Calculation method for five-axis milling cutter-workpiece contact area of ball-end cutter

Abstract

The invention provides a method for calculating a five-axis milling cutter-workpiece contact area of a ball-end cutter, and belongs to the field of numerical control milling machining.The method comprises the steps that an initial cutter-workpiece contact area information set under an initial cutter axis vector is calculated through a three-dimensional orthogonal dexel model; for any cutter axis vector, dispersing the ball head part of the cutter into a plurality of infinitesimal elements along the axial direction and the circumferential direction of the cutter; scanning along the discrete infinitesimal to obtain a discrete infinitesimal endpoint coordinate set in the initial tool-workpiece contact area information set; tool-workpiece contact area boundary point coordinates of the current tool axis vector are calculated according to the discrete infinitesimal end point coordinate set, and then tool-workpiece contact information of the current tool axis vector is obtained through calculation. According to the method, only the cutter shaft in the initial state needs to be subjected to machining simulation to calculate the cutter-workpiece contact area, simulation calculation does not need to be carried out on all cutter shaft vectors in the whole cutting process, the calculation amount is greatly reduced, and the calculation efficiency of the ball-end cutter-workpiece contact area under different cutter shaft vectors is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical control milling processing, and in particular relates to a method for calculating a contact area between a ball-end cutter five-axis milling tool and a workpiece. Background Art

[0002] Five-axis CNC machining has been widely used in the machining of complex structural parts in the aviation and aerospace industries. Cutting force, a key physical parameter in five-axis machining, is not only a criterion for determining tool wear and tool life, but also a foundation for studying the stability of cutting systems. During five-axis milling of curved parts with a ball-end mill, the tool-workpiece contact area exhibits a continuously evolving characteristic as the tool axis vector dynamically changes. Therefore, accurately extracting the tool-workpiece contact area during cutting is key to predicting cutting forces in five-axis milling with a ball-end mill.

[0003] Currently, there are two methods for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling: one is based on the 3D orthogonal Dexel method, which constructs a workpiece model using discrete vectors in three orthogonal directions for calculation; the other uses an improved Z-map method, which generates a point cloud of the tool envelope and screens the contact points to identify the contact area. However, both methods require full simulation of the entire cutting process, resulting in high computational complexity and low efficiency. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, this paper proposes a method for rapidly predicting the contact area based on initial tool axis state simulation, specifically for the case where only the ball end of a ball-end tool is involved in finishing. This method, based on the physical mechanism that tool axis inclination only affects the spatial position of the contact area on the tool surface without changing its geometry, uses a single initial tool axis simulation to deduce the contact area under different tool axis vectors, significantly reducing computational effort and improving efficiency.

[0005] To achieve the above objectives, the technical solutions provided by the present invention are:

[0006] A method for calculating the tool-workpiece contact area in a five-axis milling process using a ball-end cutter is provided, comprising the following steps:

[0007] Step 1: Use the three-dimensional orthogonal Dexel model to calculate the initial tool-workpiece contact area information set O corresponding to the initial tool axis vector CWE , including the contact element height z and the cut-in-cut-out angle θ st -θ ex ;

[0008] Step 2: For any given tool axis vector, the tool ball head is discretized into m and n microelements along the tool axial and circumferential directions respectively. The axial discrete height Δz = R0 / m, R0 is the ball head tool radius, and the circumferential discrete arc Δφ i =2π / n;

[0009] Step 3: Scan the discrete elements along the axial and circumferential directions of the tool to obtain the information set O in the initial tool-workpiece contact area. CWE The discrete element endpoint coordinate set CS m , including the following sub-steps:

[0010] Step 3.1: For the infinitesimal elements with axial and circumferential numbers k and l respectively, calculate the tool coordinate system X corresponding to the current tool axis vector. T,m -Y T,m -Z T,m The endpoint coordinates (x m ,y m ,z m ), calculate its coordinate in the initial tool coordinate system X using coordinate transformation T,O -Y T,O -Z T,O The coordinates (x o ,y o ,z o ):

[0011]

[0012] Where, Indicates the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector, Represents the transformation matrix from the workpiece coordinate system to the initial tool coordinate system;

[0013] Step 3.2, for the infinitesimal endpoint coordinates (x o ,y o ,z o ), calculate the height of the cutting element as z o , and calculate the cutting angle θ:

[0014]

