A design method and system of shape-controllable damper for milling vibration control

Abstract

The application provides a milling vibration control shape-property controllable damper design method and system, relates to the damper design field, and is based on workpiece material cutting effect, divides a workpiece-clamp system into a joint and multiple substructures; a combined structure is obtained by sequentially coupling the multiple substructures according to a milling processing sequence, the combined structure and the joint are coupled, a workpiece frequency response function prediction model is established, time-varying dynamic parameters of the workpiece are obtained, including natural frequency and vibration mode; based on a plate damping structure deformation energy model and the time-varying dynamic parameters of the workpiece, aiming at the problems that the damping structure performance is poor and the control effect cannot meet the demand, the damping performance is improved by reasonably designing the layer number, structure and material parameters of the damper, the performance is controllable, the change of the main modal vibration mode in the milling processing process of the thin-walled workpiece is considered, the shape design of the damper is guided, the shape is controllable, and vibration milling is effectively inhibited.

Description

Technical Field

[0001] This invention relates to the field of damper design, and more specifically to a design method and system for shape-controllable dampers for milling vibration control. Background Technology

[0002] Thin-walled titanium alloy structures are widely used in the aerospace field. These structures are characterized by low rigidity and difficult material machinability, making them prone to self-excited chatter during milling. This significantly impacts machining quality and efficiency, accelerates tool wear, and can even lead to part scrap. Chatter control methods primarily achieve this by altering the dynamic characteristics of the machining system. For example, improving the design of the spindle, tool, fixture, or jig can expand the stability boundary of the machining system, thereby suppressing machining vibrations. Based on their working principles, chatter control methods can be categorized into active and passive methods. Active control methods monitor the response of the machining system to determine its operating state and then use actuators to make adjustments to eliminate chatter. However, implementing active methods requires complex auxiliary equipment, lengthy control algorithms, and energy input, thus reducing their reliability and cost-effectiveness.

[0003] Unlike active control strategies, passive methods are simple in structure and easy to implement, but their dynamic characteristics are not easily altered after manufacturing. Special materials or auxiliary devices are typically used on the cutting tool, workpiece, or fixture to increase the system's stiffness or damping and improve machining stability. Regarding cutting tools, a horizontal assembly-type vibration-damping milling cutter (Chinese Patent Publication No.: CN 208437733U) and a viscoelastic constraint damping structure vibration-damping turning tool holder (Chinese Patent Publication No.: CN 106994519 B) incorporate damping structures into the tool design to improve machining stability. Regarding workpieces, Wan, M., et al. (2018). "Optimization and improvement of stable processing condition by attaching additional masses for milling of thin-walled workpiece." Mechanical Systems and Signal Processing 103:196-215, demonstrates how adding additional masses to the workpiece increases the rigidity of thin-walled workpieces, thereby expanding the stability domain. Reference: Fei, J., et al. (2017). "Chatter mitigation using moving damper." Journal of Sound and Vibration 410:49-63. A moving damper was designed to consume the vibration energy of the milling system and achieve chatter suppression.

[0004] Currently, the damping structures developed for machining vibration control have shortcomings. Most of these structures are used for tool improvement designs, such as patents CN 208437733 U and CN 106994519 B. Moreover, these damping structures are generally single-layer structures, making it difficult to achieve the effects and performance of multi-layer damping structures. Damping structure designs for workpieces often only focus on the average control effect of overall chatter, without considering the influence of changes in workpiece dynamic characteristics, resulting in control effects that fail to meet requirements. In addition, there is a lack of replicable and customized methods for related designs or systems, making it difficult to solve the chatter control problem for workpieces with different dynamic characteristics. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a shape-controllable damper design method and system for milling vibration control. This method is geared towards controlling milling vibration in thin-walled parts. On one hand, it improves damping performance and achieves controllable performance by rationally designing the number of damper layers, structure, and material parameters. On the other hand, it considers the changes in the principal mode shape during the milling process of thin-walled workpieces, guiding the shape design of the damper to achieve shape control and effectively suppressing vibration during milling.

