Free pipe bending device machining limit prediction method based on multi-body implicit interference inference

Abstract

The invention discloses a method for predicting the machining limit of a free pipe bending device based on multi-body implicit interference inference. Comprising the following steps: firstly, obtaining the overall representation of a to-be-tested free elbow device, obtaining respective joint prediction intervals of curvature and torsion of a to-be-processed elbow by using an operator fusion network, and judging whether interference occurs between the to-be-processed elbow and the to-be-tested free elbow device under each rebound axis; finally, whether interference occurs between the bent pipe to be processed and the free bent pipe device to be detected or not is obtained. And whether interference occurs between the dies is determined by using the symbol distance value. The method has excellent generalization performance, has reliable pipe section-mold interference inference capability, and can realize more comprehensive processing limit prediction of the free pipe bending device.

Description

Technical Field

[0001] This invention belongs to the field of free bending forming of pipe fittings, and specifically relates to a method for predicting the processing limit of free bending pipe devices based on multibody implicit interference inference. Background Technology

[0002] The free bending device is the core of free bending forming technology for pipe fittings. During free bending forming, interference can directly lead to bending failure. Interference in free bending mainly falls into two categories: first, the formed pipe segment ejected from the bending die, due to its complex structure and lack of die-wrapping constraints, is highly susceptible to interference with various dies on the device; second, interference between dies may occur during the position adjustment process due to the influence of structural layout and motion path. The boundary of the bending forming parameter range that the free bending device can process under interference-free conditions is defined as the processing limit of the device. Determining the processing limit requires considering both the geometric characteristics of the device and the springback behavior of the formed pipe segment.

[0003] Because free-bending pipe devices typically require customized design, their geometric structures vary widely, with significant differences in spatial configuration and dimensional parameters between different devices. Changes in the device structure directly alter its processing limits. Simultaneously, the formed pipe segment undergoes complex springback deformation after free bending. This process is influenced by a combination of factors, including pipe material parameters, geometric parameters, and free-bending process parameters, exhibiting pronounced nonlinear characteristics. The structural changes in the pipe segment caused by springback increase the uncertainty of interference between the pipe segment and the mold, making accurate determination of processing limits even more difficult. Traditional methods for determining the processing limits of free-bending pipe devices based on experience, geometric analysis, and numerical simulation suffer from low efficiency, high cost, poor accuracy, and poor generalization, making it difficult to meet the diverse needs of practical engineering applications.

[0004] Therefore, there is an urgent need for an efficient method for predicting processing limits that can simultaneously consider the customized structural features of free bending devices and the springback effect of bending pipes, so as to provide a reliable theoretical basis and technical support for device design, manufacturing and structural optimization, as well as the selection of free bending process parameters. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention provides a method for predicting the processing limits of free bending devices based on multi-body implicit interference inference. This method solves the technical problems of low efficiency, high cost, poor accuracy and generalization in current methods for determining the processing limits of free bending devices. The method of this invention is a highly efficient method for predicting processing limits that can simultaneously consider the customized structural features of the free bending device and the springback effect of the bending pipe. By integrating functions such as implicit modeling of the device, springback conformal prediction and multi-body interference inference, it achieves highly reliable and generalizable prediction of the processing limits of free bending devices.

[0006] The technical solution adopted in this invention is: A method for predicting the processing limits of a free pipe bending device based on multi-body implicit interferometry inference: S1. Divide the various molds of the free bending device under test into parametric molds and non-parametric molds, and construct implicit functions for parametric molds and non-parametric molds respectively. Perform Boolean operations on all implicit functions to obtain the overall characterization of the free bending device under test.

[0007] S2. Obtain the geometric parameters, forming parameters, and bending process parameters of the pipe to be processed, and input all parameters into an operator fusion network consisting of a deep operator network and a Fourier neural operator to perform quantile prediction of the curvature and torsion sequences, thereby obtaining the final prediction sequence. Based on the final prediction sequence, the conformal quantile regression method and the boundary adaptive super rectangle method are used sequentially to process and construct the joint prediction intervals for curvature and torsion.

[0008] S3. Based on the final prediction sequence of curvature and deflection, the joint prediction interval of curvature of the bend to be processed, the joint prediction interval of deflection, and the overall characterization of the free bending device to be tested, several springback axes are obtained using the Frenet frame. It is determined whether there is any interference between each springback axis corresponding to the bend to be processed and the free bending device to be tested. If any springback axis interferes with the free bending device to be tested, then there is interference between the bend to be processed and the free bending device to be tested.

[0009] S4. Based on the overall characterization of the free bending device under test, generate several uniformly distributed query points in the space where the free bending device under test is located. Calculate the symbolic distance value from each query point to various molds of the free bending device under test. If there is a query point whose symbolic distance value to two or more molds is negative, then interference occurs between the molds.

[0010] S5. If either the bending tube to be processed interferes with the free bending tube device to be tested, or interference occurs between the mold, the free bending tube device to be tested will be unable to process the bending tube under the current forming parameters.

[0011] S6. Each time the forming parameters are changed, a new bent tube to be processed is obtained. The same method as steps S2-S5 is used to process it several times. Finally, the result is obtained as to whether the free bending device to be tested can process the bent tube under different forming parameters.

[0012] Step S1 specifically involves: S11. Simplify the structure of various molds for the free bending pipe device to be tested, and divide all the simplified molds into two categories: parametric molds and non-parametric molds.

[0013] The criteria for classifying molds into parametric and non-parametric molds are as follows: if the simplified mold is represented by one or more combinations of cuboids, cylinders, and frustums, it is classified as a parametric mold; otherwise, it is classified as a non-parametric mold.

[0014] S12. Construct the implicit function of the parameterized mold using an implicit modeling method based on analytical formulas; construct the implicit function of the non-parametric mold using a learning-based implicit modeling method.

[0015] S13. Perform Boolean operations on all implicit functions to obtain the overall characterization of the free bending pipe device under test.

[0016] The learning-based implicit modeling method constructs the implicit function of the non-parametric mold according to the following steps: D1. Determine the variable structural parameters in a non-parametric mold. Build using Solidworks tools Group variable structure parameters STL mesh models corresponding to nonparametric molds with different values ​​are generated, and all STL mesh models are scaled down to a unit cube.

