A water medium-based inner filling bending forming method for a tubular workpiece

Abstract

The application provides a water medium-based internal filling bending forming method for a tubular workpiece, comprising the following steps: S1, obtaining initial geometric characteristics of the tubular workpiece; S2, inputting the initial geometric characteristics into a stiffness matrix solving model to obtain deformation prediction data output by the stiffness matrix solving model; S3, inputting the deformation prediction data into a regression prediction model to obtain water medium injection flow rate output by the regression prediction model; S4, inputting the water medium injection flow rate into a fluid dynamics solving model to obtain pressure distribution data output by the fluid dynamics solving model; S5, judging whether the pressure distribution data is greater than a preset pressure threshold; S6, if the pressure distribution data is greater than the preset pressure threshold, obtaining a pressure difference value between the pressure distribution data and the preset pressure threshold; S7, inputting the pressure difference value into a decision tree integrated model to obtain a springback compensation value output by the decision tree integrated model; S8, performing coordinate offset processing on the springback compensation value and the initial geometric characteristics to obtain a target forming track; and S9, performing water medium-based internal filling bending forming processing for the tubular workpiece according to the target forming track.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method for filling and bending tubular workpieces based on a water medium. Background Technology

[0002] Pipe bending and forming plays a crucial role in modern manufacturing, especially the forming process using water as the internal filler, which is a key step in manufacturing high-precision and complex pipelines. Traditional forming control methods often rely on conventional mechanical settings to regulate the fluid state. This method is difficult to respond in real time to the drastic changes in the internal physical state of the pipe during bending, which can easily lead to uneven stress on the pipe wall and thus cause serious processing defects.

[0003] In actual bending processes, fluid flow rate control is a core factor determining the forming quality. If the fluid injection speed is not properly controlled, the pressure distribution inside the pipe will become severely unbalanced. For example, when processing a metal pipe with a large bending angle, if the fluid injection is too fast, the local pressure in the outer area of ​​the bend will rise sharply. This overpressure state not only poses a risk of direct pipe wall rupture but also forcibly alters the normal plastic deformation trajectory of the metal material. After processing is completed and the internal fluid is drained, this abnormally altered plastic deformation will trigger a highly complex material springback phenomenon. It's like forcefully bending a hose filled with high-pressure fluid; the area with excessive hydraulic pressure will be overstretched. Once the pressure is released and the hands are loosened, the hose will not only rebound, but the direction and magnitude of the rebound will become unpredictable due to the previous overexpansion, ultimately causing the critical actual forming dimensions to deviate significantly from the design requirements. Conversely, if the flow rate is too slow, the internal pressure is insufficient to support the pipe wall, and the pipe will dent and become unstable when bent under force.

[0004] Therefore, accurately controlling the injection velocity of the water medium to avoid local overpressure and insufficient support, and accurately predicting and compensating for complex material springback errors when there is a risk of overpressure, and generating an accurate target forming trajectory, has become a key issue in improving the dimensional accuracy and processing quality of pipe bending forming. Summary of the Invention

[0005] This invention provides a method for filling and molding tubular workpieces based on a water medium, mainly comprising: S1: Obtain the initial geometric features of the tubular workpiece; S2: Input the initial geometric features into the stiffness matrix solving model to obtain the deformation prediction data output by the stiffness matrix solving model.

[0006] S3: Input the deformation prediction data into the regression prediction model to obtain the water medium injection flow rate output by the regression prediction model; S4: Input the water medium injection velocity into the fluid dynamics solution model to obtain the pressure distribution data output by the fluid dynamics solution model; S5: Determine whether the pressure distribution data is greater than a preset pressure threshold; S6: If the pressure distribution data is greater than the preset pressure threshold, then obtain the pressure difference between the pressure distribution data and the preset pressure threshold.

[0007] S7: Input the pressure difference value into the decision tree ensemble model to obtain the rebound compensation value output by the decision tree ensemble model; S8: Perform coordinate offset processing on the springback compensation value and the initial geometric features to obtain the target forming trajectory; S9: Perform water-based tubular workpiece infill bending forming process according to the target forming trajectory.

[0008] Further, the step of inputting the initial geometric features into the stiffness matrix solving model to obtain the deformation prediction data output by the stiffness matrix solving model includes: Obtain the node coordinate data and material property parameters of the initial geometric feature; An initial stiffness matrix is ​​constructed based on the node coordinate data and the material property parameters; The initial stiffness matrix is ​​processed by the stiffness matrix solving model to obtain nodal displacement data and stress distribution status; The deformation prediction data is determined based on the nodal displacement data and the stress distribution state.

[0009] Further, the step of inputting the deformation prediction data into the regression prediction model to obtain the water medium injection flow rate output by the regression prediction model includes: Obtain the feature vectors and historical processing sample sets corresponding to the deformation prediction data; The regression prediction model is used to perform high-dimensional spatial mapping on the feature vector and the historical processing sample set to obtain mapped feature data. Calculate the initial flow velocity value and the flow velocity fluctuation range based on the mapping feature data; The water medium injection flow rate is determined based on the initial flow rate value and the flow rate fluctuation range.

[0010] Further, the step of inputting the water medium injection velocity into the fluid dynamics solution model to obtain the pressure distribution data output by the fluid dynamics solution model includes: Obtain the boundary condition data and water medium physical property parameters corresponding to the water medium injection flow rate; Based on the boundary condition data and the physical properties of the water medium, a momentum conservation equation is constructed. The velocity distribution data of the flow field is obtained by iteratively solving the momentum conservation equation using the fluid dynamics solution model. An initial pressure distribution matrix is ​​generated based on the flow field velocity distribution data; The pressure distribution data is obtained by smoothing and filtering the initial pressure distribution matrix.

[0011] Further, the step of inputting the pressure difference value into the decision tree ensemble model to obtain the rebound compensation value output by the decision tree ensemble model includes: Obtain the difference feature sequence corresponding to the pressure difference and the ambient temperature parameter; The decision tree ensemble model is used to evaluate the difference feature sequence and the ambient temperature parameter to obtain multiple candidate compensation values; Obtain the weight coefficients and confidence indices corresponding to the multiple candidate compensation values; The comprehensive compensation value is obtained by calculating the weighted average of the multiple candidate compensation values ​​based on the weighting coefficients and the confidence index. The rebound compensation value is determined based on the comprehensive compensation value.

