3D printing path method for multi-tow continuous carbon fiber

Carbon fiber composite materials have many excellent characteristics such as high temperature resistance, friction resistance, thermal conductivity and corrosion resistance, so carbon fiber composite materials have become the first choice for printing materials. In order to improve the printing efficiency of carbon fiber 3D printing technology, it has been expanded to four side-by-side nozzles based on traditional single nozzles, and four nozzles are bound to print side by side. The four-nozzle side-by-side printing path has the problem of coordinating the motion planning of each nozzle, controlling the squeezing difference of each nozzle, and adjusting the angle of the print head, so it is necessary to reasonably control the squeezing amount of each nozzle and the angle of the print head. After the slicing processing based on the existing model, the Gcode code of the model is obtained. The Gcode code of the model is processed through the multi-tow continuous carbon fiber 3D printing path planning algorithm. The movement trajectory of each nozzle of the printer is reasonably planned based on the outer wall coordinates and the extrusion amount of each nozzle is controlled. Finally, the snipping instruction is executed after a circle of trajectory to print the next layer of motion trajectory, which ultimately improves the 3D printing while ensuring the accuracy of multi-beam model 3D printing.


Introduction
3D printing technology, also known as additive manufacturing, is used to manufacture three-dimensional models by controlling the selective stacking of materials and selectively printing the model slices on the workbench according to a predetermined G-code trajectory.It has the advantage that 3D printers with FDM can manufacture models quickly, so 3D printing technology is widely used in high-end fields such as aerospace, medicine, and electronics, and shows great advantages with outstanding advantages such as obvious digital features, high degree of automation, high precision, flexible production, and meeting customization needs [1][2].
Carbon fiber composites are known as the new generation of "king of materials" and are widely used in aerospace, automotive, sporting goods and medical fields due to their external flexibility and internal rigidity, a mass ratio less than that of aluminum, strength higher than that of steel, and excellent characteristics such as low density, high strength, high temperature, corrosion resistance and radiation resistance [3][4].Therefore, it is of extreme research importance to rapidly print customized products by combining the advantages of 3D printing technology and continuous carbon fiber composites.
When printing large-volume models or parts, traditional single-nozzle FDM fused deposition 3D are to be printed in parallel.If the printing path is not reasonably planned, it is easy to cause a lack of printing model accuracy.The third step is the extrusion control of the multi-tow nozzle, and after the reasonable planning of the path, it is also necessary to reasonably calculate the extrusion of each nozzle.If the extrusion is not reasonably planned, it is easy to cause the missing or overlapping problems of the tow trajectory, which affects the printing of the model.The fourth step is the angle adjustment of the print head.Due to the high flow rate of multiple tows and the large extrusion width, it is necessary to reasonably adjust the print head when printing the curve to prevent the winding problem of the tow and the problem of the accuracy of the printing path.The last step is to cut reasonably.Because the rotation of the robotic arm can only rotate 360 degrees in one direction, it is necessary to ensure a reasonable shear of the multiple harnesses during the printing process, and then set the angle of the print head to zero.The specific process is shown in Figure 1 below.

Extraction of model information
To plan the trajectory of multi-tow continuous carbon fiber, it is necessary to first obtain the model single nozzle slice G-code file, so that you can get the key information of the model, such as model width, layer height, line width, outer wall coordinates, etc., and then store the coordinates of each point in the set V: V (x , y ),...(x , y ) , which facilitates the subsequent operation of trajectory planning.

Planning of model path
After obtaining the coordinates of each point on the outer wall of the model and the key information of the model, it is necessary to judge the path trajectory.Since the arc trajectory of the generated Gcode file is fitted by many small line segments, it is necessary to judge the point, if the modulus length sum of the vector composed of three consecutive points P1, P2, P3 that constitute vector p1p2 ⃗ and p2p3 ⃗ .The mold length of p1p2 ⃗ and p2p3 ⃗ is less than the critical value C, it means that these 3 points fall on the arc otherwise there will be a straight line trajectory.If it is an arc trajectory, you can form a circular formula through the 3 points, the p1p2 segment trajectory will be fitted through the circular formula, and there will be clockwise and counterclockwise judgment for the circular arc trajectory.If the vector p1p2 ⃗ and p2p3 ⃗ product of the sum is positive, it means counterclockwise, otherwise, it is clockwise, and the extrusion volume and attitude of the four nozzles are calculated by similarity ratio during the fitting process.If the length of the p1p2 ⃗ or p2p3 ⃗ is greater than the critical value, it is planned as a straight trajectory, and each nozzle can be squeezed the same and the attitude remains unchanged during the linear trajectory.After each printing is completed, the tow is cut through the cut instruction to print the next turn, so as to cycle through layer printing to generate a path for multi-tow continuous carbon fiber 3D printing.

