Multi-degree-of-freedom path planning method for unsupported additive manufacturing of suspension structure

Abstract

The invention discloses a multi-degree-of-freedom path planning method for unsupported additive manufacturing of a suspension structure. According to the method, a to-be-printed model is sequentially subjected to preprocessing, cone transformation processing and slicing processing conversion, and a planned path of a cone transformation model is obtained; sequentially performing path segmentation processing and inverse cone transformation processing on the planned path of the cone transformation model to obtain a planned path of the to-be-printed model under the coordinate system of the to-be-printed model; performing exponential product kinematics modeling on the equipment to obtain a kinematics conversion relation between the coordinate system of the model to be printed and the coordinate system of the equipment; and then conversion is carried out to obtain a planned path of the to-be-printed model under the equipment coordinate system, and 3D printing is carried out. The method is suitable for most of existing slicing software, the unsupported printing overhanging structure can be realized by utilizing the generated slicing software path planning, so that the processing process after 3D printing is simplified, and the quality and the surface flatness of a printed piece are further improved.

Description

Technical Field

[0001] The present invention relates to the field of 3D printing, and in particular to a multi-degree-of-freedom path planning method for unsupported additive manufacturing of a suspended structure. Background Art

[0002] Fused Deposition Modeling (FDM) is one of the most mainstream 3D printing technologies at present. The path planning algorithm used by FDM technology usually relies on slicing three-dimensional models in the form of CAD models, point cloud data or STL files, and fills the slice contours through the corresponding filling algorithm to generate processing data files that can be recognized by the printing device. However, when printing complex structures, such as overhanging structures, such path planning algorithms are often difficult to achieve direct printing without external support; although the introduction of support structures can partially solve this problem, it also brings about complicated post-processing processes and reduced surface integrity of the printed parts, which in turn has a negative impact on the final printing effect. Therefore, how to build precise and complex structures without support or with little support has become a new challenge facing FDM technology.

[0003] To solve the problem of supporting-free printing of complex structures, we should start from the basic principle of molten lamination process, optimize the path planning algorithm and change the forming direction during the printing process to achieve supporting-free printing of structures. Therefore, multi-degree-of-freedom path planning methods have attracted widespread attention.

[0004] Since multi-DOF additive manufacturing equipment has many different mechanical configurations, these devices have significant differences in degrees of freedom, range of motion, joint restrictions, and control strategies; and the multi-DOF path planning method first needs to interpolate the model path according to the configuration space of the device to adapt to the kinematic and dynamic characteristics of the specific device. Therefore, the multi-DOF path planning method is generally not universal. In addition, in the path calculation process, factors such as path smoothness and physical interference constraints must also be considered; in the actual printing process, the impact of many factors on path planning, such as printing temperature, material extrusion speed, and material morphological characteristics, must also be considered comprehensively. The coupling relationship of these related factors requires that the multi-DOF path planning algorithm needs to take into account multiple control factors when designing, which greatly increases the complexity of the algorithm. Therefore, reducing the complexity of the algorithm has become a major challenge in the multi-DOF additive manufacturing path planning algorithm. Summary of the invention

[0005] In view of the problems in the above-mentioned background technology, the present invention proposes a multi-degree-of-freedom path planning method for support-free 3D printing of overhanging structures.

[0006] The technical solution adopted by the present invention is: The multi-degree-of-freedom path planning method of the present invention comprises the following steps: S1. Obtain a to-be-printed model of a physical product, and perform preprocessing and cone transformation processing on the to-be-printed model in sequence to obtain a cone transformation model; S2, slicing the cone transformation model to obtain hierarchical path data of the cone transformation model, and then converting the hierarchical path data of the cone transformation model to obtain the planned path and nozzle extrusion amount parameters of the cone transformation model; S3, performing path segmentation processing and inverse cone transformation processing on the planned path of the cone transformation model in sequence, obtaining the planned path and nozzle extrusion amount parameters of the model to be printed in the coordinate system of the model to be printed, and then adjusting the actual nozzle extrusion amount according to the nozzle extrusion amount parameters of the cone transformation model and the nozzle extrusion amount parameters of the model to be printed; S4, performing exponential product kinematic modeling on the turntable type additive manufacturing equipment to obtain the kinematic degree of freedom conversion relationship between the coordinate system of the model to be printed and the coordinate system of the equipment; S5. According to the kinematic transformation relationship between the coordinate system of the model to be printed and the device coordinate system, the planned path of the model to be printed in the coordinate system of the model to be printed is transformed to obtain the planned path of the model to be printed in the device coordinate system. Finally, 3D printing is performed using a turntable-type additive manufacturing device according to the planned path of the model to be printed in the device coordinate system and the actual extrusion amount of the nozzle.

[0007] The preprocessing in S1 is specifically as follows: Acquire a model to be printed, wherein the model to be printed is composed of a plurality of triangular facets, and refine and segment the triangular facet information in the model to be printed to obtain a refined and segmented model; The detailed segmentation is specifically to connect the midpoints of every two adjacent sides of the triangular facets, and then segment the triangular facets.

[0008] The cone transformation process in S1 is processed according to the following formula: [x' y' z'] T =[x 0 / cosθ y 0 / cosθz 0 +(x 0 2 +y 0 2 ) 1 / 2 ] T Among them, x 0 ,y 0 、z 0 is the position coordinate before the cone transformation, x', y', z' are the position coordinates after the cone transformation, θ is the preset cone transformation angle, and T represents matrix transpose.

