A high-precision processing and detecting method for a tire mold cavity surface

Abstract

The present application relates to the field of precision machining and detection technology, especially to a kind of tire mold cavity surface high-precision machining and detection method, comprising: obtaining three-dimensional curved surface grid generated by cavity and calculating Gaussian curvature, solving conformal factor by using discrete curvature flow algorithm and preserving angle mapping to two-dimensional parameter grid, constructing space dynamic scaling field based on conformal factor extraction area expansion coefficient, obtaining three-dimensional machining coordinates and space normal vector by reverse mapping two-dimensional machining point position, dynamically adjusting the output energy of equipment according to scaling field when machining head moves along normal vector, finally scanning point cloud to compare topography, the present application reduces the angle distortion of texture by surface angle-preserving flattening, and compensates for local energy imbalance caused by area stretching by using scaling field real-time energy regulation, and realizes high-precision manufacturing of micro-nano texture without geometric distortion and uniform etching depth on complex cavity surface.

Description

Technical Field

[0001] This invention relates to the field of precision machining and testing technology, and in particular to a method for high-precision machining and testing of the surface of a tire mold cavity. Background Technology

[0002] With the upgrading of high-end tire manufacturing processes, processing micro-nano textures with excellent optical extinction properties on the complex three-dimensional cavity surface of tire molds has become a key technical requirement in the field of precision tire manufacturing. This type of manufacturing process usually requires the use of computer-aided software to map the theoretically designed two-dimensional micro-nano array onto the three-dimensional mold surface, and then calculate the processing trajectory points including spatial position and surface normal vector. Finally, relying on multi-axis high-energy beam processing equipment, high-frequency pulse etching is performed along the morphological contour of the complex curved surface to precisely reproduce the micron-level geometric array structure on the free-form surface in space.

[0003] Existing mapping methods are prone to angular distortion and area stretching in steep curved areas, and constant energy etching cannot compensate for the resulting reduction in energy density, leading to geometric distortion and uneven depth in micro / nano structures, making it difficult to guarantee optical consistency. In addition, in 3D computer vision inspection, existing point cloud processing techniques are unable to eliminate the offset errors in on-machine measurement of large molds, resulting in inaccurate comparison of topographic features and a lack of high-precision digital vision inspection closed loop. Summary of the Invention

[0004] To address the above problems, this invention provides a high-precision machining and inspection method for the surface of tire mold cavities. By establishing a surface adaptive texture mapping model and combining dynamic solution of the surface stretching coefficient with adaptive control of etching pulse energy, the method solves the problems of micro-nano texture shape distortion caused by existing mapping and uneven depth caused by constant energy etching, effectively improving the machining accuracy and optical performance consistency of mold micro-nano textures.

[0005] This invention provides the following technical solution: a method for high-precision machining and inspection of the surface of a tire mold cavity, comprising: S1. Obtain the three-dimensional model data of the surface of the tire mold cavity and perform mesh discretization processing to generate a three-dimensional curved surface mesh and calculate the initial Gaussian curvature of each mesh vertex; S2. Set the target Gaussian curvature of the three-dimensional surface mesh to zero, and use the discrete curvature flow algorithm and the initial Gaussian curvature to solve the conformal factor of each mesh vertex, so as to convert the three-dimensional surface mesh into a two-dimensional parametric mesh in an conformal manner. S3. Based on the conformal factor, extract the area scaling coefficient of the two-dimensional parametric mesh relative to the three-dimensional curved surface mesh at each mesh vertex, and construct a spatial dynamic scaling field. S4. Generate two-dimensional processing points of the target micro-nano texture on a two-dimensional parametric mesh, and reverse map the two-dimensional processing points to a three-dimensional curved surface mesh based on the mesh topology to obtain the three-dimensional processing points and spatial normal vectors. S5. Input the three-dimensional processing point and spatial normal vector into the multi-axis high-energy beam processing equipment. When the processing head of the multi-axis high-energy beam processing equipment moves along the spatial normal vector, dynamically adjust the output energy of the multi-axis high-energy beam processing equipment for processing based on the area scaling coefficient in the spatial dynamic scaling field. S6. The surface of the processed tire mold cavity is scanned on-machine using an optical probe to obtain the measured point cloud, and the measured point cloud is compared with the morphological features of the target micro-nano texture.

[0006] The following are further optimizations to the technical solution of this invention: Step S1, which involves calculating the initial Gaussian curvature of each mesh vertex, includes: Obtain each discrete facet adjacent to each grid vertex, and calculate the sum of the interior angles of each discrete facet at the corresponding grid vertex; Calculate the difference between the preset full-angle constant and the sum of the interior angles to obtain the angle deficit value at the grid vertex; The angle loss value is normalized by using the local neighborhood area of ​​the grid vertices to obtain the initial Gaussian curvature.

[0007] Further optimization: In step S2, the step of solving the conformal factor of each mesh vertex using the discrete curvature flow algorithm and the initial Gaussian curvature includes: Construct a set of evolutionary differential equations with initial Gaussian curvature as the initial state, and establish mapping constraints between curvature variables and conformal factors; Using the target Gaussian curvature as the convergence endpoint, calculate the curvature evolution gradient of the evolutionary differential equation system at each grid vertex; The evolutionary differential equations are iteratively updated along the descent direction of the curvature evolution gradient until the preset convergence accuracy is reached, at which point the conformal factor is output.

