Mirror milling stability prediction method and system for thin-walled parts considering stiffness effect

Abstract

This application discloses a method and system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, relating to the field of machining technology. The method includes establishing a time-varying dynamic model of mirror milling stiffness; the dynamic model consists of the mass matrix, damping matrix, and stiffness matrix corresponding to the support system, workpiece system, and tooling system; using a fully discretized method to solve the stability of the dynamic model, obtaining the transformation matrix of the dynamic model; inputting the dynamic parameters of the support system, workpiece system, and tooling system during the mirror milling process of the thin-walled part into the transformation matrix of the dynamic model; and obtaining the stability leaflet diagram of the thin-walled part before and after mirror milling through MATLAB simulation. This application achieves efficient and high-precision prediction of the stability of mirror milling of thin-walled parts.

Description

Technical Field

[0001] This application relates to the field of machining technology, and in particular to a method and system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects. Background Technology

[0002] Large, thin-walled parts are characterized by their large size and low stiffness. Their machining process is highly sensitive to initial geometry and physical states, clamping constraints, and changes in structural stiffness, making them prone to machining vibrations that negatively impact machining quality. To avoid machining problems caused by the large size and low stiffness of the workpiece, a mirror milling method is proposed. Mirror milling consists of two moving heads, one supporting and the other machining. During machining, both heads move synchronously and maintain a mirror relationship at all times. During mirror milling, the support increases the local stiffness of the support position on the thin-walled workpiece, effectively suppressing deformation and vibration. In actual production, conservative parameters are typically used to avoid chatter, reducing machining efficiency and increasing production costs. Therefore, from a process perspective, this paper theoretically studies the stability of mirror milling of thin-walled parts, guiding the selection of appropriate machining parameters. This approach can avoid chatter while maximizing production efficiency, which is of great significance for practical production.

[0003] However, during mirror machining of thin-walled parts, the dynamic characteristics of the workpiece are constantly changing due to factors such as workpiece clamping, support, and material removal. This causes the support-workpiece-tool process system to be in an unstable cutting state during machining, making it prone to cutting chatter under specific machining parameters and conditions. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for predicting the stability of mirror milling of thin-walled parts that takes into account stiffness effects, which can achieve high-precision prediction of the stability of mirror milling of thin-walled parts.

[0005] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, the method comprising: A time-varying dynamic model of mirror milling stiffness is established; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system.

[0006] The dynamic model is solved for stability using the fully discrete method, and the transformation matrix of the dynamic model is obtained.

[0007] The dynamic parameters of the support system, workpiece system, and tool process system during the mirror milling of thin-walled parts are input into the transformation matrix of the dynamic model. Through MATLAB simulation, the stability lobe diagrams of the thin-walled parts before and after mirror milling are obtained.

[0008] Secondly, this application provides a system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, comprising: The model building module is used to build a dynamic model of time-varying stiffness in mirror milling; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system.

[0009] The matrix solving module is used to solve the stability of the dynamic model using the fully discrete method, and obtain the transformation matrix of the dynamic model.

[0010] The stability prediction module is used to input the dynamic parameters of the support system, workpiece system and tool process system into the transformation matrix of the dynamic model during the mirror milling of thin-walled parts. Through MATLAB simulation, the stability lobe diagrams before and after mirror milling of thin-walled parts are obtained.

[0011] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method and system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects. For nonlinear stiffness changes, a time-varying dynamic model of stiffness is established, taking into account stiffness changes such as support stiffness and workpiece stiffness after material removal, enabling the prediction of time-varying dynamic characteristics of the mirror milling process. A fully discrete method is employed to solve the stability problem of the dynamics. The fully discrete method can capture the changes in the system state at discrete time points, performing stability analysis on nonlinear and time-varying systems with high computational efficiency and without sacrificing numerical accuracy. This invention achieves efficient and high-precision prediction of the stability of mirror milling of thin-walled parts. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating a method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, as provided in Embodiment 1 of this application.

