A five-axis milling tool path planning method for lattice spherical shell components

Abstract

The application discloses a kind of five-axis milling tool path planning methods of lattice spherical shell type component.It includes: based on the equation of theoretical inner surface design, calculate the theoretical tool position of inner surface;Based on inverse distance weighted (IDW) interpolation method and in combination with nearest neighbor matching strategy, wall thickness value matching is carried out to outer surface point cloud data;Based on the normal direction of each point of outer surface point cloud data calculation, the actual inner surface is obtained by offsetting corresponding wall thickness value along normal vector;With the constraint of inner surface theoretical tool position, interpolation and fitting processing is carried out to actual inner surface point cloud data;Based on the rib shape position feature, the actual inner surface tool position is screened, and the target wall thickness is offset along the normal vector to generate the compensation tool path.The application realizes the five-axis milling tool path planning and parameterization processing of lattice spherical shell type component, improves the uniformity of wall thickness distribution, and meets the machining precision requirement of lattice spherical shell type component on site.

Description

Technical Field

[0001] This invention belongs to the field of digital machining technology, specifically relating to a five-axis milling toolpath planning method for mesh spherical shell components. Background Technology

[0002] Thin-walled components, such as those with grid-like spherical shells, serve as the primary load-bearing structures for rocket fuel tank bottoms and are widely used in the aerospace field. Their load-bearing capacity largely determines the upper limit of aerospace development. During actual machining, these components, due to their large size and poor rigidity, experience a high risk of significant deformation as initial residual stress and machining stresses combine and are released. Existing digital machining methods, which plan toolpaths based on part design models, struggle to effectively address stress-induced deformation during machining, easily leading to parts exceeding tolerances or even becoming unusable.

[0003] Currently, the machining of thin-walled mesh spherical shell components mainly employs two methods: chemical milling and "segmented machining followed by welding." The former struggles to achieve effective control over wall thickness accuracy, has a long machining cycle, and poses environmental pollution problems, while the latter leads to a decline in overall structural performance due to weld seams, failing to meet the high-performance component requirements of the aerospace industry. Therefore, this paper proposes a five-axis milling toolpath planning method for mesh spherical shell components. Based on on-machine measured profile and wall thickness data, it adaptively generates compensated toolpaths to ensure the machining accuracy of mesh spherical shell components.

[0004] In 2017, Liu Xu et al. from Nanjing University of Aeronautics and Astronautics disclosed a machining method for milling free-form surfaces with a non-ball end mill in patent CN104238456B. This method constructs a second-order tensor field for the cutting width, extracts degenerate points to divide the surface region, generates an initial machining trajectory based on the maximum cutting width direction, and finally obtains the overall toolpath through trajectory offset. However, this method mainly relies on an ideal geometric model for trajectory planning and does not consider the influence of actual workpiece profile changes on the toolpath during actual machining. In 2024, Feng Pingfa et al. from China University of Petroleum disclosed a free-form surface enveloping machining trajectory planning method based on a tool with an arbitrary curved cross-section in patent CN119806050B. This method extracts the convex envelope contour of the tool cross-section curve and performs interpolation reconstruction to construct a tool surface point cloud, and then generates a free-form surface machining trajectory based on the envelope principle. This method can control profile tolerance to a certain extent, but cannot control wall thickness accuracy.

[0005] Currently, no method has been proposed for adaptively generating five-axis milling compensation machining trajectories for mesh spherical shell components based on in-machine measurement data. Summary of the Invention

[0006] To overcome the shortcomings of existing methods, this invention proposes a five-axis milling toolpath planning method for grid spherical shell components, addressing a series of problems such as difficulty in controlling wall thickness accuracy, complex surface, and low processing efficiency.

[0007] The technical solution of this invention: A method for planning the toolpath in five-axis milling of mesh spherical shell components, the specific steps of which are as follows: The first step is to calculate the theoretical tooling point of the spherical shell's internal surface based on the design equations of the spherical shell's internal surface theory. For milling of mesh spherical shell components, the roughing stage is mainly based on the theoretical machining trajectory of the inner surface of the shell, and the tool length is adjusted in each round of machining to achieve layer-by-layer material removal. The theoretical tool path of the inner surface of the shell adopts a circumferential milling form, and the reciprocating machining is achieved by dividing the spacing between adjacent tool paths with equal arc lengths. Therefore, to ensure surface quality, based on the theoretical design equation of the inner surface of the shell, the row spacing and circumferential step distance of the machining trajectory are calculated using the equal residual height method and the equal chord height difference method, respectively. For the inner surface of the shell, its surface shape is approximately a part of a double major axis ellipsoid, thus deriving the specified height of the inner surface of the shell. Circumferential machining trajectory cross-sectional radius for: (1) in It is a double major axis ellipse. Let be the minor axis of a double major axis ellipse. Then the chord height error... The calculation formula is: (2) Then, the circumferential step distance is derived based on the equal chord height difference method. With chord height error The formula for calculating the interval is: (3) Since the curvature of the inner surface of the spherical shell is much greater than the residual height, the relationship between the row spacing of the machining trajectory and the residual height of the inner surface of the spherical shell is as follows: (4) in This refers to the line spacing of the processing trajectory. For the tool radius, This refers to the residual height of the inner surface of the spherical shell.

[0008] On the design surface of the double major axis ellipsoid, given the starting position, the row spacing and circumferential step distance are calculated by equations (1) to (4), and then the spatial distribution of the theoretical tool points of the inner surface of the spherical shell is determined, thus obtaining the set of theoretical tool points of the inner surface of the spherical shell. , This indicates the number of theoretical tool points on the internal surface of the spherical shell. Indicates the first Theoretical cutting point for the inner surface of a spherical shell.

[0009] The second step is to match the wall thickness values ​​of the actual shape surface point cloud data based on the inverse distance weighted (IDW) interpolation method and the nearest neighbor matching method. Based on digital on-machine scanning technology, the actual surface point cloud data and wall thickness data of the mesh spherical shell component are acquired. The wall thickness data is associated with a portion of the actual surface point cloud data using the nearest neighbor matching method. Then, the wall thickness value is completed for the remaining actual surface point cloud data using the IDW interpolation method, thereby achieving the assignment of wall thickness values ​​for all actual surface point cloud data.

