Method for determining the position of the four main supports of the bed of a horizontal machining center

Abstract

The present application relates to the field of numerical control machine tool design and manufacture, disclose a kind of method for determining the four-point main support position of horizontal machining center bed, the method is first according to the structure characteristics of bed bottom surface Construct alternative position set, and based on the principle of barycentric projection constraint It is divided into column working area subset and rotary table working area subset;Subsequently, a multi-working-condition whole machine finite element model containing different position combinations of moving parts is established, and an orthogonal table design test scheme is used;During the simulation process, the supporting stiffness is dynamically updated for each test group using an iterative correction mechanism based on the power function relationship of support reaction force, and the whole machine response is solved and obtained;On this basis, a comprehensive evaluation index integrating the flatness of guide rail and natural frequency is constructed;Finally, the optimal level combination is determined as the four main support positions through index mean analysis.The present application fully considers the influence of nonlinear contact stiffness and whole machine barycentric drift, effectively improves the static accuracy retention and dynamic stiffness characteristics of the whole machine.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical control machine tool design and manufacturing, in particular to a method for determining the four-point main support position of a horizontal machining center bed. BACKGROUND

[0002] As high-precision manufacturing equipment, the support layout of the bed of a horizontal machining center directly determines the gravity flow line distribution and anti-vibration performance of the whole machine. In order to ensure the precision stability of the machine tool and its adaptability to the installation environment, a structure form of four-point main support combined with auxiliary support is usually adopted. However, the rationality of the main support position of the bed is crucial to the final machining precision of the machine tool, and an improper support layout will cause a large geometric deformation of the bed guide rail, seriously affecting the machining quality.

[0003] The existing bed support position design mostly relies on the experience of designers or statics analysis based on a single fixed working condition, and often fails to fully consider the phenomenon of center of gravity drift of large mass moving parts such as columns and rotary tables during the whole stroke movement. If the support points are not properly selected, the center of gravity may deviate from the stable area of the support polygon under certain working conditions, resulting in a large overturning moment or distortion of the machine tool. At the same time, if the traditional full permutation and combination method is used to optimize all candidate points, the calculation scale is huge, and it is difficult to quickly obtain an optimal layout that meets the stability requirements within the engineering design cycle.

[0004] In the simulation analysis link of the whole machine performance optimization, the existing modeling method usually simplifies the joint surface of the anchor bolt and the foundation as a completely fixed rigid constraint or a linear spring element with constant stiffness coefficient. However, under actual physical working conditions, the contact stiffness of the support joint surface has obvious nonlinear characteristics, and its value will dynamically change with the size and distribution of the support force. Using a linear constant stiffness model cannot accurately reflect the true contact state when the load is redistributed, resulting in a large deviation between the simulation obtained whole machine response data and the actual physical prototype stress and deformation characteristics, reducing the credibility of the optimization results.

[0005] In addition, the existing support position optimization scheme usually only takes minimizing the static maximum deformation or maximizing the first-order natural frequency as a single optimization target. This single-target evaluation strategy cannot balance the static geometric precision retention and dynamic cutting stability of the machine tool. Pursuing only the optimal static stiffness may ignore the influence of modal vibration mode on machining quality, and pursuing only the optimal dynamic frequency may lead to the static straightness or flatness of the guide rail under the action of gravity. Therefore, there is an urgent need for a method for determining the main support position of the bed of a horizontal machining center that can balance the static and dynamic performance, and is efficient in calculation and accurate in boundary conditions. SUMMARY

[0006] The application provides a method for determining four-point main supporting positions of a horizontal machining center bed body, aiming to solve the technical problem that the prior art determines the supporting positions based on experience or a single static working condition, and fails to fully consider the center of gravity drift of the whole machine caused by the position change of the moving parts and the nonlinear change of the supporting contact stiffness, thereby affecting the precision retention and dynamic characteristics of the machining center.

[0007] The application provides a method for determining four-point main supporting positions of a horizontal machining center bed body, mainly comprising the following steps:

[0008] Firstly, the supporting candidate position set of the bed body is determined according to the bottom surface structure characteristics of the horizontal machining center bed body, and the supporting candidate position set is divided into a supporting position subset A located below the column working area and a supporting position subset B located below the rotary table working area; secondly, a whole machine finite element model of the horizontal machining center considering multiple working conditions is established, the multiple working conditions cover the combination of different stroke positions of the column and the rotary table on the bed body; thirdly, the supporting position subset A and the supporting position subset B are selected as test factors, an orthogonal test scheme is designed by using an orthogonal table, and multiple tests containing different main supporting position combinations are determined; subsequently, for each test in the orthogonal test scheme, the supporting stiffness at the supporting position is calculated based on an iterative correction mechanism, and the whole machine finite element model of the horizontal machining center is solved to obtain the whole machine response; then, the whole machine evaluation index is constructed according to the whole machine response, and the whole machine evaluation index comprehensively represents the static precision retention and dynamic stiffness characteristics of the whole machine; finally, the whole machine evaluation index of each test is analyzed, the level of the supporting position subset A and the level of the supporting position subset B that make the whole machine evaluation index optimal are determined, and the corresponding positions are determined as the four main supporting positions of the horizontal machining center bed body.

[0009] Further, when the supporting candidate position set of the bed body is determined, the reinforcing rib arrangement form and stress characteristics of the bottom surface of the horizontal machining center bed body are mainly used. Specifically, the corner point positions of the bed body bottom surface geometric contour, the intersection positions of the longitudinal reinforcing ribs and the transverse reinforcing ribs, the variable cross-section positions where the bed body cross-section shape changes, and the main load-bearing area positions are selected as candidate elements. These positions usually have higher local stiffness and can effectively transfer loads.

[0010] Further, in order to ensure the stability of the whole machine in various motion states, the barycentric projection constraint principle is followed in the division of the subsets. The principle requires obtaining the projection points of the barycenter of the horizontal machining center whole machine in different working conditions on the bottom surface of the bed, and determining whether these projection points are all located inside the minimum quadrilateral area formed by the combination of the elements in the selected supporting position subset A and the elements in the supporting position subset B. For the bed with structural symmetry, only the independently changed elements on one side of the symmetry axis are selected to participate in the design when the test scheme is designed, and the positions on the other side are determined according to the symmetry relationship, so as to reduce the calculation amount and ensure the balanced structure stress.

[0011] Further, the establishment process of the whole machine finite element model includes feature simplification of the three-dimensional model, removal of chamfers, non-assembly holes and small features. In the boundary condition setting, the bolted joint is simulated by binding contact, and the guide rail slider, screw nut and bearing and other moving joints are simulated by spring damping unit to reflect the axial and radial stiffness, so as to truly reflect the dynamic characteristics of the whole machine. The multiple working conditions specifically include all permutation combinations of the column at the left limit, middle and right limit positions of the bed and the rotary table at the front limit, middle and rear limit positions of the bed, so as to cover the whole process of the change of the barycenter of the whole machine.

[0012] Further, the core of the present application is to adopt a stiffness calculation method based on an iterative correction mechanism. For each test group, first, a fixed constraint and a gravity load are applied at the corresponding supporting position to pre-calculate and extract the initial support reaction force. Then, the fixed constraint is removed and an elastic element is established. In the calculation process, the normal stiffness and the tangential stiffness are updated by using the support reaction force according to the preset function relationship between the stiffness and the support reaction force. Specifically, the normal stiffness is positively correlated with the support reaction force at the supporting position, and the value of the normal stiffness is determined based on the first power index operation of the support reaction force and combined with the normal stiffness reference coefficient; similarly, the value of the tangential stiffness is determined based on the second power index operation of the support reaction force and combined with the tangential stiffness reference coefficient. The updated stiffness is assigned to the elastic element and re-solved, and whether the new and old support reaction forces meet the convergence condition is compared. If not, the above process is repeated until the calculation converges. This method overcomes the problem that the traditional linear spring element cannot simulate the nonlinear change of the contact stiffness of the foundation bolt and the ground with the pressure.