[0017] D2. For each set of variable structural parameters The corresponding STL mesh model is co-sampled on the surface of the STL mesh model corresponding to the non-parametric mold and within the unit cube. A total of 10 spatial query points are identified, and perturbations are applied only to spatial query points located on the surface of the STL mesh model to deviate them from the surface. The signed distance value from each spatial query point to the surface of the STL mesh model is calculated, using the coordinates of all spatial query points and variable structural parameters. The input is the symbolic distance value, which is used to construct a single sample dataset.

[0018] D3, Several sets of variable structural parameters The dataset is obtained by summing all the sample data obtained from the corresponding STL grid model.

[0019] D4. Input the dataset into the FC-DeepSDF model for training to obtain the trained FC-DeepSDF model. The trained FC-DeepSDF model is the implicit function of the non-parametric mold.

[0020] The forward propagation process of the FC-DeepSDF model is as follows: F1, Variable structure parameters The input is fed into two parallel fully connected layers, which respectively yield the first deep feature representation. Second deep feature representation .

[0021] F2, Representing the second deep feature With the preset shared latent vector The addition yields a mixed characteristic.

[0022] F3. Perform Fourier feature encoding on the coordinates of each spatial query point to obtain the corresponding encoded spatial query point coordinates.

[0023] F4. Concatenate the coordinates of each spatial query point with the hybrid features to obtain the input vector corresponding to the coordinates of each spatial query point.

[0024] F5, representing all input vectors and the first deep feature layer. Simultaneously, the data is input into a mapping network for processing to obtain the symbolic distance values ​​of the coordinates of all spatial query points.

[0025] The mapping network consists of several linear activation units and a last characteristic linear modulation unit (FiLM) connected in series; each linear activation unit is composed of a characteristic linear modulation unit (FiLM) and a ReLU function connected in series.

[0026] Step S2 specifically involves: S21. The geometric parameters, forming parameters, and bending process parameters of the bend to be processed are first mapped to initial prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the deflection at the 0.05, 0.50, and 0.95 quantiles respectively through a depth operator network. Then, the initial prediction sequences of the curvature and deflection at the 0.05, 0.50, and 0.95 quantiles are processed by a Fourier neural operator to finally obtain the final prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the final prediction sequences of the deflection at the 0.05, 0.50, and 0.95 quantiles respectively.

[0027] S22. Based on the final predicted sequences of the curvature and deflection of the pipe to be processed at the 0.05 and 0.95 quantiles, respectively, the conformal quantile regression method is used to construct the univariate prediction intervals for curvature and deflection.

[0028] S23. Based on the individual univariate prediction intervals of curvature and torsion, the boundary adaptive super rectangle method is used to construct the joint prediction interval of curvature and torsion.

[0029] The univariate prediction intervals for the curvature and deflection of the bend to be processed are obtained by following the formula of the conformal quantile regression method: in, For curvature; For torsion; Choose curvature or torsion; The univariate prediction interval for the curvature or deflection of the bend to be processed; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.05 quantile; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.95 quantile; For the empirical quantiles of the curvature or torsion sequence; The preset confidence level; To obtain quantiles; For indexing; To calibrate the inconsistency score of the curvature or torsion sequence of the i-th sample in the set; For calibration set; The set of inconsistencies in the curvature or torsion sequences of all samples in the calibration set; To calibrate the curvature or torsion sequence predicted for the i-th sample in the set at the 0.05 quantile; To calibrate the curvature or torsion sequence of the i-th sample in the set; This is to determine the 0.95 quantile value of the curvature or torsion sequence predicted for the i-th sample in the calibration set.

[0030] The joint prediction intervals for the curvature and deflection of the bend to be processed are obtained by applying the following formula from the boundary adaptive hyperrectangle method: ; ; ; ; ; ; ; ; ; in, and These represent the joint prediction intervals for the curvature and deflection of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the final predicted sequences of the curvature of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the final predicted sequences of the deflection of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the empirical quantiles of the curvature and torsion sequences, respectively; and These represent the empirical quantiles of the lower and upper boundaries, respectively; and They represent taking quantiles and taking quantiles; and The two components represent the confidence level; Indicates the proportionality coefficient; Indicates the preset confidence level; The lower bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. The upper bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. and Let represent the curvature and torsion sequences of the i-th sample in the calibration set, respectively; and Let represent the upper and lower boundary sequences of the curvature sequence of the i-th sample in the calibration set, respectively; and Let represent the upper and lower boundary sequences of the torsion sequence of the i-th sample in the calibration set, respectively; and These represent the sequence values ​​of the curvature sequence predicted for the i-th sample in the calibration set at the 0.05 and 0.95 quantiles, respectively. and represents the torsion sequence values ​​at the 0.05 quantile and 0.95 quantile of the i-th sample in the calibration set, respectively.

[0031] Step S3 specifically involves: S31. Based on the final predicted sequences of curvature and deflection at the 0.5 quantile, samples are taken from the joint prediction intervals of curvature and deflection of the bend to be processed. Group sequence, and thus form A combination of curvature and torsion.

[0032] S32. Integrate each curvature-deflection combination using the Frenet frame to obtain the corresponding springback axis.

[0033] S33. Based on the obtained springback axis, the overall characterization of the free bending device under test, and the Frenet frame, determine whether there is any interference between each springback axis of the bending device under test and the free bending device under test.

[0034] S34, If any one of the springback axes interferes with the free bending device under test, then the current bending pipe to be processed interferes with the free bending device under test.

[0035] Each set of curvature - Torque The combination is formed by sampling and combining according to the following formula: ; ; in, and All are indexes; No. One curvature; Let j be the j-th torsion. and These are the final predicted sequences at the 0.50 quantiles of the curvature and deflection of the bend to be processed, respectively. This represents the sampling parameter corresponding to the i-th curvature; To use the total number of groups; and These are the upper and lower boundary sequences of the joint prediction interval for curvature, respectively; and These are the upper and lower boundary sequences of the joint prediction interval for torsion, respectively. Let be the piecewise cosine function with an amplitude of 1 corresponding to the j-th torsion. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the empirical quantiles of the lower and upper boundaries, respectively.