[0006] The primary objective of this invention is to provide a design method for a shape-controlled damper for milling vibration control, employing the following scheme:

[0007] Based on the workpiece material removal effect, the workpiece-fixture system is divided into a joint and multiple substructures;

[0008] According to the milling sequence, multiple substructures are coupled sequentially to obtain the combined structure. The combined structure and the joint are coupled to establish a workpiece frequency response function prediction model and obtain the time-varying dynamic parameters of the workpiece, including natural frequency and mode shape.

[0009] Based on the deformation energy model of plate-type damping structures and the time-varying dynamic parameters of the workpiece, the number of layers, material, and shape of the damper are determined.

[0010] Furthermore, after dividing the workpiece-fixture system, all substructures are coupled using the admittance coupling method.

[0011] Furthermore, a prediction model for the frequency response function of the substructure is established and validated.

[0012] Furthermore, for the workpiece-fixture system connection, based on the fact that the contact is flexible, a genetic algorithm is introduced to identify the contact parameters of the connection and obtain the contact parameters of the connection.

[0013] Furthermore, based on the contact parameters of the joint, the combined structure and the joint are coupled using the admittance coupling method to establish a workpiece frequency response function prediction model. Through the workpiece frequency response function prediction model, the time-varying dynamic parameters of the workpiece are obtained, and the dynamic parameters of the workpiece under arbitrary processing parameters and at any time are predicted.

[0014] Furthermore, based on the predicted workpiece dynamic parameters and workpiece mode shapes, the shape of the damper is designed.

[0015] Furthermore, the number of layers and materials of the damper are determined based on the deformation energy model of plate-type damping structures, specifically including:

[0016] Based on the principle of deformation energy, a deformation energy model of a plate-type multilayer damping structure is established, and the influence of material parameters and geometric parameters on the loss factor of the damping structure is analyzed.

[0017] Various damping materials are introduced to design and fabricate single-layer, double-layer, or triple-layer damping structures. The modal characteristics of the corresponding damping structures are analyzed, and their damping performance is verified by modal testing to determine the number of layers and materials of the damping structure.

[0018] Furthermore, after determining the shape, number of layers, and material of the damper, the structural shape and parameters of the damper are optimized. The optimization process is based on the damping performance criteria of the damper to determine the shape-controllable damper with optimal parameters.

[0019] Furthermore, the obtained damper is tested in conjunction with the workpiece being processed, and the stability domain is compared with that without a damper to determine the improvement in stability caused by the damper.

[0020] A second objective of this invention is to provide a shape-controlled damper design system for milling vibration control, comprising:

[0021] The structural partitioning module is configured to divide the workpiece-fixture system into joints and multiple substructures based on the workpiece material removal effect.

[0022] The dynamic parameter acquisition module is configured to: sequentially couple multiple substructures according to the milling sequence to obtain the combined structure, couple the combined structure and the joint, establish a workpiece frequency response function prediction model, and obtain the time-varying dynamic parameters of the workpiece;

[0023] The damper design module is configured to determine the number of layers, material, and shape of the damper based on the deformation energy model of the plate-type damping structure and the modal parameters of the workpiece.

[0024] Compared with the prior art, the advantages and positive effects of this invention are:

[0025] (1) In response to the current problem of poor performance of damping structures and inability to meet the control requirements, the damping performance can be improved by rationally designing the number of layers, structure and material parameters of the damper, so as to achieve controllable performance. The change of the main mode vibration mode during the milling process of thin-walled workpieces is considered to guide the shape design of the damper, so as to achieve controllable shape and effectively suppress vibration milling.

[0026] (2) Design a shape-controllable damper, including the design of the number of damper layers, structure, and materials, to obtain the effect and performance of the multi-layer damping structure, thus achieving controllability of the damper's shape and performance. At the same time, considering the structure of the workpiece-fixture system, a workpiece frequency response function prediction model is established. Based on the predicted workpiece mode shape, the shape of the damper is designed to maximize the suppression of milling chatter.

