Assembly precision prediction method based on improved rpm-net and multi-constraint assembly surface weight distribution

Abstract

The application discloses an assembly precision prediction method based on an improved RPM-Net and multi-constraint assembly surface weight distribution, which comprises the following steps: S1, according to the assembly model analysis, the assembly surface and its measurement scheme participating in assembly positioning are obtained, the point cloud feature measurement of the surface topography of each assembly surface is carried out, and the point cloud feature extraction and segmentation are carried out; S2, according to the extracted and segmented assembly surface topography point cloud feature, the improved RPM-Net network architecture introducing a self-attention module and a cross-attention mechanism is used for point cloud registration; S3, based on the Jacobian-screw model, according to the influence degree of each assembly surface on the end pose, the assembly surface screw constituting the multi-constraint is weighted and summed, and the non-repeated constraint screw is subjected to a composite operation, so that the prediction result fully considers the influence of the assembly surface screw, the final error value of the assembly precision prediction is obtained, and the actual assembly situation is more accurately reflected, thereby providing an effective model reference for subsequent improvement of the assembly precision.

Description

Technical Field

[0001] This invention belongs to the field of assembly accuracy prediction technology, and in particular relates to an assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation. Background Technology

[0002] In modern manufacturing, the continuous advancement of manufacturing technology has significantly improved the machining precision of parts, laying a solid foundation for the high-performance manufacturing of complex mechanical equipment. However, the overall precision of complex mechanical equipment is not solely determined by manufacturing precision; precision control during assembly is equally crucial. Assembly errors not only directly affect the geometric fit between parts but also constrain the dynamic performance, stability, and long-term reliability of the equipment during operation. Therefore, how to predict assembly precision in advance using scientific prediction methods based on precision machining has become a pressing challenge for modern manufacturing, and it is also the key to truly achieving high-performance equipment manufacturing.

[0003] When predicting assembly accuracy, the selection of the method for representing and propagating assembly errors are the core factors affecting the final prediction results. For representing assembly errors, the model needs to accurately reflect the geometric deviation characteristics of components during the actual assembly process, including shape errors and orientation errors. Precise quantitative descriptions of these errors are the foundation for subsequent assembly accuracy analysis.

[0004] Traditional assembly error representation methods are mainly based on one-dimensional or two-dimensional error descriptions, such as characterizing assembly errors between parts through simple linear dimensional deviations or in-plane positional deviations. However, in actual assembly, this process occurs in three-dimensional space, and one-dimensional or two-dimensional assembly error representation methods cannot fully account for the posture deviations of parts in three-dimensional space. With the increasing complexity of mechanical structures, the increasing requirements for assembly accuracy, and the need for error propagation and accumulation, the limitations of one-dimensional and two-dimensional error representation methods become increasingly significant. Therefore, it is necessary to develop more advanced three-dimensional error representation methods to comprehensively and accurately describe assembly errors and support complex error propagation analysis and optimization. Liu Jianhua et al. summarized the more typical tolerance modeling methods, mainly including multicolor set models, small displacement screw models, and T-Map models, providing diverse theoretical foundations for assembly accuracy analysis. Among them, the small displacement screw model has attracted widespread attention because it uses six-dimensional screws to uniformly express the three-dimensional position and angle errors of rigid bodies and can perform high-fidelity propagation and accumulation in the assembly chain. Regarding the acquisition of spin, Mu et al., considering manufacturing errors and load deformation, fitted the deformed point cloud data using the least squares method to obtain the spin of each assembly surface. However, compared to point cloud registration techniques, fitted deformed point clouds often exhibit insufficient accuracy and robustness due to the lack of an iterative mechanism. To address this, Shen et al., in their study of cylindrical parts, built upon the skin model research of Schleich et al., simulated systematic and random deviations using modal decomposition and non-Gaussian random fields, and used the ICP (Iterative Closest Point) algorithm to register the cylindrical assembly surfaces to obtain the assembly deviation spin. However, the traditional ICP algorithm, due to its inherent limitations, is prone to getting trapped in local optima. Therefore, to improve the effect of point cloud registration, Zhang et al., in their study of the influence of shape errors on precision assembly, proposed an improved ICP point cloud data registration technique and combined it with a particle swarm optimization algorithm to obtain the optimal contact state for precision assembly of parts, thereby predicting the spin of the final assembly. Furthermore, some studies have also utilized deep learning frameworks to achieve end-to-end direct mapping from point cloud data to assembly errors. Shang et al. proposed a self-channel cross-attention point cloud network by combining a geometric distribution error model and point cloud deep learning, achieving high-precision coaxiality prediction in an end-to-end manner. Wu et al. proposed a spatially embedded transformer, which integrates spatial information into the transformer and uses assembly surface point clouds to achieve high-precision prediction of coaxiality of aero-engines.

[0005] In the aforementioned research methods, both traditional ICP and its improved algorithms essentially employ a hard-assignment point cloud matching strategy, which still struggles to achieve a global optimum. Similarly, end-to-end coaxiality point cloud mapping models face the challenge of effectively predicting end-point errors in multi-part coupled assemblies. To address these challenges, this paper draws upon the idea of ​​Robust Point Matching Network (RPM-Net), which uses a soft-assignment strategy to construct mappings between point clouds to alleviate local optima. Furthermore, it embeds an attention mechanism to replace the ICP method and obtain small displacement spinors. This method, on the one hand, prevents the results from getting trapped in local optima, and on the other hand, extracts features and predicts annealing parameters in a more refined manner, improving registration accuracy. Simultaneously, it is also applicable to end-point error prediction in multi-part coupled assemblies.

