An Uncertainty Analysis Method for Simulation of Assembly Performance of Mechanical Products

Abstract

This application provides a method for uncertainty analysis in mechanical product assembly performance simulation. This method considers the impact of various uncertainty factors at different stages of the simulation process on assembly performance, classifying these factors into two categories for quantitative analysis. The first category includes the measurement, modeling, and simulation analysis stages in the early stages of simulation; the uncertainty u or error of these factors can be directly calculated. The second category consists of assembly performance uncertainties caused by external loads, boundary conditions, and nonlinear processes primarily based on geometric error distribution. For this category, this method uses simulation analysis results from a physical digital twin model, combined with the construction of an optimal SVR surrogate model and Sobol global sensitivity analysis, to quantitatively analyze the sensitivity of assembly performance to process parameters. In summary, this method provides guidance for the product assembly process.

Description

Technical Field

[0001] This application relates to the field of precision mechanical assembly technology, and in particular to a method for analyzing the uncertainty of mechanical product assembly performance simulation. Background Technology

[0002] In the field of precision mechanical assembly technology, assembly quality has a significant impact on product performance. To predict and evaluate the final assembly performance of a product, finite element method (FEM) simulation analysis is typically used to analyze the assembly process of product components, and the simulation results are combined to provide quantitative guidance for specific assembly processes. However, the simulation analysis process for product assembly involves multiple factors, including modeling errors and simulation analysis errors, which affect the final simulation prediction and evaluation results, ultimately impacting the reliable guidance for the product assembly process. Therefore, it is necessary to introduce uncertainty theory into the simulation analysis process of product assembly, explore the influencing factors of uncertainty, and quantitatively analyze and evaluate the impact of various factors in the simulation process on the final assembly performance.

[0003] Currently, uncertainty analysis and evaluation methods for product assembly simulation typically only consider modeling errors and simulation analysis errors. Modeling errors only include changes to the ideal model size of components, while simulation analysis errors include errors arising from model physical material parameters, boundary conditions, load conditions, and mesh generation. However, in actual assembly processes, when simulating precision mechanical systems, existing technologies do not fully consider the impact of the actual geometric errors and their distribution on the mating surfaces of key components on the post-assembly contact state and product assembly performance. This leads to significant discrepancies between the quantitative analysis of uncertainty factors in the simulation analysis process and the actual situation, thus hindering its effective guidance in actual assembly. Therefore, there is an urgent need to innovate and invent an uncertainty analysis method for mechanical product assembly performance simulation that can fully consider the actual geometric errors and their distribution on the mating surfaces of key components in the actual assembly process, rationally classify the various uncertainty factors in the simulation analysis process, and conduct standardized quantitative analysis and evaluation of each uncertainty factor based on the classification, providing sufficient guidance for the actual product assembly process. Summary of the Invention

[0004] This application provides a method for uncertainty analysis in mechanical product assembly performance simulation, to quantify the uncertainty of various influencing factors during the simulation process. The method includes:

[0005] This paper considers the uncertainties affecting assembly performance at different stages of the simulation process and categorizes them according to these stages. The method divides these uncertainties into two categories, and then performs quantitative analysis on each category.

[0006] The first category of uncertainties includes the measurement, modeling, and simulation analysis stages in the early stages of simulation.

[0007] For the measurement stage, which is one of the first type of uncertainty factors, precise measurements are taken of the mating surfaces of key assembly components. The morphological characteristics of the complex surfaces of these key components are digitized, and an uncertainty quantification analysis of the measurement and inspection stage is performed. Ultimately, only the impact of the measurement equipment's accuracy is considered. Since the length term of the coordinates of the measured workpiece surface points is negligible, only the corresponding nominal measurement error u0 of the measurement equipment needs to be considered when calculating the uncertainty of the measurement stage.

[0008] For the modeling stage, which is part of the first type of uncertainty, the physical digital twin model of the mechanical product assembly is constructed based on the actual measured point cloud data of the key components and surfaces of the assembly obtained in the measurement stage. The accuracy of the physical digital twin model constructed using this method is then analyzed. Specifically, the accuracy analysis method for the modeling stage involves selecting a modeling point set and a test point set, generating an error surface using the modeling point set, calculating the shortest distance from each verification point in the test point set to the error surface, and calculating the MAE value as the mean absolute error (MAE) for this modeling stage.

[0009] For the simulation stage, which is one of the first type of uncertainty factors, the errors in the calculation results mainly include model errors and calculation errors. The errors in the simulation stage vary depending on the simulation software, the assignment of material physical property parameters, the mesh size, the mesh type, and other settings. The error values ​​of each influencing factor are calculated separately according to actual needs.