[0027] (3) It can meet the needs of vibration control for workpieces with different dynamic characteristics. The form-controllable damper design method for milling vibration control in this embodiment can realize the customized design of the damper and match the processing of different types of thin-walled workpieces. Attached Figure Description

[0028] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0029] Figure 1 This is a flowchart of the design of the shape-controllable damper for milling vibration control in Embodiments 1 and 2 of the present invention.

[0030] Figure 2 This is a schematic diagram of the workpiece-fixture system in Embodiments 1 and 2 of the present invention.

[0031] Figure 3 This is a schematic diagram of the damper structure optimization in Embodiments 1 and 2 of the present invention.

[0032] Figure 4 This is a schematic diagram of the cross-sectional parameters of the single-layer damper in Embodiments 1 and 2 of the present invention. Detailed Implementation

[0033] Example 1

[0034] In a typical embodiment of the present invention, such as Figures 1-4 As shown, a design method for a shape-controllable damper for milling vibration control is presented.

[0035] Current damping structures used for machining vibration control have shortcomings. Most of these structures are used for tool improvement designs, such as patents CN 208437733 U and CN 106994519 B. Moreover, these damping structures are generally single-layer structures, making it difficult to achieve the effects and performance of multi-layer damping structures. Damping structure designs for workpieces often only focus on the overall average control effect of chatter, without considering changes in workpiece dynamic characteristics, resulting in control effects that fail to meet requirements. Furthermore, there is a lack of replicable and customized methods for related designs or systems, making it difficult to solve the chatter control problem for workpieces with different dynamic characteristics.

[0036] Based on this, this embodiment provides a shape-controllable damper design method for milling vibration control, which is aimed at milling vibration control of thin-walled parts. On the one hand, by reasonably designing the number of layers, structure and material parameters of the damper, the damping performance is improved and the performance is controllable. On the other hand, the change of the main mode vibration mode during the milling process of thin-walled workpieces is considered to guide the shape design of the damper, so as to achieve shape controllability and effectively suppress vibration milling.

[0037] The design method of shape-controllable damper for milling vibration control is described in detail below with reference to the accompanying drawings.

[0038] See Figure 1 The design method of shape-controllable dampers for milling vibration control includes:

[0039] Based on the workpiece material removal effect, the workpiece-fixture system is divided into a joint and multiple substructures;

[0040] According to the milling sequence, multiple substructures are coupled sequentially to obtain the combined structure. The combined structure and the joint are coupled to establish a workpiece frequency response function prediction model and obtain workpiece modal parameters.

[0041] Based on the deformation energy model of plate-type damping structures and workpiece modal parameters, the number of layers, material, and shape of the damper are determined.

[0042] like Figure 2 As shown, based on the material removal effect of the workpiece, the workpiece-fixture system is divided into a joint and multiple substructures. In this embodiment, taking the division into three substructures and one joint as an example, the substructures are substructure A, substructure B, substructure C and joint X respectively.

[0043] Specifically, the process of sequentially coupling multiple substructures to obtain a combined structure according to the milling sequence includes: after dividing the workpiece-fixture system, coupling is performed using the admittance coupling method. First, substructure A and substructure B are coupled to obtain combined structure D. Then, combined structure D and substructure C are coupled to obtain combined structure E. A prediction model of the substructure frequency response function is established and the prediction model of the substructure frequency response function is verified.

[0044] For the frequency response function model of the substructure, its corresponding frequency response prediction model can be established using Timoshenko beam theory, and the accuracy of the prediction results can be verified using the finite element method. The frequency response function of the substructure is obtained and used in the subsequent coupling process.

[0045] Figure 2 The corresponding coordinate points 1, 2, and 3 represent the coupling relationship between substructures. Specifically, coordinate point 1 is on substructure A, coordinate point 2 is between substructure A and substructure B, and coordinate point 3 is between substructure B and substructure C.

[0046] For the workpiece-fixture system, based on the fact that the contact is flexible, a genetic algorithm is introduced to identify the contact parameters of the joint and obtain the contact parameters of the joint.