[0013] Further, the construction of the whole machine evaluation index aims to realize the comprehensive optimization of the static and dynamic performance. Specifically, the column guide rail flatness, the rotary table guide rail flatness and the first order natural frequency of the whole machine are extracted as response parameters after meeting the iterative convergence condition. By setting the global weight coefficient of the flatness index, the global weight coefficient of the natural frequency index and the local weight coefficient of each guide rail flatness, the guide rail flatness in each working condition is weighted and summed, and the comprehensive evaluation index is calculated combined with the first order natural frequency of the whole machine.

[0014] Furthermore, the final location was determined using range or mean analysis of orthogonal experiments. The mean values ​​of the overall machine evaluation index for support location subsets A and B were calculated at each test level. The level that minimized (or optimized) the mean value of the overall machine evaluation index was selected as the optimal level for that factor. These combinations yielded four main support locations. In addition, the remaining locations in the candidate set, besides the four main support locations, were designated as auxiliary support locations for auxiliary support and adjustment.

[0015] This invention provides a method for determining the positions of the four main supports of a horizontal machining center bed. It has the following beneficial effects:

[0016] 1. This invention divides the alternative positions of the bed support into a subset of the column working area and the turntable working area, and introduces the principle of center of gravity projection constraint for orthogonal experimental design. This reduces the calculation scale of all permutations and combinations, while effectively avoiding the risk of the center of gravity of the whole machine deviating from the support polygon area due to the change of the position of the moving parts. This enables the rapid and accurate determination of the main support layout that meets the anti-overturning stability requirements of the whole machine under multiple working conditions.

[0017] 2. This invention utilizes a stiffness calculation method based on an iterative correction mechanism to dynamically update the normal and tangential contact stiffness parameters according to the support reaction force at the support position. This overcomes the shortcomings of traditional linear constant stiffness models that cannot characterize the nonlinear contact behavior between anchor bolts and the ground, improves the simulation confidence of the finite element model under different load distributions, and ensures that the obtained whole-machine response data truly reflects the stress and deformation state of the actual physical system.

[0018] 3. This invention constructs a comprehensive evaluation index that integrates the flatness of the guide rail under multiple working conditions and the first-order natural frequency of the whole machine. It overcomes the one-sidedness of optimizing a single static or dynamic index and ensures that the determined four main support positions can effectively suppress the deformation of the bed guide rail caused by the redistribution of gravity load, and improve the dynamic stiffness characteristics of the whole machine, thereby ensuring the geometric accuracy retention and vibration resistance of the horizontal machining center under complex machining conditions. Attached Figure Description

[0019] Figure 1 This is a schematic diagram showing the relationship between the center of gravity movement trajectory and the support area of ​​the horizontal machining center of the present invention;

[0020] Figure 2 This is a flowchart of the initial boundary condition setting and support reaction force extraction process of the present invention;

[0021] Figure 3 This is a schematic diagram illustrating the logic for constructing the overall evaluation index of the horizontal machining center of the present invention. Detailed Implementation

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see the appendix Figure 1 - Appendix Figure 3 This invention provides a method for determining the four main support positions of a horizontal machining center bed, including determining a set of candidate support positions and dividing the support positions into subsets based on the bottom surface structural characteristics of the horizontal machining center bed; establishing a finite element model of the entire horizontal machining center considering multiple working conditions; designing an orthogonal test scheme and obtaining the initial support reaction force; calculating the support stiffness and overall machine response based on an iterative correction mechanism; constructing overall machine evaluation indicators; and analyzing the test results to determine the main support positions.

[0024] In the step of determining the set of candidate bed support locations and dividing the support location subsets based on the bottom surface structural characteristics of the horizontal machining center bed, determining the set of candidate bed support locations specifically includes: selecting the corner points, intersection points of reinforcing ribs, variable cross-section points, and main load-bearing areas of the bottom surface of the horizontal machining center bed as candidate bed support locations based on the arrangement of reinforcing ribs and stress characteristics of the bottom surface of the horizontal machining center bed.

[0025] In one specific embodiment, 12 candidate bed support positions are selected. Dividing the candidate bed support positions into subsets A and B. Subset A includes candidate bed support positions located below the column working area, and subset B includes candidate bed support positions located below the turntable working area. The selection of candidate bed support positions and the division of the support position subsets must adhere to the principle of center of gravity projection constraints.

[0026] The principle of center of gravity projection constraint means that the projection point of the center of gravity of the entire horizontal machining center onto the bottom surface of the bed must be located within the smallest quadrilateral region formed by the combination of elements in the selected support position subset A and elements in the support position subset B. For horizontal machining center beds with structural symmetry, when determining the alternative support positions and dividing the support position subsets, the alternative support positions are simplified based on the axis of symmetry, and only the independent variable elements on one side of the axis of symmetry are selected to participate in the subsequent orthogonal experimental design.

[0027] The steps for establishing a finite element model of a horizontal machining center considering multiple working conditions include: simplifying the three-dimensional model of the horizontal machining center by removing chamfers, non-assembly holes, bolt mounting holes, and local features with dimensions smaller than a preset threshold, which can be set to 5 mm; importing the simplified three-dimensional model into finite element analysis software for mesh generation to produce a complete finite element model.

[0028] Boundary conditions are set in the finite element model of the whole machine. The bolted joints are set using a binding contact configuration, while the guide rail-slider joints, lead screw-nut joints, and bearing joints use spring-damping elements to simulate axial and radial stiffness. Multiple working conditions are set, including combinations of different positions of the column and the rotary table on the machine bed. In a specific embodiment, the total number of working conditions is... The setting is 9, including combinations of the uprights being located in three positions on the left, middle, and right sides of the bed, and the turntable being located in three positions on the front, middle, and rear sides of the bed.

[0029] The steps of designing an orthogonal experimental scheme and obtaining the initial support reaction force include: selecting support location subsets A and B as experimental factors; using different combinations of positions in support location subsets A and B as experimental levels; designing an orthogonal experimental scheme using an orthogonal array; for each set of tests in the orthogonal experimental scheme, applying fixed constraints and gravity loads to the support locations corresponding to the whole machine finite element model; performing static analysis on the whole machine finite element model under various working conditions; and extracting the initial support reaction force at each support location. .

[0030] The steps for calculating support stiffness and overall machine response based on the iterative correction mechanism include: defining the normal stiffness at the support location. and tangential stiffness reaction force The functional relationship is shown in the following equation:

[0031] ;

[0032] in: This indicates the support reaction force at the support location; Indicates normal stiffness; This indicates tangential stiffness.

[0033] This step also includes performing an iterative solution process: utilizing the initial support reactions. Calculate the initial normal stiffness and initial tangential stiffness; remove the fixed constraints at the corresponding support positions in the whole machine finite element model, establish elastic elements, and assign the calculated normal stiffness and tangential stiffness to the elastic elements; perform static solution on the updated whole machine finite element model to extract new support reactions. Determine the new support reaction force Does the support reaction force used in the previous calculation satisfy the convergence condition? If it does not satisfy the convergence condition, use the new support reaction force. The normal and tangential stiffness are updated, and the elastic element parameters in the whole machine finite element model are also updated. The static solution is repeated. If the convergence condition is met, the whole machine finite element model is determined to have reached an equilibrium state. Static and modal analyses are then performed in this state to extract the flatness of the column guide rail, the flatness of the turntable guide rail, and the first natural frequency of the whole machine. The flatness of the guide rail is defined as the difference between the maximum and minimum values ​​of the guide rail deformation.

