Tool path planning method and system for mirror milling of integral box bottom

Abstract

This invention provides a method for planning toolpaths in mirror milling of an integral box bottom, comprising: establishing a trajectory planning surface; projecting the box bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then planning initial thickened area machining toolpaths, initial contour machining toolpaths, and initial thinning area machining toolpaths; projecting the initial thickened area machining toolpaths, initial contour machining toolpaths, and initial thinning area machining toolpaths onto the actual inner surface of the box bottom to obtain the final thickened area, thinned area, and contour machining toolpaths. This invention achieves efficient, residue-free machining of the thickened area of ​​the integral box bottom through the planning method of thickened area machining toolpaths, contour machining toolpaths, and thinning area machining toolpaths. The transition fillets at the contour are machined separately, and the machining program between complex contours in the thinning area is compiled using a curve-driven method, achieving residue-free and non-overlapping machining of the thinning area and ensuring precise control of the wall thickness.

Description

Technical Field

[0001] This invention relates to the field of CNC machining technology, specifically to a method and system for tool path planning in integral box bottom mirror milling. Background Technology

[0002] The fuel tank bottom is a crucial component of a launch vehicle's fuel tank, typically characterized by thin walls, large dimensions, and complex curved surfaces. The bottom's design surface is a surface of revolution around the minor axis of an elliptical first-quadrant curve. To facilitate fuel transfer, it generally incorporates several through-holes for subsequent welding to other components. Additionally, localized wall thickening serves as a weld-affected zone. Therefore, the bottom typically features through-holes and thickened areas on its external surface, resulting in a complex structure. Due to its complex structure and high quality requirements, it is one of the most difficult structural components to manufacture in launch vehicles. Currently, integrally formed fuel tank bottoms have been applied in launch vehicle models. Due to their superior strength and reliability, they are gradually replacing the traditional segmented welded tank bottoms, becoming the mainstream technological approach.

[0003] Currently, the only method for machining the integral box bottom with uniform thickness is mirror milling. During mirror milling, the wall thickness needs to be measured in real time using an ultrasonic thickness gauge and fed back to the CNC system. The wall thickness compensation amount is then calculated by a wall thickness compensation algorithm and transmitted to the compensation axis to achieve precise control of the wall thickness accuracy. According to the principle of wall thickness control in mirror milling, there can be no overlap between tool paths; otherwise, incorrect wall thickness data during measurement will lead to incorrect compensation values ​​from the measurement compensation algorithm, ultimately resulting in the wall thickness accuracy failing to meet requirements. At the same time, the trace residues from mirror milling are extremely difficult to remove through programming and can only be removed by grinding or other methods, making it difficult to meet the requirements for surface quality and wall thickness accuracy.

[0004] Therefore, when performing mirror milling of the entire box bottom, it is necessary to propose an efficient and standardized toolpath planning method to achieve residual and non-overlapping machining of the entire box bottom, and ultimately achieve precise control of wall thickness accuracy. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for planning toolpaths in integral box bottom mirror milling.

[0006] A toolpath planning method for integral box bottom mirror milling according to the present invention includes:

[0007] Step S1: Establish the trajectory planning surface;

[0008] Step S2: Project the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plan the initial thickened area machining tool path, the initial contour machining tool path and the initial thinning area machining tool path;

[0009] Step S3: Project the initial thickening area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths.

[0010] Preferably, the trajectory planning surface is established based on the equidistant offset of the inner surface of the overall box bottom theory, wherein the offset direction is away from the center of the inner surface sphere, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom.

[0011] Preferably, the initial toolpath planning step for machining the thickened area includes:

[0012] Step S2.1.1: Project the boundary line of the bottom part of the box onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines;

[0013] Step S2.1.2: Offset the intersection line of one quadrant line of the box bottom with the trajectory planning plane at equal intervals along the left and right sides to obtain two latitudinal intersection lines;

[0014] Step S2.2.3: In the driving surface formed by the two upper and lower boundary lines and the two intersecting latitudinal lines, the tool moves back and forth from top to bottom to obtain the initial tool path for machining the thickened area.

[0015] Preferably, the initial contour machining toolpath planning step includes:

[0016] Step S2.2.1: Project the outline of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened areas of each feature;

[0017] Step S2.2.2: The machining boundary line of the thickened area is offset at equal intervals in the direction away from the material to obtain the contour cutting drive curve, and then the initial contour machining tool path is obtained.

