Dynamic topology optimization design method for machine tool beam based on bimodal load spectrum driving

Abstract

The application provides a dynamic topology optimization design method of a machine tool beam based on a dual-mode load spectrum driving, and relates to the technical field of machine tool structure design and optimization. The method first acquires the working condition data of a machine tool to be optimized and converts the working condition data into a first load spectrum and a second load spectrum representing rough machining and finish machining respectively, and determines the dynamic response index calculation mode according to the first load spectrum and the second load spectrum. Then, a parameterized geometric model of the beam is established, and the two load spectrums are applied to the same or different installation areas according to the actual machining sequence to generate complete time history or driving point frequency response functions. On this basis, a topology optimization mathematical model is constructed by taking the minimization of the dynamic response index of the beam under the excitation of the two load spectrums as the target and the material volume or mass as the constraint. Finally, the optimal material distribution configuration is obtained by iterative solution as the design basis. The application integrates the time-frequency characteristics of real machining loads into the optimization model, so that the optimized configuration is directional to the dynamic stress flow and is strengthened, and the dynamic stiffness and vibration resistance of the beam in actual machining are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of machine tool structure design and optimization technology, specifically to a dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving. Background Technology

[0002] Topology optimization, as an advanced structural design method, can automatically find the optimal material distribution under given design space, load conditions, and constraints, thereby achieving lightweight and high-performance structures. It has been increasingly widely applied in machine tool structural design. For CNC machine tools, the crossbeam, as a key supporting component connecting the column and slide, directly affects the machining accuracy and surface quality of the machine tool due to its static and dynamic stiffness; therefore, it is often used as an important application object for topology optimization. Currently, mainstream topology optimization methods for large components such as machine tool crossbeams typically use maximizing static stiffness (i.e., minimizing structural flexibility) or maximizing a single low-order natural frequency as optimization objectives, and perform weighted trade-offs under multiple typical static conditions to obtain a compromise configuration. However, these methods are all based on static or quasi-static assumptions and fail to truly reflect the dynamic load characteristics experienced by the machine tool during machining.

[0003] In actual machining, the cutting force between the machine tool and the workpiece is a dynamic load that varies with time. Its amplitude, frequency, and direction change drastically with the machining parameters and material removal process. Especially in modern CNC machine tools with "roughing-finishing" composite machining capabilities, whether a dual-spindle slide structure is used or a single spindle completes roughing and finishing sequentially through automatic tool changing or automatic head changing, the dynamic loads generated in the roughing and finishing stages exhibit significant differences in both time and frequency domain characteristics. Specifically, roughing typically employs large depths of cut and feed rates, generating high-amplitude, low-frequency, strong impact pulse loads; while finishing pursues high speeds and small depths of cut, generating low-amplitude, high-frequency continuous cutting loads. These two types of loads not only have vastly different time-varying characteristics but also act sequentially in the machining sequence, placing drastically different dynamic performance requirements on the beam structure. Roughing requires the structure to have sufficiently high static stiffness to resist elastic deformation caused by large cutting forces, while finishing requires the structure to have excellent dynamic stiffness to suppress high-frequency chatter. The two requirements for material distribution often have fundamentally conflicting directions.

[0004] To address variable load conditions, existing technologies have proposed multi-condition topology optimization methods, such as using linear weighting to combine the compliance of multiple static load conditions into a single objective for optimization. While these methods can handle load variations at multiple locations or in multiple directions, their optimization objectives are still based on static compliance or its weighted average, failing to characterize the time-frequency characteristics of dynamic loads. When loads have significantly different frequency band characteristics, static optimization cannot distinguish between the different requirements of "deformation control" and "vibration suppression" on material distribution. Meanwhile, some studies have attempted to introduce dynamic topology optimization methods, such as minimizing the amplitude of the frequency response function of the structure under harmonic excitation or minimizing the root-mean-square response under random vibration. However, these methods typically assume that the load is a single-frequency harmonic excitation or a stationary random process, essentially approximating a single type of dynamic load in the frequency domain. They struggle to simultaneously characterize the distinctly different characteristics of roughing and finishing loads, and are even less capable of handling complex temporal conditions where the two loads act sequentially in time and may be in the same or different spatial locations.

[0005] Therefore, it is evident that the existing technology lacks a beam optimization method that can directly embed the time-frequency characteristics of the real dynamic load spectrum during actual composite machining of machine tools into the topology optimization model and perform material distribution design for structural dynamic response.

[0006] In view of the above, this application is hereby submitted. Summary of the Invention

[0007] This invention provides a dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving, which can at least partially improve the above-mentioned problems.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving, comprising: S1. Obtain the working condition data of the machine tool to be optimized, convert it to obtain the first load spectrum and the second load spectrum, and judge the first load spectrum and the second load spectrum to determine the calculation method of dynamic response index. S2, establish a parameterized geometric model of the machine tool to be optimized, and apply the first load spectrum and the second load spectrum to the same or different installation areas of the parameterized geometric model according to the dynamic response index calculation method, and generate a complete time history or drive point frequency response function accordingly. S3, based on the complete time history or the frequency response function of the driving point, takes the minimization of the dynamic response index of the beam structure of the machine tool to be optimized under the excitation of the first load spectrum and the second load spectrum as the optimization objective function, and constructs a topology optimization mathematical model with material volume or mass as the constraint condition; S4. The topology optimization algorithm is used to iteratively solve and optimize the topology optimization mathematical model to obtain the optimal material distribution configuration. The optimal material distribution configuration is then used as the final design basis for the beam structure of the machine tool to be optimized, so as to optimize the machine tool.

[0009] Preferably, the first load spectrum represents the roughing condition of the machine tool to be optimized, and the second load spectrum represents the finishing condition of the machine tool to be optimized. Both the first load spectrum and the second load spectrum are time history data of the three-dimensional cutting force that varies with time.

[0010] Preferably, the first load spectrum and the second load spectrum are obtained by experimental measurement or theoretical simulation.

[0011] Preferably, the first load spectrum and the second load spectrum are judged to determine the dynamic response index calculation method, specifically as follows: When it is determined that the first load spectrum and the second load spectrum possess any of the characteristics of the first judgment condition, the dynamic response index calculation method is determined to be the time domain method. The first judgment condition includes strong nonstationarity and impact characteristics, non-superposition of time-series effects, and nonlinear characteristics that need to be verified or exist. When it is determined that the number of features in the first load spectrum and the second load spectrum that meet the second judgment condition is not less than the judgment threshold, the dynamic response index calculation method is determined to be the frequency domain method. The second judgment condition includes the characteristics of the load having stationary random characteristics, the system being a linear time-invariant system, and the pursuit of extremely high computational efficiency.

[0012] Preferably, a parametric geometric model of the machine tool to be optimized is established. Based on the dynamic response index calculation method, the first load spectrum and the second load spectrum are applied to the same or different installation areas of the parametric geometric model, corresponding to the generation of a complete time history or a drive point frequency response function. Specifically: Using finite element software, a parametric geometric model of the beam of the machine tool to be optimized was established, and tetrahedral elements were used to perform structured mesh generation on the parametric geometric model. Obtain the material properties and boundary conditions of the machine tool to be optimized, and set the material properties and boundary conditions into the parametric geometric model; Based on the current engineering requirements, the self-weight of the crossbeam of the machine tool to be optimized is selectively incorporated into the parametric geometric model; Based on the preset extraction value n, the first n natural frequencies of the machine tool to be optimized are extracted using the Block Lanczos method. When it is determined that the dynamic response index calculation method is the time domain method, the first load spectrum and the second load spectrum are applied to the same installation area of ​​the parameterized geometric model according to the actual machining sequence of the machine tool, and the complete time history F(t) is obtained by splicing them together.