[0006] The method of error propagation determines how these errors are transmitted and accumulated during the assembly process through the constraints between parts, thus affecting the final assembly's precision. A reasonable error propagation method can effectively improve the accuracy and reliability of assembly precision prediction, providing strong support for optimizing assembly processes and improving product quality. Yan Yan et al., in analyzing the impact of part geometric errors on assembly precision, established a sensitivity analysis model using matrix differential method and propagated errors through homogeneous coordinate transformation. Liu Liang, in studying the prediction of aero-engine rotor assembly precision, constructed two sets of assembly precision prediction systems—a rigid stacking model and a machine learning elastic model—using homogeneous coordinate transformation and machine learning, respectively. Shi Song et al. proposed an assembly error propagation analysis method that comprehensively considers rough surface contact fits. This method improves the accuracy of aero-engine multi-stage rotor assembly precision prediction by improving the traditional homogeneous transformation matrix model for error propagation. Aoufi et al. proposed a framework combining a unified Jacobi-spinometer model and Monte Carlo simulation to analyze and optimize the assembly precision of cam clamping devices. However, in the above studies, the error propagation of the assembly chain only considered serial connections, which contradicts the situation where multiple surfaces fit between parts during actual assembly. To address this, Liu et al. proposed a virtual functional element method, which significantly improved the prediction accuracy of assembly deviations in complex assembly structures by simplifying parallel connection chains and introducing invariance effects. Chen et al. converted local parallel models into equivalent series models through intersection or compound operations. Liu Jianhua et al. performed cumulative calculations of assembly deviations in the series and parallel parts of the improved polyhedral model using summation and intersection operations, achieving assembly accuracy analysis that comprehensively considers surface morphology and stress deformation. Jin et al. transformed local parallel chains into point contact models from the perspective of primary and secondary datums, thereby achieving accurate prediction of coaxiality deviations of aero-engine rotors. Liu Gang proposed a second type of local parallel connection calculation method using the Z-axis feed system of a horizontal machining center as an example, and its validity was verified. Shen et al. combined the advantages of the Jacobi-spinator model and the non-Gaussian skin model, and extended the algebraic operation method from local parallel to global parallel, opening up new avenues for research in related fields. However, research on global parallel is currently limited, and there is still considerable room for development in related theories and applications.

[0007] Although the above schemes take into account parallel cases, the research methods used, such as algebraic operations for taking extreme values, are still based on statistical algorithms and have limitations when faced with certain deviations. The point contact model based on primary and secondary references will inevitably ignore some screws in the secondary references. These ignored screws are often amplified in actual assembly through the transmission of the assembly chain, which will have a significant impact on the end pose and cause deviations between the predicted and actual values, which urgently need to be improved. Summary of the Invention

[0008] The technical problem addressed by this invention is to provide an assembly accuracy prediction method based on an improved RPM-Net and multi-constraint assembly surface weight allocation. By embedding an attention mechanism into the RPM-Net framework, the risk of registration getting trapped in local optima is effectively suppressed, significantly improving the registration accuracy of the assembly surface point cloud. In terms of assembly error propagation, based on the degree of influence of each assembly surface on the end pose, the screws of the assembly surfaces constituting multiple constraints are weighted and summed, and the screws of non-repeating constraints are compounded to ensure that the predicted assembly error results can fully consider the influence of the screws of each assembly surface.

[0009] The technical solution adopted by this invention to solve the problem is: an assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation, comprising the following specific steps: S1 Part Surface Topography Modeling and Analysis: Based on the component model analysis, the assembly surfaces involved in assembly positioning and their measurement schemes are obtained for each part. Point cloud feature measurement is performed on the surface topography of the assembly surfaces of each part, and point cloud feature extraction and segmentation are performed. S2 Point Cloud Registration Based on Improved RPM-Net: Based on the extracted and segmented surface topography point cloud features, point cloud registration is performed using an improved RPM-Net network architecture that incorporates self-attention modules and cross-attention mechanisms. S3 Multi-Constraint Solution Based on Jacobi-Screw Model: Based on the Jacobi-screw model, according to the degree of influence of each assembly surface on the end pose, the screws of the assembly surfaces constituting multiple constraints are weighted and summed, and the screws of non-repeating constraints are compounded to obtain the final error value of assembly accuracy prediction.

[0010] Compared with existing technologies, the advantages of this invention are as follows: This method uses line laser and coordinate measuring machine (CMM) to sample the point cloud of the assembly surface to obtain the measured point cloud of the assembly surface; and it improves the RPM-Net by incorporating self-attention and cross-attention modules with attention mechanisms, enabling the improved RPM-Net network architecture to extract the relationship between point pairs in the point cloud more deeply and achieve more accurate point cloud registration; finally, it performs a weighted summation of the multi-constraint error screws based on the degree of influence of the registration error on the result, and performs a composite operation on the non-repeating constraint screws; the results show that the deviation between the predicted and actual values ​​of the shaft end pose error in the five degrees of freedom of space obtained by this method is accurately locked within 2μm and 4×10. -5 Within rad, compared with traditional serial operation methods and algebraic operation methods, the prediction accuracy is improved to a certain extent, providing an effective tool for predicting assembly accuracy, and providing a model reference for subsequent assembly error compensation.

