A Multi-Degree-of-Freedom Path Planning Method for Support-Free Additive Manufacturing of a Draping Structure

Abstract

The present invention discloses a multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure. The present invention sequentially performs preprocessing, conical transformation processing, and slicing processing on the model to be printed to convert and obtain the planned path of the conical transformation model; sequentially performs path segmentation processing and inverse conical transformation processing on the planned path of the conical transformation model to obtain the planned path of the model to be printed in the coordinate system of the model to be printed; performs exponential product kinematic modeling on the device to obtain the kinematic conversion relationship between the coordinate system of the model to be printed and the coordinate system of the device; and then performs conversion to obtain the planned path of the model to be printed in the coordinate system of the device and performs 3D printing. The present invention is applicable to most existing slicing software, and can realize unsupported printing of hanging structures by using the path planning of the generated slicing software, thereby simplifying the post-processing process after 3D printing and further improving the quality and surface flatness of the printed parts.

Description

Technical Field

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

[0002] Fused Deposition Modelling (FDM) is one of the most mainstream 3D printing technologies at present. The path planning algorithm adopted by the FDM technology usually performs slicing processing on a three-dimensional model in the form of a CAD model, point cloud data or an STL file, etc., and fills the sliced contour through a corresponding filling algorithm to generate a processing data file recognizable by a 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 introducing a support structure can partially solve this problem, it also brings problems such as a complicated post-processing process and a reduction in the surface integrity of the printed part, thereby having a negative impact on the final printing effect. Therefore, how to construct precise and complex structures under the condition of no support or less support has become a new challenge faced by the FDM technology.

[0003] To solve the problem of unsupported printing of complex structures, it is necessary to start from the basic principle of the fused deposition modeling process, and optimize the path planning algorithm and change the forming direction during the printing process to achieve unsupported printing of the structure. Thus, the multi-degree-of-freedom path planning method has attracted wide attention.

[0004] Since multi-degree-of-freedom additive manufacturing devices have many different mechanical configurations, these devices have significant differences in degrees of freedom, motion ranges, joint limitations, and control strategies; and the multi-degree-of-freedom path planning method first needs to perform interpolation calculations on 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-degree-of-freedom path planning method generally does not have universality. In addition, during the path calculation process, factors such as the smoothness of the path and physical interference constraints also need to be considered; during the actual printing process, many factors such as printing temperature, material extrusion speed, and material morphological characteristics also need to be comprehensively considered for their influence on path planning. The coupling relationship of these related factors makes it necessary to consider multiple control factors when designing the multi-degree-of-freedom path planning algorithm, greatly increasing the complexity of the algorithm. Therefore, reducing the algorithm complexity has become a major challenge in the multi-degree-of-freedom additive manufacturing path planning algorithm. Summary of the Invention

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

[0006] The technical solution adopted by the present invention is:

[0007] The multi-degree-of-freedom path planning method of the present invention includes the following steps:

[0008] S1. Obtain the model to be printed of the physical product, and successively perform preprocessing and conical transformation processing on the model to be printed to obtain a conical transformation model;

[0009] S2. Perform slicing processing on the conical transformation model to obtain the layer path data of the conical transformation model, and then convert the layer path data of the conical transformation model to obtain the planned path of the conical transformation model and the nozzle extrusion amount parameter;

[0010] S3. Successively perform path segmentation processing and inverse conical transformation processing on the planned path of the conical transformation model to obtain the planned path of the model to be printed in the coordinate system of the model to be printed and the nozzle extrusion amount parameter, and then adjust the actual nozzle extrusion amount according to the nozzle extrusion amount parameter of the conical transformation model and the nozzle extrusion amount parameter of the model to be printed;

[0011] S4. Perform 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 equipment coordinate system;

[0012] S5. According to the kinematic conversion relationship between the coordinate system of the model to be printed and the equipment coordinate system, convert the planned path of the model to be printed in the coordinate system of the model to be printed to obtain the planned path of the model to be printed in the equipment coordinate system, and finally use the turntable type additive manufacturing equipment for 3D printing according to the planned path of the model to be printed in the equipment coordinate system and the actual nozzle extrusion amount.

[0013] The specific preprocessing in S1 is as follows:

[0014] Obtain the model to be printed, which is composed of a number of triangular patches, and perform refined segmentation on the triangular patch information in the model to be printed to obtain a refined segmentation model;

[0015] The specific refined segmentation is to make a connection line of the midpoints of every two adjacent sides of the triangular patch, and then segment the triangular patch.

[0016] The conical transformation processing in S1 is processed according to the following formula:

[0017] [x' y' z'] T =[x0 / cosθ y0 / cosθ z0+(x0 2 +y0 2 ) 1 / 2 T

[0018] ​Among them, x0, y0, and z0 are the position coordinates before the conical transformation, x', y', and z' are the position coordinates after the conical transformation, θ is the preset angle of the conical transformation, and T represents matrix transpose.

