A method for generating fan-shaped high-speed machining area based on three-point arc determination

Abstract

The present invention provides a method for generating a fan-shaped high-speed machining area with three-point arc, which offsets the boundary curve of the area to be machined, obtains three points of the arc, further determines the arc and its parameter equation, and then determines the approximately longest arc in the boundary curve through Boolean operation, and finally outputs the fan-shaped high-speed machining area; and can realize high-speed machining partitioning and smooth tool path planning of the entire area to be machined through continuous iteration, effectively improving machining efficiency and reducing machining costs. And the generation method of the present invention has high universality and robustness.

Description

Technical Field

[0001] The invention belongs to the technical field of computer-aided manufacturing (CAM), and in particular relates to a method for generating a fan-shaped high-speed machining area based on three-point arc determination. Background Art

[0002] High-speed machining technology is one of the most effective advanced manufacturing technologies in mold manufacturing today. It refers to a leading technology that uses high spindle speed and high feed speed to achieve high material removal rate. According to the basic principle of high-speed cutting, after the cutting speed reaches a certain point, the cutting mechanism changes essentially. Increasing the spindle speed will actually reduce cutting heat and cutting force. Compared with traditional cutting, high-speed machining reduces unit cutting force by 30% and increases tool life by 70%. In addition, high-speed machining has the advantages of high machining efficiency, good surface finish, and small thermal stress deformation of the workpiece.

[0003] With the expansion of the application scope of high-speed machining in actual production, breakthroughs have been made in the research of new tool materials, the improvement of tool design structure, the generation of new strategies for CNC tool paths, and the improvement of cutting conditions. First, in order to achieve high-speed cutting, the current mainstream machine tools are equipped with extremely rigid spindles, powerful servo drive systems, and advanced digital controllers with fast interpolation functions. Secondly, on the one hand, a series of high-speed actuators such as electric spindles and linear motors have been widely used. On the other hand, it is the cutting parameters such as spindle speed, feed rate, axial and radial cutting depth. In the past few decades, many studies have contributed to the exploration of the optimal cutting parameters of hard materials under different cutting conditions in high-speed machining. Third, to achieve high-speed cutting, tool path characteristics are also very important. On the one hand, in order to meet motion constraints and adapt to high feed rates, the tool path should be as smooth as possible, that is, at least G1 continuous; otherwise, it will cause discontinuous points on the trajectory (such as corners) to stop completely and significantly reduce the average feed rate. On the other hand, in order to reduce tool chatter and tool wear, it is best to achieve continuous material removal throughout the high-speed cutting process.

[0004] Regarding new strategies for tool paths in CNC machining, existing research focuses on increasing the proportion of high-speed machining areas on the workpiece surface. However, existing research is highly universal, but there is little discussion on increasing the proportion of high-speed machining areas on the workpiece surface with special shapes (such as curved rings, etc.) and the effect is not particularly significant. At a time when customized product manufacturing is gradually being promoted, the machining efficiency of workpieces with special shapes needs to be improved urgently. Summary of the invention

[0005] In order to further increase the proportion of high-speed machining areas of special-shaped workpieces and make up for the performance deficiencies of existing universal partitioning algorithms, the present invention provides a method for generating a fan-shaped high-speed machining area based on three-point arc determination. Compared with other universal partitioning tool path planning algorithms, this method, while maintaining universality and robustness, determines the arc by three points and uses Boolean operations to obtain the approximate longest "center arc" in the boundary curve of certain special-shaped workpieces after layer cutting. Based on the "center arc" parameters, the parameters of four circular arcs and the maximum fan-shaped boundary are output. Through continuous iteration, high-speed machining partitioning and smooth tool path planning of the entire machining surface are realized.

