A time-varying chatter prediction method in thin-walled part milling process
By dividing thin-walled parts into eight-node hexahedrons and calculating the time-varying stiffness matrix and cutting force model, the problem of prediction efficiency and accuracy of time-varying chatter during the milling process of thin-walled parts is solved, and efficient machining stability prediction and parameter selection are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA WEAPON SCI ACADEMY NINGBO BRANCH
- Filing Date
- 2026-03-25
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies struggle to efficiently and accurately predict time-varying chatter during the milling of thin-walled parts, leading to mismatched process parameters that affect part surface quality and service life.
The thin-walled part is divided into multiple eight-node hexahedrons with the same length, width and height. The stiffness matrix of each element is obtained, and the time-varying deformation is calculated by the corrected time-varying stiffness matrix and the cutting force model to predict time-varying chatter.
It improves the efficiency and accuracy of predicting the machining stability of thin-walled parts and provides a scientific parameter selection scheme to avoid chatter.
Smart Images
Figure CN122165241A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of chatter prediction technology, and in particular to a time-varying chatter prediction method in the milling process of thin-walled parts. Background Technology
[0002] While a database of machining processes for aerospace aluminum alloys has been established in the field of CNC milling, traditional mathematical models struggle to accurately predict time-varying deformation and chatter stability during the cutting process, especially for parts with unique thin-walled structures. This leads to mismatched process parameters. Milling chatter induced by the mismatch between spindle speed and depth of cut parameters causes periodic chatter marks and microcracks on the part surface. This severely impacts the performance and service life of aerospace products.
[0003] In recent years, to accurately characterize the dynamic characteristics of the milling process, researchers have conducted multi-field coupled dynamics studies on the tool-work system. Correspondingly, these influencing factors of the machining process have also been considered in chatter prediction models. Researchers have gradually established dynamic models of tool-work coupling. Currently, researchers mainly rely on this dynamic model to solve chatter in milling. In establishing chatter models for thin-walled parts, it is necessary to simultaneously consider time-varying machining positions, time-varying dynamic characteristics caused by part material removal, and part deformation. This can improve the accuracy of chatter prediction for thin-walled parts.
[0004] For example, the existing literature "Chatter prediction for the peripheral milling of thin-walled workpieces with curved surfaces" studies the influence of different workpiece dynamics on the stability of peripheral milling of thin-walled curved workpieces. It proposes a new dynamic model of the tool and workpiece system, considering the dynamic behavior of the tool and workpiece, as well as the influence of meshing and tool feed direction. However, this method uses the commercial finite element software ABAQUS to mesh the initial workpiece and generate mass and stiffness matrices. This process relies on the efficiency of the finite element software and Matlab's call to the finite element software, which reduces the efficiency of chatter prediction.
[0005] Building upon the aforementioned literature, the paper "Chatter prediction in flank milling of thin-walled parts considering force-induced deformation" systematically studies force-induced deformation and chatter. Based on a deep understanding of the cutting process, it proposes a prediction model consistent with the actual cutting process. Although this model constructs an assembly method for the stiffness matrix, it still uses commercial software for acquiring finite element information of thin-walled parts. This process increases the number of calls to the time-varying model of thin-walled parts, reducing prediction efficiency.
[0006] Existing methods rarely consider the effects of machining deformation and material removal simultaneously when predicting chatter in thin-walled parts. Some methods require the use of finite element method (FEM) software to generate element node information for the thin-walled part or even to perform time-varying deformation calculations, which reduces the efficiency of chatter prediction for thin-walled parts. Therefore, further improvements to existing technologies are needed. Summary of the Invention
[0007] The technical problem to be solved by the present invention is to provide a time-varying chatter prediction method in the milling process of thin-walled parts that can improve prediction efficiency and accuracy, in contrast to the above-mentioned prior art.
[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a time-varying chatter prediction method in the milling process of thin-walled parts, characterized by including the following steps:
[0009] Step 1: At the initial moment, the unmilled thin-walled part is divided into multiple units, each of which is an eight-node hexahedron with the same length, width and height.
[0010] Step 2: At time t, obtain the element node information of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Based on the element node information of each element and the unit stiffness matrix of the eight-node hexahedron, obtain the stiffness matrix of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Finally, assemble the stiffness matrices of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part to obtain the time-varying stiffness matrix of the thin-walled part.