[0019] The path segmentation process in S3 is processed according to the following formula. The planned path of the conical transformation model is divided into multiple mother paths, and each mother path is segmented into m equal-length sub-paths:

[0020] dist = ((x new - x old ) 2 + (y new - y old ) 2 ) 1 / 2

[0021] m = ceil(dist / l max )

[0022] Δx = (x new - x old ) / m

[0023] Δy = (y new - y old ) / m

[0024] x k = x old + kΔx

[0025] y k = y old + kΔy

[0026] z k = z old - (x k 2 + y k 2 ) 1 / 2

[0027] Among them, P old represents the starting point of the mother path, and the coordinates of P old are (x old , y old , z old ), P new represents the end point of the mother path, and the coordinates of P new are (x new , y new , z new ), dist represents the projected length of the mother path on the XY plane, l max represents the maximum length of the segmented sub-path, x k , y k , zk Represents the end coordinates of the k-th sub-path, where the value range of k is from 1 to m, m represents the number of sub-paths into which the parent path is divided, and ceil( ) represents rounding up.

[0028] The inverse conical transformation process in S3 is processed according to the following formula:

[0029] [x0' y0' z0'] T =[x'cosθ y'cosθ z'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 T

[0030] Where x', y', z' are the position coordinates after conical transformation, x0', y0', z0' are the position coordinates of the model to be printed after inverse conical transformation, θ is the preset angle of conical transformation, and T represents matrix transpose.

[0031] The actual nozzle extrusion amount in S3 is adjusted according to the following formula:

[0032] dist k =(1 / m)((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2

[0033] dist kt =((x 0k '-x 0k-1 ') 2 +(y 0k '-y 0k-1 ') 2 ) 1 / 2

[0034] e k =e / m

[0035] e kt =cosθ(dist k / dist kt )e k

[0036] Where x new and y new represent the start coordinates of the parent path, x old and y old represent the end coordinates of the parent path, e is the basic nozzle extrusion amount for a section of the parent path, m represents the number of sub-paths into which the path is divided, e​k is the nozzle extrusion amount parameter of each sub-path of the conical transformation model, e kt is the nozzle extrusion amount of each sub-path of the model to be printed, dist k is the projected length of each sub-path on the XY plane, dist kt is the projected length of each sub-path on the XY plane after conical transformation, dist is the projected length of the parent path on the XY plane, x 0k ', y 0k ' are the coordinates of the K-th sub-path after conical transformation, x 0k-1 ', y 0k-1 ' are the coordinates of the (K - 1)-th sub-path after conical transformation, and θ is the preset angle of conical transformation.

[0037] The turntable type additive manufacturing equipment includes a four-degree-of-freedom turntable type additive manufacturing equipment and a B-axis swing - C-axis turntable type five-axis additive manufacturing equipment;

[0038] The specific steps of S5 are as follows:

[0039] S5.1. Obtain the B-axis / C-axis angles of the turntable type additive manufacturing equipment according to the planned path of the model to be printed;

[0040] When the turntable type additive manufacturing equipment is a four-degree-of-freedom turntable type additive manufacturing equipment, the C-axis angle of the turntable type additive manufacturing equipment is set according to the following formula:

[0041] Φ k = arctan((x 0k ' - x 0k-1 ') / (y 0k ' - y 0k-1 '))

[0042] where, Φ k represents the C-axis angle of the k-th sub-path, x 0k ' and y 0k ' represent the end coordinates of the k-th sub-path, x 0k-1 ' and y 0k-1 ' represent the start coordinates of the k-th sub-path;

[0043] When the turntable type additive manufacturing equipment is a B-axis swing - C-axis turntable type five-axis additive manufacturing equipment, the B-axis angle and C-axis angle of the turntable type additive manufacturing equipment are set according to the following formula:

[0044] β k = θ

[0045] Φ k = arctan((x 0k ' - x 0k-1 ') / (y0k '-y 0k-1 '))

[0046] Among them, β k represents the B-axis angle of the k-th sub-path, and Φ k represents the C-axis angle of the k-th sub-path. x 0k ' and y 0k ' represent the end coordinates of the k-th sub-path, and x 0k-1 ' and y 0k-1 ' represent the start coordinates of the k-th sub-path. θ is the angle of the preset conical transformation;

[0047] S5.2. Perform data processing on the C-axis angle of the turntable type additive manufacturing equipment to obtain the processed C-axis angle;

[0048] The data processing is carried out according to the following formula:

[0049] t k = argmin t {|Φ k + 2πt - γ k-1 |: t = -10, -9,..., 9, 10}

[0050] γ k = Φ k + 2πt k

[0051] Among them, when k = 1, γ1 = Φ1, and Φ k represents the C-axis angle of the k-th sub-path, γ k represents the processed C-axis angle of the k-th sub-path, t k represents the processing value selected for the k-th sub-path, argmin t represents the value of t when the function takes the minimum value. || represents taking the absolute value. : t = -10, -9,..., 9, 10 means that the values that t can take in the function are -10, -9,..., 9, 10, and t represents the circumferential adjustment times of the C-axis angle;

[0052] S5.3. Substitute the planned path of the model to be printed into the kinematic conversion relationship between the coordinates of the model to be printed and the equipment coordinates for conversion to obtain the position coordinates of the model to be printed in the equipment coordinates. The B-axis angle, the processed C-axis angle, and the position coordinates of the model to be printed in the equipment coordinates together constitute the planned path of the model to be printed in the equipment coordinates;

[0053] Finally, perform 3D printing using the turntable type additive manufacturing equipment according to the planned path of the model to be printed in the equipment coordinate system and the actual nozzle extrusion amount.

