Mechanical product assembly performance simulation uncertainty analysis method

Abstract

The invention provides a mechanical product assembly performance simulation uncertainty analysis method. According to the method, the influence of each uncertainty influence factor on the assembly performance in different links of the simulation process is considered, the uncertainty influence factors in the simulation process are divided into two types, and quantitative analysis of uncertainty is carried out respectively. The first class comprises a measurement link, a modeling link and a simulation analysis link in the early stage of simulation, and the influence factors of the class can be used for directly calculating the uncertainty u or error; the second type of influence factors are external loads, boundary conditions and assembly performance uncertainty caused by non-linear links caused by process parameters mainly including geometric error distribution, and for the type of influence factors, the method combines optimal SVR proxy model construction and Sobol global sensitivity analysis on the basis of a simulation analysis result of a physical digital twinborn model, so that the assembly performance uncertainty caused by the non-linear links caused by the process parameters mainly including the external loads, the boundary conditions and the process parameters mainly including the geometric error distribution is obtained. And quantitatively analyzing the sensitivity of the assembly performance to the process parameters. In conclusion, the method provides guidance for the product assembly process.

Description

Technical Field

[0001] The present application relates to the technical field of precision mechanical assembly, and in particular to a method for analyzing uncertainty in mechanical product assembly performance simulation. Background Art

[0002] In the field of precision mechanical assembly technology, assembly quality has an important impact on product performance. In order to predict and evaluate the final assembly performance of the product, the finite element simulation analysis method is usually used for the assembly process of product parts, and the simulation results are combined to provide quantitative guidance for the specific assembly process. However, since there are many factors in the simulation analysis process of product assembly, including modeling errors and simulation analysis errors, which affect the final simulation prediction and evaluation results, and ultimately affect the true and reliable guidance of the product assembly process, it is necessary to introduce uncertainty theory for the simulation analysis process of product assembly, explore the uncertainty influencing factors, and quantify and evaluate the influence of various influencing factors of the simulation process on the final assembly performance.

[0003] At present, the uncertainty analysis and evaluation methods for product assembly simulation processes usually only consider the modeling error and simulation analysis error of parts and components, where the modeling error only includes the change of the ideal model size of the parts and components, and the simulation analysis error includes the errors caused by the model's physical material parameters, boundary conditions, load conditions, mesh division, etc. However, in the actual assembly process, when simulating and analyzing the precision mechanical system, the existing technology does not fully consider the actual geometric errors and their distribution of the joint surfaces of the key parts of the assembly on the contact state after assembly and the assembly performance of the product, which leads to a large error in the quantitative analysis of the uncertainty influencing factors in the simulation analysis process compared with the actual situation, making it difficult to play a good guiding role in the actual assembly process. In summary, it is urgent to innovate and invent a mechanical product assembly performance simulation uncertainty analysis method that can fully consider the actual geometric errors and their distribution of the joint surfaces of key parts and components in the actual assembly process and reasonably classify the various uncertainty influencing factors in the simulation analysis process, and conduct standardized quantitative analysis and quantitative evaluation of each uncertainty influencing factor according to the classification, so as to provide sufficient guidance for the actual assembly process of the product. Summary of the invention

[0004] The present application provides a method for analyzing uncertainty in the simulation of mechanical product assembly performance, so as to quantitatively analyze the uncertainty of various influencing factors in the simulation process. The method includes:

[0005] The uncertainty factors affecting assembly performance in different links of the simulation process are considered and classified according to different links. This method divides the uncertainty factors in the simulation process into two categories, and then conducts quantitative analysis of the uncertainty respectively.

[0006] The first type of uncertainty influencing factors includes the measurement stage, modeling stage, and simulation analysis stage in the early stage of simulation.

[0007] For the measurement link in the first category of uncertainty influencing factors, the joint surfaces of key assembly parts are accurately measured, the topographic features of the complex surfaces of key parts are digitized, and the uncertainty of the measurement and detection link is quantitatively analyzed. Finally, only the impact of the accuracy of the measuring equipment is considered. Since the length term of the coordinates of the surface points of the workpiece 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.