[0006] A method for generating a fan-shaped high-speed machining area based on three-point arc positioning comprises the following steps:

[0007] (1) Input the boundary curve b of the current layer to be processed 0 , tool radius ρ, construction offset times N, initial minimum path area S min ;

[0008] (2) The boundary curve b 0 Offset inward once and simplify all vertices on the offset curve to obtain curve b s ;

[0009] (3) Traverse curve b s Sort all vertices on the graph into pairs according to the distance between each two vertices, and store them in the set {Pverts};

[0010] (4) Take the pair of vertices with the largest distance in the set {Pverts} as the current vertex pair, connect the current vertex pair to obtain a line segment K with a length of D, and find the curve b s The intersection points with the perpendicular bisector of line segment K are stored in the set {P};

[0011] (5) Calculate each intersection point in {P} with the midpoint P of line segment K m The arc point is determined based on the relationship between the distance and 0.5D;

[0012] (6) The arc is determined by the three-point arc determination method, and the arc and its parameters are determined by the obtained arc determination points and the current vertex pair;

[0013] (7) The discretized arc is used to construct a polyline, and the polyline is judged to be consistent with the curve b. s whether to interfere;

[0014] If no intervention is required, go directly to step (8);

[0015] If there is interference, move the arc point obtained in step (5) closer to P mThe arc point is updated and steps (6) and (7) are repeated.

[0016] (8) Output the parameters of the arc, based on the parameters of the arc and the boundary curve b 0 The fan-shaped high-speed machining area is constructed by the offset distance.

[0017] In the above step (1), the input boundary curve b 0 It is the contour curve of a layer obtained after the three-dimensional model of the workpiece is sliced ​​in a fixed direction. It is a closed polyline containing multiple points. The number of construction offsets N is to find the fan ring area with the largest area. 0 The number of offsets; the initial minimum path area S min Used to limit the minimum processing area of ​​the tool.

[0018] In step (2), for the boundary curve b 0 When biasing, the area S>S defined by the biased curve should be satisfied. min ; If S<=S min , no more biasing is performed.

[0019] In step (3), curve b s All the vertices on the grid are grouped into a vertex pair, and all the vertex pairs are sorted according to the distance between them and stored in the set {Pverts}.

[0020] In step (4), curve b s There are usually at least two intersection points with the perpendicular bisector of line segment K.

[0021] In step (6), the parametric equation of the arc includes the center P of the virtual circle where the arc lies ct , radius R arc 、The starting angle of the arc θ st , end angle θ ed The arc point obtained in step (5) and the pair of vertices with the largest distance taken out in step (4) together form three points. Based on the geometric relationship, a uniquely determined arc (arc line) can be constructed, and the center, radius, center angle, starting angle and ending angle of the virtual circle where the arc line is located can be determined.

[0022] In step (8), the output arc is used as the center arc and the boundary curve b 0 The offset distance is the distance to obtain curve b s Boundary curve b 0The final offset distance d. The boundary curve of the obtained fan-shaped high-speed machining area consists of two arcs parallel to the center arc and semicircular arcs connecting the two ends of the two arcs, wherein the radius of the semicircular arc is the offset distance d; after obtaining the fan-shaped high-speed machining area, the fan-shaped high-speed machining area is filled according to the tool radius to obtain a high-speed machining smooth tool path.

[0023] Preferably, in step (2), the boundary curve b 0 Offset distance d for offset i Calculated by the offset number N:

[0024] Use clipper to adjust the boundary curve b 0 To perform the offset operation, the offset distance starts from a small value ε (usually set to ε = 1), and ε is accumulated in sequence according to the number of times (i.e., the first offset distance is ε, the second offset distance is 2ε, and so on), until the area defined by the offset curve is S<=S min When , record the offset d at this time m , then the average offset each time is the required offset distance d i =d m / N.

[0025] Preferably, in step (2), all vertices on the offset curve are simplified by polylines by extracting vertices by distance, and the specific operation is as follows:

[0026] Start from the first vertex in order, take the first vertex as the current vertex, and delete the vertex whose distance is less than the set distance d p The vertex whose distance from the current vertex is greater than or equal to the set distance d p The next vertex is the current vertex, and so on until the last vertex; the remaining points are connected in sequence to form a simplified polyline, that is, curve b s .

[0027] As a preferred method, in step (4), the curve b is obtained s The specific steps for finding the intersection with the perpendicular bisector of line segment K are as follows:

[0028] Step 4-1: Select the pair of vertices with the largest distance in the set {Pverts} as the current vertex pair, connect the current vertex pair to form a line segment K with a length of D, and determine the midpoint P of the line segment K. m ;

[0029] Step 4-2: P m , according to the slope relationship of the straight line equation, construct the points P m Two line segments perpendicular to the line connecting the two vertices, both of which have a length of D, to ensure that each line segment can be aligned with curve bs intersect;

[0030] Step 4-3: Connect the two line segments obtained in step 4-2 to curve b. s Find the intersection and store the intersection point in the set {P}.