[0034] In the step of constructing overall machine evaluation indicators, the overall machine evaluation indicators are established. The calculation formula is as follows:

[0035] ;

[0036] in: Indicates the first Overall evaluation indicators of the suborthogonal test; This indicates the total number of analysis conditions; This indicates the operating condition number, with a value range of 1 to... ; Indicates the first In the second trial Flatness value of column guide rail under various working conditions; Indicates the first In the second trial Flatness values ​​of the turntable guide rail under various working conditions; Indicates the first In the second trial The first natural frequency of the entire machine under certain operating conditions; Represents the global weighting coefficient of the flatness index; Represents the global weighting coefficient of the inherent frequency index; Local weighting coefficient representing the flatness of the column guide rail; This represents the local weighting coefficient for the flatness of the turntable guide rails. Among them, and The signs are opposite, and they satisfy the following conditions: ; and satisfy .

[0037] The steps of analyzing test results and determining the main support location include: calculating the average values ​​of the overall machine evaluation indicators for support location subsets A and B at each test level. Select the value that makes the mean The minimum level is taken as the optimal level of the factor; the positions corresponding to the optimal levels of support position subset A and support position subset B are determined as the four main support positions of the horizontal machining center bed; the positions other than the four main support positions in the bed support candidate position set are determined as auxiliary support positions.

[0038] The process of determining the set of candidate bed support locations and dividing them into subsets based on the bottom structural characteristics of a horizontal machining center bed. First, a structural analysis of the bottom surface of the horizontal machining center bed is performed to identify the distribution network of reinforcing ribs and key stress nodes. The four corner points of the rectangular outline of the bed bottom surface are selected as basic candidate points; the intersection points of the longitudinal and transverse reinforcing ribs inside the bed are selected as core load-bearing candidate points; and locations where the bed's cross-sectional shape changes abruptly are selected as structural transition candidate points. These selected points are then summarized to form the set of candidate bed support locations. For example, in a typical horizontal machining center bed structure, 12 candidate bed support locations meeting the above conditions were identified.

[0039] Next, the set of alternative bed support locations is divided into regions based on the functional layout of the horizontal machining center. A horizontal machining center typically includes a column movement area and a rotary table fixed (or moving) area. Alternative bed support locations located below and near the column movement range are classified as support location subset A; alternative bed support locations located below and near the rotary table mounting base are classified as support location subset B. During the division process, alternative bed support locations located at the boundary of regions are categorized according to their primary load source.

[0040] Subsequently, geometric constraint verification was performed on the combinations of elements in support position subsets A and B. The verification was based on ensuring the stability of the entire machine, requiring that the projection point of the center of gravity of the horizontal machining center always fall within the support polygon. Specifically, two positions were selected from support position subset A, and two positions were selected from support position subset B; these four positions constituted a quadrilateral support region. The center of gravity position of the entire horizontal machining center under different working conditions was calculated, and the center of gravity was projected onto the bottom surface of the bed. It was then determined whether the projected center of gravity point was contained within the quadrilateral support region. If the projected center of gravity point fell outside the region, this combination was discarded, or the division of the support position subsets was readjusted to ensure that all combinations participating in subsequent orthogonal experiments met the physical feasibility condition of the minimum quadrilateral envelope of the center of gravity.

[0041] Finally, for bed frames with symmetrical structures, symmetry is used to reduce experimental variables. If the bed frame structure is symmetrical about the central axis, then the candidate bed support positions in support position subsets A and B also exhibit a symmetrical distribution. In this case, the positions on one side of the axis of symmetry are treated as independent variables, and the positions on the other side are treated as driven variables. For example, if support position subset A contains 6 positions and is symmetrical about the axis, then only the 3 positions on one side are used as the variation levels in the orthogonal experiment, and the corresponding 3 positions on the other side are determined accordingly, thereby reducing the dimensionality of the orthogonal experiment and improving the optimization efficiency.

[0042] In determining the four main support positions of a horizontal machining center bed, identifying the set of alternative support positions is fundamental to building the subsequent optimization model. Horizontal machining center beds are typically made of gray cast iron or mineral castings. Their bottom surface is not a solid plane, but rather a grid structure formed by multiple longitudinal and transverse stiffeners interwoven into a crisscross or cross-shaped pattern. This grid structure aims to provide high bending and torsional stiffness with a relatively light structural mass. The initial selection principle for the alternative support positions is based on the structural mechanical properties of the horizontal machining center bed and the load transfer path. Horizontal machining center beds typically adopt a box-type structure, with longitudinal load-bearing ribs and transverse stiffeners inside. These longitudinal load-bearing ribs and transverse stiffeners interweave to form a grid-like support structure.

[0043] When selecting alternative bed support locations, the principle of maximizing stiffness is first applied, prioritizing the physical intersection of the longitudinal load-bearing ribs and transverse reinforcing ribs on the bottom surface of the horizontal machining center bed as the preferred alternative support location. These physical intersections possess high local structural stiffness, effectively resisting local elastic deformation caused by the preload of anchor bolts and the machine tool's own weight, thus preventing warping of the bed bottom surface due to insufficient local stiffness.

[0044] Secondly, based on the principle of maximizing stability, the four corner points of the geometric contour of the bottom surface of the horizontal machining center bed are selected as alternative support locations. Selecting the corner points of the geometric contour of the bottom surface of the horizontal machining center bed can maximize the coverage area of ​​the supporting polygon, thereby increasing the lever arm length of the horizontal machining center to resist the overturning moment and improving the overturning stability of the entire horizontal machining center under extreme cutting conditions.

[0045] Furthermore, based on the principle of the shortest load transfer path, the area on the bottom surface of the bed, whose vertical projection is located directly below the mounting surface of the column guide rail and the rotary table guide rail, is selected as the alternative bed support location. Arranging the alternative bed support location on the vertical projection surface of the guide rail allows the cutting force and gravity load transmitted by the column and rotary table to be transferred to the foundation through the shortest structural path, reducing the bending moment borne by the sidewalls of the horizontal machining center bed and reducing the guide rail straightness error caused by the cantilever effect.

[0046] Furthermore, considering the variable cross-section structure of the horizontal machining center bed, the transition region where the cross-sectional shape of the horizontal machining center bed changes abruptly is selected as the alternative bed support location. At the variable cross-section location of the horizontal machining center bed, stress concentration is easily generated due to the discontinuous mass distribution. Setting the bed support alternative location at this location helps to balance the nonlinear deformation caused by the change in cross-sectional stiffness.

[0047] In the specific implementation process, interference checking is also required. This includes checking whether the selected alternative bed support locations conflict spatially with the chip removal port, coolant return channel, electrical wiring channels, and auxiliary motor mounting brackets at the bottom of the horizontal machining center bed. If a spatial conflict exists, the alternative bed support locations are fine-tuned along the extension direction of the longitudinal load-bearing ribs until the alternative bed support locations are located in the area of ​​solid ribs or thickened base plates, and have sufficient planar space for installing anchor bolts and adjusting shims. Through the above screening and verification process, multiple alternative bed support locations covering the key structural nodes of the horizontal machining center bed are finally determined, forming a set of alternative bed support locations.

[0048] The center of gravity projection constraint test aims to verify whether the selected alternative bed support positions can maintain the static stability of the horizontal machining center under various machine tool operating conditions. Since a horizontal machining center includes large moving components such as the column, spindle box, saddle, and rotary table, the overall center of gravity of the machine is not fixed but dynamically changes as these components move within their respective stroke ranges. Therefore, the core of the center of gravity projection constraint test is to ensure that the dynamic range of the center of gravity of the horizontal machining center is always contained within the geometric polygon formed by the four main support points.