[0012] Further, the process of performing coordinate offset processing on the springback compensation value and the initial geometric features to obtain the target forming trajectory includes: Obtain the initial coordinate point set and normal vector data corresponding to the initial geometric features; Based on the rebound compensation value and the normal vector data, each coordinate point in the initial coordinate point set is vector-translated to obtain the offset coordinate point set; The offset coordinate point set is subjected to NURBS fitting to obtain continuous trajectory data; The target forming trajectory is determined based on the continuous trajectory data.

[0013] Further, the step of performing water-based infill bending forming of a tubular workpiece according to the target forming trajectory includes: Obtain the end sealing device of the tubular workpiece and seal both ends of the tubular workpiece; The water medium is injected into the tubular workpiece at the specified water medium injection flow rate, and the internal pressure is maintained stable. The tubular workpiece is subjected to an external bending load according to the target forming trajectory to complete the bending forming process.

[0014] The technical solutions provided by the embodiments of the present invention can achieve the following beneficial effects: This invention discloses a water-based method for internal filling and bending of tubular workpieces. It addresses the problems of improper fluid flow rate control during tubular bending, which can easily lead to local overpressure rupture or insufficient support causing instability. Furthermore, local overpressure alters material plastic deformation, resulting in complex springback after unloading and causing deviations in the formed dimensions. This invention uses a stiffness matrix solution model to predict deformation, combines this with a regression prediction model to determine the water injection flow rate, and utilizes a fluid dynamics solution model to obtain pressure distribution data. When overpressure risk exists, this invention inputs the pressure difference into a decision tree ensemble model to predict springback compensation values, and then offsets these values ​​in the opposite direction to generate the target forming trajectory. This invention effectively avoids the risks of pipe wall instability and rupture, accurately compensates for complex springback errors, and significantly improves the dimensional accuracy and processing quality of tubular bending. Attached Figure Description

[0015] Figure 1 This is a flowchart of a water-based tubular workpiece filling and bending forming method according to the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] This invention provides a method for filling and bending tubular workpieces using a water-based medium. For example... Figure 1 As shown, this method systematically analyzes the geometric features of the tubular workpiece and combines the collaborative processing of multiple computational models to ultimately generate a precise forming trajectory and complete the bending process. The following detailed explanation of each step is provided with reference to specific embodiments.

[0018] Step S1: Obtain the initial geometric features of the tubular workpiece.

[0019] The initial geometric features of a tubular workpiece serve as the data starting point for the entire forming method, and their accuracy directly affects the reliability of all subsequent calculations. These initial geometric features typically include the outer diameter, wall thickness, bending radius, bending angle, cross-sectional shape, and axial geometric variation of the tubular workpiece. For a standard tubular workpiece with a circular cross-section, the ratio of outer diameter to wall thickness determines the stress characteristics of the tube wall during bending, while the ratio of bending radius to outer diameter directly affects the wall thinning rate and the degree of cross-sectional distortion during bending.

[0020] In one embodiment, the initial geometric features can be obtained by scanning the entire cross-section of the tubular workpiece with a coordinate measuring machine (CMM). A set of cross-sectional profile data is collected at regular intervals along the axial direction of the tube, thus forming a complete three-dimensional geometric description. For example, for an aluminum alloy tube with an outer diameter of 50 mm and a wall thickness of 2 mm, a set of cross-sectional data is collected every 5 mm along the axial direction, resulting in several sets of cross-sectional profiles. Integrating these cross-sectional data yields the initial geometric feature set of the tube. This geometric feature not only describes the macroscopic shape of the tube but also records the initial ellipticity deviation and uneven wall thickness distribution that may exist during the manufacturing process, providing a reliable geometric basis for the subsequent construction of the stiffness matrix.

[0021] It should be noted that the accuracy of the initial geometric feature acquisition has a decisive impact on the final result of the entire forming method. If the pipe has initial bending or cross-sectional ellipticity exceeding the tolerance, these deviations must be accurately reflected in the initial bonding features; otherwise, subsequent deformation prediction and trajectory planning will produce systematic errors, resulting in the final formed part failing to meet dimensional accuracy requirements.

[0022] Step S2: Input the initial geometric features into the stiffness matrix solving model to obtain the deformation prediction data output by the stiffness matrix solving model.

[0023] The stiffness matrix solution model is a numerical calculation model based on the finite element analysis principle. Its core idea is to discretize the continuous geometry of a tubular workpiece into a finite number of elements. By establishing a mechanical relationship matrix between these elements, the displacement and stress field distributions of the entire structure under external loads can be solved. The stiffness matrix describes the structure's ability to resist deformation. Each element in the matrix represents the displacement response at another node when a unit force is applied at one node. Therefore, the accurate construction of the stiffness matrix and the material property parameters are crucial.

[0024] Step S21: Obtain the node coordinate data and material property parameters of the initial geometric features.

[0025] Node coordinate data is the set of coordinates of the vertices of each discrete element in three-dimensional space after discretizing the geometry of the tubular workpiece. Material property parameters include the elastic modulus, Poisson's ratio, yield strength, strain hardening exponent, and anisotropy coefficient of the tube. The elastic modulus describes the stiffness characteristics of the material during the elastic deformation stage, Poisson's ratio describes the ratio of transverse strain to longitudinal strain when the material is under uniaxial stress, and the yield strength is the critical stress value at which the material transitions from elastic deformation to plastic deformation.

[0026] Specifically, for aluminum alloy pipe fittings, the elastic modulus is typically between 68,000 MPa and 72,000 MPa, with a Poisson's ratio of approximately 0.33. The yield strength varies depending on the alloy grade; for example, the yield strength of 6061-T6 aluminum alloy is 276 MPa. These material properties can be obtained through standard tensile tests or by querying material databases. When acquiring node coordinate data, an appropriate mesh density needs to be selected based on the geometric complexity of the pipe fitting. The mesh should be appropriately refined in areas with concentrated bending deformation to improve the calculation accuracy in those areas.