[0009] The path segmentation process in S3 is performed according to the following formula to divide the planned path of the cone transformation model into multiple mother paths, and each mother path is divided into m sub-paths of equal length: dist=((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 m = ceil(dist / l max ) Δx=(x new -x old ) / m Δy=(y new -y old ) / m x k =x old +kΔx y k =y old +kΔy z k =z old -(x k 2 +y k 2 ) 1 / 2 Among them, P old represents the starting point of the parent path, P old The coordinates are (x old ,y old ,z old ), P new represents the end point of the parent path, P new The coordinates are (x new ,y new ,z new ), dist represents the projection length of the parent path on the XY plane, l max Indicates the maximum length of the sub-path after segmentation, x k ,y k 、z k Indicates the coordinates of the end point of the kth sub-path. The value range of k is 1 to m. m indicates the number of sub-paths divided from the parent path. ceil() indicates rounding up.

[0010] The inverse cone transformation process in S3 is processed according to the following formula: [x 0 'y 0 'z 0 '] T=[x'cosθy'cosθz'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 ] T Among them, x', y', z' are the position coordinates after cone transformation, x 0 ' 、y 0 '、z 0 ' is the position coordinate of the model to be printed after the inverse cone transformation, θ is the preset cone transformation angle, and T represents the matrix transpose.

[0011] The actual nozzle extrusion amount in S3 is adjusted according to the following formula: dist k =(1 / m)((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 dist kt =((x 0k '-x 0k-1 ') 2 +(y 0k '-y 0k-1 ') 2 ) 1 / 2 e k =e / m e kt =cosθ(dist k / dist kt ) k Among them, x new and new Indicates the starting coordinates of the parent path, x old and old represents the end point coordinates of the parent path, e is the nozzle extrusion base of a parent path, m represents the number of sub-paths divided by the path, and e k is the nozzle extrusion amount parameter of each sub-path of the cone transformation model, e kt is the nozzle extrusion amount of each sub-path of the model to be printed, dist k is the projection length of each sub-path on the XY plane, dist kt is the projection length of each segment of the sub-path on the XY plane after the conical transformation, dist is the projection length of the parent path on the XY plane, 0k ',y 0k ' is the coordinate of the Kth subpath after conical transformation, x0k-1 ',y 0k-1 ' is the coordinate of the K-1th sub-path after conical transformation, and θ is the preset angle of conical transformation.

[0012] The turntable type additive manufacturing equipment includes a four-degree-of-freedom turntable type additive manufacturing equipment and a B-swing head-C turntable type five-axis additive manufacturing equipment; The specific steps of S5 are: S5.1. Obtaining the B-axis / C-axis angle of the rotary table type additive manufacturing device according to the planned path of the model to be printed; When the turntable type additive manufacturing device is a four-degree-of-freedom turntable type additive manufacturing device, the C-axis angle of the turntable type additive manufacturing device is set according to the following formula: Φ k =arctan((x 0k '-x 0k-1 ') / (y 0k '-y 0k-1 ')) Among them, Φ k represents the C-axis angle of the k-th subpath, x 0k ' and y 0k ' represents the end point coordinates of the kth subpath, x 0k-1 ' and y 0k-1 ' represents the starting point coordinates of the kth subpath; When the turntable type additive manufacturing equipment is a B-swing head-C turntable type five-axis additive manufacturing equipment, the B-axis angle and the C-axis angle of the turntable type additive manufacturing equipment are set according to the following formula: β k =θ Φ k =arctan((x 0k '-x 0k-1 ') / (y 0k '-y 0k-1 ')) Among them, β k represents the B-axis angle of the k-th sub-path, Φ k represents the C-axis angle of the k-th subpath, x 0k ' and y 0k ' represents the end point coordinates of the kth subpath, x 0k-1 ' and y 0k-1 ' represents the starting point coordinates of the kth sub-path, and θ is the preset angle of the cone transformation; S5.2, performing data processing on the C-axis angle of the turntable type additive manufacturing device to obtain a processed C-axis angle; The data processing is performed according to the following formula: t k =argmint {|Φ k +2πt-γ k-1 |:t=-10,-9,...,9,10} γ k =Φ k +2πt k Among them, when k=1, γ 1 =Φ 1 , Φ k represents the C-axis angle of the k-th subpath, γ k represents the C-axis angle of the k-th sub-path after processing, t k Indicates the processing value selected by the k-th subpath, argmin t Indicates the value of t when the function takes the minimum value, || indicates the absolute value, :t=-10,-9,...,9,10 indicates that the possible values ​​of t in the function are -10,-9,...,9,10, and t indicates the number of circumferential adjustments of the C-axis angle; S5.3, the planned path of the model to be printed is brought into the kinematic transformation relationship between the coordinates of the model to be printed and the device coordinates for transformation, so as to obtain the position coordinates of the model to be printed in the device coordinates, and the B-axis angle, the processed C-axis angle and the position coordinates of the model to be printed in the device coordinates together constitute the planned path of the model to be printed in the device coordinates; Finally, 3D printing is performed using a rotary table additive manufacturing device based on the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion volume.