[0008] Further optimization: Step S2, which involves conformally mapping the 3D surface mesh to a 2D parametric mesh, includes: Derive the length scaling factor of each mesh edge in a 3D surface mesh using the conformal factor; The edge length of each grid is updated according to the length scaling factor to generate a transition metric grid with conformal features; The transition metric mesh is mapped to a two-dimensional planar coordinate system based on the projection flattening algorithm, thus constructing a two-dimensional parametric mesh.

[0009] Further optimization: Step S3, the step of constructing the spatial dynamic scaling field, includes: Establish the local area mapping relationship between the two-dimensional parametric mesh and the three-dimensional curved surface mesh at each mesh vertex; Based on the local area mapping relationship, the deformation ratio at each grid vertex is extracted as the area scaling coefficient; By binding the area scaling factor as a scalar feature to the spatial coordinates of the 3D surface mesh, a spatial dynamic scaling field is generated.

[0010] Further optimization: Step S4, which involves reverse mapping the two-dimensional machining points to the three-dimensional surface mesh based on the mesh topology, includes: Locate the target 2D patch containing 2D machining points in a 2D parametric mesh, and calculate the corresponding relative parametric coordinates; Using the mesh mapping index, a target 3D patch that is topologically equivalent to the target 2D patch is matched in the 3D surface mesh; Spatial interpolation is performed on the geometric features of the target 3D patch based on relative parameter coordinates to calculate the 3D processing point location and spatial normal vector.

[0011] Further optimization: In step S5, the step of moving the processing head of the multi-axis high-energy beam processing equipment along the spatial normal vector includes: The spatial coordinates of the three-dimensional processing points are analyzed to generate translational displacement commands for the multi-axis high-energy beam processing equipment. The directional characteristics of the spatial normal vector are analyzed to generate attitude rotation commands for controlling the direction of the machining head to be perpendicular to the surface of the tire mold cavity. Based on the multi-axis linkage control algorithm, kinematic interpolation is performed on adjacent three-dimensional machining points to maintain the continuity of the normal attitude of the machining head during trajectory transition.

[0012] Further optimization: Step S5, the step of dynamically adjusting the output energy of the multi-axis high-energy beam processing equipment, includes: Obtain the reference energy setting parameters of the target micro / nano texture under a preset standard state; By combining the area scaling coefficients corresponding to the three-dimensional processing points, adaptive compensation calculations are performed on the benchmark energy setting parameters to obtain the target energy amplitude. The target energy amplitude is converted into equipment control commands to modulate the output energy of the multi-axis high-energy beam processing equipment in real time.

[0013] Further optimization: Step S6, which compares the morphological features of the measured point cloud with those of the target micro / nano texture, includes: Perform spatial global registration between the measured point cloud and the 3D model data to eliminate rigid body offset error of the measurement system; Extract the local micro-geometric features of the registered measured point cloud, and calculate the spatial topological parameters and morphological depth parameters of the actual processed texture; The deviation of spatial topology parameters, morphological depth parameters and theoretical design parameters of target micro-nano textures is quantitatively analyzed, and a quality judgment feedback signal is output based on the comparison results.

[0014] The present invention has the following beneficial effects: 1. In this invention, the three-dimensional curved surface is flattened in a conformal manner by using a discrete curvature flow algorithm to eliminate the angular distortion of micro-nano textures, and the area scaling coefficient is extracted to construct a dynamic scaling field. During processing, the output energy is compensated in real time to make up for the energy density imbalance caused by local area scaling, which can achieve a processing effect with no shape distortion and consistent etching depth on complex mold cavities.

[0015] 2. In this invention, the two-dimensional machining points are reverse-engineered to the three-dimensional curved surface using topological mapping rules. The three-dimensional physical coordinates and accurate spatial normal vectors are directly calculated by interpolation algorithm. While ensuring that the machining head is strictly perpendicular to the mold surface, the multi-axis interpolation algorithm maintains a smooth deflection posture, which can effectively avoid texture interference caused by direct point placement and severe mechanical vibration caused when the machine tool crosses abrupt curvature.

[0016] 3. In this invention, a high-precision in-machine inspection digital closed-loop system is constructed. By performing spatial global registration between the scanned point cloud and the theoretical model, the rigid body offset error of the measurement system is eliminated. Then, the actual morphological depth parameters are extracted for tolerance comparison and quality warning. This directly eliminates the secondary clamping and positioning error caused by repeated transfer of heavy molds, and improves the overall reliability of high-precision mass production of micro-nano structures. Attached Figure Description

[0017] Figure 1 This is a flowchart of the high-precision machining and inspection method for the surface of the tire mold cavity in this invention; Figure 2 This is a flowchart of the three-dimensional curved surface mesh conformal flattening process in steps S1-S2 of the present invention; Figure 3 This is a flowchart of the process of constructing a spatial dynamic scaling field in step S3 of the present invention; Figure 4 This is a flowchart of step S4 of the present invention, in which micro-nano texture reverse mapping is used to obtain three-dimensional processing points and spatial normal vectors; Figure 5 This is a flowchart of the spatial motion trajectory and laser output energy control in step S5 of the present invention. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] In embodiments of the present invention, a method for high-precision machining and inspection of the surface of a tire mold cavity is provided, such as... Figure 1 As shown, it includes: S1. Obtain the three-dimensional model data of the surface of the tire mold cavity and perform mesh discretization processing to generate a three-dimensional curved surface mesh and calculate the initial Gaussian curvature of each mesh vertex; Further, step S1, the step of calculating the initial Gaussian curvature of each mesh vertex, includes: Obtain each discrete facet adjacent to each grid vertex, and calculate the sum of the interior angles of each discrete facet at the corresponding grid vertex; Calculate the difference between the preset full-angle constant and the sum of the interior angles to obtain the angle deficit value at the grid vertex; The angle loss value is normalized by using the local neighborhood area of ​​the grid vertices to obtain the initial Gaussian curvature.