[0010] This method focuses on the uncertainty analysis of the second type of influencing factors, that is, to comprehensively quantify the impact of the first type of process parameters, including external loads and boundary conditions, and the second type of process parameters, which are mainly geometric error distributions that cause contact nonlinearity, on the uncertainty of assembly performance.

[0011] In the modeling stage, a physical digital twin model, i.e., a virtual assembly, is established and subjected to finite element simulation analysis. During the simulation, the mating surfaces of key components of the virtual assembly are divided into multiple regions. External loads and boundary conditions are applied to the virtual assembly and used as the first type of process parameters for finite element simulation calculation to obtain the simulation results of the virtual assembly under the assembly process. The simulation results are then post-processed, and the average displacement of the mating surfaces in each region is calculated based on the finite element simulation results.

[0012] The various process parameters that cause nonlinearity, primarily characterized by geometric error distribution, are classified as second-class process parameters. This method combines statistical description and finite element analysis models to comprehensively evaluate the geometric error distribution in each region of the mating surfaces of key components, and quantifies multiple second-class process parameters to evaluate the geometric error distribution in each region.

[0013] By using the first and second types of process parameters in each region as independent variables and the displacement of the bonding surface as the dependent variable, a sample set of process parameter-bonding surface displacement data with multiple regions is formed, which is used for subsequent surrogate model construction and uncertainty analysis.

[0014] After constructing the process parameter-combined surface displacement sample set, the single-output support vector regression (S-SVR) machine learning algorithm is used to adapt to the characteristics of strong nonlinearity and limited data volume of the sample set. Based on the known sample set, the relationship between the input and output quantities is fitted, and the values ​​of each parameter in the S-SVR method are optimized by combining the principle of genetic algorithm, and finally the optimal S-SVR surrogate model is established.

[0015] This method, based on the established optimal S-SVR surrogate model, employs the Sobol global sensitivity analysis method to quantify the uncertainty of various process parameters. It analyzes the relationship between the model output response and input variables by calculating variance, and obtains the first-order influence index Si. i This is used to quantify the sensitivity of each process parameter to the model and to calculate the total effect index S. Ti The parameter *i* represents the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the mating surface of the assembly components. This method quantifies the influence of each type I and type II process parameter on the displacement of the mating surface of the assembly components. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

[0016] As can be seen from the above technical solutions, this application considers the uncertainties affecting assembly performance at different stages of the simulation process and classifies them according to different stages. This method divides the uncertainties affecting the simulation process into two categories, and then performs quantitative analysis of the uncertainties in each category. The first category of uncertainties includes the measurement stage, modeling stage, and simulation analysis stage in the early stages of simulation. For the measurement stage, which is part of the first category of uncertainties, precise measurements are taken of the mating surfaces of key components of the assembly. The morphological features of the complex surfaces of these key components are digitized, and the uncertainty of the measurement and inspection stage is quantitatively analyzed. Ultimately, only the influence of the accuracy of the measuring equipment is considered, and the corresponding nominal measurement error u0 of the measuring equipment is calculated to determine the uncertainty of the measurement stage. For the modeling stage, which is part of the first category of uncertainties, a physical digital twin model of the mechanical product assembly is constructed based on the actual measured point cloud data of the mating surfaces of key components obtained in the measurement stage. The accuracy of the surface modeling of the physical digital twin model constructed by this method is analyzed. Modeling point sets and test point sets are selected respectively. An error surface is generated using the modeling point set, and the shortest distance from each verification point in the test point set to the error surface is calculated. The MAE value is then calculated as the average absolute error of this modeling stage. For the simulation stage, which is one of the first type of uncertainty factors, the errors in the calculation results mainly include model errors and calculation errors. The errors in the simulation stage vary depending on the simulation software, the assigned material physical property parameters, the mesh size, and the mesh type. The error values ​​for each influencing factor are calculated separately according to actual needs. This method focuses on the uncertainty analysis of the second type of influencing factors, namely, comprehensively quantifying the impact of the first type of process parameters (including external loads and boundary conditions) and the second type of process parameters (primarily geometric error distribution) that cause contact nonlinearity on the uncertainty of assembly performance. A physical digital twin model, i.e., a virtual assembly, is established in the modeling stage, and finite element simulation analysis is performed. During the simulation, the mating surfaces of key components of the virtual assembly are divided into multiple regions. External loads and boundary conditions are applied to the virtual assembly and used as the first type of process parameters for finite element simulation calculation to obtain the simulation results of the virtual assembly under the assembly process. The simulation results are then post-processed, and the average displacement of the mating surfaces in each region is calculated based on the finite element simulation results. This method treats various process parameters, primarily those related to geometric error distribution that cause nonlinearity, as second-class process parameters. Combining statistical description and finite element analysis models, it comprehensively evaluates the geometric error distribution in different regions of the mating surfaces of key components and quantifies multiple second-class process parameters to assess the geometric error distribution in each region. Using the first and second-class process parameters for each region as independent variables and the mating surface displacement as the dependent variable, a sample set of process parameter-mating surface displacement data across multiple regions is formed for subsequent surrogate model construction and uncertainty analysis.After constructing the sample set of process parameters and surface displacement, a single-output support vector regression (S-SVR) machine learning algorithm is used to adapt to the characteristics of the sample set, which is highly nonlinear and has a limited amount of data. Based on the known sample set, the relationship between the input and output quantities is fitted, and the values ​​of each parameter in the S-SVR method are optimized using the principle of genetic algorithm, ultimately establishing the optimal S-SVR surrogate model. Based on the established optimal S-SVR surrogate model, this method uses the Sobol global sensitivity analysis method to quantify the uncertainty of each process parameter. The first-order influence index S is obtained by calculating the variance to analyze the relationship between the model output response and the input variables. i This is used to quantify the sensitivity of each process parameter to the model and to calculate the total effect index S. Ti The parameter *i* represents the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the mating surface of the assembly components. This method quantifies the influence of each type I and type II process parameter on the displacement of the mating surface of the assembly components. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