[0011] Preferably, in step S1, point cloud feature extraction and segmentation, firstly, a pass-through filter is used for denoising, and the original point cloud is cropped in each direction according to a threshold; then, a combination of statistical filtering and radius filtering is used to denoise the cropped point cloud again; finally, a bilateral filtering algorithm is used to smooth the denoised point cloud. The pass-through filter is used to crop point cloud noise points with large deviations and remove unwanted parts; the combination of statistical filtering and radius filtering is used to further improve the point cloud quality; finally, a bilateral filtering algorithm is used to achieve smooth denoising to avoid interfering with subsequent registration operations and improve registration accuracy.

[0012] As a preferred approach, a self-attention module is introduced into the feature extraction and processing module of the RPM-Net network architecture. This module is used to improve the robustness of the registration process to noise and outliers, enhance the model's ability to perceive local structures, and replace coordinate features with hybrid features. This helps to more accurately establish the correspondence between point clouds and also alleviates the situation of getting trapped in local optima during the registration process to some extent, thereby improving the accuracy and robustness of the registration.

[0013] As a preferred option, a self-attention module is introduced into the feature extraction and processing module of the RPM-Net network architecture; The self-attention module first extracts the query Q, key K, and value V vectors through three different convolutional layers. Then, it generates an attention score by calculating the dot product between query Q and key K, and normalizes the result using a softmax function to obtain the attention weight of each point to other points. Attention (Q, K, V) These weights are used to weight the vector, thereby obtaining a new feature representation, as shown in the following equation. ; The results are subjected to residual connections and normalized to obtain the hybrid feature vector required for final registration.

[0014] As a preferred approach, a cross-attention module is added to the parameter prediction module of the RPM-Net network architecture to obtain point cloud features enhanced by cross-attention, calculate the matching matrix, realize the correspondence between the source point cloud and the target point cloud, and obtain the optimal rotation matrix and translation vector by weighted singular value decomposition.

[0015] Preferably, in the cross-attention module, the input features are processed by a shared multilayer perceptron in the early stage, resulting in deeper data information. Subsequently, the input features are re-divided into source point clouds and target point clouds, and the source and target point clouds can be transformed into their corresponding vectors through linear transformations of queries and keys, respectively. After performing dot product and normalization operations on the obtained vectors, their corresponding attention weights are obtained. These attention weights are used to reflect the relationship between each point in the source point cloud and each point in the target point cloud. The value vector of the target point cloud is weighted and summed using these attention weights to obtain the point cloud features enhanced by cross-attention. Finally, the source point cloud features and the target point cloud features enhanced by cross-attention are re-concatenated.

[0016] Preferably, in step S3, the assembly chain formed by introducing parallel functional elements constitutes a local multi-constraint situation. The total influence of the assembly error of each assembly surface in the assembly chain on the final pose is calculated, and the weight of the repeated constraint quantity is assigned according to the influence degree. Attached Figure Description

[0017] Figure 1 This is a diagram of the architecture of the present invention.

[0018] Figure 2 This is a three-dimensional model diagram of the bearing housing support assembly of the present invention.

[0019] Figure 3 This is a measurement scheme diagram for each assembly surface of the bearing housing support assembly of the present invention.

[0020] Figure 4 This is a point cloud image of each assembly surface of the bearing housing support assembly of the present invention after smoothing and noise reduction.

[0021] Figure 5 This is a diagram of the improved RPM-Net network architecture of the present invention.

[0022] Figure 6 This is a diagram showing the internal structure of the self-attention module of the present invention.

[0023] Figure 7 This is a diagram showing the internal structure of the cross-attention module of the present invention.

[0024] Figure 8 This is a partial multi-constraint assembly chain diagram of the present invention.

[0025] Figure 9 This is a tolerance drawing of the parts required for the bearing housing support assembly of the present invention.

[0026] Figure 10 This is a functional requirement diagram of the bearing housing support assembly of the present invention.

[0027] Figure 11 This is a partial coordinate system diagram of each component of the bearing housing support assembly of the present invention.

[0028] Figure 12 This is an assembly diagram of the bearing housing support assembly of the present invention.

[0029] Figure 13 This is a comparison chart of shaft end position errors obtained by using the traditional series connection, algebraic operation, the method of this invention, and actual measurement results for the bearing housing support assembly of this invention.

[0030] Figure 14 This is a comparison diagram of the shaft end angle errors of the bearing housing support assembly of the present invention using traditional series connection, algebraic operation, and the method of the present invention.

[0031] Figure 15 This is a comparison chart of the absolute prediction residuals of shaft end position errors using traditional series connection, algebraic operation, and the method of this invention for the bearing housing support assembly of the present invention.