[0027] Step S22: Construct an initial stiffness matrix based on the node coordinate data and material property parameters.

[0028] The initial stiffness matrix is ​​constructed by assembling the local stiffness matrices of each finite element of the tubular workpiece into the overall stiffness matrix according to the node number correspondence. The local stiffness matrix of each element is determined by the element's geometry, node coordinates, and material properties. For bending analysis of tubular workpieces, shell elements or solid elements are typically used for discretization. Shell elements are suitable for relatively thin-walled tubes, while solid elements are suitable for thicker walls or situations requiring precise description of stress distribution along the wall thickness.

[0029] In one possible implementation, for an aluminum alloy pipe with an outer diameter of 50 mm and a wall thickness of 2 mm, since the ratio of wall thickness to outer diameter is 0.04, it is considered a thin-walled pipe and suitable for discretization using shell elements. The pipe is divided into several segments along the axial direction and several equal parts along the circumference, forming a regular shell element mesh. The local stiffness matrix of each shell element is calculated based on the coordinates of the four nodes of that element and the elastic modulus and Poisson's ratio of the aluminum alloy. Then, the local stiffness matrices of all elements are superimposed according to the node numbers to form the global stiffness matrix describing the mechanical behavior of the entire pipe. The dimension of the global stiffness matrix is ​​equal to the product of the total number of nodes in the pipe and the number of degrees of freedom of each node. For a three-dimensional shell element, each node typically has 6 degrees of freedom, including 3 translational degrees of freedom and 3 rotational degrees of freedom.

[0030] Step S23: The initial stiffness matrix is ​​processed by the stiffness matrix solution model to obtain nodal displacement data and stress distribution state.

[0031] After obtaining the overall stiffness matrix, the stiffness matrix solution model combines the external load vectors applied to the pipe and the boundary conditions to obtain the displacement vectors of each node by solving linear or nonlinear iterative equations. For problems involving large deformations and material nonlinearities, such as bending forming, an incremental iterative method is usually required. This method decomposes the total load into several load increment steps, performs linearization within each increment step, and uses iterative correction to ensure solution accuracy.

[0032] Nodal displacement data describes the distance and direction of each node's deviation from its initial position under external bending loads, while the stress distribution describes the magnitude and direction of stress at various points inside the pipe. During bending, the outer side of the pipe is subjected to tensile stress, the inner side to compressive stress, and the stress near the neutral layer is close to zero. Accurate calculation of the stress distribution is crucial for determining whether the pipe has experienced local instability or cracking.

[0033] Step S24: Determine the deformation prediction data based on the nodal displacement data and stress distribution status.

[0034] Deformation prediction data integrates nodal displacement data and stress distribution information to describe the overall deformation trend and local deformation characteristics of the pipe fitting during the bending process. Specifically, the deformation prediction data includes the degree of ellipticization of the pipe section after bending, the distribution of the pipe wall thinning rate, the bending angle deviation, and the estimated springback amount.

[0035] For example, in the bending forming of an aluminum alloy pipe with a bending radius of 150 mm and a bending angle of 90 degrees, the nodal displacement data calculated by the stiffness matrix solution model shows that the maximum thinning rate of the outer wall of the pipe is approximately 8%, while the inner wall of the pipe exhibits a slight thickening, and the cross-sectional ellipticity is 3%. The stress distribution shows that the maximum tensile stress on the outer side of the bend exceeds the material's yield strength, entering the plastic deformation region, while the maximum compressive stress on the inner side of the bend is close to but does not exceed the yield strength. Combining this information, the deformation prediction data provides the expected deformation of the pipe under this bending condition, providing crucial information for determining the subsequent water injection flow rate.

[0036] Step S3: Input the deformation prediction data into the regression prediction model to obtain the water medium injection flow rate output by the regression prediction model.

[0037] In the fluid-medium-based infill bending process for tubular workpieces, the fluid medium is injected into the tube, supporting the tube wall through internal pressure and suppressing instability deformation and cross-sectional distortion during bending. The injection velocity of the fluid medium is a key parameter controlling the rate of internal pressure build-up and the uniformity of pressure distribution. Too low a velocity leads to insufficient internal pressure, failing to effectively support the tube wall; too high a velocity may cause a rapid increase in internal pressure, exceeding the tube wall's bearing capacity and leading to tube rupture. Therefore, accurately determining the injection velocity of the fluid medium based on the tube's deformation prediction data is crucial for ensuring molding quality.

[0038] Regression prediction models are mathematical mapping models based on historical processing data. Essentially, they establish a nonlinear mapping relationship between pipe deformation characteristics and the optimal water injection velocity by learning from a large number of historical processing samples. This model can comprehensively consider multiple dimensions such as pipe geometry, material properties, and deformation degree, outputting water injection velocity parameters that best match the current processing conditions.

[0039] Step S31: Obtain the feature vectors corresponding to the deformation prediction data and the historical processing sample set.

[0040] The feature vector corresponding to the deformation prediction data is a numerical vector formed by arranging and combining multiple descriptive indicators from the deformation prediction data according to certain rules. Constructing the feature vector requires extracting the features that have the most significant impact on the fluid injection velocity from the deformation prediction data, such as the maximum cross-sectional ellipticity, the maximum pipe wall thinning rate, the average stress level in the bending region, the bending angle, and the ratio of the bending radius to the outer diameter. These features collectively constitute the feature vector describing the current bending condition, serving as the input to the regression prediction model.

[0041] The historical processing sample set is a data collection accumulated through numerous actual processing experiments under the same or similar pipe materials and process conditions. Each historical processing sample contains the deformation feature vector during that processing and the corresponding optimal water medium injection flow rate record. The size and diversity of the historical processing sample set directly determine the generalization ability of the regression prediction model. The sample set covers processing conditions with different bending radii, different bending angles, different pipe specifications, and different fluid medium types.

