A five-axis linkage additive and subtractive material hybrid machining sequence planning method

Abstract

This invention discloses a five-axis linkage hybrid additive-subtractive machining sequence planning method. First, based on the equal-thickness layered cross-section of the part, the centroid of the cross-section is calculated to obtain the centroidal axis of the column structure part. Then, addressing the tool collision interference problem in the hybrid additive-subtractive machining process, a tool accessibility model is established. A bounding box acceleration structure is proposed to speed up the model solving process. Using the accessibility model and acceleration structure, the part is coarsely decomposed to establish the hybrid additive-subtractive machining sequence. Finally, the angle between the five-axis linkage printing platform and the tool is adjusted to optimize and obtain the final machining sequence. The method of this invention establishes a tool accessibility model for the hybrid additive-subtractive machining process, ensuring that tool collision interference does not occur during machining. The proposed bounding box acceleration structure speeds up the accessibility model solving process. By adjusting the angle between the five-axis linkage machining platform and the machining tool, the final hybrid additive-subtractive machining sequence is obtained, improving machining efficiency.

Description

Technical Field

[0001] This invention belongs to the field of 3D printing data processing technology, specifically relating to a five-axis linkage additive and subtractive material hybrid processing sequence planning method. Background Technology

[0002] 3D printing (also known as additive manufacturing) is a manufacturing technology that uses computer control to deposit, connect, and solidify materials layer by layer (such as plastics, liquids, or powder particles) to build three-dimensional objects from CAD models or digital 3D models. Current 3D printing has significant limitations in terms of part forming accuracy and surface quality control, making it difficult to achieve high-precision direct printing of parts. In contrast, subtractive machining, based on machining, performs well in terms of part precision and quality control. Therefore, combining additive manufacturing and machining to form a hybrid additive-subtractive manufacturing technology can leverage the advantages of additive manufacturing, such as short cycle time and high material utilization, while combining the advantages of machining, such as high surface quality and high precision, enabling efficient, high-precision, and high-performance part forming and manufacturing.

[0003] For complex structural components, such as engine components like impellers and integral bladed disks, which have complex shapes and high performance and precision requirements, existing CNC machining methods are difficult to use. Due to the complex shape of the parts, tool collision interference is prone to occur during the cutting process, making it difficult to guarantee high precision. Furthermore, the presence of tool collision interference necessitates compromises in the structural design of the parts, failing to meet performance requirements. Tool collision interference also frequently occurs during the cutting process for columnar structures, slender and curved structures, and structures containing cavities.

[0004] Hybrid additive and subtractive manufacturing provides a direction for high-precision machining of complex structural parts. The integration of additive and subtractive manufacturing can solve the problem of tool collision interference. During the additive manufacturing process, before the tool may collide and interfere, the printed part of the part is cut, which can avoid the tool and the part from colliding. This can not only obtain high-precision parts, but also avoid the risks caused by tool collision interference. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a five-axis linkage hybrid machining sequence planning method for additive and subtractive machining. This method not only calculates tool collision interference in real time during the additive and subtractive machining process to ensure its smooth operation, but also optimizes the hybrid machining sequence while ensuring that tool collision interference does not occur.

[0006] The technical solution adopted in this invention is: a five-axis linkage additive and subtractive material hybrid machining sequence planning method, the specific steps of which are as follows:

[0007] S1. Based on the equal-thickness layered slice section of the part, calculate the centroid of the slice section to obtain the centroidal axis of the column structure part;

[0008] S2. To address the tool collision and interference problem in the hybrid machining process of additive and subtractive materials, a tool reachability model is established for the hybrid machining process of additive and subtractive materials.

[0009] S3. A bounding box acceleration structure is proposed to speed up the model solution process;

[0010] S4. Using the accessibility model and acceleration structure, the part is roughly decomposed, a hybrid machining sequence of additive and subtractive materials is established, and finally the angle between the five-axis linkage printing platform and the tool is adjusted to optimize the final machining sequence.

[0011] Furthermore, step S1 is specifically as follows:

[0012] The entire part is sliced ​​by using equal-thickness layering. For each slice section, the centroid of the polygon of the current slice section is obtained.

[0013] The calculation of the centroid of the slice cross section is as follows:

[0014] The slice section is defined as a polygon with n vertices, composed of n-2 triangles. These n-2 triangles share a common vertex V1(x1,y1), and the remaining two vertices are V1(x1,y1). i (x i ,y i ) and V i+1 (x i+1 ,y i+1 ), and 1<i<n.

[0015] Let T be the centroid of the j-th triangle. j (t jx ,t jy V1(x1,y1) is a common vertex, and the remaining two points are V1(x1,y1) and V2(x1,y1). j (x j ,y j ) and V j+1 (x j+1 ,y j+1 The centroid T is obtained from the centroid formula. j (t jx ,t jy The coordinates of ) are expressed as follows:

[0016]

[0017] The centroid G(x) of the polygonal slice section g ,y g The relationship between the triangle and the centroids of the n-2 triangles that make it up is expressed as follows:

[0018]

[0019] Among them, A j Let represent the area of ​​the j-th triangle.

[0020] Let V contain n vertices. i (x i ,y i The centroid of the polygonal section of the slice is C(x). c ,y c Given a polygon with area A, the expression for calculating the centroid of the polygon is as follows:

[0021]

[0022] Each slice of the part has a cross-sectional profile that is a composite polygon. A centroid C is then determined for each slice profile. i (x i ,y i ,z i ), z i This indicates the current contour layer height. For parts with an h layer, there are C1, C2, C3..., C... h Centroid point.

[0023] Finally, connect the centroids of all the cross sections in sequence to obtain the centroidal axis of the column structure part.