[0036] Step S33 specifically involves: for any springback axis, combining the springback axis with the overall characterization of the free bending device to be tested, and correcting the springback axis according to the actual processing state. Based on the Frenet frame and the corrected springback axis, a set of discrete points located on the surface of the bending pipe to be processed is generated. The symbolic distance value from each discrete point to the free bending device to be tested is calculated. If any discrete point has a negative symbolic distance value to the free bending device to be tested, it indicates that the current springback axis corresponding to the bending pipe to be processed interferes with the free bending device to be tested.

[0037] The beneficial effects of this invention are: (1) This invention has excellent generalization performance. Based on analytical formulas and implicit modeling methods based on FC-DeepSDF, the implicit functions of the mold can be precisely controlled by adjusting the input structural parameters, thereby adapting to changes in different mold structures. When assembling and integrating the implicit functions of the mold in a shared implicit space, the spatial layout of each mold can also be flexibly adjusted according to the equipment configuration. With this characteristic, this invention can be easily extended to predict the processing limits of different types of free bending pipe devices.

[0038] (2) This invention possesses reliable pipe-mold interference inference capability. Instead of relying on single-point prediction results of springback, this invention first constructs a prediction interval for the curvature and deflection of the bend. Then, based on the actual distribution characteristics of these two parameters, it samples potential curvature and deflection sequences within the interval and obtains multiple possible springback axes through Frenet frame integration. Based on this, spatial interference inference is performed by combining the springback axes with the implicit functions of the device. This method effectively alleviates the problem of misjudgment of interference caused by inherent errors in the prediction model and improves the stability of the inference results.

[0039] (3) This invention can achieve more comprehensive prediction of the processing limits of free pipe bending devices. The proposed interference inference method can simultaneously handle two types of problems: pipe bending-mold interference and mold-mold interference, thereby obtaining complete spatial interference distribution information of pipe bending. Based on this information, the multidimensional processing limits of the device can be accurately delineated in the pipe bending forming parameter space, realizing a comprehensive evaluation and visualization of the device's processing capabilities, and providing a theoretical basis for the structural optimization of free pipe bending devices. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention.

[0041] Figure 2 This is a schematic diagram of a six-axis free bending pipe device according to an embodiment of the present invention, wherein... Figure 2 (a) and Figure 2 (b) is a schematic diagram of the device. Figure 2 (c) is the parameterized mold of the device. Figure 2(d) is the non-parametric mold of the device.

[0042] Figure 3 (a) and Figure 3 (b) are schematic diagrams of the variable structural parameters of the bending die and the bending die support in the non-parametric mold.

[0043] Figure 4 This study aims to predict the processing limits of the free bending pipe device and verify the experimental results. Detailed Implementation

[0044] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0045] like Figure 1 As shown, the method for predicting the processing limits of the free pipe bending device in this embodiment includes the following steps: S1. Divide the various molds of the free bending device under test into parametric molds and non-parametric molds, and construct implicit functions for parametric molds and non-parametric molds respectively. Perform Boolean operations on all implicit functions in a preset shared implicit space to obtain the overall characterization of the free bending device under test. The preset shared implicit space is essentially a preset, unified, and global "factory three-dimensional coordinate system," which is a unique and global three-dimensional coordinate system that all molds must adhere to.

[0046] S11. Simplify the structure of various molds for the free bending pipe device to be tested, and divide all the simplified molds into two categories: parametric molds and non-parametric molds.

[0047] The criteria for classifying molds into parametric and non-parametric molds are as follows: if the simplified mold is represented by one or more combinations of cuboids, cylinders, and frustums, it is classified as a parametric mold; otherwise, it is classified as a non-parametric mold. In other words, if it cannot be represented by one or more combinations of cuboids, cylinders, and frustums, it is classified as a non-parametric mold.

[0048] In this embodiment, as follows Figure 2 (a) and Figure 2 (b) illustrates the application of the six-axis free bending device as a case study. In the six-axis free bending device, the motors, bearings, guide mechanisms, guide mechanism supports, support beams, moving plates, and support plates of each axis are considered as parametric molds, such as... Figure 2(c); The bending die and bending die support are considered as non-parametric dies, such as Figure 2 (d). When constructing the implicit functions for these two types of molds, structural simplification is required, such as removing mold threaded holes that do not affect subsequent interference inference.

[0049] S12. Construct the implicit function of the parameterized mold using an implicit modeling method based on analytical formulas; construct the implicit function of the non-parametric mold using a learning-based implicit modeling method.

[0050] The implicit modeling method based on analytical formulas constructs the implicit functions of the parameterized mold according to the following formula: in, An implicit function representing a parameterized mold, whose output is any point in space. The symbolic distance value to the parameterized mold boundary (a positive distance value indicates a point). Outside the parametric mold, a positive distance value indicates a point. (Inside the parametric mold) Let x be the shortest distance function from any point x in space to the boundary of the cuboid. Let x be the function representing the shortest distance from any point x in space to the boundary of the cylinder; Let x be the function representing the shortest distance from any point x in space to the boundary of the frustum.

[0051] Learning-based implicit modeling methods construct implicit functions for nonparametric molds using the following steps: D1. Determine the variable structural parameters in a non-parametric mold. Build using Solidworks tools Group variable structure parameters STL mesh models corresponding to nonparametric molds with different values ​​are generated, and all STL mesh models are scaled down to a unit cube.

[0052] D2. For each set of variable structural parameters The corresponding STL mesh model is sampled on both the surface of the STL mesh model corresponding to the non-parametric mold and within the unit cube (including the interior of the STL mesh model). A set of spatial query points is used, and only those spatial query points located on the surface of the STL mesh model are subject to a small perturbation that causes them to deviate from the surface of the STL mesh model. No perturbation is applied in the space between the STL mesh model surface and the outer surface of the unit cube. The signed distance value from each spatial query point to the STL mesh model surface is calculated, using the coordinates of all spatial query points and variable structural parameters. The input is the symbolic distance value, which is used to construct a single sample dataset.