[0015] Where O is the center of the tool’s axial projection; e1 and e2 represent the x coordinates in the plane obtained by the tool’s axial projection and defined with the center of the circle as the origin. T axis and y T The unit vector of the axis; A is the projection point of the discrete element endpoint in the tool axis direction, <OA,e1> represents the angle between the vector OA and e1; <OA,e2> represents the angle between the vector OA and e2; cos -1represents the arc cosine function; [OA,e1] represents the dot product between vectors OA and e1; [OA,e2] represents the dot product between vectors OA and e2; |·| represents the modulus of the vector;

[0016] Step 3.3, determine whether the calculated results of the height and cutting angle of the cutting element are within the initial tool-workpiece contact area information set O CWE If yes, add the endpoint of the current microelement to the coordinate set CS m middle;

[0017] Step 4: According to the discrete element endpoint coordinate set CS m Calculate the coordinates of the tool-workpiece contact area boundary points of the current tool axis vector, and then calculate the tool-workpiece contact information M of the current tool axis vector CWE .

[0018] Furthermore, in step 3, the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector and the transformation matrix from the workpiece coordinate system to the initial tool coordinate system are calculated according to the transformation matrix from the tool coordinate system to the workpiece coordinate system. get, Calculate by the following steps:

[0019] The first step is to calculate the tool axis vector in the workpiece coordinate system when the tool rake angle is α and the side rake angle is β:

[0020] A(α,β)=R(C,α)R(F,β)N

[0021]

[0022] C(α)=cos(α), S(α)=sin(α), V(α)=1-cos(α), C=[c i ,c j ,c k ] T

[0023]

[0024] C(β)=cos(β), S(β)=sin(β), V(β)=1-cos(β), F=[f i ,f j ,f k ] T

[0025] Where F represents the feed direction vector, (f i ,f j ,f k) is the feed direction vector value, R(F,β) represents the generalized rotation matrix when the rotation angle around the vector F is β, C represents the direction vector perpendicular to the feed direction, (c i ,c j ,c k ) represents the direction vector value perpendicular to the feed direction, R(C,α) represents the generalized rotation matrix when the rotation angle around the vector C is α, N represents the normal vector of the workpiece surface, and the feed direction vector F is expressed as:

[0026]

[0027] Where (x1, y1, z1) and (x2, y2, z2) represent the coordinates of the tool tip points at two adjacent tool position points;

[0028] Step 2: Construct the transformation matrix from the local tool coordinate system to the workpiece coordinate system :

[0029]

[0030] Where (x, y, z) represents the three coordinate axes X and Z of the tool coordinate system. T 、Y T 、Z T Unit vector in the workpiece coordinate system.

[0031] Furthermore, in step 2, the discrete element is simplified and replaced by an arc segment at the middle position of the discrete element along the axial direction.

[0032] Furthermore, the coordinates of the tool tip points at adjacent tool position locations are obtained by using the CL file generated by setting the tool rake angle and side rake angle to 0 when programming with NX software.

[0033] Furthermore, the direction vector C perpendicular to the feed direction is obtained by cross-producting the workpiece surface normal vector N and the feed direction vector F.

[0034] The advantages of the present invention are:

[0035] The present invention proposes a method for calculating the tool-workpiece contact area for five-axis milling with a ball-end cutter. This method targets the case where only the ball end of the tool is involved in cutting during ball-end cutter finishing. Based on the principle that the tool axis inclination angle only affects the position of the contact area on the tool surface, but not the shape of the contact area, the method first uses a three-dimensional orthogonal Dexel model to calculate a tool-workpiece contact information set for the initial tool axis vector, including the contact element height and the cut-in / cut-out angle. For any tool axis vector during the cutting process, the tool ball end is divided into several discrete elements. These discrete elements are scanned to obtain a set of discrete element endpoint coordinates within the initial contact area information set. The coordinates of the tool-workpiece contact area boundary points for the current tool axis vector are then calculated based on this set of coordinates, thereby obtaining the tool-workpiece contact information for the current tool axis vector. Therefore, the method only requires the tool axis in its initial state to perform machining simulation calculations on the tool-workpiece contact area, without having to perform simulation calculations on all tool axis vectors during the entire cutting process. This greatly reduces the amount of calculations and improves the efficiency of calculating the ball-end cutter-workpiece contact area under different tool axis vectors. Testing has shown that the calculation efficiency can be increased by 7 times. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The above and / or other features and advantages of the present invention will become more readily understood through the following description with reference to the accompanying drawings, in which:

[0037] Figure 1 is a flow chart of the method for calculating the contact area between a ball-end cutter and a workpiece in a five-axis milling process according to the present invention;

[0038] Figure 2 is the projection of the tool-workpiece contact area along the tool axis in the present invention;

