A cross-scale hybrid milling force modeling method

Abstract

The present invention discloses a cross-scale hybrid milling force modeling method, comprising: 1. establishing the machine tool bed, workpiece and tool coordinate systems respectively, and establishing the milling blade trajectory equation under ideal conditions. 2. establishing the milling blade trajectory equation under tool wear based on tool runout. 3. establishing the milling blade trochoidal trajectory equation considering the minimum milling thickness and elastic recovery of the tool. 4. establishing a cross-scale instantaneous milling thickness model from micro to macro based on the principle of homogeneous coordinate transformation and comprehensive consideration of the influence of various factors on the instantaneous milling thickness. 5. establishing a cross-scale hybrid milling force model under actual milling conditions. The present invention combines various factors that affect the milling process, considers the influence of tool wear and minimum milling thickness on the milling blade trochoidal trajectory and elastic recovery, and establishes a hybrid milling force model that can be applied to both macro and micro milling states, thereby improving the prediction accuracy and versatility of the milling force model.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed micro and conventional milling processing, and more particularly to a cross-scale hybrid milling force modeling method. Background Art

[0002] Precision milling is a major metal cutting process that can produce high-precision end-user components. It can realize the processing of parts with complex geometric structures, especially some difficult-to-cut materials, and can meet the precision requirements of industries such as aviation, aerospace, precision instruments and medical devices. In high-speed and high-precision milling, milling force is one of the most important process parameters. Accurate feedback of milling force information is of great significance to ensure the stability of the processing process. However, in the process of machining some precision parts, not only the macro-milling state will appear, but also it is necessary to cross the scale to another micro-milling state. Scholars have conducted extensive research on the prediction model of milling force, but there is still a lack of research on the establishment of a universal cross-scale milling force model from macro-milling to micro-milling. Summary of the Invention

[0003] In order to solve the problem that the existing milling force model is not universal, the present invention establishes a cross-scale hybrid milling force modeling method, in order to establish a mechanical model suitable for the macro-milling to micro-milling process by analyzing the influence of multiple factors on different milling states, thereby improving the prediction accuracy and universality of the milling force model, and further improving the accuracy of the workpiece processing.

[0004] In order to achieve the above-mentioned object, the present invention adopts the following technical solutions:

[0005] The cross-scale hybrid milling force modeling method of the present invention is characterized in that it includes the following steps:

[0006] Step 1: Establish the coordinate systems of the machine bed, workpiece, and tool respectively, and establish the milling edge trajectory equation under ideal conditions;

[0007] Step 2: Based on tool runout, establish the milling edge trajectory equation under tool wear;

[0008] Step 3: Considering the minimum milling thickness and elastic recovery of the tool, establish the milling edge trochoid trajectory equation;

[0009] Step 4: Based on the principle of homogeneous coordinate transformation and taking into account the influence of multiple factors on the instantaneous milling thickness, a cross-scale instantaneous milling thickness model from micro to macro is established;

[0010] Step 5: Establish a cross-scale hybrid milling force model under actual milling conditions.

[0011] The cross-scale hybrid milling force modeling method of the present invention is also characterized in that step 1 comprises:

[0012] Step 1.1, take the machine origin O as the origin of the coordinate system, the machine tool horizontal feed direction as the X axis direction, the longitudinal feed direction as the Y axis direction, and the vertical feed direction as the Z axis direction, and establish the reference coordinate system O-XYZ; W -X W Y W Z W Fix it on the workpiece to be processed and set the tool coordinate system O T -X T Y T Z T Fixed on the tool center, the spindle coordinate system O S -X S Y S Z S Fixed on the spindle, the machine tool moving axis coordinate system is recorded as O R -X R Y R Z R , the directions of the various coordinate systems established are consistent with the direction of the reference coordinate system O-XYZ;

[0013] Step 1.2: When the machine tool is stationary, use formula (1) to obtain the tool coordinate system O T -X T Y T Z T The homogeneous coordinate transformation matrix of any point P on the milling edge:

[0014] (1)

[0015] In formula (1), R is the milling radius of the tool, k is the number of milling edges of the tool, k = 1, 2, ..., K, K is the total number of milling edges of the tool, is the tool radial lag angle, is the position angle of any point P on the milling edge; Indicates the coordinate position of point P under ideal conditions;