[0010] Define the actual shape point cloud dataset as , Indicates the first A real-world shape of a pastry. Indicates the first The coordinates of the actual external surface points, and the wall thickness dataset are as follows: ,in For the first One wall thickness data point, For the first The coordinates of the wall thickness data points, among which For the first The wall thickness value at each wall thickness data point. and They are respectively The actual number of pasta shapes and Number of data points for medium wall thickness. Calculation. and Euclidean distance : (5) For each wall thickness data point The index for searching the nearest actual shape surface point in the actual shape surface point cloud dataset is represented as: (6) in, The actual shape of the facet at the closest distance. The actual shape point at the closest distance The index. Then the wall thickness data point. Wall thickness value Mapping to the corresponding actual shape points, the wall thickness values ​​of part of the actual shape point cloud data are... Assign a value: (7) At this point, let the partial actual shape surface point cloud dataset with wall thickness values ​​already assigned be... For actual shape points that have not been assigned wall thickness values Take the one with the closest distance. The actual external surface point whose wall thickness value has been assigned. Its wall thickness is recorded as , The IDW interpolation method is used for actual surface points that have not been assigned wall thickness values. Wall thickness value Perform interpolation calculations: (8) in, For the weight function, , This is the distance decay index.

[0011] This yields a dataset of actual shape surface point clouds with wall thickness values. , Indicates the first A real-world shape point Wall thickness value.

[0012] The third step is to calculate the normal vector direction of each actual shape surface point based on the actual shape surface point cloud data with wall thickness values, and then offset the corresponding wall thickness value inward along the normal vector to obtain the actual inner shape surface point cloud dataset. First, principal component analysis (PCA) is used to calculate the normal vector direction of each actual shape surface point based on the actual shape surface point cloud data with wall thickness values. For the actual shape surface point cloud dataset with wall thickness values... One of the actual shapes of the surface point For the actual shape of the face, a neighborhood point set is selected, and a point cloud spatial index is constructed using a KD-tree. : (9) in, To obtain the actual shape surface point cloud dataset with wall thickness values The selected neighborhood point set Represents the neighborhood point set The number of actual external surface points containing wall thickness values. for The Middle An actual external surface point with a wall thickness value. Based on neighborhood point set Construct the covariance matrix : (10) Perform eigenvalue decomposition on the covariance matrix: (11) in, are eigenvalues, and ; Eigenvalues The corresponding eigenvector. Because the eigenvector corresponding to the smallest eigenvalue... As the vector, the actual shape of the facet is... The dharma vector is .

[0013] Secondly, regarding the actual shape and surface details Dharma Arrow The direction of the normal vector is calibrated for consistency. Since the normal vector direction obtained by the above method does not have global consistency, a constraint strategy based on global coordinate axes is adopted to determine the consistency of the normal vector direction. The sign of the components in the Z-coordinate direction is unified, and the correction formula is as follows: (12) Among them, actual external surface points Dharma Arrow The component is , , representing the dharma vector The component in the Z-coordinate direction. By unifying the normal vector direction inward through the correction formula, that is, along the direction inward from the center of the spherical shell surface, a point cloud dataset of the actual shape surface with a consistent normal vector direction is obtained. .

[0014] Finally, the actual shape surface point cloud data with the same normal vector direction is offset inward along its normal vector direction by the corresponding wall thickness value. The offset calculation formula is as follows: (13) in, For actual shape points The actual internal surface points after biasing. Solving for the bias yields the actual internal surface point cloud dataset. Since the actual internal surface state differs from the external surface, the point cloud normals need to be recalculated. Therefore, the actual internal surface point cloud dataset is denoted as... , Indicates the first A real-world-shaped pastry, Indicates the first The coordinates of the actual internal surface points.

[0015] The fourth step involves using the theoretical cutting point of the spherical shell's inner surface as a constraint to perform longitudinal interpolation fitting and circumferential circle fitting on the actual inner surface point cloud data. The theoretical tool positions within the spherical shell's internal surface constitute the theoretical tool trajectory. Using this trajectory as a reference, the actual internal surface point cloud data is layered and truncated, limiting the number of rows in the circumferential theoretical tool trajectory and the Z-coordinate position of each tool position. Based on this, the truncated actual internal surface point cloud dataset undergoes longitudinal interpolation fitting and circumferential circle fitting processing to obtain a uniformly distributed set of actual internal surface tool positions. The details are as follows: For the theoretical knife point set of the internal surface of the spherical shell Each different height value , , The number of rows of theoretical tool points on the inner surface of the spherical shell, and the upper and lower arc lengths along the circular arc of the inner surface of the spherical shell. The actual internal surface point cloud data is cropped to obtain the corresponding local point set. The arc length range is then converted into a Z-coordinate range, i.e.: (14) in, For The endpoints of the upper and lower Z-coordinate range centered on the sphere, with the sphere center coordinates being... ,radius , Indicates the first The coordinates of the theoretical tool point on the inner surface of the spherical shell during the process. For each theoretical tool position point on the inner surface of the spherical shell, the corresponding angle in the coordinate system of the inner surface arc is: .

[0016] Extract the actual internal shape surface point cloud dataset according to equation (14). China conforms All actual interior surface points of the given conditions constitute the actual interior surface cut-out point cloud dataset, denoted as . , ,in, Indicates the first A number of actual internal surface intercept points Indicates the first The coordinates of the actual internal surface intercept points This represents the number of point cloud datasets extracted from the actual internal surface.

[0017] Let the vertical interpolation point be... Its coordinates are In the actual internal shape point cloud dataset after truncation. In the middle, according to the height value of the cutting point of the spherical shell internal surface theory Lagrange interpolation is used to construct local functions at the vertical interpolation points. ,Right now: (15) in, The number of actual internal surface intercept points used in the longitudinal interpolation. and This indicates the sequence number of the actual inner surface intercept point participating in longitudinal interpolation within the same laser scanning line, and , and The first The and the first The spatial coordinates of the actual inner surface intercept points participating in the longitudinal interpolation.