[0018] Preferably, the initial toolpath planning step for thinning the region includes:

[0019] Step S2.3.1: Based on the contour cutting drive curve, further offset by equal distance to obtain the thinning zone machining boundary line;

[0020] Step S2.3.2: Divide the area into multiple regions based on the location of the thickened area;

[0021] Step S2.3.3: Divide the upper and lower directions equally according to the distance between the upper and lower contour lines in the area, and select the trajectory line as the driving curve one by one for reciprocating tool movement to obtain the initial thinning area machining tool path.

[0022] A toolpath planning system for integral box bottom mirror milling according to the present invention includes:

[0023] Module M1: Establishes the trajectory planning surface;

[0024] Module M2: Projects the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plans the initial thickened area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path;

[0025] Module M3: Projects the initial thickening area machining tool path, initial contour machining tool path, and initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths.

[0026] Preferably, the trajectory planning surface is established based on the equidistant offset of the inner surface of the overall box bottom theory, wherein the offset direction is away from the center of the inner surface sphere, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom.

[0027] Preferably, the initial thickened area machining toolpath planning module includes:

[0028] Module M2.1.1: Project the boundary lines of the box bottom part onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines;

[0029] Module M2.1.2: The intersection line of one quadrant line at the bottom of the box and the trajectory planning surface is offset equally on both the left and right sides to obtain two latitudinal intersection lines;

[0030] Module M2.2.3: In the driving surface formed by the two upper and lower boundary lines and the two intersecting latitudinal lines, the tool moves back and forth from top to bottom to obtain the initial tool path for machining the thickened area.

[0031] Preferably, the initial contour machining toolpath planning module includes:

[0032] Module M2.2.1: Project the outline of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened area of ​​each feature;

[0033] Module M2.2.2: The machining boundary line of the thickened area is offset at equal intervals in the direction away from the material to obtain the contour cutting drive curve, and then the initial contour machining tool path is obtained.

[0034] Preferably, the toolpath planning module for the initial thinning zone includes:

[0035] Module M2.3.1: Based on the contour cutting drive curve, further offset by equal distance to obtain the thinning zone machining boundary line;

[0036] Module M2.3.2: Divides the area into multiple regions based on the location of the thickened area;

[0037] Module M2.3.3: In the area, the upper and lower directions are evenly divided according to the distance between the upper and lower contour lines, and the reciprocating tool path is selected one by one as the driving curve to obtain the initial thinning area machining tool path.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. This invention achieves residue-free machining of the thickened area of ​​the entire box bottom by using a standardized tool path planning method for machining the thickened area, and improves its machining efficiency.

[0040] 2. The contour machining tool path planning method of the present invention enables the transition fillets at the contour to be machined separately, ensuring the connection strength at the transition fillets and avoiding stress concentration.

[0041] 3. This invention uses a curve-driven approach to program the machining process between the complex contours of the thinning zone, achieving zero-residue and non-overlapping machining of the thinning zone and ensuring precise control of the wall thickness. Attached Figure Description

[0042] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0043] Figure 1 The present invention relates to a method for planning the tool path for mirror milling of the integral bottom of a launch vehicle propellant tank.

[0044] Figure 2 This is a schematic diagram of the features required for the creation of the milling toolpath for the integral bottom of the launch vehicle tank of the present invention.

[0045] Figure 3 This is a schematic diagram of the initial thickened area tool path planning during the mirror milling of the integral bottom of the launch vehicle tank of the present invention.

[0046] Figure 4 This is a schematic diagram of the initial contour toolpath planning during the creation of the mirror milling toolpath for the integral bottom of the launch vehicle tank of the present invention.

[0047] Figure 5 This is a schematic diagram of the initial thinning area machining region planning when compiling the tool path for the mirror milling of the integral bottom of the launch vehicle tank of the present invention.

[0048] Figure 6 This is a schematic diagram of toolpath planning for an incomplete circular area during the mirror milling of the overall bottom of the launch vehicle tank in this invention.

[0049] Explanation of reference numerals in the attached figures:

[0050] Detailed Implementation

[0051] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0052] The tool path planning method for mirror milling of the entire bottom of a launch vehicle propellant tank of the present invention improves the efficiency and quality of tool path programming for mirror milling of the entire bottom of the tank by using trajectory planning surfaces for initial tool path planning based on the processing requirements of different areas, and realizes mirror milling of the entire bottom of the tank without residue and without overlap.