[0016] Step 1.3: When the tool is milling, use formula (2) to obtain the coordinates of any point P on the kth milling edge: From the tool coordinate system O T -X T Y T Z T Transform to workpiece coordinate system O W -X W Y W Z W The coordinates below :

[0017] (2)

[0018] In formula (2), The coordinate system O of the machine tool moving axis R -X R Y R Z R Relative to the workpiece coordinate system O W -X W Y W Z W The translation transformation matrix, The main axis coordinate system O S -X S Y S Z S Relative to the machine tool moving axis coordinate system O R -X R Y R Z R The rotation transformation matrix, is the tool coordinate system O T -X T Y T Z T Relative to the principal axis coordinate system O S -X S Y S Z S The transformation matrix of

[0019] Step 1.4: Use formula (3) to obtain the workpiece coordinate system O W -X W Y W Z W The trajectory equation of any point P on the milling edge of the tool is:

[0020] (3)

[0021] In formula (3), 、 、 They are workpiece coordinate system O W -X W Y W Z W Feed speed in X, Y and Z directions, is the angular velocity of the tool during rotation, and t is the milling time.

[0022] The step 2 includes:

[0023] Step 2.1: Considering the tool runout, use formula (4) to obtain the workpiece coordinate system O W -X W Y W ZW In the figure, the trajectory equation of any point P on the milling edge of the tool is:

[0024] (4)

[0025] In formula (4), is the tool runout length, is the tool runout angle, Indicates the coordinate position of point P when tool runout is considered;

[0026] Step 2.2: Use formula (5) to construct the tool flank wear VB and tool radial wear The relational expression is:

[0027] (5)

[0028] In formula (5), is the back angle of the tool, is the rake angle of the tool;

[0029] Step 2.3: Based on tool wear, use formula (6) to obtain the workpiece coordinate system O W -X W Y W Z W In the equation, the trajectory equation of any point P on the milling edge under tool wear is:

[0030] (6)

[0031] In formula (6), Indicates the coordinate position of point P based on tool runout and taking tool wear into account.

[0032] The step 3 comprises:

[0033] Step 3.1: During micro-milling, use formula (7) to obtain the tool elastic recovery :

[0034] (7)

[0035] In formula (7), E is the elastic modulus of the workpiece, is the yield limit of the workpiece;

[0036] Step 3.2: Considering the minimum milling thickness and elastic recovery of the tool, use formula (8) to obtain the trajectory equation of any point P on the tool milling edge:

[0037] (8)

[0038] In formula (8), Indicates the coordinate position of point P when considering the minimum milling thickness and elastic recovery amount of the tool.

[0039] The step 4 comprises:

[0040] Step 4.1: When the tool is milling and producing chips, use formula (9) to obtain the value of any point P on the k-th cutting edge of the tool at the k-th moment: The milling trajectory equation is:

[0041] (9)

[0042] In formula (9), Indicates the milling time of point P on the milling edge The coordinate position at time

[0043] Step 4.2: Use formula (10) to obtain the value of any point P on the km-th cutting edge of the tool at the km-th moment: The milling motion trajectory equation is:

[0044] (10)

[0045] In formula (10), Indicates the milling time of point P on the milling edge The coordinate position at time

[0046] Step 4.3: Use formula (11) to obtain the instantaneous milling thickness h of the ball end mill under the influence of comprehensive factors:

[0047] (11)

[0048] In formula (11), d is the distance between the tool center of the kth milling edge and the tool center of the k-1th milling edge, and is obtained from formula (12), is the positive angle between the two centers, and is obtained from formula (13):

[0049] (12)

[0050] (13)

[0051] In formula (12) and formula (13), Indicates that the center of the kth milling edge is in the workpiece coordinate system O W -X W Y W Z W The point on Indicates that the center of the k-1th milling edge is in the workpiece coordinate system O W -X W Y W ZW The point on

[0052] Step 4.4: During tool milling, use Equation (14) to establish a cross-scale instantaneous milling thickness model from micro to macro:

[0053] (14)

[0054] In formula (14), represents the instantaneous milling thickness of the kth cutting edge in milling state i, i∈{0,1}, when i=0, it represents the macro milling state, and when i=1, it represents the micro milling state.

