Calculation method for cutter path track and cutter shaft angle of twisted right-angle molded surface grinding undercut

Abstract

The invention relates to the technical field of numerical control machining, and discloses a method for calculating a cutter path track and a cutter shaft angle of a twisted right-angle molded surface grinding undercut, a fillet is arranged on an intersection line of two twisted linear molded surfaces, and a first curve and a second curve are respectively formed at tangent positions of the fillet and the two twisted right-angle molded surfaces; an intersection point on an intersection line of the right-angle molded surface is selected as a normal plane of the right-angle molded surface, the normal plane and the first curve intersect at a first point, the normal plane and the second curve intersect at a second point, a connecting line between the first point and the second point is a first line segment, and the distance between the middle point and the first point or the second point is the machining radius of the grinding undercut; the second line segment which forms an included angle with the first line segment and passes through the intersection point is used as a closed graph, the first straight line and the second straight line are used as tracks, the closed graph is scanned, and a tool path is established based on the scanned graph, so that the grinding undercuts can be directly machined, the machining efficiency is high, the sizes of the grinding undercuts in all positions of the twisted right-angle guide rail are equal, and the forming precision is high. And the aesthetic property is good.

Description

Technical Field

[0001] This invention relates to the field of CNC machining technology, and in particular to a method for calculating the toolpath trajectory and tool axis angle of a twisted right-angle surface overtravel groove. Background Technology

[0002] Twisted surface guides are used in cigarette packaging machinery to adjust and transport the cigarette packs, such as allowing them to flip 180° vertically or rotate 90° forward or backward. The free-form twisted surface of this type of guide is generated by sweeping the cross-sectional line of the cigarette pack along the desired motion trajectory. The cigarette pack has a rectangular cross-section, and this rectangle, swept along the motion trajectory, creates a twisted right-angled surface. In this twisted right-angled surface, all normal sections along the intersection line are right angles. The right-angled sides of the cigarette pack remain in close contact with the intersection line of the twisted right-angled surface during movement. The stability of the cigarette pack's movement within the guide rail determines its running speed.

[0003] like Figure 1 As shown, the twisted right-angle guide rail is formed by the intersection of the first surface 1' and the second surface 2' of the twisted right-angle surface, and the curve 3' is the intersection line. In order to avoid the residual material at the intersection of the first surface 1' and the second surface 2' of the cigarette pack contacting each other during the movement and affecting the running stability of the cigarette pack, the residual material at the intersection of the twisted right-angle surfaces should be removed when processing the curved surface.

[0004] For regular twisted guides, such as planes and rings, the position information of the intersection of right-angle surfaces can be obtained through mathematical calculation. The residual material can be removed by machining the overrun groove at the intersection with a CNC machine tool.

[0005] For twisted surface guideways, the position information at the intersection of the twisted right-angled surfaces cannot be directly calculated. Furthermore, since the two surfaces are freely twisted, if the machining is performed using the right angle formed by the bottom and side edges of an end mill to simulate the running trajectory, overcutting and undercutting will occur on both surfaces. Therefore, ball end mills are needed to machine the two free twisted surfaces separately. Currently, small-diameter ball end mills are generally used for root clearing or local negative allowance machining, which cannot directly machine the runout groove at the intersection of the two surfaces, resulting in low machining efficiency and an unsightly appearance at the intersection of the closed-angled surfaces. Therefore, there is an urgent need to design a method for calculating the toolpath trajectory and cutter axis angle of the runout groove for twisted right-angled surfaces to improve the above problems. Summary of the Invention

[0006] The purpose of this invention is to propose a method for calculating the toolpath trajectory and tool axis angle of a twisted right-angle surface overrun groove, so as to solve the technical problems of not being able to directly machine overrun grooves at the intersection of twisted surfaces, resulting in low machining efficiency and unsightly intersections of closed-angle surfaces.

