A method for predicting the springback amount of a solid wood bending forming

Abstract

The application provides a solid wood bending forming springback amount prediction method, relates to the technical field of digital modeling and springback prediction, and establishes layered data by acquiring thickness direction layered strain and mechanical parameters, obtains an energy imbalance index based on the energy storage area of each layer on the tension and compression sides, calculates residual stress distribution and equivalent springback torque by combining demolding cooling characteristics, and solves the curvature radius after springback and the predicted value. The scheme characterizes the non-uniformity of the interlayer mechanical properties of wood along the thickness direction, overcomes the prediction deviation of the traditional uniform material assumption, accurately describes the energy storage difference on the tension and compression sides, makes up for the defects of the existing model which ignores the asymmetric mechanical behavior of tension and compression, and includes the coupling influence of layer temperature, layer moisture content and fiber arrangement angle on the relaxation behavior in the residual stress calculation, thereby improving the fine description ability of the moisture and heat relaxation characteristics. Through a systematic calibration mechanism instead of artificial experience parameter setting, the springback amount prediction accuracy and industrial practical value are improved, and the number of trial models and material loss are reduced.

Description

Technical Field

[0001] This invention relates to the field of digital modeling and springback prediction technology, and more specifically, to a method for predicting the springback of solid wood bending. Background Technology

[0002] Solid wood bending forming technology is an important processing method that uses steam softening, mold-constrained bending, and cooling solidification to create curved components from wood. It is widely used in high-end furniture, architectural decoration, and transportation vehicles. During the bending forming process, after the solid wood material undergoes bending deformation under mold constraints, the uneven stress distribution along the thickness direction of the wood fiber layer (tensile and compressive sides) and the plastic deformation and viscoelastic relaxation of the wood cell walls under humid heat cause the internal stress to release upon demolding and cooling, leading to springback deformation of the bent component. The springback is influenced by multiple factors, including wood moisture content, softening temperature, bending radius, wood thickness, and fiber alignment, directly determining the curvature accuracy and dimensional stability of the final product. For a long time, the field of wood science and processing has conducted extensive research on the springback problem of solid wood bending. Early research mainly relied on classical beam bending theory and experimental regression methods to conduct mechanical analysis of neutral layer migration and springback deformation during bending, and established empirical relationships between springback and process parameters through mathematical fitting. Some studies have attempted to describe the viscoelastic creep behavior of wood using generalized Kelvin or Burger models, and fitted short-term creep curves based on dynamic thermomechanical analysis data. In numerical simulation, the finite element method has been introduced into wood bending analysis, with researchers using software such as ANSYS to simulate the stress distribution of bent components. Furthermore, near-infrared spectroscopy has been used to predict the bending modulus of elasticity and bending strength of wood, providing material property data support for the selection of bending parameters. Overall, existing research has recognized that springback is a core challenge restricting the accuracy of solid wood bending, and numerous explorations have been conducted from the perspectives of experimental testing, theoretical analysis, and numerical simulation.

[0003] However, existing technologies for predicting the springback of solid wood bending still have several key shortcomings. First, most existing prediction methods are based on the assumption of homogeneous materials or a single average modulus, failing to fully consider the non-uniformity of interlayer mechanical properties caused by the hygrothermal gradient, differences in fiber arrangement, and uneven distribution of bending strain along the thickness direction. As a naturally orthotropic material, wood exhibits significant differences in its elastic modulus, relaxation characteristics, and plastic deformation capacity along the thickness direction, while existing models lack effective means to characterize the layered mechanical state along the thickness direction. Second, existing springback prediction models do not adequately characterize the energy storage difference between the tensile and compressive sides during bending. When wood bends, the fibers on the tensile side bear tensile stress, while the fibers on the compressive side bear compressive stress. The cell wall deformation mechanisms and plastic flow behaviors on both sides are fundamentally different, but existing methods usually employ symmetrical elastoplastic constitutive models or ignore the tension-compression asymmetry, failing to accurately describe the mechanism by which the tension-compression imbalance energy drives springback. Third, existing methods handle the hygrothermal relaxation characteristics of wood during demolding and cooling in a rather coarse manner, often employing fixed reduction coefficients or simple exponential decay methods. They fail to incorporate the coupled effects of layer temperature, layer moisture content, and fiber alignment angle on relaxation behavior into the calculation framework for residual stress distribution. Fourth, most existing formulas for calculating springback are based on the small deformation assumption and linear bending theory. When the bending radius is small and the thickness-to-diameter ratio is large, the strain distribution in the thickness direction deviates significantly from the linear assumption, leading to a substantial decrease in prediction accuracy. Furthermore, many correction parameters in existing methods rely on manual experience and lack a systematic calibration mechanism based on batch test data, making it difficult to achieve universal predictions across tree species, thickness grades, and process conditions. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for predicting the springback amount of solid wood bending molding. This method addresses, to some extent, the problem of springback caused by residual torque resulting from uneven tensile and compressive stress after solid wood bending and demolding. Springback is influenced by multiple factors such as moisture content, temperature, radius, thickness, and fiber direction. Existing processes rely on experience-based compensation and cannot quantitatively predict the springback amount before molding, leading to inaccurate mold compensation angle settings and the need for repeated trial molding corrections.

[0005] According to one aspect of the present invention, a method for predicting the springback of solid wood during bending is provided, comprising:

[0006] Strain data and material mechanical parameters of solid wood softened by steam were obtained during the mold-constrained bending process, and layered mechanical data were established accordingly.

[0007] Based on the layered mechanical data, the energy storage of each layer is calculated and the tension side and compression side are distinguished to obtain an energy index characterizing the degree of tension-compression imbalance.

[0008] The residual stress distribution is calculated based on the energy index and demolding cooling characteristics, and the equivalent springback torque is obtained.

[0009] The predicted values ​​of the radius of curvature and rebound amount after springback are calculated based on the equivalent springback moment, the bending stiffness of the component, and the initial forming radius of curvature.

[0010] Furthermore, the calculation of energy storage in each layer includes: calculating the physical strain energy density of each fiber stress layer during the bending holding stage, and generating the rebound driving strain energy density by combining the lever arm distance of each layer relative to the bending neutral layer.

