value is determined based on the total number of moving load locations, ensuring that a design unit is identified as a migrating force transmission region only when it appears consecutively at at least two or three adjacent moving load locations; for example, when the total number of moving load locations is 10, it will be... Set it to 0.2.

[0065] The aforementioned scale connection area continuously couples the stable force transmission area and the migration force transmission area in the overall box scale design domain, the corresponding force transmission area in the internal stiffener scale design domain, and the local connection area in the connection detail scale design domain.

[0066] For the first in the overall box-shaped dimension design domain The first force transmission unit and the internal stiffener dimension design domain For each force transmission unit, the first-scale continuity criterion is expressed as: ; in, For the first The overall box-shaped design unit and the first Continuity identification between internal stiffening plate dimensional design units; For spatial mapping identifiers; This indicates whether there is a scale boundary between the two. This serves as an indicator of consistent force transmission direction.

[0067] The consistency of force transmission direction is determined by the angle between the principal stress directions of adjacent design units, and is expressed as follows: ; ; in, The angle between the principal stress directions of adjacent scale design units; For the first Principal stress direction vectors of each design unit; For the first Principal stress direction vectors of each design unit; The maximum allowable force transmission direction deviation angle.

[0068] Maximum force transmission direction deviation angle The angle is set to 30°-60°. The purpose of this setting is to avoid abrupt changes in the force transmission direction between adjacent scales, while allowing the stiffener path to make necessary turns according to the geometric space. The angle is determined by comparing the path continuity and the number of stiffeners under different angle constraints. When the path can be continuous and a large number of broken stiffeners are not generated, the corresponding angle is selected, preferably 45°.

[0069] For both the internal stiffener dimensional design domain and the connection detail dimensional design domain, the second-scale continuity criterion is constructed in the same manner. The first design domain based on the internal stiffener dimensions The first design unit and connection detail scale design domain The first design unit is the judgment object. First, the spatial mapping relationship established in S11 is read, and then the judgment is made on the... Does the design unit correspond to the first...? The design unit is located in the area where the stiffeners and wall panels connect, the area where the stiffeners intersect, the area where the guide rails connect, or the area where the columns connect; then determine whether the two have a common node, common edge, common surface, solid contact, or projection overlap relationship, and check whether a continuous material connection can be formed between them through the scale connection area; when the aforementioned spatial mapping relationship is established, and the first The design unit and the first When two design units are in direct contact, or when they are not in direct contact but can be connected through continuously retained scale connection units, the second scale continuity criterion will be applied. A value of 1 indicates a continuous force transmission relationship between the internal stiffener dimensional design domain and the connection detail dimensional design domain. When there is no spatial mapping relationship between the two, their shortest distance exceeds the preset dimensional connection distance, the connection path is interrupted by functional cavities or material removal areas, or the connection detail design unit does not cover the corresponding stiffener connection area, then... The value is assigned to 0; for design unit pairs with a criterion of 0 but belonging to the stable force transmission region or the cross-scale extension direction of the displacement force transmission region, connecting units are added layer by layer in the corresponding scale connection region, and spatial mapping, geometric contact, and path connectivity judgment are re-executed until... The change from 0 to 1 forms a continuous force transmission chain that extends from the internal stiffener scale design domain to the connecting detail scale design domain.

[0070] Combining the scale-specific constraint domain, stable force transmission region, migrating force transmission region, and cross-scale continuous connection relationship of the beam, the multi-scale beam optimization domain is represented as follows: ; in, This is the optimization domain for multi-scale beams.

[0071] The multi-scale beam optimization domain not only defines the spatial range of the overall box-shaped scale design domain, the internal stiffener scale design domain, and the connection detail scale design domain, but also retains the guide rail connection area, the column connection area, and the load application area, and maintains the load transfer continuity between different scale design domains through the scale connection area.

[0072] S2, the multi-scale beam optimization domain is input into the multi-scale topology iteration unit. The main path of bending load is determined at the overall box scale, and the anti-torsional force transmission branch connected to the main path of bending load is determined at the internal stiffener scale. The local connection between the main path of bending load and the anti-torsional force transmission branch is corrected at the connection detail scale. The data-driven performance prediction model trained according to the existing beam design scheme and the corresponding finite element verification results is used to correct the material retention priority in each round of topology iteration, so as to obtain the cross-scale beam material layout.

[0073] The multi-scale topology iteration unit includes cross-scale topology initialization, finite element response solving, bending load main path identification, torsional force transmission branch identification, local connection correction, data-driven performance prediction, material retention priority correction, material state update, and iteration convergence judgment. Specifically, cross-scale topology initialization receives the multi-scale beam optimization domain, sets non-removed regions and scale connection regions as forced material retention regions, and configures initial material retention states for the overall box-shaped scale design domain, internal stiffener scale design domain, and connection detail scale design domain. Finite element response solving obtains displacement, stress, strain energy, and low-order modal responses under load conditions corresponding to each moving load location. Bending load main path identification is based on the strain energy density, force transmission frequency, and load application area of ​​the overall box-shaped scale design unit. The connectivity between column connection areas forms the main path for bending load bearing; the identification of torsional force transmission branches is used to form torsional force transmission branches based on spatial mapping relationships and the degree of suppression of beam torsional deformation, cross-sectional distortion, and relative displacement of guide rails by candidate stiffener areas; local connection correction is used to perform material backfilling, connection width expansion, or stiffener intersection connection correction based on the first-scale continuity criterion and the second-scale continuity criterion; data-driven performance prediction is used to output the performance contribution prediction results and structural constraint risk prediction results of each design unit; material retention priority correction is used to correct the material retention priority based on the prediction results; material state update is used to update the material retention state of each scale design domain based on the corrected material retention priority; iterative convergence judgment determines whether to output the cross-scale beam material layout based on the material distribution change and structural performance change.

[0074] When constructing the multi-scale topological iterative unit, a cross-scale design unit data table is first established based on the design unit number, scale attribute, spatial coordinates, material state, non-removal attribute, and scale connection attribute in the multi-scale beam optimization domain. A first-scale mapping matrix is ​​then established based on the spatial mapping relationship between the overall box-shaped scale design domain and the internal stiffener scale design domain. A second-scale mapping matrix is ​​established based on the spatial mapping relationship between the internal stiffener scale design domain and the connection detail scale design domain. Next, an intra-scale adjacency matrix is ​​established based on the coplanarity, common edge, common node, solid contact, or projection overlap relationships between design units in the finite element mesh. The first-scale mapping matrix, the second-scale mapping matrix, and the intra-scale adjacency matrix are then connected to the bending load main path identification, torsional force transmission branch identification, and local connection correction, respectively. The strain energy density, displacement, stress, and low-temperature energy density obtained from the finite element response are then used to... The modal output, together with the bending load main path, torsional force transmission branch, and cross-scale connection state, is organized into the current round of topology iteration features and input into data-driven performance prediction. Subsequently, the basic material retention priority and the output of data-driven performance prediction are input into material retention priority correction, the corrected material retention priority is input into material state update, and the updated material state is returned to the finite element response solution to form a closed-loop iteration. The force transmission identification threshold ratio, stable force transmission frequency threshold, torsional branch screening threshold, material state update step size, and convergence threshold in the multi-scale topology iteration unit are determined by historical beam scheme playback, finite element threshold sensitivity test, and topology iteration stability test, respectively, so that the obtained bending load main path remains connected, the torsional force transmission branch can effectively suppress torsional response, the local connection meets manufacturing requirements, and the iteration process does not experience continuous oscillation.