[0018] Then, the longitudinal interpolation points are solved based on the linear fitting relationship. ,but: (16) Among them, parameters and The analytical solution is determined by minimizing the sum of squared residuals: (17) and Each represents the selected The average X-coordinate and average Y-coordinate of the actual inner surface intercept points involved in the longitudinal interpolation.

[0019] After the above vertical interpolation fitting, the actual inner surface point cloud dataset is transformed into a set of vertically uniformly distributed inner surface tool points, which is represented as: ,in Represents a point set The number of points in the middle, vertical interpolation points This is represented here as the number A longitudinally uniformly distributed inner face knife point.

[0020] For a set of longitudinally uniformly distributed internal surface cutting points For problems with random distribution in the circumferential direction, a circumferential circular fit is performed. At each fixed height section... Above, based on the inner surface tool point set The circle fitting equation is established using the least squares method: (18) in, For the height section The set of inner face knife points uniformly distributed in the upper longitudinal direction The tool points of each inner face relative to the geometric center offset value, height section The above corresponds to the offset value of the fitted circle center relative to the geometric center, the geometric center. Through height section The average values ​​of the X and Y coordinates of the tool points on the inner surface, which are uniformly distributed in the upper longitudinal direction, are obtained.

[0021] Then solve for the height section. Fitted circle center coordinates With fitted radius : (19) in, For each height section The number of internal profile cutter points evenly distributed longitudinally, these points will affect the height of the cross-section. The fitted circle is divided into A segment of circular arc.

[0022] Then, based on the C-angle relative to the height section The fitted circle is subjected to uniform circular parameter interpolation to generate a continuous and uniformly distributed set of tool marks on the inner surface. The circular parameter interpolation equation is as follows: (20) in, This is the new inner surface tooling point obtained after interpolation using circular parameters. It is in the In the arc segment The inner face tooling point generated by interpolating the circle parameters. The C-axis angle, .

[0023] The longitudinally uniformly distributed inner surface cutting edge points are mapped to the polar angle parameter space. By calculating the angular interval between adjacent inner surface cutting edge points and combining it with the angular step size of the theoretical cutting edge points of the spherical shell inner surface, circumferential uniform interpolation is achieved. The formula for calculating the angle is: (twenty one) in, The inner face cutting points are evenly distributed longitudinally. The C-axis angle, The angular step size of the theoretical cutting point on the inner surface of the spherical shell. For the first The number of inner surface tooling points that need to be inserted in the arc segment. For the first The index of the tooling point on the inner surface to be inserted in the arc segment. This represents the number of theoretical tool points on the inner surface of the spherical shell within this height section. When This indicates that the C-axis angle difference between adjacent inner surface tool points does not exceed the angle step size. Therefore, no interpolation encryption is required.

[0024] The actual set of internal surface cutting points uniformly distributed in space is obtained by performing circumferential circle fitting and circumferential uniform interpolation using equations (18) to (21). , Depend on Together with the new interpolation points generated in all circle fitting, it constitutes the inner surface knife point. For the actual internal surface tool point set The Middle One actual internal shape cutter point, Indicates the actual inner surface tooling position. coordinates Represents the actual internal shape tool point set The number of points. However, the actual set of internal cutting point locations is located on the internal surface of the spherical shell, and the shape and position characteristics of the reinforcing ribs are not considered. Therefore, it is necessary to first screen the point cloud of the actual internal cutting point locations, and then further implement equal wall thickness offset processing.

[0025] The fifth step is to screen the actual inner surface tooling points based on the shape and position characteristics of the reinforcing ribs, and generate a compensated tooling trajectory by offsetting the target wall thickness along the normal vector. Based on the design shape and position of the reinforcing ribs, the actual internal surface cutting points are screened. By limiting the range of the Z coordinate, the actual internal surface cutting points located in the transverse rib area are eliminated. Then, by giving the C-axis angle position corresponding to the center of the longitudinal rib and the offset arc length range on both sides, the actual internal surface cutting points located in the longitudinal rib area are eliminated.

[0026] First, filter the transverse rib area using a specified value. To capture the center, the upper and lower offset settings are set. To define the horizontal cutoff interval, the horizontal cutoff interval is: ,in, This represents the number of intervals to be cut off for the transverse reinforcement. This is the index for horizontally truncated intervals. The actual set of tool marks on the inner surface after horizontal filtering is represented as follows: .

[0027] Then, select the C-axis angle corresponding to the center of the longitudinal reinforcement. , This represents the number of intervals to be extracted vertically. This is the index for the vertically truncated interval. Based on the C-axis angle... Centered on the center, with equal angular steps on both sides. By applying a bias, a vertical cutoff interval is constructed. The actual set of tool marks on the inner surface after vertical screening is denoted as... .

[0028] The selected actual inner face cutting points are divided into independent grid regions. Based on the PCA principal component analysis method shown in equations (9) to (11), the normal vectors of each actual inner face cutting point are calculated for each region. According to a variation of equation (12)... The direction of the normal vector is unified so that it points outward, and the normal vector of the actual inner surface tool point is denoted as... Then, based on equation (13), the target wall thickness value is offset outward along the normal direction at the actual inner surface tool position. This allows us to obtain the target surface compensation tool location.

[0029] For digital machining on five-axis machine tools, it is necessary to further solve for the coordinates of the sway axis and the rotary axis, and to compensate for the normal vector of the tool position point based on the target outline. The formulas for calculating the coordinates of the A-axis and C-axis are as follows: (twenty two) This yields the five-axis coordinates of the tool position point for compensating the target outer surface in the workpiece coordinate system. Within the grid area, a circumferential milling method is used for machining trajectory planning, achieving five-axis milling compensation machining of the grid spherical shell component. For the multi-round milling process of the grid spherical shell component, steps two through five are repeated from the semi-finishing stage, which effectively improves machining accuracy and meets actual machining requirements.