[0054] The position coordinates of the model to be printed in the device coordinates in S5.3 are specifically as follows:

[0055] When the rotary table type additive manufacturing device is a four-degree-of-freedom rotary table type additive manufacturing device, the position coordinates of the model to be printed in the device coordinate system are set according to the following formula:

[0056] [X4 Y4 Z4] T =[x0' y0' z0'] T

[0057] Among them, X4, Y4, and Z4 represent the position coordinates of the model to be printed in the device coordinate system in the four-degree-of-freedom rotary table type additive manufacturing device, x0', y0', and z0' are the position coordinates of the model to be printed after inverse conical transformation, and T represents matrix transpose;

[0058] When the rotary table type additive manufacturing device is a B-axis swing - C-axis 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:

[0059] [X5 Y5 Z5] T

[0060] =[(x0'+P X1 )cosΦ k -(y0'+P Y1 )sinΦ k -P X2 +P X3

[0061] (x0'+P X1 ) sinΦ k -(y0'+P Y1 )cosΦ k +P Y2 +P Y3

[0062] z0'+P Z1 -P Z2 -P Z3 T

[0063] Among them, X5, Y5, and Z5 respectively represent the xyz position coordinates of the model to be printed in the device coordinate system in the five-degree-of-freedom rotary table type additive manufacturing device, x0', y0', and z0' are the position coordinates of the model to be printed after inverse conical transformation, P X1 、P Y1 、P Z1 respectively represent the xyz vector coordinates of the vector from the center of the rotating platform to the origin of the printed model in the device coordinate system, P X2 、P Y2 、P Z2 ​respectively represent the xyz position coordinates of the rotation center of the B axis in the device coordinate system, P X3 、P Y3 、P Z3 respectively represent the xyz vector coordinates of the vector pointing from the rotation center of the B axis to the end of the printing nozzle in the device coordinate system, and T represents matrix transpose.

[0064] The beneficial effects of the present invention are as follows:

[0065] 1. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of overhanging structures proposed in the present invention can achieve unsupported printing of overhanging structures, saving printing time while improving the integrity of the printed model and greatly reducing the post-processing time.

[0066] 2. The present invention takes the conical transformation algorithm as the core, only needs to perform pre-processing on the STL file of the model to be printed, and then perform post-modification on the generated G code, saving the necessary process of taking model path points for path planning, simplifying the path generation process, and greatly reducing the complexity of the path planning algorithm.

[0067] 3. The exponential product kinematic model of the present invention models the configuration of the additive manufacturing equipment to obtain the conversion relationship between the device coordinate system and the coordinate system of the model to be printed, enabling the algorithm to be applicable to various turntable-type multi-degree-of-freedom devices, and the multi-degree-of-freedom additive manufacturing path planning algorithm has high versatility.

[0068] In summary, in the process of manufacturing and printing overhanging structures, the present invention has greatly improved the surface integrity and printing efficiency of overhanging structure prints compared with traditional methods. Brief Description of the Drawings

[0069] Figure 1 is a flow block diagram of the solution of the present invention.

[0070] Figure 2 is a schematic diagram of conical transformation.

[0071] Figure 3 is a schematic diagram of the model to be printed of the Y-shaped tubular overhanging structure.

[0072] Figure 4 is a schematic diagram of the Y-shaped tubular overhanging structure model after conical transformation.

[0073] Figure 5 is a schematic diagram of slicing the conical model.

[0074] Figure 6 is a preview diagram of the final print generation of the tubular overhanging structure.

[0075] Figure 7 is a preview diagram of the process of unsupported printing of the key parts of the tubular overhanging structure. Detailed Implementation Modes

[0076] The present invention will be further described below in conjunction with the accompanying drawings and specific implementations.

[0077] As Figure 1 shown, the specific implementation example of the multi-degree-of-freedom path planning method of the present invention includes the following steps:

[0078] S1. As Figure 3 shown, obtain the model to be printed of the physical product, and perform preprocessing and conical transformation processing on the model to be printed in sequence to obtain a conical transformation model, as Figure 4 shown. Figures 3 - 6 Shows the generation process of the support-free printing G code for the tubular overhang structure;

[0079] The model to be printed includes the model height and model structure information of the model to be printed.

[0080] The preprocessing is specifically as follows:

[0081] Obtain the model to be printed. The model to be printed is composed of several triangular patches. Refine and segment the triangular patch information in the model to be printed to obtain the refined and segmented model;

[0082] The refinement and segmentation are specifically to make the connection line of the midpoints of every two adjacent sides of the triangular patch, and then segment the triangular patch, so that the original triangular patch can be segmented into four congruent small triangular patches. The model to be printed is composed of several triangular patches.

[0083] Import the model to be printed into the 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 the STL file format.

[0084] The conical transformation processing is carried out according to the following formula:

[0085] [x' y' z'] T =P(x0,y0,z0)

[0086] =[x0 / cosθ y0 / cosθ z0+(x0 2 +y0 2 ) 1 / 2 T

[0087] =1 / cosθ[x0 y0 0] T +[0 0 z0+(x0 2 +y0 2 ) 1 / 2 T

[0088] ​​Among them, x0, y0, and z0 are the position coordinates of a certain vertex of the triangular patch before the conical transformation, x', y', and z' are the position coordinates of a certain vertex of the triangular patch after the conical transformation, θ is the preset angle of the conical transformation, P( ) represents performing the conical transformation process, and T represents matrix transpose.

