An error compensation method based on binder jetting additive manufacturing

Abstract

The present invention is an error compensation method based on binder jetting additive manufacturing. The method includes the following steps: obtaining an offset error formula for triangular facets by considering the interaction between staircase error and penetration error, determining the number m of triangular facets in the input STL model, defining the set M as an array of triangular facets Tj, where m is the number of elements in the set M, and obtaining the offset errors of all triangular facets in the STL model; calculating the offset compensation value of the STL model vertices according to the projection of the offset error of the triangular facets in the vertex normal vector direction. After traversing all vertices, the vertices vi of the STL model are offset inward along the opposite direction of the vertex normal vector according to the corresponding offset compensation values, and the offset vertices are obtained, and then the compensated STL model is obtained. The present invention reduces the dimensional error caused by the interaction between staircase error and penetration error and realizes high-precision additive manufacturing.

Description

Technical Field

[0001] The present invention belongs to the field of binder jet additive manufacturing, and particularly relates to an error compensation method based on binder jet additive manufacturing. Background Art

[0002] The common file format for binder jet additive manufacturing is the STL file. Before printing, the STL model needs to be sliced to obtain two-dimensional contour information, and staircase errors will occur during the slicing process. During the printing process, the binder is ejected through the nozzle, impacts the surface of the sand bed, spreads and penetrates into the sand bed, and penetrates between the pores of the sand bed. Penetration errors will occur during this process. Through theoretical analysis and experiments, it is found that there is an interaction between the staircase error and the penetration error, and the combined error of these two errors is manifested as part size error after printing. Therefore, accurately expressing the interaction between the staircase error and the penetration error and compensating for the size error is of great significance for the forming accuracy of parts.

[0003] Currently, for the staircase errors generated by slicing the STL model, relevant research at home and abroad is relatively mature, and for the binder penetration error, some scholars have also given calculation and compensation methods for the penetration error. However, for the interaction between the staircase error and the binder penetration error and the compensation method for size error in binder jet additive manufacturing, the existing research is relatively lacking. Therefore, the present invention proposes an error compensation method based on binder jet additive manufacturing, which can achieve high-precision additive manufacturing of binder jet technology. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention aims to propose an error compensation method based on binder jet additive manufacturing. This error compensation method takes into account the interaction between the staircase error and the penetration error, and compensates for the error of the model in the way of vertex offset before printing the model, improving the forming accuracy and quality of binder jet additive manufacturing.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: an error compensation method based on binder jet additive manufacturing, the method comprising the following steps:

[0006] The offset error formula of the triangular facet obtained by considering the interaction between the staircase error and the penetration error is:

[0007]

[0008] wherein, k1 is the interaction coefficient between the negative staircase error and the penetration error in the upward triangular facet; k2 is the interaction coefficient between the positive staircase error and the penetration error in the downward triangular facet, and k1 and k2 are dimensionless quantities; L is the offset error; d xy is the penetration error in the XY direction, d zis the Z - direction penetration error; θ is the angle between the normal vector direction of the triangular facet and the forming direction, and d in formula (4) xy , d z , k1, and k2 are obtained through experiments;

[0009] Determine the number m of triangular facets in the input STL model, and define the set M as an array of triangular facets T j . m is the number of elements in the set M, and obtain the offset errors of all triangular facets in the STL model;

[0010] Calculate the offset compensation value of the vertices of the STL model according to the projection of the offset error of the triangular facet in the direction of the vertex normal vector After traversing all vertices, for the vertex v of the STL model i offset inward in the opposite direction of the vertex normal vector according to the corresponding offset compensation value to obtain the offset vertices and then obtain the compensated STL model.