[0030] The beneficial effects of this invention are as follows: This invention proposes a five-axis milling toolpath planning method for mesh spherical shell components. Compared with existing technologies, this invention reconstructs the actual internal surface point cloud based on on-machine measured actual external surface point cloud data and wall thickness data, offset inward along the normal vector, and combines longitudinal interpolation and circumferential circle fitting methods to obtain a uniformly distributed set of actual internal surface tool points, thereby improving the continuity and stability of the machining trajectory. By introducing stiffener shape and position feature constraints, the actual internal surface tool points are screened, enhancing the adaptability of the machining trajectory to complex surfaces. By offsetting the target wall thickness along the normal vector of the actual internal surface tool points, and solving the AC axis coordinates based on the normal vector, adaptive generation of tool path oriented to the actual machining state is achieved. This invention effectively improves the uniformity of wall thickness distribution while ensuring the consistency of internal and external surface profiles, thereby significantly improving machining accuracy and efficiency. Attached Figure Description

[0031] Figure 1 This is a flowchart of the five-axis milling compensation toolpath planning method for mesh spherical shell components described in this invention.

[0032] Figure 2 A schematic diagram of the theoretical tool position for generating the inner surface of the spherical shell using the equal chord height difference method and the equal residual height method is shown. Among them, (a) represents a schematic diagram of calculating the offset step length on the circumferential trajectory based on the equal chord height difference method, and (b) represents a schematic diagram of calculating the machining line spacing based on the equal residual height method.

[0033] Figure 3 This is a schematic diagram of obtaining the actual internal surface point cloud data by offsetting the external surface point cloud data inward along the normal vector to the corresponding wall thickness value. In this diagram, (a) represents the actual external surface point cloud data and the actual internal surface point cloud with wall thickness values, and (b) represents a partial schematic diagram within the dashed circle in (a).

[0034] Figure 4 This is a schematic diagram of interpolation and fitting processing for actual internal surface point cloud data. Among them, (a) shows a schematic diagram of generating a knife point with a specified Z coordinate on a single cut-out line laser point set through vertical interpolation, and (b) is a schematic diagram of fitting a circumferential circle based on the points generated by vertical interpolation.

[0035] Figure 5 This is a schematic diagram illustrating the application of five-axis milling toolpath planning for mesh spherical shell components. In this diagram, (a) represents the actual external surface tool position obtained by offsetting the actual internal surface tool position outwards along the normal vector to the target wall thickness after screening; and (b) is the mesh-compensated machining trajectory generated based on the five-axis coordinates of the actual external surface tool position.

[0036] In the figure: 1. Circumferential machining trajectory; 2. Actual external surface point cloud data with wall thickness values; 3. Actual internal surface point cloud. Detailed Implementation

[0037] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0038] This invention is implemented as a grid-like spherical shell component. Due to the involvement of key model dimensions, only approximate dimensional values ​​are provided. The theoretical internal surface equation of the spherical shell is the equation of a double-major-axis ellipsoid. The major axis of the double-major-axis ellipse is approximately 3000 mm, and the minor axis is approximately 850 mm. The wall thickness requirement is 2.5 mm in the thinnest area, with a lower tolerance of 0 mm and an upper tolerance of 0.1 mm. The external surface has 18 grid features. The centers of the longitudinal reinforcing ribs on the bottom surface are distributed according to the lower C-angle of the workpiece coordinate system, with an angle interval of 60°. The centers of the transverse reinforcing ribs on the bottom surface are distributed according to the Z-coordinate values, at -150 mm and -450 mm respectively. The origin of the workpiece coordinate system is the vertex of the spherical shell. Figure 1 This is a flowchart of the five-axis milling compensation toolpath planning method for mesh spherical shell components proposed in this invention. The specific implementation steps are as follows: The first step is to calculate the theoretical tooling point of the spherical shell's internal surface based on the design equations of the spherical shell's internal surface theory. For milling of mesh spherical shell components, the roughing stage is mainly based on the theoretical machining trajectory of the inner surface of the shell, and the tool length is adjusted in each round of machining to achieve layer-by-layer material removal. The theoretical tool path of the inner surface of the shell adopts a circumferential milling form, and the reciprocating machining is achieved by dividing the spacing between adjacent tool paths with equal arc lengths. Therefore, to ensure surface quality, based on the theoretical design equation of the inner surface of the shell, the row spacing and circumferential step distance of the machining trajectory are calculated using the equal residual height method and the equal chord height difference method, respectively. For the inner surface of the shell, its surface shape is approximately a part of a double major axis ellipsoid, thus deriving the specified height of the inner surface of the shell. Circumferential machining trajectory cross-sectional radius for: (1) in, It is a double major axis ellipse. Let be the minor axis of a double major axis ellipse. Then the chord height error... The calculation formula is: (2) Then, the circumferential step distance is derived based on the equal chord height difference method. With chord height error The formula for calculating the interval is: (3) Since the curvature of the inner surface of the spherical shell is much greater than the residual height, the relationship between the row spacing of the machining trajectory and the residual height of the inner surface of the spherical shell is as follows: (4) in, This refers to the line spacing of the processing trajectory. For the tool radius, This refers to the residual height of the inner surface of the spherical shell.

[0039] In this example, the tool radius is 10mm. On the double major axis ellipsoidal design surface, given the starting position, the travel distance is calculated to be 15mm and the circumferential step distance is 5mm using equations (1) to (4). Then, the spatial distribution of the theoretical tool position points of the inner surface of the spherical shell is determined, and the set of theoretical tool position points of the inner surface of the spherical shell is obtained. , This indicates the number of theoretical tool points on the internal surface of the spherical shell. Indicates the first The theoretical cutting point of the inner surface of the spherical shell, the specific effect is as follows: Figure 2 As shown.