[0042] In one embodiment, the historical processing sample set includes processing records for aluminum alloy pipes with outer diameters ranging from 30 mm to 80 mm and wall thicknesses ranging from 1.5 mm to 4 mm, under various working condition combinations with bending radius to outer diameter ratios ranging from 1.5 to 5 and bending angles ranging from 30 degrees to 180 degrees, totaling hundreds of sample data sets. Each sample data set has been verified through actual processing to confirm that the corresponding water medium injection flow rate can ensure that the pipes meet the quality requirements of an ellipticity rate not exceeding 5% and a wall thinning rate not exceeding 10% after bending and forming.

[0043] Step S32: The feature vector and the historical processed sample set are mapped to high-dimensional space using a regression prediction model to obtain the mapped feature data.

[0044] High-dimensional space mapping is the core mechanism for regression prediction models to handle nonlinear relationships. The relationship between pipe deformation characteristics and the optimal water medium injection velocity is usually highly nonlinear and difficult to describe with a simple linear function in the original feature space. By mapping the original feature vectors to a higher-dimensional feature space, the data relationships that were originally linearly inseparable in the low-dimensional space may exhibit an approximately linear pattern in the high-dimensional space, thus facilitating the establishment of accurate regression prediction relationships.

[0045] Specifically, high-dimensional space mapping implicitly maps each element of the original feature vector, as well as the interactions and higher-order terms between elements, to a high-dimensional feature space through kernel functions, without explicitly calculating each component of the high-dimensional feature vector. This mapping method, while maintaining computational efficiency, can capture the complex interactions between feature quantities. For example, the interaction between the ratio of the bending radius to the outer diameter and the bending angle does not simply result in the sum of their independent effects on the optimal water medium injection velocity; rather, a coupling relationship exists, and high-dimensional space mapping can effectively capture this coupling effect.

[0046] Mapped feature data is the representation of the original feature vector in a high-dimensional feature space after being mapped in a high-dimensional space. It implicitly contains nonlinear interaction information between the original feature quantities, providing a richer feature foundation for subsequent numerical calculations of flow velocity.

[0047] Step S33: Calculate the initial flow velocity value and the flow velocity fluctuation range based on the mapping feature data.

[0048] The initial flow velocity value is a predicted value obtained by the regression prediction model based on mapped feature data. It is obtained by finding the most similar historical samples in the historical processing sample set to the current operating condition, and then taking a weighted average of the optimal flow velocities corresponding to these similar samples. The similarity calculation is performed in a high-dimensional feature space; the closer a historical sample is to the feature vector of the current operating condition, the greater the contribution weight of its corresponding optimal flow velocity to the initial flow velocity value.

[0049] The velocity fluctuation range describes the uncertainty interval of the initial velocity value, reflecting the similarity between the current operating condition and historical samples, as well as the dispersion of velocity data in the historical samples. When there are historical samples that are highly similar to the current operating condition, the velocity fluctuation range is narrow, indicating a high degree of reliability in the prediction results; when the similarity between the current operating condition and historical samples is low, the velocity fluctuation range is wide, suggesting that more careful parameter adjustments are needed in subsequent steps.

[0050] For example, for an aluminum alloy pipe with a bending radius of 150 mm and a bending angle of 90 degrees, the deformation prediction data reveals that the ellipticity rate is estimated to be 3% and the pipe wall thinning rate is estimated to be 8%. After inputting the corresponding feature vector into the regression prediction model, the model finds several sets of processing records with similar working conditions in the historical processing sample set. The optimal flow rate corresponding to these records is concentrated in the range of 2.5 liters per minute to 3.2 liters per minute. After weighted averaging, the initial flow rate value is 2.8 liters per minute, and the flow rate fluctuation range is ±0.3 liters per minute.

[0051] Step S34: Determine the water medium injection flow rate based on the initial flow rate value and the flow rate fluctuation range.

[0052] The final determination of the water injection velocity requires comprehensive consideration of both the initial velocity value and the velocity fluctuation range. When the velocity fluctuation range is narrow, the initial velocity value can be directly used as the water injection velocity. When the velocity fluctuation range is wide, it is necessary to take into account the specific material properties and geometric characteristics of the pipe fittings and make appropriate adjustments within the velocity fluctuation range to select a more conservative velocity value, thereby reducing the risk of pipe fitting rupture due to velocity deviation.

[0053] Step S4: Input the water medium injection velocity into the fluid dynamics solution model and obtain the pressure distribution data output by the fluid dynamics solution model.

[0054] It should be noted that during the bending and forming process of a tubular workpiece filled with water, the flow state of the water within the cavity directly determines the magnitude and spatial distribution of the internal pressure support force on the pipe wall. The fluid dynamics solution model is a numerical simulation analysis framework based on computational fluid dynamics theory. Its core mechanism is to simulate the flow behavior of fluid within the complex and dynamically changing geometric boundaries of the pipe cavity by discretizing and solving the fluid control equations. Using the water injection velocity determined in the preceding steps as the driving input of this model, it is possible to accurately deduce the dynamic and static pressure conversion process generated when the fluid flows inside the pipe, thereby obtaining pressure distribution data for different regions of the pipe wall. This pressure distribution data is a key physical quantity for evaluating the fluid support effect and predicting the local deformation behavior of the pipe wall.

[0055] Step S41: Obtain the boundary condition data and fluid medium property parameters corresponding to the water medium injection flow rate.

[0056] Specifically, boundary condition data are the mathematical boundary settings that constrain the solution of the fluid dynamics model within a specific computational domain. In the scenario of water injection into a tubular workpiece, boundary condition data mainly includes inlet boundary conditions, outlet boundary conditions, and avoidance boundary conditions. The inlet boundary condition is directly derived from the water injection velocity determined by the humility step and is usually set as a velocity inlet boundary, specifying the initial momentum of the fluid entering the tube. The outlet boundary condition is set according to the sealing state of the other end of the tube. If it is completely closed, it is set as a wall boundary with no slip and no mass outflow; if an overflow valve is provided, it is set as a pressure outlet boundary. The wall boundary condition is used to describe the interaction between the fluid and the inner wall of the tubular workpiece and is usually set as a no-slip boundary condition, that is, the relative velocity of the fluid at the point of contact with the tube wall is zero.