[0011] The method for determining the rebound-driven strain energy density is as follows:

[0012]

[0013] in, Let be the elastic driving strain energy density of the i-th fiber stress layer. To maintain the calculation range for bending, Weights for sampling times, Let be the measurement reliability coefficient of the i-th layer at the sampling time. For lever arm sensitivity correction factor, Let be the equivalent elastic modulus of the i-th layer at the sampling time due to hygrothermal softening. The instantaneous strain of the i-th layer;

[0014] The method for determining the lever arm sensitivity correction coefficient is as follows:

[0015]

[0016] in, Let be the thickness coordinates of the center of the i-th layer. The coordinates of the neutral layer at the sampling time. For the thickness of the bending material, and These are the correction parameters obtained through the rebound calibration of the same batch of wood.

[0017] Furthermore, the aforementioned and Obtained through inverse calculation during the initial calibration phase, the inverse calculation includes:

[0018] Standard specimens of the same tree species, thickness grade, grain direction range, and moisture content adjustment process as the material to be bent are selected. Three or more sets of different forming radius conditions are set up, and the measured springback amount is measured under each condition. With the objective of minimizing the sum of squared residuals between the measured springback amount and the predicted springback amount, a nonlinear least squares algorithm or the Levberg-Marquardt algorithm is used to inversely calculate the springback amount. and The inverse calculation results are then written into the parameter library for online prediction.

[0019] Furthermore, the residual stress distribution is determined in the following manner:

[0020] The internal stress imbalance release coefficient is obtained using the energy index.

[0021] For each fiber stress layer, the relaxation retention coefficient is obtained from the wet and heat relaxation parameter library of the same batch of wood based on its layer temperature, layer moisture content and fiber arrangement angle.

[0022] The residual stress of the layer after demolding is obtained by multiplying the internal stress imbalance release coefficient, the relaxation retention coefficient, the tension-compression side residual conversion correction coefficient, and the equivalent stress converted from the physical strain energy density.

[0023] The residual stress of this layer is then multiplied by the cross-sectional area of ​​the layer and the lever arm distance relative to the neutral layer at the demolding time to obtain the contribution of this layer to the springback torque. The equivalent springback torque is obtained by summing the torque contributions of all fiber-stressed layers.

[0024] Furthermore, the relaxation preservation coefficient is obtained through the relaxation branch weights. Relaxation branch characteristics and relaxation time Determine as follows:

[0025]

[0026] in, Let be the relaxation retention coefficient of the i-th fiber stress layer. To relax the number of branches, Let be the weight coefficient of the m-th relaxation branch in the i-th layer. Let m be the characteristic relaxation time of the m-th relaxation branch in the i-th layer. For layer temperature, The water content of the layer, It is the fiber alignment angle. To preserve representative moments within the calculation interval for bending, This refers to the cooling time after demolding.

[0027] Furthermore, the residual conversion correction factor on the tension / compression side was obtained through tensile unloading and compressive unloading tests on the same batch of specimens:

[0028] Tensile strain and compressive strain corresponding to the target bending state were applied to thin-layer samples of the same batch. After being kept under the same humid heat conditions, the samples were unloaded and the residual deformation or residual stress after cooling was recorded. The difference in residual retention between the tensile side and the compressive side was compiled into a parameter table that varies with temperature, moisture content and fiber arrangement angle.

[0029] During online calculations, the tension layer uses the residual conversion correction factor on the tension side, and the compression layer uses the residual conversion correction factor on the compression side.

[0030] Furthermore, the bending stiffness of the component is a layered equivalent bending stiffness, which is obtained by multiplying and summing the equivalent elastic modulus, cooling and solidification effective coefficient, local section inertia term and parallel axis inertia term of each fiber stress layer in the demolding and cooling state.

[0031] The method for determining the predicted value of springback is as follows: the equivalent springback moment is divided by the layered equivalent bending stiffness to obtain the curvature recovery amount, the curvature recovery amount is corrected by combining the geometric nonlinearity correction coefficient, the corrected curvature recovery amount is subtracted from the initial molding curvature to obtain the curvature after demolding, the reciprocal of the curvature after demolding is taken to obtain the curvature radius after springback, and the difference between the curvature radius after springback and the initial molding curvature radius is calculated to obtain the predicted value of springback.

[0032] According to another aspect of the present invention, a solid wood bending springback prediction system is provided, comprising:

[0033] The layered mechanical data construction module is used to obtain strain data and material mechanical parameters of the thickness layer in the bending process of steam-softened solid wood under mold constraint, and to establish layered mechanical data accordingly.

[0034] The energy imbalance analysis module is used to calculate the energy storage of each layer based on the layered mechanical data and to distinguish between the tension side and the compression side, so as to obtain an energy index that characterizes the degree of tension-compression imbalance.

[0035] The residual stress and springback moment calculation module is used to calculate the residual stress distribution and obtain the equivalent springback moment based on the energy index and demolding cooling characteristics.

[0036] The curvature correction and springback prediction module is used to calculate the predicted value of the curvature radius and springback amount after springback based on the equivalent springback torque, the bending stiffness of the component, and the initial forming curvature radius.

[0037] Compared with existing technologies, the method for predicting the springback of solid wood bending molding provided by this invention establishes layered mechanical data by acquiring strain data and material mechanical parameters of each layer along the thickness direction. It then distinguishes between the tensile and compressive sides based on the energy storage calculation of each layer to obtain energy indicators characterizing the degree of tension-compression imbalance. Furthermore, it calculates the residual stress distribution and equivalent springback torque by combining demolding cooling characteristics, and finally solves for the radius of curvature and predicted springback value after springback. This fully characterizes the non-uniformity of interlayer mechanical properties of wood along the thickness direction, overcoming the prediction bias of traditional methods based on the assumption of uniform materials. Simultaneously, it accurately depicts the energy storage difference between the tensile and compressive sides, compensating for the theoretical deficiency of existing models that ignore the asymmetric mechanical behavior of tension and compression. By incorporating the coupled influence of layer temperature, layer moisture content, and fiber alignment angle on relaxation behavior into the residual stress calculation, it enhances the ability to finely describe the characteristics of hygrothermal relaxation. This invention significantly improves the accuracy of springback prediction and its industrial practical value by replacing manual empirical parameter setting with a systematic calibration mechanism, while reducing the number of trial moldings and material waste. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0039] Figure 1 This is a flowchart of a method for predicting the springback of solid wood bending forming according to an embodiment of the present invention.