[0008] For the modeling link in the first category of uncertainty influencing factors, that is, based on the actual measured point cloud data of the joint surface of the key parts of the assembly obtained in the measurement link, a physical digital twin model of the mechanical product assembly is constructed, and the surface modeling accuracy analysis of the physical digital twin model constructed by this method is performed. The accuracy analysis method of the modeling link is as follows: select the modeling point set and the test point set respectively, use the modeling point set to generate the error surface, calculate the closest distance from each verification point in the test point set to the error surface, and calculate the MAE value as the mean absolute error of the modeling link.

[0009] For the simulation link in the first category of uncertainty influencing factors, the errors in the calculation results mainly include model errors and calculation errors. The errors in the simulation link vary according to the different simulation software, the assignment of material physical property parameters, the grid size division, the grid type and other settings, and 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, the first type of process parameters including external loads and boundary conditions and the second type of process parameters mainly composed of geometric error distribution that cause contact nonlinearity, and comprehensively quantifies the impact of these two types of process parameters on the uncertainty of assembly performance.

[0011] The physical digital twin model, i.e. the virtual assembly, established in the modeling phase is subjected to finite element simulation analysis. During the simulation process, the joint 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 the loads and boundary conditions are 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 post-processed, and the average joint surface displacement of each region is calculated based on the finite element simulation calculation results.

[0012] The process parameters that cause nonlinear links and are mainly based on geometric error distribution are regarded as the second type of process parameters. This method combines statistical description with finite element analysis model, comprehensively evaluates the geometric error distribution of each area of ​​the joint surface of key components, and quantifies multiple second type process parameters to evaluate the geometric error distribution of each area.

[0013] The first and second type of process parameters in each area are taken as independent variables, and the bonding surface displacement is taken as the dependent variable to form a sample set with process parameter-bonding surface displacement data in multiple areas, which is used for subsequent proxy model construction and uncertainty analysis.

[0014] After completing the construction of the process parameter-bonding surface displacement sample set, the single output support vector regression (S-SVR) machine learning algorithm is used to adapt to the strong nonlinearity and limited data characteristics of the sample set. The relationship between the input and output is fitted based on the known sample set, and the value of each parameter in the S-SVR method is optimized in combination with the principle of genetic algorithm. Finally, the optimal S-SVR proxy model is established.

[0015] This method is based on the established optimal S-SVR proxy model, and uses the Sobol global sensitivity analysis method to quantify the uncertainty of each process parameter. The relationship between the model output response and the input variable is analyzed by calculating the variance, and the first-order influence index S i Used to quantify the sensitivity of each process parameter to the model and calculate the total effect index S Ti It is used to indicate the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the regional joint surface, where i is the i-th process parameter. This method thus quantifies the influence of each first-class process parameter and second-class process parameter on the displacement of the regional joint surface of the assembly component joint surface. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