[0024] Furthermore, step S2 is specifically as follows:

[0025] S21. Based on the centroid of the cross-section of the part slice, the tool is simplified into a ray, and a simplified tool mathematical model is established;

[0026] Simplifying cutting tools requires meeting the following three conditions:

[0027] (1) Determine the tool contact point and tool direction;

[0028] Let the radius of the ball end mill tip be R, and the contact point of the tool be the cutting point. The center of the circumscribed circle of the cutting point with radius R is regarded as the starting point of the simplified tool, that is, the starting point of the ray, and the direction of the simplified tool is the direction of the ray.

[0029] For the print head, the contact point can be regarded as the starting point of the simplified tool, that is, the starting point of the ray, and the direction of the simplified tool is the direction of the ray.

[0030] (2) Tool continuity problem;

[0031] For the print head and cutting head in the additive and subtractive material hybrid machining process, calculate the continuity on the part contour. Take any point p on the part surface contour, and calculate the tool reachability of every point in the area of ​​radius σ around that point to meet the tool continuity requirements.

[0032] Due to the layered nature of 3D printing, the layer thickness is set as the step size to discretize the vertical dimension. Calculating tool reachability at each discretized point satisfies tool continuity in the vertical dimension. Similarly, in the horizontal dimension, a small positive real number σ is used as the step size to discretize the contour lines of each layer plane. Calculating tool reachability at each discretized point satisfies tool continuity in the horizontal dimension.

[0033] The setting of the real number σ is designed according to the specific tool size. During the machining process, the tool can move continuously by one tool position. The step size setting of any point on the contour must be less than the distance of the tool moving by one tool position. The maximum value is the diameter D of the tool head.

[0034] (3) Feasible range of tools under support-free conditions;

[0035] Using a five-axis CNC machining platform to achieve supportless printing, when printing parts with a suspended structure, the printing direction of the current layer is... The outward normal vector of the triangular facet on the side of the suspended structure is The conditions for not using a supporting structure are as follows:

[0036]

[0037] The value of α is either 45° or 90°, depending on the different parts and processing environments.

[0038] If the angle between the printing direction and the normal vector of the triangular facet on the side of the suspended structure is greater than α+90°, the suspended structure will collapse, causing the machining to terminate. Therefore, the feasible range of the tool under the supportless condition is the sum of the range within which the printed layer plane of the suspended structure forms an angle α with the positive Z-axis direction, plus the range below the printed layer plane.

[0039] The simplified general equation for the cutting tool, i.e., the simplified mathematical model of the cutting tool, is expressed as follows:

[0040]

[0041] Where o represents the starting point of the ray, Let t represent the direction vector, and 0 < t < ∞, where t represents the distance the ray travels; the simplified ray is considered to be infinitely long.

[0042] S22. Based on the obtained simplified tool mathematical model, establish a tool collision interference algorithm;

[0043] Traverse all triangular faces of the STL model and find their intersection with the simplified tool mathematical model. If an intersection point exists, tool collision interference occurs; otherwise, no collision occurs. The specific intersection process is as follows:

[0044] To determine whether the simplified mathematical model equation of the cutting tool intersects the plane containing the triangular facet, let the three vertices of the triangle be P1(X1,Y1,Z1), P2(X2,Y2,Z2), and P3(X3,Y3,Z3). Then the equation of the plane containing the triangular facet is:

[0045] Mx + Ny + Oz + P = 0 (6)

[0046] Where M, N, O, and P represent the parameters of the plane equation, and the normal vector of the plane containing the triangular facet is N(M,N,O). All three vertices of the triangle lie within this plane. Substituting any point, we get:

[0047] P = -dot(N, P1) (7)

[0048] Substituting the simplified mathematical model equations of the cutting tool into the plane equations, we can obtain:

[0049]

[0050] Where t represents the distance from the starting point of the tool to the intersection point with the triangle.

[0051] If t < 0, it means the triangle is behind the cutter and will not intersect; if t > 0, it means the triangle is in front of the cutter and will intersect, obtaining the intersection point P of the cutter and the plane containing the triangle.

[0052] Then determine whether P is inside the triangle by connecting the three vertices of the triangle to the intersection point P, resulting in three vectors. and Calculate the cross product of each of the three vectors and the vector formed by the three sides of the triangle:

[0053]

[0054] If the directions of the three cross products are consistent with the direction of the triangle normal vector N, the intersection point is inside the triangle; if the directions are inconsistent, the intersection point is not inside the triangle. The tool reachability of the intersection point can be obtained based on whether the tool causes collision interference.

[0055] Furthermore, step S3 is specifically as follows:

[0056] S31. Construct bounding boxes based on triangular facet coordinates, subdivide bounding boxes and recursively build a tree-like bounding box structure.

[0057] (1) Sort all triangular facets in the model according to the centroid position of the triangular facets. The sorting method can be selected according to the size of the x-coordinate, the size of the y-coordinate, or the size of the z-coordinate, depending on the different geometric features of the model.

[0058] (2) Create nodes for the tree-shaped bounding box. Each node contains the outline information of the bounding box, leaf node information, and indexes of the left and right subtrees.

[0059] (3) Based on the triangular face data obtained in step (1), determine the number of triangular face data, set it as r, and set the starting left subscript l to 0. Construct a triangular face array and set the minimum number of triangular face data contained in each bounding box to n.

[0060] (4) Construct the bounding box of the current tree node, with the left subscript of the current tree node being l and the right subscript being r;

[0061] (5) Traverse all triangles in the triangle array with index [l,r], calculate the maximum value of x, y, z coordinates of all triangles, and construct the current bounding box outline;

[0062] (6) Check if the number of triangular faces in the bounding box is less than n. If so, directly construct the bounding box of the current node and return the current leaf node; otherwise, continue recursively building the tree.

