Curved surface integrated conformal jet printing path planning method and system

Abstract

The invention discloses a path planning method and system for curved surface integrated conformal jet printing, and belongs to the field of additive manufacturing. According to the method, the geometric data of the non-deployable curved surface are obtained and converted into the discretized grid model, then the plane pattern is designed and mapped to the three-dimensional curved surface, the mapped pattern is locally optimized, and the complete printing area model is generated. Path planning is divided into initial jet printing path generation and five-axis linkage motion path planning, conformal characteristics are achieved through an adaptive interpolation algorithm and NURBS curve optimization, five-axis motion parameters are calculated based on an inverse kinematics algorithm, and the positioning relation between a jet printing head and a curved surface is kept through the RTCP technology. The method solves the problems of precision and path planning efficiency in complex curved surface manufacturing, and is suitable for manufacturing heterogeneous complex curved surface functional structures in the fields of aerospace, medical instruments and the like.

Description

Technical Field

[0001] The present invention relates to the field of additive manufacturing technology, and more specifically to a path planning method and system for conformal printing of integrated curved surfaces, particularly a high-performance manufacturing technology for complex heterogeneous curved surface functional structures. Background Art

[0002] Electrohydrodynamic printers use an electric field to draw ink droplets from the print nozzle. Combined with a high-precision 3D printing platform, they can print micron / submicron dots and directly write micron / submicron line structures. This allows for the printing of precise micro-nano quantum dots and lines, thereby creating pre-set patterns. Electrohydrodynamic printing technology relies on electric field forces to pull ink droplets from the nozzle and eject them onto the substrate. If the nozzle is not aligned with the surface normal, the droplet's flight path will shift, affecting the accuracy and positioning of the printed pattern. Keeping the nozzle aligned with the surface normal ensures that the ink droplets reach the target location along the shortest path, thereby improving printing accuracy.

[0003] High-performance manufacturing of complex heterogeneous curved surface functional structures is an important research direction in the field of modern manufacturing, and is widely used in aerospace, defense equipment, medical equipment and other fields. When faced with complex curved surface structures, traditional manufacturing methods often face problems such as insufficient forming accuracy, low manufacturing efficiency, and difficulty in ensuring material properties. The continuous advancement of modern manufacturing technology has made the demand for manufacturing complex heterogeneous curved surface functional structures more prominent. Especially in the fields of aerospace, defense and medical equipment, complex surfaces not only need to meet high-precision requirements, but also need to meet higher standards in mechanical, electrical, thermal and other performance aspects. The development of additive manufacturing technology (electrohydrodynamic 3D printing) provides a new idea for the manufacture of complex curved surface functional structures. Compared with the traditional planar layer-by-layer stacking process, additive manufacturing technology can achieve more precise functional structure deposition on the curved surface by adding materials layer by layer.

[0004] However, the current development of complex surface manufacturing technology still faces the following technical challenges: most research still focuses on the modeling and functional optimization of simple surfaces; the efficiency and adaptability of existing path planning algorithms in multi-material printing manufacturing of complex surfaces still need to be improved.

[0005] Therefore, studying and solving the path planning and application problems of high-performance integrated conformal printing on complex heterogeneous surfaces has important theoretical and practical engineering significance. Summary of the Invention

[0006] The technical problem to be solved by the present invention is how to solve the problems of insufficient precision, low path planning efficiency and forming quality control faced in the current complex surface manufacturing.

[0007] The present invention solves the above technical problems through the following technical means:

[0008] The path planning method for integrated conformal printing on curved surfaces includes:

[0009] S1. Converting the surface geometric model into a discretized grid model consisting of grid points;

[0010] S2. Mapping the planar pattern to a discretized grid model involves interpolating the 2D model of the planar pattern and establishing XY plane indices for the grid points. For each interpolated 2D point, the nearest grid point is found on the XY plane, and the Z coordinate of the nearest grid point is used as the Z coordinate of the projected point. The projected point set is then fitted with a NURBS curve to obtain the mapped pattern.

[0011] S3. Performing local optimization on the mapped pattern to generate a complete printing area model;

[0012] S4. Path optimization for the print area model includes initial printing path generation and five-axis linkage motion path planning. Initial printing path generation uses an adaptive interpolation algorithm and NURBS curve optimization to achieve conformal characteristics. Five-axis linkage motion path planning calculates five-axis motion parameters based on an inverse kinematics algorithm and maintains the positioning relationship between the print head and the surface through RTCP technology.