[0013] When it is determined that the dynamic response index calculation method is the frequency domain method, the corresponding sub-intervals are selected from the three preset frequency scanning sub-intervals based on the first n natural frequencies, and these sub-intervals are the key focus areas. The three frequency scanning sub-intervals are the low-frequency quasi-static region, the resonance-enhanced region, and the high-frequency flat region. Based on the key focus area, the first and second load spectra were applied to different installation areas of the parametric geometric model to create remote force points (TCPs). A 1N unit harmonic excitation was applied along the X, Y, and Z axes, and the frequency response function H of the X-axis drive point was extracted. xx Y-axis driving point frequency response function H yy Z-axis driving point frequency response function H zz .

[0014] Preferably, based on the complete time history or the frequency response function of the driving point, the optimization objective function is to minimize the dynamic response index of the beam structure of the machine tool to be optimized under the excitation of the first load spectrum and the second load spectrum, and a topology optimization mathematical model is constructed with material volume or mass as a constraint. Specifically: When the dynamic response index is calculated using the time-domain method, the dynamic strain energy time integral C under full load time-history excitation is... dyn Defined as the objective function to be optimized, its formula is: T is the total duration of the load application. This is the transpose, where t is the load duration index. Let dt be the velocity vector of the structure, and dt be the time derivative. When the dynamic response index is calculated using the frequency domain method, the expected value of dynamic compliance E[C] is defined as the optimization objective function, and its formula is: N is the total number of discrete frequency points, and k is the index of the discrete frequency point, k=1,2,...,N. For frequency step size, Let k be the frequency value at the kth discrete frequency point. The self-power spectral density of the roughing load in the m-axis direction is given. The power spectral density of the finishing load in the m-axis direction is denoted as . When the beam's self-weight is not included, the material volume or mass is used as a constraint to generate the main constraints. Based on the optimization objective function and the main constraints, a topology optimization mathematical model is constructed, where the constraint condition is that the material volume or mass does not exceed a preset constraint threshold.

[0015] When the self-weight of the beam is included, performance evaluation points are set, where the response value of the objective function is the displacement or acceleration response in the same direction as the load application point. Using material volume or mass as constraints, primary constraints are generated. Static compliance constraints are added to the primary constraints. Based on the optimization objective function, primary constraints, and static compliance constraints, a topology optimization mathematical model is constructed.

[0016] Preferably, the topology optimization algorithm is a variable density method, a level set method, or an evolutionary structure optimization method.

[0017] In summary, this method includes: obtaining the cutting force time history, which characterizes the dynamic properties of roughing and finishing, as the load input; applying the load spectrum to the corresponding spindle mounting area of ​​the beam according to the working conditions in the parametric geometric model; and performing topology optimization to minimize the dynamic response (dynamic compliance / acceleration response) of the structure under the excitation of the complete load spectrum, with material volume as a constraint. This invention directly integrates the time-frequency characteristics of the actual working load into the optimization model, enabling the optimized beam configuration to strengthen the "dynamic stress flow," significantly improving the dynamic stiffness and stability of the structure in actual machining. It aims to solve the problem that existing static topology optimization methods cannot meet the dynamic performance requirements of machine tools in composite machining.

[0018] Compared with existing technologies, the advantages of this method are as follows: it uses two distinct real load spectra of roughing and finishing as inputs for topology optimization, overcoming the limitation of traditional static optimization in characterizing the time-frequency characteristics of dynamic loads. This allows the optimized configuration to be directionally strengthened for the dynamic stress flow in composite machining, simultaneously meeting the dual requirements of resisting large deformations in roughing and suppressing high-frequency vibrations in finishing, significantly improving the dynamic stiffness and vibration resistance of the beam in actual machining. This method is driven by actual working conditions, closely aligned with engineering applications, and compatible with both time-domain and frequency-domain solution strategies, providing a general technical paradigm for the design of machine tools and other structures subjected to complex time-series dynamic loads. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driven by an embodiment of the present invention.

[0020] Figure 2 This is a cutting force time history diagram for a typical roughing condition provided in an embodiment of the present invention.

[0021] Figure 3 This is a cutting force time history diagram for a typical finishing condition provided in an embodiment of the present invention.

[0022] Figure 4 This is a schematic diagram of the frequency domain method optimization solution process provided in the embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram of the time-domain method optimization solution process provided in the embodiment of the present invention.

[0024] Figure 6 This is a schematic diagram comparing the material distribution configuration of the machine tool beam before and after optimization, provided in an embodiment of the present invention. Figure 6 (a) in the diagram shows a traditional optimized configuration obtained with static stiffness as the objective. Figure 6 (b) in the figure is a schematic diagram of the dynamic optimization configuration expected to be obtained by using the method of the present invention.

[0025] Figure 7 These are the amplitude curves of the frequency response function in three directions provided in the embodiments of the present invention.

[0026] Figure 8 The integrand curves for roughing and finishing processes are provided in the embodiments of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0028] refer to Figure 1 As shown, the first embodiment of the present invention discloses a dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving, which can be executed by a dynamic topology optimization design device for machine tool beams based on dual-modal load spectrum driving (hereinafter referred to as optimization design device), specifically, by one or more processors within the optimization design device, to implement the following method: S1, acquire the operating condition data of the machine tool to be optimized, and transform it to obtain the first load spectrum and the second load spectrum (e.g., Figure 2 and Figure 3 The first load spectrum and the second load spectrum are judged to determine the calculation method of dynamic response index; Specifically, step S1 further includes: the first load spectrum represents the roughing condition of the machine tool to be optimized, and the second load spectrum represents the finishing condition of the machine tool to be optimized. Both the first load spectrum and the second load spectrum are time history data of the three-dimensional cutting force that varies with time.

[0029] The first and second load spectra can be obtained through experimental measurement or theoretical simulation: by directly acquiring the three-dimensional cutting force signals of the actual roughing and finishing processes by installing a force gauge on the machine tool; or by calculating and generating time history data based on the cutting mechanics model and process parameters.

[0030] The first load spectrum and the second load spectrum are evaluated to determine the calculation method for the dynamic response index, specifically as follows: When the first load spectrum and the second load spectrum are determined to possess any of the characteristics of the first judgment condition, the dynamic response index calculation method is determined to be the time domain method (applicable to situations where the load is highly non-stationary or nonlinear effects need to be considered). Step S2 selects to splice the data in time sequence and perform transient analysis. The first judgment condition includes strong non-stationarity and impact characteristics (the load changes drastically in the time domain, with obvious pulses, abrupt changes, or discontinuous cutting (such as discontinuous cutting in cavity milling during roughing)), non-superimposed time sequence effects (roughing (low frequency, high amplitude) and finishing (high frequency, low amplitude) act sequentially in time, and the deformation mechanisms of the two conflict (low frequency large deformation vs. high frequency vibration). In this case, splicing the data into a complete time history F(t) can accurately simulate the real physical sequence of "first bearing strong impact damage, then bearing high frequency vibration"), and the need for verification or the existence of nonlinear characteristics (when the structure may have material nonlinearity, contact state changes, or when it is used as a reliable supplementary verification of the frequency domain method results, even if it is time-consuming, the time domain method should be used to ensure physical authenticity). When the first load spectrum and the second load spectrum are determined to have at least 2 features that meet the second judgment condition, the frequency domain method is determined to be the dynamic response index calculation method. Step S2 selects unit harmonic excitation to extract the frequency response. The second judgment condition includes the characteristics of the load having stationary random characteristics (the statistical characteristics of the load do not change with time, and the frequency band characteristics are clear and concentrated), the characteristics of the system being a linear time-invariant system (the structural vibration satisfies the superposition principle. At this time, a unit harmonic excitation of 1N is applied, and the frequency response function H(f) of the driving point is extracted (i.e., the inherent transfer characteristics of the structure). This characteristic is independent of the magnitude of the external load. Once H(f) is extracted, subsequent changes in the load amplitude only require linear scaling, without the need to repeatedly solve the expensive harmonic response equation), and the pursuit of extremely high computational efficiency (in the optimization iteration (usually hundreds of times), if transient analysis is performed every time, the calculation is unacceptable). The frequency domain method converts the load into the power spectral density S(f) and integrates it in the frequency domain. The expected response value can be calculated in one go, reducing the number of calculation points from thousands of time steps to about 140 frequency points (as shown in Table 2), improving efficiency by tens of times. The discrete interval is the frequency domain integral.