[0007] To achieve this objective, the present invention adopts the following technical solution:

[0008] This invention provides a method for calculating the toolpath trajectory and tool axis angle of a twisted right-angle surface overtravel groove, comprising the following steps:

[0009] Based on the radius of the ball end mill used to machine the twisted right-angled surface of the twisted right-angled guide rail, a fillet of the same size as the radius of the ball end mill used to machine the twisted right-angled surface is set on the intersection line of the two twisted straight surfaces.

[0010] The fillet and the two twisted right-angled surfaces form a first curve and a second curve, respectively.

[0011] The intersection point on the intersection line of the right-angled surface is selected as the normal plane of the right-angled surface. The normal plane intersects the first curve at a first point and the normal plane intersects the second curve at a second point. The line connecting the first point and the second point is the first line segment. The distance between the midpoint of the first line segment and the first point or between the midpoint of the first line segment and the second point is the processing radius of the overrun groove.

[0012] Draw a closed figure around the second line segment that forms an angle with the first line segment and passes through the intersection point;

[0013] Using the first and second straight lines as trajectories, scan the closed shape;

[0014] Toolpaths are created based on scanned graphics.

[0015] Based on the ball end mill radius used when machining twisted right-angle surfaces on a twisted right-angle guideway, corresponding fillets are set on the intersection line of two twisted right-angle surfaces. The fillets are tangent to one of the twisted right-angle surfaces to form a first curve, and tangent to the other twisted right-angle surface to form a second curve. The first and second curves are used as the trajectory of the overtravel groove, ensuring that the overtravel groove is continuously distributed across the entire twisted right-angle guideway, with a continuous and smooth surface transition. The intersection point on the intersection line of the right-angle surfaces is taken as the normal plane of the right-angle surface. This ensures that the normal plane intersects the first curve at a first point and the second curve at a second point. The first point and the second point... The line connecting the two points is the first line segment. The distance between the first point and the midpoint, or the distance between the second point and the midpoint, is the machining radius of the overrun groove. The tool axis angle is set through the midpoint. The closed shape is scanned according to the trajectory and the tool trajectory is established. The overrun groove is opened using the tool. According to the above calculation method, the overrun groove can be directly machined with high machining efficiency. The size of the overrun groove is equal at all points on the twisted right-angle guide rail. Its size can be set to the minimum overrun groove that completely removes residual material. The forming accuracy is high and the aesthetics are good. It ensures that when the cigarette pack runs on the entire twisted right-angle guide rail, the edges of the cigarette pack never contact the bottom of the groove, making the running stability better.

[0016] As a preferred method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove, the machining radius of the overtravel groove is greater than the distance between the midpoint and the first point or the midpoint and the second point.

[0017] The machining of the overcut groove ensures that the residual material is removed precisely, avoiding undercutting while also preventing overcutting.

[0018] As a preferred method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove, the overtravel groove is a circular arc groove.

[0019] As a preferred method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove, the midpoint is the path formed by the first straight line and the second straight line as the trajectory scan, which is the toolpath trajectory of the center of the ball end mill.

[0020] As a preferred method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overrun groove, the two ends of the first curve and the second curve are extended respectively to form an entry track space for the tool to cut into the overrun groove.

[0021] By extending the first and second curves, when establishing the tool path scanning surface by scanning the closed pattern, the extended part facilitates the setting of the overtravel groove machining tool, ensuring that the overtravel groove machining tool can smoothly enter the machining area of ​​the subsequent overtravel groove in the entry space.

[0022] As a preferred method for calculating the overtravel groove toolpath trajectory and cutter axis angle of the twisted right-angle surface, the second line segment passing through the intersection point and perpendicular to the first line segment is the cutter axis angle of the ball end mill.

[0023] By utilizing a five-axis linkage machining method, it ensures that the tool axis angle never comes into contact with or interferes with any surface other than the overtravel groove surface, and can adapt to tortuous right-angle guideways with a large degree of angular distortion.