[0057] The physical properties of water are a set of numerical values ​​describing the inherent physical characteristics of the selected water medium, mainly including water density, dynamic viscosity, and bulk modulus. Density determines the magnitude of the inertial force of water, dynamic viscosity characterizes the magnitude of the internal friction force generated when adjacent fluid layers within the water undergo relative motion, and the bulk modulus reflects the compressibility of water under pressure.

[0058] Step S42: Construct the momentum conservation equation based on the boundary condition data and the physical properties of the water medium.

[0059] It should be noted that the momentum conservation equation is the core physical equation describing the motion of a fluid element in space; its essence is the expression of Newton's second law in fluid mechanics. Constructing the momentum conservation equation involves establishing mathematical equations between the various external forces received by the fluid element and its rate of change of momentum. In the scenario where a tubular workpiece is filled with water, the forces received by the fluid element mainly include pressure caused by the pressure gradient, internal friction caused by fluid viscosity, and volume forces such as gravity.

[0060] Specifically, based on the obtained fluid medium density and dynamic viscosity, and combined with the set boundary conditions, a momentum conservation equation can be constructed, including unsteady-state terms, convection terms, diffusion terms, and source terms. The unsteady-state term describes the rate of change of fluid velocity with time; the convection term describes the momentum transfer caused by macroscopic flow; the diffusion term reflects the momentum dissipation caused by fluid viscosity; and the source term includes gravity and other possible external forces. Since the internal geometry of the tubular workpiece is dynamically changing during bending, the constructed momentum conservation equation must be able to adapt to the characteristics of this dynamic mesh or deformable boundary, ensuring that the momentum conservation relationship of the fluid can be accurately described at any given moment of deformation.

[0061] Step S43: The momentum conservation equation is solved iteratively using a fluid dynamics solution model to obtain the flow field distribution data.

[0062] Specifically, since the momentum conservation equations are a set of highly nonlinear partial differential equations, analytical solutions cannot be obtained under the complex geometric boundaries of the tube cavity. Therefore, it is necessary to rely on a fluid dynamics solution model and employ numerical discretization methods for iterative solutions. The fluid dynamics solution model first divides the internal fluid region of the tubular workpiece into a large number of tiny control volumes, i.e., generating a computational network. Subsequently, the finite volume method is used to integrate and discretize the continuous momentum conservation equations over each control volume, transforming them into a system of algebraic equations.

[0063] In the iterative solution process, the solution model first assumes an initial pressure field and velocity field, then substitutes these assumed values ​​into a discretized system of algebraic equations to calculate a new velocity field. Since the assumed pressure field usually does not satisfy the law of conservation of mass, the solution model constructs a pressure correction equation based on the deviation of the velocity field, obtains the pressure correction amount, and then updates the pressure and velocity fields. This prediction and correction process is continuously iterated until the changes in the velocity and pressure fields calculated in two adjacent iterations are less than the preset convergence residual criterion.

[0064] For example, when performing fluid dynamics calculations on a pipe with a bending radius of 150 mm, the solution model divides the interior of the pipe cavity into 500,000 hexahedral mesh elements. Driven by a set water injection velocity, the solution model underwent thousands of iterative calculations, and the residuals of the continuity and momentum equations decreased by 10%. -6 Next, the calculation is deemed to have converged. At this point, the velocity distribution data of the flow field output by the solution model records in detail the magnitude and direction of the velocity vector of each grid node inside the cavity in three-dimensional space, clearly showing the secondary flow and vortex structure generated by the fluid in the curved region due to centrifugal force and cross-sectional changes.

[0065] Step S44: Generate an initial pressure distribution matrix based on the flow field velocity distribution data.

[0066] It should be noted that although the flow field velocity distribution data describes the motion state of the fluid, the hydrostatic pressure of the fluid directly acts on the inner wall of the tubular workpiece and provides the anti-deformation support force. According to the principles of fluid mechanics, the velocity field and pressure field of a fluid are closely coupled. After obtaining the converged flow field velocity distribution data, the fluid dynamics solution model converts the velocity information into pressure field information by solving the pressure Poisson equation.

[0067] Specifically, the solution model extracts pressure values ​​from the boundary mesh nodes adjacent to the inner wall of the tubular workpiece. These values ​​are then regularly arranged according to the axial and circumferential coordinate systems of the pipe, constructing a two-dimensional initial pressure distribution matrix. The row indices of this matrix correspond to the axial positions of the pipe, and the column indices correspond to the circumferential angles. Each element in the matrix represents the magnitude of the fluid pressure at a specific location on the inner wall of the pipe. This initial pressure distribution matrix preliminarily quantifies the spatial distribution of the supporting force exerted by the fluid medium on the pipe wall.

[0068] Step S45: Perform smoothing filtering on the initial pressure distribution matrix to obtain pressure distribution data.

[0069] In some embodiments, a spatial moving average filtering algorithm is used to process the initial pressure distribution matrix. A filtering window of a specific size is set, such as a 3×3 matrix window containing nine adjacent nodes, and this window is slid across the initial pressure distribution matrix node by node. For each central node covered by the window, the weighted average of the pressure values ​​of all nodes within the window is calculated, and this average is used to replace the original pressure value of the central node. This smoothing filter effectively eliminates non-physical pressure fluctuations caused by numerical calculations, preserves the true macroscopic pressure distribution trend, and ultimately outputs smooth and reliable pressure distribution data.

[0070] Step S5: Determine whether the pressure distribution data is greater than the preset pressure threshold.

[0071] It should be noted that the preset pressure threshold is a safety and quality critical value determined comprehensively based on the material yield strength of the tubular workpiece, the wall thickness, and the sealing pressure-bearing capacity of the forming equipment. During the bending process, the internal pressure provided by the fluid medium must be within a reasonable range. If the pressure is too low, it cannot effectively resist the thinning of the pipe wall on the outside of the bend and the wrinkling on the inside; if the pressure is too high, exceeding the preset pressure threshold, it will cause excessive expansion or even rupture of the pipe wall, and will also damage the end sealing device.