[0063] (7) Based on the x, y, z coordinates calculated in step (5), select the longest axis and sort the centroid coordinates of the triangular facets inside the bounding box according to the size of the coordinate values ​​of that axis.

[0064] (8) The midpoint of the triangular face array is mid = (l+r) / 2. Divide all triangular faces into two parts. The left half l index remains unchanged, and the r index is changed to mid. The right half l index is changed to mid+1, and the r index remains unchanged. Return to step (4) to recursively build the tree. The left subtree uses the left half triangular face and its index, and the right subtree uses the right half triangular face and its index.

[0065] Repeat steps (1)-(8) continuously to complete the creation of the tree bounding box.

[0066] S32. Intersection of simplified mathematical model of the cutting tool and tree-shaped bounding box structure;

[0067] An AABB bounding box has three opposing planes, which are three sets of planes perpendicular to the x, y, and z axes. The intersection of the three pairs of planes is calculated, and the entry and exit points of each pair of planes are calculated. Based on the coordinates of the entry and exit points, it is determined whether the tool intersects with the bounding box. If it intersects, the intersection with the triangular facets inside the bounding box is calculated to obtain the intersection point between the tool and the STL model.

[0068] Based on the simplified equation of the tool, calculate the distances t0 and t1 between the tool and the two intersection points of a set of opposite points and the starting point. Let the coordinates of the lower left point of the bounding box be L(x).l ,y l ,z l The coordinates of the upper right point are B(x). b ,y b ,z b The direction of the tool is d(x). d ,y d ,z d Then, dividing the bottom left corner coordinate L of the bounding box by the tool direction d yields a 3D vector in(x0, y0, z0), and dividing the top right corner coordinate B of the bounding box by the tool direction d yields a 3D vector out(x0, y0, z0). t ,y t ,z t The maximum value of the three coordinates in the in vector is denoted as t0, and the minimum value of the three coordinates in the out vector is denoted as t1. It is determined whether t0 < t1. If t0 < t1, the tool and the bounding box will collide and interfere; otherwise, the tool and the bounding box will not collide and interfere.

[0069] Where x0 represents the x-axis coordinate of the tool's entry point in the bounding box perpendicular to the x-axis plane, y0 represents the y-axis coordinate of the tool's entry point in the bounding box perpendicular to the y-axis plane, and z0 represents the z-axis coordinate of the tool's entry point in the bounding box perpendicular to the z-axis plane. Conversely, the three coordinate components of the vector out correspond to the coordinates of the three exit points on the opposite side.

[0070] Furthermore, step S4 is specifically as follows:

[0071] S41. Using the simplified printhead equation and tool reachability model, the tool reachability is calculated gradually from the bottom contour upwards. If a collision interference occurs, the part is decomposed from the current tool starting point and the point where the collision interference occurs. If no collision interference occurs, the tool moves up one layer until the part is completely decomposed, resulting in a machining sequence that only considers printhead collisions.

[0072] S42. Utilizing the characteristics of the five-axis linkage machining platform and the greedy algorithm, when calculating the tool accessibility of each layer, the angle between the five-axis linkage machining platform and the tool is adjusted to obtain the highest interference point when collision interference may occur, thereby reducing the number of tool changes and obtaining the optimized additive and subtractive material hybrid machining sequence.

[0073] The beneficial effects of this invention are as follows: First, based on the equal-thickness layered cross-section of the part, the centroid of the cross-section is calculated to obtain the centroidal axis of the column structure part. Then, addressing the tool collision interference problem in the hybrid additive-subtractive machining process, a tool accessibility model is established. A bounding box acceleration structure is proposed to speed up the model solving process. Using the accessibility model and acceleration structure, the part is coarsely decomposed to establish a hybrid additive-subtractive machining sequence. Finally, the angle between the five-axis linkage printing platform and the tool is adjusted to optimize and obtain the final machining sequence. This invention establishes a tool accessibility model for the hybrid additive-subtractive machining process, ensuring that tool collision interference does not occur during machining. The proposed bounding box acceleration structure speeds up the accessibility model solving process. By adjusting the angle between the five-axis linkage machining platform and the machining tool, the final hybrid additive-subtractive machining sequence is obtained, improving machining efficiency. Attached Figure Description

[0074] Figure 1 This is a flowchart of a five-axis linkage additive and subtractive material hybrid processing sequence planning method according to the present invention.

[0075] Figure 2 This is a schematic diagram of solving the centroid of a polygon in an embodiment of the present invention.

[0076] Figure 3 This is a schematic diagram of a five-axis linkage platform implementing supportless printing in an embodiment of the present invention.

[0077] Figure 4 This is a schematic diagram illustrating the intersection of a ray and a triangle in an embodiment of the present invention.

[0078] Figure 5 This is a schematic diagram of the root node bounding box of the tree-shaped bounding box in an embodiment of the present invention.

[0079] Figure 6 This is a schematic diagram illustrating the intersection of a ray and a bounding box in an embodiment of the present invention.

[0080] Figure 7 This is a schematic diagram of a complex structural component model in an embodiment of the present invention.

[0081] Figure 8 This is a diagram showing the result of a mixed processing sequence of adding and subtracting materials for complex structural components in an embodiment of the present invention. Detailed Implementation

[0082] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] like Figure 1 The flowchart of a five-axis linkage additive and subtractive material hybrid processing sequence planning method of the present invention is shown below, and the specific steps are as follows:

[0084] S1. Based on the equal-thickness layered slice section of the part, calculate the centroid of the slice section to obtain the centroidal axis of the column structure part;

[0085] S2. To address the tool collision and interference problem in the hybrid machining process of additive and subtractive materials, a tool reachability model is established for the hybrid machining process of additive and subtractive materials.