[0053] D3, Several sets of variable structural parameters The dataset is obtained by summing all the sample data obtained from the corresponding STL grid model.

[0054] D4. Input the dataset into the FC-DeepSDF model for training to obtain the trained FC-DeepSDF model. The trained FC-DeepSDF model is the implicit function of the non-parametric mold.

[0055] The forward propagation process of the FC-DeepSDF model is as follows: F1, Variable structure parameters The input is fed into two parallel fully connected layers, which respectively yield the first deep feature representation. Second deep feature representation .

[0056] F2, Representing the second deep feature With the preset shared latent vector Adding the values ​​at corresponding positions in the two feature maps yields a mixed feature.

[0057] F3. Perform Fourier feature encoding on the coordinates of each spatial query point to obtain the corresponding encoded spatial query point coordinates.

[0058] The Fourier feature encoding of the coordinates of each spatial query point is set according to the following formula: in, This represents the coordinates of the corresponding encoded spatial query point; x, y, and z represent the three dimensions of the spatial query point coordinates, respectively. Indicates an index; This indicates the preset number of frequencies.

[0059] F4. Concatenate the coordinates of each spatial query point with the hybrid features to obtain the input vector corresponding to the coordinates of each spatial query point.

[0060] F5, representing all input vectors and the first deep feature layer. Simultaneously, the data is input into a mapping network for processing to obtain the symbolic distance values ​​of the coordinates of all spatial query points.

[0061] The mapping network consists of several linear activation units and a last characteristic linear modulation unit (FiLM) connected in series; each linear activation unit is composed of a characteristic linear modulation unit (FiLM) connected in series with a ReLU function. The input of the characteristic linear modulation unit (FiLM) of the first linear activation unit serves as the input of the mapping network, and the output of the last characteristic linear modulation unit (FiLM) serves as the output of the mapping network.

[0062] Each characteristic linear modulation unit (FiLM) is configured according to the following formula: Where i represents the index; This represents the output of the i-th characteristic linear modulation unit FiLM; This represents the output of the (i-1)th ReLU function; and Both are weight matrices; This represents the first deep feature representation.

[0063] The specific formulas for processing each ReLU function are as follows: ,in, This is the output of the i-th ReLU function; This is the ReLU function.

[0064] S13. Perform Boolean operations on all implicit functions (implicit functions of all parameterized molds and implicit functions of all non-parameterized molds) in a preset shared implicit space to obtain the overall characterization of the free bending device under test.

[0065] S2. Obtain a set of geometric parameters, forming parameters, and bending process parameters for the bend to be processed. Input all parameters into an operator fusion network consisting of a DeepONets network and a Fourier neural operator (FNO) to predict the quantiles of the springback curvature and deflection sequences, obtaining the final prediction sequence. Based on the final prediction sequence, use the conformal quantile regression method and the boundary adaptive hyperrectangle method sequentially to construct the joint prediction interval for curvature and deflection. Geometric parameters include the bend diameter and wall thickness; forming parameters include the bend base circle radius and pitch; bending process parameters include the A value, compensation coefficient, boosting speed, friction coefficient, and clearance.

[0066] In this embodiment, the bending die and the bending die support each require a separate FC-DeepSDF for implicit modeling. The overall width, overall height, overall thickness, cut-off block thickness, cut-off block width, cut-off cylinder radius, and center hole radius are set as variable structural parameters of the bending die; the overall width, overall height, support column radius, corner radius, bottom cut-off length, top cut-off length, tilt angle bottom edge length, and tilt angle are set as variable structural parameters of the bending die support. Specific parameter details are as follows... Figure 3 (a) and Figure 3As shown in (b), the range of these structural parameters is shown in Table 1. Within the parameter range, 1000 sets of structural parameters for the two molds were generated using the Latin hypercube sampling method, and corresponding STL models were constructed using Solidworks. All models were then uniformly scaled to the unit cube. For each STL model, 132,500 query points were sampled on its surface and in its unit cube space, with 120,000 points sampled on the model surface and 12,500 points uniformly sampled in the spatial region. To enhance data diversity, random perturbations with variances of 0.005 and 0.05 were applied to the model surface sampling points to deviate from the model surface. Then, the symbolic distance values ​​of all query points were calculated, and two independent datasets containing the bending mold and the bending mold support were constructed. Each dataset contains 1000 spatial query points sampled from the model, the corresponding symbolic distance values, and variable structural parameters.

[0067] Table 1. Range of values ​​for variable structural parameters of bending die and bending die support Two independent FC-DeepSDF models were trained using two separate datasets. Each model was trained for 1800 epochs, and the Adam algorithm was used for optimization during training. The network learning rate was set to 5e. -4 The latent variable learning rate is set to 1e. -3 The symbol distance calculation process based on FC-DeepSDF is as follows: First, the variable structure parameters are... Input the two parallel fully connected layers respectively to extract the corresponding first deep feature representation. With the second deep feature representation Then, the second deep feature representation With the shared latent vector representing the common structure of this type of mold Add them together, and then combine the result with the coordinates of the spatial query point after Fourier feature encoding. Concatenate to form the input vector After that, The input is a mapping network consisting of three linear activation units and a last feature linear modulation unit (FiLM) connected in series. After layer-by-layer feature modulation and nonlinear transformation, the symbol distance value of the corresponding spatial point can be output.

[0068] The two FC-DeepSDFs obtained after training can be regarded as implicit representations of the bending modulus and the bending modulus support. Table 2 shows the performance of FC-DeepSDF in the implicit function construction task of the bending modulus support. The calculation formulas of CD, EMD, F1 and IoU are shown below. In the calculation of the indexes, the implicit functions are first converted into a grid using the Marching Cubes algorithm. Then, 16384, 1024 and 4096 points are sampled on the predicted grid and the real grid, respectively, to calculate the three indices CD, EMD and F1. The IoU index is calculated directly through the grid.

