A method and apparatus for online detection of the trajectory of spherical polishing.

Abstract

This invention discloses an online detection method and device for the trajectory of sphere polishing, relating to the field of precision machining online detection. The method includes: S1, acquiring a continuous image sequence during the sphere polishing process at time i using a high-speed camera; S2, preprocessing and feature recognition of the continuous image sequence; S3, a rotation angular velocity measurement module calculating the rotation angle and rotation angular velocity to obtain theoretical values; and a three-dimensional trajectory reconstruction module radially projecting discrete trajectory points onto a sphere surface determined based on the first point, to achieve visualized three-dimensional trajectory reconstruction under geometric constraints, thus completing the online detection of the sphere polishing trajectory. This invention combines a transparent grinding disc structure, a multi-view observation layout, and a dedicated image processing algorithm to achieve real-time, high-precision, and high-efficiency online detection of the sphere's rotational motion parameters and trajectory during the polishing process.

Description

Technical Field

[0001] This invention relates to the field of online inspection in precision machining. Specifically, it provides a method and apparatus for online detection of the trajectory of a sphere during polishing and grinding, applicable to the real-time monitoring and analysis of the motion trajectory of a high-precision sphere. Background Technology

[0002] Precision spheres are key components in high-precision bearings, precision instruments, and medical devices, and their surface quality and shape accuracy directly affect equipment performance. Traditional sphere polishing processes use relative motion between upper and lower grinding discs to achieve spherical surface finishing through mechanical grinding.

[0003] Online trajectory monitoring during sphere machining is a core element in ensuring the quality of precision sphere machining and overcoming accuracy bottlenecks, far exceeding the importance of offline monitoring after machining. The machining precision of spheres requires extremely high accuracy; even micron-level deviations can lead to component failure, affecting the operational stability and lifespan of the entire equipment. Minor disturbances, trajectory deviations, and abnormal rotations during machining, if not detected in time, will gradually accumulate into irreversible machining defects, ultimately leading to product scrap and significantly increasing production costs. Simultaneously, machining process monitoring is crucial for optimizing processes and improving production efficiency. Only by monitoring dynamic parameters during machining in real time can a scientific process adjustment mechanism be established, providing data support for subsequent process adjustments.

[0004] However, existing technologies have the following prominent problems:

[0005] 1) The processing process is not visualized: Traditional polishing devices are closed structures, making it impossible to observe the movement of the sphere in real time; the processing trajectory depends on experience setting and lacks a real-time feedback mechanism; abnormal movements cannot be detected in time, leading to processing defects.

[0006] 2) The limitations of existing detection methods restrict further improvement in the machining accuracy of spheres.

[0007] Compared with traditional offline and contact inspection, online trajectory detection during sphere machining has significant advantages: First, it offers strong real-time performance, simultaneously capturing dynamic information such as the sphere's motion trajectory, rotation speed, and surface condition during machining, enabling immediate warnings of abnormal situations and preventing defect expansion. Second, the non-contact detection mode effectively reduces damage to the machined precision surface, maximizing the surface quality of the sphere and reducing the rejection rate. Third, the continuity of the detection data fully presents the parameter change patterns throughout the machining process, providing comprehensive and accurate data support for process optimization and enabling real-time correction of machining parameters. Fourth, it can be linked with the machining equipment to form a closed-loop control of "detection-feedback-adjustment," significantly improving the stability and consistency of machining accuracy without interrupting the machining process, effectively increasing production efficiency.

[0008] Current inspection methods are primarily offline, which not only interrupts the processing flow and reduces efficiency but also disrupts the continuity of quality control. Contact measurement, on the other hand, carries the risk of damaging precision-machined surfaces. These methods typically only provide static final result parameters such as dimensions and roundness, failing to capture crucial dynamic information such as the sphere's trajectory and rotation during processing. This delayed, incomplete, and risky data feedback model leads to process adjustments heavily reliant on post-processing inference, hindering real-time monitoring and proactive correction, thus limiting processing accuracy and stability. Summary of the Invention

[0009] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0010] To achieve these objectives and other advantages of the present invention, an online detection method for the polishing trajectory of a sphere is provided, comprising:

[0011] S1. Use a high-speed camera to acquire a continuous image sequence during the polishing process of the sphere at time i;

[0012] S2. Perform preprocessing and feature recognition on the continuous image sequence. The preprocessing refers to grayscale conversion, threshold segmentation, and morphological processing of the image. The feature recognition refers to marker detection and multi-target tracking of the image.

[0013] S3, the rotation angular velocity measurement module calculates the real-time rotation angle and rotation angular velocity of the sphere based on the results of S2 to obtain the theoretical values;

[0014] The 3D trajectory reconstruction module projects discrete trajectory points radially onto a sphere determined by the first point based on the results of S2, so as to realize visualized 3D trajectory reconstruction under geometric constraints and complete the online detection of the sphere polishing trajectory.

[0015] In S2, the threshold segmentation constructs an optimized fuzzy clustering segmentation model by introducing an adaptive adjustment mechanism for inter-class distance in the fusion of KL divergence constraints, and the objective function of the fuzzy clustering segmentation model is... It is characterized by the following formula:

[0016] In the above formula, c The number of cluster categories. k , j This represents the increment of cluster categories during iteration. L The number of gray levels in the image. grayscale l The number of pixels, grayscale lClustering categories j The fuzzy weighted value of membership degree, l Grayscale θ The coefficients corresponding to the KL divergence regularization term are: Clustering categories k Cluster centers grayscale l Clustering categories j membership degree grayscale l Clustering categories k membership degree β The coefficient corresponding to the membership uncertainty penalty term. Clustering categories j Cluster centers m As a fuzzy factor, is the dynamic weight parameter for inter-class distance, and , t For the number of iterations, These are the initial weight parameters. , They represent the number of iterations. t Cluster centers for the two categories below.