[0040] Figure 2 This diagram illustrates an application scenario of the solid wood bending and forming springback prediction method according to an embodiment of the present invention. Detailed Implementation

[0041] Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It is obvious that the described embodiments are merely some embodiments of the present invention, and not all embodiments of the present invention, and it should be understood that the present invention is not limited to the exemplary embodiments described herein.

[0042] As mentioned in the background section, in the solid wood bending process, due to the difference in stress state between the tensile and compressive sides of the wood fibers during bending, the residual tensile stress in the inner fiber layer and the residual compressive stress in the outer fiber layer form a torque after demolding, causing the bent component to spring back inward. The amount of springback is affected by multiple factors such as wood moisture content, softening temperature, bending radius, wood thickness, and fiber arrangement direction. Existing processes rely on empirical compensation adjustments and cannot accurately quantify and predict the springback value under different combinations of process parameters before molding. This results in inaccurate mold compensation angle settings, causing the curvature error of the finished product to exceed the process tolerance, requiring repeated mold trials for correction.

[0043] Figure 1 This is a flowchart illustrating a method for predicting the springback of solid wood during bending and shaping, according to an embodiment of the present invention. Figure 1 As shown, the method for predicting the springback of solid wood during bending includes:

[0044] S1. The springback prediction system establishes a thickness-direction fiber stress layer for solid wood bentwood after steam softening. During the mold-constrained bending process, it acquires the instantaneous strain, equivalent elastic modulus of each fiber stress layer under hygrothermal softening, layer temperature, layer moisture content, and fiber arrangement direction. Then, based on the position of the bending neutral layer and the strain direction of each layer, it generates a layered mechanical dataset with stress property labels, which serves as the input data for subsequent internal stress imbalance energy calculation.

[0045] Specifically, the system first reads the species, batch number, initial moisture content, density range, grain direction, and drying and conditioning records of the timber to be bent from the timber batch database. It then reads the steam softening temperature, softening time, holding time, bending speed, demolding time, and cooling method from the process database. Subsequently, it reads the mold target curve, design radius of curvature, clamping position, and limit stroke from the mold geometry database. After reading the above data, the system establishes a cross-sectional coordinate system for the bent timber, using the thickness direction of the timber as the layer coordinate direction and the plane containing the bending axis as the calculation plane. This ensures that the thickness coordinates, layer coordinates, neutral layer coordinates, and mold radius of curvature are all represented in the same coordinate system.

[0046] Once the cross-sectional coordinate system is established, the system divides the thickness direction into multiple fiber-reinforced layers according to the bending material thickness and sampling resolution. Each fiber-reinforced layer corresponds to a layer number, layer thickness, layer center coordinates, cross-sectional width, and the position of its respective arc segment. For areas near the outer arc surface, inner arc surface, and areas where the neutral layer may shift, the system can use a relatively small layer thickness for division to preserve the strain gradient on the tensile and compressive sides during bending; for thickness areas with relatively gentle strain changes, a relatively large layer thickness can be used to reduce unnecessary data processing. If the bending member has variable curvature along its length, the system can also divide the bending material into multiple local arc segments according to the arc length position, and establish a fiber-reinforced layer in the thickness direction within each local arc segment, so that subsequent calculations can obtain the local springback of each arc segment.

[0047] Subsequently, the system retrieves sampling data from the strain acquisition device during the mold-constrained bending process. The strain acquisition device can be one or more of the following: fiber Bragg grating, moisture-resistant resistance strain gauge, flexible thin-film strain element, or digital image correlation measurement device. For high-end solid wood furniture components where it is inconvenient to directly embed sensors in the actual finished product, the system can deploy sensors in the machining allowance area, end extension section, or on accompanying monitoring samples from the same batch. These accompanying monitoring samples share the same wood species, thickness grade, grain direction range, initial moisture content adjustment process, and steam softening regime as the actual bent material, and undergo the same mold-constrained bending conditions as the actual bent material. In cases where it is impossible to directly install physical sensors in each fiber stress layer, the system can utilize the surface full-field strain, mold curvature radius, and batch-level calibration relationship obtained from digital image correlation measurements to invert the strain values ​​of each fiber stress layer. In this way, the system can obtain strain data corresponding to each layer without requiring sensors to be embedded in every internal fiber layer.

[0048] Furthermore, the system records mold displacement, clamping force, steam temperature, bending time, holding time, and demolding time simultaneously with the acquisition of strain data, ensuring that the strain value of each fiber stress layer corresponds to a specific process moment. If digital image correlation measurement is used, the system first calculates the displacement field from the speckle image on the bent material surface, and then maps the surface strain to each fiber stress layer based on the geometric relationship of the bending section and the thickness-direction strain distribution obtained from the same batch of calibrated samples. If fiber optic or strain gauge measurement is used, the system directly associates the corresponding fiber stress layer with the sensor's embedded or attached layer. For strain data obtained at the end of the bent material or in the machining allowance area, the system performs position mapping based on the consistency of the mold curvature between the end extension and the actual forming section, ensuring that the acquired data represents the in-layer deformation state of the actual forming area.

[0049] When obtaining the equivalent elastic modulus of a layer, the system does not directly call the average elastic modulus of dry wood at room temperature. Instead, it retrieves the mechanical test results of the same batch of wood under humid and softened conditions. Specifically, a thin-layer reference sample can be prepared from the same batch of wood. The reference sample undergoes the same steam softening temperature, softening time, and moisture content adjustment process as the wood to be bent. After the reference sample reaches the softened state, micro-three-point bending, sheet tension, sheet compression, or micro-area indentation tests are performed. The linear response segment between load and displacement is recorded, and the equivalent elastic modulus of the softened state is calculated from the sample size and loading method. For cases where there are differences in moisture content or temperature between different layers, the system establishes an interpolation table based on the test results of the reference sample at different temperatures and moisture contents. In actual calculations, the equivalent elastic modulus of the corresponding layer is obtained by reading or interpolating according to the current layer temperature and moisture content.