[0055] The step 5 comprises:

[0056] Step 5.1: According to the mechanical analysis method, the milling edge is discretized into a set of milling elements along the axial direction of the tool. The position angle of any milling element on the kth cutting edge is obtained using formula (15). Tangential force at , radial force and axial force :

[0057] (15)

[0058] In formula (15), 、 、 are the position angles of any milling unit on the kth cutting edge Tangential, radial and axial milling force coefficients at ; is represented by an oblique cutting element, and ,in, is the helix angle of the milling cutter, is the milling cutter rotation angle;

[0059] Step 5.2: Based on the homogeneous coordinate transformation, use formula (16) to obtain the workpiece coordinate system O W -X W Y W Z W The milling force of the kth cutting edge in any milling element along the X, Y, and Z directions is :

[0060] (16)

[0061] Step 5.3: Use formula (17) to obtain the tool coordinate system O W -X W Y W Z W Cross-scale hybrid milling forces in the X, Y, and Z directions along the lower edge :

[0062] (17)

[0063] In formula (17), and Represents the milling cutter rotation angle The upper and lower limits of .

[0064] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the hybrid milling force modeling method, and the processor is configured to execute the program stored in the memory.

[0065] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the steps of the hybrid milling force modeling method when the computer program is run by a processor.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. The present invention adopts a spatial analytical geometry method. Based on the analysis of the geometric relationship between the milling edge position, the pre-processed workpiece shape and the milling force direction, combined with the tool runout and wear effects, an instantaneous milling thickness model of the milling force is established. The improved milling thickness model can accurately reflect the real milling dynamics and the wear of each tool tooth.

[0068] 2. The present invention comprehensively considers the influence of minimum milling thickness, elastic recovery and tool runout on milling force modeling, and also takes tool wear into account in the milling force model, thereby solving the problem of insufficient versatility of milling force and improving the accuracy and versatility of the milling force model. At the same time, the accurate prediction of milling force can feedback the tool milling state information, thereby further inferring tool deformation and energy loss.

[0069] 3. In the precision milling of complex geometric parts, there are both macro-milling states and micro-milling states. Therefore, the present invention considers the multiple factors and cross-scale effects in the milling process and establishes a hybrid milling force model. This model is not only applicable to macro-milling, but also to micro-milling. It can be applied under various processing conditions and has important theoretical and practical significance for improving part processing accuracy and optimizing processing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of the hybrid milling force modeling method of the present invention;

[0071] Figure 2 is the milling motion coordinate system of the ball-end milling cutter;

[0072] Figure 3a This is a schematic diagram of the ball end mill runout;

[0073] Figure 3b Schematic diagram of the wear of the ball end mill;

[0074] Figure 4 Schematic diagram of elastic recovery between the milling cutter and the workpiece;

[0075] Figure 5 Schematic diagram of the tool milling process considering tool runout, wear, minimum chip thickness and elastic recovery;

[0076] Figure 6 Schematic diagram of milling microelement using ball end mill. DETAILED DESCRIPTION

[0077] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Referring to the accompanying drawings, a flow chart of a cross-scale hybrid milling force modeling method is shown in FIG. Figure 1 As shown, the following steps are included:

[0079] Step 1: Establish the coordinate systems of the machine bed, workpiece and tool respectively, and establish the milling edge trajectory equation under ideal conditions.

[0080] Step 1.1: During the milling process, the milling cutter not only moves in the feed direction, but also has its own rotational motion. A three-dimensional coordinate system is established in combination with the tool motion, such as Figure 2 As shown, the machine origin O is used as the origin of the coordinate system, the machine tool horizontal feed direction is the X-axis direction, the longitudinal feed direction is the Y-axis direction, and the vertical feed direction is the Z-axis direction to establish the reference coordinate system O-XYZ. Workpiece coordinate system O W -X W Y W Z W Fixed on the workpiece to be processed, tool coordinate system O T -X T Y T Z T Fixed on the tool center, spindle coordinate system O S -X S Y S Z S Fixed on the spindle, the machine tool moving axis coordinate system is O R -X R Y R Z R The directions of the various established coordinate systems are consistent with the direction of the reference coordinate system O-XYZ.

