Gear tooth surface measurement point and path cooperative optimization method

Abstract

The application relates to the technical field of gear measurement, and discloses a gear tooth surface measuring point and path cooperative optimization method, which comprises the following steps: acquiring a tooth surface point cloud of a gear, performing adaptive partitioning based on local geometric features, and dividing the tooth surface points into a plurality of sub-regions; classifying each sub-region, screening measuring points of each sub-region in combination with the geometric features of each tooth surface point in the sub-region, and generating a global measuring point set; based on the global measuring point set, constructing an open traveling salesman problem with fixed start and end points for a measuring path planning problem, and solving the problem by adopting an adaptive large neighborhood search meme method based on boundary memory to generate an optimal measuring path; and the application improves the efficiency of gear tooth surface measurement and realizes high-precision gear tooth surface measurement.

Description

Technical Field

[0001] This invention relates to the field of gear measurement technology, and specifically to a method for collaborative optimization of gear tooth surface measurement points and paths. Background Technology

[0002] Gears, as core transmission components for power and motion in rotating machinery, are widely used in aerospace, high-end equipment, precision manufacturing, and other industrial fields. They are fundamental parts that ensure the stable and efficient operation of various mechanical equipment and occupy an indispensable core position in the industrial system. However, due to limitations in machining equipment precision, differences in production processes, assembly errors, and complex production environments, there is always an unavoidable deviation between the actual machined dimensions and the theoretical design dimensions of gears. This deviation directly deteriorates gear meshing performance, exacerbates equipment vibration and noise, accelerates gear wear and aging, shortens equipment lifespan, and under extreme conditions, can even lead to mechanical failures such as gear jamming and transmission failure, and may even cause major production safety accidents.

[0003] Therefore, carrying out high-precision inspection of gear tooth surfaces, and improving the accuracy and efficiency of tooth surface inspection through scientific measurement point layout and measurement path design, is a key technical support for ensuring the consistency of gear processing quality, improving the reliability of high-end gear equipment, and avoiding equipment operation risks. It has important engineering application value and research significance.

[0004] Current gear tooth surface inspection technology is relatively mature, and the industry generally relies on gear measurement centers to complete tooth surface data acquisition and parameter testing, providing data support for gear quality assessment. However, existing gear tooth surface inspection systems mostly adopt fixed and standardized inspection modes, with independent measurement point layout and measurement path planning, and a crude design. They have not yet formed a collaborative and optimized inspection system, making it difficult to adapt to the needs of high-precision and high-efficiency batch inspection and precision quality inspection of gears, and have many technical shortcomings.

[0005] Regarding the layout of measuring points on the gear tooth surface, existing testing methods mostly employ fixed point layout strategies such as uniform or random point placement. This lacks specificity and scientific rigor, completely ignoring the local structural features, curvature variation patterns, and machining error distribution characteristics of the gear tooth surface. The machining error sensitivity and error distribution probability differ significantly across different regions of the gear, including the tooth tip, tooth root, and meshing tooth surface. Fixed point layouts easily lead to redundant measuring points on smooth tooth surfaces and missing measuring points in error-sensitive areas. This not only generates a large amount of invalid test data, increasing the computational load of subsequent data processing, but also results in insufficient detection accuracy in key error areas, failing to accurately reconstruct the true error distribution of the tooth surface, directly affecting the accuracy of gear quality testing.

[0006] In terms of measurement path planning, most gear measurement centers currently use traditional fixed scanning paths without considering the characteristics of the tooth surface structure and the distribution of measurement points to conduct dedicated path optimization design. Fixed measurement paths suffer from problems such as path redundancy, excessive backtracking, and a large proportion of idle travel. During the inspection process, the invalid movement time of the probe is too long, which significantly increases the overall inspection time, resulting in low efficiency for single-piece gear inspection. This makes it difficult to meet the requirements of batch quality inspection and rapid sampling inspection of gears in industrial production, and seriously restricts the overall efficiency of gear production and processing.

[0007] More importantly, in existing gear tooth surface inspection systems, the optimal placement of measuring points and the planning of measurement paths are two independent technical modules, operating in isolation without any coordinated matching mechanism. Optimization of measuring point placement focuses solely on improving inspection accuracy, neglecting path efficiency; path optimization focuses only on shortening the travel distance, failing to adapt to the distribution requirements of high-precision measuring points, thus failing to achieve a balance between inspection accuracy and efficiency. Solely pursuing measuring point accuracy leads to a significant increase in inspection time, while solely optimizing path efficiency sacrifices the inspection accuracy of critical areas, making it difficult to meet the integrated inspection needs of high-precision, high-efficiency gears and severely limiting the engineering application value of gear precision inspection technology. Summary of the Invention

[0008] To address the aforementioned shortcomings in existing technologies, this invention provides a method for co-optimizing gear tooth surface measurement points and paths, which solves the problems of unreasonable measurement point layout, redundant measurement paths, and the inability to simultaneously achieve both accuracy and efficiency in current gear tooth surface inspection.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A method for co-optimizing gear tooth surface measurement points and paths includes the following steps: The point cloud of the gear tooth surface is obtained, and adaptive partitioning based on local geometric features is performed to divide the tooth surface points into several sub-regions. Each sub-region is classified, and the measurement points of each sub-region are selected by combining the geometric features of each tooth surface point in the sub-region to generate a global measurement point set. Based on a global set of measurement points, the measurement path planning problem is constructed as an open-ended traveling salesman problem with a fixed start and end point. An adaptive large neighborhood search meme method based on boundary memory is used to solve the problem and generate the optimal measurement path.