[0049] The specific process of implementing the center of gravity projection constraint test includes the following steps: First, construct a dynamic distribution model of the center of gravity of the horizontal machining center. Based on the mass parameters and stroke parameters of each moving part of the horizontal machining center, determine the limit positions of the column along the X-axis, the spindle box along the Y-axis, and the slide saddle along the Z-axis. Calculate the composite center of gravity coordinates of the entire horizontal machining center under the above combination of limit positions. Traverse all combinations of limit positions to obtain the set of projection points of the center of gravity of the entire horizontal machining center on the horizontal plane (i.e., the plane where the bed bottom is located). By connecting the outermost points in the set of projection points, construct the projection envelope region of the center of gravity of the entire horizontal machining center. This projection envelope region represents the coverage area of ​​the center of gravity on the foundation plane that is likely to occur during the operation of the horizontal machining center.

[0050] Secondly, define the minimum support quadrilateral. In the already divided support position subsets A and B, select the inner bed support candidate positions closest to the geometric center of the horizontal machining center. Connect the two inner positions selected from support position subset A with the two inner positions selected from support position subset B to form the minimum support quadrilateral. The minimum support quadrilateral represents the stable support region with the smallest area that is easily formed under the current subset partitioning scheme.

[0051] Subsequently, an inclusion relationship determination is performed. The constructed center of gravity projection envelope region of the horizontal machining center is geometrically compared with the defined minimum support quadrilateral in the same coordinate system. The determination criteria are as follows: if the boundary contour of the center of gravity projection envelope region of the horizontal machining center is completely inside the boundary contour of the minimum support quadrilateral, and a preset safety margin distance is maintained between the boundary of the center of gravity projection envelope region and the boundary of the minimum support quadrilateral, then the current bed support candidate position set and subset partitioning scheme are deemed to satisfy the center of gravity projection constraint condition. If any part of the center of gravity projection envelope region exceeds the range of the minimum support quadrilateral, it indicates a risk of overturning. In this case, the bed support candidate positions that cause the range to overflow must be eliminated, or the bed support candidate positions must be reselected by expanding outwards until a complete inclusion relationship is satisfied.

[0052] Furthermore, in the verification of the center of gravity projection constraint, the influence of the overturning moment generated by the cutting force must also be considered. When calculating the composite center of gravity coordinates, the equivalent overturning moment generated by the maximum cutting force is converted into a virtual offset of the center of gravity. Specifically, the ratio of the maximum cutting moment to the total weight of the machine is calculated, and this ratio is superimposed on the coordinates of the geometric center of gravity to obtain the equivalent center of gravity position under stress. It is then verified whether the projection point of the equivalent center of gravity position also falls within the range of the minimum support quadrilateral to ensure that the four main support points of the horizontal machining center always maintain a state of pressure contact when subjected to heavy cutting loads, preventing loss of machining accuracy or equipment vibration due to support point disengagement.

[0053] In establishing a finite element model of a horizontal machining center considering multiple working conditions, model simplification and preprocessing are crucial steps in transforming the three-dimensional computer-aided design geometric model into a finite element model suitable for numerical solution. The original three-dimensional design model of a horizontal machining center typically contains numerous subtle geometric features used for manufacturing processes, assembly positioning, or aesthetic decoration. While these subtle geometric features have extremely weak impacts on the macroscopic stiffness and dynamic characteristics of the horizontal machining center, they can lead to an exponential increase in the number of meshes during finite element mesh generation, generating a large number of distorted elements and severely reducing solution efficiency and convergence accuracy. Therefore, it is essential to perform feature cleanup on the original geometric model based on Saint-Venant's principle and the equivalence principle of structural mechanics.

[0054] When implementing the model simplification operation, firstly, identify and remove the rounded and chamfered features on the non-mating surfaces of the horizontal machining center bed and its components. For cast fillets with a radius of less than 3 mm and process chamfers with a width of less than 2 mm, directly perform a chamfer removal operation to restore the arc transition surface to a right-angle intersecting surface, thus eliminating the fragmented surfaces generated during mesh generation. Secondly, fill non-critical process holes on the horizontal machining center bed and column. For threaded bottom holes, locating pin holes, oil injection holes, and non-through holes used for weight reduction that do not participate in bolt connections and have a diameter of less than 10 mm, perform a solid filling operation to restore the continuity of their planes and avoid unnecessary stress concentration near the hole openings. Thirdly, simplify local microstructures. For clearance grooves, relief grooves, cast bosses, and decorative ribs with a depth or protrusion height of less than 5 mm, ensure that they do not bear the main load transfer function, and smooth their surfaces to transform the complex local topology into a regular planar or curved surface structure. While performing the above simplified operations, it is essential to strictly preserve the geometric features of the guide rail mounting base surface of the horizontal machining center bed, the slider mounting base surface of the column, the lead screw bearing seat mounting hole, and the anchor bolt mounting hole to ensure the accuracy of subsequent boundary condition application.

[0055] After simplifying the geometric model, it was imported into the preprocessing module of the finite element analysis software for mesh discretization. Considering that the bed and column of the horizontal machining center are mostly complex cast box structures containing a large number of irregular internal reinforcing ribs and cavities, ten-node tetrahedral elements or a hybrid mesh dominated by hexahedral elements with strong adaptability were preferred for discretization. During the mesh generation process, a strategy combining global size control and local refinement was adopted. The global basic mesh size was set to ensure that the main load-bearing wall panels of the structure have at least two layers of elements in the thickness direction to capture the stress gradient during bending deformation. For the guide rail mounting surface, bearing seat holes, and bolt connection areas, local mesh refinement control was set to reduce the mesh size to one-half to one-third of the global size to improve the accuracy of contact pressure calculation in the contact area. After the mesh generation was completed, a mesh quality check was performed, focusing on checking the Jacobian determinant value, aspect ratio, and warpage of the elements. Distorted elements that did not meet the quality standards were smoothed at the node positions or re-meshed, finally generating a finite element model of the entire horizontal machining center with approximately 1 million nodes.

[0056] Finally, material properties are assigned to the generated finite element model of the horizontal machining center. Based on the actual manufacturing materials of each component, the density, elastic modulus, and Poisson's ratio of the materials are defined. For example, for the bed and column made of gray cast iron (HT300), their density, elastic modulus, and Poisson's ratio parameters are set respectively; for the lead screw and guide rail made of structural steel (45 steel), the corresponding steel material properties are set. This ensures that the finite element model maintains consistency with the actual physical prototype of the horizontal machining center in terms of mass distribution and stiffness characteristics.

[0057] In establishing a finite element model of a horizontal machining center considering multiple operating conditions, equivalent modeling of key joints is crucial to ensuring that the simulation accuracy matches the physical prototype characteristics. The horizontal machining center is not a single continuum, but a complex assembly composed of multiple components such as the bed, column, saddle, spindle box, and worktable, connected by bolts, guide rails, lead screws, and bearings. The mating surfaces between components exhibit contact stiffness and damping, and the dynamic characteristics of these surfaces often account for more than 60% of the overall flexibility of the machine. Directly modeling the mating surfaces as solid contacts would result in excessively large computational scales and difficulty in convergence; therefore, equivalent elements are needed to parametrically model the key joints.

[0058] Equivalent modeling of key joints mainly targets two types of connections: fixed joints and moving joints.