[0089] Figure 2 is a schematic diagram of the conical transformation, which presents a schematic cross-section of the model to be printed. Each unit represents the cross-section of a section of the path; among them, the vertical dotted line is the center of the conical transformation, and the angle formed by the conical layer and the horizontal layer is the angle of the conical transformation.

[0090] Here, the position coordinates 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 usually takes the center of the bottom of the model as the origin. Generally, for a centrally symmetric model, its symmetric center is selected as the transformation center line, and the intersection point of the symmetric center and the bottom surface of the model is the origin.

[0091] S2, such as Figure 5 As shown, perform slicing processing on the conical transformation model. Use slicing software to set slicing parameters, divide the conical transformation model into several horizontal layers with a certain thickness. The same horizontal layer has the same layer height, obtain the layer-by-layer path data of the conical transformation model, and then convert the layer-by-layer path data of the conical transformation model into the planned path and nozzle extrusion amount parameters of the conical transformation model obtained by the slicing software. Specifically, obtain the G-code file of the conical transformation model in the implementation;

[0092] The slicing parameters include layer height, number of outer boundary layers, extrusion width, etc.

[0093] S3. Perform path segmentation processing and inverse conical transformation processing on the planned path of the conical transformation model in sequence, that is, the post-processing of the conical 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. Specifically, obtain the G-code file of the model to be printed in the implementation, restore the path of the conical model to the path file of the model to be printed, and obtain the path planning file of the model to be printed. Then, adjust the actual nozzle extrusion amount according to the nozzle extrusion amount parameters of the conical transformation model and the nozzle extrusion amount parameters of the model to be printed;

[0094] The path segmentation processing is carried out according to the following formula. The planned path of the conical transformation model is divided into multiple parent paths, and each parent path is divided into m equal-length sub-paths:

[0095] dist=((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2

[0096] m = ceil(dist / l max )

[0097] Δx = (x new - x old ) / m

[0098] Δy = (y new - y old ) / m

[0099] x k = x old + kΔx

[0100] y k = y old + kΔy

[0101] z k = z old - (x k 2 + y k 2 ) 1 / 2

[0102] Among them, regarding the command of a section of path, i.e., G1, as a linear motion, P old represents the starting point of the mother path, i.e., the starting point of the path to be segmented. The coordinates of P old are (x old , y old , z old ). P new represents the ending point of the mother path, i.e., the ending point of the path to be segmented. The coordinates of P new are (x new , y new , z new ). dist represents the projected length of the mother path on the XY plane. l max represents the maximum length of the segmented sub - paths. m represents the number of sub - paths segmented in the mother path. x k , y k , z k represent the ending coordinates of the k - th sub - path. The value range of k is from 1 to m. ceil( ) represents rounding up. Δx and Δy respectively represent the changes projected on the X - axis and Y - axis from the starting point to the ending point of the sub - path.

[0103] Among them, k = 0, 1,... m. Re - edit the endpoints of each calculated sub - path in the format of G - code, insert them into the long - path G - code segment, and replace the original G - code to complete the refined segmentation of the long path.

[0104] The inverse conical transformation is processed according to the following formula:

[0105] [x0' y0' z0'] T =P -1 (x',y',z')

[0106] =[x'cosθ y'cosθ z'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 T

[0107] =cosθ[x' y' 0] T +[0 0 z'-((x'sinθ) 2 +(y'sinθ) 2 ) 1 / 2 T

[0108] Among them, x', y', and z' are the position coordinates of a vertex of a triangular patch after conical transformation, x0', y0', and z0' are the position coordinates of a vertex of a triangular patch of the model to be printed after inverse conical transformation, θ is the preset angle of conical transformation, P -1 ( ) represents performing inverse conical transformation processing, and T represents matrix transpose.

[0109] That is, the angle formed by the θ conical layer and the horizontal layer, and this angle should be consistent with the preset angle of conical transformation. The transformed G-code instructions are re-integrated into a new G-code file. Here, the position coordinates are the position coordinates in the coordinate system of the model to be printed, which is consistent with the coordinate system of conical transformation.

[0110] Such as Figure 5 shown, the above algorithm is used to generate the G-code process for support-free printing of a tubular overhang structure. The layer direction in the Y-shaped tubular overhang structure generated by using this algorithm is different from the layer direction obtained by a traditional slicer, and the printing and forming direction of this part is successfully transformed to achieve a support-free printing process.

[0111] The actual nozzle extrusion amount is adjusted according to the following formula:

[0112] dist k =(1 / m)dist=(1 / m)((x new -x old ) 2 +(y new -y old ) 2 ) 1 / 2

[0113] dist kt =((x 0k '-x​​0k-1 ) 2 +(y 0k '-y 0k-1 ) 2 ) 1 / 2

[0114] e k =e / m

[0115] e kt =cosθ(dist k / dist kt )e k

[0116] Among them, x new and y new represent the starting coordinates of the parent path, x old and y old represent the ending coordinates of the parent path, e is the basic extrusion amount of the nozzle for a section of the parent path, m represents the number of sub-paths into which the path is divided, e k is the nozzle extrusion amount parameter for each sub-path of the conical transformation model, e kt is the nozzle extrusion amount for each sub-path of the model to be printed, dist k is the projected length of each sub-path on the XY plane, dist kt is the projected length of each sub-path on the XY plane after conical transformation, dist is the projected length of the parent path on the XY plane, x 0k ', y 0k ' are the coordinates of the Kth sub-path after conical transformation, x 0k-1 ', y 0k-1 ' are the coordinates of the (K - 1)th sub-path after conical transformation, and θ is the preset angle of conical transformation, that is, the angle between the conical layer and the horizontal layer.

