Method, medium and equipment for predicting time-varying dynamic parameters in milling process of thin-walled workpiece

Abstract

The present invention provides a method, medium and equipment for predicting time-varying dynamic parameters in the milling process of a thin-walled workpiece, comprising: establishing a finite element model of the thin-walled workpiece and dividing the grid, dividing the substructure into a finished product area substructure and a material to be removed area substructure, and sorting the substructures according to internal nodes and interface nodes. An improved fixed interface modal synthesis method is used to establish a degree of freedom reduction model for the finished product area substructure. Considering the material removal effect, the degree of freedom reduction model for the material to be removed area substructure is updated in real time. The two substructure reduction models are coupled and connected according to the equilibrium condition of the substructure interface, and the model calculation is performed. Finally, the above steps are iterated according to the tool feed position to update the time-varying dynamic parameters in the milling process of the thin-walled workpiece. The present invention takes into account the influence of the material removal effect of the thin-walled workpiece in actual processing, reduces the calculation time while ensuring its prediction accuracy, and improves the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of thin-wall workpiece milling, and in particular relates to a method, medium and equipment for predicting time-varying dynamic parameters of a thin-wall workpiece milling process taking into account material removal effects. Background Art

[0002] To reduce structural weight while ensuring both structural strength and performance, a large number of thin-walled structural components are widely used in the manufacturing of key aerospace engine components, such as compressor blisks and turbine blades. These components, characterized by thin walls and weak rigidity, are prone to flutter instability during milling, resulting in reduced workpiece machining accuracy and surface quality. Therefore, it is necessary to analyze the stability of thin-walled workpieces during machining. Dynamic parameters are required for stability analysis in thin-walled workpiece machining, and the accuracy and speed of dynamic parameter calculations affect the stability solution. Furthermore, the material removal process in thin-walled workpieces can cause significant changes in their structural parameters, so the influence of factors such as material removal effects and tool feed position on their dynamic parameters must be considered.

[0003] Because the dynamic parameters of thin-walled workpieces are time-varying during machining, experimental methods require multiple machine shutdowns and testing to obtain results, making them costly, inefficient, and limited in scope. Therefore, experimental methods are often used to supplement and verify other methods. Finite element simulation avoids the problem of extensive repetitive experiments. However, the number of nodes in the finite element model affects the calculation speed during thin-walled workpiece dynamic simulation, and computational time increases with the number of nodes. Therefore, it is necessary to reduce the degrees of freedom during the calculation of thin-walled workpiece dynamic parameters to improve computational efficiency. Summary of the Invention

[0004] In view of the deficiencies in the prior art, the present invention provides a method, medium and equipment for predicting time-varying dynamic parameters in a thin-wall workpiece milling process.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting time-varying dynamic parameters during milling of a thin-walled workpiece, characterized by comprising:

[0007] Establish finite element model of thin-walled workpiece and divide the mesh;

[0008] The finite element model of the thin-walled workpiece is divided into substructures to form a finished product area substructure α and a material removal area substructure β, and the two substructures are sorted according to internal nodes and interface nodes;

[0009] The fixed interface modal synthesis method is used to establish the degree of freedom reduction model of the finished product area substructure α;

[0010] Considering the material removal effect, the structural dynamic modification theory is used to update the degree of freedom reduction model of the substructure β in the area where the material is to be removed in real time;

[0011] The freedom reduction models of the two substructures are coupled according to the equilibrium conditions of the substructure interface, and the dynamic parameters of the thin-walled workpiece after freedom reduction are calculated accordingly.

[0012] Update the time-varying dynamic parameters during the milling of thin-walled workpieces according to the tool feed position.

[0013] To optimize the above technical solutions, specific measures taken also include:

[0014] Furthermore, the two substructures are sorted according to internal nodes and interface nodes, specifically:

[0015] The stiffness matrix and mass matrix of the finished product area substructure α and the material to be removed area substructure β are arranged in the order of internal nodes and interface nodes.