[0072] Specifically, the system iterates through every element in the pressure distribution data matrix after smoothing and filtering, comparing it one by one with a preset pressure threshold. This comparison not only focuses on the global maximum pressure peak but also on the pressure concentration in local areas. For example, for a specific aluminum alloy pipe with a wall thickness of 2 mm, after material mechanics calculations and preliminary experimental verification, it is determined that the maximum safe internal pressure it can withstand in the bending area is 45 MPa; therefore, 45 MPa is set as the preset pressure threshold. The system rigorously checks for any numerical nodes in the pressure distribution data that exceed 45 MPa.

[0073] Step S6: If the pressure distribution data is greater than the preset pressure threshold, then obtain the pressure difference between the pressure distribution data and the preset pressure threshold.

[0074] Generally, when the judgment process detects regions in the pressure distribution data that exceed a preset pressure threshold, it indicates that the current combination of water injection velocity and initial geometric features may trigger local overpressure risks during the bending process. To quantify the severity of this overpressure risk, the system needs to calculate the specific pressure difference.

[0075] The system extracts all node values ​​in the pressure distribution data that exceed a preset pressure threshold, subtracts the preset pressure threshold from each value, and obtains a series of positive pressure differences. These pressure differences not only contain information about the magnitude of overpressure but also implicitly contain information about the spatial distribution of the overpressure region. For example, in a specific axial section on the outer side of a pipe bend, the calculated differences between multiple consecutive nodes fluctuate between 2 MPa and 5 MPa. This pressure difference data will serve as the core driving signal for triggering the subsequent process parameter compensation mechanism, instructing the system to intervene in the forming trajectory to release locally excessive fluid pressure and prevent pipe rupture.

[0076] Step S7: Input the pressure difference into the decision tree ensemble model to obtain the rebound compensation value output by the decision tree ensemble model.

[0077] It should be noted that after unloading from the bending and forming of a tubular workpiece, the release of elastic strain energy within the material inevitably leads to geometric springback, causing the final forming angle and trajectory to deviate from the target requirements. When local overpressure exists inside the tube, the plastic deformation state of the tube wall material undergoes complex changes. Local excessive expansion significantly alters the material's stress distribution history, thus exerting a highly nonlinear influence on the springback behavior after unloading. Decision tree ensemble models are powerful learning algorithm frameworks adept at handling such complex multivariate and nonlinear mapping relationships. By inputting the pressure difference into this model, the additional springback caused by local overpressure can be accurately predicted, and corresponding springback compensation values ​​can be output to correct the forming trajectory.

[0078] Step S71: Obtain the difference feature sequence corresponding to the pressure difference and the ambient temperature parameter.

[0079] Specifically, the pressure difference is spatially represented as discrete node data. To facilitate processing by the decision tree ensemble, it needs to be transformed into a structured difference feature sequence. The system extracts the pressure difference of the overpressure region according to the axial coordinate order of the pipe fitting, and calculates statistical features such as the overpressure peak value, overpressure area integral, and overpressure gradient of the region. These features are then combined into a one-dimensional difference feature sequence according to a fixed format.

[0080] Meanwhile, ambient temperature is also a crucial factor affecting the resilience of materials. The yield strength and elastic modulus of metallic materials are both temperature-sensitive; fluctuations in ambient temperature directly alter the material's deformation resistance and elastic recovery ability. Furthermore, ambient temperature affects the viscosity of fluid media, thereby fine-tuning the efficiency of internal pressure transmission. Therefore, the system uses temperature sensors deployed at the processing site to collect ambient temperature parameters in real time and concatenates them with the difference feature sequence, using them together as input features for the decision tree ensemble model.

[0081] Step S72: The difference feature sequence and the ambient temperature parameter are evaluated by the decision tree ensemble model to obtain multiple candidate compensation values.

[0082] It should be noted that decision tree ensemble models are typically composed of dozens or even hundreds of independent decision trees, such as those built using random forest or gradient boosting tree algorithms. Each decision tree uses different subsets of data and features from the historical processing dataset during the training phase, thus their evaluation perspectives on the same input features differ, effectively avoiding the overfitting problem of a single model.

[0083] Specifically, when the difference feature sequence and ambient temperature parameter are input into the decision tree ensemble model, each decision tree within the model independently performs layer-by-layer splitting judgments on these input features. For example, the root node of a decision tree might determine whether the "overpressure peak value is greater than 3 MPa." If so, it proceeds to the left subtree, then determines whether the "ambient temperature is lower than 20 degrees Celsius," and so on, traversing downwards until a leaf node is reached. Each leaf node stores a compensation value learned based on historical experience. Because the ensemble model contains multiple decision trees, each evaluation process outputs multiple different candidate compensation values ​​in parallel.

[0084] Step S73: Obtain the weight coefficients and confidence indices corresponding to multiple candidate compensation values.

[0085] Specifically, because the decision trees in the ensemble model perform differently during training, the reliability of their output candidate compensation values ​​also varies. To scientifically synthesize these candidate values, the system needs to obtain the weight coefficient and confidence index corresponding to each candidate compensation value.

[0086] Weight coefficients are typically assigned during model training based on the prediction error of each decision tree on the validation set. The smaller the prediction error of a decision tree, the greater its weight coefficient in the final decision. The confidence index reflects the purity or variance of the historical samples within a specific leaf node when the current input feature falls into that node. If the true compensation values ​​corresponding to the historical samples within a leaf node are highly consistent and have minimal variance, it indicates that the decision tree has extremely high confidence in predicting the current working condition; conversely, if the historical samples are discretely distributed, the confidence index is low.

[0087] Step S74: Calculate the comprehensive compensation value by weighting multiple candidate compensation values ​​according to the weighting coefficients and confidence index.

[0088] Generally, after obtaining the candidate compensation values ​​output by all decision trees, along with their corresponding weight coefficients and confidence indices, the system performs a composite weighted average calculation. First, the system multiplies the weight coefficient of each decision tree by its confidence index to obtain a comprehensive evaluation factor. Then, this comprehensive evaluation factor is used to weight the corresponding candidate compensation values.

[0089] Step S75: Determine the rebound compensation value based on the comprehensive compensation value.