[0117] S4. Perform exponential product kinematic modeling on the spatial configuration of the rotary table type additive manufacturing equipment to obtain the kinematic model of the equipment, and then combine the coordinate system of the model to be printed and the coordinate system of the rotary table type additive manufacturing equipment to process and obtain the conversion relationship of kinematic degrees of freedom between the coordinate system of the model to be printed and the equipment coordinate system, that is, convert the traditional three-degree-of-freedom coordinates into the coordinates of a three-degree-of-freedom, four-degree-of-freedom, or five-degree-of-freedom rotary table type additive manufacturing equipment according to the exponential product kinematic modeling, that is, the conversion relationship between the motion amounts of each axis of the equipment;

[0118] The rotary table type additive manufacturing equipment is a rotary table type multi-degree-of-freedom equipment. The three degrees of freedom mean that the equipment can move in three independent directions, usually the X, Y, and Z axis directions, specifically a traditional three-axis additive manufacturing system; the four degrees of freedom mean that a rotational degree of freedom around the C axis is added on the basis of the three degrees of freedom, specifically a rotary platform type four-axis additive manufacturing system; the five degrees of freedom mean that another rotational degree of freedom is added on the basis of the four degrees of freedom, usually the B axis, which can rotate around the Z axis, specifically a B swivel head - C rotary table type five-axis additive manufacturing system.

[0119] 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 represented by a 4×4 matrix, which can be expressed as the following formula:

[0120]

[0121] 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 represented in the form of a screw exponential matrix:

[0122] g = e ξ' θ

[0123] Among them, θ represents the angle of rotation around a certain axis.

[0124] When ω = 0, it means that the angular velocity of the rigid body motion is 0, then the motion is only linear motion, and the matrix of its screw and coordinate transformation can be expressed as:

[0125] ξ = [v T 0] T

[0126]

[0127] When ω ≠ 0, the rigid body only performs rotational motion, and the matrix of its screw and coordinate transformation can be expressed as:

[0128] ξ = [ω T ν T T = [ω1 ω2 ω3 v1 v2 v3] T

[0129]

[0130] ​In the above formula, θ is the angle of rotation during rotational motion about an axis, ω represents the angular velocity of the rigid body rotating about the axis, i.e., the unit vector in the axial direction of the rotational motion of the rigid body, ω = [ω1 ω2 ω3] T , ω1, ω2, and ω3 respectively represent the components of ω along the X, Y, and Z axes, and satisfy ω1 2 + ω2 2 + ω3 2 = 1. When the rigid body performs horizontal motion, ω = [0 0 0] T . v represents the linear velocity of the rigid body, i.e., the unit vector in the translational direction of the rigid body, v = [v1 v2 v3] T . If q represents a point on the axis of the rotational motion, then the relationship v = q × ω is satisfied. < > represents converting a vector into matrix form, and this operation symbol satisfies the relationship: 〈ω〉ν = ω × ν, where × is the cross product:

[0131]

[0132] The coordinate expression of a spinor can be represented by a 4×4 matrix:

[0133]

[0134] e <ω>θ = I 3×3 + <ω>sinθ + <ω> 2 (1 - cosθ)

[0135] For a multi-degree-of-freedom 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 spinor motion transformations, and its transformation relationship can be expressed as:

[0136] Q = e (ξn' θn) …e (ξ3'θ3 ) ⋅e (ξ2'θ2 ) ⋅e (ξ1'θ1)

[0137] Among them, e ξ'n is the nth spinor motion transformation, which means the device has n degrees of freedom.

[0138] S5. Convert the planned path of the model to be printed in the model coordinate system to the planned path of the model to be printed in the device coordinate system according to the kinematic conversion relationship between the coordinates of the model to be printed and the device coordinates. Specifically, in implementation, perform kinematic transformation on the G-code file of the model to be printed according to the configuration space of the additive manufacturing device to obtain the final G-code file. Finally, use the rotary table type additive manufacturing device to perform 3D printing according to the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion amount.