[0017] As can be seen, the technical solution provided in this embodiment is based on considering the actual geometric errors and distribution of the mating surfaces of key components during actual assembly. It categorizes the uncertainty factors influencing the simulation process and performs standardized quantitative analysis and evaluation of each uncertainty factor according to the classification. A surrogate model was constructed for the main uncertainty factors, and the reliability of the surrogate model was verified, along with corresponding global sensitivity analysis. In summary, this technical solution can fully consider the various uncertainty factors influencing the simulation analysis of the actual assembly process, providing reliable analysis methods and data for subsequent product design and assembly improvements, thereby improving assembly accuracy. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0019] Figure 1 This application provides a method for analyzing the uncertainty of mechanical product assembly performance simulation.

[0020] Figure 2 This is a schematic diagram illustrating the classification of uncertainty influencing factors provided in the embodiments of this application. This method divides the uncertainty influencing factors in the simulation process into two categories, and then performs quantitative analysis of uncertainty in each category.

[0021] Figure 3The flange-bolt connection structure assembly provided in this application provides a schematic diagram showing that the mating surfaces of key components are divided into multiple regions. This method fully considers the non-uniformity of surface geometric error distribution and investigates the average mating surface displacement Δδ in each region. k Uncertainty analysis was conducted to more comprehensively reveal the influence mechanism of various process parameters on assembly performance.

[0022] Figure 4 This is a comparison curve of the prediction results of the S-SVR proxy model training set and test set provided in the embodiments of this application. The horizontal axis represents different region numbers, and the vertical axis represents the average interfacial displacement Δδ of the corresponding region. k .

[0023] Figure 5 The Sobol global sensitivity analysis results provided in this application embodiment are shown below. The horizontal axis represents the sequence number of different process parameters, and the vertical axis represents the global sensitivity analysis evaluation index S. i S Ti , where i is the sequence number of different process parameters. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] See Figure 1 , Figure 1 This is a method for uncertainty analysis in the simulation of assembly performance of mechanical products. The method includes the following steps:

[0026] Step 101: Consider the uncertain influencing factors that affect the assembly performance at different stages during the simulation process, and classify them according to different stages. Figure 2 This diagram illustrates the classification of uncertainty factors in the simulation process using this method. The method categorizes uncertainty factors in the simulation process into two types, and then performs quantitative analysis of the uncertainty in each category.

[0027] The classification based on different stages involves dividing the uncertainty influencing factors into two categories: Category I and Category II. Category I influencing factors include the various stages in the pre-simulation phase, namely the measurement stage, the modeling stage, and the simulation stage; Category II influencing factors are the various process parameters during the assembly process.

[0028] The measurement and modeling steps in this embodiment fully consider the actual geometric errors and their distribution at the mating surfaces of key components during actual assembly, and prepare for subsequent simulation analysis and quantitative analysis of the second type of uncertainty influencing factors.