[0031] The choice between the time-domain method and the frequency-domain method depends entirely on the time-frequency characteristics of the load and the trade-off between computational efficiency and accuracy in engineering. An adaptive judgment is made based on actual processing data (such as the time history curve measured by a force gauge)—if the time history curve shows obvious spikes and pulses, time-domain splicing is selected; if the time history curve is stable and the spectrum after FFT is clean, unit excitation is selected to extract the frequency response.

[0032] In this embodiment, the working condition data of the machine tool to be optimized is first acquired and converted to obtain a first load spectrum and a second load spectrum. Then, the calculation method for the dynamic response index is determined based on the load characteristics. The first load spectrum represents the roughing condition, and the second load spectrum represents the finishing condition; both are time-history data of the three-dimensional cutting force that varies over time. Roughing typically corresponds to a large depth of cut and a high feed rate, resulting in a high-amplitude, low-frequency, strong impact pulse characteristic of the cutting force. Finishing corresponds to a high rotational speed and a small depth of cut, resulting in a low-amplitude, high-frequency continuous cutting characteristic of the cutting force. The load spectrum can be obtained by directly acquiring the three-dimensional cutting force signal of the actual machining process using a force gauge installed on the machine tool. This method most realistically reflects various random factors in the cutting process. Alternatively, time-history data can be generated through theoretical simulation calculations based on the cutting mechanics model and process parameters. This method is particularly suitable when experimental conditions are lacking. By using the actual load spectrum as the optimization input, the subsequent optimization results can be more closely aligned with engineering practice.

[0033] After obtaining the load spectrum, the calculation method for the dynamic response index needs to be determined based on its specific characteristics. When the first and second load spectra are found to possess any one of the characteristics of the first judgment condition, the time-domain method is selected. The first judgment condition includes strong non-stationarity and impact characteristics, which typically occur in periodic impact loads generated when the cutting teeth intermittently cut into the workpiece; the characteristic that the effects of sequential actions are not superimposed, meaning the responses produced by the roughing and finishing loads acting sequentially are not a linear superposition of their individual effects; and the need to verify or the existence of nonlinear characteristics, i.e., when the structure may exhibit material nonlinearity or changes in contact state. When any of the above characteristics are determined to exist, the time-domain method can directly perform transient analysis on the complete load time history, accurately capturing the impact process and sequential effects. Although the computational load is larger, the results are more reliable. When the first and second load spectra satisfy at least the number of characteristics in the second judgment condition that meet the judgment threshold, the frequency-domain method is selected. The second judgment condition includes the load having stationary random characteristics, such as the load generated by continuous steady-state cutting in finishing, which is statistically time-invariant; the system being a linear time-invariant system, which is usually satisfied by machine tool structures operating within the linear elastic range; and the pursuit of extremely high computational efficiency, because optimization iterations typically require hundreds of iterations, and performing transient analysis for each iteration would be extremely costly. The frequency domain method converts the load into power spectral density, and frequency domain integration can quickly calculate the expected response value, significantly improving computational efficiency. The specific value of the judgment threshold can be preset by those skilled in the art based on actual engineering needs. This adaptive judgment mechanism based on load characteristics enables the present invention to achieve an optimal balance between computational accuracy and computational efficiency according to different application scenarios.

[0034] S2, establish a parameterized geometric model of the machine tool to be optimized, and apply the first load spectrum and the second load spectrum to the same or different installation areas of the parameterized geometric model according to the dynamic response index calculation method, and generate a complete time history or drive point frequency response function accordingly. Specifically, step S2 further includes: using finite element software (such as ANSYS Workbench) to establish a parametric geometric model of the beam of the machine tool to be optimized (e.g., dimensions of 7460mm×1500mm×1400mm (length×height×width), corresponding to the typical span of a gantry machining center), and using tetrahedral elements to perform structured meshing on the parametric geometric model, for example: the global element size is 45mm; and performing local mesh refinement in the slide mounting area (critical area for load transfer) to ensure stress / displacement response accuracy; Obtain the material properties of the machine tool to be optimized (e.g., gray cast iron HT300: elastic modulus 130 GPa, Poisson's ratio 0.27, density 7200 kg / m³). 3 The model incorporates material properties and boundary conditions (such as applying fixed constraints to both ends of the beam to simulate column support), and sets these to the parametric geometry model. Based on the current engineering requirements, the self-weight of the crossbeam of the machine tool to be optimized is selectively included in the parametric geometric model as a prestress applied before modal analysis, or as an independent static load condition to participate in subsequent optimization (in case of insufficient material at the lower edge after optimization leading to sagging). Based on the preset extraction value n (e.g., n=50), the first n natural frequencies of the machine tool to be optimized (covering 0~2400Hz) are extracted using the Block Lanczos method, and the resonance region is determined to be 72~452Hz. This step provides a basis for the frequency segmentation of subsequent frequency response analysis and verifies whether the effective modal mass fraction meets the standard. The load is applied to the mounting area corresponding to the slide (the 8 imprinting surfaces / slider contact surfaces of the side-mounted structure). When it is determined that the dynamic response index calculation method is the time domain method (i.e., when the spindle is shared), the first load spectrum and the second load spectrum are applied to the same mounting area corresponding to the upper slide of the parametric geometric model according to the actual machining sequence of the machine tool, and the complete time history F(t) is obtained by splicing them together. The duration of the first load spectrum is T1, and the duration of the second load spectrum is T2. When the two load spectra are applied to the same mounting area, the load function is the splicing of the two time histories.

[0035] When it is determined that the dynamic response index calculation method is the frequency domain method (i.e., if the roughing and finishing spindles are independent, it is also represented as a dual-spindle structure), based on the first n natural frequencies, (in order to balance accuracy and efficiency) the corresponding sub-intervals are selected from the three preset frequency scanning sub-intervals (as shown in Table 2) as the key focus intervals. The three frequency scanning sub-intervals are the low-frequency quasi-static region (1~70Hz, step size 17.5Hz), the resonance enrichment region (70~452Hz, step size 5Hz, covering all natural frequencies), and the high-frequency flat region (452~1600Hz, step size 20.1Hz, covering 3 times the passing frequency of the finishing cutting teeth); the total number of calculation points is compressed to about 140 points / direction, which greatly shortens the solution time.

[0036] Based on the key focus area, the first and second load spectra were applied to different installation areas of the parametric geometric model to create remote force points (TCPs). A 1N unit harmonic excitation was applied along the X, Y, and Z axes, and the frequency response function H of the X-axis drive point was extracted. xx Y-axis driving point frequency response function H yy Z-axis driving point frequency response function H zz (Unit: m / N).

[0037] In simple terms, the time-domain method involves performing transient dynamic analysis on the current structure in each optimization iteration, directly calculating the time integral of its dynamic strain energy under the full load spectrum time history; the frequency-domain method converts the load spectrum into a power spectral density function, combines it with the structure's frequency response function, and calculates the expected value of the dynamic response index in the frequency domain, with the optimization objective being to minimize the amplitude of the frequency response function in the main frequency bands of the load spectrum.

[0038] In this embodiment, a parametric geometric model of the machine tool to be optimized is first established. Specifically, a parametric geometric model of the gantry beam is established in finite element analysis software. The design domain size of this model corresponds to the typical span and load-bearing requirements of a composite machining center. Tetrahedral elements are used to perform structured meshing of the design domain, and local refinement is performed in the slide mounting area to ensure the solution accuracy of this area, as this area is the direct point where the cutting force is transmitted to the beam, and its stress distribution and deformation have a significant impact on the subsequent optimization results. Through parametric modeling, parameters such as the structural dimensions and mesh density of the model can be easily adjusted, facilitating model updates during subsequent optimization iterations. Subsequently, the material properties and boundary conditions of the machine tool to be optimized are obtained and set in the parametric geometric model. The material properties include the elastic modulus, Poisson's ratio, and density of the material used in the beam. These parameters directly affect the stiffness and inertial characteristics of the structure and are the physical basis for subsequent dynamic analysis. The boundary conditions are set to apply fixed constraints to both ends of the beam, simulating the rigid connection between the beam and the column, constraining all degrees of freedom at the beam ends. Depending on the current engineering requirements, the self-weight of the machine tool's crossbeam can be selectively incorporated into the parametric geometric model. For large gantry crossbeams, their substantial mass significantly impacts structural deformation and material distribution. Incorporating self-weight into the model can be achieved by adding a static load case to the optimization model, applying standard gravitational acceleration vertically downwards; or by adding a static analysis step before modal analysis, applying gravity, and then performing prestressed modal analysis. By considering self-weight, the optimization model can more closely approximate actual service conditions, avoiding engineering problems such as insufficient lower edge material and excessive static sag.