[0047] Obtaining modal parameters includes: based on the contact parameters of the joint, coupling the combined structure E and the joint using the admittance coupling method, establishing a workpiece frequency response function prediction model, obtaining the time-varying dynamic parameters of the workpiece through this workpiece frequency response function prediction model, and predicting the workpiece modal parameters at any processing parameters and at any time.

[0048] like Figure 1 As shown, substructures A and B are first coupled to obtain composite structure D. Then, composite structure D and substructure C are coupled to obtain composite structure E. Based on this, the admittance coupling method is used to couple composite structure E and the joint to obtain the frequency response function prediction model of the workpiece.

[0049] After dividing the structure into substructures, the multiple substructures and joints are coupled step by step to form a whole, which is the workpiece remaining after material removal. The step-by-step coupling process is equivalent to gluing the disassembled substructures together step by step, finally coupling them into the remaining workpiece.

[0050] It should be noted that the assembly E only includes substructures A, B and C. Such an assembly E cannot represent the remaining workpiece because the part of the workpiece held by the clamping device is not considered, i.e., the joint. Therefore, it is necessary to couple the assembly E and the joint to obtain the complete remaining workpiece. Correspondingly, the assembly E and the joint need to be coupled again.

[0051] The workpiece after material removal has an irregular shape. To obtain the dynamic parameters of the removed workpiece, it is necessary to model the remaining workpiece, but direct modeling is not easy. Therefore, in this embodiment, the remaining workpiece after material removal is artificially divided into multiple small substructures. The substructures have regular shapes and can be modeled using Timoshenko beam theory. After each substructure is modeled, they are coupled to form the removed workpiece. Since the frequency response function model of the substructure is known, the frequency response function model of the coupled remaining workpiece can be established, thus obtaining the known frequency response function model of the remaining workpiece.

[0052] Furthermore, establishing a frequency response function prediction model for the remaining workpiece is the most crucial part of the embodiment. By establishing this model, the dynamic parameters of the remaining workpiece after partial material removal can be quickly extracted. Using this model, the dynamic parameters of the remaining workpiece after any size of material has been removed can be predicted, thereby identifying the weak points. Based on this, a more targeted damper design can be implemented. Therefore, the damper designed in this way has a better vibration suppression effect, taking into account the influence of the workpiece's time-varying characteristics.

[0053] Establishing a workpiece frequency response function prediction model specifically includes:

[0054] ① Considering the material removal effect of the workpiece, the workpiece-fixture system is divided into multiple substructures, including substructures A, B, C and the workpiece-fixture joint.

[0055] ② Building upon ①, a frequency response function prediction model for the substructures is established using Timoshenko beam theory. Simultaneously, the substructures are coupled and recombined using the admittance coupling method. For example, substructures A and B are coupled to combined structure D using the admittance coupling method, and then combined structure D is coupled with substructure C to obtain combined structure E. The corresponding coordinate points 1, 2, and 3 are used to describe the coupling relationships between the substructures.

[0056] ③ For the workpiece-fixture joint, considering that the contact between the workpiece and the fixture is flexible, a genetic algorithm is introduced to identify the contact parameters of the joint.

[0057] ④ Based on the above steps, considering the contact parameters of the workpiece-fixture joint, the admittance coupling method is used to couple the combined structure E and the clamping part, establish a workpiece frequency response function prediction model, and extract the time-varying dynamic parameters of the workpiece.

[0058] ⑤ Based on ④, the computational performance of the proposed method is verified by comparing it with the finite element method.

[0059] The shape of the damper is designed based on the predicted modal parameters and mode shapes of the workpiece.

[0060] Specifically, based on the deformation energy model of a multi-layer damping structure, the influence of the material and geometric parameters of the damper on its performance was analyzed. At this point, the dampers, whether single-layer or multi-layer, have regular shapes. On this basis, the changes in the workpiece dynamic parameters are considered. As more and more material is removed from the workpiece, the vibration mode of the workpiece deforms. Based on this trend, the shape of the damper changes accordingly, making the shape of the damper irregular and stepped, which can suppress the vibration of the workpiece to the greatest extent.