[0086] S3. A bounding box acceleration structure is proposed to speed up the model solution process;

[0087] S4. Using the accessibility model and acceleration structure, the part is roughly decomposed, a hybrid machining sequence of additive and subtractive materials is established, and finally the angle between the five-axis linkage printing platform and the tool is adjusted to optimize the final machining sequence.

[0088] In this embodiment, step S1 is specifically as follows:

[0089] The entire part is sliced ​​by using equal-thickness layering. For each slice section, the centroid of the polygon of the current slice section is obtained.

[0090] like Figure 2 As shown, a polygon with n vertices is composed of n-2 triangles. These n-2 triangles share a common vertex V1(x1,y1), and the remaining two vertices are V1(x1,y1) and V2(x1,y1). i (x i ,y i ) and V i+1 (x i+1 ,y i+1 ), and 1<i<n.

[0091] Let T be the centroid of the j-th triangle. j (t jx ,t jy V1(x1,y1) is a common vertex, and the remaining two points are V1(x1,y1) and V2(x1,y1). j (x j ,y j ) and V j+1 (x j+1 ,y j+1 The centroid T is obtained from the centroid formula. j (t jx ,t jy The coordinates of ) are expressed as follows:

[0092]

[0093] Then the centroid G(x) of the polygon g ,y g The relationship between the triangle and the centroids of the n-2 triangles that make it up is expressed as follows:

[0094]

[0095] Among them, A j Let represent the area of ​​the j-th triangle.

[0096] Let V contain n vertices. i (x i ,y i The centroid of the polygonal section of the slice is C(x). c ,y c Given a polygon with area A, the expression for calculating the centroid of the polygon is as follows:

[0097]

[0098] Each slice of the part has a cross-sectional profile that is a composite polygon. A centroid C is then determined for each slice profile. i (x i ,y i ,z i ), z i This indicates the current contour layer height. For parts with an h layer, there are C1, C2, C3..., C... h Centroid point.

[0099] In this embodiment, step S2 is specifically as follows:

[0100] S21. Based on the centroid of the cross-section of the part slice, the tool is simplified into a ray, and a simplified tool mathematical model is established;

[0101] Simplifying cutting tools requires meeting the following three conditions:

[0102] (1) Determine the tool contact point and tool direction;

[0103] Let the radius of the ball end mill tip be R. The contact point of the tool is the cutting point. However, due to the characteristics of the ball end mill, even if the contact point is the same, the angle of the end mill may be different. Therefore, the center of the circumscribed circle with radius R of the cutting point can be regarded as the starting point of the simplified tool, that is, the starting point of the ray. The direction of the simplified tool, that is, the direction of the ray, can be adjusted within a certain range according to the cutting needs. The adjustment range is affected by factors such as the feasible range of the tool after considering the support structure.

[0104] For the print head, the contact point can be regarded as the starting point of the simplified tool, that is, the starting point of the ray. The direction of the simplified tool, that is, the direction of the ray, can be adjusted within a certain range according to the cutting needs. The adjustment range is affected by factors such as the feasible range of the tool after considering the support structure.

[0105] (2) Tool continuity problem;

[0106] For the print head and cutting head in the additive and subtractive manufacturing process, the reachable range inside a layer is always greater than the reachable range of the layer outline. Therefore, only the continuity on the part outline is calculated. Take any point P on the part surface outline, and calculate the tool reachability for every point within a radius σ around that point to meet the tool continuity requirements. Due to the layered nature of 3D printing, the layer thickness can be set as the step size to discretize the vertical dimension. Calculating the tool reachability for each discretized point satisfies the tool continuity in the vertical dimension. For the horizontal dimension, a very small positive real number σ can be used as the step size to discretize the outline of each layer plane, and then calculating the tool reachability for each discretized point satisfies the tool continuity in the horizontal dimension.

[0107] The setting of the real number σ needs to be designed according to the specific tool size. In order to satisfy the tool continuity, the tool should be able to move continuously by one tool position during the machining process. Therefore, the step size setting of any point on the contour must be less than the distance of the tool moving by one tool position. Here, the maximum value is taken, which is the diameter D of the tool head.

[0108] (3) Feasible range of tools under support-free conditions;

[0109] like Figure 3 As shown, Figure 3 (a) indicates that the part may collapse when printed in three-axis mode. Figure 3 (b) Printing on a five-axis linkage platform will not result in collapse. Supportless printing can be achieved using a five-axis linkage machining platform. When printing parts with a suspended structure, the printing direction of the current layer is... The outward normal vector of the triangular facet on the side of the suspended structure is In order to avoid using a supporting structure, the following condition should be met:

[0110]

[0111] The value of α is typically 45° or 90°, but the exact value varies depending on the material and environment, so it needs to be selected for different parts and different processing environments. If the angle between the printing direction and the normal vector of the triangular facet on the side of the suspended structure exceeds α + 90°, the suspended structure will collapse, causing processing to terminate. Therefore, the feasible range of tools under supportless conditions is the sum of the range within which the printed layer plane of the suspended structure forms an angle α with the positive Z-axis direction, plus the range below the printed layer plane.

[0112] The simplified general equation for the cutting tool, i.e., the simplified mathematical model of the cutting tool, is expressed as follows:

[0113]

[0114] Where o represents the starting point of the ray, Let t represent the direction vector, and 0 < t < ∞, where t represents the distance the ray is emitted. Since there are usually other robotic arm structures above the print head and cutting tool, collisions and interference may occur. Since the mechanical structure of the print head is generally much larger than the size of the part being processed, the ray can be considered to be infinitely long.