[0031] In the present invention, the generation of the smoothing tool path requires that the arc required is a standard circular arc; therefore, in step (5), the intersection point and P are determined. m The relationship between the distance (dis) and 0.5D is to ensure that the arc (arc line) generated later is a standard arc rather than an elliptical arc. Only when the distance dis≤0.5D can the standard arc and smooth tool path be constructed according to the three-point circle method; when the distance dis>0.5D, the standard arc and smooth tool path cannot be constructed.

[0032] As a preference, in step (5), if each intersection point in {P} and P m If the distances are all greater than 0.5D, then for any untraversed intersection point, move the intersection point closer to P m The direction of translation makes it consistent with P m The distance is equal to 0.5D, and a new point is obtained, and the new point is used as the arc-fixing point; all the intersections in {P} are traversed to obtain the arc-fixing points corresponding to all the intersections, and each arc-fixing point is processed according to steps (6), (7) and (8) to obtain multiple fan-shaped high-speed machining areas, and the fan-shaped high-speed machining area with the largest area is taken as the final output result. Among them, the arc line of the fan-shaped high-speed machining area with the largest area is taken as the center arc line.

[0033] As a further preferred embodiment, if the multiple arc-fixing points obtained in step (5) respectively pass through step (6) and enter the multiple polylines obtained after step (7), there is one or more polylines that are consistent with the curve b s No interference, then with curve b s The parameters of the arc corresponding to a non-interfering polyline or the parameters of the longest arc among the multiple arcs corresponding to the multiple polylines are output to step (8), and the longest arc is the center arc. s Do not interfere with the polyline, the rest with curve b s Interfering polylines can be directly eliminated without any processing to reduce the amount of calculation.

[0034] Preferably, in step (5), if there are one or more intersection points in {P} and P m If the distance between the intersection point and P is less than or equal to 0.5D, then take the intersection point or multiple intersection points that are closest to P. m The intersection point with the largest distance is taken as the arc point.

[0035] Specifically, if {P} has only one intersection with P mIf the distance between P and the intersection point is less than or equal to 0.5D, the intersection point is used as the arc-fixing point. m If the distance between P and D is less than or equal to 0.5D, then select the intersection point with P among the multiple intersection points. m The intersection point with the largest distance is taken as the arc point.

[0036] Preferably, in step (7), for the polyline and the curve b s In case of interference, when updating the arc point, if the arc point before the update is m If the vertex pair overlaps, delete the corresponding vertex pair from {Pverts} and jump to step (4). s Interference, and the original arc point and P m When they coincide, it means that the current vertex pair corresponding to the original arc point cannot construct the corresponding curve b s For arcs that do not interfere, the current vertex pair is deleted from the set {Pverts}, and the set {Pverts} is updated while jumping to step (4) to reselect the vertex pair with the largest distance as the current vertex pair.

[0037] As a further preferred embodiment, if the set {Pverts} is empty when jumping to step (4), then jump to step (2) to further bias the offset curve inward once, and update the curve b s , go to step (3). If the vertex pairs in the set {Pverts} have been deleted (empty set), it means that the curve after the offset in step (2) in this cycle cannot be constructed in the subsequent steps to match the curve b. s There is no interference between the polylines, so the offset curve needs to be further offset inward (the offset distance is also d i ) to enter the next cycle.

[0038] Preferably, in step (7), the arc is discretized according to angle or distance to construct a polyline.

[0039] Taking discretization by angle as an example, the number of vertices of the constructed polyline is Among them, θ st is the arc starting angle, θ ed is the arc end angle, and δ is the set discrete angle value.

[0040] Preferably, in step (7), by comparing the polyline and the curve b s The difference method is used to determine whether the two interfere with each other. When the discrete angle value or distance is small enough, if the difference result is empty, the two do not interfere with each other; if the difference result is not empty, the two interfere with each other.