[0040] The second step is to match the wall thickness values ​​of the actual shape surface point cloud data based on the inverse distance weighted (IDW) interpolation method and the nearest neighbor matching method. Based on digital on-machine scanning technology, the actual surface point cloud data and wall thickness data of the mesh spherical shell component are acquired. The wall thickness data is associated with a portion of the actual surface point cloud data using the nearest neighbor matching method. Then, the wall thickness value is completed for the remaining actual surface point cloud data using the IDW interpolation method, thereby achieving the assignment of wall thickness values ​​for all actual surface point cloud data.

[0041] Define the actual shape point cloud dataset as , Indicates the first A real-world shape of a pastry. Indicates the first The coordinates of the actual external surface points, and the wall thickness dataset are as follows: ,in For the first One wall thickness data point, For the first The coordinates of the wall thickness data points, among which For the first The wall thickness value at each wall thickness data point. and They are respectively The actual number of pasta shapes and Number of data points for medium wall thickness. Calculation. and Euclidean distance : (5) For each wall thickness data point Search for the index of the nearest actual shape surface point in the actual shape surface point cloud dataset: (6) in, The actual shape of the facet at the closest distance. The actual shape point at the closest distance The index. Then the wall thickness data point. Wall thickness value Mapping to the corresponding actual shape points, the wall thickness values ​​of part of the actual shape point cloud data are... Assign a value: (7) At this point, let the partial actual shape surface point cloud dataset with wall thickness values ​​already assigned be... For actual shape points that have not been assigned wall thickness values Take the one with the closest distance. The actual external surface point whose wall thickness value has been assigned. Its wall thickness is recorded as , The IDW interpolation method is used for actual surface points that have not been assigned wall thickness values. Wall thickness value Perform interpolation calculations: (8) in, For the weight function, , Here, the distance decay exponent is... , .

[0042] This yields a dataset of actual shape surface point clouds with wall thickness values. , Indicates the first A real-world shape point Wall thickness value.

[0043] The third step is to calculate the normal vector direction of each actual shape surface point based on the actual shape surface point cloud data with wall thickness values, and then offset the corresponding wall thickness value inward along the normal vector to obtain the actual inner shape surface point cloud dataset. First, principal component analysis (PCA) is used to calculate the normal vector direction of each actual shape surface point based on the actual shape surface point cloud data with wall thickness values. For the actual shape surface point cloud dataset with wall thickness values... One of the actual shapes of the surface point For the actual shape of the face, a neighborhood point set is selected, and a point cloud spatial index is constructed using a KD-tree. : (9) in, To obtain the actual shape surface point cloud dataset with wall thickness values The selected neighborhood point set Represents the neighborhood point set The number of actual shape surface points containing wall thickness values ​​is considered. Given the large scale and dense distribution of the actual shape surface point cloud data, the number of point clouds can reach millions. Therefore, Set to 2000. for The Middle An actual external surface point with a wall thickness value. Based on neighborhood point set Construct the covariance matrix : (10) Perform eigenvalue decomposition on the covariance matrix: (11) in, are eigenvalues, and ; Eigenvalues The corresponding eigenvector. Because the eigenvector corresponding to the smallest eigenvalue... As the vector, the actual shape of the facet is... The dharma vector is .

[0044] Secondly, regarding the actual shape and surface details Dharma Arrow The direction of the normal vector is calibrated for consistency. Since the normal vector direction obtained by the above method does not have global consistency, a constraint strategy based on global coordinate axes is adopted to determine the consistency of the normal vector direction. The sign of the components in the Z-coordinate direction is unified, and the correction formula is as follows: (12) Among them, actual external surface points Dharma Arrow The component is , , representing the dharma vector The component in the Z-coordinate direction. By unifying the normal vector direction inward through the correction formula, that is, along the direction inward from the center of the spherical shell surface, a point cloud dataset of the actual shape surface with a consistent normal vector direction is obtained. .

[0045] Finally, as Figure 3 As shown, the actual surface point cloud data with the same normal vector direction is offset inward along its normal vector direction by the corresponding wall thickness value. The offset calculation formula is: (13) in, For actual shape points The actual internal surface points after biasing. Solving for the bias yields the actual internal surface point cloud dataset. Since the actual internal surface state differs from the external surface, the point cloud normals need to be recalculated. Therefore, the actual internal surface point cloud dataset is denoted as... , Indicates the first A real-world-shaped pastry, Indicates the first The coordinates of the actual internal surface points.

[0046] The fourth step involves using the theoretical cutting point of the spherical shell's inner surface as a constraint to perform longitudinal interpolation fitting and circumferential circle fitting on the actual inner surface point cloud data. The theoretical tool positions within the spherical shell's internal surface constitute the theoretical tool trajectory. Using this trajectory as a reference, the actual internal surface point cloud data is layered and truncated, limiting the number of rows in the circumferential theoretical tool trajectory and the Z-coordinate position of each tool position. Based on this, the truncated actual internal surface point cloud dataset undergoes longitudinal interpolation fitting and circumferential circle fitting processing to obtain a uniformly distributed set of actual internal surface tool positions. The details are as follows: For the theoretical knife point set of the internal surface of the spherical shell Each different height value , , The number of rows of theoretical tool points on the inner surface of the spherical shell, and the upper and lower arc lengths along the circular arc of the inner surface of the spherical shell. The actual internal surface point cloud data is cropped to obtain the corresponding local point set. The arc length range is then converted into a Z-coordinate range, i.e.: (14) in, For The endpoints of the upper and lower Z-coordinate range centered on the sphere, with the coordinates of the sphere's center being... ,radius , Indicates the first The coordinates of the theoretical tool point on the inner surface of the spherical shell during the process. For each theoretical tool position point on the inner surface of the spherical shell, the corresponding angle in the coordinate system of the inner surface arc is: .

[0047] Extract the actual internal shape surface point cloud dataset according to equation (14). China conforms All actual interior surface points of the given conditions constitute the actual interior surface cut-out point cloud dataset, denoted as . , ,in, Indicates the first A number of actual internal surface intercept points Indicates the first The coordinates of the actual internal surface intercept points This represents the number of point cloud datasets extracted from the actual internal surface.