[0016] Furthermore, the fixed interface modal synthesis method is used to establish a degree of freedom reduction model of the finished product area substructure α, specifically:

[0017] Based on the fixed interface modal synthesis method, the degrees of freedom of the interface nodes are reduced to form the coordinate transformation matrix T α，1 :

[0018]

[0019] Where, Φ α，ir is the retained modal matrix of substructure α, r represents the order of the retained modal matrix; K α，ii is the stiffness matrix of the internal nodes of substructure α, K a，ib is the stiffness matrix of the interface node between substructure α and another substructure, i and b represent the internal degree of freedom and interface degree of freedom of the substructure respectively; Φ α，b is the retained modal matrix of the reduced degree of freedom of the substructure α interface node;

[0020] Through the coordinate transformation matrix T α，l Generate the dynamic equation after the substructure α degree of freedom is reduced:

[0021]

[0022] Where, and are the mass matrix and stiffness matrix of the substructure α after reduction; P a(t) is the displacement vector of substructure α, which is composed of the displacement vectors of the substructure internal nodes and interface nodes; is the force vector of substructure α, which is composed of the force vectors of internal nodes and interface nodes; M α and K α are the mass matrix and stiffness matrix of the substructure α before reduction; the generated dynamic equation is the degree of freedom reduction model of the substructure α in the finished product area.

[0023] Furthermore, the material removal effect is considered and the structural dynamic modification theory is used to update the degree of freedom reduction model of the substructure β in the area to be removed in real time, specifically:

[0024] Determine the stiffness matrix ΔK of the removed material using structural dynamic modification technology β，l and mass matrix ΔM β，l , expressed as:

[0025]

[0026] Where K β，l and M β，l are the unit stiffness matrix and mass matrix of substructure β respectively; l is the feed position of the tool when the thin-wall workpiece material is removed; ΔV e and V e are the material removal volume and element volume, respectively;

[0027] Considering the material removal effect, the degree of freedom reduction model of the substructure β updated in real time is:

[0028]

[0029] Where, and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position; (l) M β and (l) K β are the mass matrix and stiffness matrix of the substructure β model at the lth tool feed position before reduction; (l) T β，1 is the coordinate transformation matrix of substructure β, (l) Φ β，ir is the r-order retained modal matrix of the substructure β at the l-th tool feed position, (l) K β，i i is the internal node stiffness matrix of substructure β at the lth tool feed position, (l) K β，ib is the stiffness matrix of the substructure β interface node at the lth tool feed position,(l) Φ β，b is the retained modal matrix of the reduced degree of freedom of the substructure β interface node at the lth tool feed position; P β (t) is the displacement vector of the substructure β at the lth tool feed position, which is composed of the displacement vectors of the internal nodes and the interface nodes; is the force vector of the substructure β at the lth tool feed position, which is composed of the force vectors of the internal nodes and the interface nodes.

[0030] Furthermore, the degree of freedom reduction models of the two substructures are coupled and connected according to the equilibrium condition of the substructure interface, and the dynamic parameters of the thin-walled workpiece after the degree of freedom reduction are calculated accordingly, specifically:

[0031] The coordinate transformation matrix T2 of the coupled connection is:

[0032]

[0033] Where I is the unit matrix, and its matrix dimension is related to the internal retained mode order and the interface retained mode order;

[0034] The dynamic equation of the thin-walled workpiece after the degree of freedom is reduced is:

[0035]

[0036] Where, P(t)=[P α，i (l) P β，i (l) P β，b ] T ; and are the mass matrix and stiffness matrix of the thin-walled workpiece model after reduction at the l-th tool feed position, respectively. P(t) is the displacement vector of the thin-walled workpiece model after reduction, which is composed of the displacement vectors of substructure α and substructure β. is the force vector after the thin-walled workpiece model is reduced; and are the mass matrix and stiffness matrix of the substructure α after reduction, and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position.

[0037] Furthermore, the time-varying dynamic parameters in the thin-walled workpiece milling process are updated according to the tool feed position, specifically:

[0038] After the calculation of the dynamic parameters of the thin-walled workpiece at the current tool feed position is completed, the tool feed position changes from , to l+1, and then the updated degree of freedom reduction model of the substructure β is calculated, and then coupled with the degree of freedom reduction model of the substructure α to form a new degree of freedom reduction model until the set tool feed position is traversed. The calculation is completed and the prediction of the time-varying dynamic parameters of the thin-walled workpiece during milling is completed.

[0039] Accordingly, the present invention proposes a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the method for predicting time-varying dynamic parameters in a thin-walled workpiece milling process as described above.

[0040] Accordingly, the present invention proposes an electronic device, characterized in that it includes: a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, it implements the method for predicting time-varying dynamic parameters of the thin-walled workpiece milling process as described above.

