Dynamic cutting force and dynamic modeling method of thin-walled workpiece double-sided milling system

Abstract

The application discloses a kind of thin-walled part double-sided milling processing system dynamics modeling method, the coupling effect between the tool radial vibration and the vibration in the thickness direction of thin-walled part is considered first in the method, the dynamic cutting thickness corresponding to each blade microelement of milling cutter located on the two sides of thin-walled part is calculated, then the dynamic cutting force acting on tool-thin-walled part system is calculated.The cutting force perpendicular to the thickness direction of the two sides of thin-walled part is applied to the milling cutter on the two sides respectively, the resultant force of the cutting force in the thickness direction of thin-walled part is applied to thin-walled part itself, the dynamics control equation of thin-walled part double-sided milling processing system is established, and the stability solution is carried out to the equation.Compared with the given document, the coupling effect between the tool radial vibration and the vibration in the thickness direction of thin-walled part is considered in the application to establish the cutting force and dynamics model of thin-walled part double-sided milling processing system, and the prediction accuracy of thin-walled part double-sided milling stability lobe diagram is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical processing, in particular to a cutting force and dynamics modeling method for a thin-walled part double-sided milling system. BACKGROUND

[0002] For aerospace vehicles, in order to improve the maneuverability of the vehicle, increase the carrying capacity of the load and the flight distance, a large number of thin-walled parts are used in the structure, such as aircraft skin, rocket box wall plate, etc. However, thin-walled parts often exhibit weak rigidity, large size and high material removal rate, and the surface processing modal quality requirement is extremely high, resulting in great difficulty in the manufacturing process of thin-walled parts. There are many thin-walled structures with machining requirements on both sides in the thin-walled parts of aerospace vehicles, such as rocket fuel tank bottom, engine blade and other structures, which need multiple clamping, measuring and other links in the machining process, or design complex fixtures to complete the turnover, which not only increases the process flow and cost, but also causes clamping or measurement errors, which seriously limits the machining efficiency and precision.

[0003] The double-sided milling technology of thin-walled parts appeared in recent years can meet the machining requirements of thin-walled structures on both sides. The milling cutters on both sides of the thin-walled part simultaneously perform thinning machining on the thin-walled part, and the two sides support each other without workpiece turnover clamping, which greatly improves the machining efficiency and obtains good results while reducing deformation and suppressing vibration. However, in the double-sided milling process, the cutting force on both sides is coupled, and the cutting vibration becomes extremely complex. Therefore, it is of great theoretical and engineering practical value to find a modeling method suitable for the cutting force and dynamics of the double-sided milling system of thin-walled parts to predict the stability of double-sided milling of thin-walled parts.

[0004] Document [1] discloses a dynamic modeling method for double-sided milling of cylindrical workpieces. The cutting force modeling in this method considers the influence of tool radial vibration on chip thickness and cutting force. Document [2] discloses a dynamic modeling method for double-sided milling based on double parallel machine tools. The cutting force modeling in this method considers the influence of workpiece thickness direction vibration on chip thickness and cutting force. The typical feature of the technical solutions disclosed in the above documents is that only the tool radial vibration or the workpiece thickness direction vibration is considered in the double-sided milling cutting force modeling process, and the coupling effect between the tool radial vibration and the workpiece thickness direction vibration is ignored. However, in the double-sided milling process of thin-walled parts, when the radial stiffness of the tool and the stiffness in the thickness direction of the workpiece are in the same order of magnitude, the coupling effect between the tool radial vibration and the workpiece thickness direction vibration will seriously affect the dynamic cutting force in the double-sided milling process.

[0005] [REFERENCE]

[0006] [1] Yamato, S., Nakanishi, K., Suzuki, N. et al. Development of Automatic Chatter Suppression System in Parallel Milling by Real-Time Spindle Speed Control with Observer-Based Chatter Monitoring. Int. J. Precis. Eng. Manuf. 2021, 22: 227-240.

[0007] [2] Rao Fu, Patrick Curley, Colm Higgins, Zekai Murat Kilic, Dan Sun, Adrian Murphy, Yan Jin, Double-sided milling of thin-walled parts by dual collaborative parallel kinematic machines. Journal of Materials Processing Technology, 2022, 299, 117395.

[0008] [3] Yin Li, Liu Qiang. Research on Milling Force Model Coefficient Identification Based on Partial Least Squares Regression (PLSR) Method. Mechanical Science and Technology, 2005(03): 269-272.

[0009] [4] Ye Ding, Li Min Zhu, Xiao Jian Zhang, Han Ding, A full-discretization method for prediction of milling stability, International Journal of Machine Tools and Manufacture, 2010, 50(5) 502-509. SUMMARY

[0010] In view of the above prior art, the present application provides a dynamic cutting force and dynamic modeling method for a thin-walled part double-sided milling system, which considers the coupling effect between tool radial vibration and thickness direction vibration of the thin-walled part, and can accurately predict the double-sided milling stability of the thin-walled part.