[0020] Specifically, in step S1, the basic continuous geometric model of the tire mold cavity surface is first read from the 3D design system, and the complex curved surface region that needs to be processed with velvet micro-nano texture is extracted. The Delaunay triangulation algorithm is used to discretize the complex curved surface region into a mesh, generating a 3D curved surface mesh composed of a large number of discrete triangular patches. This process transforms the continuous physical surface of the mold into a discrete topological structure containing mesh vertices and edge connectivity. Each mesh vertex in the 3D curved surface mesh corresponds to an actual spatial coordinate point on the surface of the tire mold.

[0021] For the generated 3D curved surface mesh, its topology is traversed to obtain each discrete facet adjacent to each mesh vertex, and the sum of the interior angles of each discrete facet at the corresponding mesh vertex is calculated. Specifically, the central mesh vertex of the current process is set as... Obtain the vertex containing the topological connection relationship by traversing the topological connection relationship. For any discrete triangular facet containing a vertex, all adjacent discrete triangular faces are considered. A discrete surface patch, whose other two vertices are respectively and The discrete facet at the vertex is calculated using the following formula (1). interior angle at : ................................(1) In the formula, Indicates the central grid vertex Point to adjacent vertices A three-dimensional space vector, Indicates the central grid vertex Point to adjacent vertices A three-dimensional space vector, symbol The dot product operation represents the operation of two spatial vectors, with the symbol... Represents the physical magnitude of a three-dimensional spatial vector.

[0022] After calculating a single interior angle using the above formula, sum the results with the central grid vertex. The sum of the interior angles of all adjacent discrete patches at that vertex is obtained by finding the interior angles of the corresponding mesh vertex.

[0023] In the discrete differential geometry system, taking the preset full-angle constant as 2π, the preset full-angle constant and the central grid vertex obtained from the above calculation are calculated as follows: The difference between the sums of the interior angles is used to obtain the angle deficit at the grid vertex. Simultaneously, the angle deficit at the center grid vertex is calculated. Surrounding local neighborhood area The local neighborhood area The value is related to the vertex. One-third of the total area of ​​all connected discrete triangular faces.

[0024] Finally, the normalization calculation is completed according to the following formula (2) to obtain the central grid vertex. initial Gaussian curvature : ................................(2) In the formula, This indicates the discretized surface of the tire mold cavity at the central grid vertex. The initial Gaussian curvature at that point, Represents the central grid vertex The corresponding local neighborhood area, Represents the center grid vertex The sum of the interior angles of all adjacent discrete patches at this vertex; the initial Gaussian curvature value in the above calculation results directly reflects the degree of local bending intensity of the physical surface of the tire mold at this vertex position.

[0025] While calculating the initial Gaussian curvature, the system also calculates the three-dimensional unit vertex normal vector of each grid vertex in the three-dimensional surface mesh. The specific calculation process is as follows: traverse all adjacent discrete triangular patches containing the target grid vertex, use the cross product of the spatial vectors of the two intersecting grid edges of the discrete patch to obtain the surface normal vector of each adjacent patch, and use the physical area of ​​each adjacent discrete triangular patch as the weight distribution to perform weighted summation. Finally, perform modulo operation to perform normalization processing and obtain the three-dimensional unit vertex normal vector of the grid vertex. Specifically, it is calculated according to formula (3): ............................................(3) In the formula, Represents the calculated target mesh vertices The normal vector of a three-dimensional unit vertex. Represents the target mesh vertex The adjacent first The area of ​​a discrete triangular patch Indicates the first The unit face normal vector of each discrete triangular facet is represented by the absolute value symbol, which indicates that the modulus operation is performed on the weighted sum of the composite space vector to ensure that the output vector has a standard unit length. The above calculation gives the discrete model accurate surface orientation physical properties, and the generated three-dimensional unit vertex normal vector is stored in the system's underlying data structure.

[0026] Through the above steps, the complex continuous surface of the tire mold is accurately transformed into a discrete mathematical model containing curvature information and normal physical properties, providing accurate data support for evaluating and eliminating geometric mapping deformation and inversely solving the spatial processing posture during subsequent mesh unfolding.

[0027] S2. Set the target Gaussian curvature of the three-dimensional surface mesh to zero, and use the discrete curvature flow algorithm and the initial Gaussian curvature to solve the conformal factor of each mesh vertex, so as to convert the three-dimensional surface mesh into a two-dimensional parametric mesh in an conformal manner. Furthermore, step S2, which involves using the discrete curvature flow algorithm and the initial Gaussian curvature to solve for the conformal factor of each mesh vertex, includes: Construct a set of evolutionary differential equations with initial Gaussian curvature as the initial state, and establish mapping constraints between curvature variables and conformal factors; Using the target Gaussian curvature as the convergence endpoint, calculate the curvature evolution gradient of the evolutionary differential equation system at each grid vertex; The evolutionary differential equations are iteratively updated along the descent direction of the curvature evolution gradient until the preset convergence accuracy is reached, at which point the conformal factor is output.