[0139] The rotary table type additive manufacturing device includes a four-degree-of-freedom rotary table type additive manufacturing device with a C rotation axis and a B swing head - C rotary table type five-axis additive manufacturing device;

[0140] S5.1. Obtain the B-axis / C-axis angles of the rotary table type additive manufacturing device on each sub-path according to the planned path of the model to be printed;

[0141] When the rotary table type additive manufacturing device is a four-degree-of-freedom rotary table type additive manufacturing device with a C rotation axis, the C-axis angle of the rotary table type additive manufacturing device is set according to the following formula:

[0142] Φ k = arctan((x 0k '- x 0k-1 ') / (y 0k '- y 0k-1 '))

[0143] Where, Φ k represents the C-axis angle of the k-th sub-path, x 0k ' and y 0k ' represent the coordinates of the end point of the k-th sub-path on the XY plane, x 0k-1 ' and y 0k-1 ' represent the coordinates of the start 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 start point is the start point of this mother path;

[0144] When the rotary table type additive manufacturing device is a B swing head - C rotary table type five-axis additive manufacturing device, the B-axis angle and C-axis angle of the rotary table type additive manufacturing device are set according to the following formula:

[0145] β k = θ

[0146] Φ k = arctan((x 0k '- x 0k-1 ') / (y 0k '- y 0k-1 '))

[0147] Where,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 coordinates of the k-th sub-path, x 0k-1 ' and y 0k-1 ' Represents the start coordinates of the k-th sub-path, that is, the coordinates of the end of the (k - 1)-th sub-path on the XY plane. When k = 1, the start point is the start point of the parent path of this segment, θ Is the preset angle of the conical transformation;

[0148] Calculate the angle between the printing nozzle and the model processing path, and determine the appropriate direction vector of the nozzle during processing; among them, the calculation method of the appropriate direction vector of the nozzle is: the nozzle direction is always set to be perpendicular to the printing path. Since the angle during conical transformation determines the angle of the B-axis, it is only necessary to make the nozzle perpendicular to the path on the XY plane; in the algorithm, only need to read the x old and y old as well as x new and y new values, and then use the np.arctan2 function built in the NumPy library to calculate the arctangent value of the path vector.

[0149] To ensure that the printing nozzle does not interfere with the printed model during printing, the nozzle direction is always defined as perpendicular to the printing path or at a certain angle with the printing path. For the B-C turntable type five-degree-of-freedom additive manufacturing equipment, to keep the nozzle direction always perpendicular to the printing path, the angle parameter θ during conical transformation determines the angle of the B-axis during the actual movement of the printing equipment. Therefore, it is only necessary to adjust the turntable angle of the equipment to make the printing nozzle perpendicular to the path on the XY plane. For the turntable type four-degree-of-freedom additive manufacturing equipment, the printing nozzle generally always maintains a certain fixed angle (usually vertically downward), so it is only necessary to calculate the angle of the equipment turntable to ensure that the printing nozzle and the printing path maintain a certain angle.

[0150] The turntable angle of the turntable type multi-degree-of-freedom 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:

[0151] Φ k = arctan((x 0k '- x 0k-1 ') / (y 0k '- y 0k-1 '))

[0152] It should be noted that to prevent interference between the printing nozzle and the printed model, the printing nozzle should always be kept outside the printed model. Therefore, this is the arctangent value, which is the counterclockwise angle from the origin (0, 0) to the vector (x 0k '- x 0k-1 ', y 0k '- y 0k-1 '); the range of the angle Φ k , angle Φ k is [-π, π];

[0153] S5.2. Perform data processing on the C-axis angle of the rotary table type additive manufacturing equipment to prevent angle mutation problems and obtain the processed C-axis angle on each sub-path;

[0154] The data processing is carried out according to the following formula:

[0155] t k = argmin t {|Φ k + 2πt - γ k-1 |: t = -10, -9,..., 9, 10}

[0156] γ k = Φ k + 2πt k

[0157] where, when k = 1, γ1 = Φ1, Φ k represents the C-axis angle of the k-th sub-path, γ k represents the processed C-axis angle of the k-th sub-path, t k represents the processed value selected for the k-th sub-path, that is, among the above 21 possible t k integer values of γ k select the best processed value to make γ k-1 closest to tDenote the value of \(t\) when the function takes the minimum value, \(\vert\vert\) represents taking the absolute value, \(t = - 10,-9,\cdots,9,10\) means the values that \(t\) can take in the function are \(-10,-9,\cdots,9,10\), and \(t\) represents the number of circumferential adjustments of the \(C\)-axis angle;

[0158] Process the angles calculated in step S5.1 to prevent angle mutation problems. Among the above 21 possible t k values, select the \(t\) value that makes γ k closest to γ k-1 to prevent the rotation angle from mutating.

[0159] S5.3. Substitute the planned path of the model to be printed into the kinematic conversion relationship between the coordinates of the model to be printed and the device coordinates for conversion to obtain the position coordinates \((x, y, z)\) of the model to be printed in the device coordinates. The B-axis angle, the processed C-axis angle, and the position coordinates of the model to be printed in the device coordinates on all sub-paths together constitute the planned path of the model to be printed in the device coordinates;

[0160] Finally, perform 3D printing using the rotary table type additive manufacturing equipment according to the planned path of the model to be printed in the device coordinate system and the actual nozzle extrusion amount.

[0161] Specifically, S5.3 means adjusting the movement amounts of each axis in the G-code file according to the spatial configuration of the device, and outputting the final machining file; among them, the method for adjusting the movement amounts 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 through in the coordinate system of the model to be printed, substitute these coordinates into the inverse kinematic model established in step S1 to obtain the movement amounts of the X, Y, and Z axes of the device, replace the X, Y, and Z parameters in the original G-code, and combine the B-axis angle and the processed C-axis angle to generate the final path planning file.