[0010] The present invention has the following beneficial effects: 1. The gear tooth surface measurement point and path collaborative optimization method proposed in this invention, through the integrated and collaborative optimization design of measurement point layout and measurement path, significantly improves gear inspection efficiency while ensuring high precision of tooth surface inspection, solves the inherent defects of traditional inspection technology, provides reliable technical support for high-end gear precision inspection and batch quality inspection, and solves the technical problems of unreasonable measurement point layout, redundant measurement path, and inability to balance accuracy and efficiency in current gear tooth surface inspection. 2. This invention also improves the utilization rate of tooth surface measurement points and reduces measurement costs. By adaptively partitioning the tooth surface point cloud and selecting differentiated measurement points based on information such as local curvature, Hausdorff features, and normal changes, the number of redundant measurement points can be reduced while ensuring the ability to represent key features of the tooth surface, thereby reducing measurement costs. 3. This invention also improves the efficiency of measurement paths; by modeling path planning as an open-ended traveling salesman problem with fixed start and end points, and using an improved hybrid intelligent optimization method for solving it, the total motion path of the 3D coordinate machine probe can be effectively shortened, the idle travel is reduced, and the overall measurement efficiency is improved, which is especially suitable for multi-measurement-point, high-cycle detection tasks. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating a method for co-optimization of gear tooth surface measurement points and paths proposed in this invention. Detailed Implementation

[0012] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0013] like Figure 1 As shown, a method for co-optimizing gear tooth surface measurement points and paths includes the following steps: Step 1: Obtain the point cloud of the gear tooth surface, and perform adaptive partitioning based on local geometric features to divide the tooth surface points into several sub-regions.

[0014] This step involves proposing a tooth surface partitioning method for the tooth surface point cloud (a 3D point cloud), which adaptively divides the tooth surface into several sub-regions with relatively uniform geometric features; the specific process is as follows: Define the tooth surface point cloud as:

[0015] In the formula, Add cloud-like dots to the tooth surface; For the first One tooth surface point; , , The first Each tooth surface point x axis, y axis, z Axis coordinates, where x The axial direction is upward along the gear tooth width. y The shaft is located outwards along the radius of the gear. z The axial coordinates are represented as the perpendicular deviation between the tooth surface point cloud and the ideal tooth surface; This represents the number of points on the tooth surface.

[0016] Set the number of neighborhood points For each tooth surface point in the tooth surface point cloud, search for the one with the closest Euclidean distance to that tooth surface point. For each tooth surface point, a neighborhood point set is obtained; this invention uses the K-nearest neighbor method to search for neighborhood points; simultaneously, the number of neighborhood points in this invention... The initial setting is 15.

[0017] For each tooth surface point, a local quadratic surface is fitted based on its neighborhood point set to construct the local quadratic surface equation for each tooth surface point, namely:

[0018] In the formula, , , Adding cloud-like dots to the tooth surface x axis, y axis, z Axis coordinates; , , , , , These are all coefficients of the local quadric surface equation, and these coefficients are obtained by the least squares method. Specifically, by taking the partial derivative of each coefficient and setting it to 0, the six unknown coefficients correspond to six equations. Solving these equations will yield the specific values ​​of each coefficient.

[0019] The second-order partial derivatives of the local quadratic surface equation are calculated to generate a curvature tensor matrix. Then, using an eigenvalue solving method (this invention does not impose any limitations on the specific method for solving the eigenvalues), the eigenvalues ​​of the curvature tensor matrix are solved to obtain the principal curvature parameters (including the first principal curvature) of the local quadratic surface corresponding to that tooth surface point. Second principal curvature The principal curvature parameters of the tooth surface are then used to calculate the curvature index that characterizes the degree of local bending of the tooth surface. The calculation formula is as follows:

[0020] In the formula, For the first Curvature index of each tooth surface point; The first principal curvature; It is the second principal curvature.

[0021] A Hausdorff distance metric is introduced to characterize the local morphological differences between different tooth surface points; the calculation process for the Hausdorff distance is as follows: Let X be a point on the tooth surface, and Q be its neighboring points; the first and second principal curvatures of point X are respectively... , The set of principal curvature parameters constituting the tooth surface points is denoted as K. X ={ , The first and second principal curvatures of the neighborhood point Q are respectively , The set of principal curvature parameters constituting the neighborhood points is denoted as K. Q ={ , The formula for calculating the Hausdorff distance between a point on the tooth surface and its neighboring points is as follows:

[0022] In the formula, For the first Hausdorff distance between a tooth surface point and its neighboring points; , , Both represent the operation of taking the maximum value; , Both represent the minimum value operation; The first point on the tooth surface One principal curvature; The first point on the tooth surface One principal curvature; This is an L2 norm operation.

[0023] Each tooth surface point and its corresponding neighboring points are used to form a candidate sub-region, resulting in several candidate sub-regions.

[0024] Calculate the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error for each candidate sub-region, specifically as follows:

[0025]

[0026]

[0027] In the formula, The standard deviation of curvature is used to reflect the consistency of curvature within the candidate sub-region; Candidate sub-regions The average value of the curvature index of all tooth surface points; The standard deviation of the Hausdorff distance; Candidate sub-regions The average Hausdorff distance between all tooth surface points and their neighboring points; This represents the local fitting error, used to reflect the approximate accuracy of the local quadratic surface; Candidate sub-regions Inner Each tooth surface point z Axis coordinates; Candidate sub-regions All tooth surface points z The average value of the axis coordinates; This is an operation to retrieve the maximum value.