[0011] In order to solve the above technical problems, the dynamic cutting force modeling method for a thin-walled part double-sided milling system provided by the present application comprises the following steps:

[0012] Step 1: in a half cycle of the thin-walled part vibration, infinitesimal the blade in axial height, calculate the dynamic cutting thickness of each blade of the milling cutter on both sides of the thin-walled part, the milling cutter on both sides of the thin-walled part is respectively recorded as the first milling cutter and the second milling cutter:

[0013] The dynamic cutting thickness of each blade of the first milling cutter:

[0014]

[0015] The dynamic cutting thickness of each blade of the second milling cutter (2):

[0016]

[0017] Formula and formula h 1，j (t, z i ) is the dynamic cutting thickness of the first j tooth of the first milling cutter at the i axial infinitesimal at the current time t, h 2，j (t, z i ) is the dynamic cutting thickness of the first j tooth of the second milling cutter at the i axial infinitesimal at the current time t; φ 1，j is the radial tangent angle corresponding to the current time t of the i axial infinitesimal of the first j tooth of the first milling cutter, φ 2，j is the radial tangent angle corresponding to the current time t of the i axial infinitesimal of the first j tooth of the second milling cutter; κ 1，j is the axial tangent angle corresponding to the current time t of the i axial infinitesimal of the first j tooth of the first milling cutter, κ 2，j is the axial tangent angle corresponding to the current time t of the i axial infinitesimal of the first j tooth of the second milling cutter; x1(t) and y1(t) are the dynamic displacements of the current tooth of the first milling cutter at time t, x2(t) and y2(t) are the dynamic displacements of the current tooth of the second milling cutter at time t, x1(t-τ 1,j ) and y1(t-τ 1，j ) are the dynamic displacements of the previous tooth of the first milling cutter at time t-τ 1,j , x2(t-τ 2，j ) and y2(t-τ 2，j ) are the dynamic displacements of the previous tooth of the second milling cutter at time t-τ 2，j , z w (t) is the dynamic displacement of the thin-walled part at time t, z w (t-τ 1，j ) and z w (t-τ 2，j ) are the dynamic displacements of the thin-walled part at time t-τ 1，j and t-τ 2，j respectively; τ1，j τ is the time required for the current tooth of the first milling cutter to cut to the same radial tangent angle as the previous tooth of the first milling cutter; 2，j τ is the time required for the current tooth of the second milling cutter to cut to the same radial tangent angle as the previous tooth of the second milling cutter;

[0018] Step 2: Calculate the entry angle and exit angle of the two-sided milling cutter in the forward milling and reverse milling process:

[0019] Forward milling process entry angle and exit angle calculation formula:

[0020]

[0021]

[0022] Reverse milling process entry angle and exit angle calculation formula:

[0023]

[0024]

[0025] In formula (3) to formula (6), is the entry angle, is the exit angle, a e is the radial depth of cut, and R is the radius of the milling cutter;

[0026] Step 3: Calculate the window function corresponding to each tooth of the two-sided milling cutter:

[0027]

[0028] In formula (7), g(φ p，j ) is the window function corresponding to the radial tangent angle corresponding to the current time t at the i-th axial microelement on the j-th tooth of the milling cutter p; p = 1, 2, 1 refers to the first milling cutter; 2 refers to the second milling cutter;

[0029] Step 4: Calculate the dynamic cutting force corresponding to each tooth microelement of the two-sided milling cutter:

[0030] For the first milling cutter:

[0031]

[0032]

[0033] In formula (8) and formula (9), dF t，1 (t, z i ), dF r，1 (t, z i ), and dF a，1 (t, z irespectively are tangential force, radial force and axial force of the first milling cutter at the i-th axial microelement of all teeth of the first milling cutter at the current time t, N1 is the number of teeth of the first milling cutter, K tc，1 , rc，1 , and K ac，1 are tangential cutting force coefficient, radial cutting force coefficient and axial cutting force coefficient of the first milling cutter, dz1 is the axial height of the microelement of the first milling cutter, dF x，1 (t, z i ), dF y，1 (t, z i ), and dF z，1 (t, z i ) are X-direction force, Y-direction force and Z-direction force of the first milling cutter at the i-th axial microelement of all teeth of the first milling cutter at the current time t, with the bottom of the first milling cutter as the origin of the three-dimensional coordinate system, the feeding direction of the first milling cutter is the X-axis direction, the Y-axis direction is perpendicular to the feeding direction, and the Z-axis direction is away from the thin-walled part;

[0034] For the second milling cutter:

[0035]

[0036]