[0041] As a preferred method, after obtaining the fan-shaped high-speed machining area in step (8), the boundary curve b0 Difference is calculated from the processing area to obtain multiple new areas. Each area larger than S min The boundary curve of the new area is processed according to steps (2) to (8), and this cycle is repeated to obtain all the fan-shaped high-speed machining areas.

[0042] In this technical solution, the fan-shaped high-speed machining area with the largest area obtained for the first time is moved from the boundary curve b 0 After deleting from the limited processing area, multiple new processing areas and their corresponding boundary curves will be formed. min The boundary curve of the new processing area is taken as the new boundary curve, and processed according to steps (2) to (8) to obtain the corresponding multiple fan-shaped high-speed processing areas. This cycle can be repeated on the boundary curve b 0 Generate as many fan-shaped high-speed machining areas as possible within the limited machining area to improve machining efficiency. min The new processing area can be directly defaulted to the low-speed processing area.

[0043] As a further preferred embodiment, if after multiple cycles, the area defined by the offset curve in step (2) is less than or equal to S min , the cycle is terminated and the area defined by the boundary curve is identified as the low-speed machining area.

[0044] The method for generating a fan-shaped high-speed machining area based on three-point arc positioning of the present invention comprises the following steps: inputting a machining area boundary curve b 0 and related process parameters; b 0 Offset the given distance inward and make the offset curve b i Simplified to b s polyline; traverse b s All vertices get a vertex pair set; take the vertex pair with the largest distance in the vertex pair set, and connect them by taking the perpendicular bisector and b s Intersect, after judging the geometric relationship, take out to construct b s The intersection point P of the approximate longest arc within the boundary; determine the unique arc equation and its parameters by the vertex pair and the intersection point P, and discretize it into polylines and boundary curve b according to angle (or distance) s Boolean difference operation is performed to determine whether the two interfere with each other. If there is no interference, the four arcs contained in the fan-shaped processing area are deduced from this arc. The above steps are repeated to extract the fan-shaped processing area with the largest area ratio. The fan-shaped processing area is filled according to the tool radius to obtain the final high-speed processing smooth tool path. This method generates a high-speed processing area with a high area ratio for workpieces with special shapes (large bends), high processing efficiency, and takes into account the universality of workpiece shapes. The method has simple logic and good robustness.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The fan-shaped ring-shaped high-speed machining area generation method based on three-point arc determination of the present invention determines the arc by three-point arc determination and Boolean operations to obtain the approximate longest arc and its related parameters in the boundary curve, thereby generating a fan-shaped ring-shaped high-speed machining area, and realizing high-speed machining partitioning and smooth tool path planning in the entire machining area through continuous iteration. The generation method of the present invention can generate a fan-shaped ring-shaped smooth tool path with a high proportion of high-speed machining area for workpieces of special shapes (especially curved strips and rings), and is also universal and robust for workpieces of various other shapes, generating a smooth tool path suitable for high-speed machining, and ultimately achieving the purpose of improving machining efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a method for generating a fan-shaped high-speed machining area based on three-point arc determination according to an embodiment of the present invention;

[0048] Figure 2 To obtain the process schematic diagram of the maximum high-speed machining area proportion and the longest "arc";

[0049] Figure 3 Schematic diagram of the biasing process of the boundary curve;

[0050] Figure 4 It is a schematic diagram of the process of discretizing arcs into polylines;

[0051] Figure 5 The schematic diagram of the smoothing tool path filling of the fan ring high-speed machining area is obtained;

[0052] Figure 6 The high-speed machining area (a) is generated by the method of the embodiment of the present invention and the machining area tool path (b) is generated by the common offset method. DETAILED DESCRIPTION

[0053] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0054] In order to make the workpiece processing more efficient, it is necessary to obtain as large a proportion of the high-speed processing area (here, the fan ring area) as possible within the processing area. Therefore, the problem is transformed into a geometric problem of finding one or more fan rings as large as possible inside the boundary curve of the workpiece. For this geometric problem, the solution proposed in this embodiment is to offset the original boundary curve multiple times and use the final offset distance d as the radius of the two semicircular parts at both ends of the fan ring area, such as Figure 2From a geometric point of view, the area of ​​the obtained fan-shaped ring region is obtained by scanning two semicircular parts along an arc line (hereinafter referred to as the "center arc line"), so after determining the radius of the semicircular part (the final offset distance d), the longer the "center arc line" is, the larger the area of ​​the obtained fan-shaped ring region is.