[0028] Set the standard deviation threshold for curvature. Hausdorff distance standard deviation threshold Local fitting error threshold .

[0029] Determine whether the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error of each candidate sub-region are all less than the corresponding standard deviation thresholds for curvature, Hausdorff distance, and local fitting error. If so, increment the number of neighborhood points of the tooth surface point corresponding to the candidate sub-region by 1, and continue to divide the neighborhood point set of the tooth surface point into candidate sub-regions. Otherwise, perform a bipartite division on each candidate sub-region to obtain several divided candidate sub-regions. Determine whether the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error of each divided candidate sub-region are all less than the corresponding standard deviation thresholds for curvature, Hausdorff distance, and local fitting error. If so, use each divided candidate sub-region as a sub-region. Otherwise, continue to perform bipartite division on the divided candidate sub-region until the judgment conditions are met, and finally obtain several sub-regions.

[0030] In this step, through the aforementioned judgment and binary division, the original large-scale tooth surface points can be adaptively divided into multiple sub-regions with relatively consistent geometric features, so as to enable subsequent steps to optimize the sampling of measurement points in smaller sub-regions. Among these, the curvature standard deviation threshold... Hausdorff distance standard deviation threshold Local fitting error threshold The specific value is determined in practical applications through expert experience and historical data.

[0031] Step 2: Classify each sub-region, combine the geometric features of each tooth surface point in the sub-region, filter the measurement points of each sub-region, and collect the measurement points of all sub-regions to finally generate a global measurement point set; In this step, after completing the sub-region segmentation described above, the segmented sub-regions are classified into four categories based on their curvature characteristics: flat regions, tilted regions, concave regions, and convex regions. The classification rules are as follows:

[0032] In the formula, For the first Type identifier for each sub-region; This is the sample standard deviation of the normal vector matrix of all tooth surface points in this sub-region; , These are the median of the first principal curvature and the second principal curvature of all tooth surface points in the sub-region, respectively. AND operation; , All of these are judgment criteria.

[0033] Based on the first principal curvature, the second principal curvature, and the Hausdorff distance, the information function value of each tooth surface point is calculated to serve as the geometric feature of the tooth surface point, i.e.:

[0034] In the formula, For the first The information function value of each tooth surface point; , The first The first principal curvature and the second principal curvature of each tooth surface point.

[0035] Set a minimum number of measurement points for each sub-region. .

[0036] In this step, since the minimum number of measurement points required for surface reconstruction of each sub-region using the Moving Least Squares (MLS) method in subsequent steps is 6, therefore in this invention... The value is 6.

[0037] The tooth surface points of each type of region are prioritized from high to low as follows: raised region, recessed region, inclined region, and flat region. The measurement density of each type of region is set so that the measurement density of raised region is greater than that of recessed region, the measurement density of recessed region is greater than that of inclined region, and the measurement density of inclined region is greater than that of flat region.

[0038] In this step, when implementing the measurement point selection strategy, the priority of tooth surface points in each type of region is set from high to low as follows: raised region, recessed region, inclined region, and flat region. At the same time, the measurement density of each sub-region is set according to the priority relationship. The conditions are: measurement density of raised areas > measurement density of recessed areas > measurement density of inclined areas > measurement density of flat areas; where, measurement density It is a value between 0 and 1, which determines the number of measurement points retained in the sub-region. ,Right now: , For the first The total number of tooth surface points in each sub-region.

[0039] Determine the number of measurement points to retain in each sub-region. Is it greater than or equal to the minimum number of measurement points? If so, then retain the number of measurement points in each sub-region. The number of measurement points in this sub-region Otherwise, use the minimum number of measurement points. The number of measurement points in this sub-region ; Based on the number of measurement points in the sub-region By combining priority and information content function values, each sub-region is filtered. There are 10 measurement points.

[0040] In this step, the number of measurement points for each sub-region is determined. Subsequently, for flat sub-regions, since the local geometric changes are relatively small, uniform sampling is used to select measurement points. For other types of sub-regions (such as raised, recessed, and sloping regions), information function values ​​are selected. The largest Each measurement point is used to obtain the sub-region. There are several measurement points; this ensures that the selected points can retain the characteristic information of the tooth surface to a large extent, thus reducing measurement costs from the source.

[0041] Based on the measurement points of each sub-region, tooth surface reconstruction is performed to generate the reconstructed tooth surface of each sub-region.

[0042] In this step, after the measurement points are selected, in order to verify whether the selected measurement points can effectively preserve the original geometric features of the tooth surface and avoid the loss of local morphological information due to the reduction in the number of measurement points, it is also necessary to evaluate the geometric consistency between the reconstructed tooth surface based on the measurement points and the original tooth surface. Specifically, tooth surface reconstruction is performed based on the measurement points of each sub-region to generate the reconstructed tooth surface of each sub-region; that is, this invention reconstructs each sub-region after the tooth surface point cloud is divided into blocks, and compares and analyzes each reconstructed tooth surface with the original tooth surface. Considering that the measurement points may exhibit non-uniform distribution characteristics after adaptive screening, in order to ensure the stability of the local surface fitting process and the continuity of the reconstruction results, this invention uses the Moving Least Squares (MLS) method to reconstruct the surface of each sub-region; specifically, for each sub-region, a local neighborhood model is established using its corresponding measurement points, and the continuous reconstruction of the regional surface is achieved through weighted local second-order surface fitting, thereby obtaining the reconstructed tooth surface of each sub-region.