[0028] Specifically, in step S2, in order to unfold the complex three-dimensional tire mold surface, the target Gaussian curvature value of all grid vertices in the three-dimensional surface mesh is first set to zero. Then, an evolutionary differential equation system with the initial Gaussian curvature as the initial state is constructed to establish a dynamic mapping constraint between the curvature variable of the tire mold cavity surface and the conformal factor of the grid vertex. At the initial iteration time, the initial conformal factor parameter of each grid vertex is set to zero. With the target Gaussian curvature set to zero as the convergence endpoint, the curvature evolution gradient of the evolutionary differential equation system at each grid vertex is calculated. The numerical value of this curvature evolution gradient is the difference between the target Gaussian curvature and the curvature calculated at the grid vertex at the current time.

[0029] Along the descent direction of the curvature evolution gradient, the conformal factor variables in the evolution differential equation system are iteratively updated using a fixed step size. The specific iterative update is performed according to formula (4): ................................(4) In the formula, This indicates the vertices of the tire mold mesh after the next iteration update. The conformal factor, Represents the vertex of the current iteration mesh. The conformal factor, This represents the preset evolution update step size parameter, which is preferably 0.05 in this embodiment. This indicates a target Gaussian curvature set to zero. This represents the vertices of the tire mold surface mesh calculated under the current conformal factor state. Gaussian curvature.

[0030] After each iteration, the system recalculates the current Gaussian curvature of each grid vertex and calculates the difference between the target Gaussian curvature and the current Gaussian curvature at each grid vertex, i.e., the curvature evolution gradient. The iteration terminates when the absolute value of the curvature evolution gradient is less than the preset convergence accuracy, and outputs the steady-state conformal factor of each grid vertex on the tire mold surface. In this embodiment, the preset convergence accuracy is preferably... .

[0031] Further, step S2, the step of conformally mapping the three-dimensional curved surface mesh to a two-dimensional parametric mesh, includes: Derive the length scaling factor of each mesh edge in a 3D surface mesh using the conformal factor; The edge length of each grid is updated according to the length scaling factor to generate a transition metric grid with conformal features; The transition metric mesh is mapped to a two-dimensional planar coordinate system based on the projection flattening algorithm, thus constructing a two-dimensional parametric mesh.

[0032] Specifically, all mesh edges of the three-dimensional curved surface mesh of the tire mold are traversed. For each mesh edge, the steady-state conformal factor values ​​corresponding to its two endpoints are obtained. These values ​​are added together and used as the exponent of the natural logarithm base to form the length scaling factor of the edge. The physical edge length of each original mesh edge is updated according to this length scaling factor to generate the transition metric mesh, which is calculated according to formula (5): ...............................................(5) In the formula, This represents the side length of the target plane in the updated transition metric mesh. This represents the actual edge length of the initial three-dimensional straight line connecting the corresponding mesh vertices in the original three-dimensional curved surface mesh of the tire mold. This represents the calculated length scaling factor. and These represent the conformal factors of the final output at the two vertices of the grid edge.

[0033] The system traverses all grid topology connections to calculate entirely new side length data, thereby generating a transition metric grid with conformal features.

[0034] Based on the projection flattening algorithm, the transition metric mesh containing only side length data is essentially mapped to a two-dimensional plane coordinate system. Specifically, a discrete triangle is arbitrarily specified in the transition metric mesh as the reference surface and placed at the origin of the two-dimensional coordinate plane. Then, based on the previously updated target plane side length data, the two-dimensional plane coordinates of the third vertex of the adjacent triangle sharing the same side are calculated sequentially using the cosine theorem. The process is traversed and extended in the order of topological connection until all vertices of the original three-dimensional curved surface mesh of the tire mold have obtained definite planar horizontal and vertical coordinates, and finally a completely flat two-dimensional parametric mesh is constructed.

[0035] This step flattens the curved three-dimensional mold surface of the tire into a two-dimensional design plane while strictly maintaining the angular relationships of the local geometry.

[0036] S3. Based on the conformal factor, extract the area scaling coefficient of the two-dimensional parametric mesh relative to the three-dimensional curved surface mesh at each mesh vertex, and construct a spatial dynamic scaling field. Furthermore, step S3, the step of constructing the spatial dynamic scaling field, includes: Establish the local area mapping relationship between the two-dimensional parametric mesh and the three-dimensional curved surface mesh at each mesh vertex; Based on the local area mapping relationship, the deformation ratio at each grid vertex is extracted as the area scaling coefficient; By binding the area scaling factor as a scalar feature to the spatial coordinates of the 3D surface mesh, a spatial dynamic scaling field is generated.

[0037] When performing step S3, since the conformal mapping rule used in the previous processing eliminated the angular geometric distortion of the tire mold surface, according to the conformal equivalence property of differential geometry, the target plane and the original surface will inevitably produce specific area deformation in the local neighborhood. The local area mapping relationship between the unfolded two-dimensional parametric mesh and the original three-dimensional surface mesh at each mesh vertex is established, and based on this local area mapping relationship, the physical deformation ratio at each mesh vertex of the tire mold is directly extracted as the area scaling factor.