[0013] The position coordinates of the model to be printed in the device coordinates in S5.3 are specifically: When the turntable additive manufacturing device is a four-degree-of-freedom turntable additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: [X 4 Y 4 Z 4 ] T =[x 0 'y 0 'z 0 '] T Among them, X 4 , Y 4 and Z 4 Indicates the position coordinates of the model to be printed in the equipment coordinate system of the four-degree-of-freedom turntable additive manufacturing equipment, x 0 ',y 0 '、z 0 ' is the position coordinate of the model to be printed after the inverse cone transformation, and T represents the matrix transpose; When the rotary table type additive manufacturing device is a B-swing head-C rotary table type five-axis additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: [X 5 Y 5 Z 5 ] T =[(x 0 '+P X1 )cosΦ k -(y 0 '+P Y1 )sinΦ k -P X2 +P X3 (x 0 '+P X1 ) sinΦ k -(y 0 '+P Y1 )cosΦ k +P Y2 +P Y3 z 0 '+P Z1 -P Z2 -P Z3 ] T Among them, X 5 , Y 5 and Z 5 They represent the xyz position coordinates of the model to be printed in the equipment coordinate system of the five-degree-of-freedom turntable additive manufacturing equipment, respectively. 0 ',y 0 '、z 0 ' is the position coordinate of the model to be printed after the inverse cone transformation, P X1 , P Y1 , P Z1 They represent the xyz vector coordinates of the rotating platform center pointing to the origin of the printing model in the device coordinate system, P X2 , P Y2 , P Z2 They represent the xyz position coordinates of the B-axis rotation center in the device coordinate system, P X3 , P Y3 , P Z3 They respectively represent the xyz vector coordinates pointing from the B-axis rotation center to the end of the print head in the device coordinate system, and T represents matrix transpose.

[0014] The beneficial effects of the present invention are: 1. The multi-degree-of-freedom path planning method for support-free additive manufacturing of overhanging structures proposed in the present invention can realize support-free printing of overhanging structures, save printing time, improve the integrity of the printed model, and greatly reduce post-processing time.

[0015] 2. The present invention takes the cone transformation algorithm as the core. It only needs to pre-process the STL file of the model to be printed and then post-modify the generated G code, which saves the process of model path point selection necessary for path planning, simplifies the path generation process, and greatly reduces the complexity of the path planning algorithm.

[0016] 3. The index product kinematics model of the present invention is used to model the configuration of the additive manufacturing equipment, and the conversion relationship between the equipment coordinate system and the coordinate system of the model to be printed is obtained, so that the algorithm can be applied to a variety of turntable-type multi-degree-of-freedom equipment. The multi-degree-of-freedom additive manufacturing path planning algorithm has high versatility.

[0017] In summary, in the process of manufacturing the printed overhang structure, the present invention has greatly improved the surface integrity and printing efficiency of the printed overhang structure compared with the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flowchart of the solution of the present invention.

[0019] Figure 2 It is a schematic diagram of cone transformation.

[0020] Figure 3 It is a schematic diagram of the model to be printed of the Y-shaped tubular overhang structure.

[0021] Figure 4 It is a schematic diagram of the Y-shaped tubular suspension structure model after tapered transformation.

[0022] Figure 5 This is a schematic diagram of the slicing operation on the cone model.

[0023] Figure 6 This is a preview of the final printed tubular overhang structure.

[0024] Figure 7 This is a preview of the support-free printing process of the key parts of the tubular overhang structure. DETAILED DESCRIPTION

[0025] The present invention will be further described below in conjunction with the accompanying drawings and specific implementations.

[0026] like Figure 1 As shown, the specific embodiment of the multi-degree-of-freedom path planning method of the present invention includes the following steps: S1, such as Figure 3As shown, the model to be printed of the physical product is obtained, and the model to be printed is preprocessed and cone-transformed in sequence to obtain a cone-transformed model, such as Figure 4 shown. Figure 3-Figure 6 The G-code generation process for the support-free printing of tubular overhanging structures is shown; The model to be printed includes the model height and model structure information of the model to be printed.

[0027] The specific preprocessing is: Obtaining a model to be printed, the model to be printed is composed of a number of triangular facets, and performing segmentation on the triangular facet information in the model to be printed to obtain a segmented model; The detailed segmentation is to connect the midpoints of every two adjacent sides of the triangle patch, and then segment the triangle patch, so that the original triangle patch can be segmented into four congruent small triangle patches. The model to be printed is composed of several triangle patches.

[0028] The model to be printed is imported into a 3D printing model preprocessing device to obtain the preprocessed model to be printed, that is, the three-dimensional structure information of the model to be printed. In the specific implementation, the three-dimensional structure information of the model to be printed is stored in an STL file format.

[0029] The cone transformation process is processed according to the following formula: [x' y' z'] T =P(x 0 ,y 0 ,z 0 ) =[x 0 / cosθ y 0 / cosθ z 0 +(x 0 2 +y 0 2 ) 1 / 2 ] T =1 / cosθ[x 0 y 0 0] T +[0 0 z 0 +(x 0 2 +y 0 2 ) 1 / 2 ] T Among them, x 0 ,y 0 、z 0The position coordinates of a vertex of the triangle patch before the cone transformation, x', y', z' are the position coordinates of a vertex of the triangle patch after the cone transformation, θ is the preset cone transformation angle, P( ) indicates cone transformation processing, and T indicates matrix transposition.

[0030] Figure 2 It is a schematic diagram of the conical transformation, which shows a cross-sectional diagram of the model to be built. Each unit represents the cross-section of a path. The yellow dotted line is the center of the conical transformation, and the angle between the conical layer and the horizontal layer is the angle of the conical transformation.