[0011] Step 3: Correct the time-varying stiffness matrix of the thin-walled part to obtain the corrected time-varying stiffness matrix;
[0012] Step 4: Construct a cutting force model during the milling process of thin-walled parts;
[0013] Step 5: Based on the cutting force model constructed in Step 4 and the corrected time-varying stiffness matrix in Step 3, calculate the time-varying deformation of the thin-walled part.
[0014] Step 6: Predict the time-varying chatter of the thin-walled part based on the time-varying deformation of the thin-walled part in Step 5.
[0015] Preferably, in step 3, the time-varying stiffness matrix of the thin-walled part is corrected according to the following formula to obtain the corrected time-varying stiffness matrix. , The calculation formula is:
[0016] in, , and Let represent the stiffness matrices of the cut part, the part to be cut, and the target machined part at time t, respectively, in the global coordinate system. The global coordinate system is a three-dimensional coordinate system with a vertex on the thin-walled part as the origin. , and These represent the stiffness matrices of the cut portion, the portion to be cut, and the target machined part, respectively. This represents the stiffness matrix of the elements containing common nodes between the cut and the part to be cut of a thin-walled part. The stiffness matrix represents the element containing the common nodes of the cut portion and the target machined part of the thin-walled part; This represents the stiffness matrix of the elements containing common nodes between the cut portion and the cut portion of a thin-walled part. This represents the stiffness matrix of the elements containing common nodes between the cut portion of the thin-walled part and the target machined part. This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part to be cut; This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part being cut; It is a constant, and its value is infinitely close to 0; It is a very small value.
[0017] Preferably, the calculation formula for the cutting force model constructed in step 4 is:
[0018] =
[0019] in, Let be the cutting force of the tool in the radial direction at time t. and The milling cutter is in the first position. The first tooth, the first The tangential cutting element force and radial cutting element force at time t on each cutting element. Let be the position angle of the milling cutter at time t.
[0020] Preferably, the thin-walled part is cut at a height of Actual cutting thickness for:
[0021]
[0022] in, The nominal radial cutting thickness of the cutting tool. The height of the tool along the cutting axis Deformation value at that location, , Indicates axial depth of cut. At that time, altitude The cutting force at the micro-element of the cutting process. For the overhang of the tool, The elastic modulus of the cutting tool; Let be the moment of inertia of the tool's cross section; For thin-walled parts, the height in the cutting axial direction The deformation value at point t; the deformation value of the thin-walled part at time t is: ,Should Obtained from the deformation value of the thin-walled part at time t.
[0023] Preferably, the specific process for predicting the time-varying chatter of thin-walled parts in step 6 is as follows:
[0024] Calculate the transition matrix within a cutting cycle. Determine the transition matrix If the magnitudes of all eigenvalues are less than 1, then chatter is not occurring in the current cut; otherwise, chatter is occurring in the current cut.
[0025] Transition matrix The calculation formula is:
[0026]
[0027] in, , , and The first The, the The first, ..., the 1st and 0th discrete mapping matrices; Discrete mapping matrices The calculation formula is:
[0028] This is the cutting force matrix at the instant the cutting begins. The cutting force at the endpoint of the first walk [0, Δt] is... For a single increment of walking time, , is the tooth cycle, and m is the number of discrete intervals; For a moment The instantaneous cutting force is also the kth step away from the […]. , The final cutting force; k=0,1,...,m-1, For a moment The instantaneous cutting force is also the m-2th departure point [ The final cutting force; This represents the cutting force at the end of the cutter tooth cycle, corresponding to the moment at the end of the cutter tooth cycle. The instantaneous cutting force, which is also the last thing to leave the walk [ -1, The final cutting force; ; It is an identity matrix.
[0029] Compared with existing technologies, the advantages of this invention are as follows: By dividing the unmilled thin-walled part into multiple eight-node hexahedrons with the same length, width, and height, and during the milling process of the thin-walled part, the stiffness matrix of each unit in the cut part, the part to be cut, and the target machined part of the thin-walled part is obtained, thus achieving efficient and high-precision calculation of time-varying deformation characteristics; in addition, the time-varying deformation of the thin-walled part is calculated using a cutting force model and a corrected time-varying stiffness matrix, thus considering the deformation of both the tool and the part when calculating the time-varying deformation. Therefore, this method can significantly improve the efficiency and accuracy of predicting the machining stability of thin-walled parts and provide a scientific parameter selection scheme for avoiding machining chatter. Attached Figure Description
[0030] Figure 1 This is a flowchart of the time-varying flutter prediction method in an embodiment of the present invention; Detailed Implementation
[0031] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.