[0041] The beneficial effects of the present invention are as follows: the present invention combines the actual processing conditions, takes into account the influence of the material removal effect during the processing, and the predicted dynamic parameters are more accurate. The existing fixed interface modal synthesis method can reduce the degrees of freedom of the finite element model of thin-walled workpieces, but its number of degrees of freedom is related to the number of degrees of freedom of the interface nodes. If the number of degrees of freedom of the interface is too large, it will lead to an increase in calculation time. Therefore, on the basis of the existing method, the present invention further reduces the degrees of freedom of the interface nodes to form an improved fixed interface modal synthesis method, which has the advantages of a simple model, easy programming, and short time consumption while ensuring the accuracy of dynamic parameter prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The present invention provides a flow chart of a method for predicting time-varying dynamic parameters in a thin-wall workpiece milling process.

[0043] Figure 2 Schematic diagram of the substructure division of the thin-walled workpiece provided by the present invention.

[0044] Figure 3 This is a schematic diagram of the tool feed position division when removing thin-walled workpiece material provided by the present invention.

[0045] Figure 4 This is a comparison chart of the calculation time of the original model and the reduced model of the thin-walled workpiece provided by the present invention.

[0046] Figure 5 This is the natural frequency prediction error diagram of the thin-walled workpiece reduction model provided by the present invention.

[0047] Figure 6The present invention provides a prediction diagram of time-varying dynamic parameters of thin-walled workpieces when considering the material removal effect. DETAILED DESCRIPTION

[0048] The following will be combined with the accompanying drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0049] In one embodiment, if Figure 1 As shown, the present invention provides a method for predicting time-varying dynamic parameters in a thin-walled workpiece milling process, which specifically includes the following steps:

[0050] Step 1: Mesh the thin-walled workpiece geometry to generate a finite element model. Mesh the thin-walled workpiece in finite element simulation software, and use its secondary development capabilities to derive the model's stiffness and mass matrices.

[0051] Step 2: Decompose the thin-walled workpiece into two substructures: the finished product area substructure α and the material to be removed area substructure β, as shown in Figure 2 As shown in the figure, the boundary nodes and internal nodes of the substructure are defined, and the nodes of the two substructures are reordered according to the internal nodes and interface nodes to form their stiffness matrix and mass matrix.

[0052] Step 3: Generate a reduced finite element model of substructure α using the improved fixed interface modal synthesis method. Since substructure α is a thin-walled workpiece finished area and does not involve material removal, only one model reduction is required.

[0053] Without considering the damping effect, the dynamic equation of substructure α can be expressed as:

[0054]

[0055] Where M α , K α are the mass matrix and stiffness matrix of the substructure α model before reduction; K α (t) and F α (t) are the displacement vector and force vector of the substructure respectively.

[0056] In order to improve the calculation speed, based on the fixed interface modal synthesis method, the degrees of freedom of the interface nodes are reduced to form the first coordinate transformation matrix T α，1 , expressed as:

[0057]

[0058] Where, Φ α，ir is the retained modal matrix of substructure α, r represents the order of the retained modal matrix; K α，ii is the stiffness matrix of the internal nodes of substructure α, K α，ib is the stiffness matrix of the interface nodes between substructure α and another substructure, where i and b represent the internal degrees of freedom and interface degrees of freedom of the substructure, respectively; Φ α，b is the retained modal matrix of the reduced degree of freedom of the substructure α interface node.

[0059] Through the coordinate transformation matrix T α，1 Generate the dynamic equation after the substructure α degree of freedom is reduced:

[0060]

[0061] Where, and are the mass matrix and stiffness matrix of the substructure α after reduction; P a (t) is the displacement vector of substructure α, which is composed of the displacement vectors of the substructure internal nodes and interface nodes; is the force vector of substructure α, which is composed of the force vectors of internal nodes and interface nodes, where the force vector of internal nodes is zero; M a and K α are the mass matrix and stiffness matrix of the substructure before α reduction, respectively.

[0062] Step 4: Considering the material removal effect, update the reduced model of the substructure β in the area where the material is to be removed in real time. As the material in the substructure area is continuously removed as the processing progresses, its mass and stiffness change, which in turn causes the modal parameters to change. First, according to the stiffness matrix K of the initial substructure β0 β0 and the mass matrix M β0 Perform modal analysis to obtain its modal frequency ω β0 and the modal matrix x β0 The milling path is then discretized and divided into a number of tool positions. Assuming that the number of tool feed positions is l, when the tool position changes, the thin-walled workpiece material is removed. The structural dynamic modification technology is used to determine the stiffness matrix and mass matrix of the removed material:

[0063]

[0064] Where K β，l and M β，l are the unit stiffness matrix and mass matrix of substructure β respectively; l is the feed position of the tool when the thin-wall workpiece material is removed; AV e and V eare the material removal volume and element volume, respectively.