[0016] It can be seen from the above technical scheme that the uncertainty factors affecting the assembly performance in different links of the simulation process are considered in this application, and are classified according to different links. This method divides the uncertainty factors in the simulation process into two categories, and then performs quantitative analysis of uncertainty respectively. The first category of uncertainty factors includes the measurement link, modeling link, and simulation analysis link in the early stage of simulation. For the measurement link in the first category of uncertainty factors, the joint surface of the key parts of the assembly is accurately measured, the morphological features of the complex surface of the key parts are digitized, and the uncertainty quantitative analysis of the measurement and detection link is performed. Finally, 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 calculate the uncertainty of the measurement link. For the modeling link in the first category of uncertainty factors, that is, according to the actual measurement point cloud data of the joint surface of the key parts of the assembly obtained in the measurement link, a physical digital twin model of the mechanical product assembly is constructed, and the surface modeling accuracy analysis of the physical digital twin model constructed by this method is performed, and the modeling point set and the test point set are selected respectively, and the error surface is generated using the modeling point set, and 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 link. For the simulation link in the first category of uncertainty influencing factors, the errors of the calculation results mainly include model errors and calculation errors. The errors in the simulation link vary according to the different simulation software, the assignment of material physical property parameters, the grid size division, the grid type and other settings, and the error values ​​of each influencing factor are calculated separately according to actual needs. This method focuses on the uncertainty analysis of the second category of influencing factors, that is, the first category of process parameters including external loads and boundary conditions and the second category of process parameters mainly based on geometric error distribution that cause contact nonlinearity, and comprehensively quantifies the influence of these two categories of process parameters on the uncertainty of assembly performance. The physical digital twin model established in the modeling link, that is, the virtual assembly, is subjected to finite element simulation analysis. In the simulation process, the joint surfaces of the key components of the virtual assembly are divided into multiple regions, and external loads and boundary conditions are applied to the virtual assembly, and they are used as the first category 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 post-processed, and the average joint surface displacement of each region is calculated based on the finite element simulation calculation results. The process parameters that cause nonlinear links and are mainly geometric error distribution are taken as the second type of process parameters. This method combines statistical description with finite element analysis models, conducts a comprehensive evaluation of the geometric error distribution of each region of the joint surface of key components, and quantifies multiple second type process parameters to evaluate the geometric error distribution of each region. The first and second type process parameters of each region are taken as independent variables, and the joint surface displacement is taken as the dependent variable, forming a sample set with process parameter-joint surface displacement data of multiple regions for subsequent proxy model construction and uncertainty analysis.After completing the construction of the process parameter-joint surface displacement sample set, the single output support vector regression (S-SVR) machine learning algorithm is used to adapt to the characteristics of the sample set with strong nonlinearity and limited data volume, and the relationship between the input and output is fitted based on the known sample set. 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 proxy model is established. Based on the established optimal S-SVR proxy model, this method uses the Sobol global sensitivity analysis method to quantitatively analyze the uncertainty of each process parameter, and analyzes the relationship between the model output response and the input variable by calculating the variance, and obtains the first-order influence index S respectively. i Used to quantify the sensitivity of each process parameter to the model and calculate the total effect index S Ti It is used to indicate the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the regional joint surface, where i is the i-th process parameter. This method thus quantifies the influence of each first-class process parameter and second-class process parameter on the displacement of the joint surface of the assembly parts. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

[0017] It can be seen that the technical solution provided in this embodiment is based on considering the actual geometric errors and their distribution of the joint surfaces of key components in the actual assembly process, classifying the uncertainty influencing factors in the simulation process, and conducting standardized quantitative analysis and quantitative evaluation of each uncertainty influencing factor based on the classification. Among them, a proxy model is constructed for the main uncertainty influencing factors, the reliability of the proxy model is verified, and the corresponding global sensitivity analysis is performed. In summary, this technical solution can fully consider the various uncertainty influencing factors when simulating and analyzing the actual assembly process, and provide a reliable analysis method and data basis for subsequent product improvement design and assembly links, thereby improving assembly accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0019] Figure 1 A mechanical product assembly performance simulation uncertainty analysis method provided in an embodiment of the present application;

[0020] Figure 2 A schematic diagram of the classification of uncertainty influencing factors provided in an embodiment of the present application. This method divides the uncertainty influencing factors in the simulation process into two categories, and then performs quantitative analysis of the uncertainty respectively.

[0021] Figure 3The joint surface of the key parts of the flange-bolt connection structure assembly provided in the embodiment of the present application is divided into multiple regions. The method fully considers the non-uniformity of the surface geometric error distribution and explores the average joint surface displacement Δδ of each region. k , and uncertainty analysis is performed 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 embodiment of the present application, where the horizontal axis represents the number of different regions and the vertical axis represents the average displacement Δδ of the binding surface corresponding to the region k .

[0023] Figure 5 The Sobol global sensitivity analysis results provided in the embodiment of the present application, the horizontal axis is the serial number of different process parameters, and the vertical axis is the global sensitivity analysis evaluation index S i , S Ti , i is the serial number of different process parameters. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] See also Figure 1 , Figure 1 A mechanical product assembly performance simulation uncertainty analysis method is provided, the method comprising the following steps:

[0026] Step 101 , considering the uncertain influencing factors that have an impact on assembly performance in different links during the simulation process, and classifying them according to different links. Figure 2 This is a schematic diagram of the classification of uncertainty influencing factors in the simulation process. This method divides the uncertainty influencing factors in the simulation process into two categories, and then performs quantitative analysis of the uncertainty respectively.

[0027] The classification according to different links is to divide the uncertainty influencing factors into the first category and the second category. The first category of influencing factors includes various links in the early stage of simulation, namely, measurement link, modeling link, and simulation link; the second category of influencing factors are various process parameters in the assembly process.