[0014] Figure 2 is a schematic diagram of the dynamic modeling of mirror milling of thin-walled parts, which is implemented by the method for predicting the stability of mirror milling of thin-walled parts considering stiffness effect according to Embodiment 1 of this application; Figure 2(a) is a schematic diagram of mirror milling, and Figure 2(b) is a simplified mass-spring-damping system.

[0015] Figure 3 This is a schematic diagram of the tool and workpiece modal testing platform installation for a method to predict the stability of mirror milling of thin-walled parts considering stiffness effects, as provided in Embodiment 1 of this application.

[0016] Figure 4 Stability lobe diagrams before and after machining for a method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, provided in Embodiment 1 of this application.

[0017] Figure 5 The stability lobe diagram with and without support is provided for the implementation of a method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, as provided in Embodiment 1 of this application.

[0018] Figure 6 This is a schematic diagram of a system for predicting the stability of mirror milling of thin-walled parts, which takes into account stiffness effects, provided in Embodiment 2 of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Example 1 like Figure 1 As shown, this embodiment provides a method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, including: Step 101: Establish a dynamic model of time-varying stiffness in mirror milling; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system.

[0022] Step 102: Use the fully discrete method to solve the stability of the dynamic model and obtain the transformation matrix of the dynamic model.

[0023] Step 103: Input the dynamic parameters of the support system, workpiece system and tool process system during the mirror milling of thin-walled parts into the transformation matrix of the dynamic model, and obtain the stability lobe diagram of the thin-walled parts before and after mirror milling through MATLAB simulation.

[0024] The mirror machining process is shown in Figure 2(a). The support device, workpiece, and tool are simplified into a multi-degree-of-freedom mass-spring-damping system, as shown in Figure 2(b). For this multi-degree-of-freedom mass-spring-damping system, the mass in the workpiece normal direction... m s and its damping, stiffness ( c sz , k sz ) represents the mass-spring-damping on the supporting side, the smaller mass and its damping, stiffness ( c hz , k hz This is equivalent to the contact action between the support head and the workpiece contact point. c hx , c hy )and( k hx , k hy ) represent the damping and stiffness in the radial direction of the cutting tool, respectively.

[0025] In some embodiments of this example, the formula for the dynamic model is specifically as follows: .

[0026] in M , C , K These are the mass matrix, damping matrix, and stiffness matrix corresponding to the support system, workpiece system, and tooling system, respectively. , , These are respectively the support system, workpiece system, and tooling process system. t The acceleration, velocity, and displacement vectors at time t. a p The axial cutting depth, K tc The tangential cutting force coefficient is... The vibration displacements of the support system, workpiece system, and tool process system in the X, Y, and Z directions at the current moment of cutting. The vibration displacements of the support system, workpiece system, and tool process system in the X, Y, and Z directions at the moment of the previous cutting tooth. T For the tool rotation cycle, αxx ( t ), α xy ( t ), α xz ( t ), α yx ( t ), α yy ( t ), α yz ( t ), α zx ( t ), α zy ( t ), α zz ( t () represents the cutting force coefficient.

[0027] Specifically, the time-varying dynamic model of mirror milling stiffness is a 3-DOF model of the mirror machining support-workpiece-tool system, wherein the mass matrix, damping matrix, and stiffness matrix of the support-workpiece-tool process system are: , , .in, , , , , , , , , These correspond to the modal parameters in the X, Y, and Z directions of the support-workpiece-tool process system, respectively. m x , m y and m z For modal mass, ζ x , ζ y and ζ z Let X be the damping ratio in the X, Y, and Z directions. ω x , ω y and ω z Let X be the natural frequencies in the X, Y, and Z directions. M xy , M xz ,M yx , M yz , M zx , M zy , C xy , C xz , C yx , C yz , C zx , C zy , K xy , K xz , K yx , K yz , K zx , K zy Set it to 0.

[0028] Cutting force coefficient α xx ( t ), α xy ( t ), α xz ( t ), α yx ( t ), α yy ( t ), α yz ( t ), α zx ( t ), α zy ( t ), α zz ( t This can be represented as: ; ; ; ; ; ; ; ; .