[0075] When training the multi-scale topology iterative unit, the training mainly focuses on the data-driven performance prediction. First, existing beam design schemes are collected, and each scheme is verified using finite element analysis (FEM) with the same scale division, material properties, moving load locations, and boundary constraints as the current optimization process. Material distribution characteristics, displacement response characteristics, stress response characteristics, strain energy distribution characteristics, low-order modal characteristics, and cross-scale connection characteristics are extracted. Then, the beam mass, maximum displacement, maximum stress, low-order natural frequencies, cross-scale connection status, and performance changes caused by retaining or removing design units are used as supervision labels to form training samples. These training samples are divided into training, validation, and test sets. After unifying the dimensions of the input features, the input data is used to drive performance prediction. The model parameters are updated by reducing the error between the predicted performance contribution and the actual performance changes of the finite element method, as well as the classification error between the predicted structural constraint risk and the actual force transmission interruption, stress concentration, modal deterioration, or manufacturing unachievable state. The number of model layers, number of nodes, regularization parameters, and prediction thresholds are determined using a validation set, and the prediction error for beam design schemes not involved in the training is verified using a test set. Training is completed when the average relative prediction error of the main performance indicators meets the preset model error threshold and the identification accuracy of structural constraint risks meets the preset accuracy requirement. The model error threshold is set to 5% to 10%, and the preset accuracy is set to 85% to 95%, with the specific values ​​determined based on the number of existing design samples, finite element verification error, and allowable deviations in engineering design.

[0076] S21. Input the obtained multi-scale beam optimization domain into the multi-scale topology iteration unit, and read the non-removable areas, scale connection areas, and other optimizable areas in the overall box scale design domain, internal stiffener scale design domain, and connection detail scale design domain respectively; set the guide rail connection area, column connection area, load application area, and scale connection area determined according to the spatial mapping relationship as the forced material retention area, so that the forced material retention area maintains the solid material state in the entire topology iteration process; set the areas other than the forced material retention area as the material adjustable area, so that the design units in the material adjustable area can perform retention, weakening, or removal according to the material retention priority.

[0077] For the first The first in the design domain of the scale The initial material state variables for each design unit are represented as follows: ; in, Indicates the scale type. Indicates the overall dimensions of the enclosure. Indicates the dimensions of the internal stiffeners. Indicates the detail scale of the connection; Indicates the design unit number within the corresponding scale design domain; Indicates the first In the design domain of the first scale Initial material state variables for each design unit; Indicates the first Forced material retention areas in each scale design domain; Indicates the first Adjustable material areas within a single-scale design domain; This indicates the initial material retention state of the material-adjustable area.

[0078] The material state variable ranges from 0 to 1. A value closer to 1 indicates that the corresponding design unit is closer to a solid material state, while a value closer to 0 indicates that the corresponding design unit is closer to an empty material state. The value is set according to the target material volume fraction, generally 0.4-0.8; when it is necessary to prioritize the initial structural connectivity, it is set to 0.7-0.8; when the lightweight requirement is high and there is already a stable force transmission area as the initial guide, it is set to 0.4-0.6.

[0079] To avoid material fracture in the initial state of design domains of different scales, the obtained spatial mapping relationship is used to perform consistency correction on the corresponding design units across scales. When the overall box-scale design unit and the internal stiffener-scale design unit have a spatial mapping relationship, or the internal stiffener-scale design unit and the connecting detail-scale design unit have a spatial mapping relationship, and any of the design units belongs to the scale connection area, the initial material state variables of the corresponding design units are all set to 1, thereby obtaining the cross-scale topological initial domain.

[0080] S22, apply load conditions corresponding to the locations of each moving load to the cross-scale topological initial domain; for the first... At each moving load location, the gravity of the spindle box, cutting reaction force, eccentric bending moment, and torque are applied to the corresponding contact projection area. Boundary constraints are applied according to the actual installation method of the column connection area. Static solutions are then performed on the finite element model of the beam corresponding to the current wheel topology iteration to obtain the design elements of each design unit in the overall box-shaped design domain at the [number]th [number]th [number]. Strain energy density, displacement, and stress at each moving load location.

[0081] No. The overall box-shaped design unit is in the first The strain energy density at each moving load location is expressed as: ; in, Indicates the first The overall box-shaped design unit is in the first Strain energy density at each moving load location; This represents the element strain energy of the design unit; This indicates the actual volume of the design unit.

[0082] According to the The maximum strain energy density at each moving load location determines the force transmission identification threshold, expressed as follows: ; in, Indicates the first Force identification threshold corresponding to each moving load location; This indicates the preset force transmission recognition threshold ratio.

[0083] Will satisfy The design unit is determined as the candidate force transmission unit, and adjacency relationships are established between the candidate force transmission units according to coplanarity, common edge, common node, or solid contact relationships; from the design unit with the first... Starting from the candidate force transmission unit connected to the load application area corresponding to the moving load position, search layer by layer for candidate force transmission units that can continuously extend to the column connection area. Retain candidate force transmission units that are simultaneously connected to both the load application area and the column connection area, thus obtaining the first... Load transfer area at each moving load location.

[0084] The The value is set to 0.10-0.25; its specific value is obtained through threshold sensitivity test; multiple candidate ratios are used to extract the load transfer area, and the material volume ratio, the connectivity from the load end to the support end, and the proportion of total strain energy borne by the retained area are calculated; the ratio that can maintain complete connectivity, bear a total strain energy ratio not lower than the preset strain energy retention ratio, and has a small material volume is preferred; the preset strain energy retention ratio is set to 0.80-0.95, which is set so that the extracted force transfer area can cover most of the elastic deformation energy in the structure, while avoiding the inclusion of a large number of low contribution units.

[0085] For the The frequency of force transmission in each integral box-shaped design unit, identified as a load transfer zone at various moving load locations, is expressed as follows: ; in, Indicates the first The frequency of force transmission in an overall box-shaped design unit; Indicates the total number of moving load locations; Indicates the first Load transfer area at each moving load location; Indicates the indicator function, when the first The value is 1 if the design unit belongs to the corresponding load transfer area, and 0 otherwise.

[0086] The design unit whose force transmission frequency is not lower than the stable force transmission frequency threshold is identified as the stable bending force transmission unit, and it is connected and repaired together with the load transfer units that migrate under each moving load position to form a bending load main path that extends continuously from the load action area to the column connection area.