[0038] The area scaling factor at a certain grid vertex is calculated based on the steady-state conformal factor at that vertex obtained in step S2 above, and in conjunction with the following formula (6): .............................................(6) In the formula, This indicates that the extracted 2D parametric mesh is relative to the 3D surface mesh at the mesh vertices. The area scaling factor at a given location represents the geometric area scaling factor of the local micro-processed area of ​​the tire mold during flattening transformation. The base of the natural logarithm. This indicates the corresponding mesh vertices output by solving the curvature flow algorithm in the aforementioned steps. The steady-state conformal factor.

[0039] After completing the calculation of each coefficient, all independently calculated area scaling coefficients are used as scalar feature data and bound to the original spatial coordinates of the three-dimensional surface mesh of the tire mold one by one. At the same time, in the system's data storage structure, a floating-point data attribute is added to each original spatial physical coordinate point in the three-dimensional mesh of the tire mold model. Then, the calculated area scaling coefficient is assigned to the corresponding spatial physical coordinate point.

[0040] The system traverses all mesh vertices on the model surface in the order of topological connections, attaches discrete scaling scalar data to the three-dimensional model architecture on the mold surface in all directions, and finally generates a continuous spatial dynamic scaling field covering the entire three-dimensional digital environment of the tire mold cavity.

[0041] This step accurately quantifies the local area distortion caused by the flattening operation of the tire mold surface, and establishes a data reference layer with physical mapping relationship for subsequent dynamic adjustment of the output energy of the multi-axis machining equipment.

[0042] S4. Generate two-dimensional processing points of the target micro-nano texture on a two-dimensional parametric mesh, and reverse map the two-dimensional processing points to a three-dimensional curved surface mesh based on the mesh topology to obtain the three-dimensional processing points and spatial normal vectors. Furthermore, step S4, which involves reverse mapping the two-dimensional machining points to the three-dimensional surface mesh based on the mesh topology, includes: Locate the target 2D patch containing 2D machining points in a 2D parametric mesh, and calculate the corresponding relative parametric coordinates; Using the mesh mapping index, a target 3D patch that is topologically equivalent to the target 2D patch is matched in the 3D surface mesh; Spatial interpolation is performed on the geometric features of the target 3D patch based on relative parameter coordinates to calculate the 3D processing point location and spatial normal vector.

[0043] Specifically, when performing step S4, firstly, according to the design pattern rules of the velvet micro-nano texture on the surface of the tire mold, each discrete target micro-nano texture two-dimensional processing point is generated in an array on the tiling two-dimensional parameter grid plane. Then, the topological structure of the two-dimensional parameter grid is traversed to determine the specific discrete triangular patch area that each two-dimensional processing point falls into, and it is positioned as the target two-dimensional patch.

[0044] Subsequently, a centroid coordinate algorithm model is established to calculate the relative parameter coordinates. The two-dimensional plane coordinates of the three vertices of the target two-dimensional facet are extracted. Combined with the plane coordinates of the current two-dimensional processing point, the centroid weight (i.e., relative parameter coordinates) corresponding to the two-dimensional processing point inside the triangular facet is calculated using the following formulas (7)-(9): ..........................(7) ..........................(8) ...............................................(9) In the formula, and as well as These represent the calculated centroid weights (i.e., relative parameter coordinates) of the two-dimensional processing point relative to the three vertices of the target two-dimensional surface. and Represents the actual planar coordinates of the two-dimensional processing points of the target micro / nano texture. and This represents the planar coordinates of the first vertex of the target 2D patch. and This represents the planar coordinates of the second vertex of the target 2D patch. and This represents the planar coordinates of the third vertex of the target 2D facet.

[0045] The system's underlying data stores a mesh mapping index lookup dictionary, which records the one-to-one mapping relationship between the discrete facets before and after parameterization flattening. Based on this mesh mapping index lookup dictionary, the target three-dimensional facet that is topologically equivalent to the target two-dimensional facet is accurately matched in the three-dimensional curved surface mesh. The three-dimensional coordinate data of the three physical vertices contained in the target three-dimensional facet are extracted. Based on the relative parameter coordinates obtained above, the geometric features of the target three-dimensional facet are spatially linearly interpolated using the following formula (10) to calculate the three-dimensional processing point that integrates the curvature depth information of the tire mold: ...................................(10) In the formula, This represents the actual spatial physical coordinates of the three-dimensional machining points on the surface of the tire mold generated after the reverse mapping solution. and as well as These represent the physical space coordinates of the three mesh vertices of the matched target 3D patch in the 3D model.

[0046] To ensure that the processing beam is always perpendicular to the mold surface, the system continues to perform spatial smooth interpolation calculation on the surface normal features based on the relative parameter coordinates, extracts the three-dimensional unit vertex normal vectors of the three vertices of the target three-dimensional patch obtained in step S1, performs weighted superposition calculation with the relative parameter coordinates and performs unitized direction constraint processing, and calculates the spatial normal vectors that are precisely bound to the three-dimensional processing points, specifically calculated according to formula (11): ...................................(11) In the formula, This represents the three-dimensional machining point space normal vector calculated by interpolation, used to guide the deflection angle and attitude of the machining head of a multi-axis device. and as well as These represent the independent 3D unit normal vectors of the three mesh vertices of the target 3D patch, respectively. The absolute value symbol indicates that the modulus operation is performed on the superimposed composite spatial vector to ensure that the output spatial normal vector always maintains the standard unit length.