[0013] Furthermore, the step S2 specifically includes: using a KDTree data structure to establish an XY plane index of the grid point.

[0014] Furthermore, the initial printing path generation in step S4 is specifically as follows: extracting the node positions and normal vectors of the discretized grid model as basic data for path planning; using an adaptive interpolation algorithm to supplement necessary points for the bow height error between nodes, and optimizing using NURBS curves; the parameterized error of the path is measured by the bow height error. Given three points P1, P2, and P3 on the surface, the bow height error is defined as: When the height error between adjacent points exceeds a threshold, a new sampling point is inserted between the two points:

[0015] Among them, n avg It's point P i and P i+1 The average value of the normal vectors at .

[0016] Furthermore, the five-axis motion path planning in step S4 is specifically as follows: the kinematic model of the five-axis machine tool includes the transformation matrix of three linear axes (X, Y, Z) and two rotation axes (A, B), and the kinematic equation is:

[0017]

[0018] in, Represents the transformation matrix from the workpiece coordinate system to the tool coordinate system, T x ,T y ,T z ,T a ,T b Represents the transformation matrix of X, Y, Z, A, B axis respectively, T t Represents the transformation matrix of the tool coordinate system.

[0019] Specifically, the transformation matrix of each axis can be expressed as:

[0020] For a five-axis machine tool, the position P = (x, y, z) of a point on a given surface and the normal vector n = (n x ,n y ,n z ), solve the corresponding machine coordinates (X, Y, Z, A, B):

[0021] A=arctan(n y / n x )

[0022] B=arcsin(n z )

[0023]

[0024] Among them, R a and R b are the rotation matrices of the A-axis and B-axis respectively.

[0025] Furthermore, the step S4 in which the positioning relationship between the printing head and the curved surface is maintained by using the RTCP technology is specifically as follows: obtaining the position (x w ,y w ,z w ) and the normal vector (n x ,n y ,n z ), substitute the A-axis rotation angle α and the B-axis rotation angle β into the rotation matrix:

[0026] Calculate the position change of the workpiece after rotation:

[0027] (x′ w y′ w z′ w )=R A ·R B ·(x w y w z w )

[0028] Calculate the compensation distance to return the print head to the correct position:

[0029] (ΔxΔyΔz)=(x′ w -x w y′ w -y w z′ w -z w )

[0030] Apply compensation to correct the print head position:

[0031] (X machine Y machine Z machine )=(X programmed Y programmed Z programmed )-(ΔxΔyΔz).

[0032] The present invention also provides a path planning system for curved surface integrated conformal printing, comprising:

[0033] Surface geometry modeling module: converts the surface geometry model into a discretized grid model composed of grid points;

[0034] Surface pattern modeling and integration module: This module maps a planar pattern to a discretized grid model. Specifically, after interpolating the 2D model of the planar pattern, an XY plane index of the grid points is established. For each interpolated 2D point, the nearest grid point is found on the XY plane, and the Z coordinate of the nearest grid point is used as the Z coordinate of the projected point. The projected point set is fitted with a NURBS curve to obtain the mapped pattern.

[0035] Printing area model generation module: performs local optimization on the mapped pattern to generate a complete printing area model;

[0036] Path planning module: Path optimization for the printing area model includes initial printing path generation and five-axis linkage motion path planning; initial printing path generation uses adaptive interpolation algorithm and NURBS curve optimization to achieve conformal characteristics; five-axis linkage motion path planning calculates five-axis motion parameters based on inverse kinematics algorithm and maintains the positioning relationship between the print head and the surface through RTCP technology.

[0037] Furthermore, the surface pattern modeling and integration module specifically uses a KDTree data structure to establish an XY plane index of grid points.

[0038] Furthermore, the initial printing path generation in the path planning module is specifically as follows: the node positions and normal vectors of the discretized grid model are extracted as the basic data for path planning; for the bow height error between nodes, an adaptive interpolation algorithm is used to supplement the necessary points, and NURBS curves are used for optimization; the parameterized error of the path is measured by the bow height error. Given three points P1, P2, and P3 on the surface, the bow height error is defined as: When the height error between adjacent points exceeds a threshold, a new sampling point is inserted between the two points:

[0039] Among them, n avg It's point P i and P i+1 The average value of the normal vectors at .