[0053] Example 1

[0054] According to the present invention, a method for planning toolpaths for mirror milling of an integral box bottom is provided, such as... Figure 1 As shown, it includes:

[0055] Step S1: Establish the trajectory planning surface. The trajectory planning surface is established based on the theoretical inner surface of the overall box bottom, with equidistant offsets. The offset direction is away from the center of the inner surface, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom. The offset distance is generally the wall thickness of the thickened area of ​​the box bottom plus 0mm to 5mm. The trajectory planning surface can be established in CAD / CAM software, but is not limited to this software.

[0056] like Figure 2 As shown, the overall box bottom theoretical model 1 includes a theoretical inner surface 2, a theoretical top profile 5, a theoretical bottom profile 6, and a thickened area profile 7. The theoretical inner surface 2 is offset equidistantly from the center O of the ellipsoid by 0mm to 5mm from the wall thickness of the thickened area of ​​the box bottom. The specific distance can be determined based on the deformation during box bottom processing, resulting in the trajectory planning surface 3. The actual inner surface 4, obtained through scanning or other methods, is then imported into CAD / CAM software.

[0057] Step S2: Project the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plan the initial thickened area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path. Specifically, the planning steps are described as follows:

[0058] The initial toolpath planning steps for the thickened area machining include the following sub-steps: Step S2.1.1: Project the boundary line of the box bottom part onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines. Step S2.1.2: Offset the intersection line of one quadrant line of the box bottom with the trajectory planning surface at equal intervals along the left and right sides to obtain two lateral intersection lines. Step S2.2.3: In the driving surface formed by the two upper and lower boundary lines and the two lateral intersection lines, perform a reciprocating motion from top to bottom to obtain the initial toolpath for the thickened area machining.

[0059] Specifically, the theoretical boundary line of the box bottom part is projected onto the trajectory planning surface along the curved surface, and the initial toolpath for machining the thickened area is compiled in a surface-driven manner. For example... Figure 3 As shown, the theoretical top contour 5 and theoretical bottom contour 6 of the box bottom theoretical model are first projected onto the trajectory planning surface to obtain the upper contour line 8 and the lower contour line 9, respectively. Then, the plane of one quadrant line of the box bottom is offset vertically at equal distances, with each offset distance being 25% of the effective bottom diameter of the tool for machining the thickened area, intersecting with the trajectory planning surface to obtain two auxiliary equidistant lines 10 for the region boundaries. The upper contour line 8, the lower contour line 9, and the two auxiliary equidistant lines 10 for the region boundaries form a closed "C"-shaped structure. Next, based on the length of one of the auxiliary equidistant lines 10 for the region boundaries, and following the principle that the spacing between each tool path is 50%~90% of the effective bottom diameter of the tool for machining the thickened area, the auxiliary equidistant line 10 for the region boundaries is divided into as few segments as possible to obtain the number of trajectories for machining the thickened area. Finally, the intersection point 11 of the upper contour line 8 and one of the auxiliary equidistant lines 10 for the region boundaries is used as the starting point of the tool path, and the initial tool path for machining the thickened area is obtained by using a reciprocating tool path in a top-to-bottom order.

[0060] The initial contour machining toolpath planning steps include the following sub-steps: Step S2.2.1: Project the contour line of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened areas of each feature. Step S2.2.2: Offset the machining boundary lines of the thickened areas at equal intervals in the direction away from the material to obtain the contour cutting drive curve, and thus obtain the initial contour machining toolpath.

[0061] Specifically, the theoretical thickened area contour line of the box bottom part is projected onto the trajectory planning surface, and the initial contour machining toolpath is planned in the trajectory planning surface in a curve-driven manner along the equidistant offset line of the thickened area contour line. For example... Figure 4As shown, the thickened area contour 7 of the theoretical model of the box bottom is first projected onto the trajectory planning surface to obtain the thickened area machining boundary line 12 of each feature. Then, the thickened area machining boundary line 12 is offset in a direction away from the material by a distance of 50% of the contour machining tool diameter to obtain the initial contour machining tool path 13, which is a closed curve. Finally, the endpoint of the feature or a quadrant point on the circumference is selected as the contour machining starting point 14, and the machining direction is selected by climb milling to obtain the initial contour machining tool path 13 for different features.