[0090] The comprehensive compensation value is a theoretical correction calculated purely from a data-driven model. Before determining it as the final springback compensation value, the system needs to verify its rationality in conjunction with the actual physical constraints of the tubular workpiece. The system checks whether the comprehensive compensation value exceeds the mechanical movement limits of the forming equipment, or whether it will cause the tubular part to yield during reverse compensation bending. If the comprehensive compensation value is within the physical limits of the equipment and materials, it is directly determined as the springback compensation value; if it exceeds the limits, it is truncated according to a safety threshold to ensure that the final determined springback compensation value can both correct the springback error to the greatest extent and be engineering-feasible.

[0091] Step S8: Perform coordinate offset processing on the rebound compensation value and the initial bonding feature to obtain the target forming trajectory.

[0092] It should be noted that the target forming trajectory is a set of direct instructions from the CNC pipe bending equipment to perform physical machining. The initial geometric features describe the final product form of the pipe fitting project. However, due to the existence of springback, if the pipe fitting is processed directly according to the initial geometric features, the unloaded pipe fitting will inevitably fail to meet the dimensional requirements. Therefore, the calculated springback compensation value must be superimposed onto the initial geometric features, and a target forming trajectory with "over-bending" characteristics is generated through coordinate offset processing. When the pipe fitting is processed according to this target forming trajectory and the springback is unloaded, its final form will exactly match the initial geometric features.

[0093] Step S81: Obtain the initial coordinate point set and normal vector data corresponding to the initial geometric features.

[0094] The system first discretizes the continuous dehumidifier and its features into a series of coordinate points in space, forming an initial coordinate point set. These coordinate points are typically evenly distributed along the central axis of the pipe, accurately recording the pipe's orientation in three-dimensional space. Simultaneously, to determine the direction of the coordinate offset, the system needs to calculate the normal vector data at each coordinate point in the initial coordinate point set.

[0095] In a three-dimensional curve, the normal vector is perpendicular to the tangent vector at that point and points inwards towards the curve's bend. The system calculates the tangent vector at each point by performing a difference calculation on the initial set of coordinate points, and then calculates the principal normal vector based on the oscling surface of the curve. This normal vector data provides precise directional guidance for subsequent springback compensation, ensuring that the compensation operation is strictly performed within the bending plane of the fitting and avoiding the introduction of unexpected spatial distortion.

[0096] Step S82: Based on the rebound compensation value and normal vector data, perform vector translation processing on each coordinate point in the initial coordinate point set to obtain the offset coordinate point set.

[0097] Vector translation is the core step in converting springback compensation values ​​into spatial coordinate changes. The system iterates through each coordinate point in the initial coordinate point set and extracts the corresponding normal vector data. Since springback compensation values ​​are usually expressed as angular compensation or curvature compensation, the system first converts the springback compensation value into the linear offset distance of that point in the normal direction based on the point's position on the curved arc.

[0098] The system then multiplies the straight-line offset distance by the normal vector to obtain an offset vector in three-dimensional space. Adding this offset vector to the original coordinates of the original point yields the translated coordinates. For coordinates in curved regions, the translation direction is typically along the opposite direction of the normal vector (i.e., pointing outwards from the curve) to achieve "over-curve" compensation. For coordinates in straight sections, a rigid body translation is performed based on the overall displacement of the curved section to maintain the continuity of the pipe fitting. After processing all coordinates individually, the system ultimately generates a set of offset coordinates containing compensation information.

[0099] Step S83: Perform NURBS fitting on the offset coordinate point set to obtain continuous trajectory data.

[0100] The offset coordinate point set obtained through vector translation is spatially discrete, and due to truncation errors in numerical calculations, adjacent points may exhibit jagged lines or unevenness. Directly inputting these discrete points into CNC equipment can cause drastic acceleration changes in the forming mold during movement, leading to equipment vibration and severely impacting the surface quality of the pipe fittings. NURBS curves are a high-level mathematical curve representation widely used in industrial design and CNC machining. They can accurately and smoothly fit discrete data points using control points and basis functions.

[0101] For example, the system uses the set of offset coordinate points as the fitting target and calculates the control vertex coordinates, node vectors, and weight factors of the NURBS curve using the least squares method. During the fitting process, the system strictly controls the order of the curve (usually 3rd or 4th order) to ensure that the curve is not only continuous in position but also maintains a high degree of continuity in tangent direction and curvature change. Through this NURBS fitting process, the originally discrete set of offset coordinate points, which may have slight fluctuations, is transformed into a continuous trajectory data with extremely high mathematical smoothness.

[0102] Step S84: Determine the target forming trajectory based on the continuous trajectory data.

[0103] While the trajectory data is mathematically perfectly smooth, it still needs to be converted into a machine instruction format that the forming equipment can recognize and execute. The system resamples the continuous trajectory data along the pipe's axial direction using equal-interval or equal-chord length interpolation based on the kinematic model of the specific CNC pipe bending equipment. The sampled data points contain specific motion commands such as the linear displacement of the pipe feed axis, the rotation angle of the spatial rotation axis, and the bending angle of the bending axis. These motion commands are packaged and encapsulated according to a time sequence, ultimately determining the target forming trajectory that can be directly sent to the underlying control system.

[0104] Step S9: Perform water-based tubular workpiece infill bending forming process according to the target forming trajectory.

[0105] After completing all the complex theoretical calculations, fluid simulations, overpressure assessments, and springback compensation trajectory planning, step S9 is the final step in applying the entire method to the physical world. This step requires the forming equipment to strictly calculate all parameters and trajectory instructions, coordinate mechanical motion with fluid pressure control, and complete the physical plastic deformation of the tubular workpiece.

[0106] Step S91: Obtain the end sealing device of the tubular workpiece and seal both ends of the tubular workpiece.

[0107] End sealing is a physical prerequisite for establishing a high-pressure fluid environment inside the tubular cavity. The system automatically matches or prompts the operator to install an appropriate end sealing device based on the initial assembly characteristics of the tubular workpiece (such as outer diameter and wall thickness). Commonly used sealing devices include polyurethane elastic sealing rings and axial hydraulic thrust cylinders.