[0043] After completing the surface reconstruction of each sub-region, the geometric feature parameters of the original tooth surface and the reconstructed tooth surface are extracted respectively, and a geometric consistency evaluation mechanism between the two is established. To comprehensively characterize the degree to which the reconstructed tooth surface retains the geometric information of the original tooth surface, this invention further constructs a sub-region comprehensive similarity evaluation function, which consists of the following indicators:

[0044] In the formula, Normal vector similarity is used to evaluate the consistency of normal vectors between the reconstructed point set and the reference point set, which is the set of tooth surface points corresponding to the measured points in the tooth surface point cloud. For the first The unit normal vector of the tooth surface point corresponding to each measurement point; For the set of measurement points The unit normal vector of each measurement point.

[0045]

[0046] In the formula, Geometric similarity is used to evaluate the spatial positional deviation between the measured point set and the reference point set. It is an exponential function; For the first The tooth surface points corresponding to each measurement point; For the first measurement point in the set One measurement point; This represents the average coordinates of the tooth surface points corresponding to all measurement points.

[0047]

[0048] In the formula, Curvature similarity is used to evaluate the difference between the reconstructed curvature distribution and the original curvature distribution. For the first The curvature values ​​of the tooth surface points corresponding to each measurement point; For the set of measurement points The curvature values ​​at each measurement point; ε is a positive number to prevent division by zero, used to avoid a denominator of zero.

[0049]

[0050] In the formula, Hausdorff distance feature similarity is used to evaluate the degree to which geometric mutation information is preserved after reconstruction; For the first Hausdorf distance between the tooth surface points corresponding to each measurement point; For the set of measurement points Hausdorf distance at each measurement point.

[0051] Based on the above four indicators, a comprehensive similarity evaluation function is constructed, namely:

[0052] In the formula, It is a logarithmic function; This is a comprehensive similarity evaluation function, which measures the similarity between the reconstructed tooth surface and the original tooth surface, and is used to balance the relationship between global geometric consistency and local feature consistency. , , , The weights for normal vector similarity, geometric position similarity, curvature similarity, and Hausdorff distance feature similarity are respectively assigned. This invention adopts a non-uniform weight allocation strategy with values ​​of 0.4, 0.2, 0.2, and 0.2. The non-uniform weight allocation strategy can balance the relationship between global geometric consistency and local feature consistency, and avoid a single indicator from dominating.

[0053] Determine if the overall similarity evaluation function is less than the preset similarity target; if so, then increase the number of measurement points. After adding 1, continue to perform the screening of measurement points in each sub-region and the calculation of the comprehensive similarity evaluation function; otherwise, the current number of measurement points in each sub-region will be used to form the global measurement point set.

[0054] In this step, the comprehensive similarity evaluation function and the preset similarity target are combined. A comparison is made; among which, a preset similarity target is used. This is a preset adjustable parameter, ranging from 0 to 1, defined as the required similarity threshold between the reconstructed tooth surface and the original tooth surface. When the comprehensive similarity evaluation function of the calculated sub-region is less than the similarity target... If the condition is met, the number of measurement points in the sub-region is incremented by 1, and the process of selecting measurement points and calculating the comprehensive similarity evaluation function is repeated until the condition is met. The current number of measurement points in each sub-region is then used to form the global measurement point set. Otherwise, the current number of measurement points in each sub-region is directly used to form the global measurement point set. Through this mechanism, the number of measurement points sampled in each sub-region can be adaptively adjusted according to the local geometric complexity, ultimately obtaining the globally optimal measurement point set while maintaining the tooth surface features.

[0055] Step 3: Based on the global measurement point set, the measurement path planning problem is constructed as an open-ended traveling salesman problem with a fixed start and end point, and the optimal measurement path is generated by using an adaptive large neighborhood search meme method based on boundary memory.

[0056] In this step, after the above-mentioned measurement point optimization selection is completed, the present invention further optimizes the measurement path. Considering that the probe usually has a fixed starting position and ending position in the actual gear measurement process, the path planning problem is abstracted into an open-ended traveling salesman problem with a fixed starting point and ending point; the principle is as follows: Let the global set of measurement points be the set of nodes to be visited, the starting point be the in-point of the 3D coordinate machine, the ending point be the out-point of the 3D coordinate machine, and the remaining measurement points be the intermediate nodes. Using the Euclidean distance between measurement points as the path cost, we can construct the objective function that minimizes the total length of the measurement path, as follows:

[0057]

[0058]

[0059] In the formula, To obtain the minimum value; To measure the total path length; Starting point To the first intermediate node The Euclidean distance; This represents the number of intermediate nodes. intermediate node With intermediate nodes Euclidean distance between them; For the last intermediate node To the end point Euclidean distance between them; For any point With point Euclidean distance between them; , The first , No. Each point is a measurement point or an intermediate node; To measure the path sequence; As the starting point; To measure the first intermediate node visited in the path sequence; This is for measuring the last intermediate node visited in the path sequence; This is the endpoint.