[0032] Figure 16 This is a comparison chart of the absolute prediction residuals of the shaft end angle error of the bearing housing support assembly of the present invention using traditional series connection, algebraic operation, and the method of the present invention. Detailed Implementation

[0033] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of the present invention, including various details to aid understanding. These details should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0034] The present invention is as follows Figure 1 As shown, an assembly accuracy prediction method based on an improved RPM-Net and multi-constraint assembly surface weight allocation is proposed, including the following specific steps: S1 Part Surface Topography Modeling and Analysis: Based on the component model analysis, the assembly surfaces involved in assembly positioning and their measurement schemes are obtained for each part. Point cloud feature measurement is performed on the surface topography of the assembly surfaces of each part, and point cloud feature extraction and segmentation are performed. S1.1 Point Cloud Feature Measurement In modern industrial manufacturing and quality inspection, point cloud feature measurement technology plays a crucial role, enabling the precise acquisition of three-dimensional data of object surfaces. Point cloud measurement technology is divided into two categories based on whether it involves contact with the measured surface: contact measurement, represented by coordinate measuring machines (CMMs), constructs a point cloud by contacting the surface of the object being measured. This method offers high accuracy and stability but is prone to scratching the surface; non-contact measurement, represented by line lasers, captures high-density data through scanning and is suitable for complex or difficult-to-reach curved surfaces. However, because it relies on optical sensors to capture laser light band images, it is susceptible to interference from ambient light and may contain noise points, requiring noise reduction processing.

[0035] Taking a bearing housing support assembly as an example for study, its model is as follows: Figure 2 As shown, this bearing housing support assembly mainly consists of four types of parts: a base, a bearing housing, a bearing, and a rotating shaft. It is commonly found in various industrial and mechanical fields, such as machine tools, engines, and electric motors. During measurement, a combination of line laser measurement technology and coordinate measuring machine (CMM) technology was used to extract the point cloud of the surface topography of the assembly surface of the bearing housing support assembly. The line laser measurement equipment selected was the LJ-X8060, whose repeatability reaches the sub-micron level, providing strong support for high-precision measurement.

[0036] Based on the bearing housing support assembly model, the assembly surfaces involved in assembly and positioning of each part can be analyzed. For each assembly surface, according to... Figure 3 The measurement scheme in the paper extracts the surface topography point cloud of the assembly surface of each part.

[0037] For the boss structures on both sides of the base, scanning them with a line laser would result in an angular deviation between the boss side and the placement of the line laser scanner. This angular deviation would cause compression of the obtained point cloud image, leading to errors in the scanning results. Therefore, coordinate measuring machine (CMM) measurement is used. For the bearing housing, bearing inner ring, and shaft shoulder, the reflected light is obstructed during measurement, making it easy to obtain incomplete point cloud images if line laser scanning is used. Therefore, CMM measurement is also used. For other assembly surfaces, line laser measurement can provide fast and accurate scanning results.

[0038] S1.2 Extraction and Segmentation of Point Cloud Features When using line laser scanning to scan point clouds, ambient light interference is often unavoidable. This frequently results in noise points in the final scan data, which in turn interferes with subsequent registration operations and reduces registration accuracy. Therefore, it is necessary to filter and denoise the obtained scan data.

[0039] For point cloud noise points that deviate significantly from the main part's point cloud, a direct-pass filtering method is used for noise reduction. This involves analyzing the original point cloud to obtain its three-dimensional threshold. xmin, xmax, ymin, ymax, zmin and zmax The original point cloud is then cropped in each direction according to a threshold, removing unnecessary parts to ensure that the point cloud after pass-through filtering meets the requirements. Pcloud={Pi|xmin≤xi≤xmax, ymin≤yi≤ymax, zmin≤zi≤zmax} .

[0040] After passing through filtering, to further improve the point cloud quality, a combination of statistical filtering and radius filtering was used to denoise the cropped point cloud again. For any point in the point cloud... Pi(xi, yi, zi) It and its k neighboring points Pj(xj, yj, zj) The average distance is shown in equation (1).

[0041] (1) If the average distance follows a Gaussian distribution, then the threshold can be set accordingly, as shown in equation (2).

[0042] (2) in, μ =Σ ni =1 d i / n , σ =Σ ni =1( d i -μ ) 2 / n s is the multiple of the standard deviation. By comparing di and L This allows us to determine whether the point should be retained. di > L If the number of neighboring points is too high, the point is removed; otherwise, it is retained. This result depends to some extent on the number of neighboring points and the standard deviation factor; adjusting these two factors can optimize the result. After determining the optimal parameters, using them as the nearest neighbor threshold for radius filtering allows for further processing of the point cloud.

[0043] Finally, a bilateral filtering algorithm is used to achieve smooth denoising of the point cloud after further denoising, and the result is as follows. Figure 4 As shown.

[0044] S2 Point Cloud Registration Based on Improved RPM-Net: Based on the extracted and segmented surface topography point cloud features, point cloud registration is performed using an improved RPM-Net network architecture that incorporates self-attention modules and cross-attention mechanisms. Analysis of the Advantages of Soft Assignment in RPM-Net: In point cloud registration, hard assignment and soft assignment are two key matching strategies. Hard assignment uniquely assigns each point in the source point cloud to a corresponding point in the target point cloud, forming a one-to-one precise matching relationship. Traditional ICP iterative registration uses hard assignment. This method has certain advantages in computational efficiency, but due to its deterministic nature, it often becomes one of the important reasons why point cloud registration gets stuck in local optima. In contrast, the soft assignment strategy offers a more balanced approach.

[0045] In soft assignment, the correspondence between points during the point cloud iteration process is not a simple one-to-one correspondence. Instead, each point in the source point cloud can be associated with multiple points in the target point cloud, and the correspondence is determined based on their respective probabilities. This method is used in the iterative registration process of RPM-Net. Furthermore, during the iteration process, through double random constraints and normalized annealing, the registration is gradually transitioned from a relatively fuzzy soft correspondence to a clear hard correspondence. This effectively mitigates the interference of noise and initial conditions on the optimization process, alleviates the local optimum problem caused by hard correspondence to a certain extent, and thus effectively improves the accuracy and reliability of registration.