[0011] The process of error compensation based on vertex offset is as follows:

[0012] Calculate the weighted average of the normal vectors of the triangular facets in the one - ring neighborhood of the vertex v according to formula (5) i to obtain the vertex normal vector

[0013]

[0014] where m is the number of elements in the set M, that is, the number of triangular facets in the STL model, j is an integer in the range of [1, m], λ is the shape factor, A is the area factor, is the normal vector of the triangular facet;

[0015] Calculate the projection C of the offset error of the triangular facet in the direction of the vertex normal vector j , and take the weighted average of the projections of the offset errors of the triangular facets in the one - ring neighborhood of the vertex in the direction of the vertex normal vector as the vertex offset compensation value

[0016]

[0017] where cosβ j is the vector product of the normal vector of the triangular facet and the vertex normal vector , β j is the vertex normal vector and the normal vector of the triangular facet the angle between them, is the offset error of the triangular facet T j .

[0018] The vertex offset compensation value is:

[0019]

[0020] The original vertex minus the vertex offset compensation value along the direction gives the offset vertex

[0021]

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] 1) The present invention proposes an error compensation method for binder jetting additive manufacturing. By calculating the offset error value of triangular facets, calculating the vertex offset compensation value, and offsetting the model vertices, the dimensional error caused by the interaction between the staircase error and the penetration error is reduced, and high-precision additive manufacturing is achieved.

[0024] 2) According to the flow situation of the binder in the sand bed, a three-dimensional numerical simulation model of the binder from spraying to penetration process is established, and the boundary conditions and the physical properties of the sand grains and the binder are determined. In the penetration simulation experiment, without changing other conditions, only the angle of the triangular facets is changed, which ensures the measurement accuracy of the synthesis error. For the interaction between the staircase error and the penetration error in the measurement results, an offset error formula for triangular facets based on the angle between the normal vector direction of the triangular facets and the forming direction is established, and the offset error of triangular facets with different angles after printing the STL model can be calculated.

[0025] 3) The present invention uses an error compensation method based on vertex offset. For the vertex offset of the model, based on the half-edge data structure, the triangular facets in the one-ring neighborhood of the vertex are traversed to calculate the vertex offset compensation value. After traversing all the coordinate points, the model vertices are offset towards the inside of the model in the opposite direction of the vertex normal vector. The compensated model maintains the original topological structure, avoiding complex error situations such as the crossing and overlapping of triangular facets. While ensuring the compensation accuracy, the compensation efficiency is improved, overcoming the complex error situations such as the crossing and overlapping of triangular facets caused by the use of a relatively complex spatial surface offset algorithm in the prior art. For the vertex offset compensation value, the projection of the offset error of the triangular facets in the direction of the vertex normal vector is calculated, and the shape factor and area factor of the triangular facets are used as the weight factors of the vertex normal vector. The weighted average of the offset error projections of the triangular facets in the one-ring neighborhood of the vertex is used as the vertex offset compensation value, which greatly improves the vertex offset accuracy and ensures the compensation accuracy.

[0026] ​4) Compared with the error compensation of most current binder jetting technologies that only separately consider the effects of staircase error and penetration error, the present invention compensates for the combined error considering the interaction between staircase error and penetration error. The error calculation result is more accurate, the model compensation precision is high, and the printing precision of parts is improved. Traverse all vertices of the STL model, offset inward according to the calculated vertex offset compensation value, obtain the model after error compensation, and maintain the original topological structure. Description of the Drawings

[0027] Figure 1 is the ideal penetration simulation result of the triangular facet for the inclined plane. In the figure, (a) is the penetration simulation result of the upward triangular facet, and (b) is the penetration simulation result of the downward triangular facet.

[0028] Figure 2 is the two-dimensional schematic diagram of the triangular facet offset error.

[0029] Figure 3 is an example of the sample part for the parameter calibration experiment.

[0030] Figure 4 is the schematic diagram of vertex offset. Detailed Implementation Manner

[0031] The present invention will be further explained below in conjunction with the embodiments and the drawings, but this is not used to limit the protection scope of the present application.