[0032] like Figure 1 As shown, the time-varying chatter prediction method in the milling process of thin-walled parts in this embodiment includes the following steps:
[0033] Step 1: At the initial moment, the unmilled thin-walled part is divided into multiple units, each of which is an eight-node hexahedron with the same length, width and height.
[0034] Step 2: At time t, obtain the element node information of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Based on the element node information of each element and the unit stiffness matrix of the eight-node hexahedron, obtain the stiffness matrix of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Finally, assemble the stiffness matrices of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part to obtain the time-varying stiffness matrix of the thin-walled part.
[0035] The unit stiffness matrix of the aforementioned eight-node hexahedron is a core component in finite element analysis. It is an existing technology, and the specific process of assembling the stiffness matrix is also an existing technology, so it will not be elaborated here.
[0036] Step 3: Correct the time-varying stiffness matrix of the thin-walled part to obtain the corrected time-varying stiffness matrix;
[0037] A time-varying stiffness matrix for a thin-walled part is constructed and constraints are applied to obtain time-varying machining deformation values. However, this process becomes more complex as machining progresses, and the part stiffness matrix changes at different machining locations. Therefore, in this embodiment, the time-varying stiffness matrix of the thin-walled part is corrected according to the following formula to obtain the corrected time-varying stiffness matrix. , The calculation formula is:
[0038] in, , and Let represent the stiffness matrices of the cut part, the part to be cut, and the target machined part at time t, respectively, in the global coordinate system. The global coordinate system is a three-dimensional coordinate system with a vertex on the thin-walled part as the origin. , and These represent the stiffness matrices of the cut portion, the portion to be cut, and the target machined part, respectively. This represents the stiffness matrix of the elements containing common nodes between the cut and the part to be cut of a thin-walled part. The stiffness matrix represents the element containing the common nodes of the cut portion and the target machined part of the thin-walled part; This represents the stiffness matrix of the elements containing common nodes between the cut portion and the cut portion of a thin-walled part. This represents the stiffness matrix of the elements containing common nodes between the cut portion of the thin-walled part and the target machined part. This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part to be cut; This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part being cut; It is a constant, and its value is infinitely close to 0, which can prevent singularities in matrix calculations; The value is a minimum, which means that the stiffness of the part to be cut is minimized. Thus, in this embodiment, the time-varying stiffness matrix of the thin-walled part can be calculated without re-meshing.
[0039] Step 4: Construct a cutting force model during the milling process of thin-walled parts;
[0040] A part coordinate system fixed to the bottom surface of a thin-walled part, which is used to describe the position of the tool in three-dimensional space; A workpiece coordinate system fixed on the bottom surface of the tool is used to describe the cutting edge positions of the discrete cutting micro-layers along each axis and the cutting edge forces at each cutting moment. During the cutting process, the tool is discretized into a large number of cutting micro-layers along the axial direction. Each cutting micro-layer is subjected to cutting radial and axial micro-forces when cutting a thin-walled part. The cutting micro-forces of the tool can be expressed as:
[0041]
[0042] in, , and The milling cutter is in the first position. The first tooth, the first On each cutting element The tangential force, radial force, and axial cutting element force at any given moment; It is the position angle of the milling cutter; It is a unit step function used to indicate whether the current cutting edge element participates in cutting, and it is defined as:
[0043]
[0044] and These represent the entry angle and exit angle of the milling cutter on the i-th tooth and j-th cutting micro-element, respectively; , and These are the polynomial coefficients for tangential force, radial force, and axial force, respectively. The position angle is The instantaneous undeformed chip thickness at time t; dz is the thickness of each axial discrete cutting element;
[0045] After obtaining the cutting force on the discrete micro-element cutting edge of the tool in each axis, projecting the micro-element cutting forces of all cutting micro-element layers onto the tool coordinate system yields the forces acting on the tool in each direction during the milling process. Therefore, the component forces acting on the tool coordinate system in each direction at time t can be expressed as:
[0046]
[0047] in, , and These represent the cutting forces of the tool in the x, y, and z directions of the tool coordinate system, respectively; N represents the number of teeth of the tool; and M represents the number of discrete micro-element cutting force layers along the axial direction of the tool.