[0046] Specific solutions for improving the RPM-Net network architecture include: Figure 5 As shown.

[0047] S2.1 Improved Feature Extraction and Processing Module RPM-Net aims to achieve robust point matching by learning the spatial coordinates and local geometric features of point clouds.

[0048] The RPM-Net network architecture consists of three main parts: a feature extraction and processing module, a parameter prediction module, and a matching matrix calculation module. The feature extraction and processing module extracts hybrid features from each point in the point cloud based on its spatial coordinates and local geometric attributes, which are then used for subsequent point correspondence calculations. The parameter prediction module dynamically predicts key parameters for matching matrix calculation based on the current registration state of the point cloud, namely the outlier parameter α and the annealing parameter β, to improve the robustness of registration and the accuracy of the set parameters. The matching matrix calculation module calculates the matching matrix between the source and target point clouds based on the hybrid features obtained from the feature extraction and processing module and the outlier parameter α and annealing parameter β predicted by the parameter prediction module, representing the correspondence between points.

[0049] To improve the robustness of the registration process to noise and outliers and enhance the model's ability to perceive local structures during feature extraction, this study introduces a self-attention module based on the original feature extraction module, such as... Figure 5 As shown.

[0050] For any point in the point cloud used for registration, its blending features are shown in Equation (3).

[0051] (3) in, x c Indicates the absolute position of the center of mass. Δx c,i The position of the neighboring point in the coordinate system with the centroid as the origin is shown in equation (4).

[0052] (4) PPF(xc, xi) It combines the normal angle relationship and distance relationship between the centroid and the neighboring points to describe the local geometric features between the centroid and the neighboring points, as shown in Equation (5).

[0053] (5) In improving the RPM-Net network architecture f θ This is used to represent the feature extraction structure. In this process, a shared Multilayer Perceptron (MLP) layer processes the initial features to obtain deeper information. The max-pooling layer then downsamples the obtained information, extracting vectors that represent the salient features of the local region at that point, reducing feature dimensionality while preserving key information. Subsequently, this preserved key information is further processed by the MLP to learn higher-level feature representations. After this, a self-attention module is added, with the internal structure as follows: Figure 6 As shown.

[0054] This self-attention module first extracts the query (Query, ...) through three different convolutional layers. Q ), key K ) and Value V The vector is then used. Attention scores are generated by calculating the dot product between the query and the key, and the results are normalized using a softmax function to obtain the attention weights of each point on other points. Attention (Q, K, V) These attention weights are used to weight the vector to obtain a new feature representation, as shown in Equation (6).

[0055] (6) Finally, the results undergo residual connections, which not only preserves the original feature information in the output features but also alleviates the gradient vanishing problem, thereby improving the feature extraction effect.

[0056] The introduction of the self-attention module enhances the feature representation of point cloud data, enabling the network to identify the relationships between different points in the point cloud. After the self-attention module analysis, the final hybrid feature vector required for registration is obtained through normalization. This hybrid feature vector contains rich information and can be used to replace coordinate features for registration operations, as shown in Equation (7).

[0057] (7) The improved RPM-Net replaces coordinate features with hybrid features, which helps the algorithm to establish the correspondence between point clouds more accurately. It also alleviates the problem of getting trapped in local optima during the registration process to some extent, thus improving the accuracy and robustness of the registration.

[0058] S2.2 Improved Parameter Prediction Module RPM-Net, as an advanced point cloud registration method, is based on the traditional RPM algorithm. However, unlike the traditional RPM algorithm, where outlier parameters α and annealing parameters β are empirical parameters that need to be manually tuned for different point cloud datasets, RPM-Net employs a trial-and-error process. This involves trying different parameter combinations multiple times to find the most suitable settings for a specific point cloud dataset. This is not only time-consuming but also, because parameter adjustments rely on the operator's experience and intuition, lacking objective standards, often results in suboptimal registration outcomes. In contrast, RPM-Net automatically learns and extracts features from point cloud data using a deep learning model, and then uses these features to make predictions.

[0059] To better analyze the relationships between corresponding points in the source and target point clouds, a cross-attention mechanism was introduced based on the original RPM-Net, such as... Figure 5 As shown.

[0060] In the cross-attention module, the input features, after initial processing by a shared multilayer perceptron, possess deeper data information. Subsequently, they are re-divided into source and target point clouds. This division allows the model to process and understand the features of the two point clouds separately, enabling the source and target point clouds to obtain their corresponding vectors through linear transformations of queries and keys, respectively. After performing dot product and normalization operations on the obtained vectors, their corresponding attention weights are obtained. These weights reflect the relationship between each point in the source point cloud and each point in the target point cloud. Using these weights, the value vector of the target point cloud is weighted and summed to obtain the point cloud features enhanced by cross-attention. This process allows the improved RPM-Net to pay more attention to the parts of the target point cloud that significantly influence the features of the source point cloud, thereby more accurately capturing the correspondence between the two and improving the accuracy and robustness of point cloud registration.

[0061] Finally, the source point cloud features and the target point cloud features enhanced by cross-attention are re-stitched together for subsequent parameter prediction operations, such as... Figure 7 As shown.

[0062] This data-driven parameter prediction method not only improves the accuracy and robustness of registration but also enhances the algorithm's adaptability to different point cloud data. Furthermore, predicting annealing parameters via a network enables dynamic parameter adjustment, allowing the algorithm to maintain optimal performance at different registration stages and further improving the overall point cloud registration effect.