[0048] Let the vertical interpolation point be... Its coordinates are In the actual internal shape point cloud dataset after truncation. In the middle, according to the height value of the cutting point of the spherical shell internal surface theory Lagrange interpolation is used to construct local functions at the vertical interpolation points. ,Right now: (15) in, In this example, the actual number of internal surface intercept points participating in the vertical interpolation is... , and This indicates the sequence number of the actual inner surface intercept point participating in longitudinal interpolation within the same laser scanning line, and , and The first The and the first The spatial coordinates of the actual inner surface intercept points participating in the longitudinal interpolation.

[0049] Then, the longitudinal interpolation points are solved based on the linear fitting relationship. ,but: (16) Among them, parameters and The analytical solution is determined by minimizing the sum of squared residuals: (17) and Each represents the selected The average X-coordinate and average Y-coordinate of the actual inner surface intercept points involved in the longitudinal interpolation.

[0050] The vertical interpolation process is as follows Figure 4 As shown in (a), after vertical interpolation, the actual inner surface point cloud dataset is transformed into a set of inner surface tool points that are uniformly distributed vertically, which can be represented as: ,in Represents a point set The number of points in the middle, vertical interpolation points This is represented here as the number A longitudinally uniformly distributed inner face knife point.

[0051] For a set of longitudinally uniformly distributed internal surface cutting points For problems with random distribution in the circumferential direction, a circumferential circular fit is performed. At each fixed height section... Above, based on the inner surface tool point set The circle fitting equation is established using the least squares method: (18) in, For the height section The set of inner face knife points uniformly distributed in the upper longitudinal direction The tool points of each inner face relative to the geometric center offset value, height section The above corresponds to the offset value of the fitted circle center relative to the geometric center, the geometric center. Through height section The average values ​​of the X and Y coordinates of the tool points on the inner surface, which are uniformly distributed in the upper longitudinal direction, are obtained.

[0052] Then solve for the height section. Fitted circle center coordinates With fitted radius : (19) in, For each height section The number of internal profile cutter points evenly distributed longitudinally, these points will affect the height of the cross-section. The fitted circle is divided into A segment of circular arc.

[0053] Then, based on the C-angle relative to the height section The fitted circle is subjected to uniform circular parameter interpolation to generate a continuous and uniformly distributed set of tool marks on the inner surface. The circular parameter interpolation equation is as follows: (20) in, This is the new inner surface tooling point obtained after interpolation using circular parameters. It is in the In the arc segment The inner face tooling point generated by interpolating the circle parameters. The C-axis angle, .

[0054] The longitudinally uniformly distributed inner surface tool points are mapped to the polar angle parameter space. By calculating the angular interval between adjacent inner surface tool points and combining it with the theoretical tool point angular step size of the spherical shell inner surface, circumferential uniform interpolation is achieved. The formula for calculating the angle is: (twenty one) in, The inner face cutting points are evenly distributed longitudinally. The C-axis angle, The angular step size of the theoretical cutting point on the inner surface of the spherical shell. For the first The number of inner surface tooling points that need to be inserted in the arc segment. For the first The index of the tooling point on the inner surface to be inserted in the arc segment. This represents the number of theoretical tool points on the inner surface of the spherical shell within this height section. When This indicates that the C-axis angle difference between adjacent inner surface tool points does not exceed the angle step size. Therefore, no interpolation encryption is required.

[0055] The actual set of internal surface cutting points uniformly distributed in space is obtained by performing circumferential circle fitting and circumferential uniform interpolation using equations (18) to (21). , Depend on Together with the new interpolation points generated in all circle fitting, it constitutes the inner surface knife point. For the actual internal surface tool point set The Middle One actual internal shape cutter point, Indicates the actual inner surface tooling position. coordinates Represents the actual internal shape tool point set The number of points. However, the actual set of internal cutting point locations is located on the internal surface of the spherical shell, and the shape and position characteristics of the reinforcing ribs are not considered. Therefore, it is necessary to first screen the point cloud of the actual internal cutting point locations, and then further implement equal wall thickness offset processing.

[0056] The fifth step involves screening the actual inner surface tooling points based on the shape and position characteristics of the reinforcing ribs, and generating a compensated tooling trajectory by offsetting the target wall thickness along the normal vector, such as... Figure 5 As shown; Based on the design shape and position of the reinforcing ribs, the actual internal surface cutting points are screened. By limiting the range of the Z coordinate, the actual internal surface cutting points located in the transverse rib area are eliminated. Then, by giving the C-axis angle position corresponding to the center of the longitudinal rib and the offset arc length range on both sides, the actual internal surface cutting points located in the longitudinal rib area are eliminated.

[0057] First, filter the transverse rib area using a specified value. To capture the center, the upper and lower offset settings are set. To define the horizontal cutoff interval, the horizontal cutoff interval is: ,in This represents the number of intervals to be cut off for the transverse reinforcement. This is the index for the horizontally extracted interval. In this example, , , , The actual set of tool marks on the inner surface after horizontal filtering is represented as follows: .

[0058] Then, select the C-axis angle corresponding to the center of the longitudinal reinforcement. , This represents the number of intervals to be extracted vertically. This is the index for the vertically truncated interval. Based on the C-axis angle... Centered on the center, with equal angular steps on both sides. By applying a bias, a vertical cutoff interval is constructed. The actual set of tool marks on the inner surface after vertical screening is denoted as... .

[0059] The selected actual inner face cutting points are divided into independent grid regions. Based on the PCA principal component analysis method shown in equations (9) to (11), the normal vectors of each actual inner face cutting point are calculated for each region. According to a variation of equation (12)... The direction of the normal vector is unified so that it points outward, and the normal vector of the actual inner surface tool point is denoted as... Then, based on equation (13), the target wall thickness value is offset outward along the normal direction at the actual inner surface tool position. This allows us to obtain the target surface compensation tool location.