[0024] As a preferred method for calculating the overtravel groove toolpath trajectory and cutter axis angle of the twisted right-angle surface, the second line segment that passes through the intersection point and forms an arbitrary suitable angle with the first line segment is the cutter axis angle of the ball end mill.

[0025] Using a fixed-axis machining tool, the overtravel groove is obtained by cutting along the toolpath with the same tool center coordinates but different tool axis angles, resulting in good machining stability.

[0026] As a preferred method for calculating the toolpath trajectory and cutter axis angle of the twisted right-angle surface overrun groove, the toolpath trajectory of the ball end mill's center is set with one or more segments, and the cutter axis angle of the ball end mill is adaptively selected at a suitable angle for each segment.

[0027] If the angle of a single fixed-axis tool axis interferes with the right-angled surface, the trajectory line of the midpoint can be segmented, and a suitable angle can be selected for each segment as the tool axis angle of that segment.

[0028] The beneficial effects of this invention are:

[0029] The method for calculating the toolpath trajectory and cutter axis angle of the overtravel groove on a twisted right-angle surface proposed in this invention is based on the radius of the ball end mill when machining the twisted right-angle surface on a twisted right-angle guide rail. Corresponding fillets are set on the intersection line of two twisted right-angle surfaces. The fillets are tangent to one of the twisted right-angle surfaces to form a first curve, and tangent to the other twisted right-angle surface to form a second curve. The first and second curves are used as the trajectory of the overtravel groove, ensuring that the overtravel groove is continuously distributed across the entire twisted right-angle guide rail, with a continuous and smooth surface transition. The intersection point on the intersection line of the right-angle surfaces is taken as the normal plane of the right-angle surface, ensuring that the normal plane intersects the first curve at a first point and the second curve at a second point. The first line segment is the line connecting the first and second points, which intersect at the second point. The distance between the first point and the midpoint, or the distance between the second point and the midpoint, is the machining radius of the overrun groove. The tool axis angle is set through the midpoint. The closed shape is scanned according to the trajectory and the tool trajectory is established. The overrun groove is opened using the tool. According to the above calculation method, the overrun groove can be directly machined with high machining efficiency. The size of the overrun groove is equal at all points on the twisted right-angle guide rail. Its size can be set to the minimum overrun groove that completely removes residual material. The forming accuracy is high and the aesthetics are good. It ensures that when the cigarette pack runs on the entire twisted right-angle guide rail, the edges of the cigarette pack never contact the bottom of the groove, making the running stability better. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the structure of the twisted right-angle guide rail provided in the background art of this invention;

[0031] Figure 2 This is a schematic diagram of the first structure of the tortuous right-angle guide rail provided in Embodiment 1 of the present invention;

[0032] Figure 3 This is a schematic diagram of the second structure of the twisted right-angle guide rail provided in Embodiment 1 of the present invention;

[0033] Figure 4 This is a schematic diagram of the cross-sectional structure of the closed shape provided in Embodiment 1 of the present invention;

[0034] Figure 5 This is a partial structural schematic diagram of the tool trajectory scanning surface provided in Embodiment 1 of the present invention;

[0035] Figure 6 This is a schematic diagram of the overall structure of the tool trajectory scanning surface provided in Embodiment 1 of the present invention;

[0036] Figure 7 This is a schematic diagram of the overall structure of the toolpath trajectory for five-axis linkage machining provided in Embodiment 1 of the present invention;

[0037] Figure 8 This is a partial structural schematic diagram of the toolpath trajectory for five-axis linkage machining provided in Embodiment 1 of the present invention;

[0038] Figure 9 This is a schematic diagram of the projected structure of the overrun groove and the tobacco pack on the normal cross section provided in Embodiment 1 of the present invention;

[0039] Figure 10 This is a partial structural schematic diagram of the toolpath trajectory for fixed-axis machining provided in Embodiment 2 of the present invention.