[0050] On the other hand, the system also reads the fiber arrangement direction of each fiber-bearing layer. This fiber arrangement direction can be obtained from the surface texture image of the bent wood, the direction of the annual rings on the end face, the direction of the vessel arrangement, the markings of the sawing stage, or manually entered texture angle data. If the fiber direction of a certain fiber-bearing layer forms an angle with the principal bending axis, the system corrects the softened elastic modulus according to the texture angle calibration relationship of the same batch of wood, so that the corrected equivalent elastic modulus represents the actual deformation resistance of that layer in the current bending direction. This direction correction relationship can be obtained through bending or tensile / compression tests of reference samples from the same batch at multiple texture angles and stored in the wood batch database for later retrieval.

[0051] After the strain, elastic modulus, temperature, moisture content, and fiber orientation of each layer are prepared, the system performs time synchronization and validity checks on the sampled data. If the strain data of a certain layer at a certain sampling time is discontinuous with the strain change trend of adjacent layers, or inconsistent with the change trend of the same layer at different times, the system marks the sampled data as low-reliability data and generates a measurement reliability coefficient based on sensor calibration error, sampling integrity, differential consistency between adjacent layers, and temporal continuity. If the sampled data is consistent with both spatial and temporal continuity, the system marks the data as valid data and retains a higher measurement reliability coefficient. The measurement reliability coefficient is used for data weight adjustment in the subsequent energy accumulation process, and its source is the sensor calibration and data continuity verification results.

[0052] Subsequently, the system identifies the location of the neutral layer in the bending process. The system traverses each fiber-reinforced layer along the thickness direction, reading the strain direction and layer coordinates of each layer at the same sampling time. If a continuous transition from tensile strain to compressive strain occurs between adjacent fiber-reinforced layers, the system determines the location of the neutral layer within that adjacent region. If local texture distortion or local measurement disturbances cause jumps in the strain sign of individual layers, the system verifies this by combining the neutral layer evolution trend at adjacent times, the layer-wise equivalent elastic modulus distribution, and the tensile-compressive balance relationship of the cross-section, ensuring that the location of the neutral layer is consistent with the actual stress state of the bending cross-section. After determining the neutral layer, the system marks fiber-reinforced layers located on one side of the neutral layer with strain in the tensile direction as tension layers, and fiber-reinforced layers located on the other side with strain in the compressive direction as compression layers. For fiber-reinforced layers with strain close to zero near the neutral layer, the system determines its stress nature label based on the stress continuity between adjacent layers and adjacent times.

[0053] After all fiber-reinforced layers have been labeled with their stress properties, the system writes the layer number, layer thickness, layer center coordinates, cross-sectional width, instantaneous strain, equivalent elastic modulus after hygrothermal softening, layer temperature, layer moisture content, fiber alignment angle, measurement reliability coefficient, neutral layer coordinates, and stress property labels into the layered mechanics dataset. This layered mechanics dataset is organized according to sampling time and layer number, and can represent the thickness-direction strain field, elastic modulus field, and stress property distribution of the bent material during the die-constrained bending process. This layered mechanics dataset is output at the end of S1 and then entered into S2 for calculating the strain energy of each layer and the unbalanced internal stress energy between the tensile and compressive sides.

[0054] In one embodiment, a 18mm thick and 40mm wide beechwood bend can be divided into eight fiber-reinforced layers along its thickness. During the bending holding phase, the system collects strain data for each layer using accompanying samples and obtains the softened equivalent elastic modulus in the range of 4.5GPa to 6.0GPa using thin-layer reference samples from the same batch. The system identifies the neutral layer shifting towards the compression side relative to the geometric center and accordingly marks several layers on the outer arc side as tension layers and several layers on the inner arc side as compression layers. Finally, it outputs a layered mechanical dataset containing the strain, modulus, layer position, and stress properties of each layer. This example is only for illustrating the data organization and layer labeling process and does not limit the number of layers, sensor type, or wood species.

[0055] The S2 rebound prediction system, based on the layered mechanical dataset output by S1, calculates the intralayer physical strain energy density of each fiber stress layer during the mold-constrained bending holding stage. It then generates the rebound-driven strain energy density by combining the lever arm distance of each layer relative to the neutral layer and the measurement reliability. Subsequently, the energy is summarized according to the force properties of the tension layer and the compression layer to obtain the internal stress imbalance energy and the total rebound-driven strain energy.

[0056] Specifically, the system first reads the instantaneous strain, equivalent elastic modulus of hygrothermal softening, layer center coordinates, layer thickness, cross-sectional width, measurement reliability coefficient, neutral layer coordinates, and stress property markers of each fiber stress layer at each sampling moment from the layered mechanics dataset. Then, the system determines the bending retention calculation interval from the die displacement record, clamping force record, and bending trajectory record. This bending retention calculation interval corresponds to the time period after the die reaches the target bending trajectory, the bent material is constrained by a stable die, and has completed the main bending deformation. If local steam fluctuations, die micro-vibrations, or short-term contact changes occur within the bending retention calculation interval, the system does not use a single instantaneous sampling point as the final calculation basis. Instead, it performs weighted processing on multiple sampling moments within this calculation interval to ensure that the energy result corresponds to a stable constrained bending state.

[0057] After determining the bending retention calculation interval, the system reads the strain time series and elastic modulus time series within that interval for each fiber-stressed layer and calculates the physical strain energy density of that layer. Subsequently, the system calculates a lever arm sensitivity correction coefficient based on the distance from the fiber-stressed layer to the neutral layer, allowing fiber-stressed layers farther from the neutral layer to contribute more to the springback-driven energy structure. Simultaneously, the system introduces a measurement reliability coefficient to reduce the impact of incomplete sampling or locally disturbed layer data on the springback-driven strain energy calculation. The intra-layer strain energy and internal stress imbalance energy can be determined using the following formula:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] in, Let be the physical strain energy density of the i-th fiber stress layer within the bending retention calculation interval; Let be the elastic driving strain energy density of the i-th fiber stress layer; To maintain the calculation range for bending; This refers to the sampling time within this interval; The sampling time weight is determined by the sampling interval, curvature stability, and number of effective sampling layers; Let be the equivalent elastic modulus of the i-th layer at the sampling time due to hygrothermal softening; The instantaneous strain of the i-th layer; Let be the measurement reliability coefficient of the i-th layer at the sampling time; The thickness coordinates of the center of the i-th layer; The coordinates of the neutral layer at the sampling time; For the thickness of the bent material; This is the lever arm sensitivity correction factor; and These are correction parameters obtained through springback calibration of the same batch of timber; The symbol represents the stress characteristics; positive for tension layers and negative for compression layers. The width of the i-th layer cross section; Let be the thickness of the i-th layer; This represents the energy generated by the unbalanced internal stress. This represents the total strain energy driven by the rebound.