[0060] Therefore, solving the open-ended traveling salesman problem is equivalent to finding the objective function that minimizes the total length of the measurement path; and finding the objective function is equivalent to obtaining the positions of each measurement point corresponding to the minimum total length of the measurement path. Based on this, this invention proposes an adaptive large neighborhood search meme method based on boundary memory (defined as the EMALNS-MA method) to find the positions of each measurement point corresponding to the minimum total length of the measurement path, thereby obtaining the optimal measurement path; wherein, the EMALNS-MA method is a method that integrates the meme algorithm (MA), adaptive large neighborhood search (ALNS), and edge memory mechanism, thereby achieving high efficiency in complex path problems through the synergistic effect of global search and local optimization.

[0061] The principle of the EMALNS-MA method is as follows: First, a fixed start and end point are determined based on geometric scoring rules, thus transforming the open path problem into an optimization of the arrangement of intermediate nodes. During the search process, the evolutionary operator is responsible for maintaining global exploration, while the local search operator refines the solution to accelerate convergence. Furthermore, this method introduces an adaptive large neighborhood search disruption-repair mechanism with memory guidance and simulated annealing acceptance criteria to enhance the ability to escape local optima. Through the synergistic effect of evolutionary search, local optimization, and adaptive perturbation, the EMALNS-MA method can effectively balance exploration and exploitation while satisfying the fixed endpoint constraints. Based on this, the execution process of the EMALNS-MA method is as follows: (1) Input measurement point data and construct a path model. Randomly select two different points as starting points from the global measurement point set. and termination point The remaining measurement points are the intermediate nodes. ), and construct a measurement path model, namely:

[0062] In the formula, For measuring path model; , , They are the 1st, 2nd, and 3rd respectively. There are intermediate nodes.

[0063] (2) Initialize the population and parameters. For the measurement path model constructed in step (1), the intermediate nodes are randomly arranged to generate the initial population:

[0064]

[0065] In the formula, This is the initial population; , , These are the 1st, 2nd, and Mth individuals in the initial population, meaning each individual corresponds to a path; M is the population size. Let M be the path corresponding to the Mth individual, and let M be the position sequence of each intermediate node; The intermediate node sequence of the Mth individual Memorize the edge matrix Set to 0, temperature set to The optimal path is set as ;in, For measurement points With measurement point Weight matrix constituting edge connection relationships

[0066] In this step, to improve the algorithm's ability to utilize historical high-quality path information, an edge memory matrix is ​​introduced to record the node connections in high-quality paths. High-quality edge structures are prioritized for preservation during subsequent path reconstruction, thereby enhancing the algorithm's convergence speed and search stability. The edge memory matrix is ​​defined as follows: ; This represents the number of intermediate nodes. To determine the number of measurement points, therefore This represents the connection paths (edge ​​connections) between all measured points, and there are a total of [number] paths connecting any two distinct points. strip; For measurement points With measurement point The memory weights that form the edge connections store the frequency of variations occurring in high-quality paths; since the initial optimal path... No updates were made; when initializing all elements of the edge memory matrix, let... The optimal path is updated in each subsequent iteration. That is, to obtain the current optimal path. After that, he put The corresponding optimal path in the current context The path memory weight in the path is increased by 1, which is:

[0067] In the formula, For measurement points With measurement point The memory weights after the edge connection relationship is updated; The edge of the path, i.e., the measurement point. With measurement point The edges are formed. Thus, in each update, the memory matrix is ​​based on the updated edges. The system stores the weight values ​​of different paths, which can be selectively updated for subsequent paths. The higher the weight of a path, the more likely it is to be retained in each path update. It is a high-quality path and will be prioritized for reconstruction in subsequent destruction-reconstruction operations.

[0068] (3) Path evaluation and optimal solution update. Calculate the path length for each individual in the entire population:

[0069] In the formula, For path The total length; For path The number of intermediate nodes; For path The first in The intermediate node to the first intermediate nodes Euclidean distance.

[0070] Select the current optimal path :

[0071] In the formula, To find the path The path with the shortest total length.

[0072] Determine the current optimal path Is it less than the optimal path? If so, then update the optimal path with the current optimal path, expressed as: Otherwise, maintain the original optimal path. constant; Record the current optimal path The globally optimal path And update the edge memory matrix, that is: ; (4) Perform population evolution operation. After completing step (3), the path generated by the initial population is not necessarily the optimal result of the global path. Therefore, genetic evolution operation is performed on the initial population to generate a new population (i.e., generate a new path). First, a tournament selection method is used to select a number of individuals as the parent set of the initial population. Then, sequential crossover (OX) operation is performed on the individuals in the parent set to obtain the offspring set. Finally, the offspring individuals are subjected to exchange mutation (swap) to form a new population. .

[0073] (5) Local search optimization. The new population obtained in step (4) is then optimized. and the initial population Individuals in the group, with a predetermined probability p local Local optimization is performed by first constructing a complete path; then, the 2-opt optimization method is used to eliminate path intersections and reduce path length, generating an optimized individual. Probability p local The value ranges from 0 to 1. By randomly selecting a subset of individuals using a probabilistic approach for fine-tuning, we can reduce computational complexity while ensuring solution quality and maintaining population diversity.

[0074] (6) Path perturbation based on large neighborhood search; for all optimized individuals after performing step (5), perturbation is performed with a preset probability. Perform a destruction-reconstruction operation. The value ranges from 0.1 to 0.4. When a path is destroyed, some intermediate nodes are randomly removed from the current population path to obtain a fragmented path, i.e., a fragmented individual. When rebuilding, the updated edge memory matrix recorded in step (3) is used to re-insert the removed intermediate nodes according to the edge connection information therein, and the path reconstruction is gradually completed to obtain the updated individual and the corresponding new path. This step involves setting the perturbation probability. It can preserve high-quality path structure and improve the algorithm's convergence speed and global optimization capability.