[0031] The position coordinates here are the position coordinates in the coordinate system of the model to be printed. The origin of the coordinate system of the model to be printed is usually the center of the bottom of the model. In general, for a centrosymmetric model, its symmetry center is selected as the transformation center line, and the intersection of the symmetry center and the bottom of the model is selected as the origin.

[0032] S2, such as Figure 5 As shown, the conical transformation model is sliced, and the slicing parameters are set using the slicing software, so that the conical transformation model is divided into several horizontal layers with a certain thickness, and the same horizontal layer has the same layer height, so as to obtain the layered path data of the conical transformation model, and then the planning path and nozzle extrusion amount parameters of the conical transformation model are obtained by the slicing software according to the layered path data conversion of the conical transformation model, and the G code file of the conical transformation model is obtained in the specific implementation; Slicing parameters include layer height, number of outer boundary layers, extrusion width, etc.

[0033] S3, sequentially perform path segmentation processing and inverse cone transformation processing on the planned path of the cone transformation model, i.e., post-processing of the cone transformation, to obtain the planned path and nozzle extrusion amount parameters of the model to be printed in the coordinate system of the model to be printed. In the specific implementation, the G code file of the model to be printed is obtained, and the path of the cone model is restored to the path file of the model to be printed to obtain the path planning file of the model to be printed. Then, the actual nozzle extrusion amount is adjusted according to the nozzle extrusion amount parameters of the cone transformation model and the nozzle extrusion amount parameters of the model to be printed; The path segmentation process is performed according to the following formula, dividing the planned path of the cone transformation model into multiple mother paths, and each mother path is divided into m sub-paths of equal length: dist=((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 m=ceil(dist / l max ) Δx=(xnew -x old ) / m Δy=(y new -y old ) / m x k =x old +kΔx y k =y old +kΔy z k =z old -(x k 2 +y k 2 ) 1 / 2 Among them, a path, i.e., the command of G1, is regarded as a straight line motion, P old Indicates the starting point of the mother path, that is, the starting point of the split path, P old The coordinates are (x old ,y old ,z old ), P new Indicates the end point of the parent path, that is, the end point of the split path, P new The coordinates are (x new ,y new ,z new ), dist represents the projection length of the parent path on the XY plane, l max represents the maximum length of the sub-path after segmentation, m represents the number of sub-paths segmented from the parent path, and x k ,y k 、z k Indicates the coordinates of the end point of the kth subpath. The value range of k is 1 to m. ceil() indicates rounding up. Δx and Δy indicate the changes in the projection from the subpath start point to the subpath end point on the X-axis and Y-axis directions, respectively.

[0034] Where k=0, 1, ...m. The endpoints of each sub-path obtained by calculation are re-edited according to the format of G code and inserted into the long path G code segment to replace the original G code, thereby completing the refinement segmentation of the long path.

[0035] The inverse cone transform process is processed according to the following formula: [x 0 'y 0 'z 0 '] T =P -1 (x',y',z') =[x'cosθy'cosθz'-((x'sinθ) 2+(y'sinθ) 2 ) 1 / 2 ] T =cosθ[x' y' 0] T +[0 0 z'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 ] T Among them, x', y', and z' are the position coordinates of a vertex of the triangle after the cone transformation. 0 ',y 0 '、z 0 ' is the position coordinate of a vertex of the triangular face of the model to be printed after the inverse cone transformation, θ is the preset cone transformation angle, P -1 ( ) indicates inverse cone transformation, and T indicates matrix transposition.

[0036] That is, the angle between the θ cone layer and the horizontal layer, which should be consistent with the preset angle of the cone transformation. The transformed G code instructions are reintegrated into a new G code file. The position coordinates here are the position coordinates in the coordinate system of the model to be printed, which are consistent with the coordinate system of the cone transformation.

[0037] like Figure 5 As shown in the figure, the above algorithm is used to generate the G code process for the support-free printing of the tubular overhang structure. The direction of the layers in the Y-shaped tubular overhang structure generated by the algorithm is different from the direction of the layers obtained by the traditional slicer, which successfully changes the printing direction of the part and realizes the support-free printing process.

[0038] The actual nozzle extrusion volume is adjusted according to the following formula: dist k =(1 / m)dist=(1 / m)((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 dist kt =((x 0k '-x 0k-1 ') 2 +(y 0k '-y 0k-1 ') 2 ) 1 / 2 e k =e / m e kt=cosθ(dist k / dist kt ) k Among them, x new and new Indicates the starting coordinates of the parent path, x old and old represents the end point coordinates of the parent path, e is the nozzle extrusion base of a parent path, m represents the number of sub-paths divided by the path, and e k is the nozzle extrusion amount parameter of each sub-path of the cone transformation model, e kt is the nozzle extrusion amount of each sub-path of the model to be printed, dist k is the projection length of each sub-path on the XY plane, dist kt is the projection length of each segment of the sub-path on the XY plane after the conical transformation, dist is the projection length of the parent path on the XY plane, 0k ',y 0k ' is the coordinate of the Kth subpath after conical transformation, x 0k-1 ',y 0k-1 ' is the coordinate of the K-1th sub-path after cone transformation, and θ is the preset cone transformation angle, that is, the angle between the cone layer and the horizontal layer.