[0064] In the specific calculation, the system first accumulates multiple sampled values ​​of each layer within the bending retention calculation interval to obtain the physical strain energy density of that layer. Then, it reads the distance from the center of that layer to the neutral layer at the corresponding sampling time, normalizes it by thickness, and calculates the lever arm sensitivity correction coefficient. Finally, it uses the physical strain energy density, measurement reliability coefficient, and lever arm sensitivity correction coefficient together to obtain the springback-driven strain energy density of that layer. After the springback-driven strain energy density of all layers is calculated, the system summarizes the data according to the force characteristics: tension layers are accumulated with a positive term, and compression layers with a negative term, forming a difference in energy storage between the tension and compression sides. The absolute value of this difference is used to obtain the internal stress imbalance energy. Simultaneously, the system positively accumulates the springback-driven strain energy of all fiber-loaded layers to obtain the total springback-driven strain energy. The internal stress imbalance energy and the total springback-driven strain energy are both input into S3 to establish the residual stress distribution.

[0065] Furthermore, during the initial calibration phase, the system can perform multi-radius bending-unloading springback tests on standard specimens from the same batch. Specifically, the system selects standard specimens of the same tree species, thickness grade, grain direction range, and moisture content adjustment process as the material to be bent, and sets multiple forming radius conditions. Each standard specimen first undergoes a steam softening process consistent with actual production, then is bent to the corresponding forming radius on a mold or universal testing machine. After pressure holding, it is demolded, and after cooling, the actual springback radius or springback amount is measured. Subsequently, the system writes the layer strain data, modulus data, and measured springback amount of the standard specimens into the calibration dataset and adjusts them in the calibration calculation. and This process minimizes the residual between the predicted rebound calculated from S2 to S4 and the measured rebound. This inverse calculation can be performed using nonlinear least squares, grid search followed by local optimization, or the Levenberg-Marquardt algorithm. When the predicted residuals under different radius conditions tend to stabilize, the system will... and Write it into the same batch of parameter library for use in online production prediction.

[0066] In one implementation, if the standard specimen includes three sets of molding radii of 150mm, 200mm, and 250mm, the system measures the actual radius of curvature of each set after demolding and calculates the initial strain energy distribution of each set based on the layered mechanical data obtained in S1; subsequently, the system uses the sum of the squares of the springback errors of the three sets as the optimization objective to inversely calculate... and Once calibration is complete, the online prediction phase no longer performs repeated inverse calculations; instead, it directly calls the corresponding tree species, thickness level, and moisture content range. and If the batch, thickness grade, or moisture content range of the timber changes, the system will re-calibrate or call up data from similar batches for interpolation correction.

[0067] For example, for a beech wood bend with a thickness of 18 mm and a width of 40 mm, the distance from the center of a tension layer to the neutral layer is 6.5 mm, the equivalent elastic modulus in the softened state is 5.2 GPa, the average strain is 0.003, and the measurement reliability coefficient is 0.98; the system is based on the calibration results... and Calculate the lever arm sensitivity correction factor for this layer, and obtain the springback-driven strain energy density of this layer accordingly. After performing the same processing on all tension and compression layers, the system outputs the internal stress imbalance energy and the total springback-driven strain energy. This example is only for illustrating the input, processing, and output results, and does not limit the specific parameter values.

[0068] The S3 rebound prediction system calculates the residual stress distribution of each fiber stress layer after demolding based on the internal stress imbalance energy, total rebound driving strain energy, and physical strain energy density of each fiber stress layer output by S2, combined with the wet and hot relaxation calibration data of the same batch of wood during the demolding and cooling process. It also summarizes the residual stress along the thickness direction to obtain the equivalent rebound torque.

[0069] Specifically, the system first reads the physical strain energy density, stress property sign, layer coordinates, layer thickness, cross-sectional width, internal stress imbalance energy, and total springback-driven strain energy of each fiber-stressed layer output by S2; then it reads the layer temperature, layer moisture content, fiber alignment angle, and neutral layer coordinates at the demolding time or cooling calculation time. After the above input data is prepared, the system retrieves the wet-heat relaxation parameter library of the same batch of wood. The wet-heat relaxation parameter library is established by constant strain relaxation tests of reference samples from the same batch. The reference samples are preferably wood of the same species, thickness grade, grain direction range, and moisture content adjustment process as the wood to be processed.

[0070] In the damp-heat relaxation test, the reference specimen first undergoes the same steam softening regime as the actual bent material, and is then loaded to a surface strain level corresponding to the target bending radius, maintaining a constant strain state at this strain level. The system records the stress decay curves of the specimen at different cooling times, while also recording the temperature, moisture content, and fiber alignment direction of the specimen's interior or surface. For the difference between the tension and compression sides, the system can prepare tensile unloading and compression unloading reference specimens separately, or read residual stress or residual deformation data from the outer and inner arc sides of the bending reference specimen to establish a residual conversion correction relationship between the tension and compression sides. After the test, the system groups the stress decay curves according to layer temperature, moisture content, and fiber alignment angle, and fits the relaxation branch weights and characteristic relaxation times.

[0071] In one implementation, the system uses the following relationship between residual stress and equivalent springback moment for calculation:

[0072]

[0073]

[0074]

[0075]

[0076] in, The internal stress imbalance release coefficient is determined by the total internal stress imbalance energy and the springback-driven strain energy in S2. Let be the relaxation retention coefficient of the i-th fiber stress layer at cooling time t; This represents the number of relaxed branches; Let m be the weight of the relaxed branch in the i-th layer; Let m be the feature relaxation time of the m-th relaxation branch in the i-th layer; Let i be the temperature of the i-th layer; Let be the moisture content of the i-th layer; The fiber arrangement angle of the i-th layer; To preserve the representative time of the calculation interval for bending; The calculation time is for demolding or cooling; The residual stress of the i-th fiber bearing layer after demolding; Symbols representing the nature of force; This is the residual conversion correction factor for the tension / compression side; Let be the equivalent elastic modulus of the i-th layer under the demolding and cooling state; The physical strain energy density output by S2; This is the equivalent springback torque; The coordinates of the neutral layer at the moment of demolding or cooling calculation.