[0069] in, and These represent points on the predicted grid and the actual grid, respectively. and These represent the sets of points on the predicted grid and the actual grid, respectively. Indicates the distance between CD; Indicates EMD distance; Indicates the mapping relationship Below, predict points on the grid. The corresponding points on the real grid; Represents a set of points from the prediction grid. Mapping to a set of points on the real grid; This indicates an indicator function that returns 1 if the condition is met and 0 if the condition is not met. This indicates a preset distance threshold; Indicates accuracy; Indicates recall rate; This represents the square of the L2 norm.

[0070] in, Indicates intersection, union, and ratio; and These represent the areas occupied by the predicted grid and the actual grid in space, respectively.

[0071] Table 2 Comparison between the implicit functions of the bending mode support obtained by FC-DeepSDF and the actual results. The results of these four metrics demonstrate that FC-DeepSDF can achieve high-precision implicit function construction of bending die support. For bending dies, FC-DeepSDF exhibits similar performance. To avoid redundancy, further results are not listed here. According to... Figure 2 By adjusting the actual structural parameters of the bending die and bending die support in the six-axis free bending device shown, the required non-parametric implicit function of the die can be obtained.

[0072] The implicit functions of the obtained parametric and non-parametric molds are assembled and integrated in a shared implicit space according to their actual poses, thereby obtaining the overall characterization of the entire device. This process can be expressed by the following formula: in, Represent a point The nearest distance function to the entire device (overall representation); and Let represent the global implicit functions of the parametric mold and the non-parametric mold, respectively, satisfying the following formula: in, and All are indexes. Indicates the first A parameterized mold, Indicates the first A non-parametric mold; Indicates the first Implicit functions of a parameterized mold; Indicates the first An implicit function of a non-parametric mold; and This represents the rotation matrix used for the query point; and This represents the translation matrix used for the query point; Indicates the first The variable structural parameters of a parameterized mold; Indicates the first Variable structural parameters of a non-parametric mold; and These represent the parametric and non-parametric mold sets, respectively. The implicit functions of each mold indirectly achieve pose adjustment by performing spatial transformations on the query points.

[0073] In the springback conformal prediction section, the value ranges of geometric parameters, forming parameters, and bending process parameters are shown in Table 3. Within the parameter value range, a total of 600 sets of parameters were generated using the Latin hypercube sampling method. Based on these parameters, corresponding free bending forming simulations of pipe fittings were performed in ABAQUS. After the simulation was completed, the axis of each set of bent pipes was extracted, and the corresponding curvature and deflection sequences were calculated to construct a dataset for training the deep operator network and Fourier neural operator. The dataset was divided into training, calibration, and test sets according to a ratio of 70%, 15%, and 15%, respectively.

[0074] Table 3. Range of values ​​for geometric parameters, forming parameters, and bending process parameters A deep operator network and a Fourier neural operator were trained using a training set and the Adam optimization algorithm. These two networks were trained uniformly during the training process, meaning that only the quantile prediction results of the Fourier neural operator were used as the final output and applied to the calculation of the MSE loss function. The model was trained for a total of 1500 epochs, with a network learning rate of 1e during training. -3 The training effect was evaluated on the test set, and the evaluation results at the 0.50 quantile are shown in Table 4. The formulas for calculating MSE and MAE are as follows: Table 4 Comparison of rebound prediction results and actual results of operator fusion network The results of these two metrics demonstrate that the operator fusion network, composed of a deep operator network and a Fourier neural operator connected in series, can achieve high-accuracy prediction of curvature and deflection after pipe springback. Although the prediction performance of deflection is slightly inferior to that of curvature, it still meets the required accuracy overall. Subsequent curvature and deflection sequences are obtained by sampling within the joint prediction interval, rather than relying on point prediction results at specific quantiles, which effectively reduces the impact of prediction errors on the interferometric inference results.

[0075] S21. After training, the geometric parameters, forming parameters, and bending process parameters of the bend to be processed are first mapped to initial prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the deflection at the 0.05, 0.50, and 0.95 quantiles respectively through a depth operator network. Then, the initial prediction sequences of curvature and deflection at the 0.05, 0.50, and 0.95 quantiles are processed by a Fourier neural operator to finally obtain the final prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the final prediction sequences of the deflection at the 0.05, 0.50, and 0.95 quantiles respectively.

[0076] In practice, when processing curvature (torsion), the three quantile sequences are concatenated together and input into the FNO, and then the final predicted sequences at the 0.05, 0.50 and 0.95 quantiles are output.

[0077] The deep operator network is configured according to the following formula: in, and Representing curvature and torsion respectively Initial predicted sequence at quantile; and These represent the ideal curvature and the ideal torsion, respectively. Represents the ideal mapping function; This indicates the total number of axial position parameters for the bend. This represents a set of input parameters (geometric parameters, forming parameters, and free bending process parameters of the pipe bend). Indicates the axial position parameters of the bend; Represents the bias vector; and These represent the nonlinear mapping operations of the branch network and the backbone network in a deep operator network, respectively.

[0078] The Fourier neural operator is set up according to the following formula: in, This represents the output of the Fourier neural operator; and These represent the Fourier transform and the inverse Fourier transform, respectively. Represents the weight matrix; This indicates a convolution operation with a kernel size of 1. Indicates the frequency of the Fourier transform; Indicates the frequency cutoff number; This represents the initial prediction sequence of the input curvature or torsion at the 0.05, 0.50, and 0.95 quantiles (the initial prediction sequences at the three quantiles are concatenated). This indicates the axial position parameter of the bend.

[0079] The data set construction process for training deep operator networks and Fourier neural operators is implemented according to the following steps: K1. Obtain the geometric parameters, forming parameters, and bending process parameters of the historically used pipe bends in ABAQUS software. A numerical simulation was performed, and the springback axis obtained after the simulation was completed was extracted. Based on the springback axis, the curvature sequence and deflection sequence corresponding to the bend were calculated.

[0080] K2. Construct a dataset with the geometric parameters, forming parameters, and bending process parameters of the bent pipe as input, and the curvature sequence and deflection sequence as output. Divide the dataset into a training set, a calibration set, and a test set. The training set is used to train the deep operator network and the Fourier neural operator, and the test set is used to evaluate the training effect.