[0087] The stable force transmission frequency threshold can be set to 0.6-0.8; its specific value is determined according to the number of moving load positions and the actual working range of the spindle box: when the moving load positions are relatively dense and the working range is completely covered, it is set to 0.7-0.8; when the number of moving load positions is small or the load positions are unevenly distributed, it is set to 0.6-0.7.

[0088] The first-scale material layout with the bending load-bearing main path and other currently retained material units in the overall box-scale design domain are formed by the bending load-bearing main path.

[0089] S23, read the first-scale material layout and the spatial mapping relationship between the overall box-scale design domain and the internal stiffener-scale design domain; extract the design units in the internal stiffener-scale design domain that have a projection overlap relationship with the main path of bending load, a direct connection relationship, or are connected through the scale connection area as stiffener candidate units, and form a stiffener candidate region from the stiffener candidate units.

[0090] When extracting candidate stiffener units, the bending load-bearing main path in the obtained first-scale material layout is first read, and the spatial coordinates, unit boundaries, and material retention status of each design unit in the bending load-bearing main path are obtained. Then, according to the established spatial mapping relationship between the overall box-scale design domain and the internal stiffener-scale design domain, each design unit in the bending load-bearing main path is mapped to the internal stiffener-scale design domain to obtain the corresponding stiffener-influenced area; for the first design unit in the internal stiffener-scale design domain... Each design unit is used to determine its spatial correspondence with the area affected by the stiffener; when the first design unit... When a design unit has volume projection overlap, boundary contact, node connection, or forms a continuous material path through a scale connection area with the mapped stiffener influence area, the design unit is marked as a candidate stiffener unit related to the main path of bending load; when none of the above relationships exist, it is not considered a candidate stiffener unit.

[0091] For the Each candidate stiffener element is evaluated to its degree of suppression of torsional deformation, cross-sectional distortion, and relative displacement of the guide rail. In the current finite element model of the beam, the candidate stiffener element or its corresponding local stiffener region is retained or weakened to obtain the changes in the beam's torsional angle, cross-sectional distortion, and relative displacement of the guide rail before and after the candidate element's involvement. The torsional contribution index is then obtained as follows: ; in, Indicates the first Torsional contribution index of each candidate stiffener unit; This represents the normalized suppression of the beam torsion angle by the candidate stiffener element; This represents the normalized suppression of cross-sectional distortion by the candidate stiffener element; This represents the normalized suppression amount of the relative displacement of the guide rail by the candidate stiffener element; , and Let represent the evaluation weights corresponding to the torsion angle, cross-sectional distortion, and relative displacement of the guide rail, respectively, and satisfy the following: ; The normalized suppression amount is expressed as follows, based on the proportion of change in the corresponding response before and after retaining the candidate stiffener unit: ; in, Indicates weakening the first Beam torsion angle when there are candidate stiffeners; Indicates that the first [number] is reserved. The beam torsion angle for each stiffener candidate element; the normalized suppression amount corresponding to the cross section distortion and the relative displacement of the guide rail are obtained in the same way.

[0092] The and Set according to the crossbeam design requirements; when the geometric accuracy of the guide rail is the main control target, Set to 0.4-0.6; when the torsional stiffness of the beam is the primary control target, Set to 0.4-0.6; increase when the local stability requirement of the cross-section is high. .

[0093] Candidate stiffener units with torsional contribution indices not lower than the torsional branch screening threshold are retained. Based on the design unit adjacency relationship and spatial mapping relationship, the connected components that are connected to the main path of bending load and can be continuously extended from the load area to the column connection area or the adjacent scale connection area are extracted to obtain the torsional force transmission branch.

[0094] The torsional branch screening threshold is determined by the preset quantile value of the torsional contribution index of all candidate stiffener units, taking the 60%-80% quantile value, preferably the 70% quantile value.

[0095] For candidate stiffener regions with high torsional contribution but not directly connected to the main bending load path, scale connection units are added along the shortest spatial mapping path between them and the main bending load path, so that the torsional force transmission branch and the main bending load path are continuously connected; the main bending load path, the torsional force transmission branch and the currently retained material unit form a second-scale material layout.

[0096] S24, read the spatial mapping relationship between the second-scale material layout and the internal stiffener scale design domain and the connection detail scale design domain, and perform local continuity judgment on the stiffener and wall panel connection area, stiffener intersection area, guide rail connection area and column connection area respectively.

[0097] For the first in the overall box-shaped dimension design domain The first design unit and the internal stiffener dimension design domain For each design unit, the first-scale continuity criterion is represented as follows: ; in, Indicates the first The overall box-shaped design unit and the first The first-dimensional continuity determination result among the internal stiffening plate dimensional design units; This indicates the spatial mapping relationship between the two; it is set to 1 if a spatial mapping relationship exists, and 0 otherwise. This indicates the geometric connection between the two elements. It is set to 1 when the two elements are in direct contact, have overlapping projections, or are connected through a scale-connecting region; otherwise, it is set to 0. This indicates the connectivity of the material paths between the two entities. It is set to 1 if there is a continuous material path to be retained, and 0 otherwise.

[0098] when When, it is determined that the main path of bending load and the torsional force transmission branch satisfy the first-scale continuity criterion; when When this happens, it is determined that the corresponding local area needs to be corrected.

[0099] For the design domain of internal stiffener dimensions, the first The first design unit and the connection detail scale design domain For each design unit, the second-scale continuity criterion is represented as follows: ; in, Indicates the first The internal stiffener dimension design unit and the first The result of the second-scale continuity determination between each connection detail-scale design unit; This indicates the spatial mapping relationship between the two; This indicates the geometric connection between the two. This indicates the connectivity of the material paths between the two; the rules for the values ​​of each variable are the same as the first-scale continuity criterion.

[0100] For local areas that do not meet the first-scale continuity criterion or the second-scale continuity criterion, corrections are made in the following order: First, the weakened or removed design units are restored layer by layer along the spatial mapping path, and material backfilling is performed; if an effective connection cannot be formed after material backfilling, the connection width is expanded along the contact boundary between the stiffener and the wall panel; if the discontinuous area is located at the intersection of two or more stiffeners, the connecting units in the intersection area of ​​the stiffeners are added to form a solid connection between the stiffeners.

[0101] The maximum number of backfill layers is 1-3 local design unit layers; the specific number of layers is determined based on the local mesh size and the minimum manufacturable connection width, ensuring that the actual width after backfilling is not less than the minimum stiffener connection width or minimum welded connection width specified in the manufacturing process. The connection width expansion amount is set as an integer multiple of the local mesh size, and the continuity judgment and local static analysis are re-executed after each expansion; expansion stops when both the first-scale continuity criterion and the second-scale continuity criterion are 1, and the local peak stress no longer decreases significantly with continued expansion; the phrase "no longer decreases significantly" is defined as the local peak stress reduction rate being less than 2%-5% after continuing to expand by one layer.

[0102] After correcting all discontinuous local regions, a continuous material layout across scales is obtained.

[0103] S25, for the cross-scale continuous material layout obtained by the current round topology iteration, extract material distribution characteristics, displacement response characteristics, stress response characteristics, strain energy distribution characteristics, low-order mode characteristics and cross-scale connection characteristics.