[0032] According to the flow situation of the binder in the sand bed, a three-dimensional numerical simulation model of the binder from spraying to penetration is established, the boundary conditions and the physical property parameters of the sand grains and the binder are determined. In the penetration simulation experiment, without changing other conditions, only the angle of the triangular facet is changed, the penetration simulation results of the triangular facets with different angles are measured, the position error between the ideal printing profile and the printing profile is obtained, the interaction relationship between the staircase error and the penetration error of the triangular facets with different angles is analyzed, and the triangular facet offset error formula considering the interaction between the staircase error and the penetration error is established;

[0033] Establish a three-dimensional multi-layer penetration simulation model:

[0034] Embodiment

[0035] Use COMSOL software to establish a three-dimensional numerical simulation model of the binder from spraying to infiltrating into the sand bed, and determine the physical property parameters of the sand bed, the nozzle, and the binder, as well as the boundary conditions of the model.

[0036] Determine the physical property parameters of the sand bed and the nozzle. A circular wetting wall is used to replace the actual sand grain shape. For the simulation of the sand bed, the average radius of the sand grains is γ = 71.4 μm, and the porosity of the sand bed is 0.3954. The nozzle shape and size of the array nozzle are provided by a certain manufacturer. The nozzle is an inverted trapezoid, with its upper base being 54 μm, the lower base being 50 μm, and the height being 50 μm. Set a nozzle in the two-phase flow module of the COMSOL software to simulate the array nozzle in a two-dimensional plane. This nozzle contains 28 nozzles, and the nozzle spacing is 76 μm;

[0037] Determine the physical property parameters of the binder and the model boundary conditions. Use furan resin as the binder, and its physical property parameters are shown in Table 1. To accurately simulate the penetration of the binder droplets in the sand layer, the contact angle between the binder and the sand grains should be less than π / 4. The contact angle between the furan resin and the sand grains is about 31.7°, so the contact angle is set to π / 6 in the boundary conditions. The boundary conditions of the penetration simulation model are set as shown in Table 2, where PP0 is a periodically varying pressure pulse signal.

[0038] Table 1 Physical Property Parameters of the Binder

[0039] Parameter <![CDATA[Surface tension / (N·m -1 )]]> Dynamic viscosity / (Pa·s) Contact angle / (°) <![CDATA[Density / (kg·m -3 )]]> Value 0.0432 0.009757 31.7 1120.86

[0040] Table 2 Boundary Conditions of the Simulation Model

[0041] Parameter <![CDATA[No slip / (m·s -1 )]]> Contact angle / (°) Pressure outlet / (Pa) Pressure inlet / (Pa) Value V＝0 π / 6 <![CDATA[P out = 0]]> <![CDATA[P in = PP0]]>

[0042] Ideally, the penetration morphology of the binder corresponding to different inclined triangular patches in the simulation is as Figure 1 shown. The gray part is the bonded area of the sand grains after the binder penetrates. Z is the forming direction, and F1 and F2 are the normal vector directions of the triangular patches.

[0043] The process of the binder penetration simulation experiment is as follows: Take the outermost connection line of the starting layer and the final layer of the position where the binder is ejected from the nozzle and impacts the sand bed as the two-dimensional projection of the triangular patch, that is, the ideal printing contour of the model. Take the actual boundary formed by the bonded sand grains after the binder penetrates as the printing contour. Conduct penetration simulation experiments on different-angle triangular patches by controlling the nozzle ejection behavior.

[0044] Measure the penetration simulation results of different-angle triangular patches to obtain the position error between the ideal printing contour and the printing contour. The results are shown in Table 2. The position error in the direction of the normal vector of the triangular patch upward is positive, and the reverse is negative. Among them, when the ideal inclined plane angle α is 0°, there is no position error for its upward triangular patch, and the position error of its downward triangular patch is the penetration error in the Z direction; when the ideal inclined plane angle α is 90°, the position error of its triangular patch is the penetration error in the XY direction.