[0040] Figure 1 middle:

[0041] 1' First surface; 2' Second surface; 3' Curve;

[0042] Figures 2-9 middle:

[0043] 1. First curve; 2. Second curve; 3. Rounded corner; 5. Normal plane; 6. First point; 7. Second point; 8. First line segment; 9. Midpoint; 10. Second line segment; 11. First straight line; 12. Second straight line;

[0044] 100. Cigarette pack; 101. First right-angled side; 102. Second right-angled side;

[0045] 200, First intersection line; 300, Second intersection line; 400, Third intersection line. Detailed Implementation

[0046] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar components or components having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0047] In the description of this invention, unless otherwise explicitly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection or a detachable connection; a mechanical connection or an electrical connection; a direct connection or an indirect connection through an intermediate medium; or the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0048] In the description of this invention, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0050] Currently, the positional information at the intersection of the tortuous right-angled surfaces of a twisted guideway cannot be directly calculated, and because the two surfaces are freely twisted, if the right angle formed by the bottom and side edges of an end mill is used to simulate the movement trajectory during machining, overcutting and undercutting will occur on the two surfaces.

[0051] Example 1

[0052] To solve the above problems, combined with Figures 2-9 As shown, this embodiment provides a method for calculating the toolpath trajectory and tool axis angle of a twisted right-angle surface overtravel groove, including the following steps:

[0053] Based on the radius of the ball end mill used to machine the twisted right-angled surface of the twisted right-angled guideway, a fillet 3 with the same radius as the ball end mill used to machine the twisted right-angled surface is set on the intersection line of the two twisted straight surfaces, i.e., fillet 3 operation.

[0054] See Figure 3 The rounded corner 3 formed at the tangent of the two twisted right-angled surfaces forms a first curve 1 and a second curve 2, which are parallel to each other.

[0055] The two ends of the first curve 1 and the second curve 2 are extended respectively to form an entry space for the tool to cut into the overtravel groove. By extending the first curve 1 and the second curve 2, when scanning the closed pattern to establish the tool trajectory scanning surface, the extended part facilitates the setting of the overtravel groove machining tool, ensuring that the overtravel groove machining tool can smoothly enter the machining area of ​​the subsequent overtravel groove in the entry space.

[0056] like Figure 3 and Figure 4 As shown, the intersection point on the intersection line of the right-angled surfaces is selected as the normal plane 5 of the right-angled surface. The normal plane 5 intersects the first curve 1 at the first point 6, and the normal plane 5 intersects the second curve 2 at the second point 7. The line connecting the first point 6 and the second point 7 is the first line segment 8. The distance between the midpoint 9 of the first line segment 8 and the first point 6 or between the midpoint 9 of the first line segment 8 and the second point 7 is the machining radius of the overrun groove.

[0057] To better remove residual material and avoid undercutting and overcutting. Figure 4 As shown, the machining radius of the overrun groove is greater than the distance between midpoint 9 and the first point 6 or between midpoint 9 and the second point 7. This ensures that residual material can be completely removed at every position along the entire twisted right-angle guide rail, resulting in excellent residual material removal.

[0058] In this embodiment, the cutting tool used to machine the overtravel groove is a ball end mill, and the overtravel groove is a circular arc groove.

[0059] like Figure 5 As shown, a closed figure is formed by a second line segment 10 that forms an angle with the first line segment 8 and passes through the intersection point. Preferably, the second line segment 10, which passes through the intersection point and is perpendicular to the first line segment 8, represents the cutter axis angle of the ball end mill. That is, the direction of the second line segment 10 is the optimal cutter axis direction for the ball end mill.

[0060] like Figure 6 and Figure 7 As shown, the closed shape is scanned using the first straight line 11 and the second straight line 12 as trajectories. The path formed by scanning the midpoint 9 using the first straight line 11 and the second straight line 12 as trajectories is the toolpath trajectory of the ball center of the ball end mill.

[0061] It should be noted that the line connecting the two endpoints of the first curve 1 on the normal section is the first straight line 11 (see...). Figure 4 The line connecting the two endpoints of the second curve 2 on the normal section is the second straight line 12 (see...). Figure 4 ).