[0017] Preferably, the fuzzy clustering model employs an alternating optimization strategy to iteratively update the membership degree and cluster centers during the iterative solution process;

[0018] Among them, the membership update value in iteration t+1 Characterized by the following formula:

[0019] In the above formula, The membership degree iterative adjustment coefficient, and , Representing cluster centers and The squared distance between classes, This is a dynamic weight parameter for inter-class distance. α Here, exp() represents the static weight coefficients for inter-class distance, and exp() is the exponential function. W 0 (∙) is the main branch of the Lambert W function. For Lagrange multipliers, Sample gray level l To cluster category j The squared Euclidean distance between the cluster centers, and , For the first i Each sample pair is a cluster category. k membership degree Indicates in tGray level in the next iteration l Clustering categories j The membership degree value;

[0020] exist t Cluster center iteration value after +1 iteration It is characterized by the following formula:

[0021]

[0022] In the above formula, e 0 represents the distance calculation correction factor. δ As the weight of the difference in center between classes, Clustering categories j At the cluster centers of iteration number t, Clustering categories k In the number of iterations t Cluster centers h 2、 h 3 is an adjustment term that includes inter-class distance constraints.

[0023] Preferably, in S3, the process by which the rotation angular velocity measurement module calculates the rotation angle and rotation angular velocity is as follows:

[0024] S310. If the three-dimensional coordinates of the reference marker point in two consecutive frames are P1( x 1, y 1, z 1) and P2 x 2, y 2, z 2), then the angle of rotation It is characterized by the following formula:

[0025]

[0026] S311, Obtain the center of rotation. y - z The projection point of the plane ( y 4, z 4) Then, calculate the angle of rotation of the sphere around its axis using the following formula. f :

[0027] In the above formula, h 0, h 1 represents the distance from the projection point to the center of rotation;

[0028] S312, Angle-based f Calculate angular velocity ω :

[0029]

[0030] In the above formula, This represents the inter-frame time interval.

[0031] Preferably, in S3, the workflow of the three-dimensional trajectory reconstruction module includes:

[0032] S320, based on the known radius R of the sphere and the two-dimensional image coordinates of the marker points ( x c , y c ) and the first trajectory point P1 ( x 1, y 1, z 1) Calculate the vertical coordinates of the marked point using the following formula. z c：

[0033]

[0034] S321. Sampling points are generated using the following spherical parametric equation to complete the 3D trajectory reconstruction by generating a trajectory dataset of the theoretical sphere:

[0035]

[0036] In the above formula, φ The polar angle of the sphere, θ 2 is the azimuth angle of the sphere, ( x s , y s , z s Sampling points P in the trajectory dataset i The coordinates;

[0037] S322. For each sampling point P in the trajectory dataset i The spherical projection point P is calculated using the following formula. proj，i :

[0038]

[0039] in, C i Let R be the coordinates of the marked point, R be the radius of the sphere, and ‖·‖ represent the Euclidean distance.

[0040] Preferably, in S2, the morphological processing includes:

[0041] Extract the main body region of the sphere from the binarized image after threshold segmentation;

[0042] Complementary feature regions are obtained by inverting the binarized image to obtain a target feature image containing dual marker points;

[0043] The content of the feature recognition includes:

[0044] The primary and secondary feature markers on the surface of a sphere are identified from the target feature image using a connected component labeling algorithm.

[0045] The center position and equivalent diameter of each marker point are determined by fitting the minimum circumcircle, so as to complete the automatic tracking and matching of marker points in multiple frames of images.

[0046] Preferably, it also includes:

[0047] S4. The judgment module compares the theoretical value at time i with the actual observed value. If the difference between the two does not exceed the predetermined range, the current processing parameters are not changed.

[0048] The judgment module analyzes the reconstructed trajectory at time i to determine whether there is an abnormally jumping sphere. If so, the machine stops and performs the corresponding check; otherwise, no operation is performed until the sphere polishing process is completed.

[0049] An online detection device for the trajectory of spherical polishing and grinding processes includes:

[0050] The upper and lower grinding disc assemblies are arranged opposite each other in space to form the upper grinding disc assembly and the lower grinding disc assembly of the sphere to be processed.

[0051] An axial high-speed camera group is positioned above the quartz upper grinding disc of the upper grinding disc assembly to capture motion images of the end face of the sphere.

[0052] A radial high-speed camera group positioned horizontally between the upper and lower grinding disk assemblies to capture images of motion on the equatorial plane of a large sphere.

[0053] The surface of the sphere to be processed is prepared with marker points for image tracking;

[0054] Each camera module has a supplementary lighting mechanism installed on the side of its lens.

[0055] The present invention has at least the following beneficial effects:

[0056] Firstly, while ensuring detection accuracy, this invention achieves true non-contact, all-time, and all-dimensional monitoring. The data acquisition and processing time for each processing cycle is only 1-2 minutes, and it will not cause any damage to the surface of the sphere or affect the normal processing flow.