[0040] Furthermore, the five-axis motion path planning in the path planning module is specifically as follows: the kinematic model of the five-axis machine tool includes the transformation matrix of three linear axes (X, Y, Z) and two rotation axes (A, B), and the kinematic equation is:

[0041]

[0042] in, Represents the transformation matrix from the workpiece coordinate system to the tool coordinate system, T x ,T y ,T z ,T a ,T b Represents the transformation matrix of X, Y, Z, A, B axis respectively, T t Represents the transformation matrix of the tool coordinate system.

[0043] Specifically, the transformation matrix of each axis can be expressed as:

[0044] For a five-axis machine tool, the position P = (x, y, z) of a point on a given surface and the normal vector n = (n x ,n y ,n z ), solve the corresponding machine coordinates (X, Y, Z, A, B):

[0045] A=arctan(n y / n x )

[0046] B=arcsin(n z )

[0047]

[0048] Among them, R aand R b are the rotation matrices of the A-axis and B-axis respectively.

[0049] Furthermore, the path planning module uses the RTCP technology to maintain the positioning relationship between the printing head and the surface, specifically: obtaining the position of the current path point in the surface model coordinate system (x w ,y w ,z w ) and the normal vector (n x ,n y ,n z ), substitute the A-axis rotation angle α and the B-axis rotation angle β into the rotation matrix:

[0050] Calculate the position change of the workpiece after rotation:

[0051] (x′ w y′ w z′ w )=R A ·R B ·(x w y w z w )

[0052] Calculate the compensation distance to return the print head to the correct position:

[0053] (ΔxΔyΔz)=(x′ w -x w y′ w -y w z′ w -z w )

[0054] Apply compensation to correct the print head position:

[0055] (X machine Y machine Z machine )=(X programmed Y programmed Z programmed )-(ΔxΔyΔz).

[0056] The advantages of the present invention are:

[0057] (1) The path planning method of the present invention can effectively solve the problem of pattern printing on non-developable surfaces, so that traditional two-dimensional patterns can be accurately mapped onto complex surfaces to avoid pattern distortion. After the two-dimensional model is interpolated, the KDTree data structure is used to establish the XY plane index of the grid point. For each 2D point after interpolation, the nearest grid point is found on the XY plane and the Z coordinate of the nearest grid point is used as the Z coordinate of the projection point. The projected point set is connected by a NURBS curve, which can solve the stretching, compression or distortion problems caused by curvature changes.

[0058] (2) The path planning algorithm can adapt to the curvature changes of different areas on the surface, dynamically adjust the path accuracy and printing speed, and ensure that the pattern can be accurately deposited on the surface;

[0059] (3) The five-axis linkage system can achieve precise control of the print head, ensuring that the print head always maintains the appropriate angle and distance with the curved surface during the entire printing process, achieving a stable deposition trajectory;

[0060] (4) The method of the present invention can be widely used in aerospace, medical equipment, high-end manufacturing and other fields, and has important practical value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A schematic diagram of the snowflake electrode plane pattern according to an embodiment of the present invention is drawn.

[0062] Figure 2 This is a point cloud grid model diagram of the lower half of the double-leaf hyperboloid in an embodiment of the present invention.

[0063] Figure 3 Schematic diagram of point interpolation of a snowflake electrode plane pattern according to an embodiment of the present invention.

[0064] Figure 4 Schematic diagram of the projection points and intersection paths after projection of the snowflake electrode pattern according to an embodiment of the present invention.

[0065] Figure 5 This is a schematic diagram of the path of the snowflake electrode pattern using NURBS curve fitting according to an embodiment of the present invention.

[0066] Figure 6 Schematic diagram of the processing points of the snowflake electrode pattern in the workpiece coordinate system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0068] The path planning method for high-performance, integrated conformal printing on curved surfaces provided by the present invention mainly includes two core parts: surface geometry modeling and path planning algorithm development and optimization. These two parts are described in detail below with reference to the accompanying drawings.

[0069] Step 1: Surface geometry modeling

[0070] The research on surface geometry modeling and analysis is mainly divided into two key steps: modeling of non-developable surfaces and modeling and integration of surface patterns.

[0071] 1. Modeling of non-developable surfaces

[0072] See also Figure 2 As shown, this embodiment first obtains the geometric data of the non-developable surface, including curvature distribution, normal vector and boundary features, through a scanner or 3D modeling software, and performs parametric decomposition on it to convert the complex surface into an operational discrete model. Figure 2 A typical surface point cloud grid model is shown, taking the lower half of a double-leaf hyperboloid as an example.