[0045] Table 3 Measured Values of the Position Errors of Different-Angle Triangular Patches

[0046]

[0047] Convert the ideal inclined plane angle α in the simulation experiment into the included angle θ between the normal vector direction of the triangular patch and the forming direction. When θ is in the range of 0° to 90°, it is an upward triangular patch. As the included angle increases, the negative staircase error gradually increases numerically, and the position error also gradually increases. It can be seen that the penetration error has a compensating effect on the staircase error, that is, they cancel each other out. When the ideal inclined plane angle α is 25°, the position error of the upward triangular patch is negative, reflecting the influence of the negative staircase error on the position error of the triangular patch. When θ is in the range of 90° to 180°, it is a downward triangular patch. As the included angle increases, the positive staircase error gradually increases, and the position error also gradually increases. At this time, the staircase error and the positive penetration error are superimposed on each other.

[0048] Therefore, from the above simulation experiment, it can be seen that the interaction mechanisms of the upward triangular patch and the downward triangular patch are different and need to be considered and processed separately.

[0049] By analyzing the position error between the ideal printing contour and the actual printing contour, and considering the comprehensive influence of the staircase error and the penetration error on the printing accuracy, the present invention refers to the combined error of their interaction as the offset error L of the triangular patch related to the normal vector direction of the triangular patch, simply referred to as the offset error.

[0050] When not considering the interaction between the staircase error and the penetration error, the staircase error and the penetration error generated by the triangular patch printing are as shown in the two-dimensional plane Figure 2 In the figure, the gray oblique solid line is the ideal printing contour, and the gray oblique dotted line is the actual printing contour. Figure 2 On the left in the figure is a downward triangular patch, and on the right is an upward triangular patch. l represents the distance between the two gray oblique solid lines. A serrated staircase error will be generated during layering. d xy represents the penetration error in the XY direction, and d z represents the penetration error in the Z direction. L2 is the offset error of the upward triangular patch, L1 is the offset error of the downward triangular patch, h is the layer thickness, and θ is the included angle between the normal vector direction of the triangular patch and the forming direction.

[0051] The calculation of the triangular patch offset error L can be divided into two categories:

[0052] (1) When 0 < θ < π / 2, calculate with the offset error L2 of the upward triangular patch. As can be seen from the right side in Figure 2 , the penetration error component d xy in the XY direction causes the inclined plane to shift, and the staircase error has no influence on the actual printing boundary. Therefore, the offset error of the upward triangular patch:

[0053] L2 = d xy sin(θ) (1)

[0054] (2) When π / 2 < θ < π, calculate with the offset error L1 of the downward triangular patch. Starting from Figure 2 It can be seen that both the staircase error and the penetration error have an impact on the offset of the inclined plane. Considering the penetration error d in the XY direction xy and the penetration error d in the Z direction z Calculate the offset error of the downward triangular patch:

[0055] L1 = d xy sin(θ) - (d z + h)cos(θ) (2)

[0056] When not considering the interaction between the staircase error and the penetration error, the offset error formula of the triangular patch is as follows:

[0057]

[0058] Through the penetration simulation experiment, it can be seen that there is an interaction between the staircase error and the penetration error of the binder. Therefore, formula (3) cannot be used as the calculation formula for the offset error of the triangular patch, and the interaction between these two errors needs to be further considered;

[0059] Since the staircase error is related to the normal vector direction f of the triangular patch and the layer thickness h, and the layer thickness is the component in the Z direction, the offset of the printing contour caused by the staircase error and the penetration error d in the Z direction z is related to cosθ. The offset error formula of the upward triangular patch considering the interaction is equivalent to L(θ) = d xy sin(θ) - k1cos(θ), where k1 is the interaction coefficient between the negative staircase error and the penetration error in the upward triangular patch; the offset error formula of the downward triangular patch considering the interaction is equivalent to L(θ) = d xy sin(θ) - k2cos(θ), where k2 is the interaction coefficient between the positive staircase error and the penetration error in the downward triangular patch, and k1 and k2 are dimensionless quantities. Therefore, the offset error formula of the triangular patch considering the interaction between the staircase error and the penetration error is as follows:

[0060]

[0061] The parameters in formula (4) are obtained through experiments. The parameter calibration process is:

[0062] Printing experiments were carried out on the design samples. The appearance of the samples is a cuboid with dimensions of 600mm×140mm×10mm. There are inclined planes at multiple angles inside the cuboid. Sample 1 has inclined planes at multiple angles formed by edge structures, and Sample 2 has inclined planes at multiple angles formed by hole structures. The positions and sizes of the holes and edges in Sample 1 and Sample 2 correspond. The mirror models of Sample 1 and Sample 2 obtained by mirror flipping the model are Sample 3 and Sample 4. In this embodiment, the angles between the inclined planes and the horizontal direction are 90°, 80°, 70°, 60°, 50°, 40°, 30°, and 20° in sequence. By mirror flipping the model, it is verified that the triangular facet offset error is only related to the angle between the normal vector direction and the forming direction, and the mirror models of Sample 1 and Sample 2 are Sample 3 and Sample 4.

[0063] Considering the influence of the printing equipment and material ratio on the part forming in the 3DP process, printing experiments with the same layer thickness h were carried out using the equipment of the same manufacturer, and the STL model was obtained by scanning with a 3D scanner;

[0064] The triangular facet offset error between the scanned model and the designed model of the sample was measured using the 3D detection and metrology software Geomagic Control X;

[0065] The unknown parameters in formula (4) were calibrated according to the actual measured values of the triangular facet offset error. First, the measured angle α was converted into the angle θ between the triangular facet normal vector direction and the forming direction. The offset error of the triangular facet with θ = 90° was denoted as d xy , and the offset error of the triangular facet with θ = 180° was denoted as d z . It is assumed in the present invention that the penetration error and the step error action coefficients of the upward or downward triangular facets at different angles are the same during printing. Then, the offset error data of the triangular facets at other angles were substituted into formula (4) to calculate the two parameters k1 and k2 based on the least squares method. The calculated values of the unknown parameters k1 and k2 vary within a certain range;

[0066] The average value of the interaction coefficients of all samples (Sample 1, Sample 2, Sample 3, and Sample 4) was taken to calibrate the unknown parameters in the formula. The four parameters (d xy , d z , k1, and k2) were substituted into formula (4) to obtain the triangular facet offset error formula after calibrating the parameters, and the offset error of the triangular facets at different angles θ can be calculated.

[0067] The process of error compensation based on vertex offset is as follows

[0068] Error compensation based on vertex offset can generate a compensated model by offsetting the vertices of triangular facets. This method establishes a vertex offset compensation formula for triangular facets based on the offset error formula of triangular facets, predicts the dimensional errors of binder jetting additive manufacturing parts, and compensates for the dimensional errors.

[0069] The original model is in STL file format and consists of a pair of linear lists \(M = \{v, T\}\), where \(v=\{v_{i}|1\leq i\leq n\}\) is the set of all vertices of the triangular facets in set \(M\), and \(T = \{T_{j}|1\leq j\leq m\}\) is the set of triangular facets in set \(M\). Each triangular facet \(T_{j}\) is composed of three vertices \((v_{i_{1}},v_{i_{2}},v_{i_{3}})\). Define set \(M\) as a binary array composed of vertex \(v=\{v_{i}|1\leq i\leq n\}\) and triangular facet \(T = \{T_{j}|1\leq j\leq m\}\). For the STL model, \(n\) is the number of vertices and \(m\) is the number of triangular facets. i |1\leq i\leq n\}\) is the set of all vertices of the triangular facets in set \(M\), and \(T = \{T_{j}\) j |1\leq j\leq m\}\) is the set of triangular facets in set \(M\). Each triangular facet \(T_{j}\) j is composed of three vertices \((v_{i_{1}}\) a ,v_{i_{2}}\) b ,v_{i_{3}}\) c ). Define set \(M\) as a binary array composed of vertex \(v = \{v_{i}\) i |1\leq i\leq n\}\) and triangular facet \(T = \{T_{j}\) j |1\leq j\leq m\}\). For the STL model, \(n\) is the number of vertices and \(m\) is the number of triangular facets;