[0108] During operation, the tubular workpiece is placed in the clamping mechanism of the forming equipment. The sealing devices at both ends are axially advanced under the drive of hydraulic cylinders, tightly fitting the end face or inner bore of the tube. Under axial pressure, the polyurethane sealing ring expands radially, filling the small gap between the tube wall and the sealing head, forming a reliable precision seal. This seal must be able to withstand the highest fluid pressure calculated in the preceding steps without leakage, ensuring the smooth progress of the subsequent fluid injection process.

[0109] Step S92: Inject fluid medium into the tubular workpiece according to the water medium injection flow rate and maintain stable internal pressure.

[0110] After the pipe ends are reliably sealed, the fluid pump station of the molding equipment begins to operate. The control system strictly follows the water medium injection flow rate determined in step S3, adjusting the flow rate of the water medium entering the pipe cavity through a high-frequency response proportional flow valve. As the water medium is continuously injected, the air inside the pipe cavity is expelled, water fills the entire pipe cavity, and the internal pressure begins to build up rapidly.

[0111] During the pressure build-up process, the control system monitors the actual pressure value inside the pipe cavity in real time and dynamically compares it with the pressure distribution data calculated in step S4. By adjusting the opening of the overflow valve, the system can maintain dynamic stability of the internal pressure even when the pipe is bent or deformed and the internal volume changes, ensuring that the water medium can continuously and uniformly provide anti-instability support to the pipe wall.

[0112] Step S93: Apply an external bending load to the tubular workpiece according to the target forming trajectory to complete the bending forming process.

[0113] After the fluid pressure inside the tube reaches a stable state, the mechanical actuators of the molding equipment begin to engage. The CNC system reads the target molding trajectory command determined in step S8 and drives the feeding carriage, spatial cornering mechanism, and bending die to move in a coordinated manner.

[0114] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for infilling and bending a tubular workpiece based on a water medium, comprising: S1: Obtain the initial geometric features of the tubular workpiece; S2: Input the initial geometric features into the stiffness matrix solving model to obtain the deformation prediction data output by the stiffness matrix solving model; S3: Input the deformation prediction data into the regression prediction model to obtain the water medium injection flow rate output by the regression prediction model; S4: Input the water medium injection velocity into the fluid dynamics solution model to obtain the pressure distribution data output by the fluid dynamics solution model; S5: Determine whether the pressure distribution data is greater than a preset pressure threshold; S6: If the pressure distribution data is greater than the preset pressure threshold, then obtain the pressure difference between the pressure distribution data and the preset pressure threshold; S7: Input the pressure difference value into the decision tree ensemble model to obtain the rebound compensation value output by the decision tree ensemble model; S8: Perform coordinate offset processing on the springback compensation value and the initial geometric features to obtain the target forming trajectory; S9: Perform water-based tubular workpiece infill bending forming process according to the target forming trajectory.

2. The method according to claim 1, characterized in that: The step of inputting the initial geometric features into the stiffness matrix solving model to obtain the deformation prediction data output by the stiffness matrix solving model includes: Obtain the node coordinate data and material property parameters of the initial geometric feature; An initial stiffness matrix is ​​constructed based on the node coordinate data and the material property parameters; The initial stiffness matrix is ​​processed by the stiffness matrix solving model to obtain nodal displacement data and stress distribution status; The deformation prediction data is determined based on the nodal displacement data and the stress distribution state.

3. The method according to claim 2, characterized in that, The step of inputting the deformation prediction data into the regression prediction model to obtain the water medium injection flow rate output by the regression prediction model includes: Obtain the feature vectors and historical processing sample sets corresponding to the deformation prediction data; The regression prediction model is used to perform high-dimensional spatial mapping on the feature vector and the historical processing sample set to obtain mapped feature data. Calculate the initial flow velocity value and the flow velocity fluctuation range based on the mapping feature data; The water medium injection flow rate is determined based on the initial flow rate value and the flow rate fluctuation range.

4. The method according to claim 3, characterized in that, The step of inputting the water medium injection velocity into the fluid dynamics solution model to obtain the pressure distribution data output by the fluid dynamics solution model includes: Obtain the boundary condition data and water medium physical property parameters corresponding to the water medium injection flow rate; Based on the boundary condition data and the physical properties of the water medium, a momentum conservation equation is constructed. The velocity distribution data of the flow field is obtained by iteratively solving the momentum conservation equation using the fluid dynamics solution model. An initial pressure distribution matrix is ​​generated based on the flow field velocity distribution data; The pressure distribution data is obtained by smoothing and filtering the initial pressure distribution matrix.

5. The method according to claim 4, characterized in that, The step of inputting the pressure difference value into the decision tree ensemble model to obtain the rebound compensation value output by the decision tree ensemble model includes: Obtain the difference feature sequence corresponding to the pressure difference and the ambient temperature parameter; The decision tree ensemble model is used to evaluate the difference feature sequence and the ambient temperature parameter to obtain multiple candidate compensation values; Obtain the weight coefficients and confidence indices corresponding to the multiple candidate compensation values; The comprehensive compensation value is obtained by calculating the weighted average of the multiple candidate compensation values ​​based on the weighting coefficients and the confidence index. The rebound compensation value is determined based on the comprehensive compensation value.

6. The method according to claim 5, characterized in that, The process of obtaining the target forming trajectory by performing coordinate offset processing on the springback compensation value and the initial geometric features includes: Obtain the initial coordinate point set and normal vector data corresponding to the initial geometric features; Based on the rebound compensation value and the normal vector data, each coordinate point in the initial coordinate point set is vector-translated to obtain the offset coordinate point set; The offset coordinate point set is subjected to NURBS fitting to obtain continuous trajectory data; The target forming trajectory is determined based on the continuous trajectory data.

7. The method according to claim 1, characterized in that, The step of performing water-based infill bending forming of a tubular workpiece according to the target forming trajectory includes: Obtain the end sealing device of the tubular workpiece and seal both ends of the tubular workpiece; The water medium is injected into the tubular workpiece at the specified water medium injection flow rate, and the internal pressure is maintained stable. The tubular workpiece is subjected to an external bending load according to the target forming trajectory to complete the bending forming process.

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