[0029] In some embodiments of this example, the formula for the transformation matrix of the dynamic model is specifically as follows: ; .

[0030] in, ; ; ; ; ; , , , , For time intervals, , , and They represent exist and The value of time, similarly, , , and They represent exist and The value of time, and It is a periodic coefficient matrix. It is a 3×3 transition matrix. ζ The damping ratio is denoted as .

[0031] The specific principle for obtaining the transformation matrix is ​​as follows: the dynamic equation of the 3-DOF thin-walled part mirror machining support-workpiece-tool process system can be expressed as an n-dimensional linear time-periodic system with a single discrete time delay, i.e.: .

[0032] in, A 0 is a constant matrix. A ( t )and B ( t ) is a periodic matrix, A ( t )= A ( t + T )and B ( t )= B ( t + T ).

[0033] Discretizing the rotation period, the system response within the discrete interval is: .

[0034] make ,but ,Right now X i+1 for: .

[0035] Among them, parameters It can be done through time intervals If the two boundary values ​​within the range are obtained linearly, then the above equation can be transformed into: .

[0036] in, ; ; ; ; .

[0037] In the formula, , , , , For time intervals, , , and They represent exist and The value of time, similarly, , , and They represent exist and The value of time, and It is a periodic coefficient matrix. ...is a 3×3 transition matrix, serving as... Q i , H 0 ...and A 0 Transitional effects between matrices.

[0038] The above formula It can be represented as: .

[0039] in, .

[0040] Then, define the discrete mapping: .

[0041] in, express n ( m +1) dimensional vector, D i Defined as: .

[0042] Finally, the transformation matrix within the tool rotation cycle is obtained as follows: .

[0043] According to Floquet's theorem, if the eigenvalues ​​of the transformation matrix are less than 1, the point is in a stable state; if the eigenvalues ​​are greater than 1, the point is in an unstable state; and if the eigenvalues ​​are exactly 1, the point is on the stability boundary.

[0044] .

[0045] In some embodiments of this example, before inputting the dynamic parameters of the support system, workpiece system, and tooling process system during the mirror milling of thin-walled parts into the transformation matrix of the dynamic model, the method further includes: Obtain the dynamic parameters of the support system, workpiece system, and tooling system during mirror milling of thin-walled parts, specifically including: The eddy current sensor is installed on one side of the tool tip in the tooling system.

[0046] The data acquisition instrument was set to the first preset parameters, and a hammering test was performed on the tool tip in the X and Y directions to obtain the dynamic parameters of the tool manufacturing system. The dynamic parameters of the tool manufacturing system include the natural frequency, stiffness, damping ratio, and modal mass of the tool tip.

[0047] An accelerometer is installed in the pre-machining area of ​​the workpiece on a mirror milling machine.

[0048] The data acquisition instrument parameters were set to the second preset parameters. Hammer impact tests were conducted on the workpiece before and after processing, as well as under varying support forces, to obtain the dynamic parameters of the support system and the workpiece system. The dynamic parameters of the support system and the workpiece system include the natural frequency, stiffness, damping ratio, and modal mass of the support system and the workpiece system.

[0049] Specifically, the construction is as follows Figure 3 The modal testing measurement system shown is divided into two parts. First, the eddy current sensor is placed near the tip of the tool, and the tip is hammered in the X and Y directions respectively. The computer controls the eddy current sensor and the hammer to collect data simultaneously, so as to obtain the dynamic parameters of the tip in the X and Y directions.

[0050] Then, an accelerometer is attached to the thin-walled part, and the part is hammered. The eddy current sensor and the hammer are simultaneously collected by computer control to obtain the initial state, dynamic parameters of the thin-walled part under variable support force and after processing.

[0051] In some embodiments of this example, when performing step 103, the specific steps may be as follows: Based on the dynamic parameters of the support system, the workpiece system, and the tooling system, the spindle speed during mirror milling of thin-walled parts is obtained using MATLAB simulation. n and axial depth shaft a p Stability lobe plots before and after mirror milling with variable .