[0055] In order to make the "center arc" as long as possible, according to the basic mathematical principle of three-point circle determination, first determine the two vertices on the offset boundary with a distance D, and then make a perpendicular bisector from the line connecting the two vertices to intersect the offset boundary. According to the arc length formula:

[0056]

[0057] Among them, α represents the central angle corresponding to the arc; R represents the radius of the circle where the arc lies.

[0058] Therefore, the arc length increases monotonically within the definition domain. When α=π (R=D / 2 at this time), the maximum arc length is obtained. Therefore, in the process of obtaining the third point (arc point), when the arc does not interfere with the boundary after the offset (the fan ring area will not exceed the workpiece boundary), the farther the third point is from the midpoint of the line connecting the first two points (the two vertices farthest apart), the longer the "center arc". In this embodiment, the third point is moved along the perpendicular bisector until the longest "center arc" is obtained through interference judgment. This process is as follows Figure 2 shown.

[0059] like Figure 1 As shown, a method for generating a fan-shaped high-speed machining area based on three-point arc positioning includes the following steps:

[0060] Step 101: Input the boundary curve b of the area to be processed in the current layer 0 , tool radius ρ, construction offset times N, initial minimum path area S min .

[0061] Among them, the input boundary curve b 0 It is the contour curve of a certain layer obtained after the three-dimensional model of the workpiece is cut in a fixed direction. The boundary is curve b 0 Specifically, it is a polyline composed of multiple points. 0 , it cannot be determined that the area of ​​the fan-shaped high-speed machining area with the largest area is the largest by only one offset; the number of construction offsets N refers to the number of times the fan-shaped high-speed machining area is obtained by offsetting the current boundary curve. The final result is the fan-shaped high-speed machining area {S i}(1≤i≤N) takes the largest area. The initial minimum path area S min It refers to the boundary curve b 0The accumulated bias is applied until the area defined by the obtained bias curve is S<=S min , then stop the bias process; S min Used to limit the minimum processing area of ​​the tool.

[0062] Step 102: Boundary curve b 0 Bias inward once to obtain the biased curve b i , for b i Simplify all the vertices on the polyline to get curve b s Among them, for the boundary curve b 0 The bias should satisfy curve b i The area of ​​the defined region S>S min ; If S<=S min , then stop biasing, such as Figure 3 shown.

[0063] In this step:

[0064] (1) For the boundary curve b 0 Offset distance d for offset i According to the number of offsets N, we can obtain:

[0065] Use clipper to adjust the boundary curve b 0 To perform the offset operation, the offset distance starts from a small value ε (usually given as ε = 1), and ε is accumulated in sequence according to the number of times (that is, the first offset distance is ε, the second offset distance is 2ε, and so on). When the area of ​​the area defined by the offset curve is S<=S min When , record the offset d at this time m , then the offset each time is the required offset distance d i =d m / N.

[0066] (2) The simplified part of the polyline is to extract vertices by distance:

[0067] That is, start from the first vertex in order, take the first vertex as the current vertex, and delete all the vertices that are less than the set distance d. q The vertex whose distance from the current vertex is greater than or equal to the set distance d p The next vertex is taken as the current vertex, and so on until the last vertex. The remaining points are connected in sequence to form a simplified polyline, that is, curve b. s .

[0068] Step 103: For the curve b obtained in step 102 s , perform vertex traversal, sort the vertices by distance and pair them up in pairs, and store them in the set {Pverts}.

[0069] The number of points included in the simplified polyline in step 102 is reduced exponentially. s All vertices on the vertices are grouped into pairs without duplication, and the distance d between each pair of vertices is calculated. ni , then follow d ni Put different vertex pairs into the set {Pverts} from large to small.

[0070] Step 104: Take the pair of vertices with the largest distance in the set {Pverts} as the current vertex pair, connect the current vertex pair to obtain a line segment K with a length of D, and find the curve b s The points of intersection with the perpendicular bisector of segment K are stored in the set {P}.