[0070] For any vertex \(v_{i}\) in \(v\), where \(i\) represents the number of elements in \(v\), define the set of triangular facets \(\Omega_{i}\) that share this vertex: i \(\Omega_{i}=\{T_{j}|v_{i}\in T_{j}\}\ (1)\) i :

[0071] \(\Omega_{i}\) i =\{T_{j}\) j |v_{i}\) i \in T_{j}\) j \} (1)

[0072] The normal vector of triangular facet \(T_{j}\) is calculated by the following normalized vector product: j Determine the direction of the normal vector of the triangular facet vertex: Take the weighted average of the normal vectors of the triangular facets in the first-order neighborhood of the vertex. The weight factor of the triangular facet expresses the influence size of the normal vectors of the triangular facets in the one-ring neighborhood of this point. The uneven distribution of discrete points in the STL model makes the shapes and areas of the triangular facets have large differences. Therefore, the weight factor of the triangular facet selects the area factor \(A\) and the shape factor \(\lambda\):

[0073]

[0074] where \(a\), \(b\), and \(c\) are the side lengths of the triangular facet. The value of \(\lambda\) in the range \((0, 1]\) represents the regularity degree of the triangular facet.

[0075]

[0076] The weight \(w\) of the triangular facet:

[0077] The weight \(w\) of the triangular facet:

[0078] w j = λ j A j (4)

[0079] Since the normal vector direction of the vertex is not unique, calculate the weighted average of the normal vectors of the triangular facets within the one-ring neighborhood of the vertex to obtain the vertex normal vector

[0080]

[0081] Apply the offset error L(θ) of the triangular facet to the triangular facet T in the set M j :

[0082]

[0083] Equation (6) is the dimensional error model for binder jet additive manufacturing

[0084] Consider all triangular facets T that share a vertex j and their offset errors Calculate the offset error compensation value of the vertex. The offset error compensation value of the triangular facet is along the opposite direction of the normal vector of the triangular facet with a magnitude of Since there is an angle β between the vertex normal vector and the normal vector of the triangular facet j , the projection C of the offset error of the triangular facet in the direction of the vertex normal vector j should be calculated

[0085]

[0086] where cosβ j is the vector product of and

[0087] Vertex v i is shared by several triangular facets. Calculate the weighted average of the projection C j according to the weights of the triangular facets in the one-ring neighborhood of the vertex to obtain the vertex offset compensation value

[0088]

[0089] Subtract the vertex offset compensation value in the direction of from the original vertex to obtain the offset vertex

[0090] Apply formula (9) to each vertex v of set v i to obtain the STL file M after error compensation offset : This compensation method does not change the topology of the model, and the compensated model maintains the same topological information as the original model (no gaps, no intersections). M offset The file is obtained by offsetting inward from the original STL model to compensate for the dimensional errors generated by binder jet additive manufacturing

[0091] The error compensation method based on vertex offset of binder jet additive manufacturing in the present invention is as follows

[0092] Step 1: Import the STL file to be compensated

[0093] Read the STL model data of the part in the software, and generate a triangular mesh model with a half-edge structure according to the original triangular facet data. It should be noted that. No transformation processing is performed on the model data in this process, and only the topological information of points and lines, points and faces, and lines and faces is extracted for use in the calculation process of the error compensation value in the subsequent steps to ensure the correctness of the model topological information

[0094] Step 2: Calculate the normal vectors of the triangular facets

[0095] Traverse the triangular facets within the one-ring neighborhood of any vertex v in the STL model according to the half-edge data structure, calculate the normal vector directions of the triangular facets at different angles, and after all the normal vector directions of the triangular facets are calculated, obtain the normal vectors of all the triangular facets within the one-ring neighborhood of vertex v i i

[0096] Step 3: Calculate the normal vectors of the vertices

[0097] Calculate the weight factors of each triangular facet in the software: the shape factor and the area factor, and perform a weighted average evaluation on the normal vectors of the triangular facets within the one-ring neighborhood of vertex v i After all the vertices complete the weighted average calculation of the normal vectors of the triangular facets, obtain the normal vectors of the vertices