[0060] For digital machining on five-axis machine tools, it is necessary to further solve for the coordinates of the sway axis and the rotary axis, and to compensate for the normal vector of the tool position point based on the target outline. The formulas for calculating the coordinates of the A-axis and C-axis are as follows: (twenty two) This yields the five-axis coordinates of the tool position point for compensating the target outer surface in the workpiece coordinate system. Within the mesh area, a circumferential milling method is used for machining trajectory planning to achieve five-axis milling compensation machining of mesh spherical shell components. For the multi-round milling process of mesh spherical shell components, steps two through five are repeated from the semi-finishing stage, which effectively improves machining accuracy and meets actual machining requirements. This method, while adaptively generating the five-axis milling toolpath for mesh spherical shell components, ensures the consistency of the component's internal and external profiles, effectively improving wall thickness accuracy and meeting actual machining requirements.

[0061] The method described in this invention is applicable to high-precision five-axis milling of thin-walled mesh spherical shell components and can be extended to the machining of similar structural parts in aerospace and related manufacturing fields. This method has a proven engineering foundation, effectively improving the automation level and machining accuracy of the machining process, enhancing the surface consistency and wall thickness uniformity of mesh spherical shell components, and providing a reliable technical approach for the efficient and precise machining of complex thin-walled mesh spherical shell components.

[0062] The specific implementation examples described above further illustrate the purpose, technical solution, and beneficial effects of the present invention, and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for planning the toolpath in five-axis milling of mesh spherical shell components, characterized in that, The steps are as follows: The first step is to calculate the theoretical tooling point of the inner surface based on the theoretical inner surface design equation; The second step is to perform wall thickness value matching on the point cloud data of the outer surface based on the inverse distance weighted IDW interpolation method and combined with the nearest neighbor matching strategy. The third step is to calculate the normal vector direction of each point based on the point cloud data of the outer surface, and then offset the corresponding wall thickness value inward along the normal vector to obtain the actual inner surface. The third step is as follows: Based on the point cloud data of the outer surface, the corresponding wall thickness value is offset inward along the normal vector to obtain the actual inner surface; on this basis, the target wall thickness value is offset outward along the normal vector in subsequent steps, thereby achieving effective control of wall thickness tolerance and surface tolerance. First, the normal vector of the actual shape surface point cloud is calculated based on the PCA principal component analysis method; for the shape surface point cloud dataset with wall thickness values... One point Constructing a point cloud spatial index using a KD-tree And select a set of neighborhood points for that point: （9） in, This is a dataset of point clouds representing the external surface with wall thickness values. Let be a set of neighborhood points selected from the point cloud, and the set contains One point, for The covariance matrix of the neighborhood points in the set is constructed based on the neighborhood point set. as follows: （10） Perform eigenvalue decomposition on the matrix: （11） in are eigenvalues, and ; The corresponding eigenvector; since the eigenvector corresponding to the smallest eigenvalue Since it is the normal vector, the point... normal vector ; Secondly, the normal vector direction is calibrated for consistency. Since the normal vector direction obtained by the above method lacks global consistency, a constraint strategy based on the global coordinate axes is adopted, which involves judging the normal vector... The sign of the components is unified with their direction, and the correction formula is: （12） in normal vector Quantity The normal vector is directed inwards, that is, along the direction from the center of the spherical shell, thus obtaining a set of points on the outer surface with the same normal vector direction. ; Finally, the point cloud data of the outer surface is offset inward along its normal direction by the corresponding wall thickness value. The offset calculation formula is as follows: （13） in, for The points corresponding to the offset; solving for the offset yields the actual inner surface point set. Since the actual inner surface state differs from the outer surface, the point cloud normal vector needs to be recalculated; therefore, the actual inner surface point set is denoted as... ; The fourth step is to perform interpolation and fitting on the actual internal surface point cloud data, using the theoretical tool point as a constraint. The fifth step involves screening the actual inner surface tooling points based on the shape and position characteristics of the reinforcing ribs, and generating a compensated tooling trajectory by offsetting the target wall thickness along the normal vector.

2. The method for planning the toolpath for five-axis milling of a mesh spherical shell component according to claim 1, characterized in that, The first step is as follows: For milling of grid-like spherical shell components, the roughing stage mainly involves adjusting the tool length based on the internal surface theory toolpath. The machining trajectory adopts a circumferential milling form, and the reciprocating machining is achieved by dividing the spacing between adjacent toolpaths with equal arc lengths. Therefore, for the design equation of the spherical shell's theoretical internal surface, the equal residual height method is used to calculate the row spacing of the machining trajectory to ensure surface quality. For the spherical shell's internal surface, its surface shape is approximately a part of an ellipsoid, thus deriving its specified height. The cross-sectional radius of the circumferential trajectory is: （1） in Where is the cross-sectional radius, It is a double major axis ellipse. The minor axis is the major axis of the ellipse; therefore, the chord height error... The calculation formula is: （2） Then, the circumferential dispersion step length is derived based on the chord height error method. With chord height error The formula for calculating the interval is: （3） Since the curvature of the inner surface of the spherical shell is much greater than the residual height, the relationship between the row spacing and the residual height is as follows: （4） in Line spacing, For the tool radius, The remaining height is considered; therefore, on the bimajor axis ellipsoidal design surface, given the starting position, and with the row spacing and step spacing parameters determining the spatial distribution of the tool positions, the surface is discretized using the theoretical inner surface equation to obtain the theoretical tool position set of the inner surface. .

3. The method for planning the toolpath in five-axis milling of a grid-like spherical shell component according to claim 2, characterized in that, The second step is as follows: Based on in-machine digital scanning technology, the actual external surface point cloud data and corresponding wall thickness values ​​of the mesh spherical shell component are acquired. The wall thickness data is associated with a portion of the external surface point cloud data using a nearest neighbor matching method. Then, the remaining point cloud data is padded with wall thickness values ​​using the IDW interpolation method, thereby achieving the assignment of wall thickness values ​​to all external surface point cloud data. The external surface point cloud dataset is defined as follows: The wall thickness data point set is ,in The wall thickness values ​​at each point are... and Point sets and Points; Calculation and Euclidean distance: （5） For each wall thickness data point Search for the nearest point in the shape surface point cloud dataset: （6） in, This represents the closest distance, corresponding to the closest point. Then, the wall thickness value is mapped to the corresponding surface data point: （7） At this point, some points in the shape surface point cloud dataset have already been assigned wall thickness values; let this point set be denoted as . For points that have not been assigned a wall thickness value Take the one closest to it. A known wall thickness point The wall thickness value is calculated by interpolation based on the IDW method: （8） in, For the weight function, , The distance attenuation index is used to calculate the distance between the interpolation point and the point with known wall thickness using equation (5). This yields a point cloud dataset of the external surface with wall thickness values. .