[0039] Based on the preset extraction value n, the first n natural frequencies of the machine tool to be optimized are extracted using the Block Lanczos method. The Block Lanczos method is a widely used algorithm in solving large sparse eigenvalue problems, with advantages such as fast convergence speed and high computational efficiency, especially suitable for extracting multi-modes from finite element models. The extracted natural frequencies reflect the inherent dynamic characteristics of the beam structure, including the natural frequency values ​​of each mode and the corresponding mode shapes. The range of extracted natural frequencies should cover a certain multiple of the upper frequency limit required for subsequent analysis to ensure the accuracy of high-frequency response analysis. Next, according to the previously determined dynamic response index calculation method, the corresponding load application operation is performed. When it is determined that the dynamic response index calculation method is the time domain method, the first load spectrum and the second load spectrum are applied to the same installation area of ​​the parametric geometric model according to the actual machining sequence of the machine tool, and spliced ​​to obtain a complete time history. In actual composite machining, roughing and finishing are completed by the same spindle by switching the cutting parameter sequence, so the load application positions are the same, and the two load spectra are connected end to end in time. After the first load spectrum finishes, the second load spectrum begins to apply, forming a complete load time history. This complete time history serves as input for subsequent transient dynamic analysis, enabling direct simulation of the dynamic load variation process experienced by the beam throughout the entire manufacturing process within the time domain.

[0040] When the dynamic response index calculation method is determined to be the frequency domain method, based on the extracted first n natural frequencies, corresponding sub-intervals are selected as the key focus areas from three preset frequency scanning sub-intervals. These three frequency scanning sub-intervals are the low-frequency quasi-static region, the resonance-reinforced region, and the high-frequency flat region. Specifically, based on the distribution range of the first n natural frequencies, the interval covering all natural frequencies is determined as the resonance-reinforced region, because the response amplitude of the structure near the natural frequencies will be significantly amplified, requiring fine frequency resolution to accurately capture the shape and peak value of the resonance peak. The low-frequency segment is set as the low-frequency quasi-static region, where the structural response changes gradually, allowing for a coarser frequency step size. The high-frequency segment is set as the high-frequency flat region, where the response typically tends to be smooth, also allowing for a coarser step size. This piecewise non-uniform sampling strategy significantly reduces the number of calculated frequency points while maintaining integration accuracy, thus significantly improving computational efficiency.

[0041] Based on the identified key focus areas, the first and second load spectra are applied to different mounting areas of the parametric geometric model to create remote force points. Unit harmonic excitations are then applied along the X, Y, and Z axes, and the drive point frequency response functions for each direction are extracted. Specifically, for machine tool structures with independent roughing and finishing spindles, the first and second load spectra are applied at different locations and need to be applied separately in their respective slide mounting areas. The purpose of creating remote force points is to accurately simulate the transmission path of cutting force from the tool center point to the crossbeam and to account for overhanging moments. The remote force points are set at the tool center point, and the load is transferred to the contact surface between the slide and the crossbeam through a rigid connection. Subsequently, unit harmonic excitations are applied along the three orthogonal directions, and the displacement response in the same direction is extracted at the loading point to obtain the drive point frequency response function. The drive point frequency response function reflects the inherent dynamic characteristics of the structure under unit excitation and is the fundamental data for calculating dynamic response indices using the frequency domain method. By using fine frequency steps to perform harmonic response analysis within the key focus area, accurate frequency response function curves can be obtained, ensuring the accuracy of subsequent frequency domain integral calculations of the expected value of dynamic compliance.

[0042] S3, based on the complete time history or the frequency response function of the driving point, takes minimizing the dynamic response index of the beam structure of the machine tool to be optimized under the excitation of the first load spectrum and the second load spectrum as the optimization objective function, and constructs a topology optimization mathematical model with material volume or mass as the constraint condition; that is, the beam's self-weight can be selectively taken as the static working condition to construct a multi-objective or multi-constraint optimization model, for example: minimizing dynamic compliance as the objective and static compliance or maximum static deformation as the constraint; or minimizing the weighted compliance (a combination of static compliance and dynamic compliance) as the objective. When considering self-weight, the static compliance is defined as the strain energy of the structure under gravity load.

[0043] Specifically, step S3 further includes: when the dynamic response index calculation method is the time-domain method, the dynamic strain energy C under complete load time history excitation is integrated over time. dyn Defined as the objective function to be optimized, its formula is: T is the total duration of the load application. This is the transpose, where t is the load duration index. Let dt be the velocity vector of the structure (i.e., the first derivative of the displacement vector with respect to time), and dt be the time differential; its physical meaning is to measure the cumulative deformation energy of the structure under real time-series loads.

[0044] When the dynamic response index is calculated using the frequency domain method, the expected value of dynamic compliance E[C] is defined as the optimization objective function, which is the sum of the product of the load power spectral density and the frequency response function within the frequency band. The formula is as follows: N is the total number of discrete frequency points, and k is the index of the discrete frequency point, k=1,2,...,N. This represents the frequency step size (in Hz). This represents the frequency value (in Hz) at the k-th discrete frequency point. The self-power spectral density of the roughing load in the m-axis direction (in N). 2 / Hz). The self-power spectral density of the finishing load in the m-axis direction (in N). 2 / Hz); This index comprehensively reflects the global deformation capacity of the structure under real dynamic loads.

[0045] When the beam's self-weight is not included, the material volume or mass is used as a constraint to generate the main constraint. Based on the optimization objective function and the main constraint, a topology optimization mathematical model is constructed (i.e., the final result is an explicit mathematical model with a single objective (minimizing dynamic response) and a single constraint (volume / mass fraction ≤ 40%)). The constraint is that the material volume or mass does not exceed a preset constraint threshold (e.g., the material volume of the optimized structure does not exceed 40% of the initial design domain volume (volume fraction constraint); the mass of the optimized structure does not exceed 40% of the initial design domain mass (mass fraction constraint)).

[0046] When the self-weight of the beam is included, performance evaluation points are set. The response value of the objective function is the displacement or acceleration response in the same direction as the load application point (center node) (i.e., H). xx H yy H zz This ensures that the dynamic stress flow path between the "force point → constraint end" is optimized and precisely strengthened. Using material volume or mass as constraints, primary constraints are generated. Based on these primary constraints, static compliance constraints are added (or a weighted multi-objective model is constructed (e.g., 0.3 × static compliance + 0.7 × dynamic compliance) to prevent beam sagging from exceeding tolerance). A topology optimization mathematical model is then constructed based on the objective function, primary constraints, and static compliance constraints (i.e., ultimately forming an explicit mathematical model with a single objective and multiple constraints), and passed to the solver in step S4 for iteration. See Table 1.