[0081] S22. Based on the final predicted sequences of the curvature and deflection of the pipe to be processed at the 0.05 and 0.95 quantiles, respectively, the conformal quantile regression method is used to construct the univariate prediction intervals for curvature and deflection.

[0082] The univariate prediction intervals for the curvature and deflection of the bend to be processed are obtained by following the formula of the conformal quantile regression method: in, For curvature; For torsion; Choose curvature or torsion; The univariate prediction interval for the curvature or deflection of the bend to be processed; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.05 quantile; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.95 quantile; For the empirical quantiles of the curvature or torsion sequence; The preset confidence level; To obtain quantiles; For indexing; To calibrate the inconsistency score of the curvature or torsion sequence of the i-th sample in the set; For calibration set; The set of inconsistencies in the curvature or torsion sequences of all samples in the calibration set; To calibrate the curvature or torsion sequence predicted by the operator fusion network for the i-th sample in the set at the 0.05 quantile; To calibrate the curvature or torsion sequence (true value) of the i-th sample in the set; This is to determine the 0.95 quantile value of the curvature or torsion sequence predicted by the operator fusion network for the i-th sample in the calibration set.

[0083] S23. Based on the individual univariate prediction intervals of curvature and torsion, the boundary adaptive super rectangle method is used to construct the joint prediction interval of curvature and torsion.

[0084] The joint prediction intervals for the curvature and deflection of the bend to be processed are obtained by applying the following formula from the boundary adaptive hyperrectangle method: ; ; ; ; ; ; ; ; ; in, and These represent the joint prediction intervals for the curvature and deflection of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the final predicted sequences of the curvature of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the final predicted sequences of the deflection of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the empirical quantiles of the curvature and torsion sequences, respectively; and These represent the empirical quantiles of the lower and upper boundaries, respectively; and They represent taking quantiles and taking quantiles; and Two components representing the confidence level. add equal to confidence level ; Indicates the proportionality coefficient; Indicates the preset confidence level; The lower bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. The upper bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. and Let represent the curvature and torsion sequences (true sequences) of the i-th sample in the calibration set, respectively. and Let represent the upper and lower boundary sequences of the curvature sequence of the i-th sample in the calibration set, respectively; and Let represent the upper and lower boundary sequences of the torsion sequence of the i-th sample in the calibration set, respectively; and ... and denoted as the torsion sequence values ​​at the 0.05 quantile and 0.95 quantile, respectively, obtained by predicting the torsion sequence of the i-th sample in the calibration set through the operator fusion network.

[0085] In this embodiment, a grid search method is used to determine the optimal scaling factor on the calibration set. The coverage of the joint curvature and torsion prediction interval is calculated in steps of 0.01 within the interval [0.1, 0.9], and the results for each group are recorded. While ensuring the coverage meets the requirements, the scaling factor with the smallest corresponding prediction interval volume is taken as the final result. After the search, the scaling factor was determined to be 0.55.

[0086] S3. Based on the final predicted sequence of curvature and deflection, the joint predicted interval of curvature and deflection of the bend to be processed, and the overall characterization of the free bending device to be tested, several springback axes are obtained using a Frenet frame. It is then determined whether there is interference between each springback axis corresponding to the bend to be processed and the free bending device to be tested. If any springback axis interferes with the free bending device to be tested, then interference occurs between the bend to be processed and the free bending device to be tested (the result of whether interference occurs between the bend and the mold). If no springback axis interferes with the free bending device to be tested, then no interference occurs between the bend to be processed and the free bending device to be tested.

[0087] S31. Based on the final predicted sequences of curvature and deflection at the 0.5 quantile, samples are taken from the joint prediction intervals of curvature and deflection of the bend to be processed. Group sequence, and thus form A combination of curvature and torsion.

[0088] In this embodiment, the curvature prediction sequence at the 0.50 quantile of the operator fusion network is highly consistent with the data distribution characteristics of the actual curvature. While the torsion prediction sequence at the corresponding quantile can capture the overall trend of the actual torsion, it is difficult to reflect its local fluctuation characteristics. Therefore, three sets of potential curvature and torsion sequences are sampled within their respective joint prediction intervals, and after pairing them one by one, a total of nine sets of curvature sequences are obtained. - Torque The combination of .

[0089] Each set of curvature - Torque The combination is formed by sampling and combining according to the following formula: ; ; in, and All are indexes; No. One curvature; Let j be the j-th torsion. and These are the final predicted sequences at the 0.50 quantiles of the curvature and deflection of the bend to be processed, respectively. This represents the sampling parameter corresponding to the i-th curvature; To use the total number of groups; and These are the upper and lower boundary sequences of the joint prediction interval for curvature, respectively; and These are the upper and lower boundary sequences of the joint prediction interval for torsion, respectively. Let be the piecewise cosine function with an amplitude of 1 corresponding to the j-th torsion. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the empirical quantiles of the lower and upper boundaries, respectively.

[0090] S32. Integrate each curvature-deflection combination using the Frenet frame to obtain the corresponding springback axis.

[0091] S33. Based on the obtained springback axis, the overall characterization of the free bending device under test, and the Frenet frame, determine whether there is any interference between each springback axis of the bending device under test and the free bending device under test.

[0092] For any springback axis, the springback axis is combined with the overall characterization of the free bending device under test (spatial registration), and the springback axis is corrected according to the actual processing state. A set of discrete points on the surface of the bending pipe to be processed is generated based on the Frenet frame and the corrected springback axis. The signed distance value from each discrete point to the free bending device under test is calculated. If any discrete point has a negative signed distance value to the free bending device under test, it indicates that the current springback axis corresponding to the bending pipe to be processed interferes with the free bending device under test. In specific implementation, if the current springback axis corresponding to the bending pipe to be processed interferes with the free bending device under test, it means that the free bending device method cannot process the bending pipe to be processed.

[0093] S34, If any one of the springback axes interferes with the free bending device under test, then the current bending pipe to be processed interferes with the free bending device under test, and thus it is considered that the free bending device under test cannot process the current bending pipe.