[0061] Determining the number of layers and specific materials of the damper based on the deformation energy model of plate-type damping structures includes:

[0062] Based on the principle of deformation energy, a deformation energy model of a plate-type multilayer damping structure is established, and the influence of material parameters and aggregate parameters on the loss factor of the damping structure is analyzed.

[0063] Various damping materials are introduced to design and fabricate single-layer, double-layer, or triple-layer damping structures. The modal characteristics of the corresponding damping structures are analyzed, and their damping performance is verified by modal testing to determine the number of layers and materials of the damping structure.

[0064] It is understandable that the deformation energy model for plate-type multi-layer damped structures is applicable to single-layer damped structures, which is equivalent to a single-layer damped structure being a special case of a multi-layer damped structure.

[0065] Specifically, based on the established deformation energy principle, a mathematical relationship is established between the structural loss factor and material properties and geometric parameters. The damping characteristics and stiffness characteristics of the damped structure are studied, and the influence of material mathematical and geometric parameters on modal characteristics is analyzed, providing a basis for the selection of materials and geometric parameters.

[0066] Based on the above analysis, multiple materials and geometric parameters were selected to manufacture corresponding damping structures. Modal testing was used to test the damping performance of the damping structures, and the damping structure with the best damping performance was selected.

[0067] Optionally, the damping material can be aluminum foam, polyurethane rubber, epoxy resin rubber, nitrile rubber, butyl rubber, etc. In other embodiments, the damping material can be selected according to requirements.

[0068] like Figure 1 As shown, after determining the shape, number of layers, and material of the damper, the structural shape and parameters of the damper are optimized. The optimization process is based on the damping performance criteria of the damper to determine the shape-controllable damper with optimal parameters.

[0069] Optimizing the structural shape and parameters of a damper refers to optimizing the structure, number of layers, and materials of a pre-determined damping structure. During the optimization process, to improve damper performance by optimizing materials and the number of layers, the damping structure designed based on the deformation energy principle has a regular shape. On this basis, considering the changes in the time-varying dynamic parameters of the workpiece, the damper structure is optimized, such as... Figure 3 As shown, the damper structure changes from a regular structure to an irregular structure, achieving controllable shape. Furthermore, the optimal structural loss factor is introduced. Based on the deformation energy model, the relationship between the damping performance of the damper and the structural parameters of the matrix and damping layer is derived. Taking a single-layer damping structure as an example, as... Figure 4 As shown, the loss factor η of the damping structure

[0070]

[0071]

[0072] In the formula β z H represents the loss factor of the damping material. j H represents the thickness of the matrix layer. z H represents the thickness of the damping layer. jz Ej represents the distance between the neutral layer of the matrix and the neutral layer of the damping layer, Ez represents the elastic modulus of the matrix material, and Ez represents the elastic modulus of the damping layer material.

[0073] Equation 1-2 can be used to derive the relationship between the damper performance (loss factor) of the damper and the material and geometric parameters of the matrix and damping layer, guiding the selection of materials and geometric parameters and achieving the goal of performance optimization.

[0074] After obtaining the optimal parameters of the shape-controllable damper, its stability improvement is tested. Specifically, the manufactured damper is attached to the workpiece being processed, and experimental tests are conducted. The stability domain is compared with that without the damper to determine the improvement of stability by the damper.

[0075] It should be noted that the form-controllable damper proposed in this embodiment achieves controllability of the damper's shape and performance, maximizing the suppression of milling chatter. It can meet the needs of vibration control during workpiece machining with different dynamic characteristics. The form-controllable damper design method for milling vibration control in this embodiment enables customized damper design to match the machining processes of different types of thin-walled workpieces.