[0081] Step 1.2: When the machine tool is stationary, use formula (1) to obtain the tool coordinate system OT -X T Y T Z T The homogeneous coordinate transformation matrix of any point P on the milling edge:

[0082] (1)

[0083] In formula (1), R is the milling radius of the tool, k is the number of milling edges of the tool, k = 1, 2, ..., K, K is the total number of milling edges of the tool, is the tool radial lag angle, is the position angle of any point P on the milling edge; Indicates the coordinate position of point P under ideal conditions

[0084] Step 1.3: When the tool is milling, use formula (2) to obtain the coordinates of any point P on the kth milling edge: From the tool coordinate system O T -X T Y T Z T Transform to workpiece coordinate system O W -X W Y W Z W The coordinates below :

[0085] (2)

[0086] In formula (2), The main axis translation coordinate system O R -X R Y R Z R Relative to the workpiece coordinate system O W -X W Y W Z W The translation transformation matrix, The main axis rotation coordinate system O S -X S Y S Z S Relative to the principal axis translation coordinate system O R -X R Y R Z R Rotation transformation matrix, is the tool coordinate system O T -X T Y T Z T Rotate the coordinate system O relative to the main axis S -X S Y S ZS The transformation matrix.

[0087] Step 1.4: Use formula (3) to obtain the workpiece coordinate system O W -X W Y W Z W The trajectory equation of any point P on the milling edge of the tool is:

[0088] (3)

[0089] In formula (3), 、 、 are the feed rates in the X, Y and Z directions respectively, is the angular velocity of the tool during rotation, and t is the time.

[0090] Step 2: Based on tool runout, establish the milling edge trajectory equation under tool wear:

[0091] Step 2.1: In the precision machining of small parts, the feed rate per tooth is generally in the micron level. Due to errors in the tool installation and manufacturing process and the deformation of the tool under stress during the high-speed rotation of the spindle during milling, these factors will eventually cause the tool to jump, thereby affecting the machining accuracy. Figure 3a As shown in Figure 1, due to the tool runout, its rotation center does not coincide with the rotation center of the machine tool spindle, and there is a certain deviation. Considering the tool runout, the workpiece coordinate system O is obtained using formula (4): W -X W Y W Z W In the figure, the trajectory equation of any point P on the milling edge of the tool is:

[0092] (4)

[0093] In formula (4), is the tool runout length, is the tool runout angle, Indicates the coordinate position of point P considering tool runout.

[0094] Tool wear has a nonlinear effect on milling force. As milling continues, tool wear begins to slowly appear. When the tool wear value accumulates to a certain amount, it will accelerate the friction between the tool and the workpiece, further leading to a rapid increase in milling force. At the same time, due to the existence of tool runout, the degree of wear of each tool tooth shows a different change pattern. The relationship between tool flank wear and tool radial wear is as follows: Figure 3b As shown in the figure, the tool flank wear VB and tool radial wear are constructed using formula (5). The relational expression is:

[0095] (5)

[0096] In formula (5), is the tool back angle, is the tool rake angle.

[0097] Step 2.3: Based on tool wear, use formula (6) to obtain the workpiece coordinate system O W -X W Y W Z W In the equation, the trajectory equation of any point P on the milling edge under tool wear is:

[0098] (6)

[0099] In formula (6), Indicates the coordinate position of point P based on tool runout and considering tool wear.

[0100] Step 3: Considering the minimum milling thickness and elastic recovery of the tool, establish the trochoid trajectory equation on the milling edge:

[0101] Step 3.1: In conventional milling, due to the large milling thickness, the milling edge radius of the tool is much smaller than the milling thickness. Therefore, the influence of the milling edge radius is often ignored when establishing the milling force model. In the micro-milling process, when the milling thickness is small and smaller than the minimum milling thickness, the tool will produce a tool elastic recovery. ,like Figure 4 As shown in the figure, according to the contact width between the tool and the workpiece and the geometric form of the tool deformation, the tool elastic recovery is obtained using formula (7): for:

[0102] (7)

[0103] In formula (7), E is the elastic modulus of the workpiece, is the yield limit of the workpiece, and R is the milling radius of the tool.