[0057] Secondly, this invention achieves non-contact, real-time online monitoring, overcoming the limitations of traditional polishing processes. Through the innovative combination of a transparent quartz grinding disc and a high-speed camera system, the complete trajectory of the sphere can be observed in real time during processing, obtaining rich kinematic information including three-dimensional position and velocity. Compared to existing offline detection or single-parameter monitoring methods, this invention provides full-process, multi-dimensional trajectory data, offering data support for polishing process optimization and significantly improving the controllability and predictability of the processing.

[0058] Thirdly, the detection device of this invention employs laser micropore marking feature recognition technology, solving the problem of reliable tracking of tiny spheres in complex grinding environments. Traditional visual detection methods are prone to feature loss or misidentification under interference such as polishing fluid splashes and surface reflections. However, this invention, through the dual protection of a physical micropore structure and selectively filled fluorescent material marking, maintains an extremely high success rate even under harsh working conditions. Compared to methods relying on natural features or simple markings, the marking system of this invention has stronger anti-interference capabilities and environmental adaptability, ensuring the long-term stable operation of the detection system.

[0059] Fourth, the fuzzy clustering segmentation algorithm based on the fusion of intra-class and inter-class distance measures and KL divergence adopted in this invention has stronger environmental adaptability and robustness compared with traditional threshold segmentation methods. Experiments show that it provides reliable technical support for real-time monitoring of the polishing process under complex conditions such as slurry splashing and surface reflection of spheres.

[0060] Fifth, the trajectory analysis method of this invention integrates multi-view 3D reconstruction with intelligent algorithm optimization. Through the collaborative work of axial and radial cameras, combined with an improved particle filtering algorithm and a spherical coverage analysis model, the complex motion trajectory of the sphere within the polishing cavity can be accurately reconstructed, and key indicators such as coverage uniformity and motion stability can be calculated. Compared with traditional two-dimensional observation or simple trajectory recording, the 3D motion analysis provided by this invention offers in-depth scientific basis for the study of polishing mechanisms and process optimization.

[0061] Sixth, this invention also enables timely identification and correction of processing defects through real-time trajectory monitoring and anomaly early warning, reducing the scrap rate; process optimization based on trajectory data can improve processing efficiency while reducing reliance on skilled operators; the modular design of the system allows for easy integration into existing grinding and polishing equipment, resulting in low modification costs and a short return on investment period. Compared to solutions requiring expensive dedicated testing equipment, this invention offers significant cost advantages while ensuring performance, making it easier to promote and apply in precision manufacturing enterprises.

[0062] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0063] Figure 1 This is a diagram of the online detection device for the sphere polishing trajectory of the present invention;

[0064] Figure 2 This is a flowchart of the online detection method for the sphere polishing trajectory of the present invention;

[0065] Figure 3 These are the original color images captured by the high-speed camera group during the polishing process of this invention.

[0066] Figure 4 This is a grayscale image of the precision sphere of the present invention;

[0067] Figure 5 This is a schematic diagram of the fuzzy clustering segmentation result based on the fusion of intra-class and inter-class distance measure and KL divergence according to the present invention;

[0068] Figure 6 This is a schematic diagram of the morphological corrosion results of the precision sphere of the present invention;

[0069] Figure 7 This is a schematic diagram showing the noise removal result of the precision sphere of the present invention;

[0070] Figure 8 This is a schematic diagram of the first frame marker detection results of the precision sphere of the present invention;

[0071] Figure 9 This is a schematic diagram of the second frame marker detection results of the precision sphere of the present invention;

[0072] Figure 10 This is a schematic diagram of the trajectory points after processing each frame in this invention;

[0073] Figure 11 This is a three-dimensional spatial projection image of the present invention;

[0074] Figure 12 This is a schematic diagram of the reconstruction of the theoretical sphere three-dimensional model of the present invention;

[0075] Among them, 1-worktable, 2-axial high-speed camera group, 3-fixed bracket, 4-bearing assembly, 5-transmission assembly, 6-column assembly, 7-connecting assembly, 8-upper grinding disc assembly, 9-radial high-speed camera group, 10-light source, 11-quartz upper grinding disc, 12-lower grinding disc assembly. Detailed Implementation

[0076] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0077] Example 1

[0078] like Figure 1 As shown, this invention provides an online detection device for the trajectory of spherical polishing, which is mainly used in the precision spherical polishing process in the aerospace field. It includes: a worktable 1, an axial high-speed camera group 2, a fixed bracket 3, a bearing assembly 4, a transmission assembly 5, a column assembly 6, a connecting assembly 7, an upper grinding disc assembly 8, a radial high-speed camera group 9, a light source 10, a quartz upper grinding disc 11, and a lower grinding disc assembly 12. Each high-speed camera group includes: a power supply, a high-speed camera, and a camera support. The light source 10 is set at the lens position of the high-speed camera to provide supplementary lighting.

[0079] Each high-speed camera group is mounted on the workbench 1 using corresponding fixed brackets to ensure the structural stability of the high-speed camera group. This scheme designs high-speed camera groups in two observation directions, axial and radial, to capture motion images of the sphere's end face and equatorial plane, respectively, thereby obtaining the sphere's motion information from multiple dimensions.

[0080] The column assembly 6 and the lower grinding disc assembly 12 are mounted on the worktable 1. The upper grinding disc assembly 8 is slidably connected to the column assembly 6 via the connecting assembly 7. The slidable connection allows the upper grinding disc assembly 8 to have a certain vertical movement allowance during the polishing operation.