[0063] S2.3 Matching Matrix Solving Module Finally, based on the annealing parameters and point cloud features, a corresponding matching matrix can be calculated to achieve the correspondence between the source point cloud and the target point cloud, such as... Figure 5 As shown, the optimal rotation matrix R and translation vector t are obtained by solving the problem using weighted singular value decomposition (weighted-SVD).

[0064] Comparison of S2.4 point cloud registration results To verify the accuracy of this method, we trained and validated it on the ModelNet40 dataset, using improved chamfer distance as the evaluation metric. The results are shown in Table 1. Experimental results demonstrate that the fusion of the attention mechanism reduces the error of RPM-Net under three conditions: no noise, Gaussian noise, and partial visibility, thus improving the registration accuracy.

[0065] Table 1 Comparison of Improved Chamfer Distance Table 1Comparison of improved chamfer distance In addition, to further verify the effectiveness of this method in measured point clouds, we selected... Figure 4 Using a portion of the point cloud obtained from the experiment as an example, Gaussian noise was added to it to simulate the situation where the point clouds of two assembly surfaces are inconsistent in actual assembly. Subsequently, ICP, a noisy version of RPM-Net, and an improved RPM-Net were used to register with the original point cloud with the same number of iterations to obtain the overlap of the two point clouds after registration, as shown in Table 2.

[0066] Table 2 Comparison of Overlap Table 2Comparison of overlap degree The results above show that the improved RPM-Net achieves better point cloud registration results compared to both ICP and the original RPM-Net.

[0067] S3. Multi-Constraint Solution Based on Jacobi-Screw Model: Based on the Jacobi-screw model, according to the degree of influence of each assembly surface on the end-effector pose, the screws of the assembly surfaces constituting multiple constraints are weighted and summed, and the screws of non-repeating constraints are compositely calculated to obtain the final error value for assembly accuracy prediction. The Jacobi-screw model is a mathematical model for three-dimensional tolerance analysis. It cleverly combines the transitive properties of the Jacobi matrix with the multi-degree-of-freedom expressive power of the screw model, and is widely used in assembly analysis. In assembly analysis, assembly deviation propagation is mainly divided into two categories: one is contact propagation between two functional elements, called contact functional element (CFE), and the other is propagation within a single functional element, called internal functional element (IFE). This classification allows for precise tracking of deviation paths and enables the prediction of assembly deviations.

[0068] The Jacobian matrix, as an important component of this model, can transmit small manufacturing errors of initial and intermediate parts to the end of the system. For any functional element, the Jacobian matrix is ​​represented as shown in Equation (8).

[0069] (8) Among them, [R i 0 ] 3×3 Indicates the direction of the i-th coordinate system relative to the global reference coordinate system; R Pti This indicates the relationship between the tolerance domain direction and the tolerance analysis direction; Wn i ] 3×3 It is a skew-symmetric matrix that represents the positional relationship between the i-th coordinate system and the n-th coordinate system, as shown in equation (9).

[0070] (9) in, dxn i = dx n - dx i , dyn i = dy n - dy i , dzn i = dz n - dz i .

[0071] The screw model, as another important component, can accurately express the position and orientation of a rigid body in space in the form of mathematical expressions. This model makes calculation more convenient by combining the position and angle of small displacements together, and its representation is shown in Equation (10).

[0072] (10) in, δu i , δv i and δw i This represents the positional error of the i-th functional element in the x, y, and z directions; δα i , δβ i and δγ i This represents the angular error of the i-th functional element around the x, y, and z axes.

[0073] After obtaining the above expression, it is possible to accurately calculate how the deviations of each functional element pair in an assembly chain consisting of n functional element pairs work together to affect the overall functional requirement. FR The expression is shown in equation (11). (11) (11) As can be seen from the above formula, since the Jacobian matrix of the entire system and the spin variables of each functional element are combined in a series manner, this expression is only applicable to chain assembly processes.

[0074] In the chain assembly process described above, deviations in different functional components will affect the end pose of the output part. However, in actual assembly, the connection between parts is often not a simple serial relationship; local parallel connections are inevitable.

[0075] In actual assembly processes, relying solely on chain-like calculations will inevitably reduce prediction accuracy. For example, there are multiple facets that mate between a right-angled support frame and a cubic part. Traditional assembly chain calculation methods simplify the assembly transfer chain between the two parts, often leading to the neglect of lateral constraints on the right-angled support frame during assembly error calculation. This oversight can significantly reduce the accuracy of assembly predictions.

[0076] To address assembly errors caused by parallel connections, a weighted parallel processing method based on the influence of assembly datum on the error results is proposed. Here, the concept of a Parallel Function Element (PFE) is introduced; when two or more assembly surfaces simultaneously generate fit errors during the contact and mating process of two parts, one of them is designated as a parallel function element. The resulting assembly chain is as follows: Figure 8 As shown.