[0029] Step 102: For the measurement, modeling, and simulation stages in the first category of uncertainty influencing factors, uncertainty analysis is performed respectively. In the measurement stage, the nominal measurement error u0 of the measuring equipment is considered to calculate the uncertainty of the measurement stage. In the modeling stage, a physical digital twin model of the mechanical product assembly is constructed, and the surface modeling accuracy of the constructed physical digital twin model is analyzed. In the simulation stage, model error and calculation error are calculated according to actual needs.

[0030] This embodiment performs uncertainty analysis on the first type of uncertainty influencing factors. In the measurement stage, the uncertainty is calculated by querying the specific parameters of the measuring equipment. In the modeling stage, the nearest distance from each verification point in the test point set to the error surface is calculated and the MAE value is calculated as the average absolute error of the modeling stage. The error in the simulation stage varies depending on the simulation software, the assignment of material physical property parameters, the mesh size division, the mesh type and other settings.

[0031] Step 103 focuses on the uncertainty analysis of the second type of influencing factors. Finite element simulation analysis is performed on the physical digital twin model, i.e., the virtual assembly. The mating surfaces of key components in the virtual assembly are divided into multiple regions, and simulation results are obtained. Post-processing is performed on the simulation results. Based on the finite element simulation calculation results, the average displacement of the mating surfaces in each region is calculated. A comprehensive evaluation of the geometric error distribution in each region of the mating surfaces of key components is conducted, and multiple second-type process parameters are quantified to evaluate the geometric error distribution in each region.

[0032] In this embodiment, the second type of influencing factors includes the first type of process parameters, which include external loads and boundary conditions, and the second type of process parameters, which are mainly based on geometric error distribution and cause contact nonlinearity.

[0033] Step 104: Establish a sample set of process parameters and surface displacement. Use the Single Output Support Vector Regression (S-SVR) machine learning algorithm and fit the relationship between input and output quantities based on the known sample set. Optimize the values ​​of each parameter in the S-SVR method using the principle of genetic algorithm to establish the final S-SVR surrogate model. Compare the prediction results of this S-SVR model on the training and test sets. Evaluate the predictive power of the surrogate model using the R-squared value and MAE value. If both the R-squared value and MAE value meet the thresholds set according to requirements, the S-SVR surrogate model is considered the optimal S-SVR surrogate model and used for subsequent uncertainty analysis. If the thresholds are not met, return to the iterative evolution step of the genetic algorithm to re-optimize the S-SVR model parameters.

[0034] The principle for selecting the surrogate model construction method in this step is based on two main characteristics of the process parameter-combination surface displacement sample set: (1) There is a strong nonlinearity between the process parameter and the combination surface displacement. (2) The number of samples is relatively small, mainly between tens and hundreds, which is not suitable for machine learning algorithms that require a large amount of sample data as support.

[0035] Step 105: Based on the established optimal S-SVR surrogate model, the Sobol global sensitivity analysis method is used to quantify the uncertainty of each process parameter. The first-order influence index S is obtained by calculating the variance to analyze the relationship between the model output response and the input variables. i This is used to quantify the sensitivity of each process parameter to the model and to calculate the total effect index S. Ti This is used to represent the sensitivity of the interaction between a single process parameter and other input process parameters to the regional displacement, where i is the i-th process parameter. This method thus quantifies the influence of each first-class and second-class process parameter on the displacement of the mating surface region of the assembled components.

[0036] This concludes the process. Figure 1 The description shown.

[0037] To make the above embodiments easier to understand, a specific example is given below, taking a flange-bolted connection structure as an example:

[0038] Step one involves considering the uncertainties affecting assembly performance during the simulation analysis of the flange-bolted connection structure, and classifying them according to different stages. The first category of uncertainties includes the measurement of geometric errors at the mating surfaces of key components in the early stages of simulation, the modeling stage of establishing a physical digital twin model of the assembly, and the simulation analysis stage of setting simulation parameters for the physical digital twin model, i.e., the virtual assembly. The second category of uncertainties includes external loads and boundary conditions as first-category process parameters, and the evaluation parameters of the geometric error distribution on the mating surfaces of key components in the flange-bolted connection structure as second-category process parameters.

[0039] Step two: First, conduct an uncertainty analysis on the first type of influencing factors.