[0162] When the rotary table type additive manufacturing equipment is a four-degree-of-freedom rotary table type additive manufacturing equipment 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:

[0163] [X4 Y4 Z4] T =[x0' y0' z0'] T

[0164] where X4, Y4, and Z4 represent the position coordinates of the model to be printed in the device coordinate system in the four-degree-of-freedom rotary table type additive manufacturing equipment, x 0 ' , y 0 ' ,z 0 ' are the position coordinates of the model to be printed after the inverse conical transformation, and T represents the matrix transpose;

[0165] When the turntable type additive manufacturing equipment is a B-axis swing - C-axis turntable type five-axis additive manufacturing equipment, the position coordinates of the model to be printed in the equipment coordinate system are set according to the following formula:

[0166] [X5 Y5 Z5] T

[0167] =[(x0'+P X1 )cosΦ k -(y0'+P Y1 )sinΦ k -P X2 +P X3

[0168] (x0'+P X1 ) sinΦ k -(y0'+P Y1 )cosΦ k +P Y2 +P Y3

[0169] z0'+P Z1 -P Z2 -P Z3 T

[0170] where X5, Y5, and Z5 respectively represent the xyz position coordinates of the model to be printed in the equipment coordinate system of the five-degree-of-freedom turntable type additive manufacturing equipment, x0', y0', z0' are the position coordinates of the model to be printed after the inverse conical transformation, P X1 , P Y1 , P Z1 respectively represent the xyz vector coordinates of the vector from the center of the rotating platform to the origin of the printed model in the equipment coordinate system, and the origin of the printed model is the origin of the coordinate system of the model to be printed, P X2 , P Y2 , P Z2 respectively represent the xyz position coordinates of the B-axis rotation center in the equipment coordinate system, P X3 , P Y3 , P Z3 respectively represent the xyz vector coordinates of the vector from the B-axis rotation center to the end of the printing nozzle in the equipment coordinate system, and T represents the matrix transpose.

[0171] The final printing schematic diagram is as shown in Figure 6 ​As shown, the orange part is the part for adjusting the pose of the printing nozzle, where no material is extruded, and the blue part is the physical extrusion path part where material is extruded.

[0172] Among them Figure 7 is a process preview diagram of supportless printing at the key part of the tubular overhang structure. The orange part is the part for adjusting the pose of the printing nozzle, where no material is extruded; the blue part is the physical extrusion path part where material is extruded.

[0173] This method is based on the optimized design of the existing slicer, aiming to improve the efficiency and effect of multi-degree-of-freedom 3D printing path planning, and is particularly suitable for printing overhang structures. First, determine the kinematic chain of the 3D printing platform and establish a kinematic model of the printing platform; then, perform a conical transformation on the STL model of the overhang structure to be printed, and import the transformed STL model into the slicing software to generate an initial three-degree-of-freedom G-code file; finally, perform an inverse conical transformation on the three-degree-of-freedom G-code file, calculate the rotation angle of the printing platform, and embed it into the G-code to generate the final multi-degree-of-freedom G-code file.

[0174] The above specific embodiments are used to explain the present invention, rather than limit the present invention. Any modifications and changes made within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.

[0175] The above are only the preferred embodiments of the present invention. Therefore, all equivalent changes or modifications made according to the structure, features, and principles described in the scope of the present invention patent application are included in the scope of the present invention patent application.

Claims

1. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure, characterized in that, The method includes the following steps: S1. Obtain the model to be printed of the physical product, and sequentially perform preprocessing and conical transformation processing on the model to be printed to obtain a conical transformation model; S2. Perform slicing processing on the conical transformation model to obtain the layer path data of the conical transformation model, and then convert the layer path data of the conical transformation model to obtain the planned path of the conical transformation model and the nozzle extrusion amount parameter; S3. Sequentially perform path segmentation processing and inverse conical transformation processing on the planned path of the conical transformation model to obtain the planned path of the model to be printed in the coordinate system of the model to be printed and the nozzle extrusion amount parameter of the conical transformation model, and then adjust the actual nozzle extrusion amount according to the nozzle extrusion amount parameter of the conical transformation model and the planned path of the model to be printed; In S3, the actual nozzle extrusion amount 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 y new represent the starting coordinates of the mother path, x old and y old represent the ending coordinates of the mother path, e is the nozzle extrusion base amount of a section of the mother path, m represents the number of sub-paths into which the path is divided, e k is the nozzle extrusion amount parameter of each sub-path of the conical transformation model, e kt is the nozzle extrusion amount of each sub-path of the model to be printed, dist k is the projected length of each sub-path on the XY plane, dist kt is the projected length of each sub-path on the XY plane after inverse conical transformation, dist is the projected length of the mother path on the XY plane, x 0k ', y 0k ' are the ending coordinates of the K-th sub-path after inverse conical transformation, x 0k-1 ', y 0k-1 ' are the ending coordinates of the (K - 1)-th sub-path after inverse conical transformation, and θ is the preset angle of conical transformation; S4. Perform exponential product kinematic modeling on the rotary table 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 equipment coordinate system; S5. According to the kinematic conversion relationship between the coordinate system of the model to be printed and the equipment coordinate system, convert the planned path of the model to be printed in the coordinate system of the model to be printed to obtain the planned path of the model to be printed in the equipment coordinate system, and finally use the rotary table type additive manufacturing equipment for 3D printing according to the planned path of the model to be printed in the equipment coordinate system and the actual nozzle extrusion amount.