[0077] In the specific calculation, the system first uses the output of S2. and Calculate the internal stress imbalance release coefficient This coefficient represents the proportion of energy actually involved in the tension-compression imbalance release within the full cross-section energy storage. Subsequently, the system reads the layer temperature, layer moisture content, and fiber alignment angle for each fiber stress layer, and retrieves the corresponding relaxation branch from the wet-heat relaxation parameter library or through interpolation. and characteristic relaxation time If the current layer temperature and moisture content fall between two calibration conditions, the system interpolates according to the calibration data table; if the current condition exceeds the existing calibration range, the system prioritizes extrapolating and verifying data from adjacent batches of the same tree species and thickness level, and marks this condition as one requiring supplementary calibration. After obtaining the relaxation retention coefficient, the system calculates the residual stress of the layer by combining the residual conversion correction coefficient on the tension / compression side.

[0078] The residual conversion correction coefficient on the tension / compression side The residual stress was obtained through tensile and compressive unloading tests on samples from the same batch. Specifically, the system applied tensile and compressive strains corresponding to the target bending state to thin-layer samples from the same batch, held them under the same humid and hot conditions, and then unloaded them, recording the residual deformation or residual stress after cooling. Subsequently, the system compiled the difference in residual stress between the tensile and compressive sides into a parameter table that varies with temperature, moisture content, and fiber alignment angle. During online calculation, if the i-th layer is a tension layer, the residual conversion correction factor for the tensile side is used; if the i-th layer is a compression layer, the residual conversion correction factor for the compression side is used. Through this process, the difference in residual stress between the tensile and compressive sides of the wood caused by differences in cell wall plastic compression, fiber slippage, and humid and hot relaxation can be incorporated into the calculation of the springback moment.

[0079] Furthermore, after calculating the residual stress of each fiber-loaded layer, the system multiplies the residual stress of that layer by its cross-sectional area to obtain the residual internal force of that layer. This residual force is then multiplied by the distance from the center of that layer to the demolding neutral layer to obtain the layer's contribution to the springback moment. The system iterates through all fiber-loaded layers and algebraically summarizes the moment contributions of each layer to obtain the equivalent springback moment. If the bending member is divided into multiple local arc segments along its length, the system calculates the residual stress distribution and equivalent springback moment for each local arc segment, and stores the equivalent springback moment of each arc segment in association with its corresponding arc segment number. The equivalent springback moment is output to S4 at the end of S3 and used in conjunction with the layered equivalent bending stiffness to solve for the radius of curvature after springback.

[0080] In one implementation, if the relaxation tests in the same batch show that the reference specimen experiences rapid stress release in the first few tens of seconds after demolding, followed by a slower cooling and solidification release process, the system can use two or three relaxation branches to characterize rapid and slow relaxation respectively. If the predicted residual does not decrease significantly after fitting multiple branches, the system can reduce the number of branches to avoid overfitting; if a single branch cannot cover the measured stress decay curve, the system can increase the number of branches. The selection of the number of branches is based on the fitting residual of the stress relaxation curve of the reference specimen and the consistency results of the repeated specimens, rather than being arbitrarily determined.

[0081] For example, if the unbalanced internal stress energy output by S2 is 4.8 J / m and the total springback-driven strain energy is 21.5 J / m, the system first obtains the unbalanced internal stress release coefficient. For a certain tensile fiber-loaded layer, the system reads its physical strain energy density, equivalent elastic modulus under cooling conditions, layer temperature, moisture content, and fiber alignment angle, and interpolates the corresponding relaxation retention coefficient from the relaxation parameter library. Then, it combines the tensile side residual conversion correction coefficient to obtain the residual tensile stress of the layer. After the system completes the calculation for all tensile and compressive layers, it summarizes the results along the thickness direction to obtain the equivalent springback moment. This example is only used to illustrate the generation process of residual stress and springback moment and does not limit the specific values.

[0082] S4, the springback prediction system couples the equivalent springback torque obtained in S3 with the layered equivalent bending stiffness of the bending component in the demolding and cooling state, and calculates the curvature radius correction value after demolding and the predicted value of springback in solid wood bending forming by combining the initial forming curvature radius given by the mold.

[0083] Specifically, the system first reads the target bending curve from the mold geometry database and determines the initial forming radius of curvature of the bent component based on the target bending curve. For components such as chair backs, armrests, and stair handrails, where the curvature of the main arc segments is basically the same, the system can read the design radius of curvature corresponding to the main bending arc segments as the initial forming radius of curvature. For components where the curvature changes continuously along the length direction, the system divides the component into multiple local arc segments according to the arc length position and reads the initial forming radius of curvature of each local arc segment. Subsequently, the system reads the equivalent springback torque output by S3 and reads the equivalent elastic modulus, layer thickness, cross-sectional width, layer center coordinates, and demolding neutral layer coordinates of each fiber stress layer in the demolding cooling state from the data of S1 and S3.

[0084] Before calculating the equivalent bending stiffness of each layer, the system determines the effective coefficient of cooling and curing for each fiber-bearing layer. This effective coefficient is obtained from cooling modulus recovery tests on the same batch of wood. Specifically, the system can perform dynamic thermomechanical analysis or time-sharing cooling bending tests on thin-layer reference samples from the same batch, recording the equivalent elastic modulus recovery process of the samples at different cooling times, temperatures, and moisture contents. The modulus recovery data is then compiled into a table of effective curing coefficients corresponding to layer temperature, moisture content, and cooling time. During online calculation, the system retrieves or interpolates the effective coefficients from this table based on the temperature, moisture content, and cooling time of the i-th fiber-bearing layer at the moment of demolding. If the current layer has cooled sufficiently and is close to its stable modulus, This corresponds to a higher stiffness participation ratio; if the current layer is still in a high temperature and high humidity state. This corresponds to a lower stiffness participation ratio.