[0115] S22. Based on the obtained simplified tool mathematical model, establish a tool collision interference algorithm;

[0116] In the 3D printing process, determining whether the tool and the part will collide or interfere means determining whether the tool and the STL model of the part will collide or interfere. Finding the intersection point between the tool model and the STL model involves finding the intersection of the tool and all triangles within the STL file. Finding the intersection of triangles can be divided into two parts: first, determining whether the simplified mathematical model equation of the tool intersects with the plane containing the triangle; and then determining whether the intersection point is inside the triangle.

[0117] Traverse all triangular faces of the STL model and find their intersection with the simplified tool mathematical model. If an intersection point exists, tool collision interference occurs; otherwise, no collision occurs. The specific intersection process is as follows:

[0118] like Figure 4 As shown, to calculate whether the simplified mathematical model equation of the cutting tool intersects the plane containing the triangular facet, let the three vertices of the triangle be P1(X1,Y1,Z1), P2(X2,Y2,Z2), and P3(X3,Y3,Z3). Then the equation of the plane containing the triangular facet is:

[0119] Mx + Ny + Oz + P = 0 (15)

[0120] P = -(Mx + Ny + Oz) (16)

[0121] Where M, N, O, and P represent the parameters of the plane equation, and the normal vector of the plane containing the triangular facet is N(M,N,O). All three vertices of the triangle lie within this plane. Substituting any point, we get:

[0122] P = -dot(N, P1) (17)

[0123] Suppose the cutting tool starts from the starting point and, along the tool's direction, collides and interferes with a triangle at a distance t, with the intersection point being P. Figure 4 As shown, we can obtain:

[0124]

[0125] Since point P lies on the triangle and also on the plane, substituting into equation (17) gives:

[0126] P+dot(P,N)=0 (19)

[0127] Substituting equation (18) into equation (19), we get:

[0128]

[0129] After unfolding:

[0130]

[0131] We can obtain:

[0132]

[0133] Where t represents the distance from the starting point of the tool to the intersection point with the triangle.

[0134] If t < 0, it means the triangle is behind the cutter and will not intersect; if t > 0, it means the triangle is in front of the cutter and will intersect, obtaining the intersection point P of the cutter and the plane containing the triangle.

[0135] After obtaining the intersection point P of the tool and the plane containing the triangle, it is necessary to determine whether P is inside the triangle. Connecting each of the three vertices of the triangle to the intersection point P yields three vectors. and Calculate the cross product of each of the three vectors and the vector formed by the three sides of the triangle:

[0136]

[0137] If the directions of the three cross products are consistent with the direction of the triangle's normal vector N, then the intersection point is inside the triangle. The tool reachability of that point can be determined by whether or not the tool experiences collision interference.

[0138] In this embodiment, step S3 is specifically as follows:

[0139] S31. Construct bounding boxes based on triangular facet coordinates, subdivide bounding boxes and recursively build a tree-like bounding box structure.

[0140] (1) Sort all triangular facets in the model according to the centroid position of the triangular facets. The sorting method can be selected according to the size of the x-coordinate, the size of the y-coordinate, or the size of the z-coordinate, depending on the different geometric features of the model.

[0141] (2) Create nodes for the tree-like bounding box. Each node contains the bounding box's outline information, leaf node information, and indexes of the left and right subtrees, such as... Figure 5 As shown;

[0142] (3) Based on the triangular face data obtained in step (1), determine the number of triangular face data, set it as r, and set the starting left subscript l to 0. Construct a triangular face array and set the minimum number of triangular face data contained in each bounding box to n.

[0143] (4) Construct the bounding box of the current tree node, with the left subscript of the current tree node being l and the right subscript being r;

[0144] (5) Traverse all triangles in the triangle array with index [l,r], calculate the maximum value of x, y, z coordinates of all triangles, and construct the current bounding box outline;

[0145] (6) Check if the number of triangular faces in the bounding box is less than n. If so, directly construct the bounding box of the current node and return the current leaf node; otherwise, continue recursively building the tree.

[0146] (7) Based on the x, y, z coordinates calculated in step (5), select the longest axis and sort the centroid coordinates of the triangular facets inside the bounding box according to the size of the coordinate values ​​of that axis.

[0147] (8) The midpoint of the triangular face array is mid = (l+r) / 2. Divide all triangular faces into two parts. The left half l index remains unchanged, and the r index is changed to mid. The right half l index is changed to mid+1, and the r index remains unchanged. Return to step (4) to recursively build the tree. The left subtree uses the left half triangular face and its index, and the right subtree uses the right half triangular face and its index.

[0148] Repeat steps (1)-(8) continuously to complete the creation of the tree bounding box.

[0149] S32. Intersection of simplified mathematical model of the cutting tool and tree-shaped bounding box structure;

[0150] like Figure 6 As shown, an AABB (axis aligned bounding box) has three opposing planes, which are three sets of planes perpendicular to the x, y, and z axes. The intersection of the three pairs of planes is calculated, and the entry and exit points of each set of planes are calculated. Based on the coordinates of the entry and exit points, it is determined whether the tool intersects with the bounding box. If it intersects, the intersection with the triangular facets inside the bounding box is calculated to obtain the intersection point between the tool and the STL model.

[0151] According to the simplified equation of the tool, it is only necessary to calculate the distances t0 and t1 between the tool and the two intersection points on the opposite side and the starting point. If t0 < t1, it can be proven that the tool and the bounding box collide and interfere.