[0073] The mathematical expression of non-developable surface is: S(u,v) T =[x(u,v),y(u,v),z(u,v)], where (u,v) is the parametric coordinate of the surface and u∈[u min ,u max ],v∈[v min ,v max ]. The position vector of a point on the surface is: r(u,v) T =[x(u,v),y(u,v),z(u,v)]. The surface normal vector at point (u,v) is the cross product of the two tangent vectors, then normalized: Among them, r u and r v are the tangent vectors of the surface in the u and v directions respectively.

[0074] By modeling the surface, we can deeply understand the shape characteristics of the surface and provide theoretical support for the subsequent printing process.

[0075] 2. Modeling and integration of surface patterns

[0076] Based on the non-developable surface modeling, the plane pattern is designed according to the functional requirements. Figure 1 As shown, Figure 1 This example shows a schematic diagram of a planar pattern drawing. This embodiment uses a mapping algorithm to accurately map a planar pattern onto a three-dimensional surface, resolving stretching, compression, or distortion issues caused by curvature changes. The mapped pattern is then locally optimized to better adapt to the surface's geometric characteristics.

[0077] This embodiment uses point projection to map a flat pattern to a curved surface. The flat pattern is first discretized into a set of points, and then a projection algorithm is used to map each point to a corresponding position on the three-dimensional surface. After interpolating the two-dimensional model, the KDTree data structure is used to establish the XY plane index of the grid points. For each interpolated 2D point, the nearest grid point is found on the XY plane, and the Z coordinate of the nearest grid point is used as the Z coordinate of the projected point.

[0078] like Figure 4 As shown, this embodiment determines the printing path by calculating the projection points and the intersection points. The projected point set is connected by NURBS curves to ensure the continuity and smoothness of the pattern on the surface. The mathematical definition of NURBS curve is:

[0079]

[0080] Among them, P i is the control point, w i is the weight, N i,p (t) is the p-order B-spline basis function.

[0081] like Figure 5 As shown in Figure 3, after the NURBS curve is fitted into a path, it can accurately and smoothly adapt to the surface model. Figure 6 A schematic diagram of the machining points in the workpiece coordinate system is shown. In this example, a snowflake-shaped electrode pattern was selected for experimental verification. The mapping algorithm accurately projects the two-dimensional pattern onto a three-dimensional surface, ensuring that the pattern's shape and size on the surface are not distorted. Ultimately, a complete print area model is generated, providing a precise geometric description for path planning.

[0082] Subsequently, the converted surface model is overlapped with the designed pattern model to generate a complete printing area model. The overlapping or discontinuous areas in the model are eliminated through conflict detection and correction. Finally, the superimposed model is subjected to boundary clipping and local optimization based on the process characteristics of the printing equipment to generate a processing model suitable for printing.

[0083] 2. Path Planning Algorithm Development and Optimization

[0084] The core of path planning lies in solving two problems: one is to generate the initial printing path based on the grid units discretized from the model, and the other is to plan the five-axis linkage motion path of the workbench that meets the printing path requirements.

[0085] 1. Initial printing path generation

[0086] For the initial printing path, the model is first divided into a regular grid of cells, and node positions and normal vectors are extracted as the basic data for path planning. Based on the discretized model, a path generation algorithm is designed to ensure that the path covers the target area and optimize path extension in boundary areas to ensure uniform material deposition. Furthermore, path nodes are optimized to reduce path overlap and redundant motion, thereby improving path planning efficiency and accuracy.

[0087] During the path planning process, in order to address the bow height error between points, this embodiment uses an adaptive interpolation algorithm to supplement the necessary points and uses NURBS curves for optimization, which not only ensures that the curve can accurately and smoothly adapt to the model and achieve conformal characteristics, but also ensures the smoothness and stability of the subsequent motion trajectory.

[0088] The parametric error of the path can be measured by the bow height error. Given three points P1, P2, and P3 on the surface, the bow height error is defined as:

[0089] When the height error between adjacent points exceeds a threshold, a new sampling point is inserted between the two points:

[0090]

[0091] Among them, n avg It's point P i and P i+1 The average value of the normal vectors at .

[0092] 2. Five-axis motion path planning

[0093] When planning the five-axis motion path, we focus on real-time optimization of the print head posture, so that it always remains consistent with the normal direction of the surface during movement, thereby improving the accuracy and stability of deposition.