[0076] Combination Figure 1 , Figure 2 The design method for shape-controllable dampers for milling vibration control in this embodiment specifically includes:

[0077] Step S1: Considering the material removal effect of the workpiece, the workpiece-fixture system is divided into multiple sub-parts, namely sub-structure A, sub-structure B, sub-structure C, and workpiece-fixture joint X, as follows: Figure 2 As shown;

[0078] Step S2: Based on step S1, use the admittance coupling method to couple substructure A and substructure B to obtain combined structure D, and then couple combined structure D and substructure C to obtain combined structure E.

[0079] like Figure 2 The corresponding coordinates 1, 2, and 3 are used to describe the coupling relationship between substructures.

[0080] Step S3: For the workpiece-fixture joint X, considering that the contact between the workpiece and the fixture is a flexible contact, a genetic algorithm is introduced to identify the contact parameters of the joint.

[0081] Step S4: Based on the above steps, considering the contact parameters of the workpiece-fixture joint X, the combined structure E and the clamping joint are coupled using the admittance coupling method to establish a workpiece frequency response function prediction model and extract the workpiece modal parameters at any processing parameters and at any time.

[0082] Step S5: Based on the deformation energy distance, establish a deformation energy model for a plate-type multilayer damping structure, and analyze the influence of material parameters and geometric parameters on the loss factor of the damping structure.

[0083] Step S6: Introduce various damping materials, design and fabricate single-layer, double-layer, or triple-layer damping structures, analyze the modal characteristics of the corresponding damping structures, verify their damping performance using modal testing, and determine the number of layers and materials of the damper structure.

[0084] Step S7: Based on the workpiece modal vibration conditions predicted in Step S4, design the shape of the damper; introduce the damping performance criteria of the damper, optimize the structural shape and parameters of the damper, and manufacture a shape-controllable damper with optimal parameters.

[0085] Step S8: Attach the manufactured damper to the workpiece being processed, conduct experimental tests, and compare the stability region with that without the damper to determine the improvement in stability caused by the damper.

[0086] Example 2

[0087] In another typical embodiment of the present invention, such as Figures 1-4 As shown, a shape-controllable damper design system for milling vibration control is presented.

[0088] include:

[0089] The structural partitioning module is configured to divide the workpiece-fixture system into joints and multiple substructures based on the workpiece material removal effect.

[0090] The dynamic parameter acquisition module is configured to: sequentially couple multiple substructures according to the milling sequence to obtain the combined structure, couple the combined structure and the joint, establish a workpiece frequency response function prediction model, and obtain the time-varying dynamic parameters of the workpiece;

[0091] The damper design module is configured to determine the number of layers, material, and shape of the damper based on the deformation energy model of the plate-type damping structure and the modal parameters of the workpiece.

[0092] It is understood that the working method of the above-mentioned milling vibration control form-controllable damper design system is the same as the milling vibration control form-controllable damper design method provided in Example 1. Please refer to the detailed description in Example 1 above, which will not be repeated here.

[0093] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing a shape-controlled damper for milling vibration control, characterized in that, include: Based on the workpiece material removal effect, the workpiece-fixture system is divided into a joint and multiple substructures; According to the milling sequence, multiple substructures are coupled sequentially to obtain the combined structure. The combined structure and the joint are coupled to establish a workpiece frequency response function prediction model and obtain the time-varying dynamic parameters of the workpiece, including natural frequency and mode shape. Based on the deformation energy model of plate-type damping structures and the time-varying dynamic parameters of the workpiece, the number of layers, material, and shape of the damper are determined. The number of layers and materials of the damper are determined based on the deformation energy model of plate-type damping structures, specifically including: Based on the principle of deformation energy, a deformation energy model of a plate-type multilayer damping structure is established, and the influence of material parameters and geometric parameters on the loss factor of the damping structure is analyzed. By introducing various damping materials, single-layer, double-layer, or triple-layer damping structures are designed and fabricated. The modal characteristics of the corresponding damping structures are analyzed, and their damping performance is verified by modal testing. The number of layers and materials of the damping structure are then determined. For the workpiece-fixture system, based on the fact that the contact is flexible, a genetic algorithm is introduced to identify the contact parameters of the joint and obtain the contact parameters of the joint. Based on the contact parameters of the joint, the combined structure and the joint are coupled using the admittance coupling method to establish a workpiece frequency response function prediction model. Through the workpiece frequency response function prediction model, the time-varying dynamic parameters of the workpiece are obtained, and the dynamic parameters of the workpiece under any processing parameters and at any time are predicted. Based on the predicted workpiece dynamic parameters and workpiece mode shapes, the shape of the damper is designed as follows: Based on the deformation energy model of multi-layer damping structures, the influence of the material and geometric parameters of the damper on its performance is analyzed. The shape of the single-layer or multi-layer damper is designed to be regular. On this basis, the changes in the dynamic parameters of the workpiece are considered. That is, as more and more material is removed from the workpiece, the vibration mode of the workpiece is deformed. Based on this trend, the shape of the damper is changed accordingly, making the shape of the damper irregular and stepped, which can suppress the vibration of the workpiece to the greatest extent.