[0037] In formula (10) and formula (11), dF t，2 (t, z i ), dF r，2 (t, z i ), and dF a，2 (t, z i ) are tangential force, radial force and axial force of the second milling cutter at the i-th axial microelement of all teeth of the second milling cutter at the current time t, N2 is the number of teeth of the second milling cutter, K tc，2 , K rc，2 , and K ac，2 are tangential cutting force coefficient, radial cutting force coefficient and axial cutting force coefficient of the second milling cutter, dz2 is the axial height of the microelement of the second milling cutter, dF x，2 (t, z i ), dF y，2 (t, z i ), and dF z，2 (t, z i ) are X-direction force, Y-direction force and Z-direction force of the second milling cutter at the i-th axial microelement of all teeth of the second milling cutter at the current time t, with the bottom of the second milling cutter as the origin of the three-dimensional coordinate system, the feeding direction of the second milling cutter is the X-axis direction, the Y-axis direction is perpendicular to the feeding direction, and the Z-axis direction is away from the thin-walled part;

[0038] Step 5: Model for calculating dynamic cutting forces acting on the two- sided milling cutter:

[0039] For the model of dynamic cutting forces on the first milling cutter (1), it is expressed as follows,

[0040]

[0041] In formula (12), F x，1 (t), F y，1 (t) and F z，1 (t) are the X-direction force, Y-direction force and Z-direction force of all teeth of the first milling cutter (1) at the current time t, and the elements of the dynamic milling force direction coefficient matrix are expressed as follows:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] For the model of dynamic cutting forces on the second milling cutter (2), it is expressed as follows:

[0052]

[0053] In formula (13), F x，2 (t), F y，2 (t) and F z，2 (t) are the X-direction force, Y-direction force and Z-direction force of all teeth of the second milling cutter (2) at the current time t, and the elements of the dynamic milling force direction coefficient matrix are expressed as follows:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] In the above element expression of the directional coefficient matrix, a p，1 is the axial cutting depth of the first milling cutter, a p，2 is the axial cutting depth of the second milling cutter.

[0064] Furthermore, the dynamic cutting force modeling method of the double-sided milling system for thin-walled parts, wherein the tangential cutting force coefficient K of the first milling cutter is tc，1 , radial cutting force coefficient K rc，1 and axial cutting force coefficient K ac，1 It can be obtained by numerical calculation or cutting test; the tangential cutting force coefficient K of the second milling cutter is tc，2 , radial cutting force coefficient K rc，2 and axial cutting force coefficient K ac，2 It can be obtained by numerical calculation or cutting test.

[0065] At the same time, the present invention also proposes a dynamic modeling method for a double-sided milling system of a thin-walled workpiece, wherein the milling cutters located on both sides of the thin-walled workpiece are respectively recorded as a first milling cutter and a second milling cutter. The method includes the following steps:

[0066] Step 1: Perform modal tests on the first milling cutter, the second milling cutter, and the thin-walled workpiece using a standard hammer impact method to obtain the modal mass, damping, and stiffness of the first and second milling cutters in the radial direction; the modal mass m of the thin-walled workpiece in the thickness direction z，w , damping c z，w and stiffness k z，w The radial modal mass of the first milling cutter includes the modal mass m in the X direction x，1 and the Y-direction modal mass m y，1 The radial damping of the first milling cutter includes the X-direction damping c x，1 and Y-direction damping c y，1 , the radial stiffness of the first milling cutter includes the X-direction damping k x，1 and Y-direction damping k y，1 , the radial modal mass of the second milling cutter includes the X-direction modal mass m x，2 and the Y-direction modal mass m y，2, the radial damping of the second milling cutter includes X-direction damping c x，2 and Y-direction damping c y，2 , the radial stiffness of the second milling cutter includes X-direction damping k x，2 and Y-direction damping k y，2 ;

[0067] Step 2: the dynamic cutting force of the first milling cutter and the second milling cutter is calculated by using the model obtained by the dynamic cutting force modeling method of the double-sided milling system of the thin-walled part as described above, including the X-direction force F x，1 (t), Y-direction force F y，1 (t) and Z-direction force F z，1 (t) of all teeth of the first milling cutter at the current time t, and the X-direction force F x，2 (t), Y-direction force F y，2 (t) and Z-direction force F z，2 (t) of all teeth of the second milling cutter at the current time t.

[0068] Step 3: the dynamic control equation of the double-sided milling system of the thin-walled part is established:

[0069]

[0070] The above control equation is stably solved by the full-discrete method in the time domain, and the stability blade diagram considering the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part is obtained.

[0071] Compared with the prior art, the beneficial effects of the present application are:

[0072] The dynamic cutting force modeling method in the present application first considers the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part to calculate the dynamic cutting thickness corresponding to each cutting edge element of the two-side milling cutter, and then calculates the dynamic cutting force acting on the tool-thin-walled part system. The dynamic modeling method in the present application applies the cutting forces perpendicular to the thickness direction of the thin-walled part on the two-side milling cutter, and the resultant force of the cutting forces in the thickness direction of the thin-walled part on the thin-walled part itself, establishes the dynamic control equation of the double-sided milling system of the thin-walled part, and stably solves the equation.