[0081] The upper grinding disc assembly 8 includes a transmission assembly 5, a bearing assembly 4, and a quartz upper grinding disc 11 connected in sequence. The transmission assembly 5 is mounted on the connecting assembly 7, and the output end of the transmission assembly 5 passes through the connecting assembly 7 and is connected to the bearing assembly 4, thereby transmitting the transmission force to the quartz upper grinding disc 11 connected to the bearing assembly 4. The upper grinding disc in the upper grinding disc assembly 8 is made of optically transparent quartz material (the quartz upper grinding disc is made of transparent material, which can observe the processing trajectory of the sphere to be processed), and it is connected to the revolution axis (the revolution axis is the output end of the transmission assembly 5), thereby providing a direct observation window for the observation system without stopping the machine.

[0082] The sphere to be processed is placed between the upper quartz grinding disc 11 of the upper grinding disc assembly 8 and the lower grinding disc of the lower grinding disc assembly 12, and laser-drilled marking points are prepared on the surface of the sphere to be processed as fixed features for image tracking.

[0083] Example 2

[0084] In the precision spherical polishing process used in aerospace applications, the formation of a good surface envelope during polishing is typically evaluated using parameters such as rotation angle, rotation angular velocity, and processing trajectory. Therefore, this invention proposes an online detection method for spherical polishing trajectories to acquire the aforementioned data in real time. This method integrates the following steps: image acquisition and preprocessing; dual-marker detection and positioning; three-dimensional coordinate reconstruction; rotation parameter calculation; trajectory data accumulation; spherical fitting and trajectory projection; visualization; and data management and export. Through these steps, continuous monitoring and evaluation of the surface envelope during polishing are achieved. Specifically, the workflow includes:

[0085] Step one: Real-time acquisition of image sequences containing marker points and the outline of the sphere using a high-speed camera, such as... Figure 3 As shown, a high-speed camera was used to acquire continuous images of a precision sphere. Images acquired by the high-speed camera can clearly show the outline and surface markers of the sphere. To ensure image quality, a high-resolution camera was used in the experiment to ensure accurate capture of the motion changes of the sphere's surface features.

[0086] Step two involves preprocessing and feature recognition of the image sequence to complete dual-marker detection and localization. This mainly includes grayscale conversion, threshold segmentation, morphological processing, marker detection, and multi-target tracking. Specifically, the dual-marker detection and localization employs a fuzzy clustering segmentation strategy based on the fusion of intra-class and inter-class distance measures and KL divergence. The main processing flow is as follows:

[0087] 1. Perform grayscale processing on the acquired precision microsphere images, such as... Figure 4 As shown, a function converts a color image to a grayscale image, simplifying subsequent processing. In the grayscale image, the contrast between light and dark areas on the sphere's surface is more pronounced, preparing it for subsequent thresholding.

[0088] 2. Image Feature Extraction: Calculate histogram statistical features for grayscale images. In this step, the fuzzy clustering segmentation strategy adopts a fast implementation method based on histograms, which reduces the computational complexity from O(M×N×c) to O(L×c), where M×N is the total number of image pixels, L is the number of image grayscale levels, and c is the number of cluster categories, meeting the requirements for real-time processing.

[0089] Perform histogram analysis on the input grayscale image to count the number of pixels at each grayscale level. Let the set of grayscale levels be... ,in, L This represents the number of gray levels in the image.

[0090] To further eliminate the influence of different light intensities on the statistical results, the grayscale histogram is normalized, converting the number of pixels into a probability distribution, which can be expressed as:

[0091]

[0092] in, grayscale l The probability of an element appearing in the entire image, after normalization, can accurately characterize the image's grayscale distribution. grayscale l The number of pixels.

[0093] To reduce the impact of image noise on gray-level statistical features and improve the stability and accuracy of subsequent clustering and segmentation, the normalized gray-level distribution is smoothed to obtain a smoothed gray-level feature distribution and a smoothed gray-level probability distribution. It can be represented as:

[0094]

[0095]

[0096] in, W k For smoothing weighting coefficients, r To smooth the window radius, p ( l + k (grayscale level) l + k The original probability value.

[0097] 3. Cluster initialization: Initialize the cluster centers of the marked point regions and background regions based on histogram features;

[0098] Before clustering initialization, an adaptive fuzzy clustering segmentation model based on KL divergence needs to be established. The fuzzy clustering segmentation model can be implemented in the following ways:

[0099] 1) Construction of the objective function

[0100] A. Intra-class and inter-class joint distance measure

[0101] Instead of the traditional approach of simply minimizing intra-class distance, we construct a joint distance measure between samples and cluster centers, and between cluster centers. :

[0102]

[0103] in, For the sample x i With cluster center The square of the Euclidean distance, Cluster center and The squared distance between classes, It is an adjustable balance parameter that is greater than 0.

[0104] B. Basic Fuzzy Clustering Objective Function for:

[0105]

[0106] in, For the sample i Clustering categories j membership degree m As a fuzzy factor, c The number of cluster categories. n The total number of samples, α This represents the static weighting coefficient for inter-class distance.

[0107] C. The final objective function after introducing the KL divergence regularization term.

[0108]

[0109] in, θ The KL divergence regularization parameter controls the sparsity of membership. For the sample i Clustering categories k The degree of membership.

[0110] 2) Membership optimization

[0111] A. Lagrange optimization conditions

[0112] Add membership normalization constraint Construct the Lagrange optimization function :

[0113]

[0114] in, It is a Lagrange multiplier.