[0040] Regarding the measurement process of this structure, normalization was applied to eliminate the influence of certain factors, including the measurement personnel, measurement strategy (i.e., the number of sampling points on the equipment), and the measurement environment. Furthermore, since the measured object is approximately a rigid body, the uncertainty introduced by stress concentration deformation during measurement can be ignored. Therefore, the current focus is on the errors inherent in the measuring equipment itself. And because the measured object is the coordinates of points on the workpiece surface, the L component of the indication error can be neglected. Only the nominal measurement error u0 is considered for uncertainty calculation. Therefore, the Type B uncertainty generated by the nominal measurement error of the coordinate measuring machine used is ultimately adopted.

[0041] Regarding the modeling of this structure, firstly, based on the actual measured point cloud data of the mating surfaces of key components in the flange-bolt connection structure obtained during the measurement phase, non-uniform rational B-splines (NURBS) surface modeling technology are used to interpolate and reconstruct the point cloud data model to form an error surface. This is then generated in IGES format for import into CAD software to generate the mating surface error surface. The error surface is then subjected to Boolean operations with the ideal 3D model of the target assembly to form a component mating surface with distributed errors. The target assembly is then virtually assembled within the 3D model according to certain constraints, resulting in a virtual assembly with the error surface. In the measurement phase, the obtained point cloud data is divided into a modeling point set and a verification point set. The modeling point set is used to construct the physical digital twin model, and the shortest distance from each verification point to the surface model is calculated. Finally, the mean absolute error (MAE) of all verification points is calculated; a smaller MAE value indicates higher surface modeling accuracy. Where m is the number of verification points, Q j This represents the j-th verification point. This is the nearest point on the NURBS surface to the verification point, where the coordinates of the nearest point are obtained by projecting the verification point onto the error surface.

[0042] Regarding the simulation of this structure, the physical digital twin model of the flange-bolted connection structure constructed in the modeling stage is imported into the finite element simulation analysis software ABAQUS, and simulation parameters are set. Uncertainties in the simulation parameter settings, i.e., error terms generated in the establishment of the finite element model, include model errors and calculation errors. Model errors include discretization errors, boundary condition errors, and element shape errors, with discretization errors further divided into physical discretization errors and geometric discretization errors. Calculation errors include rounding errors and truncation errors. Each error varies depending on the simulation software, the assigned material physical property parameters, mesh size, mesh type, etc., and the magnitude of each influencing factor's error value still needs to be calculated separately according to actual requirements.

[0043] Step three focuses on the uncertainty analysis of the second type of influencing factors. The physical digital twin model of the flange-bolt connection structure, i.e., the virtual assembly, established in the modeling stage, is simulated to obtain simulation results under various assembly processes. During the simulation, the mating surfaces of key components of the virtual assembly are divided into n regions, such as... Figure 3 As shown, external loads and boundary conditions are applied to the virtual assembly, and these are used as the first type of process parameters. For this object, the main first type of process parameters involved include the bolt preload F. N Tensile load, bending load, torsional load, etc. Finite element simulation calculations are performed to obtain simulation results of the virtual assembly under different assembly processes. The simulation results are post-processed. Based on equally divided regions, a set of contact surface nodes (set) is established for the upper and lower surfaces of each region. Displacement data of the upper and lower contact surfaces in each region are extracted using a Python secondary development script. The displacement data set of the node set (set) from the ABAQUS simulation software's odb file is exported in tabular form to obtain the set of node displacements ∑(x,y,z) for the upper and lower surfaces of the joint surface of each equally divided region of the flange-bolted connection structure's key component mating surface. The average joint surface displacement of each node on the upper and lower surfaces of each region is calculated based on the average node data. Then calculate the average displacement of the joint surface in each region. A comprehensive evaluation of the geometric error distribution in various regions of the mating surfaces of key components in flange-bolted connections is conducted, and multiple second-type process parameters are quantified to evaluate the geometric error distribution in each region. This part of the process parameter evaluation is based on the GW model based on Hertzian contact theory. The node data of the upper and lower surfaces of each region of the mating surfaces of key components in flange-bolted connections are extracted and calculated through finite element analysis post-processing, equivalent to a set of node data on a rough surface and another on a smooth rigid plane. The equivalent set of node data on the rough surface is then statistically analyzed, and the least-squares flatness fitting value 'a' and the average height of the convex hull are calculated. Calculation of two second-class process parameters.