[0039] S4. Performing exponential product kinematic modeling on the spatial configuration of the turntable-type additive manufacturing device to obtain a kinematic model of the device, and then combining the coordinate system of the model to be printed and the coordinate system of the turntable-type additive manufacturing device to obtain a kinematic degree of freedom conversion relationship between the coordinate system of the model to be printed and the coordinate system of the device, that is, converting the traditional three-degree-of-freedom coordinates into the coordinates of the three-degree-of-freedom, four-degree-of-freedom or five-degree-of-freedom turntable-type additive manufacturing device according to the exponential product kinematic modeling, that is, the conversion relationship between the motion quantities of each axis of the device; Turntable-type additive manufacturing equipment is a turntable-type multi-degree-of-freedom equipment. Three degrees of freedom means that the equipment can move in three independent directions, usually the X, Y, and Z axes, specifically the traditional three-axis additive manufacturing system; four degrees of freedom means that the C-axis rotational degree of freedom is added on the basis of three degrees of freedom, specifically the rotating platform four-axis additive manufacturing system; five degrees of freedom means that another rotational degree of freedom is added on the basis of four degrees of freedom, usually the B-axis, which can rotate around the Z axis, specifically the B-swing head-C turntable type five-axis additive manufacturing system.

[0040] Principle of exponential product kinematics theory: The motion of a rigid body can be decomposed into the superposition of translational motion and rotational motion. The homogeneous coordinate transformation relationship of the rigid body can be expressed by a 4×4 matrix as follows:

[0041] Among them, P represents the vector of the relative position displacement transformation of the rigid body during the transformation process, and R represents the rotation transformation matrix of the rigid body. Similarly, the rigid body motion transformation can also be expressed in the form of a spinor exponent matrix: g=e ξ' θ Here, θ represents the angle of rotation around a certain axis.

[0042] When ω=0, the angular velocity of the rigid body motion is 0, and the motion is only linear motion. The matrix of its spinor and coordinate transformation can be expressed as: ξ=[v T 0] T

[0043] When ω≠0, the rigid body only performs rotational motion, and the matrix of its spinor and coordinate transformation can be expressed as: ξ = [ω T ν T ] T =[ω 1 ω 2 ω 3 v 1 v 2 v 3 ] T

[0044] In the above formula, θ is the angle of rotation around the axis, ω represents the angular velocity of the rigid body rotating around the axis, that is, the unit vector in the direction of the axis of the rigid body rotating, ω=[ω 1 ω 2 ω 3 ] T ,ω 1 ,ω 2 ,ω 3 Respectively represent the components of ω along the X, Y, and Z axes, and satisfy ω 1 2 +ω 2 2 +ω 3 2 =1, when the rigid body moves horizontally, ω=[0 0 0] T v represents the velocity of the rigid body's linear motion, that is, the unit vector in the rigid body's translational direction, v=[ v 1 v 2 v 3 ] T , if q represents a point on the axis of rotation, then the relationship v=q×ω is satisfied. <> means converting the vector into a matrix form. This operator satisfies the relationship: 〈ω〉ν=ω×ν, where × is the cross product:

[0045] The coordinate expression of the spinor can be expressed by a 4×4 matrix:

[0046] e <ω>θ =I 3×3 +<ω>sinθ+<ω> 2 (1-cosθ) For a multi-DOF additive manufacturing device, define {M} as the device coordinate system fixed on the additive manufacturing device, and define {W} as the coordinate system of the model to be printed. {W} can be obtained from {M} through a series of screw motion transformations. The transformation relationship can be expressed as: Q=e (ξn' θn) …e (ξ3'θ3 ) ⋅e (ξ2'θ2 ) ⋅e (ξ1'θ1) Among them, e ξ'n It is the nth screw motion transformation, which means that the device has n degrees of freedom.

[0047] S5. According to the kinematic transformation relationship between the coordinates of the model to be printed and the device coordinates, the planned path of the model to be printed in the coordinate system of the model to be printed is transformed to obtain the planned path of the model to be printed in the device coordinate system. In the specific implementation, the G code file of the model to be printed is kinematically transformed according to the configuration space of the additive manufacturing device to obtain the final G code file. Finally, the 3D printing is performed using the rotary table additive manufacturing device according to the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion amount.

[0048] The turntable type additive manufacturing equipment includes a four-degree-of-freedom turntable type additive manufacturing equipment with a C rotation axis and a B-swing head-C turntable type five-axis additive manufacturing equipment; S5.1. Obtain the B-axis / C-axis angle of the turntable type additive manufacturing device on each sub-path according to the planned path of the model to be printed; When the turntable type additive manufacturing device is a four-degree-of-freedom turntable type additive manufacturing device with a C rotation axis, the C axis angle of the turntable type additive manufacturing device is set according to the following formula: Φ k =arctan((x0k '-x 0k-1 ') / (y 0k '-y 0k-1 ')) Among them, Φ k represents the C-axis angle of the k-th subpath, x 0k ' and y 0k ' represents the coordinates of the end point of the kth subpath on the XY plane, x 0k-1 ' and y 0k-1 ' represents the coordinates of the starting point of the k-th sub-path on the XY plane, that is, the coordinates of the end point of the k-1-th sub-path on the XY plane. When k=1, the starting point is the starting point of the mother path; When the turntable type additive manufacturing equipment is a B-swing head-C turntable type five-axis additive manufacturing equipment, the B-axis angle and the C-axis angle of the turntable type additive manufacturing equipment are set according to the following formula: β k =θ Φ k =arctan((x 0k '-x 0k-1 ') / (y 0k '-y 0k-1 ')) in, β k represents the B-axis angle of the k-th sub-path, Φ k represents the C-axis angle of the k-th sub-path, x 0k ' and y 0k ' represents the end point coordinates of the kth subpath, x 0k-1 ' and y 0k-1 ' Indicates the starting point coordinates of the k-th sub-path, that is, the coordinates of the end point of the k-1-th sub-path on the XY plane. When k=1, the starting point is the starting point of the mother path. θ The angle of the preset cone transformation; Calculate the angle between the print head and the model processing path to determine the appropriate direction vector of the print head during processing; the calculation method for the appropriate direction vector of the print head is as follows: the direction of the print head is always set to be perpendicular to the printing path. Since the angle of the cone transformation determines the angle of the B axis, it is only necessary to make the print head perpendicular to the path on the XY plane; in terms of the algorithm, it is only necessary to read the direction of the path. x old and y old as well asx new and y new The value of the path vector can be calculated by using the np.arctan2 function in the NumPy library.