Model nozzle extrusion control
If the vector p1p2 ⃗ segment is a straight trajectory, the extrusion of each nozzle is the same, and each nozzle moves in parallel.If the vector p1p2 ⃗ fitting trajectory is arc, you need to calculate the extrusion of each nozzle.Because the arc length of the inner and outer circles of the arc is different, there is a difference in the extrusion of the nozzle.Through the three points P1(x , y ), P2(x , y ) and P3(x , y ), the center o(x , y ) is calculated.The radius of curvature of the four nozzles can be obtained by calculating the center o(x , y ) and the radius of curvature of the four nozzles [10] R1, R2, R3, and R4 and similar ratios k1, k2, k3, and k4, and finally we can plan the extrusion amount of each nozzle.

Print head angle adjustment
The angle of the print head remains unchanged when the multi-wire bundle prints the straight line.If it is a multi-beam printing arc trajectory, you need to reasonably adjust the angle value of the print head.
Because the tangent vector of the curve is changed at any time, the angle adjustment of the print head also needs to change at all times, and the angle can be reasonably calculated to ensure the accuracy of the print model trajectory, otherwise it will cause the winding and trajectory error of the tow.

Reasonable cutting and generating Gcode files
In the case of ensuring that the first four steps are accurate, the last needs to be reasonably cut.It is necessary to ensure both the continuity of the filament and the reasonable shear of the filament, which requires rational planning of the shear process.The angle of the printhead should be zeroed in each round of trajectory.If it is not sheared before zeroing it is easy to cause the filament bundle to be tangled or even twisted.So every time you complete a trajectory, you need to shear the filament beam, so that many problems can be reasonably avoided.After planning the path of the continuous carbon fiber composite material, the corresponding G-code file can be generated, and the G-code file is the multi-tow path planning instruction.The G-code file plans the distance of each movement of the print rack and the angle adjustment during each movement, while controlling the extrusion accuracy of each nozzle.The accuracy of the printed workpiece can be guaranteed.

3D printing path planning method
In order to solve the problem of multi-tow 3D printing path planning, this paper proposes a multi-tow continuous carbon fiber 3D printing path planning method, which is to solve the path planning problem, nozzle extrusion difference problem, print head printing angle problem and nozzle printing process in the process of shearing in the process of multi-tow printing.Path planning is mainly to make reasonable planning for the travel path of the printing support, so that the printing path is correct and reliable.The printhead in the printing arc trajectory of the inner ring and the outer ring of the extrusion differences.In order to prevent the trajectory of the extrusion of insufficient or extrusion overlap must make a reasonable calculation of the amount of extrusion.The printhead angle adjustment is to prevent interference between each filament beam and affect the print trajectory of the workpiece and make adjustments, and each small section of the arc should be adjusted to the angle tangent to the arc.The final shearing problem is to solve the problem of winding the individual tows.
The overall path planning method flow is shown in Figure 2, and the method planning will be made from the following five points, the extraction of model coordinate assembly points, the path planning of the model, the extrusion planning of each nozzle, the angle planning of the printer manipulator, and the planning of the shear instruction.Through these five planning methods, the purpose of multi-tow rapid printing of the target model is realized.

Extraction of coordinate points of the outer wall of the model
After the user is given the slice file of the corresponding model, we need to extract the outer wall coordinate information of the model, and store the model information through a set and V (x , y ),...(x , y ) , so as to prepare for the later extrusion calculation and attitude adjustment.The connection between points and points, shown in Figure 3.

Model path planning method
After getting the outer wall point, it is necessary to plan the multi-beam printing trajectory.Through the slicing algorithm of the slicing software, it can be known that if the distance between the two points is greater than the critical value C, it means that the two points are in long-distance linear motion, and when the distance between the two points is less than the critical value C, it is a short straight line fitting arc trajectory.In the path planning of the multi-wire tow nozzle only arc and straight two paths, if it is a straight trajectory, the extrusion amount of each nozzle is the same, and the angle of the print head remains unchanged.If the path trajectory is arc-shaped, you need to reasonably calculate the extrusion difference of each nozzle, and the angle of the print head also needs to be adjusted.Therefore, it is necessary to calculate the set D{l ,l ,...l } of the distance between points and points through the set V (x , y ),.(1) (3)

Model path extrusion calculation
When the trajectory of the printed model walks in a straight line, each nozzle walks in parallel at this time, the extrusion of each nozzle is the same, and the straight-line distance between the two points is the extrusion amount of each nozzle.If the trajectory of the printed model is arc-shaped, the extrusion volume of each nozzle is calculated by the similarity ratio.The calculation formula is as follows.This is shown in Figure 4.