[0059] For fixed joints, these mainly include the bolted connection surfaces between the column and the saddle, the anchor bolt connection surfaces between the bed and the foundation, and the mounting surfaces between the linear guides and the bed. For these fixed joint surfaces locked by high-strength bolt preload, it is assumed that no macroscopic relative slippage or separation occurs during loading. In the finite element preprocessing, a bound contact or multi-point constraint algorithm is used for simulation. Specifically, the master and slave surfaces of the contact pair are defined. The master surface is typically selected as a surface with a sparser mesh or higher stiffness, while the slave surface is selected as a surface with a denser mesh or lower stiffness. Mathematical constraint equations force the corresponding regions of the slave surface nodes and the master surface to maintain consistent displacement in all degrees of freedom, thus simulating the rigid connection effect of bolted joints. For the anchor bolt joints, full constraints are applied at the bed anchor holes to simulate the rigid support of the foundation on the bed.

[0060] For motion joints, which mainly include linear rolling guide pairs, ball screw and nut pairs, and spindle bearing supports, these joints contain rolling elements (such as steel balls or rollers) and exhibit significant nonlinear Hertzian contact characteristics, making them weak points affecting the overall rigidity of the machine tool. This invention uses spring-damping units or bushing units for equivalent simulation.

[0061] For the equivalent modeling of a linear rolling guide pair, an independent node is first established at the geometric center of the guide slider, and this independent node is coupled to the inner surface node of the slider solid through a rigid region. Then, a reference node is established at the corresponding position on the guide rail. A connecting element is created between the slider independent node and the rail reference node. This connecting element is assigned a stiffness matrix property with six degrees of freedom. Based on the technical specification sheet provided by the rolling guide manufacturer, the contact stiffness values ​​of the guide pair in the normal (compression direction) and tangential (lateral force direction) directions are extracted, and these contact stiffness values ​​are input into the corresponding diagonal elements of the stiffness matrix. The frictional stiffness of the guide along the motion direction is typically ignored and set to zero or a minimum value to simulate the free sliding degree of freedom of the slider along the rail.

[0062] For the equivalent modeling of the ball screw and nut assembly, the screw shaft is discretized using beam or solid elements. An elastic connection is established between the nut and the screw shaft at the nut's mounting position. The axial tensile and compressive stiffness of the ball screw assembly is the primary focus of simulation, as axial stiffness directly determines the positioning accuracy and axial vibration resistance of the feed system. This is achieved by connecting multiple axially distributed spring elements in parallel between the nut and screw shaft nodes, or by defining a bushing element with only axial stiffness properties. The axial stiffness value is calculated using Hertzian contact theory based on the screw's preload level, ball diameter, and raceway curvature radius.

[0063] For the equivalent modeling of the lead screw support bearing, the bearing is simplified as an elastic element connecting the lead screw journal and the bearing housing bore. Since angular contact ball bearings or thrust roller bearings mainly bear radial and axial loads, a spring element group connecting the center node of the lead screw shaft and the center node of the bearing housing bore is established in the finite element model. The stiffness values ​​of this spring element group in the radial (X, Y directions) and axial (Z direction) directions are defined respectively. The radial stiffness is used to simulate the radial elastic deformation of the inner and outer rings and rolling elements of the bearing, and the axial stiffness is used to simulate the axial support capacity of the bearing after preload. Through the above equivalent modeling method, the complex nonlinear contact problem is transformed into a linear stiffness matrix parameter setting problem, which significantly improves the solution efficiency of the multi-condition whole machine finite element model while ensuring calculation accuracy.

[0064] In establishing a finite element model of a horizontal machining center considering multiple operating conditions, the multi-condition load boundary definition is used to simulate the mass redistribution effect caused by changes in the position of moving parts during actual machining. Horizontal machining centers typically include a large-mass column and rotary table. Movement of the column and rotary table within a large stroke range causes a significant shift in the machine's center of gravity, thereby altering the magnitude and distribution of the support reactions at each support point on the bed's bottom surface. Analyzing only a single location cannot comprehensively assess the robustness of the support layout.

[0065] The specific steps for defining multi-condition load boundaries are as follows: First, determine the extreme and intermediate positions of the moving parts' strokes. For the column component that moves laterally (usually defined as the X-axis direction) along the bed guideway, select the left limit position of the column stroke, the geometric center position of the column stroke, and the right limit position of the column stroke as three characteristic position points. For the rotary table component that moves longitudinally (usually defined as the Z-axis direction) along the bed guideway, select the front limit position of the rotary table stroke (closer to the spindle side), the geometric center position of the rotary table stroke, and the rear limit position of the rotary table stroke (away from the spindle side) as the other three characteristic position points.

[0066] Secondly, a full permutation working condition combination matrix is ​​constructed. The three characteristic positions of the column component and the three characteristic positions of the rotary table component are fully combined to generate a total of nine typical static analysis working conditions.

[0067] Working condition 1: The column is at its left limit position, and the rotary table is at its front limit position;

[0068] Working condition 2: The column is at its left extreme position, and the rotary table is at its geometric center.

[0069] Working condition 3: The column is at its left limit position, and the rotary table is at its rear limit position;

[0070] Condition 4: The column is located at the geometric center, and the rotary table is located at the front limit position;

[0071] Operating Condition 5: The column is located at the geometric center, and the rotary table is located at the geometric center.

[0072] Condition 6: The column is located at the geometric center, and the rotary table is located at the rear limit position;

[0073] Operating Condition 7: The column is at its right limit position, and the rotary table is at its front limit position;

[0074] Condition 8: The column is at its right limit position, and the rotary table is at its geometric center.

[0075] Operating Condition 9: The column is at its right limit position, and the rotary table is at its rear limit position.

[0076] For the nine operating conditions mentioned above, independent finite element models of the entire machine were constructed. During the construction process, the spatial coordinates of the bed components remained constant. Based on the relative position parameters defined for each operating condition, the spatial coordinates of the finite element mesh nodes of the column component and the rotary table component were adjusted through geometric transformation operations. After the coordinate transformation was completed, based on the equivalent modeling method of key joints, the spring damping element connection between the guide rail slider joint and the lead screw nut joint was re-searched and established at the new contact interface location to ensure the accuracy of the force transmission path under different operating conditions.

[0077] Finally, gravity load boundary conditions are applied. In the static analysis step, the gravity load generated by the machine's own weight is primarily considered. In the finite element model of the entire machine under various working conditions, the direction of gravitational acceleration in the global coordinate system is defined (usually the negative Y-axis perpendicular to the ground), and the amplitude of gravitational acceleration is set to the standard gravitational acceleration (e.g., 9.8 m / s²). The finite element solver calculates the gravity load vector distributed on all nodes of the entire machine model based on the density parameters and element volumes set in the material properties of each component, thereby simulating the stress and deformation of the horizontal machining center under natural static conditions. Through the above multi-condition load boundary definition, various center-of-gravity offset states that are prone to occur in the actual machining stroke domain of the horizontal machining center can be covered, providing complete input data for subsequent evaluation of the comprehensive performance of the support positions.

[0078] In the design of the orthogonal experimental scheme, in order to systematically evaluate the impact of different support position combinations on the static and dynamic performance of the horizontal machining center, it is necessary to transform the complex spatial position optimization problem into a parameterized orthogonal experimental design problem. Based on the region division of the bottom surface of the horizontal machining center bed in the aforementioned steps, this embodiment defines support position subset A and support position subset B as two independent experimental factors, labeled as Factor A and Factor B, respectively. Factor A represents the support layout variables under the column of the horizontal machining center bed, and Factor B represents the support layout variables under the rotary table of the horizontal machining center bed.

[0079] The level definitions for factors A and B are specifically set based on a discretized set of alternative bed support positions. In this embodiment, three discrete level values ​​are set for each factor to fit a three-level orthogonal experimental table.