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

[0029] Step 102, uncertainty analysis is performed on the measurement link, modeling link, and simulation link in the first category of uncertainty influencing factors, wherein the measurement link considers the corresponding nominal measurement error u0 of the measuring equipment to calculate the uncertainty of the measurement link; the modeling link constructs a physical digital twin model of the mechanical product assembly, and performs surface modeling accuracy analysis on the constructed physical digital twin model; the simulation link calculates model error and calculation error according to actual needs.

[0030] This embodiment performs uncertainty analysis on the first type of uncertainty influencing factors, wherein the measurement link calculates the uncertainty by querying the specific parameters of the measuring equipment, the modeling link calculates the closest distance from each verification point in the test point set to the error surface and calculates the MAE value as the mean absolute error of the modeling link, and the error in the simulation link varies according to the different simulation software, the assignment of material physical property parameters, the grid size division, the grid type and other settings.

[0031] Step 103, focusing on the uncertainty analysis of the second type of influencing factors, performs finite element simulation analysis on the physical digital twin model, i.e., the virtual assembly, divides the joint surface of the key components of the virtual assembly into multiple regions, and obtains simulation results. The simulation results are post-processed, and the average joint surface displacement of each region is calculated based on the finite element simulation calculation results. A comprehensive evaluation is performed on the geometric error distribution of each region of the joint surface of the key components, and a plurality of second-type process parameters are quantified to evaluate the geometric error distribution of each region.

[0032] In this embodiment, the second type of influencing factors are the first type of process parameters including external loads and boundary conditions and the second type of process parameters mainly composed of geometric error distribution that cause contact nonlinearity.

[0033] Step 104, establish a process parameter-joint surface displacement sample set, use a single output support vector regression (S-SVR) machine learning algorithm, and fit the relationship between the input and output based on the known sample set, combine the genetic algorithm principle to optimize the values ​​of each parameter in the S-SVR method, and establish the final S-SVR proxy model. Compare the prediction results of the training set and the test set of the S-SVR model, and evaluate the prediction degree of the proxy model by the R-square value and the MAE value. If the R-square value and the MAE value both meet the threshold set according to the requirements, the S-SVR proxy model is considered to be the optimal S-SVR proxy model for subsequent uncertainty analysis. If the threshold is not met, return to the re-iterative evolution step of the genetic algorithm to re-optimize the S-SVR model parameters.

[0034] The principle of selecting the proxy model construction method in this step is based on the two major characteristics of the process parameter-joint surface displacement sample set: (1) There is a strong nonlinearity between the process parameter and the joint surface displacement. (2) The number of samples is small, mainly between dozens 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 proxy model, the Sobol global sensitivity analysis method is used to perform quantitative analysis of the uncertainty of each process parameter, and the relationship between the model output response and the input variable is analyzed by calculating the variance to obtain the first-order influence index S i Used to quantify the sensitivity of each process parameter to the model and calculate the total effect index S Ti It is used to indicate the sensitivity of the interaction between a single process parameter and other input process parameters to the regional displacement, i is the ith process parameter. This method thus quantifies the influence of each first-class process parameter and second-class process parameter on the regional displacement of the assembly component joint surface.

[0036] So far, completed Figure 1 Description shown.

[0037] In order to make the above embodiment easier to understand, a specific example is given below, taking the flange-bolt connection structure as an example, specifically:

[0038] Step 1: Consider the uncertainty factors that affect the assembly performance during the simulation analysis of the flange-bolt connection structure, and classify them according to different links. The first category of uncertainty factors includes the measurement of the geometric errors of the joint surfaces of key components in the early stage of simulation, the modeling of the physical digital twin model of the assembly, and the simulation analysis of the simulation parameters of the physical digital twin model, i.e., the virtual assembly. The second category of uncertainty factors includes external loads and boundary conditions as the first category of process parameters, and the geometric error distribution evaluation parameters on the joint surfaces of key components of the flange-bolt connection structure as the second category of process parameters.

[0039] Step 2: First, conduct uncertainty analysis on the first type of influencing factors.

[0040] Regarding the measurement of this structure, some factors including the measurement personnel, measurement strategy, i.e., the number of sampling points of the equipment, and measurement environment are normalized to eliminate the influence of these interfering factors. The object to be measured is similar to a rigid body, so the uncertainty introduced by stress concentration deformation during measurement can be ignored. Therefore, the current research focuses on the errors existing in the measurement equipment itself, and since the measurement object is the coordinates of the surface point of the workpiece, the L component in the indication error can be ignored, and only the nominal measurement error u0 is considered for uncertainty calculation, and finally the Class B uncertainty generated by the nominal measurement error of the three-coordinate measuring machine used is adopted.