[0094] S4. Based on the overall characterization of the free bending device under test, generate several uniformly distributed query points in the space (preset shared implicit space) where the free bending device under test is located. Calculate the symbolic distance value from each query point to various molds of the free bending device under test. If there is a query point whose symbolic distance value to two or more (at least two) molds is negative, then the molds interfere with each other (the result of whether the molds interfere with each other). Otherwise, the molds do not interfere with each other.

[0095] S5. If either interference occurs between the bent tube to be processed and the free bending tube device to be tested, or interference occurs between the mold, the free bending tube device to be tested cannot process the bent tube under the current forming parameters; if neither interference occurs, the free bending tube device to be tested can process the bent tube under the current forming parameters.

[0096] S6. Each time, only the forming parameters are changed to obtain a new bent tube to be processed. The same method as steps S2-S5 is used to process it several times. Finally, the result of whether the free bending tube device to be tested can process the bent tube under different forming parameters is obtained, so as to finally determine the processing limit diagram.

[0097] Changing only the forming parameters without altering the geometric and process parameters results in a machining limit diagram. Figure 4Using forming parameters (base circle radius and pitch), by performing S2-S5 tests on bent tubes with different forming parameters, the final information obtained is whether the device will interfere with bent tubes with different forming parameters under specific geometric and process parameter conditions, thereby determining the overall processing limit diagram. In other words, for a processing limit diagram, the geometric and process parameters of bent tubes with different forming parameters are fixed and will not change.

[0098] The above process merely illustrates the interference inference process for bent tubes under specific forming parameter conditions. Interference inference is performed one by one for bent tubes with base circle radii in the range of [120, 400] and pitch in the range of [120, 480], and the processing limit of the device is finally predicted.

[0099] Figure 4 The processing limits of the six-axis free bending pipe device in this embodiment under the process parameters shown in Table 5 and their experimental verification results are presented. The consistency between the two results proves the effectiveness of the method.

[0100] Table 5. Process parameters used in the free pipe bending device The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for predicting the processing limits of a free pipe bending device based on multi-body implicit interference inference, characterized in that, Includes the following steps: S1. Divide the various molds of the free bending device under test into parametric molds and non-parametric molds, and construct implicit functions for parametric molds and non-parametric molds respectively. Perform Boolean operations on all implicit functions to obtain the overall characterization of the free bending device under test. S2. Obtain the geometric parameters, forming parameters, and bending process parameters of the pipe to be processed, and input all parameters into the operator fusion network composed of a deep operator network and a Fourier neural operator to perform quantile prediction of the curvature and torsion sequences, and obtain the final prediction sequence. Based on the final prediction sequence, the conformal quantile regression method and the boundary adaptive super rectangle method are used in sequence to process and construct the joint prediction intervals of curvature and torsion respectively. S3. Based on the final prediction sequence of curvature and deflection, the joint prediction interval of curvature of the bend to be processed, the joint prediction interval of deflection, and the overall characterization of the free bending device to be tested, several springback axes are obtained using the Frenet frame. It is determined whether there is any interference between each springback axis corresponding to the bend to be processed and the free bending device to be tested. If any springback axis interferes with the free bending device to be tested, then there is interference between the bend to be processed and the free bending device to be tested. S4. Based on the overall characterization of the free bending device under test, generate several uniformly distributed query points in the space where the free bending device under test is located. Calculate the symbolic distance value from each query point to various molds of the free bending device under test. If there is a query point whose symbolic distance value to two or more molds is negative, then interference occurs between the molds. S5. If either the bending tube to be processed interferes with the free bending tube device to be tested, or interference occurs between the molds, the free bending tube device to be tested will be unable to process the bending tube under the current forming parameters. S6. Each time the forming parameters are changed, a new bent tube to be processed is obtained. The same method as steps S2-S5 is used to process it several times. Finally, the result is obtained as to whether the free bending device to be tested can process the bent tube under different forming parameters.

2. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference as described in claim 1, characterized in that, Step S1 specifically involves: S11. Simplify the structure of various molds for the free bending pipe device to be tested, and divide all the simplified molds into two categories: parametric molds and non-parametric molds. The criteria for classifying molds into parametric and non-parametric molds are as follows: if the simplified mold is represented by one or more combinations of cuboids, cylinders, and frustums, it is classified as a parametric mold; otherwise, it is classified as a non-parametric mold. S12. Construct the implicit function of the parameterized mold using an implicit modeling method based on analytical formulas; construct the implicit function of the non-parametric mold using a learning-based implicit modeling method. S13. Perform Boolean operations on all implicit functions to obtain the overall characterization of the free bending pipe device under test.

3. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference as described in claim 2, characterized in that, The learning-based implicit modeling method constructs the implicit function of the non-parametric mold according to the following steps: D1. Determine the variable structural parameters in a non-parametric mold. Build using Solidworks tools Group variable structure parameters STL mesh models corresponding to nonparametric molds with different values, and scale all STL mesh models to a unit cube; D2. For each set of variable structural parameters The corresponding STL mesh model is co-sampled on the surface of the STL mesh model corresponding to the non-parametric mold and within the unit cube. A total of 10 spatial query points are identified, and perturbations are applied only to spatial query points located on the surface of the STL mesh model to deviate them from the surface. The signed distance value from each spatial query point to the surface of the STL mesh model is calculated, using the coordinates of all spatial query points and variable structural parameters. As input, the symbolic distance value is used to construct a single sample dataset as output; D3, Several sets of variable structural parameters The dataset is obtained by summing all sample data obtained from the corresponding STL grid model. D4. Input the dataset into the FC-DeepSDF model for training to obtain the trained FC-DeepSDF model. The trained FC-DeepSDF model is the implicit function of the non-parametric mold.

4. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference according to claim 3, characterized in that, The forward propagation process of the FC-DeepSDF model is as follows: F1, Variable structure parameters The input is fed into two parallel fully connected layers, which respectively yield the first deep feature representation. Second deep feature representation ; F2, Representing the second deep feature With the preset shared latent vector Adding them together yields mixed characteristics; F3. Perform Fourier feature encoding on the coordinates of each spatial query point to obtain the corresponding encoded spatial query point coordinates; F4. Concatenate the coordinates of each spatial query point with the hybrid features to obtain the input vector corresponding to the coordinates of each spatial query point; F5, representing all input vectors and the first deep feature layer. Simultaneously, the coordinates of all spatial query points are input into the mapping network for processing to obtain the symbolic distance values; the mapping network consists of several linear activation units and a last characteristic linear modulation unit (FiLM) connected in series; each linear activation unit is composed of a characteristic linear modulation unit (FiLM) connected in series with a ReLU function.