[0071] If there are still values ​​in the set {Pverts} (not an empty set), then take a pair of vertices with the largest distance (the current vertex pair), and record the distance between the two as D. If there are no values ​​in the set {Pverts} (it is empty), then jump to step 102.

[0072] If the curve b obtained after multiple offsets after multiple jumps to step 102 is i The area of ​​the defined region S<=S min , the cycle is terminated and the area defined by the boundary curve is identified as the low-speed machining area.

[0073] In order to minimize the time required to transform the boundary curve b of the current layer 0 The maximum fan-shaped high-speed machining area within the contour is obtained. Here, the vertex pair with the maximum distance (spacing is D) is selected from the {Pverts} set as two points in the three-point arc. And the midpoint P of the line segment between the two points is taken m , for P m , according to the slope relationship of the straight line equation, construct the points P m The two line segments perpendicular to the line connecting the two vertices have the same length of D. Find the distance between the two line segments and the curve b. s The intersection point is stored in the set {P}.

[0074] Step 105: For each point in {P} to P m The distance between and D is judged, and the arc point (the third point in the three-point arc) is determined according to the judgment result:

[0075] If every point in {P} is m If the distance dis satisfies dis>0.5D, then for any untraversed intersection point, move the intersection point closer to P m The direction of translation makes it consistent with P mThe distance is equal to 0.5D, and a new point is obtained, and the new point is used as the arc-fixing point; traverse all the intersection points in {P}, obtain the arc-fixing points corresponding to all the intersection points, and proceed to the next step for each arc-fixing point.

[0076] If there are one or more intersection points with P m If the distance dis≤0.5D, then the intersection point is used as the arc-fixing point or multiple intersection points with P are used as the arc-fixing point. m The intersection point with the largest distance is taken as the arc point and proceed to the next step.

[0077] The distance judgment in this step is to ensure that the arc generated subsequently is a standard arc rather than an elliptical arc. In this embodiment, the generation of the smoothing tool path requires that the required arc is a standard arc. m When the distance dis=0.5D, according to the three-point arc determination method, the radius of the arc (arc line) formed by the arc determination point obtained at this time and the two vertices with the largest distance taken out in step 104 is R=0.5D, and the corresponding center angle θ=180°. If dis>0.5D, it is impossible to form a standard arc and construct a smooth tool path.

[0078] Step 106: For the arc-fixing point and the current vertex pair obtained in step 105, three points are used to construct an arc (arc line) to obtain a parametric equation of the arc.

[0079] The three-point arc determination is one of the basic mathematical methods for solving arc parameter equations. The arc determination points obtained in step 105 and the currently selected vertex pair are three points. According to the geometric relationship, a unique arc can be constructed and the center coordinates P can be determined at the same time. ct , radius R arc , center angle θ, starting angle θ st , end angle θ ed .

[0080] In the case where multiple arc-fixing points are output in step 105, the multiple arc-fixing points are respectively subjected to step 106 to obtain corresponding multiple arc lines and their parameter equations, and then proceed to the next step.

[0081] Step 107: According to the parametric equation of the arc, the original arc is discretized by angle (or distance) as the fitting of the original arc to construct a polyline b p ;

[0082] Polyline b p The polygonal curve b after the current offset s The difference is calculated to determine whether the two interfere with each other, and then determine the feasibility of the tool path. If it is determined that there is interference, jump to step 108; if there is no interference, determine that the arc is the center arc and jump to step 109.

[0083] In order to facilitate the determination of whether the original arc is on curve b under the premise of approximating the longest arc length s According to the parameters such as the center angle, the original arc is discretized into multiple points in the coordinate system according to the given discrete angle value (taking angle discretization as an example) δ through the original arc parameter equation. p ,like Figure 4 As shown, the equation used is:

[0084] x i =x c +R×cos t

[0085] y i =y c +R×sin t

[0086] (x i ,y i ) is a polyline b p The vertex set (x c ,y c ) is the coordinate of the center of the circle, R is the radius, and t = i × δ. The number of points here Therefore, the difference function in the clipper library is used to p With curve b s Perform a Boolean difference operation. If the discrete angle value δ is small enough, if the difference result is zero, then curve b is considered s There is no interference with the currently obtained maximum arc, otherwise it is judged as interference.