[0041] Regarding the modeling phase of the structure, firstly, based on the actual measured point cloud data of the flange-bolt connection structure key component joint surface obtained in the measurement phase, the non-uniform rational B-spline, i.e., NURBS surface modeling technology, is used to interpolate and reconstruct the point cloud data model to form an error surface, and generate an IGES format for importing into the CAD software to generate the joint surface error surface; the error surface is subjected to Boolean operation with the ideal three-dimensional model of the target assembly to form a component joint surface with distributed errors; the target assembly is virtually assembled in the three-dimensional model according to certain constraints to obtain a virtual assembly with an 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 closest distance from each verification point to the surface model is calculated. Finally, the mean absolute error of all verification points, i.e., the MAE value, is calculated. The smaller the MAE value, the higher the surface modeling accuracy. Where m is the number of verification points, Q j represents the jth verification point, It is the closest point on the NURBS surface corresponding to the verification point, where the coordinates of the closest point are obtained by projecting the verification point onto the error surface.

[0042] Regarding the simulation phase of the structure, the physical digital twin model of the flange-bolt connection structure constructed in the modeling phase is imported into the finite element simulation analysis software ABAQUS, and the simulation parameters are set. The uncertainty influencing factors in the simulation parameter setting, that is, the error terms generated in the establishment of the finite element model, include model error and calculation error. The model error includes discrete error, boundary condition error, and unit shape error. The discrete error is divided into physical discrete error and geometric discrete error. The calculation error includes rounding error and truncation error. Each error varies according to the different simulation software, the assignment of material physical property parameters, the grid size division, the grid type and other settings. It is still necessary to calculate the error value of each influencing factor according to actual needs.

[0043] Step three, focus on the uncertainty analysis of the second type of influencing factors. Simulate the physical digital twin model of the flange-bolt connection structure established in the modeling phase, that is, the virtual assembly, to obtain its simulation results under various assembly processes. During the simulation process, the joint surface of the key components of the virtual assembly is divided into n areas, such as Figure 3 As shown. External loads and boundary conditions are applied to the virtual assembly and used as the first type of process parameters. For this object, the first type of process parameters involved mainly include bolt preload F N , tensile load, bending load, torsion 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, and the contact surface node set of the upper and lower surfaces of the region is established based on the equally divided different regions. The displacement data of the upper and lower contact surfaces of each region in the finite element analysis results are extracted in combination with the python secondary development script, and the node set set displacement data set in the odb file of the simulation software ABAQUS is exported in a table form to obtain the upper and lower surface node displacement set ∑(x, y, z) of each equally divided region of the joint surface of the key components of the flange-bolt connection structure, and the node data average calculation is used to obtain the node average joint surface displacement of the upper and lower surfaces of the region. Then calculate the average displacement of the joint surface in each area A comprehensive evaluation is conducted on the geometric error distribution of each region of the joint surface of the key components of the flange-bolt connection structure, and multiple second-category process parameters are quantified to evaluate the geometric error distribution of each region. This part of the process parameter evaluation takes the GW model based on the Hertz contact theory as the theoretical basis, extracts and calculates the upper and lower surface node data of each region of the joint surface of the key components of the flange-bolt connection structure through finite element analysis post-processing, and is equivalent to a rough surface node data set and another smooth rigid plane. The equivalent rough surface node data set is statistically analyzed, and the least squares flatness fitting value a and the average height of the convex hull of its surface node coordinate data are performed. Calculation of two second category process parameters.