[0047] Table 1 Process Table

[0048] In this embodiment, when the dynamic response index is calculated using the time-domain method, the time integral of the dynamic strain energy under complete load time history excitation is defined as the optimization objective function. This integral is obtained by accumulating the power exerted by the external force at each instant on the time axis, thus obtaining the total energy input to the structure by the external force throughout the entire processing process. The physical meaning of this objective function lies in quantifying the dynamic deformation energy borne by the structure throughout the entire roughing and finishing load history. The smaller the value, the stronger the structure's ability to resist dynamic deformation and the higher its dynamic stiffness. In this expression, the total load duration is composed of the roughing and finishing durations, reflecting the complete time history of the two working conditions. During each optimization iteration, by performing transient dynamic analysis on the current structure, this integral value can be directly calculated and fed back to the optimization algorithm as a basis for evaluating structural performance. Compared with the traditional static compliance objective, the time-domain dynamic strain energy integral can truly reflect the temporal characteristics of the load and the non-stationary impact effect, enabling the optimization results to exhibit better dynamic performance in actual processing.

[0049] When the dynamic response index is calculated using the frequency domain method, the expected value of dynamic compliance is defined as the optimization objective function. This objective function calculates the expected value of the dynamic response index in the frequency domain by converting the load spectrum into the self-power spectral density in the frequency domain and combining it with the drive point frequency response function of the structure. Specifically, the product of the square of the magnitude of the frequency response function and the corresponding load self-power spectral density is calculated in three orthogonal directions. The contributions of roughing and finishing are calculated separately and then summed, followed by integration and summation over each discrete frequency point. This expected value comprehensively reflects the dynamic deformation capability of the structure in the main frequency band of the load spectrum; the smaller the value, the higher the stiffness of the structure under actual dynamic loads. Compared to the time domain method, the frequency domain method compresses the calculation of thousands of time steps in the time domain to the integration of hundreds of frequency points, significantly improving computational efficiency while ensuring accuracy. It is particularly suitable for situations with many optimization iterations and the need to quickly obtain the optimization direction. By adaptively selecting the time domain method or the frequency domain method after judging the characteristics of the load spectrum, this invention can achieve the optimal balance between computational accuracy and computational efficiency.

[0050] Regarding the setting of constraints, when the beam's self-weight is not included, the material volume or mass is used as the primary constraint to generate the main constraint. A topology optimization mathematical model is then constructed based on the objective function and the primary constraint. This constraint is typically set to ensure that the material volume or mass does not exceed a certain percentage of the initial design domain volume or mass. This percentage can be pre-set by those skilled in the art based on lightweighting requirements, manufacturing limitations, and engineering experience. By applying volume constraints, it is ensured that the optimized configuration achieves structural lightweighting while meeting dynamic performance objectives.

[0051] When incorporating the beam's self-weight, performance evaluation points are first established, where the response value of the objective function is the displacement or acceleration response in the same direction as the load application point. Setting these evaluation points gives the optimization objective a clear physical focus, directly addressing the structural response at the cutting force application location. This aligns perfectly with the engineering requirements for controlling the displacement and vibration of the tool center point in actual machining. Based on this, primary constraints are generated using material volume or mass as constraints, and static compliance constraints are added on top of these primary constraints. Finally, a topology optimization mathematical model is constructed based on the objective function, primary constraints, and static compliance constraints. Static compliance constraints are typically defined as the strain energy of the structure under gravity load not exceeding a preset threshold, or they are considered in a weighted combination, simultaneously considering static and dynamic compliance, with the total compliance defined as the weighted sum of static and dynamic compliance. The technical significance of this approach is that for structures with heavy self-weight, such as large gantry beams, if only dynamic response is considered as the objective while ignoring the influence of self-weight, the optimization results may show insufficient material at the lower edge and excessive static sag, failing to meet actual engineering requirements. By adding static flexibility constraints to the optimization model, it can be ensured that the optimized configuration improves dynamic stiffness without losing its ability to resist static deformation, thus taking into account both the static load-bearing capacity and dynamic vibration resistance requirements of the structure.

[0052] Through the combined effect of the aforementioned objective function and constraints, a complete mathematical model for topology optimization is constructed, laying the mathematical foundation for subsequent iterative solutions. This model simultaneously considers key factors such as the time-frequency characteristics of actual processing loads and the structure's self-weight, enabling the optimization results to guide the material to the force transmission path that contributes most to the dynamic stress flow, under material volume constraints, thereby achieving targeted enhancement of structural performance.

[0053] S4. The topology optimization algorithm is used to iteratively solve and optimize the topology optimization mathematical model to obtain the optimal material distribution configuration. The optimal material distribution configuration is then used as the final design basis for the beam structure of the machine tool to be optimized, so as to optimize the machine tool.

[0054] Specifically, step S4 further includes: the topology optimization algorithm is a variable density method, a level set method, or an evolutionary structure optimization method.

[0055] In this embodiment, a topology optimization algorithm is used to iteratively solve and optimize the topology optimization mathematical model to find the optimal material distribution scheme that satisfies the constraints and minimizes the dynamic response index. The topology optimization algorithm can be any of the variable density method, level set method, or evolutionary structure optimization method, and users can flexibly choose according to the specific needs such as the scale of the problem, nonlinearity, and manufacturing constraints. In this embodiment, the variable density method is preferred. This method establishes an interpolation model between the material's elastic modulus and density by using the element density as a design variable, penalizing intermediate densities to obtain a clear 0-1 topology.

[0056] During the iterative solution process, corresponding solution paths are adopted according to the determined dynamic response index calculation method. When using the time-domain method, each iteration performs a complete transient dynamic analysis on the current structural model, calculates the time integral of dynamic strain energy under complete load spectrum time history excitation, and the optimization algorithm evaluates the performance of the current material distribution scheme and calculates element sensitivity to guide the density update direction. When using the frequency-domain method, each iteration performs harmonic response analysis to obtain the driving point frequency response function of the current structure, and calculates the expected value of dynamic compliance based on the load power spectral density. The optimization algorithm updates the design variables based on this value and its sensitivity information. The iterative process under both paths continues automatically until the convergence condition is met.

[0057] To obtain an optimized configuration with engineering manufacturability, manufacturing constraints can be applied during the iteration process. These constraints include minimum member size control to prevent the creation of narrow force transmission paths, ensuring the optimized result meets the minimum wall thickness requirements of casting or welding processes; adding symmetry constraints when necessary to maintain the symmetry of the beam structure and ensure balanced performance under bidirectional stress; and adding draft direction constraints to facilitate subsequent casting demolding or machining positioning. A proper configuration of these constraints can significantly improve the manufacturability and engineering applicability of the optimized result.

[0058] The convergence condition for iteration is typically set as follows: the maximum rate of change of the design variables in two consecutive iterations is less than a predetermined threshold. A maximum number of iterations is also set to prevent the calculation from falling into an infinite loop. The iteration terminates when the convergence condition is met, and the optimization results are output. Specifically, the obtained element density distribution is used to generate isosurfaces with a predetermined threshold as the boundary. This threshold is typically taken as the median level of the density values ​​to obtain clear topological boundaries. The isosurface model is then exported as a standard format file. The exported configuration is imported into 3D modeling software for smoothing to eliminate irregular boundaries caused by numerical noise, and then solidified to obtain a beam structure scheme that can be directly used for engineering design.

[0059] The optimal material distribution configuration is used as the final design basis for the crossbeam structure of the machine tool to be optimized, and is used to optimize the structure of the machine tool. In practical applications, the obtained configuration retains grid-shaped stiffeners at the interface between the crossbeam and the column and in the upper region to maintain basic load-bearing stiffness and installation stiffness. In the slide mounting area and along the main force transmission path extending into the crossbeam, the material is radially distributed along the direction of dynamic stress flow, forming a directional reinforcement of dynamic loads. Since the optimization objective is directly based on the actual machining load spectrum, the dynamic response index is repeatedly calculated and fed back to the optimization algorithm during the iteration process, so that the material distribution in the final configuration accurately corresponds to the force transmission path excited by the roughing impact load and the finishing high-frequency vibration load. Compared with the uniform stiffener layout obtained by traditional static topology optimization, the optimal configuration obtained by the method of this invention has higher dynamic stiffness and better vibration resistance with the same amount of material, and can simultaneously meet the dual performance requirements of roughing impact deformation resistance and finishing high-frequency flutter suppression. This invention directly incorporates the time-frequency characteristics of real machining loads into the optimization model, enabling precise matching between material distribution configuration and dynamic stress flow. This significantly improves the dynamic stiffness and vibration resistance of the beam in actual composite machining, providing efficient and reliable technical support for machine tool structure design.