[0104] Step 3.2: Considering the minimum milling thickness and elastic recovery of the tool, use formula (8) to obtain the trajectory equation of any point P on the tool milling edge:

[0105] (8)

[0106] In formula (8), Indicates the coordinate position of point P when considering the minimum milling thickness and elastic recovery of the tool.

[0107] Step 4: Based on the principle of homogeneous coordinate transformation and taking into account the influence of multiple factors on the instantaneous milling thickness, a cross-scale instantaneous milling thickness model from micro to macro is established:

[0108] Step 4.1. Due to the influence of tool runout, wear, minimum milling thickness and elastic recovery, the theoretical instantaneous milling thickness is inconsistent with the actual instantaneous milling thickness. The theoretical instantaneous milling thickness is defined as the minimum distance between the current tool tip trajectory and the surface generated by the previous tooth in one cycle. The trajectory of the point is as follows Figure 5 As shown. Point P is the position angle on the kth cutting edge. , the rotation angle is One point, The starting point is the Y axis. The direction is the rotation angle of the terminal edge; The kth cutting edge is rotated at an angle of The tool center at time The km-th cutting edge is at a rotation angle of The tool center at the time Figure 5 The geometric relationship shown in the figure shows that when the tool mills and produces chips, the equation (9) is used to obtain the value of any point P on the kth cutting edge of the tool at the kth moment. The milling trajectory equation is:

[0109] (9)

[0110] In formula (9), Indicates the milling time of point P on the milling edge The coordinate position at time.

[0111] Step 4.2: Accordingly, use formula (10) to obtain the value of any P on the km-th milling edge of the tool at time The milling motion trajectory equation at the moment is:

[0112] (10)

[0113] In formula (10), Indicates the milling time of point P on the milling edge The coordinate position at time.

[0114] Step 4.3: Use formula (11) to derive the instantaneous milling thickness h of the ball end mill under the influence of comprehensive factors:

[0115] (11)

[0116] In formula (11), d is the distance between the tool center of the kth milling edge and the tool center of the k-1th milling edge, and is obtained from formula (12), is the positive angle between the two circle centers, and is obtained from formula (13):

[0117] (12)

[0118] (13)

[0119] In formula (11) and formula (12), Indicates that the center of the kth milling edge is in the workpiece coordinate system O W -X W Y W Z W The point on Indicates that the center of the K-1th milling edge is in the workpiece coordinate system O W -X W Y W Z W The point on

[0120] Step 4.4: When the tool is milling, there are two states: one is macro milling and the other is micro milling. When machining the workpiece, the milling state may cross the scale from macro milling to micro milling state. The instantaneous milling thickness model from micro to macro cross-scale is established using formula (14):

[0121] (14)

[0122] In formula (14), represents the instantaneous milling thickness of the kth cutting edge in milling state i, i∈{0,1}, when i=0, it represents the macro milling state, and when i=1, it represents the micro milling state.

[0123] Step 5: Figure 6 As shown in Figure 2, a cross-scale hybrid milling force model is established under actual milling conditions:

[0124] Step 5.1: According to the mechanical analysis method, the milling force of the tool can be expressed as the sum of the forces of the milling elements. At this time, each cutting unit can be regarded as an orthogonal or oblique cutting process, such as Figure 6 As shown in the figure, the milling edge is discretized into a group of very small milling units along the axial direction of the tool, and the position angle of any milling element on the kth cutting edge is obtained using formula (15). Tangential force at , radial force and axial force :

[0125] (15)

[0126] In formula (15), 、 、 are the tangential, radial and axial milling force coefficients respectively; h i is the instantaneous milling thickness; Represented as an oblique cutting element, ,in is the helix angle of the milling cutter, The rotation angle of the milling cutter.