[0044] Step 4: Use the first and second type of process parameters in each area of ​​the joint surface of the key components of the flange-bolt connection structure as independent variables and the joint surface displacement as the dependent variable to form a sample set with process parameter-joint surface displacement data in multiple areas. Use the single output support vector regression (S-SVR) machine learning algorithm to construct the proxy model, divide the sample set into a training set and a test set according to a certain ratio, select the kernel function type as the radial basis kernel function RBF, and set the range of the three parameters of the penalty factor c, kernel function parameter γ, and p. Calculate the root mean square error between the predicted result and the true value, and use the root mean square error as the fitness function to generate an initial population containing the three parameters and use the genetic algorithm to iteratively evolve the three parameters. Finally, the parameter combination with the smallest fitness function value is obtained as the parameter for establishing the final S-SVR model. Set the R-square value threshold to 0.95 and the MAE value to 0.005, and compare the prediction results of the training set and the test set of the S-SVR model. The prediction results are compared. Figure 4 As shown in the figure, if both the R-square value and the MAE value meet the thresholds set according to the requirements, the S-SVR proxy model is considered to be the optimal S-SVR proxy model and can be used for subsequent uncertainty analysis.

[0045] Step 5: For the optimal S-SVR proxy model obtained in step 4, the Sobol global sensitivity analysis method is used to quantitatively analyze the uncertainty of each process parameter. For the joint surface of the key parts of the flange-bolt connection structure, the screw preload F is selected. N , the least squares flatness fitting value a of the regional equivalent rough surface and the average height of the convex hull The three process parameters were used as the first, second, and third influencing factors to establish the optimal S-SVR proxy model for the displacement of the regional bonding surface, and the Sobol global sensitivity analysis was performed. The distribution intervals of each process parameter were set respectively, and the sample space was randomly generated. The relationship between the model output response and the input variable was analyzed by calculating the variance, and the first-order influence index S i Used to quantify the sensitivity of each process parameter to the model and calculate the total effect index S Ti It is used to indicate the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the regional joint surface. The statistical results are as follows: Figure 5 As shown in the figure, the distribution range that can be set, the sensitivity of each process parameter to the displacement of the regional joint surface is ranked as follows: the average height of the convex hull >Screw preload F N>The least squares flatness fitting value a of the regional equivalent rough surface is obtained, and the sensitivity is quantified. This completes the quantification of the influence of process parameters on assembly performance during the simulation process. 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-bolt connection structure.

[0046] Regarding the existing common simulation uncertainty analysis methods, when conducting uncertainty analysis on the assembly performance of mechanical products during the simulation process, ideal models are often used to set simulation parameters, without considering the geometric error distribution of the real morphology of the joint surface and conducting a more systematic and scientific statistical analysis. This method establishes a physical digital twin model of the assembly based on measured point cloud data to accurately characterize the real morphology of the joint surface of key components of the assembly and conduct simulation analysis, considering the uncertainty impact brought by the measurement link, modeling link, and simulation setting link; the joint surface is averaged and the surface geometric error distribution is comprehensively evaluated and calculated by combining the comprehensive finite element model with the statistical description; according to the sample set established by the simulation results and process parameters, the S-SVR machine learning algorithm, which is more suitable for objects with small sample size and strong sample nonlinearity, is combined with the genetic algorithm to optimize the parameters. The proxy model of assembly performance is constructed and the model accuracy is verified. Then, the Sobol global sensitivity analysis method is used to comprehensively evaluate the influence of each process parameter on the assembly performance and the influence of each process parameter on the assembly performance, so that the uncertainty analysis results are more comprehensive. In summary, this method is used to analyze the uncertainty influencing factors of the assembly performance of mechanical products during the simulation process, which has good reliability.

[0047] Taking a mechanical product with a structure similar to a flange-bolt connection structure as an example, the effectiveness of this method is demonstrated, and it can be applied to the summary and induction of uncertainty analysis of assembly performance in the simulation process of mechanical products with similar structures. This method provides a reliable analysis method and data basis for subsequent product improvement design and assembly links, 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 in the scope of protection of the present invention.