[0115] B. Optimal membership degree It is characterized by the following formula:

[0116]

[0117] in, W 0 (∙) is the main branch of the Lambert W function. This is the membership degree iterative adjustment coefficient. , For the sample x i With cluster center The square of the Euclidean distance, αThis represents the static weighting coefficient for inter-class distance.

[0118] C. The Lagrange multiplier constraint satisfies: At the same time, constraints To ensure that the membership degree takes legal values, the upper and lower constraint thresholds of the Lagrange multipliers are used. P 3. P 4. Characterized by the following formula:

[0119]

[0120]

[0121] D. Cluster center update

[0122] Regarding the objective function Differentiate and set to zero to obtain the cluster centers. Iterative:

[0123]

[0124] in, h 2. h 3 represents the adjustment term that includes inter-class distance constraints, and is characterized by the following formula:

[0125]

[0126]

[0127] In the above formula, e 0 represents the distance calculation correction factor.

[0128] Furthermore, to measure the distance between grayscale values ​​and cluster centers, inter-class distance constraints are used to enhance the separation between different categories; therefore, an inter-class distance constraint term is introduced into the objective function. To measure the differences in membership distributions between different categories and improve the discriminative power of clustering results, a KL divergence regularization term is introduced into the objective function. To further reduce the uncertainty of blurred regions, a penalty is applied to pixels with membership degrees close to 0.5, thereby improving the stability and accuracy of segmentation results; a membership degree uncertainty penalty term is introduced into the objective function. To avoid the fixed inter-class distance weights affecting the clustering results, the inter-class distance weight parameters need to be dynamically adjusted in the objective function based on the current distance between cluster centers during each iteration; therefore, the improved objective function... Represented as:

[0129]

[0130] In the above formula, c The number of cluster categories. k , jThis represents the increment of cluster categories during iteration. L The number of gray levels in the image. grayscale l The number of pixels, grayscale l Clustering categories j The fuzzy weighted value of membership degree, l Grayscale θ for KL The coefficient corresponding to the divergence regularization term ( θ >0 controls the sparsity of membership degrees. Clustering categories k Cluster centers grayscale l Clustering categories j membership degree grayscale l Clustering categories k membership degree β The coefficient corresponding to the membership uncertainty penalty term. Clustering categories j Cluster centers m As a fuzzy factor, is the dynamic weight parameter for inter-class distance, and , t For the number of iterations, These are the initial weight parameters. , These are the cluster centers of the two categories at iteration number t.

[0131] 4. Membership degree iterative calculation: The KL divergence regularization fuzzy clustering algorithm is used to calculate the membership degree of each pixel to the two types of regions. In this step, the KL divergence regularization term penalizes the uniformly distributed membership degree, so that the marked point region has higher sparsity and interpretability, and improves robustness under interference conditions such as polishing fluid splash and surface reflection.

[0132] This step primarily employs an alternating optimization strategy in the membership degree iterative calculation to achieve iterative updates of membership degrees and cluster centers:

[0133] 1) Due to the existence of multiple ambiguous regions in membership, especially at the boundaries of image grayscale distribution, the segmentation results become unstable when the pixel membership is close to 0.5. To automatically suppress the uncertainty in ambiguous regions and improve segmentation stability, an uncertainty penalty factor is added to fix the cluster centers and update the membership values ​​in iteration t+1. Characterized by the following formula:

[0134] Among them, the membership update value in iteration t+1 Characterized by the following formula:

[0135]

[0136] In the above formula, The membership degree iterative adjustment coefficient, and , Representing cluster centers and The squared distance between classes, This is a dynamic weight parameter for inter-class distance. α This refers to the static weight coefficient for inter-class distance. exp ( ) is an exponential function. W 0 (∙) is the main branch of the Lambert W function. For Lagrange multipliers, Sample gray level l To cluster category j The squared Euclidean distance between the cluster centers, and , For the first i Each sample pair is a cluster category. k membership degree Indicates in t Gray level in the next iteration l Clustering categories j The membership degree value;

[0137] 2) To avoid center overlap, when cluster centers are close, an inter-cluster center difference weight δ is added for automatic adjustment to improve convergence stability. t Cluster center iteration value after +1 iteration Characterized by the following formula:

[0138]

[0139] In the above formula, e 0 represents the distance calculation correction factor. δ As the weight of the difference in center between classes, Clustering categories j At the cluster centers of iteration number t, Clustering categories k At the cluster centers of iteration number t, h 2. h 3 is an adjustment term that includes inter-class distance constraints.

[0140] 5. Region Separation: Based on the principles of intra-class minimization and inter-class maximization, the marker region and the background region are separated. That is, according to the final membership matrix, each pixel is assigned to the category with the highest membership degree, generating a binary segmentation image.

[0141] 6. Post-processing optimization: Morphological erosion and area filtering are performed on the segmentation results to extract the regions of the main and reference markers. Morphological erosion includes... Figure 6 As shown, a disk structuring element is used for erosion to remove small noise points and smooth the edges of the sphere. This step corresponds to "initial morphological processing to extract features of the sphere region";

[0142] Area filtration effect Figure 7 As shown, a function is used to remove connected regions with an area of ​​less than 10,000 pixels to eliminate small noise in the background, and a custom function is used to remove excessively large regions to accurately extract the main body region of the sphere.

[0143] 7. Geometric Verification and Localization (Localization is parameter calibration): Verify the circular features using the minimum bounding rectangle algorithm, calculate the diameter of the bounding circle, and determine the sub-pixel-level center coordinates of the marker point in each frame of the image based on the midpoint of the rectangle's diagonal.