[0094] The kinematic model of the five-axis machine tool is key to the path planning of this embodiment. In a five-axis machine tool, the relative position and posture between the workpiece and the tool can be controlled via five motion axes: three linear axes (X, Y, Z) and two rotary axes (A, B). The five-axis machine tool structure used in this embodiment is a "three-axis mobile + two-axis rotary table" configuration. The kinematic equations of the five-axis machine tool can be expressed as:

[0095]

[0096] in, Represents the transformation matrix from the workpiece coordinate system to the tool coordinate system, T x ,T y ,T z ,T a ,T b Represents the transformation matrix of X, Y, Z, A, B axis respectively, T t Represents the transformation matrix of the tool coordinate system.

[0097] Specifically, the transformation matrix of each axis can be expressed as:

[0098] The inverse kinematics problem is to solve the position and posture of a given workpiece coordinate system and calculate the corresponding angles of each joint of the five-axis machine tool. For a five-axis machine tool, the position P = (x, y, z) of a point on a given surface and the normal vector n = (n x ,n y ,n z ), solve the corresponding machine coordinates (X, Y, Z, A, B):

[0099] A=arctan(n y / n x )

[0100] B=arcsin(n z )

[0101]

[0102] Among them, R a and R b are the rotation matrices of the A-axis and B-axis respectively.

[0103] This embodiment uses kinematics calculation of the print head posture to ensure that the print head always remains consistent with the normal direction of the curved surface, thereby ensuring the accuracy and consistency of material deposition.

[0104] 3. Five-axis inverse kinematics calculation of fixed-orientation tool

[0105] To ensure printing stability and process consistency, the printing system of this embodiment adopts a "fixed downward-facing tool" design principle. This means the print head always maintains a vertical downward orientation, and the worktable's rotational motion establishes the desired relative position between the curved surface and the print head. This design significantly simplifies the structural complexity of the printing system while ensuring stable ink droplet deposition.

[0106] Kinematics of fixed orientation printheads

[0107] In this kinematic configuration, the system has the following characteristics:

[0108] 1. Fixed orientation of the print head: The Z axis of the print head is always parallel to the Z axis of the machine tool and points vertically downward, that is:

[0109] 2. Workpiece rotation positioning: By rotating the A-axis and B-axis, the local normal vector of the surface is aligned with the Z-axis of the print head, achieving the correct relative posture between the "surface-print head".

[0110] 3. Workpiece position compensation: The three linear axes X, Y, and Z move in coordination to compensate for the spatial position changes caused by the rotation of the workpiece, ensuring that the printing point is accurately aligned with the target position.

[0111] Inverse kinematics calculation process

[0112] Based on the above characteristics, the inverse kinematics calculation process is modified as follows:

[0113] 1. Rotation angle calculation: Since the print head is fixed downward, the workpiece needs to be rotated to align the surface normal vector with the Z axis direction of the print head. Let the surface normal vector be but: Where A is the rotation angle of the worktable around the X-axis, and B is the rotation angle of the worktable around the Y-axis.

[0114] 2. Rotation transformation matrix: Combined rotation matrix: R = R A ·R B

[0115] 3. Position compensation calculation: In order to compensate for the position change caused by the rotation of the workpiece, the position difference before and after the rotation needs to be calculated. Let the original position be P0 = (x0, y0, z0), and the position relative to the rotation center be P r =(x r ,y r ,z r ), then: P r =P0-P c Among them, P c is the coordinate of the rotation center. Position after rotation: P r′ =R·P r Position compensation: ΔP=P r′ -P r

[0116] 4. Linear axis position calculation: Where h is the print head height compensation, which is used to adjust the working distance between the print head and the curved surface.

[0117] Through the above-mentioned inverse kinematics calculation method and trajectory planning strategy, this embodiment can achieve high-precision printing on complex surfaces under the constraint of a fixed nozzle orientation, effectively improving manufacturing efficiency and product quality.

[0118] RTCP function implementation

[0119] To achieve precise positioning between the print head and the curved surface, this embodiment employs RTCP (Real-Time Control Point) technology. In processing equipment, RTCP maintains the print head's posture and position relative to the workpiece even as the worktable rotates, simplifying path planning and improving printing accuracy.