[0127] Step 5.2: Based on the homogeneous coordinate transformation, use formula (16) to obtain the workpiece coordinate system O W -X W Y W Z W The milling force of the kth cutting edge in any milling element along the X, Y, and Z directions is :

[0128] (16)

[0129] Step 5.3: Integrate the micro-element milling force along the tool axis and sum the micro-element milling forces on each milling edge. Finally, the cross-scale integrated milling force of the tool in the three directions in the workpiece coordinate system is obtained. The tool in the workpiece coordinate system O is obtained using formula (17). W -X W Y W Z W Cross-scale hybrid milling forces in the X, Y, and Z directions along the lower edge :

[0130] (17)

[0131] In formula (17), and Represents the milling cutter rotation angle The upper and lower limits of .

[0132] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0133] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

[0134] This example considers a kinematically-based, cross-scale integrated milling force modeling approach. To better understand the mechanics of precision milling, the impact of key factors on milling forces, such as tool wear, tool runout, elastic deformation, and minimum cutting thickness, is comprehensively considered. Based on milling kinematics, the impact of these factors on instantaneous cutting thickness is comprehensively considered, resulting in a cross-scale hybrid milling force model with good adaptability and predictive accuracy. This hybrid model is applicable not only to macro-milling conditions but also to micro-milling conditions.

Claims

1. A cross-scale hybrid milling force modeling method, characterized in that: The following steps are involved: Step 1: Establish the coordinate systems of the machine bed, workpiece, and tool respectively, and establish the milling edge trajectory equation under ideal conditions; Step 2: Based on tool runout, establish the milling edge trajectory equation under tool wear; Step 3: Considering the minimum milling thickness and elastic recovery of the tool, establish the milling edge trochoid trajectory equation; Step 4: Based on the principle of homogeneous coordinate transformation and taking into account the influence of multiple factors on the instantaneous milling thickness, a cross-scale instantaneous milling thickness model from micro to macro is established; Step 4.1: When the tool is milling and producing chips, use formula (9) to obtain the value of any point P on the k-th cutting edge of the tool at the k-th moment: The milling trajectory equation is: (9) In formula (9), Indicates the milling time of point P on the milling edge The coordinate position at the time of cutting; R is the milling radius of the tool, k is the number of milling edges of the tool, k = 1, 2, ..., K, K is the total number of milling edges of the tool, is the tool radial lag angle, is the position angle of any point P on the milling edge; 、 、 They are workpiece coordinate system O W -X W Y W Z W Feed speed in X, Y and Z directions; is the angular velocity of the tool during rotation; VB is the tool flank wear; is the radial wear of the tool; is the runout angle of the tool; Step 4.2: Use formula (10) to obtain the value of any point P on the km-th cutting edge of the tool at the km-th moment: The milling motion trajectory equation is: (10) In formula (10), Indicates the milling time of point P on the milling edge The coordinate position at time is the elastic recovery amount of the tool; is the runout length of the tool; Step 4.3: Use formula (11) to obtain the instantaneous milling thickness h of the ball end mill under the influence of comprehensive factors: (11) In formula (11), d is the distance between the tool center of the kth milling edge and the tool center of the k-1th milling edge, and is obtained from formula (12), is the positive angle between the two centers, and is obtained from formula (13): (12) (13) In formula (11) and formula (12), Indicates that the center of the kth milling edge is in the workpiece coordinate system O W -X W Y W Z W The point on Indicates that the center of the k-1th milling edge is in the workpiece coordinate system O W -X W Y W Z W The point on Step 4.4: During tool milling, use Equation (11) to establish a cross-scale instantaneous milling thickness model from micro to macro: (14) In formula (11), represents the instantaneous milling thickness of the kth cutting edge in milling state i, i∈{0,1}, when i=0, it represents the macro-milling state, when i=1, it represents the micro-milling state; Step 5: Establish a cross-scale hybrid milling force model under actual milling conditions; Step 5.1: According to the mechanical analysis method, the milling edge is discretized into a set of milling elements along the axial direction of the tool. The position angle of any milling element on the kth cutting edge is obtained using formula (15). Tangential force at , radial force and axial force : (15) In formula (15), 、 、 are the position angles of any milling unit on the kth cutting edge Tangential, radial and axial milling force coefficients at ; is represented by an oblique cutting element, and ,in, is the helix angle of the milling cutter, is the milling cutter rotation angle; Step 5.2: Based on the homogeneous coordinate transformation, use formula (16) to obtain the workpiece coordinate system O W -X W Y W Z W The milling force of the kth cutting edge in any milling element along the X, Y, and Z directions is : (16) Step 5.3: Use formula (17) to obtain the tool coordinate system O W -X W Y W Z W Cross-scale hybrid milling forces in the X, Y, and Z directions along the lower edge : (17) In formula (17), and Represents the milling cutter rotation angle The upper and lower limits of .