[0073] The present application considers the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part to establish the cutting force and dynamic model of the double-sided milling system of the thin-walled part, and improves the prediction accuracy of the stability blade diagram of the double-sided milling of the thin-walled part. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 is a schematic diagram of the double-sided milling of the thin-walled part of the present application;

[0075] Figure 2 is a stability blade diagram predicted by the present application according to a full-discrete method in time domain. DETAILED DESCRIPTION

[0076] The design idea of the thin-walled part double-sided milling machining system dynamic modeling method provided by the present application is that the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part is considered to calculate the dynamic cutting thickness corresponding to each blade microelement of the milling cutter on the two sides of the thin-walled part, and then the dynamic cutting force acting on the tool-thin-walled part system is calculated. The cutting force perpendicular to the thickness direction of the thin-walled part on the two sides is respectively applied to the milling cutter on the two sides, and the resultant force of the cutting force in the thickness direction of the thin-walled part is applied to the thin-walled part itself, the dynamic control equation of the thin-walled part double-sided milling machining system is established, and the stability solution is carried out on the equation. Compared with the given literature, the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part is considered to establish the cutting force and dynamic model of the thin-walled part double-sided milling machining system, the double-sided milling machining stability of the thin-walled part 3 can be accurately predicted, and the prediction accuracy of the double-sided milling stability blade diagram of the thin-walled part is improved.

[0077] The present application will be further described below in conjunction with the drawings and specific embodiments, but the following embodiments are by no means any limitation on the present application. In the description of the present embodiment, the terms "first", "second" are only used to distinguish in the description, and have no special meaning.

[0078] Embodiment 1

[0079] The thin-walled part double-sided milling machining system cutting force modeling method provided by the present embodiment specifically includes the following steps:

[0080] Step 1: in a half cycle of the vibration of the thin-walled part 3, the blade is microelementized in the axial height, the dynamic cutting thickness of each blade of the milling cutter on the two sides of the thin-walled part 3 is calculated, Figure 1 The schematic diagram of the thin-walled part double-sided milling provided by the present application is shown, and the milling cutters on the two sides of the thin-walled part 3 are respectively denoted as the first milling cutter 1 and the second milling cutter 2.

[0081] For the dynamic cutting thickness of each blade of the first milling cutter 1:

[0082]

[0083] For the dynamic cutting thickness of each blade of the second milling cutter (2):

[0084]

[0085] In formula (1) and formula (2): h 1，j (t, z i) is the dynamic cutting thickness of the first milling cutter 1 at the i-th axial microelement of the j-th tooth at the current time t, h 2，j (t, z i ) is the dynamic cutting thickness of the second milling cutter 2 at the i-th axial microelement of the j-th tooth at the current time t; φ 1，j is the radial cutting angle corresponding to the current time t at the i-th axial microelement of the j-th tooth of the first milling cutter 1, φ 2，j is the radial cutting angle corresponding to the current time t at the i-th axial microelement of the j-th tooth of the second milling cutter 2, κ 1，j is the axial cutting angle corresponding to the current time t at the i-th axial microelement of the j-th tooth of the first milling cutter 1, κ 2，j is the axial cutting angle corresponding to the current time t at the i-th axial microelement of the j-th tooth of the second milling cutter 2; x1(t) and y1(t) are the dynamic displacements of the first milling cutter 1 at the current tooth time t, x2(t) and y2(t) are the dynamic displacements of the second milling cutter 2 at the current tooth time t, x1(t-τ 1，j ) and y1(t-τ 1，j ) are the dynamic displacements of the first milling cutter 1 at the previous tooth time t-τ 1，j , x2(t-τ 2，j ) and y2(t-τ 2，j ) are the dynamic displacements of the second milling cutter 2 at the previous tooth time t-τ 2，j , z w (t) is the dynamic displacement of the thin-walled part 3 at time t, z w (t-τ 1，j ) and z w (t-τ 2，j ) are the dynamic displacements of the thin-walled part 3 at times t-τ 1，j and t-τ 2，j , respectively; τ 1，j is the time required for the current tooth of the first milling cutter 1 to cut to the same radial cutting angle as the previous tooth of the first milling cutter 1, τ 2，j is the time required for the current tooth of the second milling cutter 2 to cut to the same radial cutting angle as the previous tooth of the second milling cutter 2.

[0086] It can be understood that during the double-sided milling of the thin-walled part 3, when the radial stiffness of the cutter and the stiffness in the thickness direction of the workpiece are in the same order of magnitude, both the radial direction of the cutter and the thickness direction of the thin-walled part 3 will vibrate. The vibration of the milling cutter on both sides of the thin-walled part 3 caused by the dynamic cutting force is in the milling cutter itself, therefore, the dynamic displacement of the first milling cutter 1 and the second milling cutter 2 in the radial direction, i.e. x1(t), y1(t), x1(t-τ 1，j ), y1(t-τ 1，jx2(t), y2(t), x2(t-τ 2，j ), y2(t-τ 2，j ) are measured from the milling cutter itself. In the thickness direction of the thin-walled part 3, they are measured from the dynamic displacement of the thin-walled part 3. Exemplarily, in the first half of the vibration period of the thin-walled part 3, the dynamic displacement difference of the first milling cutter 1 in the thickness direction of the thin-walled part 3 is z w (t)-z w (t-τ 1，j ), and the dynamic displacement difference of the second milling cutter 2 in the thickness direction of the thin-walled part 3 is z w (t-τ 2，i )-z w (t), which indicates that the thin-walled part 3 is currently vibrating towards the side of the first milling cutter 1 at the tooth time t, and also indicates that in the thickness direction of the thin-walled part 3, the dynamic displacement difference on the side of the first milling cutter 1 increases while the dynamic displacement difference on the side of the second milling cutter 2 decreases. It can be understood that in the second half of the vibration period of the thin-walled part 3, the above-mentioned situation is reversed for the second milling cutter 2, which will not be described here.