[0047] This step uses precise mathematical inverse mapping to seamlessly restore the two-dimensional design to a complex three-dimensional physical surface, avoiding texture distortion or overlap problems caused by directly placing points on a free-form surface in space.

[0048] S5. Input the three-dimensional processing point and spatial normal vector into the multi-axis high-energy beam processing equipment. When the processing head of the multi-axis high-energy beam processing equipment moves along the spatial normal vector, dynamically adjust the output energy of the multi-axis high-energy beam processing equipment for processing based on the area scaling coefficient in the spatial dynamic scaling field. Further, in step S5, the step of moving the processing head of the multi-axis high-energy beam processing equipment along the spatial normal vector includes: Analyze the spatial coordinates of the three-dimensional processing points to generate translational displacement commands for the multi-axis high-energy beam processing equipment; The directional characteristics of the spatial normal vector are analyzed to generate attitude rotation commands for controlling the direction of the machining head to be perpendicular to the surface of the tire mold cavity. Based on the multi-axis linkage control algorithm, kinematic interpolation is performed on adjacent three-dimensional machining points to maintain the continuity of the normal attitude of the machining head during trajectory transition.

[0049] Furthermore, step S5, the step of dynamically adjusting the output energy of the multi-axis high-energy beam processing equipment, includes: Obtain the reference energy setting parameters of the target micro / nano texture under a preset standard state; By combining the area scaling coefficients corresponding to the three-dimensional processing points, adaptive compensation calculations are performed on the benchmark energy setting parameters to obtain the target energy amplitude. The target energy amplitude is converted into equipment control commands to modulate the output energy of the multi-axis high-energy beam processing equipment in real time.

[0050] Specifically, when executing step S5, the system first extracts the preprocessed three-dimensional machining points and parses their spatial coordinate data. The extracted lateral position, longitudinal position, and depth position are converted into translation displacement commands for the three linear servo control axes of the multi-axis high-energy beam machining equipment. At the same time, the system parses the directional feature data of the spatial normal vector accompanying the three-dimensional machining points and generates attitude rotation commands for the multi-axis high-energy beam machining equipment to control the beam output direction of the machining head to be strictly perpendicular to the surface of the tire mold cavity.

[0051] Assuming the multi-axis equipment adopts a double-swivel head machine tool structure with two rotary axes to control the attitude, the rotational swivel angle is calculated using the inverse kinematics algorithm based on the three-dimensional components of the given spatial normal vector, specifically according to formulas (12)-(13): ...................................(12) ......................................(13) In the formula, This indicates the target control angle of the pitch and rotation axes of the multi-axis high-energy beam processing equipment. This indicates the target control angle of the yaw rotation axis of the multi-axis high-energy beam processing equipment. and as well as These represent the unit projection components of the calculated 3D spatial normal vector in three mutually perpendicular directions in the system's Cartesian coordinate system.

[0052] To maintain the continuity of the normal attitude of the machining head during trajectory transition, the control system reads the two adjacent three-dimensional machining points and their spatial normal vectors. Based on the multi-axis linkage control algorithm, kinematic interpolation is performed between the two points. The system performs linear interpolation processing on the linear displacement interval to ensure smooth spatial translation trajectory, and performs spherical linear interpolation operation on the rotational attitude angles corresponding to the spatial normal vectors of the starting point and the ending point. It outputs continuous and dense small rotation angle control quantities to prevent the machining head from experiencing severe mechanical vibration and wobbling when passing over the curvature change area of ​​the tire mold.

[0053] In the process of synchronously controlling the processing energy, the system acquires the reference energy setting parameters of the target micro / nano texture under a preset standard deformation-free state. These parameters characterize the ideal single-pulse beam output energy value required to process a velvet-like micro-pit structure with a design standard depth in a planar region without any geometric stretching interference. In this scheme, for the ultrafast laser micro / nano processing of tire mold steel, the reference energy setting parameters are... Preferred The single pulse energy.

[0054] Subsequently, the system retrieves and extracts the area scaling coefficient corresponding to the current three-dimensional processing point in the spatial dynamic scaling field. Combining this coefficient with the following formula (14), the system performs adaptive compensation calculation on the reference energy setting parameters to obtain the target energy amplitude: ......................................(14) In the formula, This represents the single-point target energy amplitude, calculated using adaptive compensation, that will be sent to the processing equipment. This indicates the reference energy setting parameters obtained under the preset standard conditions. This represents the unique area scaling coefficient of the current 3D processing point extracted from the spatial dynamic scaling field. Through this mapping operation, the target output energy calculated by the system and the physical area deformation rate generated by the local mesh mapping exhibit a strictly proportional change.

[0055] The calculated target energy amplitude is directly converted into a device control command that conforms to the underlying hardware communication format and sent to the energy generator controller of the multi-axis high-energy beam processing equipment. The controller adjusts the modulation duty cycle signal or the physical amplitude of the driving voltage of the radio frequency source in real time. At the same time that the processing head accurately reaches the interpolation set physical space coordinates and completes the normal rotation attitude adjustment, the actual beam output energy of the multi-axis high-energy beam processing equipment is modulated.