[0144] Step 3: Set up a rotation angular velocity measurement module and a 3D trajectory reconstruction module that work in parallel, and the two modules share the basic processing flow of image acquisition and marker detection from Step 2;

[0145] The rotation angular velocity measurement module extracts the sub-pixel-level center coordinates of the marker points in each frame of the image; based on the trajectory of the marker point coordinates changing in consecutive frames, combined with the known radius of the sphere and the image acquisition time interval, it calculates the real-time rotation angle and rotation angular velocity of the sphere. The workflow of the rotation angular velocity measurement module includes:

[0146] 1. The basic processing of image acquisition and marker detection in step two is adopted, namely, acquiring continuous frame images of a rotating object containing markers and performing grayscale conversion on the continuous frame images;

[0147] 2. Perform dual-marker point detection and localization on each frame of the image, use the adaptive threshold segmentation method to binarize the image, use multi-level morphological processing to extract the main body region of the sphere, and then obtain the complementary feature region by inverting the binary image to finally obtain the target feature image containing dual-marker points.

[0148] It should be noted that the dual-marked points include a primary marker point and a reference marker point, and the detection and localization of the dual-marked points adopts a fuzzy clustering segmentation strategy based on the fusion of intra-class and inter-class distance measures and KL divergence. Figure 8 Demonstrates the detection and positioning of precision sphere surface markers (wherein, Figure 8The purple circle represents the sphere to be detected, and the yellow circle represents the micropore marker. A connected component labeling algorithm is used to identify the primary and secondary feature markers on the sphere's surface, and circular bounding boxes are drawn on the original image for visualization. The purple circle represents the detection result of the main sphere region, and the yellow circle represents the second marker detected in the complementary region. Furthermore, the precise center position and equivalent diameter of each marker are determined through minimum circumcircle fitting, enabling automatic tracking and matching of markers across multiple frames of images.

[0149] 3. Reconstruct the 3D spatial coordinates of the marker points based on the spherical constraint model, and calculate the object's rotation angle and angular velocity based on the changes in the 3D coordinates of the marker points in two consecutive frames. The specific processing flow is as follows:

[0150] Let P1 be the three-dimensional coordinates of the reference marker point in two consecutive frames. x 1, y 1, z 1) and P2 x 2, y 2, z 2):

[0151] a) Calculate the rotation angle :

[0152]

[0153] b) Determine the center of rotation at y - z The projection point of the plane ( y 4, z 4):

[0154]

[0155] c) Calculate the angle of rotation of the sphere about its axis of rotation. f :

[0156]

[0157] in, h 0, h 1 represents the distance from the projection point to the center of rotation;

[0158] d) Calculate angular velocity ω :

[0159]

[0160] in, This represents the inter-frame time interval.

[0161] Figure 9The detection results of the marker points in the second frame image are shown. Using the same processing flow as the first frame, the positions of the surface marker points on the sphere at another moment are obtained. This provides comparative data for the analysis of rotational motion by analyzing the spatial position changes of the marker points between consecutive frames. Based on the positional changes of the marker points in the two frames, the rotational motion of the sphere in three-dimensional space is reconstructed through coordinate transformation and geometric calculations, including key kinematic parameters such as rotation angle and angular velocity. This allows for more scientific optimization of the polishing process. Furthermore, a batch processing mode is used to statistically average multiple sets of data, improving measurement accuracy.

[0162] Table 1 compares the actual and theoretical values ​​of the ball blanks with the values ​​obtained under the condition of 0.2 N / ball and no grinding fluid. The differences in rotation angle, rotation angular velocity, and revolution angular velocity are given respectively, and the errors are basically within 20%.

[0163] Table 1: Measured and Theoretical Values ​​of the Motion State of the Ball Blank

[0164]

[0165] Furthermore, using a load of 0.2 N / ball on the billet as the measurement index, the billet's rotation angle, rotational angular velocity, and revolution angular velocity were measured under conditions of water filling and non-water filling in the V-groove. The billet's motion states are obtained in Tables 2 and 3 (where the data in parentheses in the columns containing the experimental values ​​in Tables 2 and 3 represent the error relative to the theoretical values):

[0166] Table 2: Measurement of the motion state of the ball billet under the conditions of a load of 0.2 N / ball and water injection in the V-groove.

[0167]

[0168] Table 3: Measurement of the motion state of the ball billet under the condition of a load of 0.2 N / ball and no water injection into the V-groove.

[0169]

[0170] A comparison of the data measured in Tables 2 and 3 shows that the orbital speed and rotational angular velocity of the spherical blank decreased. Observations revealed that the slippage of the spherical blank was more severe when water was added to the V-groove than during dry grinding. This may be because a liquid film forms on the surface of the spherical blank, reducing the friction between the blank and the grinding disc, resulting in insufficient friction to provide a large gyroscopic torque. At the three contact points, slippage occurs between the silicon sphere and the grinding disc along the great circle of the silicon sphere's longitudinal profile, simultaneously intensifying the collisions between the spherical blanks. The above research indicates that although there is a certain error (within 20%) between the theoretical and experimental values ​​calculated according to the formula, it is basically acceptable in engineering terms, suggesting that the geometric motion state of the spherical blank is good. By comparing and observing the motion parameters under different working conditions, further process improvements can be made.