[0120] In RTCP mode, when the workpiece coordinate system changes due to the rotation of the A-axis and B-axis, the system will calculate and compensate the position of the print head in real time to keep it in the expected position relationship with the surface. The mathematical implementation of the RTCP function can be expressed as: compensated =T initial ·(T rotation ) -1 , where T compensated is the compensated print head pose matrix, T initial is the initial print head pose matrix, T rotation is the rotation axis transformation matrix.

[0121] Specifically, the implementation of RTCP involves the following transformation calculations:

[0122] 1. First, obtain the position of the current path point in the workpiece coordinate system (x w ,y w ,z w ) and the normal vector (n x ,n y ,n z ). Substitute the A-axis rotation angle α and the B-axis rotation angle β into the rotation matrix:

[0123] 2. Calculate the position change of the workpiece after rotation:

[0124] (x′ w y′ w z′ w )=R A ·R B ·(x w y w z w )

[0125] 3. Calculate the compensation distance to return the print head to the correct position:

[0126] (ΔxΔyΔz)=(x′ w -x w y′ w -y wz′ w -z w )

[0127] 4. Apply compensation to correct the position of the print head:

[0128] (X machine Y machine Z machine )=(X programmed Y programmed Z programmed )-(ΔxΔyΔz)

[0129] For complex curved areas (such as high curvature and boundary transition areas), this embodiment requires dynamic adjustment of the five-axis path and printing speed to ensure the continuity and consistency of material deposition. The greater the curvature of the area, the higher the path point density should be. The relationship can be expressed as: Δs = min (Δs max ,k / κ), where Δs is the arc length distance between path points, Δs max is the maximum allowed point spacing, k is the scaling factor, and κ is the curvature.

[0130] The relationship between the printing speed v and the curvature κ can be expressed as: Among them, v max is the maximum printing speed, and α is the adjustment coefficient.

[0131] The above embodiments are only used to illustrate the technical solutions of this embodiment, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A path planning method for conformal printing on curved surfaces, characterized in that: include: S1. Converting the surface geometric model into a discretized grid model consisting of grid points; S2. Mapping the planar pattern to a discretized grid model involves interpolating the 2D model of the planar pattern and establishing XY plane indices for the grid points. For each interpolated 2D point, the nearest grid point is found on the XY plane, and the Z coordinate of the nearest grid point is used as the Z coordinate of the projected point. The projected point set is then fitted with a NURBS curve to obtain the mapped pattern. S3. Performing local optimization on the mapped pattern to generate a complete printing area model; S4. Path optimization for the print area model includes initial printing path generation and five-axis linkage motion path planning. Initial printing path generation uses an adaptive interpolation algorithm and NURBS curve optimization to achieve conformal characteristics. Five-axis linkage motion path planning calculates five-axis motion parameters based on an inverse kinematics algorithm and maintains the positioning relationship between the print head and the surface through RTCP technology.

2. The path planning method for curved surface integrated conformal printing according to claim 1, characterized in that: The step S2 specifically includes: using the KDTree data structure to establish the XY plane index of the grid point.

3. The path planning method for curved surface integrated conformal printing according to claim 1, characterized in that: The initial printing path generation in step S4 is specifically as follows: extracting the node positions and normal vectors of the discretized grid model as basic data for path planning; using an adaptive interpolation algorithm to supplement necessary points for the bow height error between nodes, and optimizing using NURBS curves; the parameterized error of the path is measured by the bow height error. Given three points P1, P2, and P3 on the surface, the bow height error is defined as: When the height error between adjacent points exceeds a threshold, a new sampling point is inserted between the two points: Among them, n avg It's point P i and P i+1 The average value of the normal vectors at .

4. The path planning method for curved surface integrated conformal printing according to claim 1, characterized in that: The five-axis motion path planning in step S4 is specifically as follows: the kinematic model of the five-axis machine tool includes the transformation matrix of three linear axes (X, Y, Z) and two rotation axes (A, B), and the kinematic equation is: in, Represents the transformation matrix from the workpiece coordinate system to the tool coordinate system, T x ,T y ,T z ,T a ,T b Represents the transformation matrix of X, Y, Z, A, B axis respectively, T t Represents the transformation matrix of the tool coordinate system. Specifically, the transformation matrix of each axis can be expressed as: For a five-axis machine tool, the position P = (x, y, z) of a point on a given surface and the normal vector n = (n x ,n y ,n z ), solve the corresponding machine coordinates (X, Y, Z, A, B): A=arctan(n y / n x ) B=arcsin(n z ) Among them, R a and R b are the rotation matrices of the A-axis and B-axis respectively.