[0039] Figure 3 Schematic diagram of the workpiece coordinate system, tool coordinate system, feed coordinate system, and tool axis rake angle and side rake angle in the present invention;

[0040] Figure 4 The comparison of the tool-workpiece contact area calculated by the proposed method and the existing three-dimensional orthogonal Dexel discrete model when the tool axis rake angle is 10° and the side rake angle is 20° in the example of the present invention;

[0041] Figure 5 Comparison of the tool-workpiece contact area calculated by the proposed method and the existing three-dimensional orthogonal Dexel discrete model when the tool axis rake angle is 20° and the side rake angle is 20° in the example;

[0042] Figure 6 Comparison of the tool-workpiece contact area calculated by the proposed method and the existing three-dimensional orthogonal Dexel discrete model when the tool axis rake angle is 30° and the side rake angle is 20° in the example;

[0043] Figure 7 The figure shows a comparison of the tool-workpiece contact area calculated by the proposed method and the existing three-dimensional orthogonal Dexel discrete model when the tool axis rake angle is 40° and the side rake angle is 20° in the example of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is only for the purpose of illustration and is not intended to limit the present invention.

[0045] Aiming at the situation where only the ball head part is involved in cutting during ball-end cutter finishing, the present invention provides a tool-workpiece contact area calculation method for ball-end cutter five-axis milling that can quickly predict the contact area based on the principle that the tool axis inclination angle only affects the position of the contact area on the tool surface but does not affect the shape of the contact area.

[0046] Reference Figure 1 The method for calculating the contact area between a ball-end cutter and a workpiece provided by the present invention includes:

[0047] Step S1, using a three-dimensional orthogonal Dexel model to calculate the initial tool-workpiece contact area information set O corresponding to the initial tool axis vector CWE , including the contact element height z and the cut-in-cut-out angle θ st -θ ex ;

[0048] Step S2: for any given tool axis vector, the tool ball head is discretized into m and n microelements along the tool axial and circumferential directions respectively. The axial discrete height Δz = R0 / m, R0 is the ball head tool radius, and the circumferential discrete arc Δφ i =2π / n, the discrete element can be simplified and replaced by a circular arc segment at the middle position of the discrete element along the axial direction;

[0049] Step S3, scanning the discrete elements along the axial and circumferential directions of the tool to obtain the information set O in the initial tool-workpiece contact area CWE The discrete element endpoint coordinate set CS m ;

[0050] Step S4: Based on the discrete element endpoint coordinate set CS m Calculate the coordinates of the tool-workpiece contact area boundary points of the current tool axis vector, and then calculate the tool-workpiece contact information M of the current tool axis vector CWE .

[0051] According to the present invention, step S3 may include the following sub-steps:

[0052] Step S3.1: For the infinitesimal element with axial and circumferential numbers k and l respectively, calculate the tool coordinate system X corresponding to the current tool axis vector. T,m -Y T,m -Z T,m The endpoint coordinates (x m ,y m ,z m ), calculate its coordinate in the initial tool coordinate system X using coordinate transformation T,O -Y T,O -Z T,O The coordinates (x o ,y o ,z o ):

[0053]

[0054] Where, Indicates the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector, Represents the transformation matrix from the workpiece coordinate system to the initial tool coordinate system;

[0055] Step S3.2, refer to Figure 2 , for the infinitesimal endpoint coordinates (x o ,y o ,z o ), calculate the height of the cutting element as z o , the corresponding cutting angle θ is calculated by the following formula:

[0056] like

[0057] like

[0058] like

[0059] Where O is the center of the tool’s axial projection; e1 and e2 represent the x coordinates in the plane obtained by the tool’s axial projection and defined with the center of the circle as the origin. T axis and y T The unit vector of the axis; A is the projection point of the discrete element endpoint in the tool axis direction, <OA,e1> represents the angle between the vector OA and e1; <OA,e2> represents the angle between the vector OA and e2; cos -1 represents the arc cosine function; [OA,e1] represents the dot product between vectors OA and e1; [OA,e2] represents the dot product between vectors OA and e2; |·| represents the modulus of the vector;

[0060] Step 3.3, determine whether the calculated results of the height and cutting angle of the cutting element are within the initial tool-workpiece contact area information set O CWE If yes, add the endpoint of the current microelement to the coordinate set CS m It should be understood that in this step, for the judgment of the cutting angle calculation result, if the calculated cutting angle is within the range of the cutting-in-cutting-out angle, it is determined that the cutting angle is within the information set.