[0048] When calculating the time-varying deformation of thin-walled parts, the interaction force between the tool and the thin-walled part is mainly the radial cutting force perpendicular to the part surface. Specifically, in the coordinate system established in this paper, the force on the thin-walled part is mainly the force on the tool in the y-direction. Compared to the force exerted on the tool in the y-direction, the force in the x-direction mainly acts on the tangential direction of the thin-walled part; therefore, in this invention, the stiffness of the thin-walled part in the x-direction (i.e., tangential) is much greater than its stiffness in the y-direction (i.e., radial); therefore, during the force application process of the thin-walled part, the selected force is... ;
[0049] That is: the calculation formula for the cutting force model constructed in step 4 is:
[0050] =
[0051] in, This represents the cutting force of the tool in the radial direction. and The milling cutter is in the first position. The first tooth, the first The tangential cutting element force and radial cutting element force at time t on each cutting element. This refers to the position angle of the milling cutter;
[0052] Step 5: Based on the cutting force model constructed in Step 4 and the corrected time-varying stiffness matrix in Step 3, calculate the time-varying deformation of the thin-walled part.
[0053] Select axial cutting height as The cutting micro-elements at the location are analyzed. and These represent the tool center when the tool is deformed and when it is not deformed, respectively. and The angle of entry when the tool is deformed and when it is not deformed. Indicates the cutting angle of the tool. and These represent the cutting axial height. The deformation values of the parts and tools at that location. and These represent the nominal radial cutting thickness and the actual radial cutting thickness of the tool, respectively. Tool deformation can be calculated using the following formula:
[0054]
[0055] in, Indicates the tool at height Deformation value at; Indicates axial depth of cut. hour, The cutting force of a highly ductile micro-element; Indicates the overhang of the tool. The elastic modulus of the cutting tool; Let be the moment of inertia of the tool's cross section;
[0056] Then we can get Highly realistic cutting thickness for:
[0057]
[0058] in, The nominal radial cutting thickness of the cutting tool. The height of the tool along the cutting axis Deformation value at that location, For thin-walled parts, the height in the cutting axial direction The deformation value at point t; the deformation value of the thin-walled part at time t is: ,Should Obtained from the deformation value of the thin-walled part at time t; It is to obtain the cutting axial height of the thin-walled part during the machining process at time t. Deformation value at;
[0059] Step 6: Predict the time-varying chatter of the thin-walled part based on the time-varying deformation of the thin-walled part in Step 5.
[0060] The specific process for predicting time-varying chatter of thin-walled parts in this embodiment is as follows:
[0061] Calculate the transition matrix within a cutting cycle. Determine the transition matrix If the magnitudes of all eigenvalues are less than 1, then chatter is not occurring in the current cut; otherwise, chatter is occurring in the current cut.
[0062] Transition matrix The calculation formula is:
[0063]
[0064] in, , , and The first The, the The first, ..., the 1st and 0th discrete mapping matrices; Discrete mapping matrices The calculation formula is:
[0065] This is the cutting force matrix at the instant the cutting begins. The cutting force at the endpoint of the first walk [0, Δt] is... For a single increment of walking time, , is the tooth cycle, and m is the number of discrete intervals; For a moment The instantaneous cutting force is also the kth step away from the […]. , The final cutting force; k=0,1,...,m-1, For a moment The instantaneous cutting force is also the m-2th departure point [ The final cutting force; This represents the cutting force at the end of the cutter tooth cycle, corresponding to the moment at the end of the cutter tooth cycle. The instantaneous cutting force, which is also the last thing to leave the walk [ -1, The final cutting force; ; It is an identity matrix.
[0066] The cutting tool and thin-walled part exhibit time-varying characteristics during the milling process. The dynamic equation of the contact process between the cutting tool and the thin-walled part can be expressed as:
[0067]
[0068] in, , and Let represent the stiffness matrix, damping matrix, and mass matrix of the part and the thin-walled part at time t, respectively; , and These represent the acceleration, velocity, and displacement matrices of the contact node, respectively.
[0069] Discrete mapping matrix It originates from the transition matrix, which is derived from solving the aforementioned dynamic equations. In the dynamic equations, It is the cutting force. The cutting thickness is related to the cutting thickness at each moment, which in turn is related to the time-varying deformation. If the part does not deform, more material is cut; if it deforms, less material is cut, and the corresponding cutting force is reduced. Therefore, in this step, the time-varying chatter of the thin-walled part is predicted based on the time-varying deformation of the thin-walled part in step 5. The above technology is known to those skilled in the art and will not be elaborated further here.
[0070] The above uses a transition matrix The principle of predicting time-varying chatter in thin-walled parts is existing technology. It can be found in the Chinese invention patent "A Reliability Optimization Method for Milling Process Parameters" with patent number ZL201710631126.2 (authorization announcement number CN107480352B), which will not be elaborated here.