[0085] In one implementation, the system employs the following radius of curvature correction relationship:

[0086]

[0087]

[0088]

[0089]

[0090] in, The layered equivalent bending stiffness of the bending member in the demolding and cooling state; Let be the equivalent elastic modulus of the i-th fiber under the condition of demolding and cooling. The effective coefficient for cooling and curing of the i-th layer; The width of the i-th layer cross section; The thickness of the i-th layer Let i be the coordinates of the center of the i-th layer; The coordinates of the neutral layer at the moment of demolding; Let be the initial forming curvature, and be determined by the initial forming curvature radius. Sure; The equivalent springback torque output by S3, These are geometric nonlinearity correction coefficients; For the thickness of the bent material; The radius of curvature after springback; This is the predicted value for rebound.

[0091] In the specific solution process, the system first calculates the local cross-sectional inertial contribution and the parallel axis inertial contribution relative to the demolding neutral layer for each fiber-loaded layer. This is then multiplied by the equivalent elastic modulus of the layer in its cooling state and the effective coefficient of cooling and solidification to obtain the layer's contribution to the overall bending stiffness. After calculating the stiffness contributions of all fiber-loaded layers, the system accumulates these contributions to obtain the layered equivalent bending stiffness. Subsequently, the system couples the equivalent springback torque output from S3 with the layered equivalent bending stiffness to obtain the curvature recovery caused by residual stress release. This is then combined with a geometric correction term formed by the thickness and the initial radius of curvature to correct the curvature recovery under small-radius bending. Finally, the curvature recovery is subtracted from the initial forming curvature to obtain the demolded curvature, which is then converted into the springback radius. The system subtracts the springback radius from the initial forming radius to obtain the predicted value of the solid wood bending springback.

[0092] Furthermore, the geometric nonlinearity correction coefficient The springback was calibrated using multiple radii of standard specimens from the same batch. Specifically, the system selected standard specimens of the same wood species, thickness grade, and grain direction as the material to be bent, and set multiple forming radius conditions. Each standard specimen underwent steam softening, die bending, pressure holding, demolding, and cooling in sequence, and the actual radius of curvature was measured after cooling. The system compared the measured springback amount under each condition with the predicted springback amount calculated from S2 to S4, and adjusted accordingly. This reduces the overall prediction error across multiple radius conditions. After calibration, the system will... The parameters are written into the corresponding tree species, thickness grade, moisture content range, and radius range. During online production, the system calls the corresponding parameters based on the current bending batch and forming radius. If the current forming radius is between two calibrated radii, the system will interpolate according to the calibrated data.

[0093] For a component with multiple local curvature segments along its length, the system calls upon the corresponding initial radius of curvature, equivalent springback moment, and layered equivalent bending stiffness for each local arc segment to calculate the springback radius and local springback amount after springback. Once all local arc segments have been calculated, the system combines the local springback amounts in arc length order to form the springback curve of the entire bent component. This springback curve can be output to the mold compensation module, which converts the local springback amount into mold compensation radius, press stroke compensation amount, or fixture positioning compensation amount. Alternatively, it can be output to the finished product quality prediction module to determine whether the finished product curvature under the current combination of process parameters can meet the drawing tolerance requirements before actual molding.

[0094] In one implementation, the initial forming radius of curvature of a handrail component is 180mm. The system reads the equivalent springback torque output by S3 and calculates the layered equivalent bending stiffness based on the equivalent elastic modulus of the cooling state of the eight fiber stress layers, the effective coefficient of cooling and solidification, layer thickness, cross-sectional width, and the coordinates of the demolding neutral layer. Subsequently, the system calls the geometric nonlinear correction coefficient obtained from the multi-radius calibration of the same batch to calculate the radius of curvature after demolding and outputs the predicted value of springback. If the predicted springback indicates that the radius of curvature of the finished product will be greater than the design requirement, the system can convert the difference into the mold compensation amount for the next batch. This example is only used to illustrate the input, processing, and output process of S4 and does not limit the specific component size or compensation method.

[0095] In summary, the method for predicting the springback of solid wood bending molding based on embodiments of the present invention is explained. It establishes layered mechanical data by acquiring strain data and material mechanical parameters of each layer along the thickness direction. Based on the energy storage calculation of each layer, it distinguishes between the tensile and compressive sides to obtain energy indicators characterizing the degree of tension-compression imbalance. Then, it calculates the residual stress distribution and equivalent springback torque by combining demolding cooling characteristics, and finally solves for the radius of curvature and predicted springback value after springback. This fully characterizes the non-uniformity of interlayer mechanical properties of wood along the thickness direction, overcoming the prediction bias of traditional methods based on the assumption of uniform materials. Simultaneously, it accurately depicts the energy storage difference between the tensile and compressive sides, compensating for the theoretical deficiency of existing models that ignore the asymmetric mechanical behavior of tension and compression. Furthermore, by incorporating the coupled influence of layer temperature, layer moisture content, and fiber alignment angle on relaxation behavior into the residual stress calculation, it improves the ability to finely describe the characteristics of hygrothermal relaxation. The present invention significantly improves the accuracy of springback prediction and its industrial practical value by replacing manual empirical parameter setting with a systematic calibration mechanism, while reducing the number of mold trials and material waste.

[0096] Here, those skilled in the art will understand that the specific operations of each step in the above-mentioned solid wood bending and springback prediction system have been referenced above. Figure 1 and Figure 2 The method for predicting the springback of solid wood bending is described in detail in the description of the method, and therefore, its repeated description will be omitted.

[0097] In summary, the solid wood bending and forming springback prediction system based on the embodiments of the present invention is explained. It establishes layered mechanical data by acquiring strain data and material mechanical parameters of each layer along the thickness direction, and distinguishes between the tensile and compressive sides based on the energy storage calculation of each layer to obtain energy indicators characterizing the degree of tension-compression imbalance. Then, it calculates the residual stress distribution and equivalent springback torque by combining demolding cooling characteristics, and finally solves for the radius of curvature and predicted springback value after springback. This fully characterizes the non-uniformity of interlayer mechanical properties of wood along the thickness direction, overcoming the prediction bias of traditional methods based on the assumption of uniform materials; it also accurately depicts the energy storage difference between the tensile and compressive sides, compensating for the theoretical deficiency of existing models that ignore the asymmetric mechanical behavior of tension and compression; and by incorporating the coupled influence of layer temperature, layer moisture content, and fiber arrangement angle on relaxation behavior into the residual stress calculation, it improves the ability to finely describe the wet-heat relaxation characteristics. The present invention significantly improves the accuracy of springback prediction and its industrial practical value by replacing manual empirical parameter setting with a systematic calibration mechanism, while reducing the number of mold trials and material waste.