[0061] like Figure 3 As shown, in some embodiments of the present invention, the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector in step 3 and the transformation matrix from the workpiece coordinate system to the initial tool coordinate system are calculated according to the transformation matrix from the tool coordinate system to the workpiece coordinate system. The transformation matrix is calculated by the following steps:

[0062] Step 1: Define the feed coordinate system (FCS), workpiece coordinate system (WCS), and tool coordinate system (TCS). In the FCS coordinate system, F represents the feed direction, C represents the direction perpendicular to the feed direction, and N represents the direction normal to the workpiece surface. The rake angle α is defined as the angle of rotation of the tool axis about C, and the side rake angle β is defined as the angle of rotation of the tool axis about F.

[0063] Step 2: Calculate the tool axis vector in the workpiece coordinate system when the tool rake angle is α and the side rake angle is β:

[0064] A(α,β)=R(C,α)R(F,β)N

[0065]

[0066] C(α)=cos(α), S(α)=sin(α), V(α)=1-cos(α), C=[c i ,c j ,c k ] T

[0067]

[0068] C(β)=cos(β), S(β)=sin(β), V(β)=1-cos(β), F=[f i ,f j ,f k ] T

[0069] Where F represents the feed direction vector, (fi ,f j ,f k ) is the feed direction vector value, R(F,β) represents the generalized rotation matrix when the rotation angle around the vector F is β, C represents the direction vector perpendicular to the feed direction, (c i ,c j ,c k ) represents the direction vector value perpendicular to the feed direction, R(C,α) represents the generalized rotation matrix when the rotation angle around the vector C is α, N represents the normal vector of the workpiece surface, and the feed direction vector F is expressed as:

[0070]

[0071] Where (x1, y1, z1) and (x2, y2, z2) represent the coordinates of the tool tip at two adjacent tool locations. The normal vector of the workpiece surface and the coordinates of adjacent tool tip points can be obtained by setting the tool rake angle and side rake angle to 0 when programming with NX software. The workpiece normal vector at the tool location is the same as the tool axis vector. Vector C is obtained by cross-producting the workpiece surface normal vector N and the feed direction vector F.

[0072] Step 3: Construct the transformation matrix from local TCS to WCS

[0073]

[0074] Where (x, y, z) represents the three coordinate axes X and Z of the tool coordinate system. T 、Y T 、Z T Unit vector in the workpiece coordinate system.

[0075] For step S4, the coordinate set of each discrete element endpoint of the tool obtained in step S3 includes the height and cutting angle of each discrete element. Since the two endpoints of the arc formed by connecting the end to end of the circumferential discrete elements with equal axial height in the coordinate set form the boundary of the tool-workpiece contact area, one is the entry point and the other is the exit point, the coordinates of the boundary points of the tool-workpiece contact area can be calculated based on the height and cutting angle of each discrete element in the discrete element endpoint coordinate set. The cutting angle calculated at the entry point is the entry angle, and the cutting angle calculated at the exit point is the exit angle. Thus, the tool-workpiece contact information of the current tool axis vector including the height of each element and its entry-exit angle is obtained.

[0076] As described above, the method of the present invention only needs to perform processing simulation calculation of the tool-workpiece contact area on the initial state tool axis, and there is no need to perform simulation calculations for all tool axis vectors in the entire cutting process, which greatly reduces the amount of calculation and improves the calculation efficiency of the ball-end tool-workpiece contact area under different tool axis vectors.

[0077] Next, the ball-end cutter five-axis milling tool-workpiece contact area calculation method provided by the present invention is further explained with reference to examples.

[0078] This example calculates the tool-workpiece contact area for multiple different tool axis rake angles and side rake angles using the method provided by the present invention and the existing three-dimensional orthogonal Dexel method. The calculation and comparison results are shown in Figure 2. Figures 4 to 7 As shown in the figures, it can be seen that by using the method of the present invention, the calculation efficiency of the contact area between the ball-end cutter five-axis milling tool and the workpiece is improved by 7 times, and the relative error is small, which verifies the effectiveness of the method provided by the present invention.

[0079] Finally, it should be noted that the features mentioned and / or illustrated in the above description of the exemplary embodiments of the present invention may be incorporated into one or more other embodiments in the same or similar manner, combined with features in other embodiments, or substituted for corresponding features in other implementations. The technical solutions obtained by such combination or substitution shall also be deemed to be included in the scope of protection of the present invention.