[0104] The material distribution characteristics include the material volume fraction, material centroid position, number of continuous material branches, width of the main bending load path, number of torsional force transmission branches, and spatial distribution of stiffeners in each design domain at each scale. The displacement response characteristics include the maximum displacement of the beam, the displacement of the guide rail mounting surface, the relative displacement of the two guide rails, and the displacement variation range under each moving load position. The stress response characteristics include the maximum equivalent stress, the proportion of high-stress elements, and the stress concentration in the connection area. The strain energy distribution characteristics include the total strain energy, the proportion of strain energy at each scale, the strain energy concentration, and the strain energy variation under each moving load position. The low-order modal characteristics include the first few natural frequencies, the main mode shapes, and the frequency interval between adjacent orders. The cross-scale connection characteristics include the design unit comparison scale that satisfies the first scale continuity criterion, the design unit comparison scale that satisfies the second scale continuity criterion, the width of the scale connection area, and the number of local fractures.

[0105] The normalized features described above form the performance prediction input vector for the current round of topology iteration, which is represented as follows: ; in, Indicates the topology iteration round; This represents the performance prediction input vector for the current round of topology iteration; Indicates the material distribution characteristics; Indicates the characteristics of displacement response; Indicates stress response characteristics; Indicates the characteristics of strain energy distribution; Represents low-order modal characteristics; This represents cross-scale connectivity features.

[0106] Output the first The performance contribution prediction results and structural constraint risk prediction results of each design unit are expressed as follows: ; in, Indicates the first The design unit in the first Performance contribution prediction results in round topology iteration; This indicates the corresponding structural constraint risk prediction result; This indicates data-driven performance prediction; Indicates the first The local material state, local strain energy density, local stress, scale, distance from the main bending load path or torsional load transmission branch, and connection status of each design unit.

[0107] S26, calculate the first round of finite element analysis results based on the current round's results. The basic material retention priority for each design unit is determined by the normalized strain energy density, force transmission frequency, path connectivity contribution, and scale connection contribution, and is expressed as follows: ; in, Indicates the first The design unit in the first Priority for retaining basic materials in round topology iteration; This represents the normalized strain energy density; Indicates the frequency of force transmission; This indicates the contribution of the design unit to the connectivity of the main bending load path or the torsional force transmission branch; This indicates the contribution of the design unit to continuous force transmission across scales; , , and This represents the corresponding basic evaluation weight, and satisfies: .

[0108] The basic evaluation weights are set according to the design objectives, with the strain energy density weight and the force transmission frequency weight set to relatively large values, such as... Set it to 0.25-0.40. Set it to 0.20-0.35. Set it to 0.15-0.30. Set it to 0.10-0.25.

[0109] The modification of the basic material retention priority based on the performance contribution prediction results and structural constraint risk prediction results from data-driven performance prediction is expressed as follows: ; in, Indicates the priority of material retention after revision; Indicates the performance contribution adjustment weight; Indicates the structural constraint risk correction weight; This means that the calculation result will be limited to the range of 0 to 1.

[0110] The larger the predicted performance contribution, the more significant the comprehensive positive contribution of the corresponding design unit to the reduction of beam mass, displacement suppression, stress reduction, natural frequency enhancement, or cross-scale continuous force transmission. Therefore, its material retention priority is increased. The larger the predicted structural constraint risk, the more likely the removal of the design unit will cause local stress concentration, force transmission interruption, modal deterioration, or manufacturing failure. Therefore, its material removal priority is reduced by increasing the material retention priority.

[0111] and The values ​​were set to 0.05-0.30 respectively; to avoid the data-driven performance prediction model from excessively interfering with the traditional topology sensitivity, Not exceeding 0.4.

[0112] For design units in non-removed areas and scale transition areas, regardless of the calculated material retention priority value, their material retention priority is forcibly set to 1.

[0113] S27. Update the material retention status in the overall box-shaped dimension design domain, the internal stiffener dimension design domain, and the connection detail dimension design domain according to the revised material retention priority; sort all material-adjustable design units from high to low according to material retention priority, and retain design units with higher priority while reducing or removing design units with lower priority, provided that the target material volume fraction of the current round is met.

[0114] No. The material status of each design unit is updated incrementally as follows: ; in, Indicates the first In the round topology iteration, the first Material condition of each design unit; Indicates the current material state; This indicates the target material state obtained based on the modified material retention priority and target material volume fraction; Indicates the material status update step size; Set to 0.1-0.5, preferably 0.3.

[0115] After updating the material status, a new finite element model corresponding to the current material layout is established, and finite element solution, bending load main path identification, torsional force transmission branch identification, local connection correction, performance prediction, and material retention priority correction are performed in sequence.

[0116] The change in material distribution between two adjacent topological iterations is expressed as: ; in, Indicates the first Wheel and the first The change in material distribution between wheels; This indicates that the number of design units for all materials can be adjusted.

[0117] The change in structural performance is expressed as follows: ; in, This represents the change in structural performance between two consecutive topology iterations; Indicates the first Wheel crossbeam material quality; Indicates the first The maximum displacement of the wheel under each moving load position; Indicates the first Maximum equivalent stress of the wheel; Indicates the first The first-order natural frequency of the wheel.

[0118] When the change in material distribution satisfies: ; And the change in structural performance satisfies: ; When the preset number of convergence rounds is maintained, the multi-scale topology iteration is determined to be converged, and the cross-scale beam material layout is output.

[0119] The material distribution convergence threshold Set to 0.005-0.02; structural performance convergence threshold. Set to 0.005-0.03, and preset the number of convergence rounds to 3-5 rounds.

[0120] The final output cross-scale beam material layout retains the main path of bending load, the branch path of torsional force transmission, and the local connection area that satisfies the first-scale continuity criterion and the second-scale continuity criterion.

[0121] S3. The cross-scale beam material layout is converted into a candidate beam structure composed of wall panels and continuous stiffeners. The candidate beam structure is subjected to static verification under moving load and low-order modal verification. Based on the verification results, cross-scale backfilling or stiffener connection correction is performed on local areas that do not meet the requirements until the candidate beam structure meets the preset mass, displacement, stress, natural frequency and manufacturing constraints. The beam optimization design result is then output.

[0122] S31. After completing the cross-scale topology iteration, the cross-scale beam material layout is obtained. The cross-scale beam material layout includes the material retention state, material removal state, scale connection area, and cross-scale continuous force transmission area in the overall box scale design domain, the internal stiffener scale design domain, and the connection detail scale design domain.

[0123] Based on the material retention status of each design unit, continuous material regions are extracted. The material retention units continuously distributed in the overall box-scale design domain are then fitted along the outer contour of the beam to form the outer wall panel region and the inner wall panel region.