[0171] The 3D trajectory reconstruction module radially projects discrete trajectory points onto a sphere determined by the first point, achieving trajectory reconstruction under geometric constraints and completing online detection of the sphere polishing trajectory. Its main functions include: coordinate transformation, marker point localization, 3D trajectory reconstruction, and sphere mapping. The workflow of the 3D trajectory reconstruction module includes:

[0172] The image acquisition and marker detection method in step two is used to batch process the image sequence and extract the position of markers frame by frame; the data of multiple frames are accumulated to form a motion trajectory dataset, and the motion trajectory sphere is fitted based on spherical geometric constraints; the original trajectory points are projected onto the fitted sphere to reconstruct a smooth motion trajectory.

[0173] The 3D trajectory reconstruction is achieved using spherical fitting with a first-point constraint method. The specific process includes:

[0174] 1. Given the radius R of the sphere and the coordinates of the marked point in a two-dimensional image ( x c , y c In the case of ), based on the first trajectory point P1 ( x 1, y 1, z 1) Calculate the vertical coordinates of the marker point z c :

[0175]

[0176] Sampling points are generated using the following spherical parametric equation, which in turn generates the theoretical sphere:

[0177]

[0178] In the above formula, φ The polar angle of the sphere, θ 2 is the azimuth angle of the sphere, ( x s , y s , z s Sampling points P in the trajectory dataset i The coordinates;

[0179] The trajectory projection is implemented using a radial normalization method, that is, for each sampling point P in the trajectory dataset... i Its spherical projection point P proj，i The calculation is as follows:

[0180]

[0181] in, Ci Let R be the coordinates of the marked point, R be the radius of the sphere, and ‖·‖ represent the Euclidean distance.

[0182] Step four, visualization processing, mainly includes:

[0183] Real-time processing visualization: Each frame of the image displays the detection results of the marker points and the fitted circle. Figure 10 This demonstrates real-time trajectory visualization in batch processing (where, Figure 10 The red area in the image represents the position of the marker point in each frame. By updating and displaying the red trajectory points in real time after each frame is processed, a two-dimensional motion trajectory of the marker point in the image plane is formed, intuitively showing the motion trend;

[0184] Trajectory accumulation visualization: Displays the distribution of trajectory points on a two-dimensional plane. Figure 11 The complete visualization of the 3D motion trajectory of the sphere is presented. All batch-processed 3D coordinate points are plotted in a 3D coordinate system using a function, demonstrating the complete motion trajectory distribution characteristics of the marker points on the sphere's surface from a spatial perspective. The actual coordinates of the batch-processed 3D coordinate points are shown in Table 4.

[0185] Table 4 shows the true coordinates of the 3D coordinate points after batch processing.

[0186]

[0187] 3D reconstruction visualization: Displays 3D trajectory points, fitted sphere, and marker point positions. Figure 12 For accurate reconstruction of a precision sphere's three-dimensional geometric model Figure 12 The red trajectory in the image represents the movement trajectory of the marker point. Based on the detected trajectory data and the known radius of the sphere, the precise position of the marker point is calculated using the spherical equation. A theoretical sphere model is constructed using a high-resolution spherical mesh and displayed in a semi-transparent manner, allowing for a more intuitive observation of the polishing trajectory of the spherical blank and providing guidance for subsequent process improvements.

[0188] Dynamic projection visualization: Displaying the projection process of a trajectory point onto a sphere point by point;

[0189] Parameter display: Real-time display of calculated parameters such as rotation angle and angular velocity.

[0190] Step 5: At any given time, the judgment module compares the theoretical value with the actual observed value. If the difference between the two does not exceed the predetermined range, the current processing parameters will not be changed. Here, processing parameters refer to pressure, rotation speed, etc.

[0191] The judgment module analyzes the reconstructed trajectory at time i to determine whether there is an abnormally jumping sphere. If so, the machine stops and performs the corresponding check; otherwise, no operation is performed until the sphere polishing process is completed.

[0192] This invention innovatively employs a technical solution combining dual-marker detection and 3D trajectory reconstruction. By analyzing the relative motion relationship between primary and secondary markers, it eliminates projection errors and mismatches inherent in single-point detection. The method described in this invention eliminates the need for complex camera calibration and coordinate system transformation, directly extracting 3D motion information from image sequences, thus achieving fully automated, non-contact online detection of the rotational motion of a precision sphere.

[0193] The precision sphere rotation motion detection method of the present invention can monitor the rotation state of the sphere in real time during the processing. It is applicable to the motion analysis of precision spheres of different sizes and materials. It has the advantages of high detection accuracy, strong real-time performance and high degree of automation, and provides an effective technical means for the optimization of precision sphere processing technology and quality control.