[0056] This step achieves rigorous hardware-based compensation between the motion trajectory of complex curved surfaces in space and the physical processing energy, ensuring uniform etching depth of micro-nano textures in each deformation area of ​​the tire mold and reducing etching depth deviation at different locations.

[0057] S6. The surface of the processed tire mold cavity is scanned on-machine using an optical probe to obtain the measured point cloud, and the measured point cloud is compared with the morphological features of the target micro-nano texture.

[0058] Furthermore, step S6, which compares the measured point cloud with the morphological features of the target micro / nano texture, includes: Perform spatial global registration between the measured point cloud and the 3D model data to eliminate rigid body offset error of the measurement system; Extract the local micro-geometric features of the registered measured point cloud, and calculate the spatial topological parameters and morphological depth parameters of the actual processed texture; The deviation of spatial topology parameters, morphological depth parameters and theoretical design parameters of target micro-nano textures is quantitatively analyzed, and a quality judgment feedback signal is output based on the comparison results.

[0059] Specifically, after completing the multi-axis high-energy beam processing, the system controls the optical probe mounted on the machine tool to perform on-machine three-dimensional morphological scanning of the surface of the tire mold cavity, and obtains the measured point cloud reflecting the local microscopic physical fluctuations. The measured point cloud is then imported into the registration calculation module for performing spatial registration between the point cloud and the three-dimensional model, and performs global spatial registration with the original three-dimensional model data of the tire mold to compensate for the overall rigid body rotation and translation offset errors of the measured point cloud relative to the theoretical model caused by the physical installation deviation of the optical probe and the zeroing deviation of the machine tool motion axis.

[0060] The system employs an iterative nearest-point algorithm to traverse and find the closest matching point pairs between the measured point cloud sampling points and the 3D model data surface. By constructing and minimizing the mean square error objective function, the optimal rotation transformation matrix and translation transformation vector are solved, specifically calculated according to formula (15): .................(15) In the formula, The mean square error cost function represents the accuracy of spatial registration between measured data and theoretical data of a tire mold. This represents the total number of valid sample point pairs participating in the registration iteration calculation. This represents the three-dimensional spatial coordinate vector of the actual surface sampling point in the measured point cloud. This represents the three-dimensional spatial coordinate vector of the theoretical reference point that matches the surface of the three-dimensional model data. This represents the third-order rotation transformation matrix used to correct the overall spatial attitude deviation of the measured point cloud. This represents the three-dimensional translation transformation vector used to correct the overall spatial position deviation of the measured point cloud. |·| represents the vector 2-norm operation, i.e., calculating the magnitude of the orientation vector. The calculated rotation transformation matrix and translation transformation vector are directly applied to the measured point cloud to complete the global spatial registration and alignment.

[0061] The local micro-geometric features are further extracted using the registered measured point cloud, thereby calculating the spatial topological parameters and morphological depth parameters of the actual processed texture. In order to calculate the morphological depth parameters, the system projects the registered measured micro-concave feature points along the local cross-sectional normal of the three-dimensional model surface and calculates the morphological depth parameters that reflect the processing depth of the velvet micro-pit array according to formula (16): ................................(16) In the formula, The morphological depth parameter represents the actual single-point etching depth of the micro / nano texture of the tire mold target. This represents the three-dimensional physical coordinate vector of the microscopic feature measurement point after rigid body pose registration transformation. This represents the fundamental mapping coordinate vector corresponding to the theoretical surface of the three-dimensional model. The symbol represents the unit outward normal vector of the 3D surface at the base mapped coordinate point. This represents the vector dot product operation, used to calculate the relative depth displacement along the normal direction of a surface.

[0062] Meanwhile, the system identifies the extreme points at the bottom of two adjacent micro-nano pits in the registered measured point cloud, calculates the three-dimensional Euclidean distance between the two extreme points, and extracts the spatial topological parameters that characterize the spacing of the actual texture array.

[0063] Subsequently, the system will subtract the morphological depth parameter obtained by formula (16) from the theoretically designed machining depth value to obtain the absolute value of the depth machining deviation, and subtract the extracted spatial topology parameter from the theoretically designed array spacing value to obtain the topological geometric offset. The obtained absolute value of the depth machining deviation and the topological geometric offset will be compared with the micron-level form and position tolerance allowable thresholds stored in the system. If the deviation of any extracted parameter exceeds the tolerance allowable threshold, a quality anomaly judgment feedback signal including coordinate positioning will be output to the machine tool bottom control system to trigger an early warning. If all deviations are within the threshold range, a release confirmation signal indicating that the area has been processed is directly output.

[0064] In this scheme, the micron-level form and position tolerance allowable threshold is specifically the depth machining deviation allowable threshold for the topography depth. The allowable threshold for the topological geometric offset of the spatial topological array spacing is preferably... .

[0065] This step establishes a closed-loop measurement mechanism from physical processing to data verification, effectively ensuring the reliability of the processing accuracy of complex curved surface micro-nano structures.