[0087] Step 2: Calculate the entry angle and exit angle of the two-sided milling cutter in the forward milling and reverse milling processes:

[0088] Forward milling process entry angle and exit angle calculation formula:

[0089]

[0090]

[0091] Reverse milling process entry angle and exit angle calculation formula:

[0092]

[0093]

[0094] In formula (3) to formula (6), is the entry angle, is the exit angle, a e is the radial depth of cut, and R is the radius of the milling cutter.

[0095] Step 3: Calculate the window function corresponding to each tooth of the two-sided milling cutter:

[0096]

[0097] In formula (7), g(φ p，j ) is the window function corresponding to the radial contact angle at the current time t at the i-th axial microelement on the j-th tooth of the p-th milling cutter; p = 1, 2, 1 refers to the first milling cutter; 2 refers to the second milling cutter.

[0098] Step 4: Calculate the dynamic cutting force of each infinitesimal of the two- sided milling cutter:

[0099] For the first milling cutter 1:

[0100]

[0101]

[0102] In formula (8) and formula (9), dF t，1 (t, z i ), dF r，1 (t, z i ), and dF a，1 (t, z i ) are the tangential force, radial force, and axial force of the i-th axial infinitesimal of all teeth of the first milling cutter 1 at the current time t, N1 is the number of teeth of the first milling cutter 1, K tc，1 , K rc，1 , and K ac，1 are the tangential cutting force coefficient, radial cutting force coefficient, and axial cutting force coefficient of the first milling cutter 1, dz1 is the axial height of the infinitesimal of the first milling cutter 1, dF x，1 (t, z i ), dF y，1 (t, z i ), and dF z，1 (t, z i ) are the X-direction force, Y-direction force, and Z-direction force of the i-th axial infinitesimal of all teeth of the first milling cutter 1 at the current time t, with the bottom of the first milling cutter 1 as the origin of the three-dimensional coordinate system, the feed direction of the first milling cutter 1 is the X-axis direction, the Y-axis direction is perpendicular to the feed direction, and the Z-axis direction is away from the thin-walled part 3.

[0103] According to the literature [3], for example, the tangential cutting force coefficient K tc，1 , radial cutting force coefficient K rc，1 , and axial cutting force coefficient K ac，1 of the first milling cutter 1 and the tangential cutting force coefficient K tc，2 , radial cutting force coefficient K rc，2 , and axial cutting force coefficient K ac，2 of the second milling cutter 2 are obtained by cutting test. In other embodiments, the above-mentioned cutting force coefficients can also be obtained by numerical calculation, which is not limited in the implementation of the present application.

[0104] Step 5: Model for calculating the dynamic cutting force acting on the two- sided milling cutter:

[0105] The model expression of the dynamic cutting force on the first milling cutter 1 is as follows,

[0106]

[0107] In formula (12), F x，1 (t), F y，1 (t) and F z，1 (t) are the X-direction force, Y-direction force and Z-direction force of all teeth of the first milling cutter 1 at the current time t, and the elements of the dynamic milling force direction coefficient matrix are expressed as follows:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] The model of the dynamic cutting force on the second milling cutter 2 is expressed as follows:

[0118]

[0119] In formula (13), F x，2 (t), F y，2 (t) and F z，2 (t) are the X-direction force, Y-direction force and Z-direction force of all teeth of the second milling cutter 2 at the current time t, and the elements of the dynamic milling force direction coefficient matrix are expressed as follows:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] In the above element expression of the directional coefficient matrix, a p，1 is the axial cutting depth of the first milling cutter (1), a p，2 is the axial cutting depth of the second milling cutter 2.

[0130] By comparing a 13 and b 13 、a 23 and b 23 、a 33 and b 33 It can be seen that the vibration of the thin-walled part 3 in the thickness direction increases the dynamic cutting force direction coefficient on one side of the thin-walled part 3, while the dynamic cutting force direction coefficient on the other side decreases.

[0131] Example 2

[0132] The dynamic modeling method of the double-sided milling processing system of thin-walled parts provided in this embodiment is as follows: Figure 1 As shown, the milling cutters located on both sides of the thin-walled part 1 are respectively recorded as the first milling cutter 1 and the second milling cutter 2. The method includes the following steps:

[0133] Step 1: Perform modal tests on the first milling cutter 1, the second milling cutter 2, and the thin-walled part 3 using the standard hammer impact method to obtain the modal mass, damping, and stiffness of the first milling cutter 1 and the second milling cutter 2 in the radial direction; the modal mass m of the thin-walled part 3 in the thickness direction z，w , damping c z，w and stiffness k z，w .