[0060] To further illustrate the effectiveness of this method, this embodiment uses a fixed-column, moving-beam overhead crane-type gantry machining center as an example. The machine tool's crossbeam is equipped with a slide, and a five-axis milling head is installed in the slide, allowing for the roughing and finishing of cast iron parts in a single setup. The same 10mm diameter solid carbide end mill (4 teeth) is used for both roughing and finishing. The machining mode is switched only by modifying the cutting parameters, without changing the tool during the process. The implementation steps of this invention are described below in conjunction with this actual machining process.

[0061] The first step is load spectrum acquisition (experimental data collection). In this embodiment, both the first and second load spectra are obtained through actual cutting experiments. The experiment was conducted on the gantry machining center, using a Kistler three-axis force gauge to collect cutting force signals in real time at a sampling frequency of 30000Hz. Roughing condition (first load spectrum): Plane milling was performed with a spindle speed of 3000 r / min, axial depth of cut of 0.3 mm, radial width of cut of 8 mm, and appropriate feed per tooth. The three-axis force time history (i.e., for the X, Y, and Z axes respectively) for 5 consecutive seconds during the stable cutting phase was captured. This time period contains approximately 1000 cutting cycles (4 teeth × 50 r / s × 5 s), sufficient to characterize the impact features of roughing. Finishing condition (second load spectrum): Slot milling is performed on the plane after roughing, with a spindle speed of 8000 r / min, radial depth of cut of 0.05 mm, and axial depth of cut of 5 mm. The three-dimensional force time history (i.e., for the X, Y, and Z axes respectively) for a continuous 10 seconds during the stable cutting phase is captured. This period contains approximately 5333 cycles, fully reflecting the smooth characteristics of high-frequency continuous cutting.

[0062] The acquired force signals are filtered, de-trended, and saved as a text file, which serves as the load input for subsequent optimization. Alternatively, the load spectrum can also be generated based on the same process parameters using a cutting mechanics theoretical model or commercial cutting simulation software; this embodiment does not impose any limitations on this.

[0063] The second step is to establish a finite element model and apply dynamic loading. Specifically, a parametric geometric model of the gantry beam is established in the finite element analysis software ANSYS Workbench. In this embodiment, the design domain dimensions of the gantry beam are 7460mm × 1500mm × 1400mm (L × H × W, i.e., length, width, and height), corresponding to the typical span and load-bearing requirements of a composite machining center. Tetrahedral elements are used to create a structured mesh of the design domain, with an element size of 45mm, and local refinement is applied in the slide mounting area. This embodiment uses gray cast iron HT300 material, with a typical value being the elastic modulus. Poisson's ratio ,density The boundary conditions are set to apply fixed constraints to both ends of the beam. Depending on the required accuracy, the beam's own weight can be further considered, either as prestress applied to the model or as an independent static load condition in subsequent optimization.

[0064] First, constrained modal analysis is performed on the beam to determine its natural frequency range and provide a basis for frequency segmentation in subsequent harmonic response analysis. This embodiment uses the Block Lanczos method to extract all modes within a frequency range covering 1.5 times (i.e., 2400Hz) of the upper limit of the subsequent harmonic response scan (1600Hz). The results show that the first 50 natural frequencies are between 72 and 451Hz, and their cumulative modal effective mass fractions in the X, Y, and Z directions all reach 1, indicating that higher-order modes contribute no further to the global dynamic response. Therefore, subsequent harmonic response analysis only needs to use the first 50 modes for modal superposition, ensuring accuracy while avoiding redundancy.

[0065] Defining the load application area: The crossbeam has a side-mounted structure, with the slide contacting the crossbeam's linear guide via three sets of upper and lower sliders (a total of eight imprinted surfaces). To accurately simulate the transmission of cutting force from the tool center point (TCP) to the crossbeam and to account for overhanging torque, remote force loading is employed. In the harmonic response analysis, three independent remote points TCP are created (i.e., for the three axes). X TCP Y TCP Z Their coordinates are all set to the spatial location of TCP, the geometry is selected from all slider contact surfaces, and the behavior is set to "rigid". Then, three remote forces are created. X ForceY Force Z Each force references its own remote point, and the components of the force are respectively set as , , (Other directions are 0). Using "Step Selection" in "Step Control," activate these three remote forces in load step 1 (X direction), load step 2 (Y direction), and load step 3 (Z direction), respectively. Thus, each load step applies a unit harmonic excitation along only one coordinate axis to extract the frequency response function of the driving point. , , .

[0066] Since the ANSYS Workbench harmonic response module does not support non-uniform frequency step sizes within a single load step, this embodiment subdivides the frequency scan in each direction into three sub-intervals, solving them with different frequency step sizes, resulting in 9 load steps (load steps 1-3 for the X direction, 4-6 for the Y direction, and 7-9 for the Z direction). The frequency range and number of sub-steps for each load step are shown in Table 2.

[0067] Table 2 Load step frequency settings for harmonic response analysis

[0068] In Table 2, the frequency range of the resonance encryption zone, 70~452Hz, completely covers all the natural frequencies (72~451Hz) of the aforementioned first 50 modes, and is finely scanned with a 5Hz step size to ensure that the frequency response function can accurately capture all resonance peaks. The upper limit of the scan, 1600Hz, is obtained by taking three times (1599Hz) the passing frequency of the finishing cutter teeth (4 teeth × 8000r / min / 60≈533Hz) and rounding it upwards, which can completely include the main harmonic energy of the cutting force. This piecewise non-uniform sampling strategy reduces the total number of calculated frequency points from 320 points with uniform 5Hz sampling to about 140 points / direction, significantly shortening the solution time, while the integral accuracy of the dynamic compliance expectation value remains unaffected.

[0069] The third step is to optimize the problem definition. Specifically, the optimization objective is to minimize the expected dynamic compliance value E[C] of the beam structure under a time-sequential alternating load spectrum. This index comprehensively reflects the global deformation capacity of the structure under real dynamic loads; the smaller the value, the higher the dynamic stiffness. The constraint condition is set to ensure that the material volume of the optimized structure does not exceed 40% of the initial design domain volume, and static compliance constraints or weighted combined objectives under gravity conditions can be selectively added to ensure the beam's ability to bear its own weight.

[0070] Step 4: Topology optimization solution settings. In the structural optimization module of ANSYS Workbench, the standard operations are as follows: the objective function is specified as the dynamic compliance response calculated in step 3; volumetric response constraints are added to the response constraints, with the upper limit of volume fraction set to 40%; the optimization method is the variable density method (SIMP), with a material penalty factor of 3; the density update uses the optimization criterion method (OC); manufacturing constraints are applied with minimum member size control (3 times the element size, i.e., 135mm), and symmetry constraints and draft direction constraints can be added if necessary; the convergence condition is that the maximum rate of change of the design variables in two consecutive iterations is less than 0.1%, and the maximum number of iterations is set to 200. After optimization, the isosurface STL file with a density threshold of 0.5 is output and imported into SpaceClaim for smoothing and solidification.

[0071] Specifically, two examples illustrate the calculation and closed-loop optimization of dynamic response indices. The first example uses frequency domain topology optimization based on ANSYS Workbench (see...). Figure 4 The frequency domain method balances computational accuracy and efficiency, and is suitable for situations where the load spectrum frequency band characteristics are clear. Frequency response function calculation: After solving the harmonic response analysis for 9 load steps, the displacement frequency response curves in the X, Y, and Z directions are extracted at the central node (the geometric center of the slide mounting area, selected as a solid mesh node). Since each direction is composed of three frequency segments, the real and imaginary parts are merged in ascending frequency order during post-processing to obtain the complete complex frequency response function. , , (Unit: m / N). Figure 7 The extracted frequency response function amplitude diagrams in three directions are provided as an example, clearly showing multiple peaks within the resonance region (72~452Hz). The analysis set a global constant structural damping coefficient of 0.02 (equivalent to cast iron and mating surfaces) and enabled the "modal equivalent damping ratio" option, ensuring the frequency response function has a reasonable finite amplitude and phase at resonance, thus avoiding the loss of the imaginary part.