[0065] When the material removal effect is considered, the dynamic equation of the substructure β at the lth tool feed position can be expressed as:

[0066]

[0067] in, (l) M β = (0) M β +ΔM β，l , (l) K β = (0) K β +ΔK β，l ; (l) M β 、 (l) K β are the mass matrix and stiffness matrix of the substructure β model at the lth tool feed position before reduction; X β (t) and (l) F β (t) are the displacement vector and force vector of the substructure respectively.

[0068] Similar to the reduction process of substructure α, the reduction model of substructure β considering the material removal effect can be expressed as:

[0069]

[0070] Where, P β (t)=[ (l) P β，i (l) P β，b ] T , and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position; (l) M β and (l) K β are the mass matrix and stiffness matrix of the substructure β model at the lth tool feed position before reduction; (l) T β，1 is the coordinate transformation matrix of substructure β, which is similar to the coordinate transformation matrix of substructure α and plays the role of reducing the degree of freedom of the model; (l) Φ β，ir is the r-order retained modal matrix of the substructure β at the l-th tool feed position, (l) K β，iiis the internal node stiffness matrix of substructure β at the lth tool feed position, (l) K β，ib is the stiffness matrix of the substructure β interface node at the lth tool feed position, (l) Φ β，b is the retained modal matrix of the reduced degree of freedom of the substructure β interface node at the lth tool feed position; P β (t) is the displacement vector of the substructure β at the lth tool feed position, which is composed of the displacement vectors of the internal nodes and the interface nodes; is the force vector of the substructure β at the lth tool feed position, which is composed of the force vectors of the internal nodes and the interface nodes, where the internal node force vector is zero.

[0071] Step 5: Figure 2 It can be seen that substructure α and substructure β are connected by an interface, and the force and displacement equilibrium conditions on the interface are consistent. Therefore, based on the interface equilibrium conditions, the two substructure reduced models can be coupled and connected through the coordinate transformation matrix to form a complete thin-walled workpiece degree of freedom reduction model. The second coordinate transformation matrix is ​​expressed as follows:

[0072]

[0073] Where I is the unit matrix, and its matrix dimension is related to the retained modal order and the retained modal order of the interface.

[0074] The dynamic model of the thin-walled workpiece with reduced degrees of freedom is formed by coupling through the T2 coordinate transformation matrix. When the tool is in the first feed position, the dynamic equation of the thin-walled workpiece can be expressed as:

[0075]

[0076] Where, P(t)=[P a，i (l) P β，i (l) P β，b ] T ; and are the mass matrix and stiffness matrix of the thin-walled workpiece model after reduction at the l-th tool feed position, respectively. P(t) is the displacement vector of the thin-walled workpiece model after reduction, which is composed of the displacement vectors of substructure α and substructure β. is the force vector after the thin-walled workpiece model is reduced; and are the mass matrix and stiffness matrix of the substructure α after reduction, and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position.

[0077] Step 6: Solve the dynamic parameters of the thin-walled workpiece according to the reduced dynamic equations to obtain its modal frequency and modal matrix, which will then be used for subsequent flutter stability analysis.

[0078] Step 7: After the calculation of the dynamic parameters of the thin-walled workpiece at the current tool feed position is completed, the tool feed position changes from l to l+1, and jumps to step 4 to continue calculating the reduced model of substructure β, and then couples it with substructure α to form a new reduced model until the set tool feed position is traversed and the calculation ends.

[0079] To illustrate the prediction process of time-varying dynamic parameters during the milling of thin-walled workpieces with material removal effects, a cantilever plate structure is used as an example to analyze the time-varying dynamic parameters with material removal effects. The selected thin-walled workpiece has dimensions of 80 mm × 60 mm × 5 mm, with a fixture clamping length of 10 mm. The thin-walled workpiece is made of aluminum alloy with a Young's modulus of E = 70 GPa and a density of ρ = 2820 kg / m 3 , Poisson's ratio is 0.32. During the milling process, 2.5 mm of material is removed along the thickness direction of the workpiece.