[0044] Step four involves using the first and second types of process parameters for each region of the mating surface of key components in the flange-bolted connection structure as independent variables and the mating surface displacement as the dependent variable, forming a sample set of process parameter-mating surface displacement data for multiple regions. A surrogate model is constructed using a single-output support vector regression (S-SVR) machine learning algorithm. The sample set is divided into training and testing sets according to a certain ratio. A radial basis function (RBF) kernel is selected, and the ranges of the penalty factor c, kernel parameter γ, and p are set. The root mean square error (RMSE) between the predicted results and the true values ​​is calculated, and this RMSE is used as the fitness function. An initial population containing the three parameters is generated, and a genetic algorithm is used to iteratively evolve the three parameters. The parameter combination with the smallest fitness function value is then used as the parameters for the final S-SVR model. The R-squared threshold is set to 0.95, and the MAE value is 0.005. The prediction results of this S-SVR model are compared between the training and testing sets. Figure 4 As shown, if both the R-squared value and the MAE value meet the thresholds set according to the requirements, then the S-SVR surrogate model is considered to be the optimal S-SVR surrogate model and can be used for subsequent uncertainty analysis.

[0045] Step 5: The optimal S-SVR surrogate model obtained in Step 4 is analyzed using the Sobol global sensitivity analysis method to quantify the uncertainty of each process parameter. For the mating surfaces of key components in the flange-bolted connection structure, the screw preload F is selected. N The least squares flatness fitting value 'a' of the equivalent rough surface of the region and the average height of the convex hull. An optimal S-SVR surrogate model for the displacement of the regional interface was established, with three process parameters as the first, second, and third influencing factors. A Sobol global sensitivity analysis was performed, setting the distribution intervals for each process parameter, randomly generating a sample space, and analyzing the relationship between the model output response and input variables by calculating variance. The first-order influence index S was then obtained. i This is used to quantify the sensitivity of each process parameter to the model and to calculate the total effect index S. Ti This is used to represent the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the region interface surface. Statistical results are as follows: Figure 5 As shown, the configurable distribution range, the sensitivity of each process parameter to the displacement of the interface surface in the region is ranked as follows: average height of the convex hull. Screw preload F NThe least-squares flatness fitting value 'a' of the equivalent rough surface of the region was obtained, and the sensitivity was quantified. This quantifies the influence of process parameters on assembly performance during simulation. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators, including transferring the uncertainty of each influencing factor to the coaxiality error of the final assembly of the flange-bolted connection structure.

[0046] Existing common simulation uncertainty analysis methods often use ideal models for simulation parameter settings when analyzing the uncertainty of mechanical product assembly performance during simulation, without considering the geometric error distribution of the actual morphology of the mating surfaces or conducting more systematic and scientific statistical analysis. This paper establishes a physical digital twin model of the assembly based on measured point cloud data to accurately characterize the actual morphology of the mating surfaces of key components and conducts simulation analysis. It considers the uncertainties introduced by the measurement, modeling, and simulation settings. The mating surfaces are evenly divided, and a comprehensive evaluation calculation combining finite element model and statistical description is performed to analyze the surface geometric error distribution. Based on the simulation results and the sample set established by the process parameters, a surrogate model for assembly performance is constructed using the S-SVR machine learning algorithm combined with a genetic algorithm, which is more suitable for objects with small sample sizes and strong nonlinearity. The model accuracy is verified, and then the Sobol global sensitivity analysis method is used to comprehensively evaluate the individual influence of each process parameter on assembly performance and the influence of their interaction on assembly performance, making the uncertainty analysis results more comprehensive. In summary, this method demonstrates good reliability in analyzing the influencing factors of uncertainty in the assembly performance of mechanical products during simulation.

[0047] Taking a mechanical product with a flange-bolted connection structure as an example, the effectiveness of this method is demonstrated, and it can be applied to the summary and generalization of assembly performance uncertainty analysis in the simulation process of similar mechanical products. This method provides a reliable analytical approach and data basis for subsequent product design and assembly improvements, thereby improving assembly accuracy.