[0052] Based on stability assessment, the spindle speed can be obtained by substituting the dynamic parameters of mirror machining. n and axial depth shaft a p Leaf-shaped stability diagram for mirror milling with variable spindle speed. This invention considers the influence of time-varying stiffness on the stability of mirror milling, and selects commonly used machining parameters, such as spindle speed. n =4000~9000r / min a p =1.0mm a e =2mm f z =0.02mm / tooth. Substituting the dynamic parameters obtained from modal testing into the formula, the 3-DOF stability lobe diagram of the time-varying stiffness dynamic model was plotted using MATLAB simulation, as shown below. Figure 4 As shown in the figure. The solid and dashed lines represent the Lobe curves before and after processing, respectively. The area above the Lobe curve is the unstable region, and the area below the curve is the stable region.

[0053] The stability region is analyzed below. Figure 4 The processing parameters are as follows n A =6000rpm, a pA =1.0mm A point( n A , a pAFor example, if we consider the stability before machining, and the machining parameter is below the Lobe curve, then it is considered to be in the cutting stability region. However, in actual machining, the nonlinear change in stiffness caused by material removal affects the system stability, and the machining parameter is now in the cutting instability region. Studies show that material removal reduces the workpiece stiffness; as material is continuously removed, the workpiece stiffness gradually decreases, and the machining stability region also gradually shrinks.

[0054] Leaf-shaped stability diagrams with varying support forces, plotted using MATLAB simulations, are shown below. Figure 5 As shown, the stability lobe diagrams obtained with and without support, as well as with increased support force, differ significantly. Changes in support force affect support stiffness, thus impacting stability. Research indicates that the stable regions with and without support differ considerably. Applying support force increases the overall system size, significantly enlarging the stable region and the critical depth of cut. However, as the support force increases, the increase in stable region becomes less pronounced, and the impact of continuously increasing support force on machining stability diminishes.

[0055] Example 2 like Figure 6 As shown, this embodiment provides a stability prediction system for mirror milling of thin-walled parts considering stiffness effects, including: The model building module 601 is used to build a dynamic model of time-varying stiffness in mirror milling; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system.

[0056] The matrix solving module 602 is used to solve the stability of the dynamic model using the fully discrete method to obtain the transformation matrix of the dynamic model.

[0057] The stability prediction module 603 is used to input the dynamic parameters of the support system, workpiece system and tool process system during the mirror milling of thin-walled parts into the transformation matrix of the dynamic model, and obtain the stability lobe diagram before and after mirror milling of thin-walled parts through MATLAB simulation.

[0058] The system also includes a parameter acquisition module, used to acquire the dynamic parameters of the support system, workpiece system and tool process system during the mirror milling of thin-walled parts.

[0059] In summary, this application has the following technical effects: The advantages and technical effects of this invention are as follows: This invention establishes a time-varying dynamic model for stiffness nonlinear changes, considering stiffness changes such as support stiffness and workpiece stiffness after material removal, enabling the prediction of time-varying dynamic characteristics in the mirror milling process. It employs a fully discrete method for stability solving of the dynamics. The fully discrete method can capture the changes in the system state at discrete time points, performing stability analysis on nonlinear and time-varying systems with high computational efficiency and without sacrificing numerical accuracy. This invention achieves efficient and high-precision prediction of stability in mirror milling of thin-walled parts, avoiding chatter and improving machining quality and efficiency.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, characterized in that, The method for predicting the stability of mirror milling of thin-walled parts includes: A time-varying dynamic model of mirror milling stiffness is established; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system; The stability of the dynamic model is solved using the fully discrete method, and the transformation matrix of the dynamic model is obtained. The dynamic parameters of the support system, workpiece system, and tool process system during the mirror milling of thin-walled parts are input into the transformation matrix of the dynamic model. Through MATLAB simulation, the stability lobe diagrams of the thin-walled parts before and after mirror milling are obtained.

2. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 1, characterized in that, The specific formula for the dynamic model is as follows: ； in M , C , K These are the mass matrix, damping matrix, and stiffness matrix corresponding to the support system, workpiece system, and tooling system, respectively. , , These are respectively the support system, workpiece system, and tooling process system. t The acceleration, velocity, and displacement vectors at time t. a p This is the axial cutting depth. K tc The tangential cutting force coefficient is... The vibration displacements of the support system, workpiece system, and tool process system in the X, Y, and Z directions at the current moment of cutting. The vibration displacements of the support system, workpiece system, and tool process system in the X, Y, and Z directions at the moment of the previous cutting tooth. T For the tool rotation cycle, α xx ( t ), α xy ( t ), α xz ( t ), α yx ( t ), α yy ( t ), α yz ( t ), α zx ( t ), α zy ( t ), α zz ( t () represents the cutting force coefficient.

3. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 1, characterized in that, The specific formula for the transformation matrix of the dynamic model is as follows: ； ； in, ; ; ; ; ; , , , , For time intervals, , , and They represent exist and The value of time, similarly, , , and They represent exist and The value of time, and It is a periodic coefficient matrix. It is a 3×3 transition matrix. ζ The damping ratio is denoted as .

4. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 1, characterized in that, Before inputting the dynamic parameters of the support system, workpiece system, and tooling process system during the mirror milling of thin-walled parts into the transformation matrix of the dynamic model, the following steps are also included: Obtain the dynamic parameters of the support system, workpiece system, and tool process system during mirror milling of thin-walled parts.

5. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 4, characterized in that, Obtain the dynamic parameters of the support system, workpiece system, and tooling system during mirror milling of thin-walled parts, specifically including: Install the eddy current sensor on one side of the tool tip in the tooling system; Set the parameters of the data acquisition instrument to the first preset parameters, perform hammering tests on the tool tip in the X and Y directions, and obtain the dynamic parameters of the tool process system; Install the accelerometer in the pre-machining area of ​​the workpiece on the mirror milling machine; The data acquisition instrument parameters were set to the second preset parameters. Hammering tests were conducted on the workpiece before and after processing, as well as under varying support forces, to obtain the dynamic parameters of the support system and the workpiece system.

6. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 5, characterized in that, The dynamic parameters of the cutting tool process system include the natural frequency, stiffness, damping ratio, and modal mass of the cutting tool tip.

7. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 6, characterized in that, The dynamic parameters of the support system and the workpiece system include the natural frequency, stiffness, damping ratio, and modal mass of the support system and the workpiece system.

8. The method for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 1, characterized in that, The dynamic parameters of the support system, workpiece system, and tool process system during the mirror milling of thin-walled parts are input into the transformation matrix of the dynamic model. Through MATLAB simulation, the stability lobe diagrams of the thin-walled parts before and after mirror milling are obtained, specifically including: Based on the dynamic parameters of the support system, the workpiece system, and the tooling system, the spindle speed during mirror milling of thin-walled parts is obtained using MATLAB simulation. n and axial depth shaft a p Stability lobe plots before and after mirror milling with variable .

9. A system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects, characterized in that, include: The model building module is used to build a dynamic model of time-varying stiffness in mirror milling; the dynamic model consists of the mass matrix, damping matrix and stiffness matrix corresponding to the support system, workpiece system and tool process system; The matrix solving module is used to solve the stability of the dynamic model using the fully discrete method to obtain the transformation matrix of the dynamic model; The stability prediction module is used to input the dynamic parameters of the support system, workpiece system and tool process system into the transformation matrix of the dynamic model during the mirror milling of thin-walled parts. Through MATLAB simulation, the stability lobe diagrams before and after mirror milling of thin-walled parts are obtained.

10. A system for predicting the stability of mirror milling of thin-walled parts considering stiffness effects according to claim 9, characterized in that, Also includes: The parameter acquisition module is used to acquire the dynamic parameters of the support system, workpiece system, and tool process system during the mirror milling process of thin-walled parts.

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