[0124] Specifically, based on the spatial coordinates and material states of each material retention unit within the overall box-scale design domain in the cross-scale beam material layout, a set of continuous material units whose material states meet the retention conditions is selected. Then, the material retention units are sorted along the beam length direction and the cross-sectional circumference, and the unit nodes located at the outer boundary and the inner cavity boundary of the beam are extracted. The outer node boundary and the inner node boundary are fitted by spline fitting to form a continuous outer contour surface and an inner contour surface. The solid area corresponding to the outer contour surface is determined as the outer wall panel area, and the solid area corresponding to the inner contour surface is determined as the inner wall panel area.

[0125] The material retention units that are continuously distributed along the main path of bending load and the branch path of torsional force transmission in the internal stiffening plate scale design domain are directionally aggregated, and the connection relationship between adjacent material units is identified to form a continuous stiffening plate region.

[0126] Specifically, based on the positional relationship between the main bending load path and the torsional force transmission branch in the cross-scale beam material layout, material retention units corresponding to their spatial dimensions are selected in the internal stiffener scale design domain. Then, based on the center coordinates, main direction vector, and unit adjacency relationship of each material retention unit, the material retention units continuously arranged along the same force direction are aggregated in direction, and it is determined whether there are common nodes, common edges, or solid contact relationships between adjacent material units. When adjacent material units meet the connection conditions, they are merged into the same stiffener region, and the stiffener boundary is smoothed to obtain a continuous stiffener region continuously distributed along the main bending load path and the torsional force transmission branch.

[0127] The retained material units located in the connection areas of stiffeners and wall panels, stiffener intersection areas, guide rail connection areas, and column connection areas in the connection detail scale design domain are extracted as connection transition areas.

[0128] Specifically, based on the area identification information in the connection detail scale design domain, the spatial ranges corresponding to the stiffener and wall panel connection area, stiffener intersection area, guide rail connection area, and column connection area are located respectively. Then, the design units located in the above areas and whose material state is retained are screened, and based on their spatial mapping relationship with the overall box scale design domain or the internal stiffener scale design domain, it is determined whether they participate in cross-scale load transfer. Material retained units that meet the regional position constraints and cross-scale connection relationships are merged to form a connection transition area.

[0129] For regions where there are discontinuities between discrete material elements but the manufacturing connection requirements are met, structural merging is performed based on material continuity constraints, and the adjacency relationship of the material elements is established as follows: ; in: For the first The design unit and the first The value for determining the continuity relationship between design units; The spatial distance between two design units; The threshold for continuous material merging distance; To determine whether there are shared nodes, shared edges, or entity connections between two design units.

[0130] The material continuous merging distance threshold The dimensions are determined based on the finite element mesh size and the actual minimum connection size during processing, and are set to 1-2 times the average size of the elements. When the beam is manufactured by welding, the dimensions are determined based on the effective connection width of the weld. When it is manufactured by integral casting or additive manufacturing, the dimensions are determined based on the continuous forming capability of the material. When the continuity relationship judgment value meets the preset conditions, the corresponding discrete material elements are merged into continuous structural elements, and the boundary of the merged structure is smoothed to maintain a continuous curved surface transition in the wall panel area and a continuous force transmission direction in the stiffener area, ultimately forming a candidate beam structure composed of wall panels and continuous stiffeners.

[0131] S32, after obtaining the candidate structure of the crossbeam, establish a set of moving load conditions based on the actual working state of the crossbeam; set multiple spindle box moving positions along the crossbeam guide rail direction, take the load action area corresponding to each moving position as the static analysis input, and keep the constraint state of the guide rail connection area and column connection area consistent with the actual installation state to form a static check of the moving load.

[0132] For the For each moving load location, the candidate beam structure is solved using the finite element method, and the corresponding nodal displacement field is expressed as follows: ; in: For the first Displacement response results at each moving load location; For the first Displacement response of each finite element node.

[0133] The maximum displacement is extracted from the displacement response results and represented as follows: ; in: This represents the maximum displacement response of the candidate beam structure at all moving load locations.

[0134] The stress response of each design element obtained from the finite element method is expressed as follows: ; in: For the first Equivalent stress of each design unit.

[0135] Extracting maximum stress: ; Modal analysis was performed on the candidate beam structure, and the low-order modal response results are expressed as follows: ; in: These are the results for low-order modal responses; For the first The first natural frequency.

[0136] The structural verification results are established based on the candidate beam structure's mass, maximum displacement, maximum stress, natural frequency, and manufacturing constraints; the structural verification results are defined as follows: ; in: For the candidate structural mass of the beam, To generate constraint verification results, including minimum wall thickness, stiffener connection width, and machining accessibility.

[0137] The mass threshold is determined based on the original beam structure mass, the overall lightweight requirements of the machine tool, and the requirements for maintaining the beam load-bearing capacity. First, the initial mass of the existing beam design is obtained. Then, the allowable weight reduction ratio is determined based on the machine tool dynamic response requirements and the structural lightweighting target. The original mass is multiplied by the allowable retention ratio to obtain the mass threshold. The allowable retention ratio is determined through historical beam optimization cases and finite element verification results, and is set to 70%-90% of the original structural mass.

[0138] The displacement threshold is determined based on the accuracy requirements of the crossbeam guide rail, the positioning error requirements of the spindle box, and the allowable deformation range during the machining process. First, the allowable deformation range of the machine tool guide rail and the positioning accuracy index of the spindle box are obtained. The allowable displacement error of the guide rail installation area, the machining accuracy requirements of the spindle, and the thermal deformation compensation capability are comprehensively analyzed to determine the maximum allowable displacement range of the crossbeam. Then, through finite element static analysis of multiple historical crossbeam structures, the maximum displacement value corresponding to meeting the machining accuracy requirements is statistically analyzed. The maximum displacement value that can ensure the stable operation of the guide rail and the machining accuracy is taken as the displacement threshold.

[0139] The stress threshold is determined based on the mechanical properties of the beam material, the structural safety factor, and the long-term cyclic load conditions. First, the yield strength or allowable fatigue strength of the beam material is obtained. Then, a safety factor is set according to the frequency of moving loads, impact loads, and service life requirements of the beam. The stress threshold is obtained by calculating the allowable stress of the material. The safety factor is set to 1.5-2.5 according to the machine tool operating environment.

[0140] The natural frequency threshold is determined based on the excitation frequency range, spindle speed range, and dynamic design requirements to avoid resonance during the beam's operation. First, the spindle rotation frequency, cutting cycle frequency, spindle box reciprocating frequency, and other periodic excitation frequencies are obtained to form the beam's working excitation frequency range. Then, modal analysis is performed on the original beam structure and several optimized structures to obtain the distribution of each natural frequency, avoiding frequency regions close to the working excitation frequency. Typically, the lowest natural frequency is set to 1.2-1.5 times or more of the maximum working excitation frequency, or a safe frequency interval is set based on engineering experience. By comparing the beam's vibration response and machining stability under different natural frequency thresholds, the frequency value that avoids resonance and meets dynamic stiffness requirements is selected as the natural frequency threshold.