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for uncertainty analysis in simulation of assembly performance of mechanical products, characterized in that, The method includes: Considering the uncertainties that affect assembly performance at different stages of the simulation process, and classifying them according to different stages, the uncertainties in the simulation process are divided into two categories, and then the uncertainties are quantitatively analyzed separately. The first category of uncertainties includes the measurement, modeling, and simulation analysis stages in the early stages of simulation. For the measurement link in the first category of uncertainty factors, the morphological features of the complex surfaces of the key components of the assembly are digitized by accurately measuring the mating surfaces of the key components, and the uncertainty of the measurement and inspection link is quantitatively analyzed. Finally, only the influence of the accuracy of the measuring equipment is considered. Since the length of the coordinates of the workpiece surface points can be ignored, only the corresponding nominal measurement error u0 of the measuring equipment needs to be considered to calculate the uncertainty of the measurement link. For the modeling stage in the first category of uncertainty factors, which involves constructing a physical digital twin model of the mechanical product assembly based on the actual measured point cloud data of the key components and surfaces of the assembly obtained in the measurement stage, and performing surface modeling accuracy analysis on the constructed physical digital twin model; by selecting modeling point sets and test point sets respectively, using the modeling point set to generate an error surface, and calculating the shortest distance from each verification point in the test point set to the error surface, and calculating the MAE value as the mean absolute error of this modeling stage; For the simulation stage in the first category of uncertain influencing factors, the error in the calculation results includes model error and calculation error. The error in the simulation stage varies depending on the simulation software, the assignment of material physical property parameters, the mesh size division, and the mesh type setting. Therefore, the error value of each influencing factor should be calculated separately according to actual needs. Uncertainty analysis of the second type of influencing factors: This type of influencing factors includes the first type of process parameters of external load and boundary conditions, and the second type of process parameters that cause contact nonlinearity mainly by geometric error distribution. Uncertainty analysis is performed on these factors to comprehensively quantify the impact of these two types of process parameters on the uncertainty of assembly performance. First, a physical digital twin model, i.e., a virtual assembly, is established in the modeling stage, and finite element simulation analysis is performed. During the simulation, the mating surfaces of the key components of the virtual assembly are divided into multiple regions. External loads and boundary conditions are applied to the virtual assembly and used as the first type of process parameters for finite element simulation calculation to obtain the simulation results of the virtual assembly under the assembly process. The simulation results are then post-processed, and the average displacement of the mating surfaces in each region is calculated based on the finite element simulation results. The various process parameters that cause nonlinearity, mainly based on geometric error distribution, are designated as second-class process parameters. Combining statistical description and finite element analysis models, a comprehensive evaluation is conducted on the geometric error distribution of each region on the mating surfaces of key components of the assembly. Multiple second-class process parameters are quantified to evaluate the geometric error distribution of each region. The first and second type process parameters of each region are used as independent variables, and the combined surface displacement is used as the dependent variable to form a sample set of process parameter-combined surface displacement data for multiple regions, which is used for subsequent proxy model construction and uncertainty analysis. After completing the construction of the process parameter-combined surface displacement sample set, the single-output support vector regression (S-SVR) machine learning algorithm is used. Based on the known sample set, the relationship between the input and output quantities is fitted. The value of each parameter in the S-SVR method is optimized by combining the principle of genetic algorithm, and finally the optimal S-SVR surrogate model is established. Based on the established optimal S-SVR surrogate model, the Sobol global sensitivity analysis method is used to quantify the uncertainty of each process parameter. The relationship between the model output response and input variables is analyzed by calculating the variance, and the first-order influence index S is obtained. i This is used to quantify the sensitivity of each process parameter to the model and to calculate the total effect index. This is used to represent the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the mating surface in the region, where i is the i-th process parameter; thus, the influence of each first-class and second-class process parameter on the displacement of the mating surface in the region of the assembly parts is quantified during the simulation process; this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

2. The method for simulation analysis of assembly performance of mechanical products according to claim 1, characterized in that, Uncertainty factors are categorized into two types based on different stages: Uncertainty influencing factors are categorized into two types: Type I and Type II. Type I factors include all stages of the measurement and modeling process, namely the measurement stage, the modeling stage, and the simulation stage. The measurement and modeling stages fully consider the actual geometric errors and their distribution at the mating surfaces of key components in the actual assembly process to conduct uncertainty analysis and prepare for subsequent simulation analysis and quantitative analysis of Type II uncertainty influencing factors. Type II factors are various process parameters in the assembly process, which are further divided into Type I process parameters, including external loads and boundary conditions, and Type II process parameters, mainly based on geometric error distribution, that cause contact nonlinearity. Type II factors represent the uncertainty influencing factors in the simulation analysis of mechanical product assembly performance.

3. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, The modeling process involves establishing a physical-digital twin model, including: Point cloud data is extracted from the mating surfaces of key components in the assembly. Non-uniform rational B-splines, i.e., NURBS surface modeling technology, are used to interpolate and reconstruct the point cloud data model to form error surfaces. The resulting IGES format is then imported into CAD software to generate the error surfaces. Boolean operations are performed between the error surfaces and the ideal 3D model of the target assembly to form component mating surfaces with distributed errors. The target assembly is then virtually assembled in the 3D model according to certain constraints to obtain a virtual assembly with error surfaces.

4. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, Perform surface modeling accuracy analysis, including: The point cloud data obtained in the measurement process is divided into a modeling point set and a verification point set. A NURBS surface is constructed using the modeling point set, and the shortest distance from each verification point to the surface model is calculated. Finally, the mean absolute error (MAE) of all verification points is calculated; a smaller MAE value indicates higher surface modeling accuracy. Where m is the number of verification points, Q j This represents the j-th verification point. This is the nearest point on the NURBS surface to the verification point, where the coordinates of the nearest point are obtained by projecting the verification point onto the error surface.

5. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, The mating surfaces of key components in the assembly are divided into multiple regions, and the displacement of the mating surfaces in each region is calculated through post-processing, including: For the mating surfaces of key components in the assembly, they are divided into n regions. For the k-th region, based on the node data set Σ(x,y,z) extracted from the finite element analysis post-processing of that region, the average mating surface displacement of the nodes on the upper and lower surfaces of that region is calculated by averaging the node data. Then calculate the displacement of the interface in this region. Where δ is the displacement of the bonding surface and k is the region number.

6. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, Combining statistical description and finite element analysis models, a comprehensive evaluation of the geometric error distribution in each region of the mating surfaces of key components in the assembly is conducted, and the results are quantified into multiple second-type process parameters to evaluate the geometric error distribution in each region, including: Based on the GW model of Hertzian contact theory, the node data of the upper and lower surfaces of each region of the joint surface of key components of the assembly are extracted and calculated through finite element analysis post-processing. This is equivalent to a set of node data of a rough surface and another smooth rigid plane. Then, the geometric error distribution of the equivalent rough surface node data set is evaluated, including the calculation of the least squares flatness fitting of the equivalent rough surface and the average height of the convex hull, and the entropy parameter of the convex hull height distribution as the second type of process parameters.

7. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, The optimal S-SVR proxy model is established using the S-SVR method, including: The sample set is divided into a training set and a test set according to a certain ratio. A radial basis function (RBF) kernel is selected, and the ranges of three parameters—penalty factor c, kernel parameter γ, and p—are set. An initial population containing these three parameters is generated based on the principles of a genetic algorithm. The crossover probability, mutation probability, and number of iterations required by the genetic algorithm are determined. The initial population is decoded to obtain different parameter sets, which are then substituted into the S-SVR model to predict the output of the training set. The root mean square error (RMSE) between the predicted results and the true values ​​is calculated, and this RMSE is used as the fitness function. The population undergoes selection, crossover, and mutation operations using the genetic algorithm to obtain a new generation of population. Decoding this new population generates a new parameter set. Based on the multiple sets of parameters in the parameter set and the training set, multiple S-SVR models based on the new parameter sets are formed and calculated. The fitness values ​​of each individual in the new generation are calculated. Evolution proceeds along the path of individuals with decreasing fitness values ​​until the termination condition is met. At this point, the individual with the smallest fitness function value is selected from all individuals in the current population, and the optimal parameter set is decoded and used as the parameters for the final S-SVR model. The corresponding S-SVR surrogate model is then obtained. The prediction results of this S-SVR model on the training and test sets are compared. The predictive power of the surrogate model is evaluated using the R-squared value and MAE value. If both the R-squared value and MAE value meet the thresholds set according to requirements, the S-SVR surrogate model is considered the optimal S-SVR surrogate model and is used for subsequent uncertainty analysis. If the thresholds are not met, the process returns to the iterative evolution step of the genetic algorithm to re-optimize the S-SVR model parameters.

8. The method for uncertainty analysis of mechanical product assembly performance simulation according to claim 1, characterized in that, The Sobol global sensitivity analysis method is used to quantify the uncertainty of various process parameters, including: Set the upper and lower limits V for each process parameter. maxi V mini Given a sample size N, a Sobol sequence of input process parameter variable data is generated based on N. The input process parameter variable data matrix R is then split, with the first D columns forming matrix A and the last D columns forming matrix B. Multiple new input process parameter variable matrices AB are constructed by replacing the columns of these matrices. 1 AB 2 ...AB D Substitute multiple sets of new input process parameter variable matrices and matrices A and B into the previously constructed S-SVR optimal surrogate model to generate multiple sets of Y-value matrices YA, YB, and YAB corresponding to each set of process parameter variables. 1 YAB 2 ...YAB D Finally, the first-order influence index S is calculated based on each Y-value matrix. i With the total effect index in This ultimately quantified the influence of various first-class and second-class process parameters on the displacement of the mating surface area of ​​the assembly parts during the simulation process. Based on the sensitivity of each process parameter, the process parameters were adjusted to optimize the assembly performance.

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