2. The design method for a shape-controlled damper for milling vibration control as described in claim 1, characterized in that, After dividing the workpiece-fixture system, all substructures are coupled using the admittance coupling method.

3. The design method for a shape-controlled damper for milling vibration control as described in claim 2, characterized in that, A prediction model for the frequency response function of the substructure is established and validated.

4. The design method for a shape-controlled damper for milling vibration control as described in claim 1, characterized in that, After determining the shape, number of layers, and material of the damper, the structural shape and parameters of the damper are optimized. The optimization process is based on the damping performance criteria of the damper to determine the shape-controllable damper with optimal parameters.

5. The design method for a shape-controlled damper for milling vibration control as described in claim 1, characterized in that, The obtained damper was tested in conjunction with the workpiece being processed, and the stability region was compared with that without the damper to determine the improvement of stability by the damper.

6. A design system for a form-controlled damper for milling vibration control, characterized in that, include: The structural partitioning module is configured to divide the workpiece-fixture system into joints and multiple substructures based on the workpiece material removal effect. The dynamic parameter acquisition module is configured to: sequentially couple multiple substructures according to the milling sequence to obtain the combined structure, couple the combined structure and the joint, establish a workpiece frequency response function prediction model, and obtain the time-varying dynamic parameters of the workpiece, including natural frequencies and mode shapes; The damper design module is configured to determine the number of layers, material, and shape of the damper based on the deformation energy model of plate-type damped structures and time-varying dynamic parameters. The number of layers and materials of the damper are determined based on the deformation energy model of plate-type damping structures, specifically including: Based on the principle of deformation energy, a deformation energy model of a plate-type multilayer damping structure is established, and the influence of material parameters and geometric parameters on the loss factor of the damping structure is analyzed. By introducing various damping materials, single-layer, double-layer, or triple-layer damping structures are designed and fabricated. The modal characteristics of the corresponding damping structures are analyzed, and their damping performance is verified by modal testing. The number of layers and materials of the damping structure are then determined. For the workpiece-fixture system, based on the fact that the contact is flexible, a genetic algorithm is introduced to identify the contact parameters of the joint and obtain the contact parameters of the joint. Based on the contact parameters of the joint, the combined structure and the joint are coupled using the admittance coupling method to establish a workpiece frequency response function prediction model. Through the workpiece frequency response function prediction model, the time-varying dynamic parameters of the workpiece are obtained, and the dynamic parameters of the workpiece under any processing parameters and at any time are predicted. Based on the predicted workpiece dynamic parameters and workpiece mode shapes, the shape of the damper is designed as follows: Based on the deformation energy model of multi-layer damping structures, the influence of the material and geometric parameters of the damper on its performance is analyzed. The shape of the single-layer or multi-layer damper is designed to be regular. On this basis, the changes in the dynamic parameters of the workpiece are considered. That is, as more and more material is removed from the workpiece, the vibration mode of the workpiece is deformed. Based on this trend, the shape of the damper is changed accordingly, making the shape of the damper irregular and stepped, which can suppress the vibration of the workpiece to the greatest extent.

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