[0080] For Factor A (support layout in the column area), the following three levels are set:

[0081] Level 1: Select the two corner points located at the rear end of the bottom surface of the horizontal machining center bed. This position corresponds to the end of the longitudinal guide rail of the bed, at the limit edge of the column travel, and can provide the maximum longitudinal support span. Since the horizontal machining center bed has a symmetrical structure, selecting Level 1 means simultaneously activating the two rear corner points that are symmetrically distributed about the axis of symmetry of the bed as the main support points.

[0082] Level 2: Select the symmetrical node positions located at the intersection of the first transverse stiffener and the longitudinal load-bearing wall panel within the column area of ​​the horizontal machining center bed. This position is typically located at the latter third of the column's travel, possessing high local structural rigidity and being close to the column's center of gravity.

[0083] Level 3: Select a symmetrical node position at the junction of the column area and the chip conveyor transition area of ​​the horizontal machining center bed. This position is close to the geometric center of the column stroke, which can effectively shorten the maximum cantilever length during the column movement.

[0084] For Factor B (turntable area support layout), the following three levels are set:

[0085] Level 1: Select the two corner points located at the front end of the bottom edge of the horizontal machining center bed. This position is directly in front of the rotary table, which can minimize torsional deformation of the bed front end caused by the eccentric rotation of the workpiece. Similarly, selecting Level 1 means simultaneously activating the two front corner points that are symmetrically distributed about the bed's axis of symmetry.

[0086] Level 2: Select a symmetrical node position located directly below the vertical projection line of the rotary table's rotation center. This position represents the shortest path for the cutting force to be transmitted to the foundation, theoretically providing the maximum vertical support stiffness and reducing forced vibration during Z-axis feed.

[0087] Level 3: Select a symmetrical node position located on the rear side of the rotary table area of ​​the horizontal machining center bed, near the boundary between the column area and the rotary table area. This position helps to balance the deformation in the middle of the bed and enhance the connection rigidity of the middle section of the bed.

[0088] Based on the above definition, each experimental level essentially represents a pair of symmetrically distributed support point coordinate combinations. The three levels of factor A and the three levels of factor B, through orthogonal combinations, constitute all potential topologies of the four main support positions of the horizontal machining center bed. In the orthogonal experimental design matrix, each row represents a specific four-point support layout scheme, which clearly specifies which two pairs of points are activated as main support points, thus providing clear geometric boundary inputs for subsequent finite element simulation analysis.

[0089] In designing an orthogonal experimental scheme, the selection and configuration of the orthogonal array serves as a bridge connecting the physical model and mathematical optimization, aiming to cover the most comprehensive parameter space with the fewest simulation iterations. Given that the two core experimental factors—the support layout of the column area (defined as factor A) and the support layout of the turntable area (defined as factor B)—have been established in the preceding steps, and three discrete geometric position levels have been set for factors A and B respectively, this embodiment explicitly selects… Standard orthogonal arrays serve as the logical framework for experimental design.

[0090] The standard orthogonal array contains nine row vectors and four column vectors. The number 9 represents the total number of test schemes, which means that the design space can be effectively sampled through nine independent whole-machine finite element simulation analyses; the number 3 represents that each test column can accommodate three factor levels, which perfectly matches the level division of factor A and factor B in this embodiment; the number 4 represents that the array can accommodate a maximum of four independent test factors.

[0091] The specific steps for configuring the orthogonal array are as follows: First, establish the mapping relationship between the experimental factors and the column vectors of the orthogonal array. Map factor A, representing the support layout of the column area, to... The first column vector of the standard orthogonal array; maps factor B, representing the support layout of the turntable area, to... The second column vector of the standard orthogonal array. To minimize the interference of inter-factor interactions on the main effect assessment and to simplify the data analysis model, this embodiment will... The third and fourth column vectors of the standard orthogonal array are left idle, set as empty columns or error columns, and no geometric variables or physical parameters are assigned to them.

[0092] Based on the above mapping rules, a test matrix containing nine independently configured sets is constructed, with each set of tests corresponding to a specific four-point main support topology of a horizontal machining center bed:

[0093] The first set of experiments: configuring the first level of factor A and the first level of factor B. Physically, this corresponds to selecting the rear corner position of the column area and the front corner position of the turntable area as the main support points.

[0094] The second set of experiments: configuring the first level of factor A and the second level of factor B. Physically, this corresponds to selecting the rear corner point of the column area and the center projection point of the turntable area as the main support points.

[0095] The third group of experiments: configuring the first level of factor A and the third level of factor B. Physically, this corresponds to selecting the rear corner point of the column area and the rear transition point of the turntable area as the main support point.

[0096] The fourth group of experiments: the second level of factor A and the first level of factor B.

[0097] Fifth group of experiments: the second level of factor A and the second level of factor B.

[0098] The sixth group of experiments: the second level of factor A and the third level of factor B.

[0099] Seventh group of experiments: the third level of factor A and the first level of factor B.

[0100] Group 8: The third level of factor A and the second level of factor B.

[0101] Group 9: The third level of factor A and the third level of factor B.

[0102] The above configuration scheme follows the principle of balanced dispersion in orthogonal design, meaning that in any column, each of the three levels appears three times; and in any combination of two columns, each of the nine level pairs (e.g., 1-1, 1-2, ..., 3-3) appears once. This mathematical characteristic ensures that in subsequent analysis, the contribution of factor A or factor B to the overall machine evaluation index at different levels can be calculated independently, thereby achieving decoupled optimization of the optimal support position.

[0103] In the simulation calculation process based on stiffness deformation iterative correction, setting the initial boundary conditions is a prerequisite for starting the nonlinear iterative solution algorithm. Since the main support stiffness of the horizontal machining center bed is a function of the support reaction force, and the support reaction force depends on the stiffness matrix of the system, a definite initial state must first be introduced to break the cyclic dependence of stiffness forces. This embodiment uses the assumption of ideal rigid support as the logical starting point for iterative calculation.

[0104] The specific process for setting and calculating the initial boundary conditions is as follows: First, for each test configuration determined in the orthogonal test scheme, the corresponding four main support points are located in the finite element model of the horizontal machining center. Based on the factor A level and factor B level specified by the current orthogonal test row vector, the specific four mesh nodes or node groups are indexed in the node set of the bed bottom surface.

[0105] Next, fully constrained boundary conditions are applied to the four main support points. Fully constrained boundary conditions mean that all three translational degrees of freedom (displacement along the X-axis, Y-axis, and Z-axis) and three rotational degrees of freedom (rotation about the X-axis, Y-axis, and Z-axis) of the selected nodes in the Cartesian coordinate system are limited to zero. This operation is physically equivalent to assuming that the horizontal machining center bed is rigidly fixed to an absolutely rigid foundation, in which case the contact stiffness of the support mating surfaces is considered infinite. For the alternative support positions on the bed bottom surface other than the four main support points, no constraints are applied, leaving them in a free-floating state to simulate the condition where the entire machine weight is borne only by the four main supports.

[0106] Subsequently, a gravity load was applied to the finite element model of the horizontal machining center with fully constrained boundary conditions. The direction of the gravity load was set to the negative Y-axis of the global coordinate system, and the magnitude of the gravitational acceleration was set to 9.8 m / s². At this point, it was necessary to iterate through all nine multi-condition load boundaries defined in the preceding steps (i.e., different combinations of the column and turntable positions). For each condition, the finite element solver applied Hooke's law. (In this specific step, displacement boundary) Given that the value is 0, the solver calculates the constraint reaction force required to maintain this zero displacement and performs a linear statics solution.