[0062] like Figure 8 As shown, a toolpath is established based on the scanned image. Since the trajectory of midpoint 9 is the ball-end mill's center toolpath trajectory, and the direction of the second line segment 10 is the optimal tool axis direction, a five-axis linkage machining toolpath can be generated.

[0063] Using a ball end mill to create the overrun groove, the overrun groove can be directly machined according to the above calculation method, which has high machining efficiency. The size of the overrun groove is equal at all points on the twisted right-angle guide rail. Its size can be set to the minimum overrun groove to completely remove residual material. The forming accuracy is high and the aesthetics are good. It ensures that when the cigarette pack 100 runs on the entire twisted right-angle guide rail, the edges of the cigarette pack 100 never come into contact with the bottom of the groove, which makes the running stability better.

[0064] To further illustrate the core logic of the above calculation method, such as Figure 9 As shown, the projection of the overrun groove on the normal section of the intersection line of two twisted right-angled surfaces and the cross-sectional structure diagram of the cigarette pack 100 are displayed. The two adjacent right-angled sides of the cigarette pack 100 are defined as the first right-angled side 101 and the second right-angled side 102. A fillet 3 is set on the intersection line of the first right-angled side 101 and the second right-angled side 102, i.e., the two twisted right-angled surfaces. The shaded area formed by the fillet 3 and the first right-angled side 101 and the second right-angled side 102 is the residual material from machining the two twisted right-angled surfaces. The circle in the figure is the overrun groove to be machined. The overrun groove needs to cover the shaded area so that all the residual material can be removed. The size of the circle is preferably the smallest circle that completely covers the shaded area. The center of the circle is the center coordinate of the ball end mill used to machine the overrun groove, and the arrow direction is the direction of the cutter axis of the ball end mill used to machine the overrun groove.

[0065] For example, such as Figure 2 As shown, taking the twisted right-angle guide rail as an example, this twisted right-angle guide rail has three pairs of twisted right-angle surfaces, that is, three intersecting lines, namely the first intersecting line 200, the second intersecting line 300, and the third intersecting line 400. The curved part of this twisted right-angle guide rail is machined using a ball end mill with a radius of 4cm for five-axis linkage. Now, taking the first intersecting line 200 as an example, the calculation method of the toolpath trajectory and tool axis angle of the twisted right-angle surface overrun groove is further described in detail:

[0066] The ball end mill used for machining the twisted right-angled guide rail has a radius of 4cm, and a fillet with a radius of 4cm is set on the intersection line of the two twisted straight surfaces.

[0067] The fillet 3 forms the first curve 1 and the second curve 2 at the tangent of the two twisted right-angled surfaces, respectively.

[0068] The two ends of the first curve 1 and the second curve 2 are extended respectively to form an entry space for the tool to cut into the overrun groove.

[0069] Select the intersection point on the intersection line of the right-angled surfaces to form the normal plane 5 of the right-angled surfaces. The normal plane 5 intersects the first curve 1 at the first point 6, and the normal plane 5 intersects the second curve 2 at the second point 7.

[0070] Connect the first point 6 and the second point 7 to form the first line segment 8, which is 5.6cm long.

[0071] Using the center of the first line segment 8 as the center, select a ball end mill with a radius of 3cm to machine the overrun groove.

[0072] Draw a second line segment 10 perpendicular to the first line segment 8 through the midpoint 9. The second line segment 10 is the cutter axis angle of the ball end mill.

[0073] The first straight line 11 and the second straight line 12 serve as the trajectory, scanning the closed pattern to form the tool trajectory scanning surface.

[0074] The five-axis toolpath is established based on the scanned image. The trajectory of the midpoint 9 is the toolpath trajectory of the ball end mill's center. The second line segment 10 is the optimal tool axis angle, which can generate the toolpath trajectory of the five-axis linkage machining tool.