[0134] The radial modal mass of the first milling cutter 1 includes the X-direction modal mass m x，1 and the Y-direction modal mass m y，1 The radial damping of the first milling cutter 1 includes the X-direction damping c x，1 and Y-direction damping c y，1 The radial stiffness of the first milling cutter 1 includes the X-direction damping k x，1 and Y-direction damping k y，1 .

[0135] The radial modal mass of the second milling cutter 2 includes the X-direction modal mass m x，2 and the Y-direction modal mass m y，2 The radial damping of the second milling cutter 2 includes the X-direction damping c x，2 and Y-direction damping cy，2 The radial stiffness of the second milling cutter 2 includes X-direction damping k x，2 and Y-direction damping k y，2 .

[0136] Step 2: Calculate the dynamic cutting forces of the first milling cutter 1 and the second milling cutter 2 using the model obtained by the dynamic cutting force modeling method of the thin-walled part double-sided milling system according to any one of claims 1 to 2, including the X-direction force F x，1 (t), Y-direction force F y，1 (t), and Z-direction force F z，1 (t) of all teeth of the first milling cutter 1 at the current time t, and the X-direction force F x，2 (t), Y-direction force F y，2 (t), and Z-direction force F z，2 (t) of all teeth of the second milling cutter 2 at the current time t.

[0137] Step 3: Establish the dynamic control equation of the thin-walled part double-sided milling system:

[0138]

[0139] According to the full-discrete method in the time domain, the above control equation is solved for stability to obtain a stability blade diagram considering the coupling effect between the radial vibration of the cutter and the vibration in the thickness direction of the thin-walled part 3.

[0140] It can be understood that, in order to offset the cutting forces on both sides of the thin-walled part 3, the geometric structure parameters of the first milling cutter 1 and the second milling cutter 2 can be set to be consistent, and the milling parameters of the first milling cutter 1 and the second milling cutter 2 are also set to be consistent in the thin-walled part double-sided milling test.

[0141] In this embodiment, the above cutting force and dynamic modeling method of the thin-walled part double-sided milling system of the application is further illustrated by the following parameters.

[0142] First, the formula

[0143]

[0144] can be arranged as

[0145]

[0146] where the natural frequency the damping ratio The above formula can be further arranged as

[0147]

[0148] Exemplarily, the first milling cutter 1 and the second milling cutter 2 are both bull-nose end milling cutters, the modal mass m x，1 of the first milling cutter 1 in the X direction is 0.514 kg, the natural frequency ω nx，1 is 1413.062 rad / s, and the damping ratio is 0.022, the modal mass m y，1 of the first milling cutter 1 in the Y direction is 0.602 kg, the natural frequency ω ny，1 is 1414.071 rad / s, and the damping ratio is 0.021, the modal mass m x，2 of the second milling cutter in the 2X direction is 0.516 kg, the natural frequency ω nx，2 is 1425.053 rad / s, and the damping ratio is 0.024, the modal mass m y，2 of the first milling cutter 1 in the Y direction is 0.606 kg, the natural frequency ω ny，2 is 1430.068 rad / s, and the damping ratio is 0.030, the modal mass m w of the thin-walled part 3 is 37.9151 kg, the natural frequency ω nw is 88.1491 rad / s, and the damping ratio is 0.024. The tangential cutting force coefficient, the radial cutting force coefficient and the axial cutting force coefficient of the first milling cutter 1 and the second milling cutter 2 are all 780.2 × 10 6 N / m 2 , 480.2 × 10 6 N / m 2 and 200.5 × 10 6 N / m 2 . The number of teeth of the first milling cutter 1 and the second milling cutter 2 is both 3, the diameter is both 20 mm, the helix angle is both 38°, and the circular arc radius is both 5 mm. The milling process is reverse milling, the cutting-in angle is 0°, and the cutting-out angle is 180°.

[0149] The time required for half a period of vibration of the thin-walled part 3 can be calculated from the natural frequency of the thin-walled part 3 described above, which is 0.0356 seconds. In order to ensure stability, it is necessary to set the spindle speed to be 562 rpm or above within half a period of vibration of the thin-walled part 3. According to the literature [4], the control equation is solved for stability in the time domain by using the full-discrete method, and the predicted stability lobe diagram is as shown in Figure 2 .

[0150] It can be seen from the above embodiments that the thin-walled part double-sided milling processing system cutting force and dynamics modeling method provided by the embodiments firstly considers the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part 3 to calculate the dynamic cutting thickness corresponding to each blade microelement of the two-side milling cutter, and then calculates the dynamic cutting force acting on the entire tool-thin-walled part 3 system. The dynamics modeling method applies the cutting forces perpendicular to the thickness direction of the thin-walled part 3 on the two-side milling cutter, and applies the resultant force of the cutting forces in the thickness direction of the thin-walled part 3 on the thin-walled part 3 itself, establishes the dynamics control equation of the thin-walled part 3 double-sided milling processing system, and solves the equation for stability. Compared with the given literature, the embodiments consider the coupling effect between the tool radial vibration and the vibration in the thickness direction of the thin-walled part 3 to establish the cutting force and dynamics model of the thin-walled part 3 double-sided milling processing system, and improve the prediction accuracy of the thin-walled part 3 double-sided milling stability lobe diagram.