2. The multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure according to claim 1, wherein: The preprocessing in S1 is specifically: Obtain the model to be printed, which is composed of a number of triangular patches, and perform refined segmentation on the triangular patch information in the model to be printed to obtain the refined segmentation model; The refined segmentation is specifically to make the connection line of the midpoints of every two adjacent sides of the triangular patch, and then segment the triangular patch.

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

4. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure according to claim 3, characterized in that: The path segmentation processing in S3 is processed according to the following formula, and the planned path of the conical transformation model is divided into multiple mother paths, and each mother path is segmented into m equal-length sub-paths: 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 mother path, and P old has coordinates (x old , y old , z old ). P new represents the end point of the mother path, and P new has coordinates (x new , y new , z new ). dist represents the projected length of the mother path on the XY plane, l max represents the maximum length of the sub-path after segmentation. Δx and Δy respectively represent the changes in the X-axis and Y-axis directions projected from the starting point to the ending point of the sub-path. x k , y k , z k represent the end coordinates of the k-th sub-path. The value range of k is from 1 to m, where m represents the number of sub-paths segmented from the mother path, and ceil( ) represents rounding up.

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

6. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure according to claim 1, characterized in that: The rotary table type additive manufacturing equipment includes a four-degree-of-freedom rotary table type additive manufacturing equipment and a B-axis swing - C-axis rotary table type five-axis additive manufacturing equipment; The specific steps of S5 are: S5.

1. Obtain the B-axis / C-axis angles of the rotary table type additive manufacturing equipment according to the planned path of the model to be printed; When the rotary table type additive manufacturing equipment is a four-degree-of-freedom rotary table type additive manufacturing equipment, the C-axis angle of the rotary table type additive manufacturing equipment 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 sub-path, x 0k ' and y 0k ' represent the end coordinates of the k-th sub-path, x 0k-1 ' and y 0k-1 ' represent the start coordinates of the k-th sub-path; When the rotary table type additive manufacturing equipment is a B-axis swing - C-axis rotary table type five-axis additive manufacturing equipment, the B-axis angle and C-axis angle of the rotary table 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 ')) where, 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 ' represent the end coordinates of the k-th sub-path, x 0k-1 ' and y 0k-1 ' represent the start coordinates of the k-th sub-path, and θ is the angle of a preset conical transformation; S5.

2. Perform data processing on the C-axis angle of the turntable type additive manufacturing equipment according to the following formula to obtain the processed C-axis angle: t k = arg min t {|Φ k + 2πt - γ k-1 |: t = -10, -9,..., 9, 10} γ k = Φ k + 2πt k where, Φ k represents the C-axis angle of the k-th sub-path, γ k represents the C-axis angle of the processed k-th sub-path, t k represents the processing value selected for the k-th sub-path, arg min t represents the value of t when the function takes the minimum value, || represents taking the absolute value, t = -10, -9,..., 9, 10 means that the values that t can take in the function are -10, -9,..., 9 or 10, and t represents the circumferential adjustment times of the C-axis angle; S5.

3. Substitute the planned path of the model to be printed into the kinematic conversion relationship between the coordinates of the model to be printed and the equipment coordinates for conversion, and obtain the position coordinates of the model to be printed in the equipment coordinates. The B-axis angle, the processed C-axis angle, and the position coordinates of the model to be printed in the equipment coordinates together constitute the planned path of the model to be printed in the equipment coordinates; Finally, perform 3D printing using the turntable type additive manufacturing equipment according to the planned path of the model to be printed in the equipment coordinate system and the actual nozzle extrusion amount.

7. A multi-degree-of-freedom path planning method for unsupported additive manufacturing of a hanging structure according to claim 6, characterized in that: The position coordinates of the model to be printed in the equipment coordinates in S5.3 are specifically: When the turntable type additive manufacturing equipment is a four-degree-of-freedom turntable type additive manufacturing equipment, the position coordinates of the model to be printed in the equipment coordinate system are set according to the following formula: [X4 Y4 Z4] 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 in the four-degree-of-freedom turntable type additive manufacturing equipment, x0', y0', and z0' are the position coordinates of the model to be printed after inverse conical transformation, and T represents matrix transpose; When the turntable type additive manufacturing equipment is a B-swing head - C-turntable type five-axis additive manufacturing equipment, the position coordinates of the model to be printed in the equipment coordinate system are set according to the following formula: [X5 Y5 Z5] 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 respectively represent the xyz position coordinates of the model to be printed in the equipment coordinate system of the five-degree-of-freedom turntable type additive manufacturing equipment. x0', y0', and z0' are the position coordinates of the model to be printed after inverse conical transformation, P X1 , P Y1 , P Z1 respectively represent the xyz vector coordinates pointing from the center of the rotating platform to the origin of the printed model in the equipment coordinate system. P X2 , P Y2 , P Z2 respectively represent the xyz position coordinates of the rotation center of the B axis in the equipment coordinate system. P X3 , P Y3 , P Z3 respectively represent the xyz vector coordinates pointing from the rotation center of the B axis to the end of the printing nozzle in the equipment coordinate system. T represents matrix transpose.

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