[0152] First, calculate the distance from the tool's starting point to each face of the bounding box. Let the coordinates of the lower left point of the bounding box be L(x). l ,y l ,z l The coordinates of the upper right point are B(x). b ,y b ,z b The direction of the tool is d(x). d ,y d ,zd Dividing the lower left corner coordinate L of the bounding box by the tool direction d yields a 3D vector in(x0, y0, z0), and dividing the upper right corner coordinate B of the bounding box by the tool direction d yields a 3D vector out(x0, y0, z0). t ,y t ,z t Let t0 be the maximum value of the three coordinates in the in vector and t1 be the minimum value of the three coordinates in the out vector. We only need to determine whether t0 < t1 to determine whether the tool has collided or interfered with the bounding box.

[0153] Where x0 represents the x-axis coordinate of the tool's entry point in the bounding box perpendicular to the x-axis plane, y0 represents the y-axis coordinate of the tool's entry point in the bounding box perpendicular to the y-axis plane, and z0 represents the z-axis coordinate of the tool's entry point in the bounding box perpendicular to the z-axis plane. Conversely, the three coordinate components of the vector out correspond to the coordinates of the three exit points on the opposite side.

[0154] In this embodiment, step S4 is specifically as follows:

[0155] S41. Using the simplified printhead equation and tool reachability model, the tool reachability is calculated gradually upwards from the bottom contour. If a collision interference occurs, the part is decomposed from the current tool starting point and the point of collision interference. If no collision interference occurs, the tool moves up one layer until the part is completely decomposed, resulting in a machining sequence that only considers printhead collisions. Using the simplified cutting equation and tool reachability model, the part is coarsely decomposed to obtain a machining sequence that only considers cutting tool collisions. Finally, the two sequences are combined to obtain a hybrid additive and subtractive machining sequence under the coarse decomposition.

[0156] The specific steps of the decomposition are as follows:

[0157] 1) Determine the tool direction on each layer based on the tangent direction of the part's centroidal axis;

[0158] 2) Perform tool reachability calculations on all points on the bottom contour line of the part, and the interval between points needs to meet the step size of tool continuity.

[0159] 3) If tool collision interference occurs, record the tool starting point and the point where the collision interference occurred, and decompose the part from the current tool starting point; otherwise, move the tool up one layer and repeat step 2).

[0160] 4) Calculate the tool reachability upwards from the bottom contour line of the column structure to which the interference point belongs, until the layer to which the collision interference point belongs. If a collision interference occurs, record the current tool starting point and the collision interference point. Decompose the part from the current tool starting point and repeat step 4). Otherwise, move the tool up one layer.

[0161] 5) If the current column structure is decomposed, select the next column structure and repeat step 2) until the column structure is decomposed.

[0162] S42. Utilizing the characteristics of the five-axis linkage machining platform and the greedy algorithm, when calculating the tool reachability of each layer, the angle between the five-axis linkage machining platform and the tool is adjusted to obtain the highest interference point when collision interference may occur, thereby reducing the number of tool changes and obtaining the optimized additive and subtractive material hybrid machining sequence.

[0163] The specific steps of the method for calculating the mixed additive and subtractive material processing sequence based on the greedy algorithm are as follows:

[0164] 1. Based on the tangent direction of the part's centroidal axis in each layer and the range of motion of the supportless tool, determine the angle that the tool can move along the contour line of that layer. Due to the characteristics of 3D printing, the tool angle is the same within the same layer.

[0165] 2. Perform tool reachability calculations on all points on the bottom contour line of the part. The interval between points needs to meet the step size of tool continuity. The tool angle is selected within the movable angle in step 1, and the step size is set.

[0166] 3. If tool collision interference occurs, record the tool starting point and the point where the collision interference occurs. If the previously recorded collision interference point is smaller than the current collision interference point, update the collision interference point and record the tool direction; otherwise, adjust the tool angle.

[0167] 4. Check if all tool angles in this layer have been traversed. If yes, skip to step 5; otherwise, skip to step 3.

[0168] 5. Disassemble the part based on the latest recorded collision interference point;

[0169] 6. Calculate the tool reachability upwards from the bottom contour line of the column structure to which the collision interference point belongs, until the layer to which the collision interference point belongs. If a collision interference occurs, skip to step 3; otherwise, move the tool up one layer.

[0170] 7. If the current column structure has been decomposed, select the next column structure and jump to step 2; otherwise, jump to step 6.

[0171] 8. If all column structures have been decomposed, the current algorithm ends; otherwise, proceed to step 7.

[0172] The present invention also provides Embodiment 2 to further illustrate the method of the present invention.

[0173] In this embodiment 2, the following is adopted: Figure 7 The results of the additive and subtractive material hybrid processing sequence of the present invention, shown in the complex structural component test, are based on C++ programming. Specific steps are as follows:

[0174] A1. Set the equal thickness layering parameters, with a layer thickness of 1mm. After obtaining the layering results, calculate the centroid of each layer section to obtain the centroidal axis of the part.

[0175] A2. Calculate the contact point and direction of the print head and the cutting head based on the centroidal axis obtained in step A1. Calculate the feasible range of the tool under unsupported conditions based on the tangential angle of the centroidal axis to obtain a simplified model of the print head and the cutting head.

[0176] A3. Establish a tree-like bounding box structure for the STL model of complex structural parts. For the simplified tool model where the tool contact point is located on the contour line of each layer of the part, find the intersection between the simplified tool model and the tree-like bounding box structure to obtain the collision interference situation of the tool on each layer of the contour line, and then coarsely decompose the part.

[0177] A4. Based on the greedy algorithm, adjust the tool direction of each layer of the tool simplification model to obtain the optimized part decomposition and the mixed machining sequence of material addition and subtraction.