5. The path planning method for curved surface integrated conformal printing according to claim 4, characterized in that: In step S4, the positioning relationship between the printing head and the curved surface is maintained by using the RTCP technology as follows: obtaining the position (x w ,y w ,z w ) and the normal vector (n x ,n y ,n z ), substitute the A-axis rotation angle α and the B-axis rotation angle β into the rotation matrix: Calculate the position change of the workpiece after rotation: (x′ w y′ w z′ w )=R A ·R B ·(x w y w z w ) Calculate the compensation distance to return the print head to the correct position: (ΔxΔyΔz)=(x′ w -x w y′ w -y w z′ w -z w ) Apply compensation to correct the print head position: (X machine Y machine Z machine )=(X programmed Y programmed Z programmed )-(ΔxΔyΔz)。 6. Path planning system for integrated conformal printing on curved surfaces, characterized by: include: Surface geometry modeling module: converts the surface geometry model into a discretized grid model composed of grid points; Surface pattern modeling and integration module: This module maps a planar pattern to a discretized grid model. Specifically, after interpolating the 2D model of the planar pattern, an XY plane index of the grid points is established. For each interpolated 2D point, the nearest grid point is found on the XY plane, and the Z coordinate of the nearest grid point is used as the Z coordinate of the projected point. The projected point set is fitted with a NURBS curve to obtain the mapped pattern. Printing area model generation module: performs local optimization on the mapped pattern to generate a complete printing area model; Path planning module: Path optimization for the printing area model includes initial printing path generation and five-axis linkage motion path planning; initial printing path generation uses adaptive interpolation algorithm and NURBS curve optimization to achieve conformal characteristics; five-axis linkage motion path planning calculates five-axis motion parameters based on inverse kinematics algorithm and maintains the positioning relationship between the print head and the surface through RTCP technology.

7. The path planning system for curved surface integrated conformal printing according to claim 6, characterized in that: The surface pattern modeling and integration module specifically uses a KDTree data structure to establish an XY plane index of a grid point.

8. The path planning system for curved surface integrated conformal printing according to claim 6, characterized in that: The initial printing path generation in the path planning module is specifically as follows: the node positions and normal vectors of the discretized grid model are extracted as the basic data for path planning; the necessary points are supplemented by an adaptive interpolation algorithm for the bow height error between nodes, and the NURBS curve is used for optimization; the parameterized error of the path is measured by the bow height error. Given three points P1, P2, and P3 on the surface, the bow height error is defined as: When the height error between adjacent points exceeds a threshold, a new sampling point is inserted between the two points: Among them, n avg It's point P i and P i+1 The average value of the normal vectors at .

9. The path planning system for curved surface integrated conformal printing according to claim 6, characterized in that: The five-axis motion path planning in the path planning module is specifically as follows: the kinematic model of the five-axis machine tool includes the transformation matrix of three linear axes (X, Y, Z) and two rotation axes (A, B), and the kinematic equation is: in, Represents the transformation matrix from the workpiece coordinate system to the tool coordinate system, T x ,T y ,T z ,T a ,T b Represents the transformation matrix of X, Y, Z, A, B axis respectively, T t Represents the transformation matrix of the tool coordinate system. Specifically, the transformation matrix of each axis can be expressed as: For a five-axis machine tool, the position P = (x, y, z) of a point on a given surface and the normal vector n = (n x ,n y ,n z ), solve the corresponding machine coordinates (X, Y, Z, A, B): A=arctan(n y / n x ) B=arcsin(n z ) Among them, R a and R b are the rotation matrices of the A-axis and B-axis respectively.

10. The path planning system for curved surface integrated conformal printing according to claim 9, characterized in that: The path planning module uses RTCP technology to maintain the positioning relationship between the printing head and the surface. Specifically, the following steps are performed: obtaining the position of the current path point in the surface model coordinate system (x w ,y w ,z w ) and the normal vector (n x ,n y ,n z ), substitute the A-axis rotation angle α and the B-axis rotation angle β into the rotation matrix: Calculate the position change of the workpiece after rotation: (x′ w y′ w z′ w )=R A ·R B ·(x w y w z w ) Calculate the compensation distance to return the print head to the correct position: (ΔxΔyΔz)=(x′ w -x w y′ w -y w z′ w -z w ) Apply compensation to correct the print head position: (X machine Y machine Z machine )=(X programmed Y programmed Z programmed )-(ΔxΔyΔz)。

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