[0075] Example 2

[0076] Compared with five-axis linkage machining, this embodiment uses the same CNC milling tools and sets the machining radius of the overtravel groove. The difference between this embodiment and embodiment one is that it uses a fixed-axis machining method, that is, the tool axis angle is set differently.

[0077] like Figure 10 As shown, in this embodiment, the appropriate angle between the midpoint 9 and the first line segment 8 is the tool axis angle of the fixed-axis machining tool. The path formed by scanning the midpoint 9 using the first curve 1 and the second curve 2 is the toolpath trajectory of the fixed-axis machining tool. By using the fixed-axis machining tool method, the overtravel groove obtained by cutting along the toolpath trajectory with the same tool center coordinates but different tool axis angles has good machining stability.

[0078] Furthermore, the toolpath of a fixed-axis machining tool can be set to one or more segments, with each segment having a suitable tool axis angle. If the tool axis angle of a single fixed-axis tool interferes with a right-angled surface, the trajectory line of the midpoint 9 can be segmented, and a suitable angle can be selected for each segment as the tool axis angle for that segment.

[0079] like Figure 9 As shown, as the cross section of the cigarette pack 100 sweeps along the running trajectory, the circular part and the tool axis direction sweep together along the running trajectory to form the tool path trajectory for machining the overrun groove. Since the overrun groove is machined with a ball end mill, for the same tool center coordinates, the cutting results obtained in different tool axis directions are the same, which is beneficial for segmented machining using the fixed axis machining method.

[0080] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the toolpath trajectory and tool axis angle of a twisted right-angle surface overtravel groove, characterized in that, Includes the following steps: Based on the radius of the ball end mill used to process the twisted right-angled surface of the twisted right-angled guide rail, a fillet of the same size as the radius of the ball end mill used to process the twisted right-angled surface is set on the intersection line of the two twisted straight surfaces (3). The fillet (3) forms a first curve (1) and a second curve (2) at the tangent points of the two twisted right-angle surfaces, respectively. The intersection point on the intersection line of the right angle surface is selected as the normal plane (5) of the right angle surface. The normal plane (5) intersects the first curve (1) at the first point (6) and the normal plane (5) intersects the second curve (2) at the second point (7). The line connecting the first point (6) and the second point (7) is the first line segment (8). The distance between the midpoint (9) of the first line segment (8) and the first point (6) or between the midpoint (9) of the first line segment (8) and the second point (7) is the processing radius of the overrun groove. Draw a closed figure from the second line segment (10) that forms an angle with the first line segment (8) and passes through the intersection point; Using the first straight line (11) and the second straight line (12) as trajectories, the closed shape is scanned; Toolpaths are created based on scanned graphics.

2. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to claim 1, characterized in that, The processing radius of the overrun groove is greater than the distance between the midpoint (9) and the first point (6) or between the midpoint (9) and the second point (7).

3. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to claim 1, characterized in that, The overrun groove is a circular arc groove.

4. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to claim 1, characterized in that, The midpoint (9) is the path formed by the first straight line (11) and the second straight line (12) as the trajectory scan, which is the tool path trajectory of the ball center of the ball end mill.

5. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to claim 1, characterized in that, The two ends of the first curve (1) and the second curve (2) are extended respectively to form an entry space for the tool to cut into the overrun groove.

6. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to any one of claims 1-5, characterized in that, The second line segment (10), which passes through the intersection point and is perpendicular to the first line segment (8), is the cutter axis angle of the ball end mill.

7. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to any one of claims 1-5, characterized in that, The second line segment (10), which passes through the intersection point and forms an arbitrary suitable angle with the first line segment (8), is the cutter axis angle of the ball end mill.

8. The method for calculating the toolpath trajectory and tool axis angle of the twisted right-angle surface overtravel groove according to claim 7, characterized in that, The ball end mill's toolpath trajectory is set in one or more segments, and each segment adaptively selects a suitable angle for the ball end mill's cutter axis angle.

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