[0087] In the case where multiple arc points are output in step 105, multiple arc lines and their parameter equations are output after step 106, in step 107, each arc line is discretized to obtain multiple polylines. If one or more polylines are aligned with curve b, s No interference, then with curve b s The parameters of the arc (center arc) corresponding to a non-interfering polyline or the parameters of the longest arc (center arc) among the multiple arcs corresponding to the multiple polylines are output to step 109; in addition, for the arcs other than those with curve b s Do not interfere with the polyline, the rest with curve b s Interfering polylines can be directly eliminated without any processing to reduce the amount of calculation.

[0088] If all the obtained polylines are consistent with curve b s If there is interference, each polyline is processed according to step 108.

[0089] Step 108: Move the arc point closer to P m Move a small value r in the direction of P to update the arc point.m If they coincide, the current pair of vertices is deleted from the set {Pverts}, and the process jumps to step 104 to reselect a pair of vertices with the largest distance in the set {Pverts} as the current pair of vertices.

[0090] In determining the polyline b p With curve b s After the interference occurs, move the originally specified third point of the arc (arc point) along the perpendicular bisector of line segment K to the midpoint P of line segment K. m The direction is shifted by a given distance r, and the arc point is updated. If the original arc point is already close to the midpoint P m coincide with curve b, then it means that the current vertex pair cannot construct a s Interference occurs in the standard arc, so the current vertex pair is deleted from the set {Pverts}.

[0091] Step 109: Output the parameters of the current arc (arc line), including the center P ct , radius R arc 、Arc starting angle θ st 、Arc end angle θ ed , according to the parameters of the arc and the boundary curve b 0 The offset distance d constructs a fan-shaped high-speed machining area.

[0092] The non-interfering center arc obtained in step 107 is obtained according to the parametric equation of the center arc and the boundary curve b 0 The offset distance d can be used to obtain the center, radius and other parameter information of the four arcs contained in the fan-shaped high-speed machining area. Figure 5 As shown, the fan-shaped high-speed machining area is filled in sequence, and finally a smooth tool path is output.

[0093] If multiple lines that do not match curve b are output in step 107 s If there are interfering polylines, the parameters of the arc corresponding to each polyline are output in step 109, and the corresponding fan-shaped high-speed machining area is obtained, and the fan-shaped high-speed machining area with the largest area is taken as the final output.

[0094] After a cycle of processing according to the above steps 101 to 109, the boundary curve b can be obtained. 0 The maximum area of ​​the fan-shaped high-speed machining area within the limited machining area is selected to further improve the machining efficiency; optionally, the maximum area of ​​the fan-shaped high-speed machining area obtained in the first cycle is moved from the boundary curve b 0 After deleting from the limited processing area, multiple new processing areas and their corresponding boundary curves will be formed. minThe boundary curve of the new processing area is used as the new boundary curve, and is processed according to steps 102 to 109 to obtain the corresponding multiple fan-shaped high-speed processing areas. This cycle can be repeated on the boundary curve b. 0 Generate as many fan-shaped high-speed machining areas as possible within the limited machining area, and finally output the final fan-shaped high-speed machining area. min The new processing area can be directly defaulted to the low-speed processing area.

[0095] The generation method of this embodiment is implemented by C++ programming language, and a typical application example is as follows:

[0096] For example, select a processing area with a certain curved shape, such as Figure 6 As shown in the figure, the maximum width of the figure is 5210mm and the maximum height is 2424mm. The special feature of this figure is that there are multiple folded edges and the whole has a certain curvature. These areas have multiple sharp corners during the ordinary offset processing and cannot achieve high-speed processing. In the test program, the tool radius ρ is set to 5mm, the number of offsets is constructed to N = 10, and the initial minimum path area S is set to min =10000mm 2 . Figure 6 (a) shows the fan-shaped high-speed machining area generated by the generation method of this embodiment. It can be seen from the figure that the fan-shaped high-speed machining area on the workpiece surface accounts for a high proportion, and the remaining low-speed machining area is small. This path is suitable for high-speed machining and has high machining efficiency. Figure 6 (b) shows the circular tool path obtained by the common offset method. It can be seen from the figure that the common offset method may produce more sharp corners, and the existence of sharp corners is not conducive to high-speed processing. Therefore, the tool path obtained by the generation method of this embodiment has a higher processing efficiency than the tool path obtained by the common offset method.