[0075] (7) Determine the new solution acceptance strategy based on the simulated annealing mechanism. For the population individuals that performed the destruction-reconstruction operation in step (6), calculate the difference in the old and new path costs of the updated individuals, i.e.:

[0076] In the formula, The cost difference between the old and new paths; The updated individual corresponds to a new path. The total length; For the optimized individual corresponding path The total length.

[0077] Based on the cost difference between the old and new paths, the new solution is accepted according to the following criteria: the updated individual is calculated to accept the new path. The probability of:

[0078] In the formula, To accept the new path for the updated individual The probability of; where, When the new path is better Directly accept the new path Otherwise, with a certain probability Accepting poorer solutions improves the algorithm's ability to escape local optima; (8) Dynamically adjust the perturbation probability. When the algorithm obtains the optimal path in the previous step (3), During the normal convergence phase, reduce the probability of disturbance:

[0079] In the formula, The updated perturbation probability; When the algorithm iterates multiple times and step (3) fails to find the optimal path... When this happens, the probability of the disturbance increases: ; (9) Temperature update; update the temperature according to the annealing strategy: ,in The coefficient of performance is the cooling factor, and .

[0080] (10) Determine the termination condition and output the result. Repeat steps (3) to (9) until either of the following conditions is met: 1) the maximum number of iterations is reached; 2) the optimal solution is found for several consecutive generations. No longer changing; the globally optimal path will be used. Output as the optimal measurement path.

[0081] In summary, the gear tooth surface measurement point and path collaborative optimization method proposed in this invention achieves the following technical effects: 1. Improved the utilization rate of tooth surface measurement points and reduced measurement costs; by adaptively partitioning the tooth surface point cloud and selecting differentiated measurement points based on information such as local curvature, Hausdorff features and normal changes, the number of redundant measurement points can be reduced while ensuring the ability to represent key features of the tooth surface, thereby reducing measurement costs. 2. Improved measurement path efficiency: By modeling path planning as an open-ended traveling salesman problem with fixed start and end points and using an improved hybrid intelligent optimization method for solving it, the total motion path of the 3D coordinate machine probe can be effectively shortened, idle travel reduced, and overall measurement efficiency improved. It is especially suitable for multi-point, high-cycle detection tasks.

[0082] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0083] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for collaborative optimization of gear tooth surface measurement points and paths, characterized in that, Includes the following steps: The point cloud of the gear tooth surface is obtained, and adaptive partitioning based on local geometric features is performed to divide the tooth surface points into several sub-regions. Each sub-region is classified, and the measurement points of each sub-region are selected by combining the geometric features of each tooth surface point in the sub-region to generate a global measurement point set. Based on a global set of measurement points, the measurement path planning problem is constructed as an open-ended traveling salesman problem with a fixed start and end point. An adaptive large neighborhood search meme method based on boundary memory is used to solve the problem and generate the optimal measurement path.

2. The gear tooth surface measurement point and path collaborative optimization method according to claim 1, characterized in that, The process of acquiring the point cloud of the gear tooth surface and performing adaptive partitioning based on local geometric features to divide the tooth surface points into several sub-regions is as follows: Define the tooth surface point cloud as: in, Add cloud-like dots to the tooth surface; For the first One tooth surface point; , , The first Each tooth surface point x axis, y axis, z Axis coordinates; The number of points on the tooth surface; Set the number of neighborhood points For each tooth surface point in the tooth surface point cloud, search for the one with the closest Euclidean distance to that tooth surface point. For each tooth surface point, obtain the neighborhood point set of each tooth surface point; Based on the neighborhood point set, the local quadratic surface equation for each tooth surface point is constructed, namely: in, , , , , , These are all coefficients of the local quadric surface equation; Take the second-order partial derivative of the local quadratic surface equation for each tooth surface point, construct the curvature tensor matrix, solve the eigenvalues ​​of the curvature tensor matrix, and obtain the principal curvature parameters for each tooth surface point, including the first principal curvature and the second principal curvature. Based on the first principal curvature and the second principal curvature, calculate the curvature index of each tooth surface point; Based on the principal curvature parameter, the Hausdorff distance between each tooth surface point and its neighboring points is calculated, i.e.: in, For the first Hausdorff distance between a tooth surface point and its neighboring points; , , Both represent the operation of taking the maximum value; , Both represent the minimum value operation; The first point on the tooth surface One principal curvature; The first point on the tooth surface One principal curvature; L2 norm operations; Each tooth surface point and its corresponding neighboring points are used to form a candidate sub-region, resulting in several candidate sub-regions. Calculate the standard deviation of curvature, standard deviation of Hausdorff distance, and local fitting error for each candidate sub-region; Set the standard deviation threshold for curvature. Hausdorff distance standard deviation threshold Local fitting error threshold ; Determine whether the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error of each candidate sub-region are all less than the corresponding standard deviation thresholds for curvature, Hausdorff distance, and local fitting error. If so, increment the number of neighborhood points of the tooth surface point corresponding to the candidate sub-region by 1, and continue to divide the neighborhood point set of the tooth surface point into candidate sub-regions. Otherwise, perform a bipartite division on each candidate sub-region to obtain several divided candidate sub-regions. Determine whether the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error of each divided candidate sub-region are all less than the corresponding standard deviation thresholds for curvature, Hausdorff distance, and local fitting error. If so, use each divided candidate sub-region as a sub-region. Otherwise, continue to perform bipartite division on the divided candidate sub-region until the judgment conditions are met, and finally obtain several sub-regions.