Claims

1. A method for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling, characterized in that: The following steps are involved: Step 1: Use the three-dimensional orthogonal Dexel model to calculate the initial tool-workpiece contact area information set O corresponding to the initial tool axis vector CWE , including the contact element height z and the cut-in-cut-out angle θ st -θ ex ; Step 2: For any given tool axis vector, the tool ball head is discretized into m and n microelements along the tool axial and circumferential directions respectively. The axial discrete height Δz = R0 / m, R0 is the ball head tool radius, and the circumferential discrete arc Δφ i =2π / n; Step 3: Scan the discrete elements along the axial and circumferential directions of the tool to obtain the information set O in the initial tool-workpiece contact area. CWE The discrete element endpoint coordinate set CS m , including the following sub-steps: Step 3.1: For the infinitesimal elements with axial and circumferential numbers k and l respectively, calculate the tool coordinate system X corresponding to the current tool axis vector. T,m -Y T,m -Z T,m The endpoint coordinates (x m ,y m ,z m ), calculate its coordinate in the initial tool coordinate system X using coordinate transformation T,O -Y T,O -Z T,O The coordinates (x o ,y o ,z o ): Where, Indicates the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector, Represents the transformation matrix from the workpiece coordinate system to the initial tool coordinate system; Step 3.2, for the infinitesimal endpoint coordinates (x o ,y o ,z o ), calculate the height of the cutting element as z o , and calculate the cutting angle θ: like like like Where O is the center of the tool’s axial projection; e1 and e2 represent the x coordinates in the plane obtained by the tool’s axial projection and defined with the center of the circle as the origin. T axis and y T The unit vector of the axis; A is the projection point of the discrete element endpoint in the tool axis direction, <OA,e1> represents the angle between the vector OA and e1; <OA,e2> represents the angle between the vector OA and e2; cos -1 represents the arc cosine function; [OA,e1] represents the dot product between vectors OA and e1; [OA,e2] represents the dot product between vectors OA and e2; |·| represents the modulus of the vector; Step 3.3, determine whether the calculated results of the height and cutting angle of the cutting element are within the initial tool-workpiece contact area information set O CWE If yes, add the endpoint of the current microelement to the coordinate set CS m middle; Step 4: According to the discrete element endpoint coordinate set CS m Calculate the coordinates of the tool-workpiece contact area boundary points of the current tool axis vector, and then calculate the tool-workpiece contact information M of the current tool axis vector CWE .

2. The method for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling according to claim 1, wherein: In step 3, the transformation matrix from the tool coordinate system to the workpiece coordinate system corresponding to the current tool axis vector and the transformation matrix from the workpiece coordinate system to the initial tool coordinate system are calculated according to the transformation matrix from the tool coordinate system to the workpiece coordinate system. get, Calculate by the following steps: The first step is to calculate the tool axis vector in the workpiece coordinate system when the tool rake angle is α and the side rake angle is β: A(α,β)=R(C,α)R(F,β)N C(α)=cos(α),S(α)=sin(α),V(α)=1-cos(α),C=[c i ,c j ,c k ] T C(β)=cos(β),S(β)=sin(β),V(β)=1-cos(β),F=[f i ,f j ,f k ] T Where F represents the feed direction vector, (f i ,f j ,f k ) is the feed direction vector value, R(F,β) represents the generalized rotation matrix when the rotation angle around the vector F is β, C represents the direction vector perpendicular to the feed direction, (c i ,c j ,c k ) represents the direction vector value perpendicular to the feed direction, R(C,α) represents the generalized rotation matrix when the rotation angle around the vector C is α, N represents the normal vector of the workpiece surface, and the feed direction vector F is expressed as: Where (x1, y1, z1) and (x2, y2, z2) represent the coordinates of the tool tip points at two adjacent tool position points; Step 2: Construct the transformation matrix from the local tool coordinate system to the workpiece coordinate system Where (x, y, z) represents the three coordinate axes X and Z of the tool coordinate system. T 、Y T 、Z T Unit vector in the workpiece coordinate system.

3. The method for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling according to claim 1 or 2, characterized in that: In step 2, the discrete element is simplified and replaced by an arc segment at the middle position of the discrete element along the axial direction.

4. The method for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling according to claim 2, wherein: The coordinates of the tool tip points at adjacent tool positions are obtained by using the CL file generated by setting the tool rake angle and side rake angle to 0 when programming with NX software.

5. The method for calculating the contact area between a ball-end cutter and a workpiece in five-axis milling according to claim 2, wherein: The direction vector C perpendicular to the feed direction is obtained by cross-producting the workpiece surface normal vector N and the feed direction vector F.

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