[0077] The fit error between the bottom surface of the right-angle support frame and the cubic part can be expressed as: E 1=[0 0 δw 1 δα 1 δβ 10] T The fit error between the side surface and the cubic part can be expressed as: E 2=[0 δv 20 δα 2 0δγ 2] T Both constrain the cubic part, forming a local multi-constraint situation. As can be seen from the above fitting error, in the direction of rotation around the x-axis, the bottom and side surfaces of the right-angle support frame both constrain the cubic part. If the two repeated constraint quantities are simply added together as the final predicted value, the constraint quantity will be calculated repeatedly, which may lead to the final prediction result being over-amplified and thus deviating from the actual deviation range. If the smallest of the two is used as the final prediction quantity, the final prediction value may be too conservative due to ignoring the larger value, and may also deviate from the actual deviation value. To this end, a weight allocation method based on multi-constraint assembly surfaces is proposed. For the multi-constraint assembly surfaces in this example, the total influence of the assembly error of the bottom and side surfaces on the final pose can be calculated separately, and the repeated constraint quantities can be weighted according to the influence degree and weighted summed to obtain the final error value. As shown in equations (12) to (14).

[0078] (12) (13) (14) in, Ui Indicates fit error Ei The impact on the end effector pose after error propagation; Si Through the Ui Perform 2-norm summation to obtain the assembly surface. iThe degree of influence of the fit error on the end-effector pose error was determined; finally, the influence weight of each assembly surface error on the functional requirements was obtained through normalization. ωi .

[0079] After obtaining the above weights, the weighted operation of the repeated constraint quantity can be performed, as shown in equation (15).

[0080] (15) For independent variables, since each variable is constrained by only a single surface and is not affected by other surfaces, it can be calculated by combining operations, that is, taking the local maximum value of the two deviations.

[0081] Finally, the local multi-constraint error formed by the right-angle support frame and the cubic part is shown in Equation (16).

[0082] (16) The weighting method based on multi-constraint assembly surfaces, when dealing with local multi-constraint situations, takes two advantages. First, it considers the overlapping constraints of two pairs of assembly surfaces simultaneously in a weighted manner, theoretically avoiding both overestimating and overly conservative prediction results. Second, it combines independent variables, cleverly transforming the local multi-constraint problem into a new serial connection, simplifying computation while effectively ensuring assembly prediction accuracy. Finally, this method can also be extended to the study of global parallel problems.

[0083] Verification Example To verify the accuracy of the assembly accuracy prediction method based on the improved RPM-Net and multi-constraint assembly surface weight allocation proposed in this invention, a bearing housing support assembly is used as an example to compare and analyze the predicted and measured results. For simplified calculation, all assembly surfaces are considered rigid, i.e., the deformation effect during assembly is not considered. The required tolerances for the components are as follows: Figure 9 As shown.

[0084] During assembly, the pose accuracy of the rotary shaft end is crucial, directly affecting the performance and function of the entire component. In machine tools, the pose accuracy of the shaft end directly impacts the machining quality of the workpiece; in electric motors, the pose accuracy affects the uniformity and stability of the motor torque, thus influencing the efficiency and reliability of power transmission. Furthermore, long-term pose errors can also affect the lifespan of the electric motor. Therefore, to study the pose accuracy of the rotary shaft end during actual machining, this verification example assumes the left end of the shaft as the output end and defines its pose relative to the global coordinate system 0 as the functional requirement, such as... Figure 10 As shown.

[0085] The accuracy of this pose is affected by a variety of factors, including errors in the manufacturing and assembly of the base, bearing housing, bearing, and the rotating shaft itself. These errors propagate and accumulate through the assembly surfaces, thus affecting the precise positioning of the rotating shaft's end. The local coordinate systems of the components constituting the assembly are as follows: Figure 11 As shown in the figure, the relative positions and assembly relationships of the various parts are displayed in detail.

[0086] To facilitate better positioning between components, there are localized multiple constraints between the base and bearing housing, and between the bearing and shaft. Furthermore, since errors in the bearing housings and bearings on both sides are transmitted and accumulated to the shaft end through the rotating shaft, affecting the shaft's orientation, this assembly also exhibits a global parallel connection. The corresponding assembly diagram is shown below. Figure 12 As shown.

[0087] As can be seen from the figure, the local multi-constraints of the entire component are CFE1 and PFE1, CFE2 and PFE2, CFE5 and PFE3, and CFE6 and PFE4, respectively; the two serial constraint chains IFE1-CFE1-IFE3-CFE3-IFE5-CFE5-IFE7 and IFE2-CFE2-IFE4-CFE4-IFE6-CFE6-IFE8 in the component constitute a global parallel constraint.

[0088] To verify the effectiveness of the proposed weighted parallel processing method based on error influence, in addition to using this method, the axis-end pose will also be predicted by traditional calculation methods that only consider series connection and algebraic operation methods that take local minima. All prediction results will be compared and analyzed with the actual values.

[0089] In this verification example, based on the local coordinate system of each assembly surface, the Jacobian matrix of each functional element can be obtained, as shown in Table 3.

[0090] Table 3 Jacobian Matrix Table 3 Jacobian matrix Furthermore, by registering the denoised point cloud using an improved RPM-Net, the fit error between each contact assembly surface can be obtained. For the registration of internal functional components, an ideal point cloud model can be used. Subsequently, the corresponding weighting factors can be obtained according to equations (12) to (14), as shown in Table 4. The fit errors are then weighted and calculated to obtain the final shaft end prediction value.

[0091] Table 4. Fitting errors and weighting distribution between assembly surfaces Table 4Fitting errors and weight distribution between each assembly surface When measuring the actual results, this paper uses coordinate measuring machine (CMM) technology to accurately measure the end of the rotation axis to obtain its center coordinates. Based on this, the attitude is further accurately determined by registering the point cloud data of the end of the rotation axis with the ideal model.