Claims

1. A method for predicting the springback of solid wood during bending and shaping, characterized in that, include: Strain data and material mechanical parameters of solid wood softened by steam were obtained during the mold-constrained bending process, and layered mechanical data were established accordingly. Based on the layered mechanical data, the energy storage of each layer is calculated and the tension side and compression side are distinguished to obtain an energy index characterizing the degree of tension-compression imbalance. The residual stress distribution is calculated based on the energy index and demolding cooling characteristics, and the equivalent springback torque is obtained. The predicted values ​​of the radius of curvature and rebound amount after springback are calculated based on the equivalent springback moment, the bending stiffness of the component, and the initial forming radius of curvature.

2. The method for predicting the springback of solid wood during bending and shaping according to claim 1, characterized in that, The calculation of energy storage in each layer includes: calculating the physical strain energy density of each fiber stress layer during the bending holding stage, and generating the rebound driving strain energy density by combining the lever arm distance of each layer relative to the bending neutral layer. The method for determining the rebound-driven strain energy density is as follows: ； in, Let be the elastic driving strain energy density of the i-th fiber stress layer. To maintain the calculation range for bending, Weights for sampling times, Let be the measurement reliability coefficient of the i-th layer at the sampling time. For lever arm sensitivity correction factor, Let be the equivalent elastic modulus of the i-th layer at the sampling time due to hygrothermal softening. The instantaneous strain of the i-th layer; The method for determining the lever arm sensitivity correction coefficient is as follows: ； in, Let be the thickness coordinates of the center of the i-th layer. The coordinates of the neutral layer at the sampling time. For the thickness of the bending material, and These are the correction parameters obtained through the rebound calibration of the same batch of wood.

3. The method for predicting the springback of solid wood during bending and shaping according to claim 2, characterized in that, The and Obtained through inverse calculation during the initial calibration phase, the inverse calculation includes: Standard specimens of the same tree species, thickness grade, grain direction range, and moisture content adjustment process as the material to be bent are selected. Three or more sets of different forming radius conditions are set up, and the measured springback amount is measured under each condition. With the objective of minimizing the sum of squared residuals between the measured springback amount and the predicted springback amount, a nonlinear least squares algorithm or the Levberg-Marquardt algorithm is used to inversely calculate the springback amount. and The inverse calculation results are then written into the parameter library for online prediction.

4. The method for predicting the springback of solid wood during bending and shaping according to claim 3, characterized in that, The residual stress distribution is determined in the following way: The internal stress imbalance release coefficient is obtained using the energy index. For each fiber stress layer, the relaxation retention coefficient is obtained from the wet and heat relaxation parameter library of the same batch of wood based on its layer temperature, layer moisture content and fiber arrangement angle. The residual stress of the layer after demolding is obtained by multiplying the internal stress imbalance release coefficient, the relaxation retention coefficient, the tension-compression side residual conversion correction coefficient, and the equivalent stress converted from the physical strain energy density. The residual stress of this layer is then multiplied by the cross-sectional area of ​​the layer and the lever arm distance relative to the neutral layer at the demolding time to obtain the contribution of this layer to the springback torque. The equivalent springback torque is obtained by summing the torque contributions of all fiber-stressed layers.

5. The method for predicting the springback of solid wood during bending and shaping according to claim 4, characterized in that, The relaxation preservation coefficient is obtained through the relaxation branch weight. Relaxation branch characteristics and relaxation time Determine as follows: ； in, Let be the relaxation retention coefficient of the i-th fiber stress layer. To relax the number of branches, Let be the weight coefficient of the m-th relaxation branch in the i-th layer. Let m be the characteristic relaxation time of the m-th relaxation branch in the i-th layer. For layer temperature, The water content of the layer, The fiber alignment angle, To preserve representative moments within the calculation interval for bending, This refers to the cooling time after demolding.

6. The method for predicting the springback of solid wood during bending and shaping according to claim 5, characterized in that, The residual conversion correction factor on the tension and compression sides was obtained through tensile unloading and compressive unloading tests of the same batch of samples: Tensile strain and compressive strain corresponding to the target bending state were applied to thin-layer samples of the same batch. After being kept under the same humid heat conditions, the samples were unloaded and the residual deformation or residual stress after cooling was recorded. The difference in residual retention between the tensile side and the compressive side was compiled into a parameter table that varies with temperature, moisture content and fiber arrangement angle. During online calculations, the tension layer uses the residual conversion correction factor on the tension side, and the compression layer uses the residual conversion correction factor on the compression side.

7. The method for predicting the springback of solid wood during bending and shaping according to claim 6, characterized in that, The bending stiffness of the component is a layered equivalent bending stiffness, which is obtained by multiplying and summing the equivalent elastic modulus, cooling and solidification effective coefficient, local section inertia term and parallel axis inertia term of each fiber stress layer in the demolding and cooling state. The method for determining the predicted value of springback is as follows: the equivalent springback torque is divided by the layered equivalent bending stiffness to obtain the curvature recovery amount, the curvature recovery amount is corrected by combining the geometric nonlinearity correction coefficient, the corrected curvature recovery amount is subtracted from the initial molding curvature to obtain the curvature after demolding, the reciprocal of the curvature after demolding is taken to obtain the curvature radius after springback, and the difference between the curvature radius after springback and the initial molding curvature radius is calculated to obtain the predicted value of springback.

8. A system for predicting the springback of solid wood during bending and shaping, characterized in that, include: The layered mechanical data construction module is used to obtain strain data and material mechanical parameters of the thickness layer in the bending process of steam-softened solid wood under mold constraint, and to establish layered mechanical data accordingly. The energy imbalance analysis module is used to calculate the energy storage of each layer based on the layered mechanical data and to distinguish between the tension side and the compression side, so as to obtain an energy index that characterizes the degree of tension-compression imbalance. The residual stress and springback moment calculation module is used to calculate the residual stress distribution and obtain the equivalent springback moment based on the energy index and demolding cooling characteristics. The curvature correction and springback prediction module is used to calculate the predicted value of the curvature radius and springback amount after springback based on the equivalent springback torque, the bending stiffness of the component, and the initial forming curvature radius.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the solid wood bending and forming springback prediction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the solid wood bending and forming springback prediction method as described in any one of claims 1 to 7.

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