[0178] The results of the additive and subtractive material hybrid processing sequence obtained in Example 2 are as follows: Figure 8 As shown, where A i S represents additive manufacturing mode. i This indicates a subtractive machining mode. A→S represents a tool change that occurs when adding material before subtracting material during the machining of this sub-part, while S→A represents a tool change for adding material to the next sub-part after the subtractive machining of the previous sub-part is completed. A pair {A i ,S i} indicates that a cutting tool collision interference has occurred, and the i-th sub-component must be subtracted before the next sub-component can be additively processed. A pair {A1,A2} indicates that a printhead collision interference has occurred, but multiple sub-components can be additively processed first and then subtracted together.

[0179] Table 1 shows a comparison of the running time of the intersection algorithm between the tool and the STL model with and without the use of a tree-bound box structure for acceleration. The method of the present invention has a significant improvement in algorithm efficiency compared with other additive and subtractive material hybrid machining sequence planning methods.

[0180] Table 1

[0181]

[0182] In summary, the method of this invention establishes a tool accessibility model for the additive-subtractive machining process, ensuring that tool collisions and interference do not occur during machining. It proposes a bounding box acceleration structure to speed up the solution process of the accessibility model. By adjusting the angle between the five-axis linkage machining platform and the machining tool, the final additive-subtractive machining sequence is obtained, thereby improving machining efficiency.

[0183] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A five-axis linkage additive and subtractive material hybrid machining sequence planning method, the specific steps of which are as follows: S1. Based on the equal-thickness layered slice section of the part, calculate the centroid of the slice section to obtain the centroidal axis of the column structure part; S2. To address the tool collision and interference problem in the hybrid machining process of additive and subtractive materials, a tool reachability model is established for the hybrid machining process of additive and subtractive materials. S21. Based on the centroid of the cross-section of the part slice, the tool is simplified into a ray, and a simplified tool mathematical model is established; Simplifying cutting tools requires meeting the following three conditions: (1) Determine the tool contact point and tool direction; Let the radius of the ball end mill tip be R, and the contact point of the tool be the cutting point. The center of the circumscribed circle of the cutting point with radius R is regarded as the starting point of the simplified tool, that is, the starting point of the ray. The direction of the simplified tool is the direction of the ray. For the print head, the contact point can be regarded as the starting point of the simplified tool, that is, the starting point of the ray, and the direction of the simplified tool is the direction of the ray. (2) Tool continuity problem; For the print head and cutting head in the additive and subtractive material hybrid machining process, calculate the continuity on the part contour. Take any point p on the part surface contour, and calculate the tool reachability of each point in the area of ​​radius σ around the point to meet the tool continuity requirements. Due to the layered nature of 3D printing, the layer thickness is set as the step size to discretize the vertical dimension. The tool reachability of each discretized point can be calculated to satisfy the tool continuity in the vertical dimension. For the horizontal dimension, a very small positive real number σ can be used as the step size to discretize the contour line of each layer plane. The tool reachability of each discretized point can then be calculated to satisfy the tool continuity in the horizontal dimension. in, The setting of the real number σ is designed according to the specific tool size. During the machining process, the tool can move continuously by one tool position. The step size setting of any point on the contour must be less than the distance of the tool moving by one tool position. The maximum value is the diameter D of the tool head. (3) Feasible range of cutting tools under support-free conditions; Using a five-axis CNC machining platform to achieve supportless printing, when printing parts with a suspended structure, the printing direction of the current layer is... The outward normal vector of the triangular facet on the side of the suspended structure is The conditions for not using a supporting structure are as follows: （1）； in, The value is or Choose according to different parts and different processing environments; If the angle between the printing direction and the normal vector of the triangular facet on the side of the suspended structure is greater than... The collapse of the suspended structure led to the termination of processing; therefore, the feasible range of tools under the unsupported condition is the plane of the printed layer of the suspended structure. positive axis direction The sum of the range of angles and the range below the printed layer plane; The simplified general equation for the cutting tool, i.e., the simplified mathematical model of the cutting tool, is expressed as follows: （2）； in, Indicates the origin of the ray. Represents the direction vector, and , This represents the distance the ray travels; the simplified ray is considered to be infinitely long. S22. Based on the obtained simplified tool mathematical model, establish a tool collision interference algorithm; Traverse all triangular faces of the STL model and find their intersection with the simplified tool mathematical model. If an intersection point exists, tool collision interference occurs; otherwise, no collision occurs. The specific intersection process is as follows: Calculate whether the simplified mathematical model equation of the cutting tool intersects the plane containing the triangular facet. Let the three vertices of the triangle be... , and Then the equation of the plane containing the triangular facet is: （3）； Where M, N, O, and P represent the parameters of the plane equation, and the normal vector of the plane containing the triangular facet is... Since all three vertices of the triangle lie in this plane, substituting any point, we get: （4）； Substituting the simplified mathematical model equations of the cutting tool into the plane equations, we can obtain: （5）； in, This represents the distance from the starting point of the cutting tool to the intersection point with the triangle; like This indicates that the triangles will not intersect after the cutter; if This means that the triangle will intersect before the cutting tool, and the intersection point of the cutting tool and the plane containing the triangle will be obtained. ; Then determine Whether it is inside the triangle, consider the three vertices of the triangle and their intersection. Connect them to obtain three vectors. , and Calculate the cross product of each of the three vectors and the vector formed by the three sides of the triangle: （6）； If the directions of the three cross products are perpendicular to the normal vector of the triangle If the directions are the same, the intersection point is inside the triangle; if the directions are different, the intersection point is not inside the triangle. The tool reachability of the intersection point can be obtained by whether the tool causes collision interference. S3. A bounding box acceleration structure is proposed to speed up the model solution process; S4. Using the accessibility model and acceleration structure, the part is roughly decomposed, a hybrid machining sequence of additive and subtractive materials is established, and finally the angle between the five-axis linkage printing platform and the tool is adjusted to optimize the final machining sequence.