Angle adjustment of the print head
When printing the work-piece by the nozzle of the print head, it is also necessary to constantly adjust the direction, so that the nozzle movement direction of the print head and the normal vector of the line segment formed between the two points are tangent.The angle of the print head should be adjusted every time the trajectory is printed, so as to ensure that the printing trajectory of each nozzle of the print head nozzle will not overlap, so it is very important to adjust the angle of the print head [11].At the same time, the angular rotation of the printhead can only be guaranteed to rotate 360° in one direction, so the angle of the printhead needs to be reset to zero after each print to ensure that the angle of the printhead is initialized for the next layer of the trace.The angle of the print head is adjusted as shown in Figure 5 below.The calculation formula is as follows.When the print head is located at point A, the print head and the vector α ⃗ coincide.When moving to point B, the angle of the print head must coincide with β ⃗ .When the print head is located at point A, the vector angle α ⃗ and μ ⃗ constitute the angle θ .When the print head is located at point B, the angle of the vector β ⃗ and the reference line μ ⃗ constitute the angle is θ , so the nozzle of the print head is adjusted from the angle of point A to point B, that is, θ -θ , the angle θ of the vector formed by the vector α ⃗ and the vector β ⃗ .According to Formula 2, coordinate points A(x ,y ) and B(x ,y ) and circular coordinate o(x ,y ) and radius r can be known, and the circle Formula ( 6) and the tangent formula of the point on the circle can be obtained.If α ⃗=(m ,n ), and β ⃗ =(m ,n ), then the angle θ is calculated in Formula ( 7):

Insertion of the cut instruction
Not only the angle of the print head should be set to the initialized state, but the Gcode cutting instruction needs to be inserted between the printing layer and the printing layer, so as to avoid the extrusion winding of each nozzle when the print head initializes the angle, thereby affecting the accuracy of printing.At the same time, the cutting device must be cut fast and accurately.This requires inserting a cutting instruction at a reasonable position to make the print head quickly jump freely and make the model accurately formed [12][13].The insertion of the cut command is generally controlled between the jump points of the Z axis, as shown in Figure 6.

Experimental analysis
The process of continuous carbon fiber printing through single nozzle and multi-tow four-nozzle continuous carbon fiber is shown in Figure 7 below, the printing time of single nozzle is 98 seconds, and the printing time of multi-tow is 356 seconds, as shown in Table 1 below.Multi-tow 98 Second 100%

Conclusion
The multi-tow continuous carbon fiber 3D printing path planning method proposed in this paper is mainly aimed at the parallel printing of large models and multiple nozzles to make up for the efficiency problem of continuous carbon fiber 3D printing of single nozzles.The planning method obtains model features through discrete model outer wall points while using multiple small line segments to fit arc trajectories, which will have angle adjustment problems, shearing problems, extrusion problems, etc., to prevent the accuracy of extrusion on the path and the printing error of the trajectory.Through experimental comparison, it is found that both methods can completely print out the model.The method of multi-tow continuous carbon fiber 3D printing proposed in this paper increases the efficiency by 3 to 4 times, and this path planning method in this paper improves the printing efficiency while satisfying the accuracy, which greatly makes up for the shortcomings of traditional 3D printing.

Figure 2 .
Figure 2. Flow chart of multi-tow continuous carbon fiber 3D printing path planning method.

Figure 3 .
Figure 3. Extracts a collection of model exterior wall coordinates.
..(x , y ) .Through the set D{l ,l ,...l } we can determine whether each section of the trajectory is a straight line or an arc.If the distance L is larger than C, it is a straight line otherwise an arc.If it is an arc, three points P1 (x1, y1), P2 (x2, y2), and P3 (x3, y3) can be used to calculate the arc trajectory, by obtaining the circle formula can calculate the center of the circle, the arc angle and the arc trajectory of the P1 to P2 segment.The calculation formula is as follows.

Figure 4 .
Figure 4.The extrusion amount of each nozzle in the arc trajectory is calculated by similar triangle.

Figure 7 .
Figure 7.The printing process.Table 1. Print the time table.

Table 1 .
Print the time table.