[0092] To more comprehensively evaluate the reliability of this method, the results obtained by this method were compared with those obtained by traditional methods that only consider series connections and algebraic operations that take local minima, as shown in Table 5 and... Figures 13 to 16 As shown in the figure, the shaft end position errors (δu, δv, δw) and shaft end angle errors (δα, δγ) under different prediction methods are intuitively displayed, along with their corresponding measured values.

[0093] Table 5 Calculation results of different methods Table 5The calculation results of different methods The comparison results above show that the absolute prediction residuals of the shaft-end pose error calculated by this method in the five degrees of freedom of space are within 2 μm and 4 × 10⁻⁶ m. -5 Within rad. Compared to traditional serial and algebraic methods, this method improves position prediction accuracy by approximately 3 μm and angle prediction accuracy by approximately 5 × 10⁻⁶. -5 rad. This shows that, for the end pose of the rotating shaft, this method reflects the actual assembly situation better than existing methods.

[0094] To predict assembly accuracy, this invention proposes an assembly accuracy prediction method based on an improved RPM-Net and multi-constraint assembly surface weight allocation. Point cloud sampling of the assembly surface is performed using line laser and a coordinate measuring machine (CMM) to obtain the measured point cloud of the assembly surface. Subsequently, an attention mechanism is incorporated into RPM-Net to improve it, enabling the improved RPM-Net to extract the relationships between point pairs in the point cloud more deeply, achieving more accurate point cloud registration. Finally, the multi-constraint error screws are weighted and summed according to the degree of influence of the registration error on the result, and composite calculations are performed on the non-repeating constraint screws. Results show that the predicted values ​​of the shaft end pose error in the five degrees of freedom of space obtained by this method are precisely locked to within 2 μm and 4 × 10⁻⁴ μm of the actual values. -5Within rad, compared to traditional series operation methods and algebraic operation methods, the prediction accuracy is improved to a certain extent. This provides an effective tool for predicting assembly accuracy. At the same time, it provides a model reference for subsequent assembly error compensation.

[0095] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can occur depending on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for predicting assembly accuracy based on improved RPM-Net and multi-constraint assembly surface weight allocation, characterized in that, The specific steps include the following: S1 Part Surface Topography Modeling and Analysis: Based on the component model analysis, the assembly surfaces involved in assembly positioning and their measurement schemes are obtained for each part. Point cloud feature measurement is performed on the surface topography of the assembly surfaces of each part, and point cloud feature extraction and segmentation are performed. S2 Point Cloud Registration Based on Improved RPM-Net: Based on the extracted and segmented surface topography point cloud features, point cloud registration is performed using an improved RPM-Net network architecture that incorporates self-attention modules and cross-attention mechanisms. S3 Multi-Constraint Solution Based on Jacobi-Screw Model: Based on the Jacobi-screw model, according to the degree of influence of each assembly surface on the end pose, the screws of the assembly surfaces constituting multiple constraints are weighted and summed, and the screws of non-repeating constraints are compounded to obtain the final error value of assembly accuracy prediction.

2. The assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation according to claim 1, characterized in that, In step S1, point cloud feature extraction and segmentation, firstly, a pass-through filter is used for denoising, and the original point cloud is cropped in each direction according to the threshold. Then, a combination of statistical filtering and radius filtering is used to denoise the cropped point cloud again. Finally, a bilateral filtering algorithm is used to smooth the denoised point cloud.

3. The assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation according to claim 1, characterized in that, A self-attention module was introduced into the feature extraction and processing module of the RPM-Net network architecture; The self-attention module first extracts the query Q, key K, and value V vectors through three different convolutional layers. Then, it generates an attention score by calculating the dot product between query Q and key K, and normalizes the result using a softmax function to obtain the attention weight of each point to other points. Attention (Q, K, V) These weights are used to weight the vector, thereby obtaining a new feature representation, as shown in the following equation. ； The results are subjected to residual connections and normalized to obtain the hybrid feature vector required for final registration.

4. The assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation according to claim 3, characterized in that, A cross-attention module is added to the parameter prediction module of the RPM-Net network architecture to obtain point cloud features enhanced by cross-attention, calculate the matching matrix, realize the correspondence between the source point cloud and the target point cloud, and obtain the optimal rotation matrix and translation vector by weighted singular value decomposition.

5. The assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation according to claim 4, characterized in that, In the cross-attention module, the input features are processed by a shared multilayer perceptron in the early stage, which gives them deeper data information. Then, the input features are re-divided into source point clouds and target point clouds, and the source point clouds and target point clouds can be transformed by the linear transformation of the query and the key to obtain their corresponding vectors. After performing dot product and normalization operations on the obtained vectors, their corresponding attention weights are obtained. These attention weights are used to reflect the relationship between each point in the source point cloud and each point in the target point cloud. The value vector of the target point cloud is weighted and summed using these attention weights to obtain the point cloud features enhanced by cross attention; finally, the source point cloud features and the target point cloud features enhanced by cross attention are re-stitched together.

6. The assembly accuracy prediction method based on improved RPM-Net and multi-constraint assembly surface weight allocation according to claim 2, characterized in that, In step S3, the assembly chain formed by introducing parallel functional elements constitutes a local multi-constraint situation. The total influence of the assembly error of each assembly surface in the assembly chain on the final pose is calculated, and the weight of the repeated constraint quantity is assigned according to the influence degree.

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