[0071] In this embodiment, the element node information, stiffness matrix assembly, time-varying deformation calculation, and time-varying flutter prediction in the time-varying flutter prediction method are all run in Matlab software.
[0072] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for predicting time-varying chatter during the milling process of thin-walled parts, characterized in that... Includes the following steps: Step 1: At the initial moment, the unmilled thin-walled part is divided into multiple units, each of which is an eight-node hexahedron with the same length, width and height. Step 2: At time t, obtain the element node information of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Based on the element node information of each element and the unit stiffness matrix of the eight-node hexahedron, obtain the stiffness matrix of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part. Finally, assemble the stiffness matrices of each element in the cut part, the part to be cut, and the target machined part of the thin-walled part to obtain the time-varying stiffness matrix of the thin-walled part. Step 3: Correct the time-varying stiffness matrix of the thin-walled part to obtain the corrected time-varying stiffness matrix; Step 4: Construct a cutting force model during the milling process of thin-walled parts; Step 5: Based on the cutting force model constructed in Step 4 and the corrected time-varying stiffness matrix in Step 3, calculate the time-varying deformation of the thin-walled part. Step 6: Predict the time-varying chatter of the thin-walled part based on the time-varying deformation of the thin-walled part in Step 5.
2. The time-varying flutter prediction method according to claim 1, characterized in that: In step 3, the time-varying stiffness matrix of the thin-walled part is corrected according to the following formula to obtain the corrected time-varying stiffness matrix. , The calculation formula is: ； in, , and Let represent the stiffness matrices of the cut part, the part to be cut, and the target machined part at time t, respectively, in the global coordinate system. The global coordinate system is a three-dimensional coordinate system with a vertex on the thin-walled part as the origin. , and These represent the stiffness matrices of the cut portion, the portion to be cut, and the target machined part, respectively. This represents the stiffness matrix of the elements containing common nodes between the cut and the part to be cut of a thin-walled part. The stiffness matrix represents the element containing the common nodes of the cut portion and the target machined part of the thin-walled part; This represents the stiffness matrix of the elements containing common nodes between the cut portion and the cut portion of a thin-walled part. This represents the stiffness matrix of the elements containing common nodes between the cut portion of the thin-walled part and the target machined part. This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part to be cut; This represents the stiffness matrix of the elements containing common nodes between the target machined part and the part being cut; It is a constant, and its value is infinitely close to 0; It is a very small value.
3. The time-varying flutter prediction method according to claim 2, characterized in that: The calculation formula for the cutting force model constructed in step 4 is as follows: = ； in, Let be the cutting force of the tool in the radial direction at time t. and The milling cutter is in the first position. The first tooth, the first The tangential cutting element force and radial cutting element force at time t on each cutting element. Let be the position angle of the milling cutter at time t.
4. The time-varying flutter prediction method according to claim 3, characterized in that: Thin-walled parts at a cutting height of Actual cutting thickness for: ； in, The nominal radial cutting thickness of the cutting tool. The height of the tool along the cutting axis Deformation value at that location, , Indicates axial depth of cut. At that time, altitude The cutting force at the micro-element of the cutting process. For the overhang of the tool, The elastic modulus of the cutting tool; Let be the moment of inertia of the tool's cross section; For thin-walled parts, the height in the cutting axial direction The deformation value at point t, and the deformation value of the thin-walled part at time t: ,Should Obtained from the deformation value of the thin-walled part at time t.
5. The time-varying flutter prediction method according to any one of claims 1 to 4, characterized in that: The specific process for predicting the time-varying chatter of thin-walled parts in step 6 is as follows: Calculate the transition matrix within a cutting cycle. Determine the transition matrix If the magnitudes of all eigenvalues are less than 1, then chatter is not occurring in the current cut; otherwise, chatter is occurring in the current cut. Transition matrix The calculation formula is: ； in, , , and The first The, the The first, ..., the 1st and 0th discrete mapping matrices; Discrete mapping matrices The calculation formula is: ; This is the cutting force matrix at the instant the cutting begins. The cutting force at the endpoint of the first walk [0, Δt] is... For a single increment of walking time, , is the tooth cycle, and m is the number of discrete intervals; For a moment The instantaneous cutting force is also the kth step away from the […]. , The final cutting force; k=0,1,...,m-1, For a moment The instantaneous cutting force is also the m-2th departure point [ The final cutting force; This represents the cutting force at the end of the cutter tooth cycle, corresponding to the moment at the end of the cutter tooth cycle. The instantaneous cutting force, which is also the last thing to leave the walk [ -1, The final cutting force; ; It is an identity matrix.