[0098] Step 4: Calculate the offset error of the triangular facets

[0099] Calculate the included angle between the normal vector directions of the triangular facets at different angles and the forming direction in the software, and after all the triangular facets are calculated for the included angle, substitute it into formula (4) to calculate the offset error of the triangular facets, and obtain the offset error data of the triangular facets

[0100] Step 5: Calculate the projection of the offset error of the triangular facets in the direction

[0101] ​​Calculate the angle between the normal vector of the triangular patch and the vertex normal vector in the software. After the calculation of the triangular patches within the one-ring neighborhood of the vertex (the triangular patches directly adjacent to vertex v are called one-ring neighborhood triangular patches) is completed, obtain the projection of the triangular patch offset error in the direction;

[0102] Step Six: Calculate the vertex offset compensation value

[0103] In the software, calculate the weighted average of the projection of the triangular patch offset error in the direction of the vertex normal vector according to the weights (shape factor and area factor) of the triangular patches. After all vertices have completed the operation, obtain the vertex offset compensation value.

[0104] Step Seven: Calculate the offset vertex

[0105] Subtract the vertex offset compensation value in the direction from the original vertex coordinates to obtain the offset vertex.

[0106] Step Eight: Output the compensated STL model

[0107] Repeat Step Seven. After traversing all vertices, complete the compensation calculation and obtain the compensated STL model.

[0108] Matters not described in the present invention are applicable to the prior art.

Claims

1. An error compensation method based on binder jetting additive manufacturing, the method comprising the following steps: The offset error formula of the triangular facets is obtained by considering the interaction between the staircase error and the penetration error as: Among them, k1 is the interaction coefficient between the negative step error and the penetration error in the upward triangular patch; k2 is the interaction coefficient between the positive step error and the penetration error in the downward triangular patch, and k1 and k2 are dimensionless quantities; L is the offset error; d xy is the penetration error in the XY direction, d z is the penetration error in the Z direction; θ is the angle between the direction of the triangular patch normal vector and the forming direction, and d xy , d z , k1, and k2 are obtained through experiments; Determine the number m of triangular patches in the input STL model, and define the set M as an array of triangular patches T j , where m is the number of elements in the set M, and obtain the offset errors of all triangular patches in the STL model; Calculate the offset compensation value of the STL model vertex according to the projection of the offset error of the triangular facet in the direction of the vertex normal vector After traversing all vertices, the vertex v of the STL model i According to the corresponding offset compensation value Offset inward along the opposite direction of the vertex normal vector to obtain the offset vertex Furthermore, obtain the compensated STL model 2. The error compensation method based on binder jetting additive manufacturing according to claim 1, wherein In the offset error formula of the triangular facet, d xy , d z , the calibration process of the parameters k1 and k2 is as follows: Design a sample for printing experiment. The appearance of the sample is a cuboid, and there are inclined planes at multiple angles inside the cuboid. Sample 1 has inclined planes at multiple angles formed by edge structures, and sample 2 has inclined planes at multiple angles formed by hole structures. The positions and sizes of the holes and edges in sample 1 and sample 2 correspond and are the same. The mirror models of sample 1 and sample 2 are obtained by mirroring and flipping the model as sample 3 and sample 4; Conduct a printing experiment with the same layer thickness h using equipment from the same manufacturer, and use a 3D scanner to scan and obtain the STL model; Use the 3D inspection and metrology software Geomagic Control X to measure the offset error of the triangular facets between the scanned model and the designed model of the sample; Calibrate the unknown parameters in formula (4) according to the actual measured value of the offset error of the triangular facet: convert the measured inclined plane angle α into the angle θ between the direction of the triangular facet normal vector and the forming direction, and denote the offset error of the triangular facet with θ = 90° as d xy , and denote the offset error of the triangular facet with θ = 180° as d z , assume that the penetration error and the step error action coefficients of the upward or downward triangular facets with different angles are the same during printing, and then substitute the offset error data of the triangular facets with other angles into formula (4) to calculate the two parameters k1 and k2 based on the least squares method. The calculated values of the unknown parameters k1 and k2 vary within a certain range; Calibrate the unknown parameters in the formula by taking the average value of the interaction coefficients of all the samples (Sample 1, Sample 2, Sample 3, and Sample 4), and substitute the four parameters (d xy , d z , k1, and k2) into formula (4) to obtain the triangular facet offset error formula after calibration parameters, and calculate the offset error of the triangular facets at different angles θ.