[0151] Although the present application is described above with reference to the drawings, the present application is not limited to the specific embodiments described above, and the specific embodiments described above are merely illustrative, but not restrictive, and those skilled in the art can make many modifications under the inspiration of the present application without departing from the purpose of the present application, and these all belong to the protection of the present application.

Claims

1. A dynamic cutting force modeling method for a double-sided milling system of a thin-walled workpiece, characterized in that: The steps include: Step 1: Within a half cycle of vibration of the thin-walled part (3), the blade is microelemented in the axial height, and the dynamic cutting thickness of each blade of the milling cutter located on both sides of the thin-walled part (3) is calculated. The milling cutters located on both sides of the thin-walled part (3) are respectively recorded as the first milling cutter (1) and the second milling cutter (2): Dynamic cutting thickness of each cutting edge of the first milling cutter (1): Dynamic cutting thickness of each cutting edge of the second milling cutter (2): In formula (1) and formula (2): h 1,j (t,z i ) is the dynamic cutting thickness of the i-th axial microelement on the j-th tooth of the first milling cutter (1) at the current time t, h 2,j (t,z i ) is the dynamic cutting thickness at the i-th axial microelement on the j-th tooth of the second milling cutter (2) at the current moment t; φ 1,j is the radial cutting angle corresponding to the i-th axial microelement on the j-th tooth of the first milling cutter (1) at the current time t, φ 2,j is the radial cutting angle corresponding to the i-th axial microelement on the j-th tooth of the second milling cutter (2) at the current time t, κ 1,j is the axial cutting angle corresponding to the i-th axial microelement on the j-th tooth of the first milling cutter (1) at the current time t, κ 2,j is the axial cutting angle corresponding to the i-th axial infinitesimal point on the j-th tooth of the second milling cutter (2) at the current moment t; x1(t) and y1(t) are the dynamic displacements of the first milling cutter (1) when the current tooth passes through the tooth at time t, x2(t) and y2(t) are the dynamic displacements of the second milling cutter (2) when the current tooth passes through the tooth at time t, x1(t-τ 1,j ) and y1(t-τ 1,j ) is the moment t-τ of the previous tooth of the first milling cutter (1) 1,j Dynamic displacement of the tooth, x2(t-τ 2,j ) and y2(t-τ 2,j ) is the moment t-τ of the previous tooth of the second milling cutter (2) 2,j Dynamic displacement across the tooth, z w (t) is the dynamic displacement of the thin-walled part (3) at time t, z w (t-τ 1,j ) and z w (t-τ 2,j ) are respectively the time t-τ of the thin-walled part (3) 1,j and t-τ 2,j Dynamic displacement; τ 1,j is the time required for the first milling cutter (1) to cut to the same radial cutting angle as the previous tooth of the first milling cutter (1), τ 2,j The time required for the current tooth of the second milling cutter (2) to cut to the same radial cutting angle as the previous tooth of the second milling cutter (2); Step 2: Calculate the entry and exit angles of the two-sided milling cutter during the down milling and up milling process: Calculation formula for cutting-in angle and cutting-out angle in down milling process: The calculation formula for the cutting angle and cutting angle in the reverse milling process is: In formula (3) to formula (6), is the entry angle, is the cut-out angle, a e is the radial cutting depth, R is the cutter radius; Step 3: Calculate the window function corresponding to each cutting edge of the double-sided milling cutter: In formula (7), g(φ p,j ) is the window function corresponding to the radial tangent angle at the i-th axial element on the j-th tooth of the milling cutter p at the current time t; p = 1, 2, 1 refers to the first milling cutter; 2 refers to the second milling cutter; Step 4: Calculate the dynamic cutting force corresponding to each edge element of the two-sided milling cutter: Regarding the first milling cutter (1): In formula (8) and formula (9), dF t,1 (t,z i ), dF r,1 (t,z i ) and dF a,1 (t,z i ) are respectively the tangential force, radial force and axial force at the i-th axial element of all teeth of the first milling cutter (1) at the current moment t, N1 is the number of teeth of the first milling cutter (1), K tc,1 , K rc,1 and K ac,1 are the tangential cutting force coefficient, radial cutting force coefficient and axial cutting force coefficient of the first milling cutter (1), dz1 is the microelement axial height of the first milling cutter (1), dF x,1 (t,z i ), dF y,1 (t,z i ) and dF z,1 (t,z i ) is the X-direction force, Y-direction force, and Z-direction force at the i-th axial microelement of all teeth of the first milling cutter (1) at the current moment t, with the bottom of the first milling cutter (1) as the origin of the three-dimensional coordinate system, the feed direction of the first milling cutter (1) is the X-axis direction, the direction perpendicular to the feed direction is the Y-axis direction, and the direction facing away from the thin-walled workpiece (3) is the Z-axis direction; For the second milling cutter (2): In formula (10) and formula (11), dF t,2 (t,z i ), dF r,2 (t,z i ) and dF a,2 (t,z i ) are respectively the tangential force, radial force and axial force at the i-th axial element of all the teeth of the second milling cutter (2) at the current moment t, N2 is the number of teeth of the second milling cutter (2), K tc,2 , K rc,2 and K ac,2 are the tangential cutting force coefficient, radial cutting force coefficient and axial cutting force coefficient of the second milling cutter (2), dz2 is the microelement axial height of the second milling cutter (2), dF x,2 (t,z i ), dF y,2 (t,z i ) and dF z,2 (t,z i ) is the X-direction force, Y-direction force and Z-direction force at the i-th axial microelement of all teeth of the second milling cutter (2) at the current moment t, with the bottom of the second milling cutter (2) as the origin of the three-dimensional coordinate system, the feed direction of the second milling cutter (2) is the X-axis direction, the direction perpendicular to the feed direction is the Y-axis direction, and the direction facing away from the thin-walled workpiece (3) is the Z-axis direction; Step 5: Model for calculating the dynamic cutting forces acting on the double-sided milling cutter: The model expression of the dynamic cutting force on the first milling cutter (1) is as follows: In formula (12), F x,1 (t), F y,1 (t) and F z,1 (t) is the X-direction force, Y-direction force and Z-direction force of all teeth of the first milling cutter (1) at the current moment t, wherein the elements of the dynamic milling force direction coefficient matrix are expressed as follows: The model expression of the dynamic cutting force of the second milling cutter (2) is as follows: In formula (13), F x,2 (t), F y,2 (t) and F z,2 (t) is the X-direction force, Y-direction force and Z-direction force of all teeth of the second milling cutter (2) at the current moment t, wherein the elements of the dynamic milling force direction coefficient matrix are expressed as follows: In the above element expression of the directional coefficient matrix, a p,1 is the axial cutting depth of the first milling cutter (1), a p,2 is the axial cutting depth of the second milling cutter (2).