[0062] The initial toolpath planning steps for the thinning area machining include the following sub-steps: Step S2.3.1: Further offset the contour cutting drive curve by an equal distance to obtain the machining boundary line of the thinning area. Step S2.3.2: Divide the area into multiple regions according to the location of the thickened area. Step S2.3.3: Divide the vertical direction equally in each region according to the distance between the upper and lower contour lines, and select the trajectory line as the drive curve for each reciprocating toolpath to obtain the initial toolpath for the thinning area machining.

[0063] Specifically, such as Figure 5 As shown, the thickened area processing boundary lines 12 of each feature are first offset equidistantly in the direction away from the material. The offset distance is 50% of the contour processing tool diameter plus 50% to 75% of the effective diameter of the thinning area processing tool bottom, resulting in the thinning area processing boundary line 15. Further, circles are drawn around the center O at the highest point of each of the thinning area processing boundary lines 15. If other thinning area processing boundary lines 15 are encountered, the circle is broken, leaving only the arc, forming the thinning area auxiliary processing boundary line 16. In this way, the area to be processed is divided into thinning area processing areas 17 to 22, numbered 1 to 6.

[0064] In the aforementioned regions, areas 17 (region 1) and 22 (region 6) of the thinning zone are annular regions. The initial toolpath planning method for this region can be implemented based on the initial toolpath planning method for the thickening zone.

[0065] In the thinning zone processing, regions 2-5, and 18-21, are all incomplete annular regions. Further, taking region 2, 18, as an example... Figure 6As shown in the diagram. First, the auxiliary machining boundary line 16 of the larger diameter thinning area is offset by 50% of the effective bottom diameter of the thinning area machining tool at its outer and inner sides, resulting in the boundary line 23 of region 2. Then, this boundary line forms the machining area with the original thinning area machining boundary line 15 and the auxiliary machining boundary line 16. Next, the boundary line 23 of region 2 is offset at equal intervals, with the offset distance determined by dividing it into equal parts according to the principle of 50%~90% of the effective bottom diameter of the thinning area machining tool, and the step distance is calculated. Finally, the intersection point 24 of the upper left corner of the thinning area machining boundary line 15 and the auxiliary machining boundary line 16 is selected as the program starting point. Using a reciprocating tool path, the straightness is connected end to end to obtain the initial machining tool path for region 2 of the thinning area.

[0066] Step S3: Project the initial thickening area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths.

[0067] Specifically, the actual internal surface obtained through scanning is imported into CAD / CAM software. The initial tool path created in step S2 is projected in the opposite direction along the trajectory planning surface normal vector onto the actual internal surface as the tool position point. The normal vector at the tool position point on the actual internal surface is used as the tool axis to obtain all tool position points and tool axes, forming the final tool path for thickening, thinning and contour machining, which is used for mirror milling.

[0068] Example 2

[0069] The present invention also provides a tool path planning system for integral box bottom mirror milling. Those skilled in the art can implement the integral box bottom mirror milling tool path planning system by executing the steps of the integral box bottom mirror milling tool path planning method. That is, the integral box bottom mirror milling tool path planning method can be understood as a preferred embodiment of the integral box bottom mirror milling tool path planning system.

[0070] A toolpath planning system for integral box bottom mirror milling according to the present invention includes:

[0071] Module M1: Establishes the trajectory planning surface. The trajectory planning surface is established based on the equidistant offset of the inner surface of the overall box bottom theory, wherein the offset direction is away from the center of the inner surface sphere, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom.

[0072] Module M2: Projects the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plans the initial thickened area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path.

[0073] The initial thickened area machining toolpath planning module includes: Module M2.1.1: Projecting the boundary line of the box bottom part onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines. Module M2.1.2: Equivalently offsetting the intersection line of one quadrant line of the box bottom with the trajectory planning surface along both sides to obtain two lateral intersection lines. Module M2.2.3: Reciprocating the tool path from top to bottom in the driving surface formed by the two upper and lower boundary lines and the two lateral intersection lines to obtain the initial thickened area machining toolpath.

[0074] The initial contour machining toolpath planning module includes: Module M2.2.1: Projecting the contour line of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened areas of each feature. Module M2.2.2: Equivalently offsetting the machining boundary lines of the thickened areas in the direction away from the material to obtain the contour cutting drive curve, and thus obtaining the initial contour machining toolpath.