[0097] The above is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, the present invention may be modified and varied in various ways. Any modification, equivalent substitution, improvement, etc. made without departing from the principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for generating a fan-shaped high-speed machining area based on three-point arc determination, characterized in that: The following steps are involved: (1) Input the boundary curve b0 of the current layer to be processed, the tool radius ρ, the number of construction offsets N, and the initial minimum path area S min ; (2) The boundary curve b0 is offset inward once, and all vertices on the offset curve are simplified to obtain curve b s ; (3) Traverse curve b s Sort all vertices on the graph into pairs according to the distance between each two vertices, and store them in the set {Pverts}; (4) Take the pair of vertices with the largest distance in the set {Pverts} as the current vertex pair, connect the current vertex pair to obtain a line segment K with a length of D, and find the curve b s The intersection points with the perpendicular bisector of line segment K are stored in the set {P}; (5) Calculate each intersection point in {P} with the midpoint P of line segment K m The arc point is determined based on the relationship between the distance and 0.5D; (6) The arc is determined by the three-point arc determination method, and the arc and its parameter equation are determined by using the obtained arc determination points and the current vertex; (7) The discretized arc is used to construct a polyline, and the polyline is judged to be consistent with the curve b. s whether to interfere; If no intervention is required, go directly to step (8); If there is interference, move the arc point obtained in step (5) closer to P m The arc point is updated and steps (6) and (7) are repeated. (8) Outputting the parameters of the arc line, and constructing the fan-shaped high-speed machining area according to the parameters of the arc line and the offset distance of the boundary curve b0.

2. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1 is characterized in that: In step (5), if every intersection point in {P} and P m If the distances are all greater than 0.5D, then for any untraversed intersection point, move the intersection point closer to P m The direction of translation makes it consistent with P m The distance is equal to 0.5D, and a new point is obtained, and the new point is used as the arc-fixing point; Traverse all the intersection points in {P} to obtain the arc-determining points corresponding to all the intersection points. Process each arc-determining point according to steps (6), (7) and (8) to obtain multiple fan-shaped high-speed machining areas. Take the fan-shaped high-speed machining area with the largest area as the final output result.

3. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 2 is characterized in that: If the multiple arc-fixing points obtained in step (5) pass through step (6) and enter step (7) respectively, among the multiple polylines obtained, there is one or more polylines that are consistent with curve b s No interference, then with curve b s The parameters of the arc corresponding to a non-interfering polyline or the parameters of the longest arc among multiple arcs corresponding to multiple polylines are input as output to step (8).

4. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1, characterized in that: In step (5), if there are one or more intersection points in {P} with P m If the distance between the intersection point and P is less than or equal to 0.5D, then take the intersection point or multiple intersection points with P m The intersection point with the largest distance is taken as the arc point.

5. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1, characterized in that: In step (7), for the polyline and curve b s In case of interference, when updating the arc point, if the arc point before the update is m If they overlap, delete the current vertex pair from {Pverts} and jump to step (4).

6. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 5, characterized in that: If the set {Pverts} is empty when jumping to step (4), then jump to step (2) to further bias the offset curve inward once and update the curve b s , proceed to step (3).

7. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1, characterized in that: In step (7), by comparing the polyline and curve b s The difference method is used to determine whether the two interfere with each other. If the difference result is empty, the two do not interfere with each other; if the difference result is not empty, the two interfere with each other.

8. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1, characterized in that: In step (2), the boundary curve b0 is offset by an offset distance d i Calculated by the offset number N: Use clipper to perform offset calculation on the boundary curve b0. The offset distance starts from a small value ε and accumulates ε in sequence until the area defined by the offset curve is S<=S min When , record the offset d at this time m , then the average offset each time is the offset distance d i =d m / N.

9. The method for generating a fan-shaped high-speed machining area based on three-point arc positioning according to claim 1, characterized in that: After the fan-shaped high-speed machining area is obtained in step (8), the boundary curve b0 and the machining area are subtracted to obtain multiple new areas. min The boundary curve of the new area is processed according to steps (2) to (8), and this cycle is repeated to obtain all the fan-shaped high-speed machining areas.

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