[0107] Finally, the initial support reaction force is applied. Data extraction is performed. After completing the statics solution, the finite element post-processing module is entered, and the nodes corresponding to the four main support points are selected. The support reaction force values ​​of each node in the Y-axis direction (i.e., the normal direction perpendicular to the foundation plane) are extracted from the solution result database. Due to the multi-condition analysis, each support point will obtain nine support reaction force values ​​corresponding to nine different conditions. In the initialization stage of this embodiment, to simplify the selection of initial values ​​for iteration, the arithmetic mean or maximum value of the support reaction force under the nine conditions is selected as the initial support reaction force of that support point. The initial support reaction force This will be directly substituted into the subsequent stiffness calculation formula to estimate the support stiffness parameters required for the first round of iteration, thereby transforming the ideal rigid model into a physically realistic elastic support model.

[0108] In finite element simulation, to simulate the nonlinear load-dependent characteristics exhibited by a horizontal machining center bed when installed on a foundation using adjusting shims and anchor bolts—that is, the physical phenomenon where contact stiffness hardens with increasing load—this embodiment constructs a mathematical model of support stiffness based on power functions. The specifically defined normal stiffness function and tangential stiffness function are as follows:

[0109] ;

[0110] ;

[0111] In the formula, This is the normal support reaction force borne at the support position of the horizontal machining center bed, expressed in Newtons (N). This value is derived from the nodal reaction force results of the previous static analysis. Normal contact stiffness, measured in Newtons per millimeter (N / mm), characterizes the ability to resist compressive deformation in the vertical direction; coefficient 10000 is the normal stiffness reference coefficient, determined by the pad material, the elastic modulus of the foundation, and the contact area; index 0.4425 is the normal stiffness hardening index. The tangential contact stiffness, expressed in Newtons per millimeter (N / mm), characterizes the ability to resist shear slip in the horizontal plane. A coefficient of 5000 is the tangential stiffness baseline coefficient, reflecting the characteristic that tangential constraints are weaker than normal supports. The exponent of 0.2846 is the tangential stiffness hardening exponent, characterizing the nonlinear growth of maximum static friction and tangential resistance. Through this function definition, the model can automatically adjust the stiffness of the spring elements according to the actual load distributed at each support point, realistically simulating the non-uniform elastic support state.

[0112] To select the optimal support position from orthogonal experiments that balances static accuracy retention and dynamic stiffness characteristics, this embodiment constructs a minimum-type comprehensive evaluation index function for the entire machine based on weighted summation under multiple working conditions. This indicator comprehensively reflects the impact of changes in the positions of the column and turntable on the overall machine performance. Its calculation formula is as follows:

[0113] ;

[0114] In the formula, For the first Dimensionless comprehensive evaluation index for orthogonal experimental schemes; The total number of working conditions (9 in this embodiment) covers the full stroke combination of the column and the turntable; This is the operating condition sequence number. For the first Group 1 trial The straightness error (mm) of the column guide rail mounting surface under various working conditions is obtained by calculating the absolute value of the difference between the maximum and minimum displacement in the direction of gravity. The flatness error value (mm) of the turntable guide rail mounting surface is obtained in the same way as above. The first-order natural frequency of the entire machine (Hz); It is the frequency normalization constant (Hz), used to unify the dimensions and transform the frequency maximization objective into the numerical minimization objective. and These are the global weighting coefficients for static accuracy and dynamic stiffness, respectively, and satisfy... and These are the local weighting coefficients for the deformation of the column guide rail and the turntable guide rail, respectively. Based on the dominant influence of the column on machining accuracy, they are typically set as follows: and This scoring mechanism achieves both penalty and collaborative optimization for schemes that lead to large guide rail deformation and easy excitation of low-frequency modes.

[0115] In the calculation of the overall machine evaluation index, the weighting coefficient allocation strategy directly determines the optimal direction of the four main support positions of the horizontal machining center bed. Since the application scenarios of horizontal machining centers vary, a single fixed weighting combination cannot meet all design requirements. Therefore, this invention adopts a dynamic weighting allocation strategy based on the analytic hierarchy process (AHP) combined with application condition-driven principles to ensure that the selected main support positions of the bed maximally match the final performance indicators of the horizontal machining center.

[0116] First, regarding the global weight coefficients (Static precision weights) and The allocation of (dynamic stiffness weight) is set with two basic configuration modes: precision machining priority mode and heavy cutting efficiency priority mode.

[0117] When the design goals of a horizontal machining center focus on precision mold making or the manufacturing of precision aerospace parts, a precision machining-first mode is adopted. In this mode, the geometric accuracy retention of the horizontal machining center is considered the primary constraint. Designers assign a global weighting factor to static accuracy. The value range is set between 0.65 and 0.80, and the global weighting coefficient of dynamic stiffness is adjusted accordingly. Set between 0.20 and 0.35. Higher values... The value can force the optimization algorithm to select support position schemes that can control the deformation of the guide rail within the micrometer level even under conditions of large center of gravity shift, thereby ensuring the dimensional consistency of the final workpiece.

[0118] When the design goal of a horizontal machining center focuses on roughing high-removal-rate automotive engine blocks or engineering machinery components, a heavy-cutting efficiency-first mode is adopted. In this mode, suppressing chatter and increasing the critical depth of cut are the core requirements. Designers appropriately reduce the global weighting coefficient for static accuracy. The value of (e.g., set to 0.40 to 0.50) significantly improves the global weight coefficient of dynamic stiffness. The value can be set (e.g., from 0.50 to 0.60). Increase. The proportion of [something] can guide the optimization process to favor support layouts that can significantly improve the first-order natural frequency of the machine, thereby widening the stable cutting range of the machine tool.

[0119] Secondly, regarding the local weight coefficients (Column guide rail deformation weight) and The allocation of (rotary table guideway deformation weight) is set based on the sensitivity of component deformation to the machining error transmission chain. In a horizontal machining center, the column component supports the spindle box and cutting tools. Bending deformation of the column guideway directly leads to Abbe error at the tool tip, which is amplified by the suspension structure, severely affecting machining accuracy. In contrast, the rotary table component supports the workpiece; its guideway deformation mainly causes rigid displacement of the workpiece, with a relatively smaller impact on final accuracy and easier compensation through the CNC system. Based on the above error transmission mechanism, this embodiment consistently follows... Greater than The allocation principle. Typically, the local weighting coefficient for column guide rail deformation is used. Set the local weighting coefficient for turntable guide rail deformation to 0.6 to 0.7. The value is set to 0.3 to 0.4 to reflect the dominant role of column support stability in the overall machine precision system.

[0120] Furthermore, to eliminate the subjective arbitrariness in weight assignment, this embodiment introduces the analytic hierarchy process (AHP) to construct the judgment matrix. A comparison matrix is ​​established containing three criterion layers: static straightness, static flatness, and first-order natural frequency. Machine tool design experts are invited to score the relative importance of each pair of the three criteria (e.g., using a 1-9 scale). By calculating the largest eigenvalue of this judgment matrix and its corresponding normalized eigenvector, the exact solution is obtained. and The specific numerical values ​​are determined. Simultaneously, the consistency ratio is calculated. If the consistency ratio is less than 0.10, the weight allocation logic is considered mathematically self-consistent; otherwise, the judgment matrix needs to be readjusted. This quantitative decision-making process ensures that the optimal selection of the four main support positions of the bed has a rigorous mathematical basis and engineering rationality.