[0141] The manufacturing constraint thresholds are determined based on the capabilities of the beam processing equipment, material forming processes, welding process requirements, and assembly connection requirements. First, the actual manufacturing process parameters of the beam are obtained, including the minimum machinable wall thickness, minimum stiffener thickness, minimum stiffener spacing, effective weld connection width, and the space accessible to the machining tools. Then, these process constraints are converted into structural constraints, such as minimum wall thickness thresholds, minimum stiffener width thresholds, and minimum connection area size thresholds, which are treated as inviolable conditions during topology optimization. Specific threshold values ​​are determined based on the precision of the manufacturing equipment and process specifications. For example, when using machining, the thresholds are determined based on tool size and machining stiffness; when using welded structures, they are determined based on weld size and thermal deformation control requirements. Finally, the manufacturing constraint thresholds that guarantee structural manufacturability are determined through trial processing verification or statistical analysis of historically manufactured qualified structural dimensions.

[0142] S33. Based on the structural verification results, the constraint satisfaction of the candidate beam structure is judged. First, the maximum displacement, maximum stress, natural frequency and manufacturing constraint results in the structural verification results are compared with the corresponding thresholds to determine the local areas that do not meet the constraint requirements.

[0143] For abnormal areas located in the overall box-shaped design domain, the judgment is made based on the force transmission relationship between the area and the main bending load path, the load application area, and the column connection area; when the interruption of the material continuous path, the concentration of strain energy, or the reduction of load transmission efficiency is detected, cross-scale backfilling is performed on the corresponding area.

[0144] The cross-scale backfill area is represented as follows: ; in: This is a set of design units to be backfilled. For the first The continuous force transmission evaluation value of each design unit; The threshold for determining continuous force transmission is determined by: material regions in different beam design schemes that can maintain continuous transmission from the load application area to the column connection area as effective force transmission samples, and material regions where force transmission is interrupted, local stress concentration occurs, or displacement suddenly increases as invalid force transmission samples. The distribution range of the continuous force transmission evaluation values ​​of the corresponding design units is statistically analyzed. Then, the boundary value between the lowest evaluation value in the effective force transmission samples and the highest evaluation value in the invalid force transmission samples is used as the threshold for determining continuous force transmission.

[0145] For abnormal areas in the internal stiffener dimensional design domain, the judgment is based on the continuity of the torsional force transmission branches; when there are discontinuities between stiffeners, discontinuous torsional paths, or increased cross-sectional distortion response, continuous stiffener paths are supplemented through stiffener connectivity correction; specifically including: 1. Search for the nearest consecutive stiffening element in the area of ​​the broken stiffening element; 2. Connect the disconnected areas along the load transfer direction; 3. Adjust the width of the supplementary area to meet the requirements for stiffener manufacturing.

[0146] For anomalous areas in the connection detail-scale design domain, connection area expansion or local material reinforcement is performed based on the degree of local stress concentration and connection manufacturing constraints.

[0147] The extent of localized material reinforcement is based on: Sure.

[0148] in: For localized material reinforcement areas; For the first Stress in each design unit; The threshold for stress concentration is set at 80%-90% of the allowable stress of the material, in order to avoid the risk of local plasticity in advance.

[0149] After modification, the revised candidate beam structure was obtained.

[0150] S34. The modified candidate beam structure is re-input into the finite element model. The displacement response results, stress distribution results, and low-order modal response results are recalculated according to the moving load static verification method and low-order modal verification method in S32. The structural verification results are then regenerated.

[0151] The optimization convergence state is determined by the change in structural performance during two consecutive iterations, as expressed in the following: ; in: This refers to the change in structural performance. For the first The structural verification results of the round iteration; For the first The results of the structural verification of the round of iterations.

[0152] The candidate beam structure is considered to have reached an optimized state when the following conditions are met: 1. The quality meets the quality threshold requirements; 2. The maximum displacement is less than the displacement threshold; 3. The maximum stress is less than the stress threshold; 4. The low-order natural frequency meets the dynamic performance requirements; 5. The wall panels, stiffening ribs, and connection areas meet manufacturing constraints; 6. The change in structural performance between two adjacent iterations is less than the convergence threshold.

[0153] The convergence threshold is determined based on the stability of topology optimization and is set to 1%-5%. If the change in structural performance is below this range, it is considered that continuing the iteration will not produce a significant optimization effect.

[0154] If any of the above conditions are not met, the abnormal area will be relocated based on the new structural verification results, and cross-scale backfilling, stiffener connection correction and connection area optimization will continue to be performed until all constraints are met, and finally the beam optimization design results that meet the requirements of lightweight, load-bearing performance, dynamic performance and manufacturing will be output.

[0155] Example 2 like Figure 4 As shown, the beam optimization design system based on multi-scale topology and data-driven methods includes the following modules: A multi-scale optimization domain construction module is used to divide the beam design domain into an overall box-shaped scale design domain, an internal stiffener scale design domain, and a connection detail scale design domain, set non-removal areas and scale connection areas, and construct a multi-scale beam optimization domain based on the load transfer continuity under moving loads. A multi-scale topology iteration module is used to identify the main path of bending load and the branch of torsional force transmission based on the multi-scale beam optimization domain, perform local continuity correction on the cross-scale connection area, and use the performance contribution prediction results and structural constraint risk prediction results output by the data-driven performance prediction model to correct the material retention priority, and obtain the cross-scale beam material layout through iterative updates. The structural reconstruction and verification module is used to convert the cross-scale beam material layout into a candidate beam structure composed of wall panels and continuous stiffeners. The module performs static verification of moving loads and low-order modal verification on the candidate beam structure, and performs cross-scale backfilling, stiffener connectivity correction or connection area correction according to the structural verification results, until the preset mass, displacement, stress, natural frequency and manufacturing constraints are met, and outputs the beam optimization design results.

[0156] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0157] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A beam optimization design method based on multi-scale topology and data-driven approach, characterized in that, Includes the following steps: The beam design domain is divided according to the overall box dimensions, internal stiffener dimensions, and connection detail dimensions. Non-removable areas are set in the guide rail connection area, column connection area, and load application area. Based on the load transfer continuity under moving load, the design domains of each scale are coupled to obtain the multi-scale beam optimization domain. Based on the multi-scale beam optimization domain input multi-scale topology iteration unit, the main path of bending load is determined at the overall box scale. Based on the internal stiffener dimensions, the torsional force transmission branch connected to the main bending load path is determined, and the local connection between the main bending load path and the torsional force transmission branch is corrected at the connection detail dimensions. Based on the data-driven performance prediction trained by the existing design scheme of the beam and the corresponding finite element verification results, the material retention priority in each round of topology iteration is corrected to obtain the cross-scale beam material layout. Based on the cross-scale beam material layout, the candidate beam structure is converted into a beam composed of wall panels and continuous stiffeners. The candidate beam structure is then subjected to static verification under moving load and low-order modal verification. Based on the verification results, cross-scale backfilling or stiffener plate connection correction is performed on the local areas that do not meet the requirements, and the beam optimization design results are output.

2. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 1, characterized in that, The overall box-shaped dimensional design domain, determined based on the outer and inner wall panels of the crossbeam and the outer profile of the cross section, is expressed as follows: ;in, Design domain for overall enclosure dimensions; This refers to the spatial area corresponding to the outer wall panel. For the space area corresponding to the inner wall panel, the internal stiffening dimensional design domain is determined based on the internal space between the outer and inner wall panels used for setting the stiffening ribs, and is expressed as follows: ;in, Design domain for internal stiffener dimensions; This refers to the internal cavity region formed between the outer and inner wall panels; The reserved space for assembly passages, maintenance passages, and chip removal passages must not include stiffening slabs. The detailed design domain for connections is determined based on the areas where stiffening slabs connect to wall panels, where stiffening slabs intersect, where guide rails connect, and where columns connect. ;in, Design domains for connecting detailed scales; This is the area where the stiffening slab connects to the wall panel; This is the area where the stiffening plates intersect; This is the guide rail connection area; For the column connection area, the spatial mapping relationship between the overall box-shaped dimensional design domain, the internal stiffening rib dimensional design domain, and the connection detail dimensional design domain is expressed as follows: ； ； in, The spatial mapping matrix between the overall box-shaped design domain and the internal stiffening plate design domain; The spatial mapping matrix between the internal stiffener scale design domain and the connection detail scale design domain; The first in the overall box-shaped design domain Design unit; The first in the internal stiffener dimensional design domain Design unit; To connect the first in the detailed scale design domain Each design unit yields the segmented design domain for the beam.

3. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 2, characterized in that, In the aforementioned crossbeam segmented design domain, the guide rail connection area corresponding to guide rail installation and force transmission, the column connection area corresponding to the connection between the crossbeam end and the column, and the load application area covered by the load during the movement of the spindle box are marked as non-removable areas and represented as follows: ;in, This is the area that will not be removed. This is the guide rail connection area; This is the area where the columns connect; The load application area is defined as the material region directly connected to the non-removed area and used to transfer loads to adjacent scales, which is then labeled as the scale transition area. ； in, This is the area where scales connect; For the first The shortest distance between each design unit and the non-removed area; The distance between scale connections; For scale-related identifiers, when the first When establishing a spatial mapping relationship between a design unit and an adjacent scale design domain This yields a beam-scale constraint domain with non-removal constraints and scale connection constraints.

4. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 3, characterized in that, Multiple moving load positions are set along the direction of the crossbeam guide rail, and the moving load positions are arranged in an equally spaced manner as follows: ;in, For the first The coordinates of the moving load position in the direction of the crossbeam guide rail; The starting position of the allowable range of movement of the spindle box; The end position of the allowable movement range of the spindle box; This represents the total number of moving load locations. Based on the crossbeam's segmental constraint domain, the load transfer area extending from the load application area to the column connection area at each moving load position is represented as follows: ;in, For the first Load transfer area at each moving load location; This indicates the extraction of a design element from candidate force transmission elements that is simultaneously connected to both the load application area and the column connection area. For the first A set of candidate force transmission units at each moving load location; For the first The load action sub-region corresponding to each moving load location; For the column connection area; for any design unit in the beam's segmented constraint domain, the frequency of its identification as a load transfer area under all moving load positions is represented as follows: ； in, For the first The frequency of force transmission in each design unit; For indicator functions; This represents the total number of moving load locations. For the first The load transfer area under each moving load position is defined as the stable force transfer area, and the load transfer area that migrates with the change of the moving load position is defined as the migrating force transfer area. The stable force transfer area and the migrating force transfer area in the overall box-shaped design domain, the corresponding force transfer area in the internal stiffener design domain, and the local connection area in the connection detail design domain are continuously coupled through the scale connection area to obtain the multi-scale beam optimization domain.

5. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 1, characterized in that, The non-removed regions and scale connection regions in the multi-scale beam optimization domain are set as forced material retention regions, and the remaining regions are set as material adjustable regions. Initial material retention states are configured for the overall box-shaped scale design domain, the internal stiffener scale design domain, and the connection detail scale design domain, respectively. The initial material state variables are represented as follows: ;in, Indicates the scale type. Indicates the overall dimensions of the enclosure. Indicates the dimensions of the internal stiffeners. Indicates the detail scale of the connection; Indicates the design unit number within the corresponding scale design domain; Indicates the first In the design domain of the first scale Initial material state variables for each design unit; Indicates the first Forced material retention areas in each scale design domain; Indicates the first Adjustable material areas within a single-scale design domain; The initial material retention state of the material-adjustable region is represented to obtain the cross-scale topological initial domain; The load conditions corresponding to each moving load position are applied to the cross-scale topological initial domain and finite element analysis is performed. Based on the strain energy density, force transmission frequency, and connectivity between each design element in the overall box-scale design domain and the load application area and column connection area at each moving load position, the strain energy density is expressed as: ;in, Indicates the first The overall box-shaped design unit is in the first Strain energy density at each moving load location; This represents the element strain energy of the design unit; The actual volume of the design unit is represented, and the bending load-bearing main path extending continuously from the load-bearing area to the column connection area is determined, resulting in the first-scale material layout with the bending load-bearing main path.

6. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 5, characterized in that, Based on the spatial mapping relationship between the first-scale material layout and the overall box-shaped design domain and the internal stiffener design domain, candidate stiffener regions corresponding to the main bending load path are extracted from the internal stiffener design domain. Based on the degree to which each candidate stiffener region suppresses the torsional deformation of the beam, cross-sectional distortion, and relative displacement of the guide rail, the torsional contribution index is obtained as follows: ;in, Indicates the first Torsional contribution index of each candidate stiffener unit; This represents the normalized suppression of the beam torsion angle by the candidate stiffener element; This represents the normalized suppression of cross-sectional distortion by the candidate stiffener element; This represents the normalized suppression amount of the relative displacement of the guide rail by the candidate stiffener element; , and Let represent the evaluation weights corresponding to the torsion angle, cross-sectional distortion, and relative displacement of the guide rail, respectively, and satisfy the following: Determine the torsional force transmission branch that is connected to the main bending load path and extends from the load application area to the column connection area, and obtain a second-scale material layout with the main bending load path and the torsional force transmission branch. Based on the spatial mapping relationship between the material layout of the second scale and the internal stiffener scale design domain and the connection detail scale design domain, local continuity judgment is performed on the stiffener-wall panel connection area, stiffener intersection area, guide rail connection area and column connection area. The first-scale continuity criterion is expressed as: ;in, Indicates the first The overall box-shaped design unit and the first The first-dimensional continuity determination result among the internal stiffening plate dimensional design units; This indicates the spatial mapping relationship between the two; This indicates the geometric connection between the two. This indicates the connectivity of the material paths between the two. The second-scale continuity criterion is expressed as: ;in, Indicates the first The internal stiffener dimension design unit and the first The result of the second-scale continuity determination between each connection detail-scale design unit; This indicates the spatial mapping relationship between the two; This indicates the geometric connection between the two. This indicates the connectivity of the material paths between the two. Local areas that do not meet the first or second scale continuity criteria are corrected by material backfilling, connection width expansion, or stiffener intersection connection to obtain a cross-scale continuous material layout. The material distribution characteristics, displacement response characteristics, stress response characteristics, strain energy distribution characteristics, low-order modal characteristics, and cross-scale connection characteristics of the cross-scale continuous material layout are extracted in the current round topology iteration. These characteristics are then input into the data-driven performance prediction trained based on the existing beam design scheme and corresponding finite element verification results. The performance contribution prediction results and structural constraint risk prediction results of each design unit are expressed as follows: ;in, Indicates the first The design unit in the first Performance contribution prediction results in round topology iteration; This indicates the corresponding structural constraint risk prediction result; This indicates data-driven performance prediction; Indicates the first The local material state, local strain energy density, local stress, scale, distance from the main bending load path or torsional load transmission branch, and connection status of each design unit. This represents the performance prediction input vector for the current round topology iteration.

7. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 6, characterized in that, The material retention priority for design units that positively contribute to beam mass reduction, displacement suppression, stress reduction, natural frequency enhancement, or cross-scale continuous force transmission, based on the performance contribution prediction results, is expressed as follows: ;in, Indicates the first The design unit in the first Priority for retaining basic materials in round topology iteration; This represents the normalized strain energy density; Indicates the frequency of force transmission; This indicates the contribution of the design unit to the connectivity of the main bending load path or the torsional force transmission branch; This indicates the contribution of the design unit to continuous force transmission across scales; , , and This represents the corresponding basic evaluation weight, and satisfies: Based on the structural constraint risk prediction results, the material removal priority of design units that may cause local stress concentration, force transmission interruption, modal deterioration, or manufacturing impracticality is reduced, resulting in the corrected material retention priority expressed as: ;in, Indicates the priority of material retention after revision; Indicates the performance contribution adjustment weight; Indicates the structural constraint risk correction weight; This means that the calculation result will be limited to the range of 0 to 1; Indicates the first The design unit in the first Performance contribution prediction results in round topology iteration; This indicates the corresponding structural constraint risk prediction result; Update the material retention status in the overall box-shaped dimension design domain, the internal stiffener dimension design domain, and the connection detail dimension design domain according to the revised material retention priority, and re-execute the finite element solution, bending load main path identification, torsional force transmission branch identification, local connection correction, and material retention priority correction. No. The material status of each design unit is updated incrementally as follows: ;in, Indicates the first In the round topology iteration, the first Material condition of each design unit; Indicates the current material state; This indicates the target material state obtained based on the modified material retention priority and target material volume fraction; Indicates the material status update step size; The change in material distribution between two adjacent topological iterations is expressed as: ;in, Indicates the first Wheel and the first The change in material distribution between wheels; This indicates that the number of design units for all materials can be adjusted; The change in structural performance is expressed as follows: ;in, This represents the change in structural performance between two consecutive topology iterations; Indicates the first Wheel crossbeam material quality; Indicates the first The maximum displacement of the wheel under each moving load position; Indicates the first Maximum equivalent stress of the wheel; Indicates the first The first-order natural frequency is used until the changes in material distribution and structural performance in two adjacent rounds of topological iteration satisfy the preset convergence condition, and then the cross-scale beam material layout is output.

8. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 1, characterized in that, The cross-scale beam material layout is geometrically reconstructed. Based on the material retention state in each scale design domain, continuous wall panel regions, stiffening plate regions, and connecting transition regions are extracted. Discrete material elements are then merged into continuous structural elements according to material continuity constraints. The adjacency relationship of the material elements is represented as follows: ； in: For the first The design unit and the first The value for determining the continuity relationship between design units; The spatial distance between two design units; The threshold for continuous material merging distance; To determine whether there is a relationship between two design units, generate candidate beam structures consisting of wall panels and continuous stiffening plates; Static load conditions and modal analysis conditions corresponding to various moving load positions are applied to the candidate beam structure, and finite element analysis is performed to obtain the beam displacement response, stress distribution, and low-order modal response results under different moving load positions. Based on the candidate beam structure's mass, maximum displacement, local stress, natural frequency, and manufacturing constraints, a comprehensive verification of the candidate beam structure is performed, and the structural verification results are expressed as follows: ;in: For the candidate structural mass of the beam, To generate constraint verification results; These are the results for low-order modal responses; This represents the maximum displacement response of the candidate beam structure at all moving load locations; This represents the maximum stress.

9. The beam optimization design method based on multi-scale topology and data-driven approach according to claim 9, characterized in that, Based on the structural verification results, local areas that do not meet the preset mass, displacement, stress, natural frequency, or manufacturing constraints are located, and corresponding corrections are performed according to the scale type of the local area. For areas in the overall box-shaped design domain where performance degrades due to interrupted force transmission paths, continuous material areas are restored through cross-scale backfilling. The cross-scale backfilled areas are represented as follows: ;in: This is a set of design units to be backfilled. For the first The continuous force transmission evaluation value of each design unit; The threshold for continuous force transmission is set. For areas in the internal stiffener scale design domain where the torsional resistance is reduced due to stiffener discontinuity, continuous stiffener paths are supplemented by stiffener connection correction. For areas in the connection detail scale design domain where stress concentration or manufacturing is impossible due to insufficient local connection, correction is made by connection area expansion or local material reinforcement to obtain the corrected beam candidate structure. The modified candidate beam structure is re-verified with static load and low-order modal verification. Based on the updated structural verification results, it is determined whether the preset mass, displacement, stress, natural frequency and manufacturing constraints are met. If the requirements are not met, cross-scale backfilling or stiffener connection correction is performed according to the corresponding scale of the unmet area until the candidate beam structure meets all the constraints. The optimized design result of the beam is then output.

10. A beam optimization design system based on multi-scale topology and data-driven approach, used to implement the beam optimization design method based on multi-scale topology optimization and data-driven approach as described in any one of claims 1-9, characterized in that, Includes the following modules: A multi-scale optimization domain construction module is used to divide the beam design domain into an overall box-shaped scale design domain, an internal stiffener scale design domain, and a connection detail scale design domain, set non-removal areas and scale connection areas, and construct a multi-scale beam optimization domain based on the load transfer continuity under moving loads. A multi-scale topology iteration module is used to identify the main path of bending load and the branch of torsional force transmission based on the multi-scale beam optimization domain, perform local continuity correction on the cross-scale connection area, and use the performance contribution prediction results and structural constraint risk prediction results output by the data-driven performance prediction model to correct the material retention priority, and obtain the cross-scale beam material layout through iterative updates. The structural reconstruction and verification module is used to convert the cross-scale beam material layout into a candidate beam structure composed of wall panels and continuous stiffeners. The module performs static verification of moving loads and low-order modal verification on the candidate beam structure, and performs cross-scale backfilling, stiffener connectivity correction or connection area correction according to the structural verification results, until the preset mass, displacement, stress, natural frequency and manufacturing constraints are met, and outputs the beam optimization design results.

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