[0194] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0195] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for online detection of the trajectory of a sphere polishing process, characterized in that, include: S1. Use a high-speed camera to acquire a continuous image sequence during the polishing process of the sphere at time i; S2. Perform preprocessing and feature recognition on the continuous image sequence. The preprocessing refers to grayscale conversion, threshold segmentation, and morphological processing of the image. The feature recognition refers to marker detection and multi-target tracking of the image. S3, the rotation angular velocity measurement module calculates the real-time rotation angle and rotation angular velocity of the sphere based on the results of S2 to obtain the theoretical values; The 3D trajectory reconstruction module projects discrete trajectory points radially onto a sphere determined by the first point based on the results of S2, so as to realize visualized 3D trajectory reconstruction under geometric constraints and complete the online detection of the sphere polishing trajectory. In S2, the threshold segmentation constructs an optimized fuzzy clustering segmentation model by introducing an adaptive adjustment mechanism for inter-class distance in the fusion of KL divergence constraints, and the objective function of the fuzzy clustering segmentation model is... It is characterized by the following formula: In the above formula, c The number of cluster categories. k , j This represents the increment of cluster categories during iteration. L The number of gray levels in the image. grayscale l The number of pixels, grayscale l Clustering categories j The fuzzy weighted value of membership degree, l Grayscale θ The coefficients corresponding to the KL divergence regularization term are: Clustering categories k Cluster centers grayscale l Clustering categories j membership degree grayscale l Clustering categories k membership degree β The coefficient corresponding to the membership uncertainty penalty term. Clustering categories j Cluster centers m As a fuzzy factor, is the dynamic weight parameter for inter-class distance, and , t For the number of iterations, These are the initial weight parameters. , They are the number of iterations. t Cluster centers of the two categories below; The fuzzy clustering model employs an alternating optimization strategy to iteratively update membership and cluster centers during the iterative solution process. Among them, the membership update value in iteration t+1 Characterized by the following formula: In the above formula, The membership degree iterative adjustment coefficient, and , Representing cluster centers and The squared distance between classes, This is a dynamic weight parameter for inter-class distance. α This refers to the static weight coefficient for inter-class distance. exp ( ) is an exponential function. W 0 (∙) is the main branch of the Lambert W function. For Lagrange multipliers, Sample gray level l To cluster category j The squared Euclidean distance between the cluster centers, and , For the first i Each sample pair is a cluster category. k membership degree Indicates in t Gray level in the next iteration l Clustering categories j The membership degree value; exist t Cluster center iteration value after +1 iteration Characterized by the following formula: In the above formula, e 0 represents the distance calculation correction factor. δ As the weight of the difference in center between classes, Clustering categories j At the cluster centers of iteration number t, Clustering categories k In the number of iterations t Cluster centers h 2. h 3 is an adjustment term that includes inter-class distance constraints.

2. The online detection method for the trajectory of sphere polishing as described in claim 1, characterized in that, In S3, the process by which the rotation angular velocity measurement module calculates the rotation angle and rotation angular velocity is as follows: S310. If the three-dimensional coordinates of the reference marker point in two consecutive frames are P1( x 1, y 1, z 1) and P2 x 2, y 2, z 2), then the angle of rotation It is characterized by the following formula: S311, Obtain the center of rotation. y - z Projection points of the plane ( y 4, z 4) Then, calculate the angle of rotation of the sphere around its axis using the following formula. f : In the above formula, h 0, h 1 represents the distance from the projection point to the center of rotation; S312, Angle-based f Calculate angular velocity ω : In the above formula, This represents the inter-frame time interval.

3. The online detection method for the trajectory of sphere polishing as described in claim 1, characterized in that, In S3, the workflow of the three-dimensional trajectory reconstruction module includes: S320, based on the known radius R of the sphere and the two-dimensional image coordinates of the marker points ( x c , y c ) and the first trajectory point P1 ( x 1, y 1, z 1) Calculate the vertical coordinates of the marked point using the following formula. z c： S321. Sampling points are generated using the following spherical parametric equation to complete the 3D trajectory reconstruction by generating a trajectory dataset of the theoretical sphere: In the above formula, φ The polar angle of the sphere, θ 2 is the azimuth angle of the sphere, ( x s , y s , z s Sampling points P in the trajectory dataset i The coordinates; S322、For each sampling point P in the trajectory dataset i , the spherical projection point P is calculated using the following formula proj，i : In the above formula, C i is the coordinate of the marker point, R is the radius of the sphere, and ||·|| represents the Euclidean distance.

4. The online detection method for the trajectory of sphere polishing as described in claim 1, characterized in that, In S2, the morphological processing includes: Extract the main body region of the sphere from the binarized image after threshold segmentation; Complementary feature regions are obtained by inverting the binarized image to obtain a target feature image containing dual marker points; The content of the feature recognition includes: The primary and secondary feature markers on the surface of a sphere are identified from the target feature image using a connected component labeling algorithm. The center position and equivalent diameter of each marker point are determined by fitting the minimum circumcircle, so as to complete the automatic tracking and matching of marker points in multiple frames of images.

5. The online detection method for the trajectory of sphere polishing as described in claim 1, characterized in that, Also includes: S4. The judgment module compares the theoretical value at time i with the actual observed value. If the difference between the two does not exceed the predetermined range, the current processing parameters are not changed. The judgment module analyzes the reconstructed trajectory at time i to determine whether there is an abnormally jumping sphere. If so, the machine stops and performs the corresponding check; otherwise, no operation is performed until the sphere polishing process is completed.

6. An online detection device for the trajectory of sphere polishing, applied in the online detection method for the trajectory of sphere polishing as described in any one of claims 1-5, characterized in that, include: The upper and lower grinding disc assemblies are arranged opposite each other in space to form the upper grinding disc assembly and the lower grinding disc assembly of the sphere to be processed. An axial high-speed camera group is positioned above the quartz upper grinding disc of the upper grinding disc assembly to capture motion images of the end face of the sphere. A radial high-speed camera group positioned horizontally between the upper and lower grinding disk assemblies to capture images of motion on the equatorial plane of a large sphere. The surface of the sphere to be processed is prepared with marker points for image tracking; Each camera module has a supplementary lighting mechanism installed on the side of its lens.

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