[0049] To ensure that the print head does not interfere with the printed model during the printing process, the direction of the print head is always defined as perpendicular to the printing path or at a certain angle to the printing path. For BC turntable type five-degree-of-freedom additive manufacturing equipment, in order to keep the direction of the print head always perpendicular to the printing path, the angle parameter θ during the cone transformation determines the angle of the B axis during the actual movement of the printing device. Therefore, it is only necessary to adjust the turntable angle of the equipment so that the print head is perpendicular to the path in the XY plane. For turntable type four-degree-of-freedom additive manufacturing equipment, the print head generally always maintains a fixed angle (usually vertically downward), so it is only necessary to calculate the angle of the equipment turntable to ensure that the print head maintains a certain angle with the printing path.

[0050] The turntable angle of the turntable multi-DOF additive manufacturing equipment, that is, the angle of the C axis during the movement of the printing equipment Φ k The calculation formula is as follows: Φ k =arctan((x 0k '-x 0k-1 ') / (y 0k '-y 0k-1 ')) It is worth noting that in order to prevent the print head from interfering with the printed model, the print head should always be kept outside the printed model. Therefore, the inverse tangent value here is the value from the origin (0,0) to the vector (x 0k '-x 0k-1 ',y 0k '-y 0k-1 ')'s counterclockwise angle Φ k ,angle Φ k The range of is [-π, π]; S5.2. Process the C-axis angle of the turntable additive manufacturing equipment to prevent angle mutations and obtain the processed C-axis angle on each sub-path. Data processing is performed according to the following formula: t k =argmin t {|Φ k +2πt-γ k-1 |:t=-10,-9,...,9,10} γ k =Φk + 2πt k Among them, when k=1, γ 1 =Φ 1 , Φ k represents the C-axis angle of the k-th sub-path, γ k represents the C-axis angle of the k-th sub-path after processing, t k represents the processing value selected by the kth subpath, that is, among the 21 possible t k Among the integer values ​​of γ k Closest γ k-1 The t value, argmin t Indicates the value of t when the function takes the minimum value, || indicates the absolute value, :t=-10,-9,...,9,10 indicates that the possible values ​​of t in the function are -10,-9,...,9,10, and t indicates the number of circumferential adjustments of the C-axis angle; The angle calculated in step S5.1 is processed to prevent angle mutation. t k In the value of γ k Closest γ k-1 The t value is used to prevent the rotation angle from changing suddenly.

[0051] S5.3, the planned path of the model to be printed is brought into the kinematic transformation relationship between the coordinates of the model to be printed and the device coordinates for transformation, and the position coordinates (x, y, z) of the model to be printed in the device coordinates are obtained. The B-axis angles on all sub-paths, the processed C-axis angles and the position coordinates of the model to be printed in the device coordinates together constitute the planned path of the model to be printed in the device coordinates; Finally, 3D printing is performed using a rotary table additive manufacturing device based on the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion volume.

[0052] S5.3 is to be specific, that is, according to the spatial configuration of the equipment, adjust the movement of each axis in the G code file, and output the final processing file; wherein, the method for adjusting the movement of each axis is: regard the X, Y, and Z values ​​in the G code of the model to be printed as the coordinates of each path point that the nozzle needs to pass in the coordinate system of the model to be printed, bring these coordinates into the inverse kinematics model established in step S1, obtain the movement of the three axes of the device X, Y, and Z, replace the X, Y, and Z parameters in the original G code, combine the B-axis angle and the processed C-axis angle, and generate the final path planning file.

[0053] When the turntable additive manufacturing device is a four-degree-of-freedom turntable additive manufacturing device with a C rotation axis, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: [X 4 Y 4 Z 4 ] T =[x 0 'y 0 'z 0 '] T Among them, X 4 , Y 4 and Z 4 It represents the position coordinates of the model to be printed in the equipment coordinate system of the four-degree-of-freedom turntable additive manufacturing equipment. x 0 ' ,y 0 ' , z 0 ' is the position coordinate of the model to be printed after the inverse cone transformation, and T represents the matrix transpose; When the rotary table type additive manufacturing device is a B-swing head-C rotary table type five-axis additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: [X 5 Y 5 Z 5 ] T =[(x 0 '+P X1 )cosΦ k -(y 0 '+P Y1 )sinΦ k -P X2 +P X3 (x 0 '+P X1 ) sinΦ k -(y 0'+P Y1 )cosΦ k +P Y2 +P Y3 z 0 '+P Z1 -P Z2 -P Z3 ] T Among them, X 5 , Y 5 and Z 5 They represent the xyz position coordinates of the model to be printed in the equipment coordinate system of the five-degree-of-freedom turntable additive manufacturing equipment, respectively. 0 ',y 0 '、z 0 ' is the position coordinate of the model to be printed after the inverse cone transformation, P X1 , P Y1 , P Z1 They respectively represent the xyz vector coordinates of the rotating platform center pointing to the printing model origin in the device coordinate system. The printing model origin is the origin of the coordinate system of the model to be printed. X2 , P Y2 , P Z2 They represent the xyz position coordinates of the B-axis rotation center in the device coordinate system, P X3 , P Y3 , P Z3 They respectively represent the xyz vector coordinates pointing from the B-axis rotation center to the end of the print head in the device coordinate system, and T represents matrix transpose.