[0072] Load spectrum frequency domain conversion: Converting the roughing and finishing time force signals obtained in the first step... , Import the data into MATLAB and calculate the three-dimensional power spectral density using Fast Fourier Transform (FFT). and These PSDs are then interpolated onto a frequency list that is identical to the frequency response function, generating a text file (such as psd_x_c.txt) that can be read by ANSYS. To make the numerical processing more stable, the force amplitude can be scaled proportionally according to the actual sensitivity coefficient of the force gauge. After scaling, the power spectral density is adjusted according to the square relationship, but the optimization direction remains unchanged.

[0073] Calculation of expected dynamic compliance value: Calculate the dynamic compliance contribution under rough and finish loads respectively, and then sum them to obtain the total expected value. Figure 8 This demonstrates the integrand function during roughing and finishing. The area under the spectrum curve represents the dynamic compliance contribution of each element. This expected value is directly used as the objective function for topology optimization.

[0074] Topology Optimization Loop (APDL): Since the Workbench standard optimization module cannot directly use user-defined dynamic compliance as the objective, this embodiment inserts an APDL command object into the harmonic response analysis and writes an adaptive optimization loop based on SIMP. The core logic is as follows: each iteration executes the harmonic response solution, reads the displacement of the center node and splices the frequency response, reads the external PSD file and integrates it according to the trapezoidal rule to obtain E[C], uses it as the objective function, calculates the element sensitivity using the built-in adjoint method, and updates the design variables using the OC criterion. The optimization process is fully automatic until the objective converges. An example of its main command snippets (file reading and integration parts) is as follows: DIM,FRQ_X,ARRAY,140! Read the list of frequencies in the X direction. VREAD,FRQ_X(1),freq_x,txt (F10.0) DIM,PSD_XC,TABLE,140,1,1,FREQ TREAD, PSD_XC, psd_x_c, txt! Reads the roughing PSD file in the X direction. ... ECMP = 0.0 DO,ILS,1,3! Iterate through 9 load steps DO,IFR,1,140 SET, ILS, IFR GET,UX,NODE,N_LOAD,U,X ECMP = ECMP + UX UX PSD_XC(IFR) (FRQ_X(IFR+1)-FRQ_X(IFR)) ENDDO ENDDO After accumulating the contributions from the Y and Z directions and finishing processes, the final ECMP input is used to optimize the response. TOREVISE,DYN_COMP,ECMP This macro is seamlessly integrated with the Workbench interface, allowing those skilled in the art to implement complete dynamic topology optimization iterations.

[0075] The second example is a time-domain topology optimization solution based on ANSYS Workbench (see...). Figure 5 The time-domain method directly performs transient dynamic analysis on the complete load time history, providing direct physical meaning, but it has a high computational cost and is suitable for situations where the load is highly non-stationary or requires consideration of nonlinear effects. This embodiment uses the same model, load spectrum, and constraints as the frequency-domain method; the only difference is the calculation method of the dynamic response index in step four. All operations are performed in ANSYS Workbench. This embodiment aims to demonstrate the flexibility and universality of the method of the present invention in processing dynamic load spectra.

[0076] Time-domain method-specific settings: Transient dynamics analysis settings. In ANSYS Workbench, a transient structure module is created for the structural model of the current iteration step. Rayleigh damping coefficients are defined as α=15, β=8×10⁻⁶, and the time step is set to 0.0005s to ensure accurate capture of the high-frequency components of the finishing load; the total duration is T=15s, covering the entire roughing and finishing load history. The two force time histories are sequentially spliced ​​and applied to the loading points using the load data table.

[0077] Calculate the time-domain dynamic compliance. After solving, insert the user-defined results into the Solution, and use the Result Tracker function to calculate the formula. Calculate the dynamic strain energy integral, which is the objective function.

[0078] Optimization Iteration: The transient analysis process is invoked in the structural optimization module. The built-in adjoint method automatically calculates the time-domain sensitivity and updates the density using the OC criterion. Each iteration performs a complete transient solution. The iteration termination criterion is the same as that of the frequency domain method. Although the time-domain method is time-consuming, its accurate capture of non-stationary shocks makes it a reliable supplement to verifying the results of the frequency domain method.

[0079] The fifth step is result output and verification. Specifically, after optimization, the obtained cell density distribution is used to generate isosurfaces with a threshold of 0.5, which yields results such as... Figure 6The diagram (b) shows the material distribution of the crossbeam. In the figure, the crossbeam-column interface and upper region retain the grid-like stiffeners to maintain basic load-bearing and installation stiffness; however, in the slide mounting area and along the main force transmission path extending into the crossbeam, a star-shaped radial stiffener structure with a central ring appears. This radial stiffener corresponds precisely to the direction of the "dynamic stress flow" excited by the dynamic load spectrum of roughing and finishing, distributing the cutting force to both ends of the crossbeam with the shortest force transmission path, and forming circumferential constraints at the ring, effectively suppressing high-frequency vibrations. In contrast, Figure 6 The traditional optimized configuration shown in (a) aims to minimize static compliance. It presents a uniform grid-like stiffener layout and does not show any reinforcement features for areas with concentrated dynamic loads.

[0080] To verify the optimization effect, the measured composite load spectra of roughing and finishing were simultaneously applied to two configurations, and the results were compared through transient dynamic simulation. The results show that, under the same volume fraction constraint, the optimized configuration of this invention (…) Figure 6 In (b) of the design, the maximum dynamic deformation at the loading point is reduced by approximately 15% compared to the traditional configuration, and the root mean square value of the triaxial acceleration is reduced by approximately 25%. The vibration amplitude attenuation is particularly significant in the high-frequency range near the passing frequency of the finishing teeth. This improvement is attributed to the precise guidance of the material to the force transmission path that contributes most to the dynamic flexibility, thus satisfying the stiffness requirements of the structure in both low-frequency large deformation and high-frequency flutter modes.

[0081] These examples demonstrate that this method can automatically generate rib configurations with directional reinforcement for roughing-finishing composite conditions, providing an efficient and operable design solution for gantry machining center beams and other large structures subjected to time-sequential dynamic loads. This invention can be directly integrated into commercial topology optimization software (such as ANSYS and OptiStruct) or self-developed finite element programs, providing methodological support for the dynamic design of various gantry machining center beams using single / dual spindles and single / dual slides. It can also be applied to press bodies, high-speed electric spindles, and other mechanical structures subjected to time-sequential dynamic loads.

[0082] In addition, due to the large self-weight of the beam, in order to obtain an optimized configuration that better matches the actual working conditions, gravity can be included in the optimization model. The specific operation is as follows: (1). Static equivalence of multiple working conditions: Add a static load working condition in the topology optimization module, apply standard Earth gravity, and the direction is vertically downward. The compliance of the static working condition and the expected value of the dynamic compliance of the dynamic load spectrum working condition are weighted and combined. The total compliance = a·static compliance + (1-a)·dynamic compliance, where a is 0.2~0.5, or can be automatically adjusted by the optimization algorithm. The volume constraint remains unchanged.

[0083] (2) Prestressed dynamic analysis: Add a static analysis step before modal analysis, apply gravity, solve the problem, pass the results to modal analysis and enable the "prestress" option; subsequent harmonic response or transient analysis is based on the prestressed mode. This method is more accurate, but the computational cost is higher, and it is suitable for structures that are sensitive to gravity effects.

[0084] Experience shows that, for the gantry beam in this embodiment, the influence of its own weight on the final topology is mainly reflected in strengthening the material distribution in the support areas at both ends and increasing the thickness of the lower longitudinal stiffeners. If the self-weight is not considered, the optimized configuration may result in insufficient material at the lower edge and excessive static sag. Therefore, it is recommended to use at least method (1) for verification in engineering implementation.