Claims

1. A mechanical product assembly performance simulation uncertainty analysis method, characterized in that: The method includes: The uncertainty factors affecting assembly performance in different links of the simulation process are considered and classified according to different links. This method divides the uncertainty factors in the simulation process into two categories, and then conducts quantitative analysis of the uncertainty respectively. The first type of uncertainty influencing factors includes the measurement stage, modeling stage, and simulation analysis stage in the early stage of simulation. For the measurement link in the first category of uncertainty influencing factors, the topographic features of the complex surfaces of the key components of the assembly are digitized by accurately measuring the joint surfaces of the key components, and the uncertainty quantitative analysis of the measurement and detection link is performed. Finally, only the impact of the accuracy of the measuring equipment is considered. Since the length term of the coordinates of the surface points of the workpiece 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 link in the first category of uncertainty influencing factors, that is, based on the actual measured point cloud data of the joint surface of the key parts of the assembly obtained in the measurement link, a physical digital twin model of the mechanical product assembly is constructed, and the surface modeling accuracy analysis of the physical digital twin model constructed by this method is performed. By selecting the modeling point set and the test point set respectively, the error surface is generated using the modeling point set, and the closest distance from each verification point in the test point set to the error surface is calculated, and the MAE value is calculated as the mean absolute error of this modeling link. For the simulation link in the first category of uncertainty influencing factors, the errors in the calculation results mainly include model errors and calculation errors. The errors in the simulation link vary according to the simulation software, the material physical property parameters, the grid size division, the grid type and other settings. Therefore, the error values ​​of each influencing factor are calculated separately according to actual needs. This method focuses on the uncertainty analysis of the second type of influencing factors, which are the first type of process parameters including external loads and boundary conditions and the second type of process parameters mainly composed of geometric error distribution that cause contact nonlinearity. Uncertainty analysis is performed to comprehensively quantify the impact of these two types of process parameters on the uncertainty of assembly performance. This method first establishes a physical digital twin model, i.e., a virtual assembly, in the modeling process, and performs finite element simulation analysis. During the simulation process, the joint surfaces of the key components of the virtual assembly are divided into multiple regions, and external loads and boundary conditions are applied to the virtual assembly, and the loads and boundary conditions are 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 post-processed, and the average joint surface displacement of each region is calculated based on the finite element simulation calculation results. The process parameters that cause nonlinear links and are mainly based on geometric error distribution are regarded as the second type of process parameters. This method combines statistical description with finite element analysis model, comprehensively evaluates the geometric error distribution of each area of ​​the joint surface of key parts of the assembly, and quantifies multiple second type process parameters to evaluate the geometric error distribution of each area. The first and second type of process parameters in each area are taken as independent variables, and the bonding surface displacement is taken as the dependent variable to form a sample set with process parameter-bonding surface displacement data in multiple areas, which is used for subsequent proxy model construction and uncertainty analysis. After completing the construction of the process parameter-bonding surface displacement sample set, the single output support vector regression (S-SVR) machine learning algorithm is used to adapt to the strong nonlinearity and limited data characteristics of the sample set. The relationship between the input and output is fitted based on the known sample set, and the value of each parameter in the S-SVR method is optimized in combination with the principle of genetic algorithm. Finally, the optimal S-SVR proxy model is established. This method is based on the established optimal S-SVR proxy model, and uses the Sobol global sensitivity analysis method to quantify the uncertainty of each process parameter. The relationship between the model output response and the input variable is analyzed by calculating the variance, and the first-order influence index S i Used to quantify the sensitivity of each process parameter to the model and calculate the total effect index S Ti It is used to indicate the sensitivity of the interaction between a single process parameter and other input process parameters to the displacement of the regional joint surface, where i is the i-th process parameter. This method thus quantifies the influence of each first-class process parameter and second-class process parameter on the displacement of the regional joint surface of the assembly parts during the simulation process. Similarly, this method can be used to evaluate the uncertainty analysis of process parameters on other assembly performance indicators.

2. A mechanical product assembly performance simulation analysis method according to claim 1, characterized in that: According to different links, the uncertainty influencing factors are divided into two categories, including: The uncertainty influencing factors are divided into the first and second categories of uncertainty influencing factors. The first category of influencing factors includes all links in the measurement and modeling process, namely the measurement link, modeling link, and simulation link; the measurement link and the modeling link fully consider the actual geometric errors and their distribution on the joint surfaces of key parts of the assembly in the actual assembly process to conduct uncertainty analysis, and prepare for the subsequent simulation analysis link and the quantitative analysis of the second category of uncertainty influencing factors. The second category of influencing factors are various process parameters in the assembly process, which are divided into the first category of process parameters including external loads and boundary conditions and the second category of process parameters mainly based on geometric error distribution that cause contact nonlinearity. The second category of influencing factors are the main types of uncertainty influencing factors in the simulation analysis process of mechanical product assembly performance.