2. The five-axis linkage additive and subtractive material hybrid machining sequence planning method according to claim 1, characterized in that, The specific steps of S1 are as follows: The entire part is sliced ​​by using equal-thickness layering. For each slice section of the part, the centroid of the polygon of the current slice section is obtained. The calculation of the centroid of the slice cross section is as follows: Set the slice section to contain A polygon with vertices, composed of It is composed of a combination of triangles. a triangle The two points are a common vertex and the remaining two points are respectively and ,and ; Let the first The centroid of the triangle is , The two points are a common vertex and the remaining two points are respectively and The center of gravity is obtained from the formula for the center of gravity. The coordinates are expressed as follows: （7）； centroid of a sliced ​​polygon With what makes it The relationship between the centroids of the two triangles is expressed as follows: （8）； in, Indicates the first The area of ​​each triangle; Suppose it contains vertices The centroid of the polygonal slice section is The area is The expression for calculating the centroid of the polygon is as follows: （9）； Each slice of the part is a composite polygon, and a centroid is determined for each slice. , Indicates the current contour layer height; for those with The components of the layer have One centroid point; Finally, connect the centroids of all the cross sections in sequence to obtain the centroidal axis of the column structure part.

3. The five-axis linkage additive and subtractive material hybrid machining sequence planning method according to claim 1, characterized in that, Step S3 is as follows: S31. Construct bounding boxes based on triangular facet coordinates, subdivide bounding boxes and recursively build a tree-like bounding box structure. (1) Sort all triangular facets in the model according to their centroid positions. The sorting method can be selected according to the different geometric features of the model. Sort by coordinate size, according to Sort by coordinate size or by Sort by coordinate size; (2) Create nodes of the tree-shaped bounding box. Each node contains the outline information of the bounding box, the leaf node information, and the indexes of the left and right subtrees. (3) Based on the triangular facet data obtained in step (1), determine the number of triangular facets, and set it as follows: Starting left subscript Set the value to 0, construct an array of triangular faces, and set the minimum number of triangular faces that each bounding box must contain. ; (4) Construct the bounding box of the current tree node, with the lower left index of the current tree node being... The subscript is ; (5) Traverse the indices of the triangular face array Calculate all triangular faces. The maximum value of the coordinates is used to construct the current bounding box outline; (6) Is the number of triangular facets in the bounding box less than 100? If so, directly construct the bounding box of the current node and return the current leaf node; otherwise, continue recursively building the tree. (7) Calculated according to step (5) Coordinates: Select the longest axis and sort the centroid coordinates of the triangular facets within the bounding box according to the coordinate values ​​of that axis. (8) Midpoint of the triangular facet array Divide all the triangular pieces into two parts, the left half The subscript remains unchanged. Subscript changed right half Subscript changed , With the index unchanged, return to step (4) to recursively build the tree. Use the left half-triangle face and index for the left subtree, and the right half-triangle face and index for the right subtree. Repeat steps (1)-(8) continuously to complete the creation of the tree-shaped bounding box; S32. Intersection of simplified mathematical model of the cutting tool and tree-shaped bounding box structure; An AABB bounding box has three opposing planes, which are respectively... The axis is perpendicular to three sets of faces. The intersection of the three pairs of planes is calculated. The entry and exit points of each set of planes are calculated. Based on the coordinates of the entry and exit points, it is determined whether the tool intersects with the bounding box. If it intersects, the intersection with the triangular facet inside the bounding box is calculated to obtain the intersection point between the tool and the STL model. Based on the simplified equation of the tool, calculate the distance between the tool and the starting point of the two intersection points of a set of opposite points. Let the coordinates of the bottom left point of the bounding box be... The coordinates of the upper right point are The direction of the cutting tool is Then the coordinates of the bottom left corner of the bounding box will be... Divide by the tool direction This yields a three-dimensional vector. Set the top right coordinates of the bounding box Divide by the tool direction This yields a three-dimensional vector. ;Pick The maximum value of the three coordinates in a vector is denoted as , The minimum value of the three coordinates in a vector is denoted as Determine if there is ,like If the tool does not collide with the bounding box, then the tool will interfere with the bounding box; otherwise, the tool will not collide with the bounding box. in, This indicates that the cutter is perpendicular to the enclosure. The point of entry into the axial surface Axis coordinates This indicates that the cutter is perpendicular to the enclosure. The point of entry into the axial surface Axis coordinates This indicates that the cutter is perpendicular to the enclosure. The point of entry into the axial surface Axis coordinates; in contrast, vectors. The three coordinate components correspond to the coordinates of the three exit points on the opposite side.

4. The five-axis linkage additive and subtractive material hybrid machining sequence planning method according to claim 1, characterized in that, Step S4 is as follows: S41. Using the simplified printhead equation and tool reachability model, the tool reachability is calculated gradually from the bottom contour upwards. If a collision interference occurs, the part is decomposed from the current tool starting point and the point where the collision interference occurs. If no collision interference occurs, the tool moves up one layer until the part is completely decomposed, resulting in a machining sequence that only considers printhead collisions. S42. Utilizing the characteristics of the five-axis linkage machining platform and the greedy algorithm, when calculating the tool accessibility of each layer, the angle between the five-axis linkage machining platform and the tool is adjusted to obtain the highest interference point when collision interference may occur, thereby reducing the number of tool changes and obtaining the optimized additive and subtractive material hybrid machining sequence.

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