3. The gear tooth surface measurement point and path collaborative optimization method according to claim 2, characterized in that, The formula for calculating the curvature index of each tooth surface point is: in, For the first Curvature index of each tooth surface point; The first principal curvature; It is the second principal curvature.

4. The gear tooth surface measurement point and path collaborative optimization method according to claim 3, characterized in that, The formulas for calculating the standard deviation of curvature, the standard deviation of Hausdorff distance, and the local fitting error for each candidate sub-region are as follows: in, The standard deviation of curvature; Candidate sub-regions The average value of the curvature index of all tooth surface points; The standard deviation of the Hausdorff distance; Candidate sub-regions The average Hausdorff distance between all tooth surface points and their neighboring points; This represents local fitting error; Candidate sub-regions Inner Each tooth surface point z Axis coordinates; Candidate sub-regions All tooth surface points z The average value of the axis coordinates; This is an operation to retrieve the maximum value.

5. The gear tooth surface measurement point and path collaborative optimization method according to claim 1, characterized in that, The process of classifying each sub-region, combining the geometric features of each tooth surface point in the sub-region, filtering the measurement points of each sub-region, and generating a global measurement point set is as follows: Obtain the median of the first and second principal curvatures of all tooth surface points in each sub-region. Simultaneously, calculate the sample standard deviation of the normal vector matrix of all tooth surface points in each sub-region. Then, classify each sub-region into flat, inclined, concave, and convex regions to obtain the type of each sub-region. in, For the first Type identifier for each sub-region; , , , These are respectively flat areas, sloping areas, concave areas, and convex areas; is the sample standard deviation of the normal vector matrix of all tooth surface points in the sub-region; , These are the median of the first principal curvature and the second principal curvature of all tooth surface points in the sub-region, respectively. AND operation; , All of these are judgment conditions; Based on the first principal curvature, the second principal curvature, and the Hausdorff distance, the information function value of each tooth surface point is calculated to serve as the geometric feature of the tooth surface point, i.e.: in, For the first The information function value of each tooth surface point; , The first The first principal curvature and the second principal curvature of each tooth surface point; For the first Hausdorff distance between a tooth surface point and its neighboring points; Set a minimum number of measurement points for each sub-region. ; The tooth surface point priority of each type of region is set from high to low as: raised region, recessed region, inclined region, and flat region. The measurement density of each type of region is set, and the measurement density of each type of region satisfies the following conditions: the measurement density of raised region is greater than that of recessed region, the measurement density of recessed region is greater than that of inclined region, and the measurement density of inclined region is greater than that of flat region. Based on the measurement density of each type of region and the number of tooth surface points in each type of region, the number of measurement points retained in each sub-region is calculated. ,Right now: in, For the first The total number of tooth surface points in each sub-region; For measuring density; Determine the number of measurement points to retain in each sub-region. Is it greater than or equal to the minimum number of measurement points? If so, then retain the number of measurement points for each sub-region. The number of measurement points in this sub-region Otherwise, use the minimum number of measurement points. The number of measurement points in this sub-region ; Based on the number of measurement points in the sub-region By combining priority and information content function values, each sub-region is filtered. One measurement point; Based on the measurement points of each sub-region, tooth surface reconstruction is performed to generate the reconstructed tooth surface of each sub-region; Based on the reconstructed tooth surface and the original tooth surface, the similarity of normal vectors, geometric position, curvature, and Hausdorff distance features are calculated, namely: in, The similarity is the similarity of the normal vectors; For the first The unit normal vector of the tooth surface point corresponding to each measurement point; For the set of measurement points Unit normal vector of each measurement point; Geometric similarity; It is an exponential function; For the first The tooth surface points corresponding to each measurement point; For the first measurement point in the set One measurement point; This is the average coordinate of the tooth surface points corresponding to all measurement points; Curvature similarity; For the first The curvature values ​​of the tooth surface points corresponding to each measurement point; For the set of measurement points The curvature values ​​at each measurement point; ε is a positive number to prevent division by zero; For Hausdorff distance feature similarity; For the first Hausdorf distance between the tooth surface points corresponding to each measurement point; For the set of measurement points Hausdorf distance at each measurement point; A comprehensive similarity evaluation function is constructed based on normal vector similarity, geometric position similarity, and Hausdorff distance feature similarity. Determine if the overall similarity evaluation function is less than the preset similarity target; if so, then increase the number of measurement points. After incrementing by 1, the measurement point selection and comprehensive similarity evaluation function calculation for each sub-region are performed; otherwise, the current number of measurement points in each sub-region is used to form a global measurement point set.

6. The gear tooth surface measurement point and path collaborative optimization method according to claim 5, characterized in that, Number of measurement points retained in each sub-region As the number of measurement points in this area By combining priority and information content function values, each sub-region is filtered. There are 1 measurement point, specifically: For sub-regions of the flat region type, a uniform sampling method is used for screening. One measurement point; for sub-regions other than flat areas, select the one with the largest information function value. Each measurement point ultimately yields the results for each sub-region. There are 10 measurement points.