[0066] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. 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 high-precision machining and inspection of the surface of a tire mold cavity, characterized in that, include: S1. Obtain the three-dimensional model data of the surface of the tire mold cavity and perform mesh discretization processing to generate a three-dimensional curved surface mesh and calculate the initial Gaussian curvature of each mesh vertex; S2. Set the target Gaussian curvature of the three-dimensional surface mesh to zero, and use the discrete curvature flow algorithm and the initial Gaussian curvature to solve the conformal factor of each mesh vertex, so as to convert the three-dimensional surface mesh into a two-dimensional parametric mesh in an conformal manner. S3. Based on the conformal factor, extract the area scaling coefficient of the two-dimensional parametric mesh relative to the three-dimensional curved surface mesh at each mesh vertex, and construct a spatial dynamic scaling field. S4. Generate two-dimensional processing points of the target micro-nano texture on a two-dimensional parametric mesh, and reverse map the two-dimensional processing points to a three-dimensional curved surface mesh based on the mesh topology to obtain the three-dimensional processing points and spatial normal vectors. S5. Input the three-dimensional processing point and spatial normal vector into the multi-axis high-energy beam processing equipment. When the processing head of the multi-axis high-energy beam processing equipment moves along the spatial normal vector, dynamically adjust the output energy of the multi-axis high-energy beam processing equipment for processing based on the area scaling coefficient in the spatial dynamic scaling field. S6. The surface of the processed tire mold cavity is scanned on-machine using an optical probe to obtain the measured point cloud, and the measured point cloud is compared with the morphological features of the target micro-nano texture.

2. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S1, which involves calculating the initial Gaussian curvature of each mesh vertex, includes: Obtain each discrete facet adjacent to each grid vertex, and calculate the sum of the interior angles of each discrete facet at the corresponding grid vertex; Calculate the difference between the preset full-angle constant and the sum of the interior angles to obtain the angle deficit value at the grid vertex; The angle loss value is normalized by using the local neighborhood area of ​​the grid vertices to obtain the initial Gaussian curvature.

3. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S2, the step of solving the conformal factor of each mesh vertex using the discrete curvature flow algorithm and the initial Gaussian curvature, includes: Construct a set of evolutionary differential equations with initial Gaussian curvature as the initial state, and establish mapping constraints between curvature variables and conformal factors; Using the target Gaussian curvature as the convergence endpoint, calculate the curvature evolution gradient of the evolutionary differential equation system at each grid vertex; The evolutionary differential equations are iteratively updated along the descent direction of the curvature evolution gradient until the preset convergence accuracy is reached, at which point the conformal factor is output.

4. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S2, which involves conformally mapping the three-dimensional surface mesh to a two-dimensional parametric mesh, includes: Derive the length scaling factor of each mesh edge in a 3D surface mesh using the conformal factor; The edge length of each grid is updated according to the length scaling factor to generate a transition metric grid with conformal features; The transition metric mesh is mapped to a two-dimensional planar coordinate system based on the projection flattening algorithm, thus constructing a two-dimensional parametric mesh.

5. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S3, the step of constructing the spatial dynamic scaling field, includes: Establish the local area mapping relationship between the two-dimensional parametric mesh and the three-dimensional curved surface mesh at each mesh vertex; Based on the local area mapping relationship, the deformation ratio at each grid vertex is extracted as the area scaling coefficient; By binding the area scaling factor as a scalar feature to the spatial coordinates of the 3D surface mesh, a spatial dynamic scaling field is generated.

6. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S4, which involves reverse mapping the two-dimensional machining points to the three-dimensional surface mesh based on the mesh topology, includes: Locate the target 2D patch containing 2D machining points in a 2D parametric mesh, and calculate the corresponding relative parametric coordinates; Using the mesh mapping index, a target 3D patch that is topologically equivalent to the target 2D patch is matched in the 3D surface mesh; Spatial interpolation is performed on the geometric features of the target 3D patch based on relative parameter coordinates to calculate the 3D processing point location and spatial normal vector.

7. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S5, the step of moving the processing head of the multi-axis high-energy beam processing equipment along the spatial normal vector, includes: The spatial coordinates of the three-dimensional processing points are analyzed to generate translational displacement commands for the multi-axis high-energy beam processing equipment. The directional characteristics of the spatial normal vector are analyzed to generate attitude rotation commands for controlling the direction of the machining head to be perpendicular to the surface of the tire mold cavity. Based on the multi-axis linkage control algorithm, kinematic interpolation is performed on adjacent three-dimensional machining points to maintain the continuity of the normal attitude of the machining head during trajectory transition.

8. The method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S5, the step of dynamically adjusting the output energy of the multi-axis high-energy beam processing equipment, includes: Obtain the reference energy setting parameters of the target micro / nano texture under a preset standard state; By combining the area scaling coefficients corresponding to the three-dimensional processing points, adaptive compensation calculations are performed on the benchmark energy setting parameters to obtain the target energy amplitude. The target energy amplitude is converted into equipment control commands to modulate the output energy of the multi-axis high-energy beam processing equipment in real time.

9. A method for high-precision machining and inspection of the surface of a tire mold cavity according to claim 1, characterized in that, Step S6, which compares the measured point cloud with the morphological features of the target micro / nano texture, includes: Perform spatial global registration between the measured point cloud and the 3D model data to eliminate rigid body offset error of the measurement system; Extract the local micro-geometric features of the registered measured point cloud, and calculate the spatial topological parameters and morphological depth parameters of the actual processed texture; The deviation of spatial topology parameters, morphological depth parameters and theoretical design parameters of target micro-nano textures is quantitatively analyzed, and a quality judgment feedback signal is output based on the comparison results.

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