[0075] The initial thinning zone machining toolpath planning module includes: Module M2.3.1: Based on the contour cutting drive curve, further offset by equal distance to obtain the thinning zone machining boundary line. Module M2.3.2: Divide the area into multiple regions according to the location of the thickened area. Module M2.3.3: Divide the vertical direction equally in each region according to the distance between the upper and lower contour lines, and select the trajectory line as the drive curve for reciprocating toolpath to obtain the initial thinning zone machining toolpath.

[0076] Module M3: Projects the initial thickening area machining tool path, initial contour machining tool path, and initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths.

[0077] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0078] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for planning toolpaths in a mirror milling process for an integral box bottom, characterized in that, include: Step S1: Establish the trajectory planning surface; Step S2: Project the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plan the initial thickened area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path; Step S3: Project the initial thickening area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths; The trajectory planning surface is established based on the equidistant offset of the inner surface of the overall box bottom theory, wherein the offset direction is away from the center of the inner surface sphere, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom. The initial toolpath planning steps for machining the thickened area include: Step S2.1.1: Project the boundary line of the bottom part of the box onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines; Step S2.1.2: Offset the intersection line of one quadrant line of the box bottom with the trajectory planning plane at equal intervals along the left and right sides to obtain two latitudinal intersection lines; Step S2.2.3: In the driving surface formed by the two upper and lower boundary lines and the two intersecting latitudinal lines, the tool moves back and forth from top to bottom to obtain the initial tool path for machining the thickened area. The initial contour machining toolpath planning steps include: Step S2.2.1: Project the outline of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened areas of each feature; Step S2.2.2: The machining boundary line of the thickened area is offset at equal intervals in the direction away from the material to obtain the contour cutting drive curve, and then the initial contour machining tool path is obtained.

2. The toolpath planning method for integral box bottom mirror milling according to claim 1, characterized in that, The initial toolpath planning steps for thinning the region include: Step S2.3.1: Based on the contour cutting drive curve, further offset by equal distance to obtain the thinning zone machining boundary line; Step S2.3.2: Divide the area into multiple regions based on the location of the thickened area; Step S2.3.3: Divide the upper and lower directions equally according to the distance between the upper and lower contour lines in the area, and select the trajectory line as the driving curve one by one for reciprocating tool movement to obtain the initial thinning area machining tool path.

3. A toolpath planning system for integral box bottom mirror milling, characterized in that, include: Module M1: Establishes the trajectory planning surface; Module M2: Projects the bottom boundary line and the thickened area contour line onto the trajectory planning surface, and then plans the initial thickened area machining tool path, the initial contour machining tool path, and the initial thinning area machining tool path; Module M3: Projects the initial thickening area machining tool path, initial contour machining tool path, and initial thinning area machining tool path onto the actual box bottom inner surface to obtain the final thickening area, thinning area, and contour machining tool paths; The trajectory planning surface is established based on the equidistant offset of the inner surface of the overall box bottom theory, wherein the offset direction is away from the center of the inner surface sphere, and the offset distance is greater than the wall thickness of the thickened area of ​​the box bottom. The initial toolpath planning module for machining the thickened area includes: Module M2.1.1: Project the boundary lines of the box bottom part onto the trajectory planning surface along the curved surface to obtain two upper and lower boundary lines; Module M2.1.2: The intersection line of one quadrant line at the bottom of the box and the trajectory planning surface is offset equally on both the left and right sides to obtain two latitudinal intersection lines; Module M2.2.3: In the driving surface formed by the two upper and lower boundary lines and the two intersecting latitudinal lines, the tool moves back and forth from top to bottom to obtain the initial tool path for machining the thickened area; The initial contour machining toolpath planning module includes: Module M2.2.1: Project the outline of the thickened area of ​​the box bottom part onto the trajectory planning surface to obtain the machining boundary lines of the thickened area of ​​each feature; Module M2.2.2: The machining boundary line of the thickened area is offset at equal intervals in the direction away from the material to obtain the contour cutting drive curve, and then the initial contour machining tool path is obtained.

4. The integral box bottom mirror milling toolpath planning system according to claim 3, characterized in that, The initial thinning zone machining toolpath planning module includes: Module M2.3.1: Based on the contour cutting drive curve, further offset by equal distance to obtain the thinning zone machining boundary line; Module M2.3.2: Divides the area into multiple regions based on the location of the thickened area; Module M2.3.3: In the area, the upper and lower directions are evenly divided according to the distance between the upper and lower contour lines, and the reciprocating tool path is selected one by one as the driving curve to obtain the initial thinning area machining tool path.

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