[0085] In summary, the dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving is applicable to mechanical structures subjected to time-varying, non-stationary, and multi-source dynamic loads, such as gantry machining center beams, press bodies, and high-speed spindles. Specifically, this invention first acquires the working condition data of the machine tool to be optimized and converts it into a first load spectrum and a second load spectrum representing roughing and finishing, respectively. Based on the load characteristics, it adaptively judges and determines whether the calculation method for the dynamic response index is the time domain method or the frequency domain method. Then, it establishes a parametric geometric model of the machine tool beam, and applies the two load spectra to the same or different installation areas according to the actual machining sequence, generating corresponding complete time histories or drive point frequency response functions. On this basis, it constructs a topology optimization mathematical model with the optimization objective of minimizing the dynamic response index of the beam structure under the sequential excitation of the two load spectra and the material volume or mass as constraints. Finally, iteratively solving the topology optimization algorithm yields the optimal material distribution configuration as the final design basis. This invention directly incorporates the time-frequency characteristics of actual machining loads into the optimization model, precisely guiding the material to the force transmission path that contributes most to dynamic flexibility. This simultaneously meets the dual performance requirements of resisting large deformations in rough machining and suppressing high-frequency vibrations in finish machining, significantly improving the dynamic stiffness and vibration resistance of beams in actual composite machining. This method is also applicable to other mechanical structures subjected to time-series dynamic loads, such as press bodies and high-speed electric spindles, demonstrating good versatility and engineering application value.

[0086] Compared with existing technologies, the advantages of this method are as follows: Firstly, it simultaneously uses two distinct dynamic load spectra—roughing and finishing—as input for topology optimization, directly addressing the actual composite machining process of machine tools, thus possessing greater engineering significance. Aiming to minimize dynamic response (dynamic compliance, acceleration), it guides material distribution along the critical path of dynamic stress flow, significantly improving the dynamic stiffness and vibration resistance of the structure under operating conditions. It provides both time-domain and frequency-domain solution strategies, balancing accuracy and efficiency. The deep integration of load spectrum construction and dynamic topology optimization forms a closed-loop design from load characterization to performance-driven design, providing a new paradigm for the design of machine tools and other structures subjected to complex dynamic loads.

[0087] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A dynamic topology optimization design method for machine tool beams based on dual-modal load spectrum driving, characterized in that, include: S1. Obtain the working condition data of the machine tool to be optimized, convert it to obtain the first load spectrum and the second load spectrum, and judge the first load spectrum and the second load spectrum to determine the calculation method of dynamic response index. S2, establish a parameterized geometric model of the machine tool to be optimized, and apply the first load spectrum and the second load spectrum to the same or different installation areas of the parameterized geometric model according to the dynamic response index calculation method, and generate a complete time history or drive point frequency response function accordingly. S3, based on the complete time history or the frequency response function of the driving point, takes the minimization of the dynamic response index of the beam structure of the machine tool to be optimized under the excitation of the first load spectrum and the second load spectrum as the optimization objective function, and constructs a topology optimization mathematical model with material volume or mass as the constraint condition; S4. The topology optimization algorithm is used to iteratively solve and optimize the topology optimization mathematical model to obtain the optimal material distribution configuration. The optimal material distribution configuration is then used as the final design basis for the beam structure of the machine tool to be optimized, so as to optimize the machine tool.

2. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 1, characterized in that, The first load spectrum represents the roughing condition of the machine tool to be optimized, and the second load spectrum represents the finishing condition of the machine tool to be optimized. Both the first and second load spectra are time history data of the three-dimensional cutting force that varies with time.

3. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driving according to claim 2, characterized in that, The first and second load spectra can be obtained through experimental measurement or theoretical simulation.

4. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 1, characterized in that, The first load spectrum and the second load spectrum are evaluated to determine the calculation method for the dynamic response index, specifically as follows: When it is determined that the first load spectrum and the second load spectrum possess any of the characteristics of the first judgment condition, the dynamic response index calculation method is determined to be the time domain method. The first judgment condition includes strong nonstationarity and impact characteristics, non-superposition of time-series effects, and nonlinear characteristics that need to be verified or exist. When it is determined that the number of features in the first load spectrum and the second load spectrum that meet the second judgment condition is not less than the judgment threshold, the dynamic response index calculation method is determined to be the frequency domain method. The second judgment condition includes the characteristics of the load having stationary random characteristics, the system being a linear time-invariant system, and the pursuit of extremely high computational efficiency.

5. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 1, characterized in that, A parametric geometric model of the machine tool to be optimized is established. Based on the dynamic response index calculation method, the first load spectrum and the second load spectrum are applied to the same or different installation areas of the parametric geometric model, generating a complete time history or drive point frequency response function. Specifically: Using finite element software, a parametric geometric model of the beam of the machine tool to be optimized was established, and tetrahedral elements were used to perform structured mesh generation on the parametric geometric model. Obtain the material properties and boundary conditions of the machine tool to be optimized, and set the material properties and boundary conditions into the parametric geometric model; Based on the current engineering requirements, the self-weight of the crossbeam of the machine tool to be optimized is selectively incorporated into the parametric geometric model; Based on the preset extraction value n, the first n natural frequencies of the machine tool to be optimized are extracted using the Block Lanczos method. When it is determined that the dynamic response index calculation method is the time domain method, the first load spectrum and the second load spectrum are applied to the same installation area of ​​the parameterized geometric model according to the actual machining sequence of the machine tool, and the complete time history F(t) is obtained by splicing them together.

6. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 5, characterized in that, Also includes: When it is determined that the dynamic response index calculation method is the frequency domain method, the corresponding sub-intervals are selected from the three preset frequency scanning sub-intervals based on the first n natural frequencies, and these sub-intervals are the key focus areas. The three frequency scanning sub-intervals are the low-frequency quasi-static region, the resonance-enhanced region, and the high-frequency flat region. Based on the key focus area, the first and second load spectra were applied to different installation areas of the parametric geometric model to create remote force points (TCPs). A 1N unit harmonic excitation was applied along the X, Y, and Z axes, and the frequency response function H of the X-axis drive point was extracted. xx Y-axis driving point frequency response function H yy Z-axis driving point frequency response function H zz .

7. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 6, characterized in that, Based on the complete time history or the frequency response function of the driving point, the optimization objective function is to minimize the dynamic response index of the beam structure of the machine tool to be optimized under the excitation of the first load spectrum and the second load spectrum. A topology optimization mathematical model is constructed with material volume or mass as a constraint. Specifically: When the dynamic response index is calculated using the time-domain method, the dynamic strain energy time integral C under full load time-history excitation is... dyn Defined as the objective function to be optimized, its formula is: T is the total duration of the load application. This is the transpose, where t is the load duration index. Let dt be the velocity vector of the structure, and dt be the time derivative. When the dynamic response index is calculated using the frequency domain method, the expected value of dynamic compliance E[C] is defined as the optimization objective function, and its formula is: N is the total number of discrete frequency points, and k is the index of the discrete frequency point, k=1,2,...,N. For frequency step size, Let k be the frequency value at the kth discrete frequency point. The self-power spectral density of the roughing load in the m-axis direction is given. The power spectral density of the finishing load in the m-axis direction is denoted as . When the beam's self-weight is not included, the material volume or mass is used as a constraint to generate the main constraints. Based on the optimization objective function and the main constraints, a topology optimization mathematical model is constructed, where the constraint condition is that the material volume or mass does not exceed a preset constraint threshold.

8. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 7, characterized in that, Also includes: When the self-weight of the beam is included, performance evaluation points are set, where the response value of the objective function is the displacement or acceleration response in the same direction as the load application point. Using material volume or mass as constraints, primary constraints are generated. Static compliance constraints are added to the primary constraints. Based on the optimization objective function, primary constraints, and static compliance constraints, a topology optimization mathematical model is constructed.

9. The machine tool beam dynamic topology optimization design method based on dual-modal load spectrum driven according to claim 1, characterized in that, The topology optimization algorithm is a variable density method, a level set method, or an evolutionary structure optimization method.

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