[0054] The final printed diagram is as follows Figure 6 As shown, the orange part is the print head posture adjustment part, where there is no material extrusion, and the blue part is the actual extrusion path part with material extrusion.

[0055] in Figure 7 This is a preview of the process of support-free printing of the key parts of the tubular overhang structure. The orange part is the print head posture adjustment part, where no material is extruded; the blue part is the actual extrusion path part where material is extruded.

[0056] This method is based on the optimization design of the existing slicer and aims to improve the efficiency and effect of multi-DOF 3D printing path planning, which is particularly suitable for printing overhanging structures. First, the motion chain of the 3D printing platform is determined and the kinematic model of the printing platform is established; then, the STL model of the overhanging structure to be printed is subjected to a conical transformation and the transformed STL model is imported into the slicing software to generate the initial three-DOF G-code file; finally, the three-DOF G-code file is subjected to a reverse conical transformation, the rotation angle of the printing platform is calculated, and it is embedded in the G-code to generate the final multi-DOF G-code file.

[0057] The above specific implementation modes are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

[0058] The above description is only a preferred embodiment of the present invention, so all equivalent changes or modifications made according to the structure, characteristics and principles described in the scope of the patent application of the present invention are included in the scope of the patent application of the present invention.

Claims

1. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures, characterized in that: The method comprises the following steps: S1. Obtain a to-be-printed model of a physical product, and perform preprocessing and cone transformation processing on the to-be-printed model in sequence to obtain a cone transformation model; S2, slicing the cone transformation model to obtain hierarchical path data of the cone transformation model, and then converting the hierarchical path data of the cone transformation model to obtain the planned path and nozzle extrusion amount parameters of the cone transformation model; S3, performing path segmentation processing and inverse cone transformation processing on the planned path of the cone transformation model in sequence, obtaining the planned path and nozzle extrusion amount parameters of the model to be printed in the coordinate system of the model to be printed, and then adjusting the actual nozzle extrusion amount according to the nozzle extrusion amount parameters of the cone transformation model and the nozzle extrusion amount parameters of the model to be printed; S4, performing exponential product kinematic modeling on the turntable type additive manufacturing equipment to obtain the kinematic degree of freedom conversion relationship between the coordinate system of the model to be printed and the coordinate system of the equipment; S5. According to the kinematic transformation relationship between the coordinate system of the model to be printed and the device coordinate system, the planned path of the model to be printed in the coordinate system of the model to be printed is transformed to obtain the planned path of the model to be printed in the device coordinate system. Finally, 3D printing is performed using a turntable-type additive manufacturing device according to the planned path of the model to be printed in the device coordinate system and the actual extrusion amount of the nozzle.

2. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 1, characterized in that: The preprocessing in S1 is specifically as follows: Acquire a model to be printed, wherein the model to be printed is composed of a plurality of triangular facets, and refine and segment the triangular facet information in the model to be printed to obtain a refined and segmented model; The detailed segmentation is specifically to connect the midpoints of every two adjacent sides of the triangular facets, and then segment the triangular facets.

3. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 2, characterized in that: The cone transformation process in S1 is processed according to the following formula: [x'y'z'] T =[x0 / cosθy0 / cosθz0+(x0 2 +y0 2 ) 1 / 2 ] T Among them, x0, y0, z0 are the position coordinates before the cone transformation, x', y', z' are the position coordinates after the cone transformation, θ is the preset angle of the cone transformation, and T represents the matrix transpose.

4. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 3, characterized in that: The path segmentation process in S3 is performed according to the following formula to divide the planned path of the cone transformation model into multiple mother paths, and each mother path is divided into m sub-paths of equal length: dist=((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 m=ceil(dist / l max ) Δx=(x new -x old ) / m Δy=(y new -y old ) / m x k =x old +kΔx and k =and old +kΔy z k =z old -(x k 2 +y k 2 ) 1 / 2 Among them, P old represents the starting point of the parent path, P old The coordinates are (x old ,y old ,z old ), P new represents the end point of the parent path, P new The coordinates are (x new ,y new ,z new ), dist represents the projection length of the parent path on the XY plane, l max represents the maximum length of the sub-path after segmentation, Δx and Δy represent the changes in the projection from the sub-path starting point to the sub-path end point on the X-axis and Y-axis directions, respectively. k ,y k 、z k Indicates the coordinates of the end point of the kth sub-path. The value range of k is 1 to m. m indicates the number of sub-paths divided from the parent path. ceil() indicates rounding up.

5. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 1, characterized in that: The inverse cone transformation process in S3 is processed according to the following formula: [x0'y0'z0'] T =[x'cosθy'cosθz'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 ] T Among them, x', y', z' are the position coordinates after cone transformation, x0', y0', z0' are the position coordinates of the model to be printed after inverse cone transformation, θ is the preset cone transformation angle, and T represents matrix transpose.

6. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 1, characterized in that: The actual nozzle extrusion amount in S3 is adjusted according to the following formula: dist k =(1 / m)((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2 dist kt =((x 0k '-x 0k-1 ') 2 +(y 0k '-y 0k-1 ') 2 ) 1 / 2 e k =e / m e kt =cosθ(dist k / dist kt )e k Among them, x new and new Indicates the starting coordinates of the parent path, x old and old represents the end point coordinates of the parent path, e is the nozzle extrusion base of a parent path, m represents the number of sub-paths into which the path is divided, and e k is the nozzle extrusion amount parameter of each sub-path of the cone transformation model, e kt is the nozzle extrusion amount of each sub-path of the model to be printed, dist k is the projection length of each sub-path on the XY plane, dist kt is the projection length of each segment of the sub-path on the XY plane after the conical transformation, dist is the projection length of the parent path on the XY plane, 0k ',y 0k ' is the coordinate of the Kth subpath after conical transformation, x 0k-1 ',y 0k-1 ' is the coordinate of the K-1th sub-path after conical transformation, and θ is the preset angle of conical transformation.

7. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 1, characterized in that: The turntable type additive manufacturing equipment includes a four-degree-of-freedom turntable type additive manufacturing equipment and a B-swing head-C turntable type five-axis additive manufacturing equipment; The specific steps of S5 are: S5.

1. Obtaining the B-axis / C-axis angle of the rotary table type additive manufacturing device according to the planned path of the model to be printed; When the turntable type additive manufacturing device is a four-degree-of-freedom turntable type additive manufacturing device, the C-axis angle of the turntable type additive manufacturing device is set according to the following formula: Φ k =arctan((x 0k '-x 0k-1 ') / (and 0k '-and 0k-1 ')) Among them, Φ k represents the C-axis angle of the k-th subpath, x 0k ' and y 0k ' represents the end point coordinates of the kth subpath, x 0k-1 ' and y 0k-1 ' represents the starting point coordinates of the kth subpath; When the turntable type additive manufacturing equipment is a B-swing head-C turntable type five-axis additive manufacturing equipment, the B-axis angle and the C-axis angle of the turntable type additive manufacturing equipment are set according to the following formula: b k =θ Φ k =arctan((x 0k '-x 0k-1 ') / (and 0k '-and 0k-1 ')) Among them, β k represents the B-axis angle of the k-th sub-path, Φ k represents the C-axis angle of the k-th subpath, x 0k ' and y 0k ' represents the end point coordinates of the kth subpath, x 0k-1 ' and y 0k-1 ' represents the starting point coordinates of the kth sub-path, and θ is the preset angle of the cone transformation; S5.

2. The C-axis angle of the rotary table type additive manufacturing equipment is processed according to the following formula to obtain the processed C-axis angle: t k =arg min t {|F k +2πt-γ k-1 |:t=-10,-9,...,9,10} c k =Φ k +2πt k Among them, Φ k represents the C-axis angle of the k-th subpath, γ k represents the C-axis angle of the k-th sub-path after processing, t k Indicates the processing value selected by the k-th subpath, arg min t Indicates the value of t when the function takes the minimum value, | | indicates the absolute value, :t=-10,-9,...,9,10 indicates that the possible values ​​of t in the function are -10,-9,...,9,10, and t indicates the number of circumferential adjustments of the C-axis angle; S5.3, the planned path of the model to be printed is brought into the kinematic transformation relationship between the coordinates of the model to be printed and the device coordinates for transformation, so as to obtain the position coordinates of the model to be printed in the device coordinates, and the B-axis angle, the processed C-axis angle and the position coordinates of the model to be printed in the device coordinates together constitute the planned path of the model to be printed in the device coordinates; Finally, 3D printing is performed using a rotary table additive manufacturing device based on the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion volume.

8. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures according to claim 7, characterized in that: The position coordinates of the model to be printed in the device coordinates in S5.3 are specifically: When the turntable additive manufacturing device is a four-degree-of-freedom turntable additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: [X4Y4Z4] T =[x0'y0'z0'] T Among them, X4, Y4 and Z4 represent the position coordinates of the model to be printed in the equipment coordinate system of the four-degree-of-freedom turntable additive manufacturing equipment, x0', y0', z0' are the position coordinates of the model to be printed after inverse cone transformation, and T represents matrix transposition; When the rotary table type additive manufacturing device is a B-swing head-C rotary table type five-axis additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula: <h2 style=";text-align:left;direction:ltr">[X5Y5Z5]<h2 style=";text-align:left;direction:ltr"> T =[(x0'+P X1 )cosΦ k -(y0'+P Y1 )sinΦ k -P X2 +P X3 (x0'+P X1 ) sinΦ k -(y0'+P Y1 )cosΦ k +P Y2 +P Y3 z0'+P Z1 -P Z2 -P Z3 ] T Among them, X5, Y5 and Z5 represent the xyz position coordinates of the model to be printed in the equipment coordinate system of the five-degree-of-freedom turntable additive manufacturing equipment, x0', y0', z0' are the position coordinates of the model to be printed after the inverse cone transformation, P X1 , P Y1 , P Z1 They represent the xyz vector coordinates of the rotating platform center pointing to the origin of the printing model in the device coordinate system, P X2 , P Y2 , P Z2 They represent the xyz position coordinates of the B-axis rotation center in the device coordinate system, P X3 , P Y3 , P Z3 They respectively represent the xyz vector coordinates pointing from the B-axis rotation center to the end of the print head in the device coordinate system, and T represents matrix transpose.

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