3. The error compensation method based on binder jetting additive manufacturing according to claim 2, wherein The size of the sample is 600mm×140mm×10mm, and the angles between the multiple inclined planes and the horizontal direction are 90°, 80°, 70°, 60°, 50°, 40°, 30°, 20° in sequence.

4. The error compensation method based on binder jetting additive manufacturing according to claim 1, wherein After obtaining the offset error of all triangular facets in the STL model, the error compensation based on vertex offset is performed. The specific process is: Calculate vertex v according to formula (5) i The weighted average of the normal vectors of the triangular patches in the first-ring neighborhood to obtain the vertex normal vector where j is an integer in the range of [1, m], λ is a shape factor, and A is an area factor. is the normal vector of the triangular facet; Calculate the projection C of the offset error of the triangular patch in the direction of the vertex normal vector j Take the weighted average of the projections of the offset errors of the triangular patches in the one-ring neighborhood of the vertex in the direction of the vertex normal vector as the vertex offset compensation value where cosβ j is the cross product of the normal vector of the triangular patch and the vertex normal vector , β j is the angle between the vertex normal vector and the normal vector of the triangular patch , and is the offset error of the triangular patch T j . The vertex offset compensation value is as follows: The original vertex minus the vertex offset compensation value along the direction to obtain the offset vertex 5. An error compensation method for vertex offset based on binder jetting additive manufacturing, which is: Step 1: Import the STL file to be compensated Read the STL model data of the part in the software, generate a triangular mesh model with a half-edge structure according to the original triangular facet data, and only extract the topological information of point-line, point-face, and line-face; Step 2: Calculate the normal vector of the triangular facet Traverse the triangular patches in the one-ring neighborhood of any vertex v in the STL model according to the half-edge data structure, calculate the normal vector directions of the triangular patches at different angles, and after the normal vector directions of all triangular patches are calculated, obtain the normal vectors of all triangular patches in the one-ring neighborhood of vertex v i i ​​ Step 3: Calculate the normal vector of the vertex Calculate the weight factors of each triangular patch in the software: the shape factor and the area factor; and for vertex v i Perform a weighted average evaluation on the normal vectors of the triangular patches within the one-ring neighborhood. After all vertices have completed the weighted average calculation of the normal vectors of the triangular patches, the normal vector of the vertex is obtained Step 4: Calculate the offset error of the triangular facet Calculate the angle between the normal vector direction of the triangular facet at different angles and the forming direction in the software, and use this angle to further obtain the offset error data of the triangular facet; Step 5: Calculate the projection of the triangular facet offset error in the direction Calculate the angle between the normal vector of the triangular patch and the vertex normal vector in the software. After the calculation of the triangular patches in the one-ring neighborhood of the vertex is completed, obtain the projection C of the triangular patch offset error in the direction j ; Step 6: Calculate the vertex offset compensation value In the software, calculate the weighted average of the projection of the offset error of the triangular facet in the direction of the vertex normal vector according to the weight factor of the triangular facet. After all vertices are completed, obtain the vertex offset compensation value; Step 7: Calculate the offset vertex After subtracting the vertex offset compensation value along the direction from the original vertex coordinates, the offset vertex is obtained; Step 8: Output the compensated STL model Repeat step 7. After traversing all vertices, complete the compensation calculation and obtain the compensated STL model.

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