[0080] First, a finite element simulation model of a thin-walled workpiece is established and meshed. The number of degrees of freedom of this model is 12,300, and there is no degree of freedom interface. The time for calculating the dynamic parameters using this model is 273.3 seconds. Then, the thin-walled workpiece is divided into the finished product area substructure α and the material to be removed area (thickness 2.5mm) substructure β. The improved fixed interface modal synthesis method is used to reduce the model of the finished product area substructure α. The material to be removed area is divided into 4 milling cutter feed positions, such as Figure 3 As shown in Figure 1, considering the influence of material removal effect on the thin-wall workpiece structure, a reduction model of the substructure β in the material processing area is established, and then the two substructures are coupled to solve their dynamic parameters. The calculation results are shown in Figure 1. Figure 4As shown in the figure, the model solution time is related to the number of degrees of freedom retained during model reduction. A larger number of degrees of freedom is retained, resulting in increased computational time and correspondingly improved accuracy. However, for thin-walled workpieces used in milling, low-order modes often affect machining stability. Therefore, during the dynamic parameter calculation, only the first few modes are retained, ensuring accuracy while also improving computational efficiency. When the fixed interface modal synthesis method is used to reduce the model's degrees of freedom while retaining 10 main modes, the number of degrees of freedom for the thin-walled workpiece becomes 3085, with 3075 at the interface. The computational time is reduced to 52.8 seconds, a significant reduction in computational time. However, since the reduction in degrees of freedom using the fixed interface modal synthesis method is related to the number of degrees of freedom at the interface nodes, a larger number of degrees of freedom at the interface nodes increases computational time. Therefore, based on the fixed interface method, the number of degrees of freedom at the interface nodes is reduced to improve computational efficiency. When the number of degrees of freedom of the interface is reduced from 3075 to 1500, the total number of degrees of freedom of the model becomes 1510, and the calculation time is reduced from 52.8s to 30.7s.

[0081] Then the accuracy of the calculation results of the reduced degree of freedom model is analyzed. Assuming that the calculation results of the full model are the exact solution, when the improved fixed interface modal synthesis method is used for solution, the calculation results of the two are relatively consistent, and the calculation error is less than 2.7%. Figure 5 As shown. Therefore, this method can be used to reduce the calculation time while maintaining the calculation accuracy. Furthermore, this method is used to calculate the time-varying dynamic parameters of thin-walled workpieces considering the material removal process, as shown in Figure 6 As shown in the figure, it can be seen that as the tool feed position changes, the first four modal frequencies of the thin-walled workpiece change accordingly. Therefore, the time-varying dynamic parameters of the thin-walled workpiece must be considered in the subsequent stability calculation process.

[0082] In another embodiment, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the method for predicting time-varying dynamic parameters in a thin-walled workpiece milling process as described in the first embodiment.

[0083] In another embodiment, the present invention proposes an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for predicting time-varying dynamic parameters of a thin-walled workpiece milling process as described in Example 1 is implemented.