7. The gear tooth surface measurement point and path collaborative optimization method according to claim 6, characterized in that, The formula for calculating the comprehensive similarity evaluation function is: in, It is a logarithmic function; This is a comprehensive similarity evaluation function; , , , These are the weights for normal vector similarity, geometric position similarity, curvature similarity, and Hausdorff distance feature similarity, respectively.

8. The gear tooth surface measurement point and path collaborative optimization method according to claim 1, characterized in that, Based on a global set of measurement points, the measurement path planning problem is constructed as an open-ended traveling salesman problem with fixed start and end points. An adaptive large neighborhood search meme method based on boundary memory is used to solve this problem, and the process of generating the optimal measurement path is as follows: Based on the global set of measurement points, the measurement path planning problem is constructed as an open-ended traveling salesman problem with a fixed start and end point, and an objective function is constructed to minimize the total length of the measurement path. An adaptive large neighborhood search meme method based on boundary memory is adopted to transform the problem of solving the objective function of minimizing the total length of the measurement path into the problem of arranging and optimizing the intermediate nodes. The optimal measurement path is generated through global and local search.

9. The gear tooth surface measurement point and path collaborative optimization method according to claim 8, characterized in that, Based on a global set of measurement points, the measurement path planning problem is constructed as an open-ended traveling salesman problem with a fixed start and end point. The objective function for minimizing the total length of the measurement path is then developed, as follows: Let the global set of measurement points be the set of nodes to be visited. Set the starting point as the entry point of the 3D coordinate machine, the ending point as the exit point of the 3D coordinate machine, and the remaining measurement points as intermediate nodes. Using the Euclidean distance between measurement points as the path cost, we construct an objective function that minimizes the total length of the measurement path, namely: in, To obtain the minimum value; To measure the total path length; From the starting point to the first intermediate node The Euclidean distance; This represents the number of intermediate nodes. intermediate node With intermediate nodes Euclidean distance between them; For the last intermediate node To the end point Euclidean distance between them; For any node With nodes Euclidean distance between them; , The first , No. One point; To measure the path sequence; As the starting point; This is to measure the first intermediate node visited in the path sequence; This is to measure the last intermediate node visited in the path sequence; This is the endpoint.

10. The gear tooth surface measurement point and path collaborative optimization method according to claim 8, characterized in that, An adaptive large neighborhood search meme method based on boundary memory is adopted to transform the problem of minimizing the total length of the measurement path into an optimization problem of arranging intermediate nodes. The process of generating the optimal measurement path through global and local searches is as follows: Step 1: Randomly select two measurement points from the global measurement point set as the starting points. End point Using the remaining measurement nodes as intermediate nodes, a measurement path model is constructed, namely: in, For measuring path model; , , They are the 1st, 2nd, and 3rd respectively. One intermediate node; Step 2: Based on the measurement path model, the intermediate nodes are randomly arranged to form a number of individuals, generating an initial population, i.e.: in, This is the initial population; , , These are the 1st, 2nd, and Mth individuals in the initial population, respectively; M is the population size. The path corresponding to the Mth individual; Let M be the sequence of intermediate nodes of the Mth individual; Memorize the edges using the matrix Set to 0, temperature set to The optimal path is set as ;in, For measurement points With measurement point The memory weights that constitute the edge connection relationships; Step 3: Calculate the path length of each entity, i.e.: in, For path The total length; For path The number of intermediate nodes; For path The first in The intermediate node to the first intermediate nodes Euclidean distance; Select the current optimal path ,Right now: in, To find the path The path with the minimum total length; Determine the current optimal path Is it less than the optimal path? If so, then update the optimal path with the current optimal path, expressed as: ； Otherwise, maintain the optimal path. constant; Record the current optimal path The globally optimal path And update the edge memory, that is: in, For measurement points With measurement point The memory weights are used to update the edge connection relationships; The edges of the path, i.e., nodes ,node The edges formed; Step 4: Use the tournament selection method to select individuals from the initial population to form the parent set; Perform a sequential crossover operation on the individuals in the parent set to obtain the child set; Exchange and mutate offspring individuals to generate a new population. ; Step 5: For the new population Initial population Individuals in the group, with a predetermined probability p local After screening, the 2-opt optimization method is used to adjust the node order within an individual to generate an optimized individual; Step 6: For all optimized individuals, apply a preset perturbation probability. To perform the destruction-reconstruction operation, firstly, some intermediate nodes are randomly removed from each optimized individual to generate incomplete individuals. Then, based on the updated edge memory, the removed intermediate nodes are re-inserted into the corresponding individuals to generate updated individuals. Step 7: Calculate the difference between the old and new path costs for the updated individual, i.e.: in, The cost difference between the old and new paths; The updated individual corresponds to a new path. The total length; For the optimized individual corresponding path The total length; Based on the cost difference between the old and new paths, calculate the updated individual's reception of the new path. The probability of that, that is: In the formula, To accept the new path for the updated individual The probability of; Step 8: Determine if the optimal path has been obtained. If so, decrease the perturbation probability; otherwise, increase the perturbation probability to obtain the updated perturbation probability. Step 9: Introduce the cooling coefficient and update the temperature, i.e.: in, The updated temperature; The coefficient of performance is the cooling factor. Step 10: Determine if the maximum number of iterations or the optimal path has been reached in a series of consecutive iterations. If nothing has changed, then the globally optimal path will be used. Output the optimal measurement path; otherwise, continue with Steps 3 through 9.

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