3. The method for analyzing uncertainty in mechanical product assembly performance simulation according to claim 1, characterized in that: Establishing a physical digital twin model in the modeling phase includes: The point cloud data of the key parts joint surfaces of the assembly are extracted, and the point cloud data model is interpolated and reconstructed using non-uniform rational B-spline, i.e., NURBS surface modeling technology, to form an error surface, and an IGES format is generated for importing into CAD software to generate the error surface; the error surface is Boolean operated with the ideal three-dimensional model of the target assembly to form a parts joint surface with distributed errors; the target assembly is virtually assembled in the three-dimensional model according to certain constraints to obtain a virtual assembly with an error surface.

4. The method for analyzing uncertainty in mechanical product assembly performance simulation according to claim 1, characterized in that: Conduct surface modeling accuracy analysis, including: The point cloud data obtained in the measurement phase is divided into a modeling point set and a verification point set. The modeling point set is used to establish a NURBS surface, and the closest distance from each verification point to the surface model is calculated. Finally, the mean absolute error of all verification points, i.e., the MAE value, is calculated. The smaller the MAE value, the higher the surface modeling accuracy. Where m is the number of verification points, Q j represents the jth verification point, It is the closest point on the NURBS surface corresponding to the verification point, where the coordinates of the closest point are obtained by projecting the verification point onto the error surface.

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

6. The method for analyzing uncertainty in mechanical product assembly performance simulation according to claim 1, characterized in that: Combining statistical description with finite element analysis model, the geometric error distribution of each area of ​​the joint surface of key parts of the assembly is comprehensively evaluated and quantified into multiple second-class process parameters to evaluate the geometric error distribution of each area, including: Taking the GW model based on Hertz contact theory as the theoretical basis, the upper and lower surface node data of each area of ​​the joint surface of the key components of the assembly are extracted and calculated through finite element analysis post-processing, which is equivalent to a rough surface node data set 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, the information entropy of the convex hull height distribution and other parameters as the second type of process parameters.

7. The method for analyzing uncertainty in 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. The kernel function type is selected as the radial basis kernel function RBF, and the ranges of the three parameters of the penalty factor c, the kernel function parameter γ, and p are set. The initial population containing the three parameters is generated in combination with the genetic algorithm principle, and the parameters required by the genetic algorithm such as the crossover probability, the mutation probability, and the number of iterations are determined. The initial population is decoded and different parameter groups are obtained. They are substituted into the S-SVR model to predict the output of the training set, and the root mean square error between the predicted result and the true value is calculated, and the root mean square error is used as the fitness function. The population is subjected to genetic algorithm operations such as selection, crossover, and mutation to obtain a new generation of populations. The population decoding generates a new parameter set. According to the multiple sets of parameters of the parameter set and the training set, multiple S-SVR models based on the new parameter set are formed and the fitness values ​​of each individual of the new generation are calculated. According to the individual direction with gradually decreasing fitness value, it evolves until the termination iteration condition is reached. At this time, the individual with the smallest fitness function value is selected from all individuals in the current population, and the optimal parameter group is decoded to obtain the parameters for the final establishment of the S-SVR model, and the corresponding S-SVR proxy model is finally obtained. The prediction results of the training set and the test set of the S-SVR model are compared, and the prediction degree of the proxy model is evaluated by the R-square value and the MAE value. If the R-square value and the MAE value both meet the threshold set according to the requirements, the S-SVR proxy model is considered to be the optimal S-SVR proxy model for subsequent uncertainty analysis. If the threshold is not met, return to the re-iterative evolution step of the genetic algorithm to re-optimize the S-SVR model parameters.

8. The method for analyzing uncertainty in 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 each process parameter, including: Set the upper and lower limits V of each process parameter maxi 、V mini With the sample sampling number N, generate the Sobol sequence input process parameter variable data according to the sampling number N, and split the input process parameter variable data matrix R, the first D columns are matrix A, and the last D columns are matrix B. By replacing the columns of the matrix, multiple sets of new input process parameter variable matrices AB are constructed 1 , A.B. 2 ...AB D , substitute multiple sets of new input process parameter variable matrices and matrices A and B into the S-SVR optimal proxy model constructed earlier to generate multiple sets of Y value matrices YA, YB, 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 Total effect index in In this way, the influence of each first-class process parameter and second-class process parameter on the displacement of the assembly component joint surface area during the simulation process is quantified, and each process parameter can be adjusted according to its sensitivity to achieve the effect of optimizing assembly performance.

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