[0084] In the embodiments disclosed herein, computer storage media can be tangible media that can contain or store programs for use by or in conjunction with an instruction execution system, device, or apparatus. Computer storage media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROMs), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0085] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0086] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting time-varying dynamic parameters in the milling process of thin-walled workpieces, characterized in that: include: Establish finite element model of thin-walled workpiece and divide the mesh; The finite element model of the thin-walled workpiece is divided into substructures to form a finished product area substructure α and a material removal area substructure β, and the two substructures are sorted according to internal nodes and interface nodes; The fixed interface modal synthesis method is used to establish the degree of freedom reduction model of the finished product area substructure α; specifically: Based on the fixed interface modal synthesis method, the degrees of freedom of the interface nodes are reduced to form the coordinate transformation matrix T α,1 : Where, Φ α,ir is the retained modal matrix of substructure α, r represents the order of the retained modal matrix; K α,ii is the stiffness matrix of the internal nodes of substructure α, K α,ib is the stiffness matrix of the interface node between substructure α and another substructure, i and b represent the internal degree of freedom and interface degree of freedom of the substructure respectively; Φ α,b is the retained modal matrix of the reduced degree of freedom of the substructure α interface node; Through the coordinate transformation matrix T α,1 Generate the dynamic equation after the substructure α degree of freedom is reduced: Where, P α (t)=[P α,i P α,b ] T , and are the mass matrix and stiffness matrix of the substructure α after reduction; P α (t) is the displacement vector of substructure α, which is composed of the displacement vectors of the substructure internal nodes and interface nodes; is the force vector of substructure α, which is composed of the force vectors of internal nodes and interface nodes; M α and K α are the mass matrix and stiffness matrix of the substructure α before reduction respectively; the generated dynamic equation is the degree of freedom reduction model of the substructure α in the finished product area; Considering the material removal effect, the structural dynamic modification theory is used to update the degree of freedom reduction model of the substructure β in the area where the material is to be removed in real time; specifically: Determine the stiffness matrix ΔK of the removed material using structural dynamic modification technology β,l and mass matrix ΔM β,l , expressed as: Where K β,l and M β,l are the unit stiffness matrix and mass matrix of substructure β respectively; l is the feed position of the tool when the thin-wall workpiece material is removed; ΔV e and V e are the material removal volume and element volume, respectively; Considering the material removal effect, the degree of freedom reduction model of the substructure β updated in real time is: Where, P β (t)=[ (l) P β,i (l) P β,b ] T , and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position; (l) M β and (l) K β are the mass matrix and stiffness matrix of the substructure β model at the lth tool feed position before reduction; (l) T β,1 is the coordinate transformation matrix of substructure β, (l) Φ β,ir is the r-order retained modal matrix of the substructure β at the l-th tool feed position, (l) K β,ii is the internal node stiffness matrix of substructure β at the lth tool feed position, (l) K β,ib is the stiffness matrix of the substructure β interface node at the lth tool feed position, (l) Φ β,b is the retained modal matrix of the reduced degree of freedom of the substructure β interface node at the lth tool feed position; P β (t) is the displacement vector of the substructure β at the lth tool feed position, which is composed of the displacement vectors of the internal nodes and the interface nodes; is the force vector of the substructure β at the lth tool feed position, which is composed of the force vectors of the internal nodes and the interface nodes; The freedom reduction models of the two substructures are coupled according to the equilibrium conditions of the substructure interface, and the dynamic parameters of the thin-walled workpiece after freedom reduction are calculated accordingly. Update the time-varying dynamic parameters during the milling of thin-walled workpieces according to the tool feed position.

2. The method for predicting time-varying dynamic parameters during milling of a thin-walled workpiece according to claim 1, characterized in that: The two substructures are sorted according to internal nodes and interface nodes, specifically: The stiffness matrix and mass matrix of the finished product area substructure α and the material to be removed area substructure β are arranged in the order of internal nodes and interface nodes.

3. The method for predicting time-varying dynamic parameters during milling of a thin-walled workpiece according to claim 1, wherein: The degree of freedom reduction models of the two substructures are coupled and connected according to the equilibrium condition of the substructure interface, and the dynamic parameters of the thin-walled workpiece after the degree of freedom reduction are calculated accordingly, specifically: The coordinate transformation matrix T2 of the coupled connection is: Where I is the unit matrix, and its matrix dimension is related to the internal retained mode order and the interface retained mode order; The dynamic equation of the thin-walled workpiece after the degree of freedom is reduced is: Where, P(t)=[P α,i (l) P β,i (l) P β,b ] T ; and are the mass matrix and stiffness matrix of the thin-walled workpiece model after reduction at the l-th tool feed position, respectively. P(t) is the displacement vector of the thin-walled workpiece model after reduction, which is composed of the displacement vectors of substructure α and substructure β. is the force vector after the thin-walled workpiece model is reduced; and are the mass matrix and stiffness matrix of the substructure α after reduction, and are the mass matrix and stiffness matrix of the substructure β after reduction at the lth tool feed position.

4. The method for predicting time-varying dynamic parameters during milling of a thin-walled workpiece according to claim 1, wherein: The time-varying dynamic parameters of the thin-walled workpiece milling process are updated according to the tool feed position, specifically: After the calculation of the dynamic parameters of the thin-walled workpiece at the current tool feed position is completed, the tool feed position changes from l to l+1, and then the updated degree of freedom reduction model of the substructure β is calculated, and then coupled with the degree of freedom reduction model of the substructure α to form a new degree of freedom reduction model until the set tool feed position is traversed. The calculation is completed and the prediction of the time-varying dynamic parameters of the thin-walled workpiece during milling is completed.

5. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables a computer to execute the method for predicting time-varying dynamic parameters in a thin-walled workpiece milling process according to any one of claims 1 to 4.

6. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for predicting time-varying dynamic parameters in a thin-walled workpiece milling process as described in any one of claims 1 to 4 is implemented.

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