5. The method for predicting the processing limits of a free pipe bending device based on multi-body implicit interference inference according to claim 1, characterized in that, Step S2 specifically involves: S21. The geometric parameters, forming parameters, and bending process parameters of the bend to be processed are first mapped to initial prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the deflection at the 0.05, 0.50, and 0.95 quantiles respectively through a depth operator network. Then, the initial prediction sequences of the curvature and deflection at the 0.05, 0.50, and 0.95 quantiles are processed by a Fourier neural operator to finally obtain the final prediction sequences of the curvature at the 0.05, 0.50, and 0.95 quantiles and the final prediction sequences of the deflection at the 0.05, 0.50, and 0.95 quantiles respectively. S22. Based on the final predicted sequences of the curvature and deflection of the bend to be processed at the 0.05 and 0.95 quantiles respectively, the conformal quantile regression method is used to construct the univariate prediction intervals for curvature and deflection respectively. S23. Based on the individual univariate prediction intervals of curvature and torsion, the boundary adaptive super rectangle method is used to construct the joint prediction interval of curvature and torsion.

6. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference according to claim 5, characterized in that: The univariate prediction intervals for the curvature and deflection of the bend to be processed are obtained by following the formula of the conformal quantile regression method: in, For curvature; For torsion; Choose curvature or torsion; The univariate prediction interval for the curvature or deflection of the bend to be processed; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.05 quantile; The final predicted sequence of curvature or deflection of the bend to be processed at the 0.95 quantile; For the empirical quantiles of the curvature or torsion sequence; The preset confidence level; To obtain quantiles; For indexing; To calibrate the inconsistency score of the curvature or torsion sequence of the i-th sample in the set; For calibration set; The set of inconsistencies in the curvature or torsion sequences of all samples in the calibration set; To calibrate the curvature or torsion sequence predicted for the i-th sample in the set at the 0.05 quantile; To calibrate the curvature or torsion sequence of the i-th sample in the set; This is to determine the 0.95 quantile value of the curvature or torsion sequence predicted for the i-th sample in the calibration set.

7. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference according to claim 5, characterized in that: The joint prediction intervals for the curvature and deflection of the bend to be processed are obtained by applying the following formula from the boundary adaptive hyperrectangle method: ； ； ； ； ； ； ； ； ； in, and These represent the joint prediction intervals for the curvature and deflection of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the final predicted sequences of the curvature of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the final predicted sequences of the deflection of the bend to be processed at the 0.05 and 0.95 quantiles, respectively. and These represent the empirical quantiles of the curvature and torsion sequences, respectively; and These represent the empirical quantiles of the lower and upper boundaries, respectively; and They represent taking quantiles and taking quantiles; and The two components represent the confidence level; Indicates the proportionality coefficient; Indicates the preset confidence level; The lower bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. The upper bound joint consistency score of curvature and torsion for the i-th sample in the calibration set is represented. and Let represent the curvature and torsion sequences of the i-th sample in the calibration set, respectively; and Let represent the upper and lower boundary sequences of the curvature sequence of the i-th sample in the calibration set, respectively; and Let represent the upper and lower boundary sequences of the torsion sequence of the i-th sample in the calibration set, respectively; and These represent the sequence values ​​of the curvature sequence predicted for the i-th sample in the calibration set at the 0.05 and 0.95 quantiles, respectively. and represents the torsion sequence values ​​at the 0.05 quantile and 0.95 quantile of the i-th sample in the calibration set, respectively.

8. The method for predicting the processing limits of a free pipe bending device based on multi-body implicit interference inference according to claim 1, characterized in that, Step S3 specifically involves: S31. Based on the final predicted sequences of curvature and deflection at the 0.5 quantile, samples are taken from the joint prediction intervals of curvature and deflection of the bend to be processed. Group sequence, and thus form Curvature-torsion combination; S32. Integrate each curvature-deflection combination using a Frenet frame to obtain the corresponding springback axis; S33. Based on the obtained springback axis, the overall characterization of the free bending device under test, and the Frenet frame, determine whether there is any interference between each springback axis of the bending device under test and the free bending device under test. S34, If any one of the springback axes interferes with the free bending device under test, then the current bending pipe to be processed interferes with the free bending device under test.

9. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference according to claim 8, characterized in that: Each set of curvature - Torque The combination is formed by sampling and combining according to the following formula: ； ； in, and All are indexes; No. One curvature; Let j be the j-th torsion. and These are the final predicted sequences at the 0.50 quantiles of the curvature and deflection of the bend to be processed, respectively. This represents the sampling parameter corresponding to the i-th curvature; To use the total number of groups; and These are the upper and lower boundary sequences of the joint prediction interval for curvature, respectively; and These are the upper and lower boundary sequences of the joint prediction interval for torsion, respectively. Let be the piecewise cosine function with an amplitude of 1 corresponding to the j-th torsion. and These represent the lower and upper boundary sequences of the univariate prediction interval for the curvature of the bend to be processed, respectively. and These represent the lower and upper boundary sequences of the univariate prediction interval for the deflection of the bend to be processed, respectively. and These represent the empirical quantiles of the lower and upper boundaries, respectively.

10. The method for predicting the processing limit of a free pipe bending device based on multi-body implicit interference inference according to claim 8, characterized in that, Step S33 specifically involves: For any springback axis, the springback axis is combined with the overall characterization of the free bending device under test, and the springback axis is corrected according to the actual processing state. A set of discrete points on the surface of the bending pipe to be processed is generated based on the Frenet frame and the corrected springback axis. The sign distance value from each discrete point to the free bending device under test is calculated. If the sign distance value from any discrete point to the free bending device under test is negative, it indicates that the current springback axis corresponding to the bending pipe to be processed interferes with the free bending device under test.

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