2. The dynamic cutting force modeling method for a double-sided milling system for thin-walled parts according to claim 1 is characterized in that: The tangential cutting force coefficient K of the first milling cutter (1) tc,1 , radial cutting force coefficient K rc,1 and axial cutting force coefficient K ac,1 Obtained by numerical calculation or cutting test; the tangential cutting force coefficient K of the second milling cutter (2) tc,2 , radial cutting force coefficient K rc,2 and axial cutting force coefficient K ac,2 Obtained by numerical calculation or cutting test.

3. A dynamic modeling method for double-sided milling of thin-walled parts, characterized in that: The milling cutters located on both sides of the thin-walled part (3) are respectively referred to as a first milling cutter (1) and a second milling cutter (2). The method comprises the following steps: Step 1: Perform modal testing on the first milling cutter (1), the second milling cutter (2) and the thin-walled part (3) by a standard hammer impact method to obtain the modal mass, damping and stiffness of the first milling cutter (1) and the second milling cutter (2) in the radial direction; the modal mass m of the thin-walled part (3) in the thickness direction z,w , damping c z,w and stiffness k z,w ; The radial modal mass of the first milling cutter (1) includes the X-direction modal mass m x,1 and the Y-direction modal mass m y,1 The radial damping of the first milling cutter (1) includes the X-direction damping c x,1 and Y-direction damping c y,1 The radial stiffness of the first milling cutter (1) includes the X-direction damping k x,1 and Y-direction damping k y,1 , The radial modal mass of the second milling cutter (2) includes the X-direction modal mass m x,2 and the Y-direction modal mass m y,2 The radial damping of the second milling cutter (2) includes the X-direction damping c x,2 and Y-direction damping c y,2 The radial stiffness of the second milling cutter (2) includes the X-direction damping k x,2 and Y-direction damping k y,2 ; Step 2: Calculate the dynamic cutting forces of the first milling cutter (1) and the second milling cutter (2) using the model obtained by the dynamic cutting force modeling method of the thin-walled double-sided milling system according to any one of claims 1 to 2, including the X-direction force F of all teeth of the first milling cutter (1) at the current time t. x,1 (t), Y direction force F y,1 (t) and Z-direction force F z,1 (t) and the X-direction force F of all teeth of the second milling cutter (2) at the current moment t x,2 (t), Y direction force F y,2 (t) and Z-direction force F z,2 (t); Step 3: Establish the dynamic control equation of the double-sided milling system of the thin-walled workpiece: The stability of the control equations is solved by a fully discrete method in the time domain, and a stability lobe diagram is obtained that takes into account the coupling effect between the radial vibration of the tool and the vibration in the thickness direction of the thin-walled part (3).

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