[0121] Range analysis was used to decouple the influence of factors. The indices and sums of each factor at the same level were calculated. , and average response value , Given the overall machine evaluation indicators Defined as a cost function reflecting the deformation and vibration risk of a machine tool (i.e., the smaller the value, the better the static accuracy and dynamic stiffness of the machine tool), when determining the optimal level, the average response values ​​of different levels under the same factor should be compared. Select The level corresponding to the minimum value is taken as the optimal level for that factor. Calculate the range. The difference between the maximum and minimum average responses is used to assess factor sensitivity. If... This indicates that the position of the column support has a more significant impact. The horizontal combination selected through comprehensive optimization constitutes the theoretically optimal solution.

[0122] The process involves theoretical optimization, simulation verification, and local search. First, a theoretical scheme is obtained by combining the optimization levels. Then, a refined model is built, and the nonlinear stiffness is substituted to recalculate the indices. Verification was then performed. Finally, a local neighborhood search was conducted, traversing neighboring nodes within a small radius centered on the theoretical point. The coordinates were fine-tuned through sensitivity analysis to determine the final position. And to intervene and avoid interference.

[0123] Auxiliary supports are used to suppress vibration in the suspended area and to reinforce stiffness. The layout strategy is based on deformation cloud maps and modal shapes: the first group is arranged in the long span area of ​​the longitudinal guide rail of the bed (the area of ​​maximum gravity deformation); the second group is arranged in the high-stress area of ​​the column stroke (where the ribs are dense); and the third group is arranged below external components (such as the tool magazine). In the simulation, dead and live element technology is used to simulate the process state: the auxiliary supports are deactivated in the gravity loading step (simulating leveling), and activated in the cutting / modal step and set to uniaxial compression attribute (stiffness of 50%-70% of the main support), constructing a 4 main plus N auxiliary composite support system.

Claims

1. A method for determining the positions of the four main supports of a horizontal machining center bed, characterized in that, include: S1. Based on the bottom structure characteristics of the horizontal machining center bed, determine the set of alternative bed support positions, and divide the set of alternative bed support positions into a subset A of support positions located below the column working area and a subset B of support positions located below the rotary table working area. S2. Establish a finite element model of the horizontal machining center considering multiple working conditions, including combinations of the column and rotary table at different positions on the machine bed. S3. Select the support position subset A and the support position subset B as test factors, design orthogonal test schemes using orthogonal arrays, and determine multiple sets of tests containing different combinations of main support positions; S4. For each set of tests in the orthogonal test scheme, calculate the support stiffness at the support position based on the iterative correction mechanism, and solve the finite element model of the horizontal machining center to obtain the overall machine response. S5. Construct an overall machine evaluation index based on the overall machine response. The overall machine evaluation index comprehensively characterizes the static accuracy retention and dynamic stiffness characteristics of the overall machine. S6. Analyze the overall machine evaluation index of each group of tests, determine the level of the optimal support position subset A and the level of the support position subset B, and determine the corresponding positions as the four main support positions of the horizontal machining center bed.

2. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The step S1, which involves determining the set of candidate positions for the bed support based on the bottom structural characteristics of the horizontal machining center bed, specifically includes: Based on the arrangement of reinforcing ribs and stress characteristics of the bottom surface of the horizontal machining center bed, the corner points of the geometric contour of the bottom surface of the bed, the intersection of the longitudinal and transverse reinforcing ribs, the location of the variable cross-section where the cross-sectional shape of the bed changes abruptly, and the location of the main load-bearing area are selected as elements for the set of alternative bed support locations.

3. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, In step S1, when dividing the set of candidate bed support positions into support position subset A and support position subset B, the principle of center of gravity projection constraint is followed; the principle of center of gravity projection constraint includes: Obtain the projection points of the center of gravity of the entire horizontal machining center on the bottom surface of the bed under different working conditions, and determine whether the projection points are all located inside the smallest quadrilateral region formed by the combination of elements in the selected support position subset A and elements in the support position subset B. For a horizontal machining center bed with structural symmetry, when dividing the subset, only the independent variation elements on one side of the axis of symmetry are selected to participate in the design of the orthogonal experimental scheme, and the position on the other side is determined according to the symmetry relationship.

4. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The establishment of the finite element model of the horizontal machining center considering multiple working conditions in step S2 includes: The 3D model of the horizontal machining center is simplified by removing chamfers, non-assembly holes, and local features with dimensions smaller than a preset threshold, and a finite element model of the whole machine is generated. Boundary conditions are set in the finite element model of the whole machine. The bolt fixing joint adopts the binding contact setting, and the guide rail slider joint, the lead screw nut joint and the bearing joint adopt the spring damping unit to simulate the axial stiffness and radial stiffness.

5. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The multiple working conditions mentioned in step S2 include all permutations and combinations of different travel positions of the column on the machine bed and different travel positions of the turntable on the machine bed; The different travel positions of the upright on the bed include the upright being located at the left extreme position, the middle position and the right extreme position of the bed; The different travel positions of the turntable on the bed include the turntable being located at the front limit position, the middle position, and the rear limit position of the bed.

6. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The step S4, which involves calculating the support stiffness at the support location based on the iterative correction mechanism and solving the finite element model of the horizontal machining center to obtain the overall machine response, includes: For each set of tests, fixed constraints and gravity loads are applied to the support positions corresponding to the finite element model of the whole machine, and static analysis is performed to extract the initial support reaction force. Based on the preset stiffness and support reaction function relationship, the initial normal stiffness and initial tangential stiffness are calculated using the initial support reaction. Remove the fixed constraints at the corresponding support positions in the finite element model of the whole machine, establish elastic elements, and assign the calculated normal stiffness and tangential stiffness to the elastic elements; The updated finite element model of the whole machine is statically solved to extract new support reactions and determine whether the new support reactions and the support reactions used in the previous calculation meet the convergence conditions. If the convergence condition is not met, the normal stiffness and tangential stiffness, as well as the elastic element parameters, are updated using the new support reaction forces. The static solution is repeated until the convergence condition is met, at which point the overall machine response is extracted.

7. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 6, characterized in that, The preset stiffness and support reaction function relationship is a power function relationship; the calculation of the initial normal stiffness and initial tangential stiffness using the initial support reaction includes: The normal stiffness is set to be positively correlated with the support reaction force at the support location, and the value of the normal stiffness is calculated based on the first power exponent of the support reaction force and determined in combination with the normal stiffness reference coefficient. The tangential stiffness is set to be positively correlated with the support reaction force at the support location, and the value of the tangential stiffness is calculated based on the second power exponent of the support reaction force and determined in combination with the tangential stiffness reference coefficient.

8. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The step S5, which involves constructing overall machine evaluation indicators based on the overall machine response, specifically includes: The flatness of the column guide rail, the flatness of the turntable guide rail, and the first natural frequency of the whole machine after the convergence condition are satisfied are extracted as the whole machine response parameters. Set the global weight coefficient for the flatness index, the global weight coefficient for the natural frequency index, the local weight coefficient for the flatness of the column guide rail, and the local weight coefficient for the flatness of the turntable guide rail; The flatness of the column guide rail and the flatness of the turntable guide rail under various working conditions are weighted and summed, and the whole machine evaluation index is calculated by combining the first-order natural frequency of the whole machine and the corresponding global weight coefficient.

9. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, The determination of the levels of the support position subset A and the support position subset B that optimize the overall machine evaluation index in step S6 specifically includes: Calculate the average values ​​of the overall machine evaluation index for the support position subset A and the support position subset B at each test level; The level that minimizes the average value of the overall machine evaluation index is selected as the optimal level of the test factor. The positions corresponding to the optimal levels of support position subset A and support position subset B are combined to determine the four main support positions.

10. The method for determining the positions of the four main supports of a horizontal machining center bed according to claim 1, characterized in that, Also includes: The locations other than the four main support locations are selected as auxiliary support locations from the pooled candidate bed support locations.

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