2. A cross-scale hybrid milling force modeling method according to claim 1, characterized in that: The step 1 comprises: Step 1.1, take the machine origin O as the origin of the coordinate system, the machine tool horizontal feed direction as the X axis direction, the longitudinal feed direction as the Y axis direction, and the vertical feed direction as the Z axis direction, and establish the reference coordinate system O-XYZ; W -X W Y W Z W Fix it on the workpiece to be processed and set the tool coordinate system O T -X T Y T Z T Fixed on the tool center, the spindle coordinate system O S -X S Y S Z S Fixed on the spindle, the machine tool moving axis coordinate system is recorded as O R -X R Y R Z R , the directions of the various coordinate systems established are consistent with the direction of the reference coordinate system O-XYZ; Step 1.2: When the machine tool is stationary, use formula (1) to obtain the tool coordinate system O T -X T Y T Z T The homogeneous coordinate transformation matrix of any point P on the milling edge: (1) In formula (1), R is the milling radius of the tool, k is the number of milling edges of the tool, k = 1, 2, ..., K, K is the total number of milling edges of the tool, is the tool radial lag angle, is the position angle of any point P on the milling edge; Indicates the coordinate position of point P under ideal conditions; Step 1.3: When the tool is milling, use formula (2) to obtain the coordinates of any point P on the kth milling edge: From the tool coordinate system O T -X T Y T Z T Transform to workpiece coordinate system O W -X W Y W Z W The coordinates below : (2) In formula (2), The coordinate system O of the machine tool moving axis R -X R Y R Z R Relative to the workpiece coordinate system O W -X W Y W Z W The translation transformation matrix, The main axis coordinate system O S -X S Y S Z S Relative to the machine tool moving axis coordinate system O R -X R Y R Z R The rotation transformation matrix, is the tool coordinate system O T -X T Y T Z T Relative to the principal axis coordinate system O S -X S Y S Z S The transformation matrix of Step 1.4: Use formula (3) to obtain the workpiece coordinate system O W -X W Y W Z W The trajectory equation of any point P on the milling edge of the tool is: (3) In formula (3), 、 、 They are workpiece coordinate system O W -X W Y W Z W Feed speed in X, Y and Z directions, is the angular velocity of the tool during rotation, and t is the milling time.

3. The cross-scale hybrid milling force modeling method according to claim 2, characterized in that: The step 2 includes: Step 2.1: Considering the tool runout, use formula (4) to obtain the workpiece coordinate system O W -X W Y W Z W In the figure, the trajectory equation of any point P on the milling edge of the tool is: (4) In formula (4), is the tool runout length, is the tool runout angle, Indicates the coordinate position of point P when tool runout is considered; Step 2.2: Use formula (5) to construct the tool flank wear VB and tool radial wear The relational expression is: (5) In formula (5), is the back angle of the tool, is the rake angle of the tool; Step 2.3: Based on tool wear, use formula (6) to obtain the workpiece coordinate system O W -X W Y W Z W In the equation, the trajectory equation of any point P on the milling edge under tool wear is: (6) In formula (6), Indicates the coordinate position of point P based on tool runout and taking tool wear into account.

4. The cross-scale hybrid milling force modeling method according to claim 3, characterized in that: The step 3 comprises: Step 3.1: During micro-milling, use formula (7) to obtain the tool elastic recovery : (7) In formula (7), E is the elastic modulus of the workpiece, is the yield limit of the workpiece; Step 3.2: Considering the minimum milling thickness and elastic recovery of the tool, use formula (8) to obtain the trajectory equation of any point P on the tool milling edge: (8) In formula (8), Indicates the coordinate position of point P when considering the minimum milling thickness and elastic recovery amount of the tool.

5. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the hybrid milling force modeling method according to any one of claims 1 to 4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the hybrid milling force modeling method according to any one of claims 1 to 4 are executed.

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