4. The method for planning the toolpath for five-axis milling of a grid-like spherical shell component according to claim 3, characterized in that, The fourth step is as follows: Based on the theoretical tool path trajectory of the internal shape, the actual internal shape point cloud data is layered and cropped, limiting the number of rows of the circumferential tool path trajectory and the length of each row. The location is determined by the direction of the cut-off points. Based on this, longitudinal interpolation and circumferential circle fitting are performed on the cut-off point set to obtain a uniformly distributed actual inner surface cut-off point set. For the set of tool points in the theory of inner surface Each different height value , The theoretical number of tool positions, the vertical arc length along the arc. The actual internal surface point cloud data is cropped to obtain the corresponding local point set; the arc length range is converted into the Z value range, i.e.: （14） in, For The range of values ​​in the Z-direction above and below the center. The coordinates of the center of the sphere along the Z direction, and the radius. , For each theoretical tool position point, the corresponding angle in the circular arc coordinate system is: ; According to equation (14), the actual inner shape surface point set is extracted. China conforms Given all points according to the given conditions, the actual set of points intercepting the inner surface is: , ,in, The number of points to be selected from the actual internal surface; The actual inner shape point set after truncation In the middle, according to the inner surface theory, the height of the tool point is... Lagrange interpolation is used to construct local functions at interpolation points. ,Right now: （15） in The number of points participating in the interpolation, and these points must be on the same line of the laser beam. and The points are selected for interpolation; then, the interpolation points are solved based on the linear fitting relationship. ,but: （16） Where parameters and The analytical solution is determined by minimizing the sum of squared residuals: （17） and For the selected One interpolation point and The average value; after the above longitudinal interpolation fitting, the actual inner surface laser point set is transformed into a longitudinally uniformly distributed tool point set, which is expressed as: ,in Represents a point set The number of points in the middle; against For problems with random distribution in the circumferential direction, a circumferential circle fit is performed; at each fixed height section... Above, based on discrete point sets A circle fitting model is established using the least squares method: （18） in for Each point in the middle relative to the geometric center The offset value; The offset of the center of the circle relative to the geometric center is given; then the coordinates of the center of the cross section are solved. With fitted radius : （19） in, The number of points within each cross section, which divide the circle of that cross section into... Segmented arc; then, based on The angle is uniformly interpolated across the cross section to generate a continuous and uniformly distributed set of tool points. The circular parameter interpolation equation is: （20） in, For the newly interpolated points, It is in the In a segment of a circle, the first Interpolation generation points The C-axis angle is calculated; point cloud data is mapped to polar angle parameter space, and circumferential uniform interpolation is achieved by calculating the angular interval between adjacent points and combining it with the theoretical tool position angle step size. The formula for calculating angles is: （21） in, The theoretical tool position angle step size, For the first The number of points to be inserted in the segment. The number of theoretical tool points within this cross section; when This indicates that the axial angle difference between adjacent tool points does not exceed the angular step size. Therefore, no interpolation encryption is required; thus, the theoretical tool point set of the actual inner surface with equal row spacing and equal step spacing in space is obtained. ,in Represents a point set The number of points; however, the tool point set at this time is located on the inner surface and the shape and position characteristics of the reinforcing ribs are not considered. Therefore, the tool point points need to be screened first, and then the equal wall thickness offset processing is further implemented.

5. The method for planning the toolpath for five-axis milling of a mesh spherical shell component according to claim 4, characterized in that, The fifth step is as follows: Based on the design shape and position of the reinforcing ribs, the actual internal surface cutting points are screened. The cutting points located in the transverse rib area are eliminated by limiting the range of Z. Then, the cutting points located in the longitudinal rib area are eliminated by giving the C-axis angle position corresponding to the center of the longitudinal rib and the offset arc length range on both sides. First, filter the transverse rib area by a specified value. To capture the center, the upper and lower offset settings are set. To define the cutoff interval, the Z-axis cutoff interval is: ,in Let be the number of intervals selected by the horizontal ribs; then the point set after horizontal filtering is: Then, select the angle corresponding to the center of the longitudinal reinforcement. , The number of longitudinal reinforcement sections; at the stated angle Centered on the same angle on both sides By applying an offset, the longitudinal reinforcement screening interval is constructed. The point set after vertical filtering is denoted as... ; The actual inner surface tool points after screening are divided into independent grid regions. According to the PCA principal component analysis method shown in equations (9) to (11), the normal vector of each tool point is calculated in each region; according to the variation of equation (12) The direction of the normal vector is unified so that it points to the outward normal direction, and the normal vector of the actual inner surface tool point is denoted as... ; Then, based on equation (13), the target wall thickness value is offset outward along the normal vector at the tool position. This allows us to obtain the compensation tool position point for the target surface. Furthermore, for digital machining on a five-axis machine tool, it is necessary to further solve for the coordinates of the swing axis and the rotary axis, based on the normal vector of the tool position point. The coordinates of the A-axis and C-axis are determined using the following formulas: （22） This yields the five-axis coordinates of the compensated tool position in the workpiece coordinate system. Within the grid area, a circumferential milling method with equal arc length is used for machining trajectory planning, realizing five-axis milling compensation machining of grid spherical shell components. For the multi-round milling process of grid spherical shell components, steps two to five are repeated from the semi-finishing stage, which can effectively improve machining accuracy and meet actual machining requirements.

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